Identifier
Images
=>
Cc0009;cc-rep-1
[]=>{}
[1]=>{{1}}
[1,2]=>{{1},{2}}
[2,1]=>{{1,2}}
[1,2,3]=>{{1},{2},{3}}
[1,3,2]=>{{1},{2,3}}
[2,1,3]=>{{1,2},{3}}
[2,3,1]=>{{1,2,3}}
[3,1,2]=>{{1,2,3}}
[3,2,1]=>{{1,3},{2}}
[1,2,3,4]=>{{1},{2},{3},{4}}
[1,2,4,3]=>{{1},{2},{3,4}}
[1,3,2,4]=>{{1},{2,3},{4}}
[1,3,4,2]=>{{1},{2,3,4}}
[1,4,2,3]=>{{1},{2,3,4}}
[1,4,3,2]=>{{1},{2,4},{3}}
[2,1,3,4]=>{{1,2},{3},{4}}
[2,1,4,3]=>{{1,2},{3,4}}
[2,3,1,4]=>{{1,2,3},{4}}
[2,3,4,1]=>{{1,2,3,4}}
[2,4,1,3]=>{{1,2,3,4}}
[2,4,3,1]=>{{1,2,4},{3}}
[3,1,2,4]=>{{1,2,3},{4}}
[3,1,4,2]=>{{1,2,3,4}}
[3,2,1,4]=>{{1,3},{2},{4}}
[3,2,4,1]=>{{1,3,4},{2}}
[3,4,1,2]=>{{1,3},{2,4}}
[3,4,2,1]=>{{1,2,3,4}}
[4,1,2,3]=>{{1,2,3,4}}
[4,1,3,2]=>{{1,2,4},{3}}
[4,2,1,3]=>{{1,3,4},{2}}
[4,2,3,1]=>{{1,4},{2},{3}}
[4,3,1,2]=>{{1,2,3,4}}
[4,3,2,1]=>{{1,4},{2,3}}
[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[1,2,3,5,4]=>{{1},{2},{3},{4,5}}
[1,2,4,3,5]=>{{1},{2},{3,4},{5}}
[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[1,2,5,3,4]=>{{1},{2},{3,4,5}}
[1,2,5,4,3]=>{{1},{2},{3,5},{4}}
[1,3,2,4,5]=>{{1},{2,3},{4},{5}}
[1,3,2,5,4]=>{{1},{2,3},{4,5}}
[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[1,3,4,5,2]=>{{1},{2,3,4,5}}
[1,3,5,2,4]=>{{1},{2,3,4,5}}
[1,3,5,4,2]=>{{1},{2,3,5},{4}}
[1,4,2,3,5]=>{{1},{2,3,4},{5}}
[1,4,2,5,3]=>{{1},{2,3,4,5}}
[1,4,3,2,5]=>{{1},{2,4},{3},{5}}
[1,4,3,5,2]=>{{1},{2,4,5},{3}}
[1,4,5,2,3]=>{{1},{2,4},{3,5}}
[1,4,5,3,2]=>{{1},{2,3,4,5}}
[1,5,2,3,4]=>{{1},{2,3,4,5}}
[1,5,2,4,3]=>{{1},{2,3,5},{4}}
[1,5,3,2,4]=>{{1},{2,4,5},{3}}
[1,5,3,4,2]=>{{1},{2,5},{3},{4}}
[1,5,4,2,3]=>{{1},{2,3,4,5}}
[1,5,4,3,2]=>{{1},{2,5},{3,4}}
[2,1,3,4,5]=>{{1,2},{3},{4},{5}}
[2,1,3,5,4]=>{{1,2},{3},{4,5}}
[2,1,4,3,5]=>{{1,2},{3,4},{5}}
[2,1,4,5,3]=>{{1,2},{3,4,5}}
[2,1,5,3,4]=>{{1,2},{3,4,5}}
[2,1,5,4,3]=>{{1,2},{3,5},{4}}
[2,3,1,4,5]=>{{1,2,3},{4},{5}}
[2,3,1,5,4]=>{{1,2,3},{4,5}}
[2,3,4,1,5]=>{{1,2,3,4},{5}}
[2,3,4,5,1]=>{{1,2,3,4,5}}
[2,3,5,1,4]=>{{1,2,3,4,5}}
[2,3,5,4,1]=>{{1,2,3,5},{4}}
[2,4,1,3,5]=>{{1,2,3,4},{5}}
[2,4,1,5,3]=>{{1,2,3,4,5}}
[2,4,3,1,5]=>{{1,2,4},{3},{5}}
[2,4,3,5,1]=>{{1,2,4,5},{3}}
[2,4,5,1,3]=>{{1,2,4},{3,5}}
[2,4,5,3,1]=>{{1,2,3,4,5}}
[2,5,1,3,4]=>{{1,2,3,4,5}}
[2,5,1,4,3]=>{{1,2,3,5},{4}}
[2,5,3,1,4]=>{{1,2,4,5},{3}}
[2,5,3,4,1]=>{{1,2,5},{3},{4}}
[2,5,4,1,3]=>{{1,2,3,4,5}}
[2,5,4,3,1]=>{{1,2,5},{3,4}}
[3,1,2,4,5]=>{{1,2,3},{4},{5}}
[3,1,2,5,4]=>{{1,2,3},{4,5}}
[3,1,4,2,5]=>{{1,2,3,4},{5}}
[3,1,4,5,2]=>{{1,2,3,4,5}}
[3,1,5,2,4]=>{{1,2,3,4,5}}
[3,1,5,4,2]=>{{1,2,3,5},{4}}
[3,2,1,4,5]=>{{1,3},{2},{4},{5}}
[3,2,1,5,4]=>{{1,3},{2},{4,5}}
[3,2,4,1,5]=>{{1,3,4},{2},{5}}
[3,2,4,5,1]=>{{1,3,4,5},{2}}
[3,2,5,1,4]=>{{1,3,4,5},{2}}
[3,2,5,4,1]=>{{1,3,5},{2},{4}}
[3,4,1,2,5]=>{{1,3},{2,4},{5}}
[3,4,1,5,2]=>{{1,3},{2,4,5}}
[3,4,2,1,5]=>{{1,2,3,4},{5}}
[3,4,2,5,1]=>{{1,2,3,4,5}}
[3,4,5,1,2]=>{{1,2,3,4,5}}
[3,4,5,2,1]=>{{1,3,5},{2,4}}
[3,5,1,2,4]=>{{1,3},{2,4,5}}
[3,5,1,4,2]=>{{1,3},{2,5},{4}}
[3,5,2,1,4]=>{{1,2,3,4,5}}
[3,5,2,4,1]=>{{1,2,3,5},{4}}
[3,5,4,1,2]=>{{1,3,4},{2,5}}
[3,5,4,2,1]=>{{1,2,3,4,5}}
[4,1,2,3,5]=>{{1,2,3,4},{5}}
[4,1,2,5,3]=>{{1,2,3,4,5}}
[4,1,3,2,5]=>{{1,2,4},{3},{5}}
[4,1,3,5,2]=>{{1,2,4,5},{3}}
[4,1,5,2,3]=>{{1,2,4},{3,5}}
[4,1,5,3,2]=>{{1,2,3,4,5}}
[4,2,1,3,5]=>{{1,3,4},{2},{5}}
[4,2,1,5,3]=>{{1,3,4,5},{2}}
[4,2,3,1,5]=>{{1,4},{2},{3},{5}}
[4,2,3,5,1]=>{{1,4,5},{2},{3}}
[4,2,5,1,3]=>{{1,4},{2},{3,5}}
[4,2,5,3,1]=>{{1,3,4,5},{2}}
[4,3,1,2,5]=>{{1,2,3,4},{5}}
[4,3,1,5,2]=>{{1,2,3,4,5}}
[4,3,2,1,5]=>{{1,4},{2,3},{5}}
[4,3,2,5,1]=>{{1,4,5},{2,3}}
[4,3,5,1,2]=>{{1,4},{2,3,5}}
[4,3,5,2,1]=>{{1,2,3,4,5}}
[4,5,1,2,3]=>{{1,2,3,4,5}}
[4,5,1,3,2]=>{{1,3,4},{2,5}}
[4,5,2,1,3]=>{{1,4},{2,3,5}}
[4,5,2,3,1]=>{{1,2,3,4,5}}
[4,5,3,1,2]=>{{1,4},{2,5},{3}}
[4,5,3,2,1]=>{{1,2,4,5},{3}}
[5,1,2,3,4]=>{{1,2,3,4,5}}
[5,1,2,4,3]=>{{1,2,3,5},{4}}
[5,1,3,2,4]=>{{1,2,4,5},{3}}
[5,1,3,4,2]=>{{1,2,5},{3},{4}}
[5,1,4,2,3]=>{{1,2,3,4,5}}
[5,1,4,3,2]=>{{1,2,5},{3,4}}
[5,2,1,3,4]=>{{1,3,4,5},{2}}
[5,2,1,4,3]=>{{1,3,5},{2},{4}}
[5,2,3,1,4]=>{{1,4,5},{2},{3}}
[5,2,3,4,1]=>{{1,5},{2},{3},{4}}
[5,2,4,1,3]=>{{1,3,4,5},{2}}
[5,2,4,3,1]=>{{1,5},{2},{3,4}}
[5,3,1,2,4]=>{{1,2,3,4,5}}
[5,3,1,4,2]=>{{1,2,3,5},{4}}
[5,3,2,1,4]=>{{1,4,5},{2,3}}
[5,3,2,4,1]=>{{1,5},{2,3},{4}}
[5,3,4,1,2]=>{{1,2,3,4,5}}
[5,3,4,2,1]=>{{1,5},{2,3,4}}
[5,4,1,2,3]=>{{1,3,5},{2,4}}
[5,4,1,3,2]=>{{1,2,3,4,5}}
[5,4,2,1,3]=>{{1,2,3,4,5}}
[5,4,2,3,1]=>{{1,5},{2,3,4}}
[5,4,3,1,2]=>{{1,2,4,5},{3}}
[5,4,3,2,1]=>{{1,5},{2,4},{3}}
[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[1,2,3,6,4,5]=>{{1},{2},{3},{4,5,6}}
[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[1,2,4,6,3,5]=>{{1},{2},{3,4,5,6}}
[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[1,2,5,3,4,6]=>{{1},{2},{3,4,5},{6}}
[1,2,5,3,6,4]=>{{1},{2},{3,4,5,6}}
[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[1,2,6,3,4,5]=>{{1},{2},{3,4,5,6}}
[1,2,6,3,5,4]=>{{1},{2},{3,4,6},{5}}
[1,2,6,4,3,5]=>{{1},{2},{3,5,6},{4}}
[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}
[1,2,6,5,3,4]=>{{1},{2},{3,4,5,6}}
[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}}
[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[1,3,2,6,4,5]=>{{1},{2,3},{4,5,6}}
[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}
[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[1,3,4,6,2,5]=>{{1},{2,3,4,5,6}}
[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[1,3,5,2,4,6]=>{{1},{2,3,4,5},{6}}
[1,3,5,2,6,4]=>{{1},{2,3,4,5,6}}
[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[1,3,6,2,4,5]=>{{1},{2,3,4,5,6}}
[1,3,6,2,5,4]=>{{1},{2,3,4,6},{5}}
[1,3,6,4,2,5]=>{{1},{2,3,5,6},{4}}
[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}
[1,3,6,5,2,4]=>{{1},{2,3,4,5,6}}
[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}}
[1,4,2,3,5,6]=>{{1},{2,3,4},{5},{6}}
[1,4,2,3,6,5]=>{{1},{2,3,4},{5,6}}
[1,4,2,5,3,6]=>{{1},{2,3,4,5},{6}}
[1,4,2,5,6,3]=>{{1},{2,3,4,5,6}}
[1,4,2,6,3,5]=>{{1},{2,3,4,5,6}}
[1,4,2,6,5,3]=>{{1},{2,3,4,6},{5}}
[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}
[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[1,4,3,6,2,5]=>{{1},{2,4,5,6},{3}}
[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}
[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[1,4,5,6,2,3]=>{{1},{2,3,4,5,6}}
[1,4,5,6,3,2]=>{{1},{2,4,6},{3,5}}
[1,4,6,2,3,5]=>{{1},{2,4},{3,5,6}}
[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}
[1,4,6,3,2,5]=>{{1},{2,3,4,5,6}}
[1,4,6,3,5,2]=>{{1},{2,3,4,6},{5}}
[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}
[1,4,6,5,3,2]=>{{1},{2,3,4,5,6}}
[1,5,2,3,4,6]=>{{1},{2,3,4,5},{6}}
[1,5,2,3,6,4]=>{{1},{2,3,4,5,6}}
[1,5,2,4,3,6]=>{{1},{2,3,5},{4},{6}}
[1,5,2,4,6,3]=>{{1},{2,3,5,6},{4}}
[1,5,2,6,3,4]=>{{1},{2,3,5},{4,6}}
[1,5,2,6,4,3]=>{{1},{2,3,4,5,6}}
[1,5,3,2,4,6]=>{{1},{2,4,5},{3},{6}}
[1,5,3,2,6,4]=>{{1},{2,4,5,6},{3}}
[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}
[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}
[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}
[1,5,3,6,4,2]=>{{1},{2,4,5,6},{3}}
[1,5,4,2,3,6]=>{{1},{2,3,4,5},{6}}
[1,5,4,2,6,3]=>{{1},{2,3,4,5,6}}
[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}}
[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}}
[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[1,5,6,2,3,4]=>{{1},{2,3,4,5,6}}
[1,5,6,2,4,3]=>{{1},{2,4,5},{3,6}}
[1,5,6,3,2,4]=>{{1},{2,5},{3,4,6}}
[1,5,6,3,4,2]=>{{1},{2,3,4,5,6}}
[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}
[1,5,6,4,3,2]=>{{1},{2,3,5,6},{4}}
[1,6,2,3,4,5]=>{{1},{2,3,4,5,6}}
[1,6,2,3,5,4]=>{{1},{2,3,4,6},{5}}
[1,6,2,4,3,5]=>{{1},{2,3,5,6},{4}}
[1,6,2,4,5,3]=>{{1},{2,3,6},{4},{5}}
[1,6,2,5,3,4]=>{{1},{2,3,4,5,6}}
[1,6,2,5,4,3]=>{{1},{2,3,6},{4,5}}
[1,6,3,2,4,5]=>{{1},{2,4,5,6},{3}}
[1,6,3,2,5,4]=>{{1},{2,4,6},{3},{5}}
[1,6,3,4,2,5]=>{{1},{2,5,6},{3},{4}}
[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}}
[1,6,3,5,2,4]=>{{1},{2,4,5,6},{3}}
[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}}
[1,6,4,2,3,5]=>{{1},{2,3,4,5,6}}
[1,6,4,2,5,3]=>{{1},{2,3,4,6},{5}}
[1,6,4,3,2,5]=>{{1},{2,5,6},{3,4}}
[1,6,4,3,5,2]=>{{1},{2,6},{3,4},{5}}
[1,6,4,5,2,3]=>{{1},{2,3,4,5,6}}
[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}}
[1,6,5,2,3,4]=>{{1},{2,4,6},{3,5}}
[1,6,5,2,4,3]=>{{1},{2,3,4,5,6}}
[1,6,5,3,2,4]=>{{1},{2,3,4,5,6}}
[1,6,5,3,4,2]=>{{1},{2,6},{3,4,5}}
[1,6,5,4,2,3]=>{{1},{2,3,5,6},{4}}
[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}}
[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}
[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}
[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}
[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}
[2,1,3,6,4,5]=>{{1,2},{3},{4,5,6}}
[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}}
[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}
[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}
[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}
[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}
[2,1,4,6,3,5]=>{{1,2},{3,4,5,6}}
[2,1,4,6,5,3]=>{{1,2},{3,4,6},{5}}
[2,1,5,3,4,6]=>{{1,2},{3,4,5},{6}}
[2,1,5,3,6,4]=>{{1,2},{3,4,5,6}}
[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}}
[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}}
[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}}
[2,1,5,6,4,3]=>{{1,2},{3,4,5,6}}
[2,1,6,3,4,5]=>{{1,2},{3,4,5,6}}
[2,1,6,3,5,4]=>{{1,2},{3,4,6},{5}}
[2,1,6,4,3,5]=>{{1,2},{3,5,6},{4}}
[2,1,6,4,5,3]=>{{1,2},{3,6},{4},{5}}
[2,1,6,5,3,4]=>{{1,2},{3,4,5,6}}
[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}}
[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}
[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}
[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}
[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}
[2,3,1,6,4,5]=>{{1,2,3},{4,5,6}}
[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}}
[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}
[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}
[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}
[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}
[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}
[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}}
[2,3,5,1,4,6]=>{{1,2,3,4,5},{6}}
[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}
[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}}
[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}}
[2,3,5,6,1,4]=>{{1,2,3,5},{4,6}}
[2,3,5,6,4,1]=>{{1,2,3,4,5,6}}
[2,3,6,1,4,5]=>{{1,2,3,4,5,6}}
[2,3,6,1,5,4]=>{{1,2,3,4,6},{5}}
[2,3,6,4,1,5]=>{{1,2,3,5,6},{4}}
[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}}
[2,3,6,5,1,4]=>{{1,2,3,4,5,6}}
[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}}
[2,4,1,3,5,6]=>{{1,2,3,4},{5},{6}}
[2,4,1,3,6,5]=>{{1,2,3,4},{5,6}}
[2,4,1,5,3,6]=>{{1,2,3,4,5},{6}}
[2,4,1,5,6,3]=>{{1,2,3,4,5,6}}
[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}
[2,4,1,6,5,3]=>{{1,2,3,4,6},{5}}
[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}}
[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}}
[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}}
[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}}
[2,4,3,6,1,5]=>{{1,2,4,5,6},{3}}
[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}}
[2,4,5,1,3,6]=>{{1,2,4},{3,5},{6}}
[2,4,5,1,6,3]=>{{1,2,4},{3,5,6}}
[2,4,5,3,1,6]=>{{1,2,3,4,5},{6}}
[2,4,5,3,6,1]=>{{1,2,3,4,5,6}}
[2,4,5,6,1,3]=>{{1,2,3,4,5,6}}
[2,4,5,6,3,1]=>{{1,2,4,6},{3,5}}
[2,4,6,1,3,5]=>{{1,2,4},{3,5,6}}
[2,4,6,1,5,3]=>{{1,2,4},{3,6},{5}}
[2,4,6,3,1,5]=>{{1,2,3,4,5,6}}
[2,4,6,3,5,1]=>{{1,2,3,4,6},{5}}
[2,4,6,5,1,3]=>{{1,2,4,5},{3,6}}
[2,4,6,5,3,1]=>{{1,2,3,4,5,6}}
[2,5,1,3,4,6]=>{{1,2,3,4,5},{6}}
[2,5,1,3,6,4]=>{{1,2,3,4,5,6}}
[2,5,1,4,3,6]=>{{1,2,3,5},{4},{6}}
[2,5,1,4,6,3]=>{{1,2,3,5,6},{4}}
[2,5,1,6,3,4]=>{{1,2,3,5},{4,6}}
[2,5,1,6,4,3]=>{{1,2,3,4,5,6}}
[2,5,3,1,4,6]=>{{1,2,4,5},{3},{6}}
[2,5,3,1,6,4]=>{{1,2,4,5,6},{3}}
[2,5,3,4,1,6]=>{{1,2,5},{3},{4},{6}}
[2,5,3,4,6,1]=>{{1,2,5,6},{3},{4}}
[2,5,3,6,1,4]=>{{1,2,5},{3},{4,6}}
[2,5,3,6,4,1]=>{{1,2,4,5,6},{3}}
[2,5,4,1,3,6]=>{{1,2,3,4,5},{6}}
[2,5,4,1,6,3]=>{{1,2,3,4,5,6}}
[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}}
[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}}
[2,5,4,6,1,3]=>{{1,2,5},{3,4,6}}
[2,5,4,6,3,1]=>{{1,2,3,4,5,6}}
[2,5,6,1,3,4]=>{{1,2,3,4,5,6}}
[2,5,6,1,4,3]=>{{1,2,4,5},{3,6}}
[2,5,6,3,1,4]=>{{1,2,5},{3,4,6}}
[2,5,6,3,4,1]=>{{1,2,3,4,5,6}}
[2,5,6,4,1,3]=>{{1,2,5},{3,6},{4}}
[2,5,6,4,3,1]=>{{1,2,3,5,6},{4}}
[2,6,1,3,4,5]=>{{1,2,3,4,5,6}}
[2,6,1,3,5,4]=>{{1,2,3,4,6},{5}}
[2,6,1,4,3,5]=>{{1,2,3,5,6},{4}}
[2,6,1,4,5,3]=>{{1,2,3,6},{4},{5}}
[2,6,1,5,3,4]=>{{1,2,3,4,5,6}}
[2,6,1,5,4,3]=>{{1,2,3,6},{4,5}}
[2,6,3,1,4,5]=>{{1,2,4,5,6},{3}}
[2,6,3,1,5,4]=>{{1,2,4,6},{3},{5}}
[2,6,3,4,1,5]=>{{1,2,5,6},{3},{4}}
[2,6,3,4,5,1]=>{{1,2,6},{3},{4},{5}}
[2,6,3,5,1,4]=>{{1,2,4,5,6},{3}}
[2,6,3,5,4,1]=>{{1,2,6},{3},{4,5}}
[2,6,4,1,3,5]=>{{1,2,3,4,5,6}}
[2,6,4,1,5,3]=>{{1,2,3,4,6},{5}}
[2,6,4,3,1,5]=>{{1,2,5,6},{3,4}}
[2,6,4,3,5,1]=>{{1,2,6},{3,4},{5}}
[2,6,4,5,1,3]=>{{1,2,3,4,5,6}}
[2,6,4,5,3,1]=>{{1,2,6},{3,4,5}}
[2,6,5,1,3,4]=>{{1,2,4,6},{3,5}}
[2,6,5,1,4,3]=>{{1,2,3,4,5,6}}
[2,6,5,3,1,4]=>{{1,2,3,4,5,6}}
[2,6,5,3,4,1]=>{{1,2,6},{3,4,5}}
[2,6,5,4,1,3]=>{{1,2,3,5,6},{4}}
[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}}
[3,1,2,4,5,6]=>{{1,2,3},{4},{5},{6}}
[3,1,2,4,6,5]=>{{1,2,3},{4},{5,6}}
[3,1,2,5,4,6]=>{{1,2,3},{4,5},{6}}
[3,1,2,5,6,4]=>{{1,2,3},{4,5,6}}
[3,1,2,6,4,5]=>{{1,2,3},{4,5,6}}
[3,1,2,6,5,4]=>{{1,2,3},{4,6},{5}}
[3,1,4,2,5,6]=>{{1,2,3,4},{5},{6}}
[3,1,4,2,6,5]=>{{1,2,3,4},{5,6}}
[3,1,4,5,2,6]=>{{1,2,3,4,5},{6}}
[3,1,4,5,6,2]=>{{1,2,3,4,5,6}}
[3,1,4,6,2,5]=>{{1,2,3,4,5,6}}
[3,1,4,6,5,2]=>{{1,2,3,4,6},{5}}
[3,1,5,2,4,6]=>{{1,2,3,4,5},{6}}
[3,1,5,2,6,4]=>{{1,2,3,4,5,6}}
[3,1,5,4,2,6]=>{{1,2,3,5},{4},{6}}
[3,1,5,4,6,2]=>{{1,2,3,5,6},{4}}
[3,1,5,6,2,4]=>{{1,2,3,5},{4,6}}
[3,1,5,6,4,2]=>{{1,2,3,4,5,6}}
[3,1,6,2,4,5]=>{{1,2,3,4,5,6}}
[3,1,6,2,5,4]=>{{1,2,3,4,6},{5}}
[3,1,6,4,2,5]=>{{1,2,3,5,6},{4}}
[3,1,6,4,5,2]=>{{1,2,3,6},{4},{5}}
[3,1,6,5,2,4]=>{{1,2,3,4,5,6}}
[3,1,6,5,4,2]=>{{1,2,3,6},{4,5}}
[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}}
[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}}
[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}}
[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}}
[3,2,1,6,4,5]=>{{1,3},{2},{4,5,6}}
[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}}
[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}}
[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}}
[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}}
[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}}
[3,2,4,6,1,5]=>{{1,3,4,5,6},{2}}
[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}}
[3,2,5,1,4,6]=>{{1,3,4,5},{2},{6}}
[3,2,5,1,6,4]=>{{1,3,4,5,6},{2}}
[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}}
[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}}
[3,2,5,6,1,4]=>{{1,3,5},{2},{4,6}}
[3,2,5,6,4,1]=>{{1,3,4,5,6},{2}}
[3,2,6,1,4,5]=>{{1,3,4,5,6},{2}}
[3,2,6,1,5,4]=>{{1,3,4,6},{2},{5}}
[3,2,6,4,1,5]=>{{1,3,5,6},{2},{4}}
[3,2,6,4,5,1]=>{{1,3,6},{2},{4},{5}}
[3,2,6,5,1,4]=>{{1,3,4,5,6},{2}}
[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}}
[3,4,1,2,5,6]=>{{1,3},{2,4},{5},{6}}
[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}}
[3,4,1,5,2,6]=>{{1,3},{2,4,5},{6}}
[3,4,1,5,6,2]=>{{1,3},{2,4,5,6}}
[3,4,1,6,2,5]=>{{1,3},{2,4,5,6}}
[3,4,1,6,5,2]=>{{1,3},{2,4,6},{5}}
[3,4,2,1,5,6]=>{{1,2,3,4},{5},{6}}
[3,4,2,1,6,5]=>{{1,2,3,4},{5,6}}
[3,4,2,5,1,6]=>{{1,2,3,4,5},{6}}
[3,4,2,5,6,1]=>{{1,2,3,4,5,6}}
[3,4,2,6,1,5]=>{{1,2,3,4,5,6}}
[3,4,2,6,5,1]=>{{1,2,3,4,6},{5}}
[3,4,5,1,2,6]=>{{1,2,3,4,5},{6}}
[3,4,5,1,6,2]=>{{1,2,3,4,5,6}}
[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}}
[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}}
[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}}
[3,4,5,6,2,1]=>{{1,2,3,4,5,6}}
[3,4,6,1,2,5]=>{{1,2,3,4,5,6}}
[3,4,6,1,5,2]=>{{1,2,3,4,6},{5}}
[3,4,6,2,1,5]=>{{1,3,5,6},{2,4}}
[3,4,6,2,5,1]=>{{1,3,6},{2,4},{5}}
[3,4,6,5,1,2]=>{{1,2,3,4,5,6}}
[3,4,6,5,2,1]=>{{1,3,6},{2,4,5}}
[3,5,1,2,4,6]=>{{1,3},{2,4,5},{6}}
[3,5,1,2,6,4]=>{{1,3},{2,4,5,6}}
[3,5,1,4,2,6]=>{{1,3},{2,5},{4},{6}}
[3,5,1,4,6,2]=>{{1,3},{2,5,6},{4}}
[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}}
[3,5,1,6,4,2]=>{{1,3},{2,4,5,6}}
[3,5,2,1,4,6]=>{{1,2,3,4,5},{6}}
[3,5,2,1,6,4]=>{{1,2,3,4,5,6}}
[3,5,2,4,1,6]=>{{1,2,3,5},{4},{6}}
[3,5,2,4,6,1]=>{{1,2,3,5,6},{4}}
[3,5,2,6,1,4]=>{{1,2,3,5},{4,6}}
[3,5,2,6,4,1]=>{{1,2,3,4,5,6}}
[3,5,4,1,2,6]=>{{1,3,4},{2,5},{6}}
[3,5,4,1,6,2]=>{{1,3,4},{2,5,6}}
[3,5,4,2,1,6]=>{{1,2,3,4,5},{6}}
[3,5,4,2,6,1]=>{{1,2,3,4,5,6}}
[3,5,4,6,1,2]=>{{1,2,3,4,5,6}}
[3,5,4,6,2,1]=>{{1,3,4,6},{2,5}}
[3,5,6,1,2,4]=>{{1,3,4,6},{2,5}}
[3,5,6,1,4,2]=>{{1,2,3,4,5,6}}
[3,5,6,2,1,4]=>{{1,2,3,4,5,6}}
[3,5,6,2,4,1]=>{{1,3,6},{2,4,5}}
[3,5,6,4,1,2]=>{{1,2,3,5,6},{4}}
[3,5,6,4,2,1]=>{{1,3,6},{2,5},{4}}
[3,6,1,2,4,5]=>{{1,3},{2,4,5,6}}
[3,6,1,2,5,4]=>{{1,3},{2,4,6},{5}}
[3,6,1,4,2,5]=>{{1,3},{2,5,6},{4}}
[3,6,1,4,5,2]=>{{1,3},{2,6},{4},{5}}
[3,6,1,5,2,4]=>{{1,3},{2,4,5,6}}
[3,6,1,5,4,2]=>{{1,3},{2,6},{4,5}}
[3,6,2,1,4,5]=>{{1,2,3,4,5,6}}
[3,6,2,1,5,4]=>{{1,2,3,4,6},{5}}
[3,6,2,4,1,5]=>{{1,2,3,5,6},{4}}
[3,6,2,4,5,1]=>{{1,2,3,6},{4},{5}}
[3,6,2,5,1,4]=>{{1,2,3,4,5,6}}
[3,6,2,5,4,1]=>{{1,2,3,6},{4,5}}
[3,6,4,1,2,5]=>{{1,3,4},{2,5,6}}
[3,6,4,1,5,2]=>{{1,3,4},{2,6},{5}}
[3,6,4,2,1,5]=>{{1,2,3,4,5,6}}
[3,6,4,2,5,1]=>{{1,2,3,4,6},{5}}
[3,6,4,5,1,2]=>{{1,3,4,5},{2,6}}
[3,6,4,5,2,1]=>{{1,2,3,4,5,6}}
[3,6,5,1,2,4]=>{{1,2,3,4,5,6}}
[3,6,5,1,4,2]=>{{1,3,4,5},{2,6}}
[3,6,5,2,1,4]=>{{1,3,5},{2,4,6}}
[3,6,5,2,4,1]=>{{1,2,3,4,5,6}}
[3,6,5,4,1,2]=>{{1,3,5},{2,6},{4}}
[3,6,5,4,2,1]=>{{1,2,3,5,6},{4}}
[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}}
[4,1,2,3,6,5]=>{{1,2,3,4},{5,6}}
[4,1,2,5,3,6]=>{{1,2,3,4,5},{6}}
[4,1,2,5,6,3]=>{{1,2,3,4,5,6}}
[4,1,2,6,3,5]=>{{1,2,3,4,5,6}}
[4,1,2,6,5,3]=>{{1,2,3,4,6},{5}}
[4,1,3,2,5,6]=>{{1,2,4},{3},{5},{6}}
[4,1,3,2,6,5]=>{{1,2,4},{3},{5,6}}
[4,1,3,5,2,6]=>{{1,2,4,5},{3},{6}}
[4,1,3,5,6,2]=>{{1,2,4,5,6},{3}}
[4,1,3,6,2,5]=>{{1,2,4,5,6},{3}}
[4,1,3,6,5,2]=>{{1,2,4,6},{3},{5}}
[4,1,5,2,3,6]=>{{1,2,4},{3,5},{6}}
[4,1,5,2,6,3]=>{{1,2,4},{3,5,6}}
[4,1,5,3,2,6]=>{{1,2,3,4,5},{6}}
[4,1,5,3,6,2]=>{{1,2,3,4,5,6}}
[4,1,5,6,2,3]=>{{1,2,3,4,5,6}}
[4,1,5,6,3,2]=>{{1,2,4,6},{3,5}}
[4,1,6,2,3,5]=>{{1,2,4},{3,5,6}}
[4,1,6,2,5,3]=>{{1,2,4},{3,6},{5}}
[4,1,6,3,2,5]=>{{1,2,3,4,5,6}}
[4,1,6,3,5,2]=>{{1,2,3,4,6},{5}}
[4,1,6,5,2,3]=>{{1,2,4,5},{3,6}}
[4,1,6,5,3,2]=>{{1,2,3,4,5,6}}
[4,2,1,3,5,6]=>{{1,3,4},{2},{5},{6}}
[4,2,1,3,6,5]=>{{1,3,4},{2},{5,6}}
[4,2,1,5,3,6]=>{{1,3,4,5},{2},{6}}
[4,2,1,5,6,3]=>{{1,3,4,5,6},{2}}
[4,2,1,6,3,5]=>{{1,3,4,5,6},{2}}
[4,2,1,6,5,3]=>{{1,3,4,6},{2},{5}}
[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}}
[4,2,3,1,6,5]=>{{1,4},{2},{3},{5,6}}
[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}}
[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}}
[4,2,3,6,1,5]=>{{1,4,5,6},{2},{3}}
[4,2,3,6,5,1]=>{{1,4,6},{2},{3},{5}}
[4,2,5,1,3,6]=>{{1,4},{2},{3,5},{6}}
[4,2,5,1,6,3]=>{{1,4},{2},{3,5,6}}
[4,2,5,3,1,6]=>{{1,3,4,5},{2},{6}}
[4,2,5,3,6,1]=>{{1,3,4,5,6},{2}}
[4,2,5,6,1,3]=>{{1,3,4,5,6},{2}}
[4,2,5,6,3,1]=>{{1,4,6},{2},{3,5}}
[4,2,6,1,3,5]=>{{1,4},{2},{3,5,6}}
[4,2,6,1,5,3]=>{{1,4},{2},{3,6},{5}}
[4,2,6,3,1,5]=>{{1,3,4,5,6},{2}}
[4,2,6,3,5,1]=>{{1,3,4,6},{2},{5}}
[4,2,6,5,1,3]=>{{1,4,5},{2},{3,6}}
[4,2,6,5,3,1]=>{{1,3,4,5,6},{2}}
[4,3,1,2,5,6]=>{{1,2,3,4},{5},{6}}
[4,3,1,2,6,5]=>{{1,2,3,4},{5,6}}
[4,3,1,5,2,6]=>{{1,2,3,4,5},{6}}
[4,3,1,5,6,2]=>{{1,2,3,4,5,6}}
[4,3,1,6,2,5]=>{{1,2,3,4,5,6}}
[4,3,1,6,5,2]=>{{1,2,3,4,6},{5}}
[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}}
[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}}
[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}}
[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}}
[4,3,2,6,1,5]=>{{1,4,5,6},{2,3}}
[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}}
[4,3,5,1,2,6]=>{{1,4},{2,3,5},{6}}
[4,3,5,1,6,2]=>{{1,4},{2,3,5,6}}
[4,3,5,2,1,6]=>{{1,2,3,4,5},{6}}
[4,3,5,2,6,1]=>{{1,2,3,4,5,6}}
[4,3,5,6,1,2]=>{{1,2,3,4,5,6}}
[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}}
[4,3,6,1,2,5]=>{{1,4},{2,3,5,6}}
[4,3,6,1,5,2]=>{{1,4},{2,3,6},{5}}
[4,3,6,2,1,5]=>{{1,2,3,4,5,6}}
[4,3,6,2,5,1]=>{{1,2,3,4,6},{5}}
[4,3,6,5,1,2]=>{{1,4,5},{2,3,6}}
[4,3,6,5,2,1]=>{{1,2,3,4,5,6}}
[4,5,1,2,3,6]=>{{1,2,3,4,5},{6}}
[4,5,1,2,6,3]=>{{1,2,3,4,5,6}}
[4,5,1,3,2,6]=>{{1,3,4},{2,5},{6}}
[4,5,1,3,6,2]=>{{1,3,4},{2,5,6}}
[4,5,1,6,2,3]=>{{1,3,4,6},{2,5}}
[4,5,1,6,3,2]=>{{1,2,3,4,5,6}}
[4,5,2,1,3,6]=>{{1,4},{2,3,5},{6}}
[4,5,2,1,6,3]=>{{1,4},{2,3,5,6}}
[4,5,2,3,1,6]=>{{1,2,3,4,5},{6}}
[4,5,2,3,6,1]=>{{1,2,3,4,5,6}}
[4,5,2,6,1,3]=>{{1,2,3,4,5,6}}
[4,5,2,6,3,1]=>{{1,4,6},{2,3,5}}
[4,5,3,1,2,6]=>{{1,4},{2,5},{3},{6}}
[4,5,3,1,6,2]=>{{1,4},{2,5,6},{3}}
[4,5,3,2,1,6]=>{{1,2,4,5},{3},{6}}
[4,5,3,2,6,1]=>{{1,2,4,5,6},{3}}
[4,5,3,6,1,2]=>{{1,2,4,5,6},{3}}
[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}}
[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}}
[4,5,6,1,3,2]=>{{1,4},{2,3,5,6}}
[4,5,6,2,1,3]=>{{1,2,4,5},{3,6}}
[4,5,6,2,3,1]=>{{1,2,3,4,5,6}}
[4,5,6,3,1,2]=>{{1,2,3,4,5,6}}
[4,5,6,3,2,1]=>{{1,3,4,6},{2,5}}
[4,6,1,2,3,5]=>{{1,2,3,4,5,6}}
[4,6,1,2,5,3]=>{{1,2,3,4,6},{5}}
[4,6,1,3,2,5]=>{{1,3,4},{2,5,6}}
[4,6,1,3,5,2]=>{{1,3,4},{2,6},{5}}
[4,6,1,5,2,3]=>{{1,2,3,4,5,6}}
[4,6,1,5,3,2]=>{{1,3,4,5},{2,6}}
[4,6,2,1,3,5]=>{{1,4},{2,3,5,6}}
[4,6,2,1,5,3]=>{{1,4},{2,3,6},{5}}
[4,6,2,3,1,5]=>{{1,2,3,4,5,6}}
[4,6,2,3,5,1]=>{{1,2,3,4,6},{5}}
[4,6,2,5,1,3]=>{{1,4,5},{2,3,6}}
[4,6,2,5,3,1]=>{{1,2,3,4,5,6}}
[4,6,3,1,2,5]=>{{1,4},{2,5,6},{3}}
[4,6,3,1,5,2]=>{{1,4},{2,6},{3},{5}}
[4,6,3,2,1,5]=>{{1,2,4,5,6},{3}}
[4,6,3,2,5,1]=>{{1,2,4,6},{3},{5}}
[4,6,3,5,1,2]=>{{1,4,5},{2,6},{3}}
[4,6,3,5,2,1]=>{{1,2,4,5,6},{3}}
[4,6,5,1,2,3]=>{{1,4},{2,3,5,6}}
[4,6,5,1,3,2]=>{{1,4},{2,6},{3,5}}
[4,6,5,2,1,3]=>{{1,2,3,4,5,6}}
[4,6,5,2,3,1]=>{{1,2,4,6},{3,5}}
[4,6,5,3,1,2]=>{{1,3,4,5},{2,6}}
[4,6,5,3,2,1]=>{{1,2,3,4,5,6}}
[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}}
[5,1,2,3,6,4]=>{{1,2,3,4,5,6}}
[5,1,2,4,3,6]=>{{1,2,3,5},{4},{6}}
[5,1,2,4,6,3]=>{{1,2,3,5,6},{4}}
[5,1,2,6,3,4]=>{{1,2,3,5},{4,6}}
[5,1,2,6,4,3]=>{{1,2,3,4,5,6}}
[5,1,3,2,4,6]=>{{1,2,4,5},{3},{6}}
[5,1,3,2,6,4]=>{{1,2,4,5,6},{3}}
[5,1,3,4,2,6]=>{{1,2,5},{3},{4},{6}}
[5,1,3,4,6,2]=>{{1,2,5,6},{3},{4}}
[5,1,3,6,2,4]=>{{1,2,5},{3},{4,6}}
[5,1,3,6,4,2]=>{{1,2,4,5,6},{3}}
[5,1,4,2,3,6]=>{{1,2,3,4,5},{6}}
[5,1,4,2,6,3]=>{{1,2,3,4,5,6}}
[5,1,4,3,2,6]=>{{1,2,5},{3,4},{6}}
[5,1,4,3,6,2]=>{{1,2,5,6},{3,4}}
[5,1,4,6,2,3]=>{{1,2,5},{3,4,6}}
[5,1,4,6,3,2]=>{{1,2,3,4,5,6}}
[5,1,6,2,3,4]=>{{1,2,3,4,5,6}}
[5,1,6,2,4,3]=>{{1,2,4,5},{3,6}}
[5,1,6,3,2,4]=>{{1,2,5},{3,4,6}}
[5,1,6,3,4,2]=>{{1,2,3,4,5,6}}
[5,1,6,4,2,3]=>{{1,2,5},{3,6},{4}}
[5,1,6,4,3,2]=>{{1,2,3,5,6},{4}}
[5,2,1,3,4,6]=>{{1,3,4,5},{2},{6}}
[5,2,1,3,6,4]=>{{1,3,4,5,6},{2}}
[5,2,1,4,3,6]=>{{1,3,5},{2},{4},{6}}
[5,2,1,4,6,3]=>{{1,3,5,6},{2},{4}}
[5,2,1,6,3,4]=>{{1,3,5},{2},{4,6}}
[5,2,1,6,4,3]=>{{1,3,4,5,6},{2}}
[5,2,3,1,4,6]=>{{1,4,5},{2},{3},{6}}
[5,2,3,1,6,4]=>{{1,4,5,6},{2},{3}}
[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}}
[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}}
[5,2,3,6,1,4]=>{{1,5},{2},{3},{4,6}}
[5,2,3,6,4,1]=>{{1,4,5,6},{2},{3}}
[5,2,4,1,3,6]=>{{1,3,4,5},{2},{6}}
[5,2,4,1,6,3]=>{{1,3,4,5,6},{2}}
[5,2,4,3,1,6]=>{{1,5},{2},{3,4},{6}}
[5,2,4,3,6,1]=>{{1,5,6},{2},{3,4}}
[5,2,4,6,1,3]=>{{1,5},{2},{3,4,6}}
[5,2,4,6,3,1]=>{{1,3,4,5,6},{2}}
[5,2,6,1,3,4]=>{{1,3,4,5,6},{2}}
[5,2,6,1,4,3]=>{{1,4,5},{2},{3,6}}
[5,2,6,3,1,4]=>{{1,5},{2},{3,4,6}}
[5,2,6,3,4,1]=>{{1,3,4,5,6},{2}}
[5,2,6,4,1,3]=>{{1,5},{2},{3,6},{4}}
[5,2,6,4,3,1]=>{{1,3,5,6},{2},{4}}
[5,3,1,2,4,6]=>{{1,2,3,4,5},{6}}
[5,3,1,2,6,4]=>{{1,2,3,4,5,6}}
[5,3,1,4,2,6]=>{{1,2,3,5},{4},{6}}
[5,3,1,4,6,2]=>{{1,2,3,5,6},{4}}
[5,3,1,6,2,4]=>{{1,2,3,5},{4,6}}
[5,3,1,6,4,2]=>{{1,2,3,4,5,6}}
[5,3,2,1,4,6]=>{{1,4,5},{2,3},{6}}
[5,3,2,1,6,4]=>{{1,4,5,6},{2,3}}
[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}}
[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}}
[5,3,2,6,1,4]=>{{1,5},{2,3},{4,6}}
[5,3,2,6,4,1]=>{{1,4,5,6},{2,3}}
[5,3,4,1,2,6]=>{{1,2,3,4,5},{6}}
[5,3,4,1,6,2]=>{{1,2,3,4,5,6}}
[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}}
[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}}
[5,3,4,6,1,2]=>{{1,5},{2,3,4,6}}
[5,3,4,6,2,1]=>{{1,2,3,4,5,6}}
[5,3,6,1,2,4]=>{{1,2,3,4,5,6}}
[5,3,6,1,4,2]=>{{1,4,5},{2,3,6}}
[5,3,6,2,1,4]=>{{1,5},{2,3,4,6}}
[5,3,6,2,4,1]=>{{1,2,3,4,5,6}}
[5,3,6,4,1,2]=>{{1,5},{2,3,6},{4}}
[5,3,6,4,2,1]=>{{1,2,3,5,6},{4}}
[5,4,1,2,3,6]=>{{1,3,5},{2,4},{6}}
[5,4,1,2,6,3]=>{{1,3,5,6},{2,4}}
[5,4,1,3,2,6]=>{{1,2,3,4,5},{6}}
[5,4,1,3,6,2]=>{{1,2,3,4,5,6}}
[5,4,1,6,2,3]=>{{1,2,3,4,5,6}}
[5,4,1,6,3,2]=>{{1,3,5},{2,4,6}}
[5,4,2,1,3,6]=>{{1,2,3,4,5},{6}}
[5,4,2,1,6,3]=>{{1,2,3,4,5,6}}
[5,4,2,3,1,6]=>{{1,5},{2,3,4},{6}}
[5,4,2,3,6,1]=>{{1,5,6},{2,3,4}}
[5,4,2,6,1,3]=>{{1,5},{2,3,4,6}}
[5,4,2,6,3,1]=>{{1,2,3,4,5,6}}
[5,4,3,1,2,6]=>{{1,2,4,5},{3},{6}}
[5,4,3,1,6,2]=>{{1,2,4,5,6},{3}}
[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}}
[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}}
[5,4,3,6,1,2]=>{{1,5},{2,4,6},{3}}
[5,4,3,6,2,1]=>{{1,2,4,5,6},{3}}
[5,4,6,1,2,3]=>{{1,2,4,5},{3,6}}
[5,4,6,1,3,2]=>{{1,2,3,4,5,6}}
[5,4,6,2,1,3]=>{{1,5},{2,4},{3,6}}
[5,4,6,2,3,1]=>{{1,3,5,6},{2,4}}
[5,4,6,3,1,2]=>{{1,5},{2,3,4,6}}
[5,4,6,3,2,1]=>{{1,2,3,4,5,6}}
[5,6,1,2,3,4]=>{{1,3,5},{2,4,6}}
[5,6,1,2,4,3]=>{{1,2,3,4,5,6}}
[5,6,1,3,2,4]=>{{1,2,3,4,5,6}}
[5,6,1,3,4,2]=>{{1,3,4,5},{2,6}}
[5,6,1,4,2,3]=>{{1,2,3,5,6},{4}}
[5,6,1,4,3,2]=>{{1,3,5},{2,6},{4}}
[5,6,2,1,3,4]=>{{1,2,3,4,5,6}}
[5,6,2,1,4,3]=>{{1,4,5},{2,3,6}}
[5,6,2,3,1,4]=>{{1,5},{2,3,4,6}}
[5,6,2,3,4,1]=>{{1,2,3,4,5,6}}
[5,6,2,4,1,3]=>{{1,5},{2,3,6},{4}}
[5,6,2,4,3,1]=>{{1,2,3,5,6},{4}}
[5,6,3,1,2,4]=>{{1,2,4,5,6},{3}}
[5,6,3,1,4,2]=>{{1,4,5},{2,6},{3}}
[5,6,3,2,1,4]=>{{1,5},{2,4,6},{3}}
[5,6,3,2,4,1]=>{{1,2,4,5,6},{3}}
[5,6,3,4,1,2]=>{{1,5},{2,6},{3},{4}}
[5,6,3,4,2,1]=>{{1,2,5,6},{3},{4}}
[5,6,4,1,2,3]=>{{1,2,3,4,5,6}}
[5,6,4,1,3,2]=>{{1,3,4,5},{2,6}}
[5,6,4,2,1,3]=>{{1,5},{2,3,4,6}}
[5,6,4,2,3,1]=>{{1,2,3,4,5,6}}
[5,6,4,3,1,2]=>{{1,5},{2,6},{3,4}}
[5,6,4,3,2,1]=>{{1,2,5,6},{3,4}}
[6,1,2,3,4,5]=>{{1,2,3,4,5,6}}
[6,1,2,3,5,4]=>{{1,2,3,4,6},{5}}
[6,1,2,4,3,5]=>{{1,2,3,5,6},{4}}
[6,1,2,4,5,3]=>{{1,2,3,6},{4},{5}}
[6,1,2,5,3,4]=>{{1,2,3,4,5,6}}
[6,1,2,5,4,3]=>{{1,2,3,6},{4,5}}
[6,1,3,2,4,5]=>{{1,2,4,5,6},{3}}
[6,1,3,2,5,4]=>{{1,2,4,6},{3},{5}}
[6,1,3,4,2,5]=>{{1,2,5,6},{3},{4}}
[6,1,3,4,5,2]=>{{1,2,6},{3},{4},{5}}
[6,1,3,5,2,4]=>{{1,2,4,5,6},{3}}
[6,1,3,5,4,2]=>{{1,2,6},{3},{4,5}}
[6,1,4,2,3,5]=>{{1,2,3,4,5,6}}
[6,1,4,2,5,3]=>{{1,2,3,4,6},{5}}
[6,1,4,3,2,5]=>{{1,2,5,6},{3,4}}
[6,1,4,3,5,2]=>{{1,2,6},{3,4},{5}}
[6,1,4,5,2,3]=>{{1,2,3,4,5,6}}
[6,1,4,5,3,2]=>{{1,2,6},{3,4,5}}
[6,1,5,2,3,4]=>{{1,2,4,6},{3,5}}
[6,1,5,2,4,3]=>{{1,2,3,4,5,6}}
[6,1,5,3,2,4]=>{{1,2,3,4,5,6}}
[6,1,5,3,4,2]=>{{1,2,6},{3,4,5}}
[6,1,5,4,2,3]=>{{1,2,3,5,6},{4}}
[6,1,5,4,3,2]=>{{1,2,6},{3,5},{4}}
[6,2,1,3,4,5]=>{{1,3,4,5,6},{2}}
[6,2,1,3,5,4]=>{{1,3,4,6},{2},{5}}
[6,2,1,4,3,5]=>{{1,3,5,6},{2},{4}}
[6,2,1,4,5,3]=>{{1,3,6},{2},{4},{5}}
[6,2,1,5,3,4]=>{{1,3,4,5,6},{2}}
[6,2,1,5,4,3]=>{{1,3,6},{2},{4,5}}
[6,2,3,1,4,5]=>{{1,4,5,6},{2},{3}}
[6,2,3,1,5,4]=>{{1,4,6},{2},{3},{5}}
[6,2,3,4,1,5]=>{{1,5,6},{2},{3},{4}}
[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}}
[6,2,3,5,1,4]=>{{1,4,5,6},{2},{3}}
[6,2,3,5,4,1]=>{{1,6},{2},{3},{4,5}}
[6,2,4,1,3,5]=>{{1,3,4,5,6},{2}}
[6,2,4,1,5,3]=>{{1,3,4,6},{2},{5}}
[6,2,4,3,1,5]=>{{1,5,6},{2},{3,4}}
[6,2,4,3,5,1]=>{{1,6},{2},{3,4},{5}}
[6,2,4,5,1,3]=>{{1,3,4,5,6},{2}}
[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}}
[6,2,5,1,3,4]=>{{1,4,6},{2},{3,5}}
[6,2,5,1,4,3]=>{{1,3,4,5,6},{2}}
[6,2,5,3,1,4]=>{{1,3,4,5,6},{2}}
[6,2,5,3,4,1]=>{{1,6},{2},{3,4,5}}
[6,2,5,4,1,3]=>{{1,3,5,6},{2},{4}}
[6,2,5,4,3,1]=>{{1,6},{2},{3,5},{4}}
[6,3,1,2,4,5]=>{{1,2,3,4,5,6}}
[6,3,1,2,5,4]=>{{1,2,3,4,6},{5}}
[6,3,1,4,2,5]=>{{1,2,3,5,6},{4}}
[6,3,1,4,5,2]=>{{1,2,3,6},{4},{5}}
[6,3,1,5,2,4]=>{{1,2,3,4,5,6}}
[6,3,1,5,4,2]=>{{1,2,3,6},{4,5}}
[6,3,2,1,4,5]=>{{1,4,5,6},{2,3}}
[6,3,2,1,5,4]=>{{1,4,6},{2,3},{5}}
[6,3,2,4,1,5]=>{{1,5,6},{2,3},{4}}
[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}}
[6,3,2,5,1,4]=>{{1,4,5,6},{2,3}}
[6,3,2,5,4,1]=>{{1,6},{2,3},{4,5}}
[6,3,4,1,2,5]=>{{1,2,3,4,5,6}}
[6,3,4,1,5,2]=>{{1,2,3,4,6},{5}}
[6,3,4,2,1,5]=>{{1,5,6},{2,3,4}}
[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}}
[6,3,4,5,1,2]=>{{1,2,3,4,5,6}}
[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}}
[6,3,5,1,2,4]=>{{1,4,6},{2,3,5}}
[6,3,5,1,4,2]=>{{1,2,3,4,5,6}}
[6,3,5,2,1,4]=>{{1,2,3,4,5,6}}
[6,3,5,2,4,1]=>{{1,6},{2,3,4,5}}
[6,3,5,4,1,2]=>{{1,2,3,5,6},{4}}
[6,3,5,4,2,1]=>{{1,6},{2,3,5},{4}}
[6,4,1,2,3,5]=>{{1,3,5,6},{2,4}}
[6,4,1,2,5,3]=>{{1,3,6},{2,4},{5}}
[6,4,1,3,2,5]=>{{1,2,3,4,5,6}}
[6,4,1,3,5,2]=>{{1,2,3,4,6},{5}}
[6,4,1,5,2,3]=>{{1,3,6},{2,4,5}}
[6,4,1,5,3,2]=>{{1,2,3,4,5,6}}
[6,4,2,1,3,5]=>{{1,2,3,4,5,6}}
[6,4,2,1,5,3]=>{{1,2,3,4,6},{5}}
[6,4,2,3,1,5]=>{{1,5,6},{2,3,4}}
[6,4,2,3,5,1]=>{{1,6},{2,3,4},{5}}
[6,4,2,5,1,3]=>{{1,2,3,4,5,6}}
[6,4,2,5,3,1]=>{{1,6},{2,3,4,5}}
[6,4,3,1,2,5]=>{{1,2,4,5,6},{3}}
[6,4,3,1,5,2]=>{{1,2,4,6},{3},{5}}
[6,4,3,2,1,5]=>{{1,5,6},{2,4},{3}}
[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}}
[6,4,3,5,1,2]=>{{1,2,4,5,6},{3}}
[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}}
[6,4,5,1,2,3]=>{{1,2,3,4,5,6}}
[6,4,5,1,3,2]=>{{1,2,4,6},{3,5}}
[6,4,5,2,1,3]=>{{1,3,5,6},{2,4}}
[6,4,5,2,3,1]=>{{1,6},{2,4},{3,5}}
[6,4,5,3,1,2]=>{{1,2,3,4,5,6}}
[6,4,5,3,2,1]=>{{1,6},{2,3,4,5}}
[6,5,1,2,3,4]=>{{1,2,3,4,5,6}}
[6,5,1,2,4,3]=>{{1,3,6},{2,4,5}}
[6,5,1,3,2,4]=>{{1,3,4,6},{2,5}}
[6,5,1,3,4,2]=>{{1,2,3,4,5,6}}
[6,5,1,4,2,3]=>{{1,3,6},{2,5},{4}}
[6,5,1,4,3,2]=>{{1,2,3,5,6},{4}}
[6,5,2,1,3,4]=>{{1,4,6},{2,3,5}}
[6,5,2,1,4,3]=>{{1,2,3,4,5,6}}
[6,5,2,3,1,4]=>{{1,2,3,4,5,6}}
[6,5,2,3,4,1]=>{{1,6},{2,3,4,5}}
[6,5,2,4,1,3]=>{{1,2,3,5,6},{4}}
[6,5,2,4,3,1]=>{{1,6},{2,3,5},{4}}
[6,5,3,1,2,4]=>{{1,4,6},{2,5},{3}}
[6,5,3,1,4,2]=>{{1,2,4,5,6},{3}}
[6,5,3,2,1,4]=>{{1,2,4,5,6},{3}}
[6,5,3,2,4,1]=>{{1,6},{2,4,5},{3}}
[6,5,3,4,1,2]=>{{1,2,5,6},{3},{4}}
[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}}
[6,5,4,1,2,3]=>{{1,3,4,6},{2,5}}
[6,5,4,1,3,2]=>{{1,2,3,4,5,6}}
[6,5,4,2,1,3]=>{{1,2,3,4,5,6}}
[6,5,4,2,3,1]=>{{1,6},{2,3,4,5}}
[6,5,4,3,1,2]=>{{1,2,5,6},{3,4}}
[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}}
[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},{6,7}}
[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},{5,6,7}}
[1,2,3,4,7,5,6]=>{{1},{2},{3},{4},{5,6,7}}
[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,5,7,4,6]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[1,2,3,6,4,5,7]=>{{1},{2},{3},{4,5,6},{7}}
[1,2,3,6,4,7,5]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,7,4,5,6]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,7,4,6,5]=>{{1},{2},{3},{4,5,7},{6}}
[1,2,3,7,5,4,6]=>{{1},{2},{3},{4,6,7},{5}}
[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[1,2,3,7,6,4,5]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,7,6,5,4]=>{{1},{2},{3},{4,7},{5,6}}
[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[1,2,4,3,7,5,6]=>{{1},{2},{3,4},{5,6,7}}
[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,4,5,7,3,6]=>{{1},{2},{3,4,5,6,7}}
[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[1,2,4,6,3,5,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,4,6,3,7,5]=>{{1},{2},{3,4,5,6,7}}
[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,4,7,3,5,6]=>{{1},{2},{3,4,5,6,7}}
[1,2,4,7,3,6,5]=>{{1},{2},{3,4,5,7},{6}}
[1,2,4,7,5,3,6]=>{{1},{2},{3,4,6,7},{5}}
[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[1,2,4,7,6,3,5]=>{{1},{2},{3,4,5,6,7}}
[1,2,4,7,6,5,3]=>{{1},{2},{3,4,7},{5,6}}
[1,2,5,3,4,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[1,2,5,3,4,7,6]=>{{1},{2},{3,4,5},{6,7}}
[1,2,5,3,6,4,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,5,3,6,7,4]=>{{1},{2},{3,4,5,6,7}}
[1,2,5,3,7,4,6]=>{{1},{2},{3,4,5,6,7}}
[1,2,5,3,7,6,4]=>{{1},{2},{3,4,5,7},{6}}
[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[1,2,5,4,7,3,6]=>{{1},{2},{3,5,6,7},{4}}
[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,5,6,7,3,4]=>{{1},{2},{3,4,5,6,7}}
[1,2,5,6,7,4,3]=>{{1},{2},{3,5,7},{4,6}}
[1,2,5,7,3,4,6]=>{{1},{2},{3,5},{4,6,7}}
[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[1,2,5,7,4,3,6]=>{{1},{2},{3,4,5,6,7}}
[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,6,3,4,5,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,6,3,4,7,5]=>{{1},{2},{3,4,5,6,7}}
[1,2,6,3,5,4,7]=>{{1},{2},{3,4,6},{5},{7}}
[1,2,6,3,5,7,4]=>{{1},{2},{3,4,6,7},{5}}
[1,2,6,3,7,4,5]=>{{1},{2},{3,4,6},{5,7}}
[1,2,6,3,7,5,4]=>{{1},{2},{3,4,5,6,7}}
[1,2,6,4,3,5,7]=>{{1},{2},{3,5,6},{4},{7}}
[1,2,6,4,3,7,5]=>{{1},{2},{3,5,6,7},{4}}
[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[1,2,6,5,3,4,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,6,5,3,7,4]=>{{1},{2},{3,4,5,6,7}}
[1,2,6,5,4,3,7]=>{{1},{2},{3,6},{4,5},{7}}
[1,2,6,5,4,7,3]=>{{1},{2},{3,6,7},{4,5}}
[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,6,7,3,4,5]=>{{1},{2},{3,4,5,6,7}}
[1,2,6,7,3,5,4]=>{{1},{2},{3,5,6},{4,7}}
[1,2,6,7,4,3,5]=>{{1},{2},{3,6},{4,5,7}}
[1,2,6,7,4,5,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[1,2,7,3,4,5,6]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,3,4,6,5]=>{{1},{2},{3,4,5,7},{6}}
[1,2,7,3,5,4,6]=>{{1},{2},{3,4,6,7},{5}}
[1,2,7,3,5,6,4]=>{{1},{2},{3,4,7},{5},{6}}
[1,2,7,3,6,4,5]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,3,6,5,4]=>{{1},{2},{3,4,7},{5,6}}
[1,2,7,4,3,5,6]=>{{1},{2},{3,5,6,7},{4}}
[1,2,7,4,3,6,5]=>{{1},{2},{3,5,7},{4},{6}}
[1,2,7,4,5,3,6]=>{{1},{2},{3,6,7},{4},{5}}
[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}}
[1,2,7,4,6,3,5]=>{{1},{2},{3,5,6,7},{4}}
[1,2,7,4,6,5,3]=>{{1},{2},{3,7},{4},{5,6}}
[1,2,7,5,3,4,6]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,5,3,6,4]=>{{1},{2},{3,4,5,7},{6}}
[1,2,7,5,4,3,6]=>{{1},{2},{3,6,7},{4,5}}
[1,2,7,5,4,6,3]=>{{1},{2},{3,7},{4,5},{6}}
[1,2,7,5,6,3,4]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,5,6,4,3]=>{{1},{2},{3,7},{4,5,6}}
[1,2,7,6,3,4,5]=>{{1},{2},{3,5,7},{4,6}}
[1,2,7,6,3,5,4]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,6,4,3,5]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,6,4,5,3]=>{{1},{2},{3,7},{4,5,6}}
[1,2,7,6,5,3,4]=>{{1},{2},{3,4,6,7},{5}}
[1,2,7,6,5,4,3]=>{{1},{2},{3,7},{4,6},{5}}
[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[1,3,2,4,7,5,6]=>{{1},{2,3},{4},{5,6,7}}
[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,5,7,4,6]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[1,3,2,6,4,5,7]=>{{1},{2,3},{4,5,6},{7}}
[1,3,2,6,4,7,5]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,7,4,5,6]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,7,4,6,5]=>{{1},{2,3},{4,5,7},{6}}
[1,3,2,7,5,4,6]=>{{1},{2,3},{4,6,7},{5}}
[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}}
[1,3,2,7,6,4,5]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,7,6,5,4]=>{{1},{2,3},{4,7},{5,6}}
[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[1,3,4,2,7,5,6]=>{{1},{2,3,4},{5,6,7}}
[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,3,4,5,7,2,6]=>{{1},{2,3,4,5,6,7}}
[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,3,4,6,2,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,4,6,2,7,5]=>{{1},{2,3,4,5,6,7}}
[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,3,4,7,2,5,6]=>{{1},{2,3,4,5,6,7}}
[1,3,4,7,2,6,5]=>{{1},{2,3,4,5,7},{6}}
[1,3,4,7,5,2,6]=>{{1},{2,3,4,6,7},{5}}
[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[1,3,4,7,6,2,5]=>{{1},{2,3,4,5,6,7}}
[1,3,4,7,6,5,2]=>{{1},{2,3,4,7},{5,6}}
[1,3,5,2,4,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,3,5,2,4,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,3,5,2,6,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,5,2,6,7,4]=>{{1},{2,3,4,5,6,7}}
[1,3,5,2,7,4,6]=>{{1},{2,3,4,5,6,7}}
[1,3,5,2,7,6,4]=>{{1},{2,3,4,5,7},{6}}
[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,3,5,4,7,2,6]=>{{1},{2,3,5,6,7},{4}}
[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[1,3,5,6,7,2,4]=>{{1},{2,3,4,5,6,7}}
[1,3,5,6,7,4,2]=>{{1},{2,3,5,7},{4,6}}
[1,3,5,7,2,4,6]=>{{1},{2,3,5},{4,6,7}}
[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[1,3,5,7,4,2,6]=>{{1},{2,3,4,5,6,7}}
[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[1,3,6,2,4,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,6,2,4,7,5]=>{{1},{2,3,4,5,6,7}}
[1,3,6,2,5,4,7]=>{{1},{2,3,4,6},{5},{7}}
[1,3,6,2,5,7,4]=>{{1},{2,3,4,6,7},{5}}
[1,3,6,2,7,4,5]=>{{1},{2,3,4,6},{5,7}}
[1,3,6,2,7,5,4]=>{{1},{2,3,4,5,6,7}}
[1,3,6,4,2,5,7]=>{{1},{2,3,5,6},{4},{7}}
[1,3,6,4,2,7,5]=>{{1},{2,3,5,6,7},{4}}
[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[1,3,6,5,2,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,6,5,2,7,4]=>{{1},{2,3,4,5,6,7}}
[1,3,6,5,4,2,7]=>{{1},{2,3,6},{4,5},{7}}
[1,3,6,5,4,7,2]=>{{1},{2,3,6,7},{4,5}}
[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,3,6,7,2,4,5]=>{{1},{2,3,4,5,6,7}}
[1,3,6,7,2,5,4]=>{{1},{2,3,5,6},{4,7}}
[1,3,6,7,4,2,5]=>{{1},{2,3,6},{4,5,7}}
[1,3,6,7,4,5,2]=>{{1},{2,3,4,5,6,7}}
[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[1,3,7,2,4,5,6]=>{{1},{2,3,4,5,6,7}}
[1,3,7,2,4,6,5]=>{{1},{2,3,4,5,7},{6}}
[1,3,7,2,5,4,6]=>{{1},{2,3,4,6,7},{5}}
[1,3,7,2,5,6,4]=>{{1},{2,3,4,7},{5},{6}}
[1,3,7,2,6,4,5]=>{{1},{2,3,4,5,6,7}}
[1,3,7,2,6,5,4]=>{{1},{2,3,4,7},{5,6}}
[1,3,7,4,2,5,6]=>{{1},{2,3,5,6,7},{4}}
[1,3,7,4,2,6,5]=>{{1},{2,3,5,7},{4},{6}}
[1,3,7,4,5,2,6]=>{{1},{2,3,6,7},{4},{5}}
[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}
[1,3,7,4,6,2,5]=>{{1},{2,3,5,6,7},{4}}
[1,3,7,4,6,5,2]=>{{1},{2,3,7},{4},{5,6}}
[1,3,7,5,2,4,6]=>{{1},{2,3,4,5,6,7}}
[1,3,7,5,2,6,4]=>{{1},{2,3,4,5,7},{6}}
[1,3,7,5,4,2,6]=>{{1},{2,3,6,7},{4,5}}
[1,3,7,5,4,6,2]=>{{1},{2,3,7},{4,5},{6}}
[1,3,7,5,6,2,4]=>{{1},{2,3,4,5,6,7}}
[1,3,7,5,6,4,2]=>{{1},{2,3,7},{4,5,6}}
[1,3,7,6,2,4,5]=>{{1},{2,3,5,7},{4,6}}
[1,3,7,6,2,5,4]=>{{1},{2,3,4,5,6,7}}
[1,3,7,6,4,2,5]=>{{1},{2,3,4,5,6,7}}
[1,3,7,6,4,5,2]=>{{1},{2,3,7},{4,5,6}}
[1,3,7,6,5,2,4]=>{{1},{2,3,4,6,7},{5}}
[1,3,7,6,5,4,2]=>{{1},{2,3,7},{4,6},{5}}
[1,4,2,3,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[1,4,2,3,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[1,4,2,3,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[1,4,2,3,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[1,4,2,3,7,5,6]=>{{1},{2,3,4},{5,6,7}}
[1,4,2,3,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[1,4,2,5,3,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,4,2,5,3,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,4,2,5,6,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,2,5,6,7,3]=>{{1},{2,3,4,5,6,7}}
[1,4,2,5,7,3,6]=>{{1},{2,3,4,5,6,7}}
[1,4,2,5,7,6,3]=>{{1},{2,3,4,5,7},{6}}
[1,4,2,6,3,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,2,6,3,7,5]=>{{1},{2,3,4,5,6,7}}
[1,4,2,6,5,3,7]=>{{1},{2,3,4,6},{5},{7}}
[1,4,2,6,5,7,3]=>{{1},{2,3,4,6,7},{5}}
[1,4,2,6,7,3,5]=>{{1},{2,3,4,6},{5,7}}
[1,4,2,6,7,5,3]=>{{1},{2,3,4,5,6,7}}
[1,4,2,7,3,5,6]=>{{1},{2,3,4,5,6,7}}
[1,4,2,7,3,6,5]=>{{1},{2,3,4,5,7},{6}}
[1,4,2,7,5,3,6]=>{{1},{2,3,4,6,7},{5}}
[1,4,2,7,5,6,3]=>{{1},{2,3,4,7},{5},{6}}
[1,4,2,7,6,3,5]=>{{1},{2,3,4,5,6,7}}
[1,4,2,7,6,5,3]=>{{1},{2,3,4,7},{5,6}}
[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[1,4,3,2,7,5,6]=>{{1},{2,4},{3},{5,6,7}}
[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}
[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,4,3,5,7,2,6]=>{{1},{2,4,5,6,7},{3}}
[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[1,4,3,6,2,5,7]=>{{1},{2,4,5,6},{3},{7}}
[1,4,3,6,2,7,5]=>{{1},{2,4,5,6,7},{3}}
[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[1,4,3,7,2,5,6]=>{{1},{2,4,5,6,7},{3}}
[1,4,3,7,2,6,5]=>{{1},{2,4,5,7},{3},{6}}
[1,4,3,7,5,2,6]=>{{1},{2,4,6,7},{3},{5}}
[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}
[1,4,3,7,6,2,5]=>{{1},{2,4,5,6,7},{3}}
[1,4,3,7,6,5,2]=>{{1},{2,4,7},{3},{5,6}}
[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,5,2,7,3,6]=>{{1},{2,4},{3,5,6,7}}
[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,4,5,3,7,2,6]=>{{1},{2,3,4,5,6,7}}
[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,4,5,6,2,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,5,6,2,7,3]=>{{1},{2,3,4,5,6,7}}
[1,4,5,6,3,2,7]=>{{1},{2,4,6},{3,5},{7}}
[1,4,5,6,3,7,2]=>{{1},{2,4,6,7},{3,5}}
[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,4,5,7,2,3,6]=>{{1},{2,3,4,5,6,7}}
[1,4,5,7,2,6,3]=>{{1},{2,3,4,5,7},{6}}
[1,4,5,7,3,2,6]=>{{1},{2,4,6,7},{3,5}}
[1,4,5,7,3,6,2]=>{{1},{2,4,7},{3,5},{6}}
[1,4,5,7,6,2,3]=>{{1},{2,3,4,5,6,7}}
[1,4,5,7,6,3,2]=>{{1},{2,4,7},{3,5,6}}
[1,4,6,2,3,5,7]=>{{1},{2,4},{3,5,6},{7}}
[1,4,6,2,3,7,5]=>{{1},{2,4},{3,5,6,7}}
[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,6,3,2,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,6,3,2,7,5]=>{{1},{2,3,4,5,6,7}}
[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,4,6,5,7,2,3]=>{{1},{2,3,4,5,6,7}}
[1,4,6,5,7,3,2]=>{{1},{2,4,5,7},{3,6}}
[1,4,6,7,2,3,5]=>{{1},{2,4,5,7},{3,6}}
[1,4,6,7,2,5,3]=>{{1},{2,3,4,5,6,7}}
[1,4,6,7,3,2,5]=>{{1},{2,3,4,5,6,7}}
[1,4,6,7,3,5,2]=>{{1},{2,4,7},{3,5,6}}
[1,4,6,7,5,2,3]=>{{1},{2,3,4,6,7},{5}}
[1,4,6,7,5,3,2]=>{{1},{2,4,7},{3,6},{5}}
[1,4,7,2,3,5,6]=>{{1},{2,4},{3,5,6,7}}
[1,4,7,2,3,6,5]=>{{1},{2,4},{3,5,7},{6}}
[1,4,7,2,5,3,6]=>{{1},{2,4},{3,6,7},{5}}
[1,4,7,2,5,6,3]=>{{1},{2,4},{3,7},{5},{6}}
[1,4,7,2,6,3,5]=>{{1},{2,4},{3,5,6,7}}
[1,4,7,2,6,5,3]=>{{1},{2,4},{3,7},{5,6}}
[1,4,7,3,2,5,6]=>{{1},{2,3,4,5,6,7}}
[1,4,7,3,2,6,5]=>{{1},{2,3,4,5,7},{6}}
[1,4,7,3,5,2,6]=>{{1},{2,3,4,6,7},{5}}
[1,4,7,3,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[1,4,7,3,6,2,5]=>{{1},{2,3,4,5,6,7}}
[1,4,7,3,6,5,2]=>{{1},{2,3,4,7},{5,6}}
[1,4,7,5,2,3,6]=>{{1},{2,4,5},{3,6,7}}
[1,4,7,5,2,6,3]=>{{1},{2,4,5},{3,7},{6}}
[1,4,7,5,3,2,6]=>{{1},{2,3,4,5,6,7}}
[1,4,7,5,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,4,7,5,6,2,3]=>{{1},{2,4,5,6},{3,7}}
[1,4,7,5,6,3,2]=>{{1},{2,3,4,5,6,7}}
[1,4,7,6,2,3,5]=>{{1},{2,3,4,5,6,7}}
[1,4,7,6,2,5,3]=>{{1},{2,4,5,6},{3,7}}
[1,4,7,6,3,2,5]=>{{1},{2,4,6},{3,5,7}}
[1,4,7,6,3,5,2]=>{{1},{2,3,4,5,6,7}}
[1,4,7,6,5,2,3]=>{{1},{2,4,6},{3,7},{5}}
[1,4,7,6,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,2,3,4,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,5,2,3,4,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,5,2,3,6,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,5,2,3,6,7,4]=>{{1},{2,3,4,5,6,7}}
[1,5,2,3,7,4,6]=>{{1},{2,3,4,5,6,7}}
[1,5,2,3,7,6,4]=>{{1},{2,3,4,5,7},{6}}
[1,5,2,4,3,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[1,5,2,4,3,7,6]=>{{1},{2,3,5},{4},{6,7}}
[1,5,2,4,6,3,7]=>{{1},{2,3,5,6},{4},{7}}
[1,5,2,4,6,7,3]=>{{1},{2,3,5,6,7},{4}}
[1,5,2,4,7,3,6]=>{{1},{2,3,5,6,7},{4}}
[1,5,2,4,7,6,3]=>{{1},{2,3,5,7},{4},{6}}
[1,5,2,6,3,4,7]=>{{1},{2,3,5},{4,6},{7}}
[1,5,2,6,3,7,4]=>{{1},{2,3,5},{4,6,7}}
[1,5,2,6,4,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,5,2,6,4,7,3]=>{{1},{2,3,4,5,6,7}}
[1,5,2,6,7,3,4]=>{{1},{2,3,4,5,6,7}}
[1,5,2,6,7,4,3]=>{{1},{2,3,5,7},{4,6}}
[1,5,2,7,3,4,6]=>{{1},{2,3,5},{4,6,7}}
[1,5,2,7,3,6,4]=>{{1},{2,3,5},{4,7},{6}}
[1,5,2,7,4,3,6]=>{{1},{2,3,4,5,6,7}}
[1,5,2,7,4,6,3]=>{{1},{2,3,4,5,7},{6}}
[1,5,2,7,6,3,4]=>{{1},{2,3,5,6},{4,7}}
[1,5,2,7,6,4,3]=>{{1},{2,3,4,5,6,7}}
[1,5,3,2,4,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[1,5,3,2,4,7,6]=>{{1},{2,4,5},{3},{6,7}}
[1,5,3,2,6,4,7]=>{{1},{2,4,5,6},{3},{7}}
[1,5,3,2,6,7,4]=>{{1},{2,4,5,6,7},{3}}
[1,5,3,2,7,4,6]=>{{1},{2,4,5,6,7},{3}}
[1,5,3,2,7,6,4]=>{{1},{2,4,5,7},{3},{6}}
[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}}
[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[1,5,3,4,7,2,6]=>{{1},{2,5,6,7},{3},{4}}
[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}
[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,5,3,6,7,2,4]=>{{1},{2,4,5,6,7},{3}}
[1,5,3,6,7,4,2]=>{{1},{2,5,7},{3},{4,6}}
[1,5,3,7,2,4,6]=>{{1},{2,5},{3},{4,6,7}}
[1,5,3,7,2,6,4]=>{{1},{2,5},{3},{4,7},{6}}
[1,5,3,7,4,2,6]=>{{1},{2,4,5,6,7},{3}}
[1,5,3,7,4,6,2]=>{{1},{2,4,5,7},{3},{6}}
[1,5,3,7,6,2,4]=>{{1},{2,5,6},{3},{4,7}}
[1,5,3,7,6,4,2]=>{{1},{2,4,5,6,7},{3}}
[1,5,4,2,3,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,5,4,2,3,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,5,4,2,6,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,5,4,2,6,7,3]=>{{1},{2,3,4,5,6,7}}
[1,5,4,2,7,3,6]=>{{1},{2,3,4,5,6,7}}
[1,5,4,2,7,6,3]=>{{1},{2,3,4,5,7},{6}}
[1,5,4,3,2,6,7]=>{{1},{2,5},{3,4},{6},{7}}
[1,5,4,3,2,7,6]=>{{1},{2,5},{3,4},{6,7}}
[1,5,4,3,6,2,7]=>{{1},{2,5,6},{3,4},{7}}
[1,5,4,3,6,7,2]=>{{1},{2,5,6,7},{3,4}}
[1,5,4,3,7,2,6]=>{{1},{2,5,6,7},{3,4}}
[1,5,4,3,7,6,2]=>{{1},{2,5,7},{3,4},{6}}
[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,5,4,6,7,2,3]=>{{1},{2,3,4,5,6,7}}
[1,5,4,6,7,3,2]=>{{1},{2,5,7},{3,4,6}}
[1,5,4,7,2,3,6]=>{{1},{2,5},{3,4,6,7}}
[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[1,5,4,7,3,2,6]=>{{1},{2,3,4,5,6,7}}
[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[1,5,6,2,3,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,5,6,2,3,7,4]=>{{1},{2,3,4,5,6,7}}
[1,5,6,2,4,3,7]=>{{1},{2,4,5},{3,6},{7}}
[1,5,6,2,4,7,3]=>{{1},{2,4,5},{3,6,7}}
[1,5,6,2,7,3,4]=>{{1},{2,4,5,7},{3,6}}
[1,5,6,2,7,4,3]=>{{1},{2,3,4,5,6,7}}
[1,5,6,3,2,4,7]=>{{1},{2,5},{3,4,6},{7}}
[1,5,6,3,2,7,4]=>{{1},{2,5},{3,4,6,7}}
[1,5,6,3,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,5,6,3,4,7,2]=>{{1},{2,3,4,5,6,7}}
[1,5,6,3,7,2,4]=>{{1},{2,3,4,5,6,7}}
[1,5,6,3,7,4,2]=>{{1},{2,5,7},{3,4,6}}
[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,5,6,4,7,2,3]=>{{1},{2,3,5,6,7},{4}}
[1,5,6,4,7,3,2]=>{{1},{2,5,7},{3,6},{4}}
[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[1,5,6,7,4,2,3]=>{{1},{2,3,4,5,6,7}}
[1,5,6,7,4,3,2]=>{{1},{2,4,5,7},{3,6}}
[1,5,7,2,3,4,6]=>{{1},{2,3,4,5,6,7}}
[1,5,7,2,3,6,4]=>{{1},{2,3,4,5,7},{6}}
[1,5,7,2,4,3,6]=>{{1},{2,4,5},{3,6,7}}
[1,5,7,2,4,6,3]=>{{1},{2,4,5},{3,7},{6}}
[1,5,7,2,6,3,4]=>{{1},{2,3,4,5,6,7}}
[1,5,7,2,6,4,3]=>{{1},{2,4,5,6},{3,7}}
[1,5,7,3,2,4,6]=>{{1},{2,5},{3,4,6,7}}
[1,5,7,3,2,6,4]=>{{1},{2,5},{3,4,7},{6}}
[1,5,7,3,4,2,6]=>{{1},{2,3,4,5,6,7}}
[1,5,7,3,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,5,7,3,6,2,4]=>{{1},{2,5,6},{3,4,7}}
[1,5,7,3,6,4,2]=>{{1},{2,3,4,5,6,7}}
[1,5,7,4,2,3,6]=>{{1},{2,5},{3,6,7},{4}}
[1,5,7,4,2,6,3]=>{{1},{2,5},{3,7},{4},{6}}
[1,5,7,4,3,2,6]=>{{1},{2,3,5,6,7},{4}}
[1,5,7,4,3,6,2]=>{{1},{2,3,5,7},{4},{6}}
[1,5,7,4,6,2,3]=>{{1},{2,5,6},{3,7},{4}}
[1,5,7,4,6,3,2]=>{{1},{2,3,5,6,7},{4}}
[1,5,7,6,2,3,4]=>{{1},{2,5},{3,4,6,7}}
[1,5,7,6,2,4,3]=>{{1},{2,5},{3,7},{4,6}}
[1,5,7,6,3,2,4]=>{{1},{2,3,4,5,6,7}}
[1,5,7,6,3,4,2]=>{{1},{2,3,5,7},{4,6}}
[1,5,7,6,4,2,3]=>{{1},{2,4,5,6},{3,7}}
[1,5,7,6,4,3,2]=>{{1},{2,3,4,5,6,7}}
[1,6,2,3,4,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,2,3,4,7,5]=>{{1},{2,3,4,5,6,7}}
[1,6,2,3,5,4,7]=>{{1},{2,3,4,6},{5},{7}}
[1,6,2,3,5,7,4]=>{{1},{2,3,4,6,7},{5}}
[1,6,2,3,7,4,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,2,3,7,5,4]=>{{1},{2,3,4,5,6,7}}
[1,6,2,4,3,5,7]=>{{1},{2,3,5,6},{4},{7}}
[1,6,2,4,3,7,5]=>{{1},{2,3,5,6,7},{4}}
[1,6,2,4,5,3,7]=>{{1},{2,3,6},{4},{5},{7}}
[1,6,2,4,5,7,3]=>{{1},{2,3,6,7},{4},{5}}
[1,6,2,4,7,3,5]=>{{1},{2,3,6},{4},{5,7}}
[1,6,2,4,7,5,3]=>{{1},{2,3,5,6,7},{4}}
[1,6,2,5,3,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,2,5,3,7,4]=>{{1},{2,3,4,5,6,7}}
[1,6,2,5,4,3,7]=>{{1},{2,3,6},{4,5},{7}}
[1,6,2,5,4,7,3]=>{{1},{2,3,6,7},{4,5}}
[1,6,2,5,7,3,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,2,5,7,4,3]=>{{1},{2,3,4,5,6,7}}
[1,6,2,7,3,4,5]=>{{1},{2,3,4,5,6,7}}
[1,6,2,7,3,5,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,2,7,4,3,5]=>{{1},{2,3,6},{4,5,7}}
[1,6,2,7,4,5,3]=>{{1},{2,3,4,5,6,7}}
[1,6,2,7,5,3,4]=>{{1},{2,3,6},{4,7},{5}}
[1,6,2,7,5,4,3]=>{{1},{2,3,4,6,7},{5}}
[1,6,3,2,4,5,7]=>{{1},{2,4,5,6},{3},{7}}
[1,6,3,2,4,7,5]=>{{1},{2,4,5,6,7},{3}}
[1,6,3,2,5,4,7]=>{{1},{2,4,6},{3},{5},{7}}
[1,6,3,2,5,7,4]=>{{1},{2,4,6,7},{3},{5}}
[1,6,3,2,7,4,5]=>{{1},{2,4,6},{3},{5,7}}
[1,6,3,2,7,5,4]=>{{1},{2,4,5,6,7},{3}}
[1,6,3,4,2,5,7]=>{{1},{2,5,6},{3},{4},{7}}
[1,6,3,4,2,7,5]=>{{1},{2,5,6,7},{3},{4}}
[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}}
[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}
[1,6,3,4,7,2,5]=>{{1},{2,6},{3},{4},{5,7}}
[1,6,3,4,7,5,2]=>{{1},{2,5,6,7},{3},{4}}
[1,6,3,5,2,4,7]=>{{1},{2,4,5,6},{3},{7}}
[1,6,3,5,2,7,4]=>{{1},{2,4,5,6,7},{3}}
[1,6,3,5,4,2,7]=>{{1},{2,6},{3},{4,5},{7}}
[1,6,3,5,4,7,2]=>{{1},{2,6,7},{3},{4,5}}
[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[1,6,3,7,2,4,5]=>{{1},{2,4,5,6,7},{3}}
[1,6,3,7,2,5,4]=>{{1},{2,5,6},{3},{4,7}}
[1,6,3,7,4,2,5]=>{{1},{2,6},{3},{4,5,7}}
[1,6,3,7,4,5,2]=>{{1},{2,4,5,6,7},{3}}
[1,6,3,7,5,2,4]=>{{1},{2,6},{3},{4,7},{5}}
[1,6,3,7,5,4,2]=>{{1},{2,4,6,7},{3},{5}}
[1,6,4,2,3,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,4,2,3,7,5]=>{{1},{2,3,4,5,6,7}}
[1,6,4,2,5,3,7]=>{{1},{2,3,4,6},{5},{7}}
[1,6,4,2,5,7,3]=>{{1},{2,3,4,6,7},{5}}
[1,6,4,2,7,3,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,4,2,7,5,3]=>{{1},{2,3,4,5,6,7}}
[1,6,4,3,2,5,7]=>{{1},{2,5,6},{3,4},{7}}
[1,6,4,3,2,7,5]=>{{1},{2,5,6,7},{3,4}}
[1,6,4,3,5,2,7]=>{{1},{2,6},{3,4},{5},{7}}
[1,6,4,3,5,7,2]=>{{1},{2,6,7},{3,4},{5}}
[1,6,4,3,7,2,5]=>{{1},{2,6},{3,4},{5,7}}
[1,6,4,3,7,5,2]=>{{1},{2,5,6,7},{3,4}}
[1,6,4,5,2,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,4,5,2,7,3]=>{{1},{2,3,4,5,6,7}}
[1,6,4,5,3,2,7]=>{{1},{2,6},{3,4,5},{7}}
[1,6,4,5,3,7,2]=>{{1},{2,6,7},{3,4,5}}
[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,6,4,7,2,3,5]=>{{1},{2,3,4,5,6,7}}
[1,6,4,7,2,5,3]=>{{1},{2,5,6},{3,4,7}}
[1,6,4,7,3,2,5]=>{{1},{2,6},{3,4,5,7}}
[1,6,4,7,3,5,2]=>{{1},{2,3,4,5,6,7}}
[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[1,6,5,2,3,4,7]=>{{1},{2,4,6},{3,5},{7}}
[1,6,5,2,3,7,4]=>{{1},{2,4,6,7},{3,5}}
[1,6,5,2,4,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,5,2,4,7,3]=>{{1},{2,3,4,5,6,7}}
[1,6,5,2,7,3,4]=>{{1},{2,3,4,5,6,7}}
[1,6,5,2,7,4,3]=>{{1},{2,4,6},{3,5,7}}
[1,6,5,3,2,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,5,3,2,7,4]=>{{1},{2,3,4,5,6,7}}
[1,6,5,3,4,2,7]=>{{1},{2,6},{3,4,5},{7}}
[1,6,5,3,4,7,2]=>{{1},{2,6,7},{3,4,5}}
[1,6,5,3,7,2,4]=>{{1},{2,6},{3,4,5,7}}
[1,6,5,3,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,6,5,4,2,3,7]=>{{1},{2,3,5,6},{4},{7}}
[1,6,5,4,2,7,3]=>{{1},{2,3,5,6,7},{4}}
[1,6,5,4,3,2,7]=>{{1},{2,6},{3,5},{4},{7}}
[1,6,5,4,3,7,2]=>{{1},{2,6,7},{3,5},{4}}
[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[1,6,5,7,2,3,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,5,7,2,4,3]=>{{1},{2,3,4,5,6,7}}
[1,6,5,7,3,2,4]=>{{1},{2,6},{3,5},{4,7}}
[1,6,5,7,3,4,2]=>{{1},{2,4,6,7},{3,5}}
[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[1,6,7,2,3,4,5]=>{{1},{2,4,6},{3,5,7}}
[1,6,7,2,3,5,4]=>{{1},{2,3,4,5,6,7}}
[1,6,7,2,4,3,5]=>{{1},{2,3,4,5,6,7}}
[1,6,7,2,4,5,3]=>{{1},{2,4,5,6},{3,7}}
[1,6,7,2,5,3,4]=>{{1},{2,3,4,6,7},{5}}
[1,6,7,2,5,4,3]=>{{1},{2,4,6},{3,7},{5}}
[1,6,7,3,2,4,5]=>{{1},{2,3,4,5,6,7}}
[1,6,7,3,2,5,4]=>{{1},{2,5,6},{3,4,7}}
[1,6,7,3,4,2,5]=>{{1},{2,6},{3,4,5,7}}
[1,6,7,3,4,5,2]=>{{1},{2,3,4,5,6,7}}
[1,6,7,3,5,2,4]=>{{1},{2,6},{3,4,7},{5}}
[1,6,7,3,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[1,6,7,4,2,3,5]=>{{1},{2,3,5,6,7},{4}}
[1,6,7,4,2,5,3]=>{{1},{2,5,6},{3,7},{4}}
[1,6,7,4,3,2,5]=>{{1},{2,6},{3,5,7},{4}}
[1,6,7,4,3,5,2]=>{{1},{2,3,5,6,7},{4}}
[1,6,7,4,5,2,3]=>{{1},{2,6},{3,7},{4},{5}}
[1,6,7,4,5,3,2]=>{{1},{2,3,6,7},{4},{5}}
[1,6,7,5,2,3,4]=>{{1},{2,3,4,5,6,7}}
[1,6,7,5,2,4,3]=>{{1},{2,4,5,6},{3,7}}
[1,6,7,5,3,2,4]=>{{1},{2,6},{3,4,5,7}}
[1,6,7,5,3,4,2]=>{{1},{2,3,4,5,6,7}}
[1,6,7,5,4,2,3]=>{{1},{2,6},{3,7},{4,5}}
[1,6,7,5,4,3,2]=>{{1},{2,3,6,7},{4,5}}
[1,7,2,3,4,5,6]=>{{1},{2,3,4,5,6,7}}
[1,7,2,3,4,6,5]=>{{1},{2,3,4,5,7},{6}}
[1,7,2,3,5,4,6]=>{{1},{2,3,4,6,7},{5}}
[1,7,2,3,5,6,4]=>{{1},{2,3,4,7},{5},{6}}
[1,7,2,3,6,4,5]=>{{1},{2,3,4,5,6,7}}
[1,7,2,3,6,5,4]=>{{1},{2,3,4,7},{5,6}}
[1,7,2,4,3,5,6]=>{{1},{2,3,5,6,7},{4}}
[1,7,2,4,3,6,5]=>{{1},{2,3,5,7},{4},{6}}
[1,7,2,4,5,3,6]=>{{1},{2,3,6,7},{4},{5}}
[1,7,2,4,5,6,3]=>{{1},{2,3,7},{4},{5},{6}}
[1,7,2,4,6,3,5]=>{{1},{2,3,5,6,7},{4}}
[1,7,2,4,6,5,3]=>{{1},{2,3,7},{4},{5,6}}
[1,7,2,5,3,4,6]=>{{1},{2,3,4,5,6,7}}
[1,7,2,5,3,6,4]=>{{1},{2,3,4,5,7},{6}}
[1,7,2,5,4,3,6]=>{{1},{2,3,6,7},{4,5}}
[1,7,2,5,4,6,3]=>{{1},{2,3,7},{4,5},{6}}
[1,7,2,5,6,3,4]=>{{1},{2,3,4,5,6,7}}
[1,7,2,5,6,4,3]=>{{1},{2,3,7},{4,5,6}}
[1,7,2,6,3,4,5]=>{{1},{2,3,5,7},{4,6}}
[1,7,2,6,3,5,4]=>{{1},{2,3,4,5,6,7}}
[1,7,2,6,4,3,5]=>{{1},{2,3,4,5,6,7}}
[1,7,2,6,4,5,3]=>{{1},{2,3,7},{4,5,6}}
[1,7,2,6,5,3,4]=>{{1},{2,3,4,6,7},{5}}
[1,7,2,6,5,4,3]=>{{1},{2,3,7},{4,6},{5}}
[1,7,3,2,4,5,6]=>{{1},{2,4,5,6,7},{3}}
[1,7,3,2,4,6,5]=>{{1},{2,4,5,7},{3},{6}}
[1,7,3,2,5,4,6]=>{{1},{2,4,6,7},{3},{5}}
[1,7,3,2,5,6,4]=>{{1},{2,4,7},{3},{5},{6}}
[1,7,3,2,6,4,5]=>{{1},{2,4,5,6,7},{3}}
[1,7,3,2,6,5,4]=>{{1},{2,4,7},{3},{5,6}}
[1,7,3,4,2,5,6]=>{{1},{2,5,6,7},{3},{4}}
[1,7,3,4,2,6,5]=>{{1},{2,5,7},{3},{4},{6}}
[1,7,3,4,5,2,6]=>{{1},{2,6,7},{3},{4},{5}}
[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,3,4,6,2,5]=>{{1},{2,5,6,7},{3},{4}}
[1,7,3,4,6,5,2]=>{{1},{2,7},{3},{4},{5,6}}
[1,7,3,5,2,4,6]=>{{1},{2,4,5,6,7},{3}}
[1,7,3,5,2,6,4]=>{{1},{2,4,5,7},{3},{6}}
[1,7,3,5,4,2,6]=>{{1},{2,6,7},{3},{4,5}}
[1,7,3,5,4,6,2]=>{{1},{2,7},{3},{4,5},{6}}
[1,7,3,5,6,2,4]=>{{1},{2,4,5,6,7},{3}}
[1,7,3,5,6,4,2]=>{{1},{2,7},{3},{4,5,6}}
[1,7,3,6,2,4,5]=>{{1},{2,5,7},{3},{4,6}}
[1,7,3,6,2,5,4]=>{{1},{2,4,5,6,7},{3}}
[1,7,3,6,4,2,5]=>{{1},{2,4,5,6,7},{3}}
[1,7,3,6,4,5,2]=>{{1},{2,7},{3},{4,5,6}}
[1,7,3,6,5,2,4]=>{{1},{2,4,6,7},{3},{5}}
[1,7,3,6,5,4,2]=>{{1},{2,7},{3},{4,6},{5}}
[1,7,4,2,3,5,6]=>{{1},{2,3,4,5,6,7}}
[1,7,4,2,3,6,5]=>{{1},{2,3,4,5,7},{6}}
[1,7,4,2,5,3,6]=>{{1},{2,3,4,6,7},{5}}
[1,7,4,2,5,6,3]=>{{1},{2,3,4,7},{5},{6}}
[1,7,4,2,6,3,5]=>{{1},{2,3,4,5,6,7}}
[1,7,4,2,6,5,3]=>{{1},{2,3,4,7},{5,6}}
[1,7,4,3,2,5,6]=>{{1},{2,5,6,7},{3,4}}
[1,7,4,3,2,6,5]=>{{1},{2,5,7},{3,4},{6}}
[1,7,4,3,5,2,6]=>{{1},{2,6,7},{3,4},{5}}
[1,7,4,3,5,6,2]=>{{1},{2,7},{3,4},{5},{6}}
[1,7,4,3,6,2,5]=>{{1},{2,5,6,7},{3,4}}
[1,7,4,3,6,5,2]=>{{1},{2,7},{3,4},{5,6}}
[1,7,4,5,2,3,6]=>{{1},{2,3,4,5,6,7}}
[1,7,4,5,2,6,3]=>{{1},{2,3,4,5,7},{6}}
[1,7,4,5,3,2,6]=>{{1},{2,6,7},{3,4,5}}
[1,7,4,5,3,6,2]=>{{1},{2,7},{3,4,5},{6}}
[1,7,4,5,6,2,3]=>{{1},{2,3,4,5,6,7}}
[1,7,4,5,6,3,2]=>{{1},{2,7},{3,4,5,6}}
[1,7,4,6,2,3,5]=>{{1},{2,5,7},{3,4,6}}
[1,7,4,6,2,5,3]=>{{1},{2,3,4,5,6,7}}
[1,7,4,6,3,2,5]=>{{1},{2,3,4,5,6,7}}
[1,7,4,6,3,5,2]=>{{1},{2,7},{3,4,5,6}}
[1,7,4,6,5,2,3]=>{{1},{2,3,4,6,7},{5}}
[1,7,4,6,5,3,2]=>{{1},{2,7},{3,4,6},{5}}
[1,7,5,2,3,4,6]=>{{1},{2,4,6,7},{3,5}}
[1,7,5,2,3,6,4]=>{{1},{2,4,7},{3,5},{6}}
[1,7,5,2,4,3,6]=>{{1},{2,3,4,5,6,7}}
[1,7,5,2,4,6,3]=>{{1},{2,3,4,5,7},{6}}
[1,7,5,2,6,3,4]=>{{1},{2,4,7},{3,5,6}}
[1,7,5,2,6,4,3]=>{{1},{2,3,4,5,6,7}}
[1,7,5,3,2,4,6]=>{{1},{2,3,4,5,6,7}}
[1,7,5,3,2,6,4]=>{{1},{2,3,4,5,7},{6}}
[1,7,5,3,4,2,6]=>{{1},{2,6,7},{3,4,5}}
[1,7,5,3,4,6,2]=>{{1},{2,7},{3,4,5},{6}}
[1,7,5,3,6,2,4]=>{{1},{2,3,4,5,6,7}}
[1,7,5,3,6,4,2]=>{{1},{2,7},{3,4,5,6}}
[1,7,5,4,2,3,6]=>{{1},{2,3,5,6,7},{4}}
[1,7,5,4,2,6,3]=>{{1},{2,3,5,7},{4},{6}}
[1,7,5,4,3,2,6]=>{{1},{2,6,7},{3,5},{4}}
[1,7,5,4,3,6,2]=>{{1},{2,7},{3,5},{4},{6}}
[1,7,5,4,6,2,3]=>{{1},{2,3,5,6,7},{4}}
[1,7,5,4,6,3,2]=>{{1},{2,7},{3,5,6},{4}}
[1,7,5,6,2,3,4]=>{{1},{2,3,4,5,6,7}}
[1,7,5,6,2,4,3]=>{{1},{2,3,5,7},{4,6}}
[1,7,5,6,3,2,4]=>{{1},{2,4,6,7},{3,5}}
[1,7,5,6,3,4,2]=>{{1},{2,7},{3,5},{4,6}}
[1,7,5,6,4,2,3]=>{{1},{2,3,4,5,6,7}}
[1,7,5,6,4,3,2]=>{{1},{2,7},{3,4,5,6}}
[1,7,6,2,3,4,5]=>{{1},{2,3,4,5,6,7}}
[1,7,6,2,3,5,4]=>{{1},{2,4,7},{3,5,6}}
[1,7,6,2,4,3,5]=>{{1},{2,4,5,7},{3,6}}
[1,7,6,2,4,5,3]=>{{1},{2,3,4,5,6,7}}
[1,7,6,2,5,3,4]=>{{1},{2,4,7},{3,6},{5}}
[1,7,6,2,5,4,3]=>{{1},{2,3,4,6,7},{5}}
[1,7,6,3,2,4,5]=>{{1},{2,5,7},{3,4,6}}
[1,7,6,3,2,5,4]=>{{1},{2,3,4,5,6,7}}
[1,7,6,3,4,2,5]=>{{1},{2,3,4,5,6,7}}
[1,7,6,3,4,5,2]=>{{1},{2,7},{3,4,5,6}}
[1,7,6,3,5,2,4]=>{{1},{2,3,4,6,7},{5}}
[1,7,6,3,5,4,2]=>{{1},{2,7},{3,4,6},{5}}
[1,7,6,4,2,3,5]=>{{1},{2,5,7},{3,6},{4}}
[1,7,6,4,2,5,3]=>{{1},{2,3,5,6,7},{4}}
[1,7,6,4,3,2,5]=>{{1},{2,3,5,6,7},{4}}
[1,7,6,4,3,5,2]=>{{1},{2,7},{3,5,6},{4}}
[1,7,6,4,5,2,3]=>{{1},{2,3,6,7},{4},{5}}
[1,7,6,4,5,3,2]=>{{1},{2,7},{3,6},{4},{5}}
[1,7,6,5,2,3,4]=>{{1},{2,4,5,7},{3,6}}
[1,7,6,5,2,4,3]=>{{1},{2,3,4,5,6,7}}
[1,7,6,5,3,2,4]=>{{1},{2,3,4,5,6,7}}
[1,7,6,5,3,4,2]=>{{1},{2,7},{3,4,5,6}}
[1,7,6,5,4,2,3]=>{{1},{2,3,6,7},{4,5}}
[1,7,6,5,4,3,2]=>{{1},{2,7},{3,6},{4,5}}
[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}}
[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}}
[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}}
[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}}
[2,1,3,4,7,5,6]=>{{1,2},{3},{4},{5,6,7}}
[2,1,3,4,7,6,5]=>{{1,2},{3},{4},{5,7},{6}}
[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}}
[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}}
[2,1,3,5,6,4,7]=>{{1,2},{3},{4,5,6},{7}}
[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}}
[2,1,3,5,7,4,6]=>{{1,2},{3},{4,5,6,7}}
[2,1,3,5,7,6,4]=>{{1,2},{3},{4,5,7},{6}}
[2,1,3,6,4,5,7]=>{{1,2},{3},{4,5,6},{7}}
[2,1,3,6,4,7,5]=>{{1,2},{3},{4,5,6,7}}
[2,1,3,6,5,4,7]=>{{1,2},{3},{4,6},{5},{7}}
[2,1,3,6,5,7,4]=>{{1,2},{3},{4,6,7},{5}}
[2,1,3,6,7,4,5]=>{{1,2},{3},{4,6},{5,7}}
[2,1,3,6,7,5,4]=>{{1,2},{3},{4,5,6,7}}
[2,1,3,7,4,5,6]=>{{1,2},{3},{4,5,6,7}}
[2,1,3,7,4,6,5]=>{{1,2},{3},{4,5,7},{6}}
[2,1,3,7,5,4,6]=>{{1,2},{3},{4,6,7},{5}}
[2,1,3,7,5,6,4]=>{{1,2},{3},{4,7},{5},{6}}
[2,1,3,7,6,4,5]=>{{1,2},{3},{4,5,6,7}}
[2,1,3,7,6,5,4]=>{{1,2},{3},{4,7},{5,6}}
[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}}
[2,1,4,3,5,7,6]=>{{1,2},{3,4},{5},{6,7}}
[2,1,4,3,6,5,7]=>{{1,2},{3,4},{5,6},{7}}
[2,1,4,3,6,7,5]=>{{1,2},{3,4},{5,6,7}}
[2,1,4,3,7,5,6]=>{{1,2},{3,4},{5,6,7}}
[2,1,4,3,7,6,5]=>{{1,2},{3,4},{5,7},{6}}
[2,1,4,5,3,6,7]=>{{1,2},{3,4,5},{6},{7}}
[2,1,4,5,3,7,6]=>{{1,2},{3,4,5},{6,7}}
[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}}
[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}}
[2,1,4,5,7,3,6]=>{{1,2},{3,4,5,6,7}}
[2,1,4,5,7,6,3]=>{{1,2},{3,4,5,7},{6}}
[2,1,4,6,3,5,7]=>{{1,2},{3,4,5,6},{7}}
[2,1,4,6,3,7,5]=>{{1,2},{3,4,5,6,7}}
[2,1,4,6,5,3,7]=>{{1,2},{3,4,6},{5},{7}}
[2,1,4,6,5,7,3]=>{{1,2},{3,4,6,7},{5}}
[2,1,4,6,7,3,5]=>{{1,2},{3,4,6},{5,7}}
[2,1,4,6,7,5,3]=>{{1,2},{3,4,5,6,7}}
[2,1,4,7,3,5,6]=>{{1,2},{3,4,5,6,7}}
[2,1,4,7,3,6,5]=>{{1,2},{3,4,5,7},{6}}
[2,1,4,7,5,3,6]=>{{1,2},{3,4,6,7},{5}}
[2,1,4,7,5,6,3]=>{{1,2},{3,4,7},{5},{6}}
[2,1,4,7,6,3,5]=>{{1,2},{3,4,5,6,7}}
[2,1,4,7,6,5,3]=>{{1,2},{3,4,7},{5,6}}
[2,1,5,3,4,6,7]=>{{1,2},{3,4,5},{6},{7}}
[2,1,5,3,4,7,6]=>{{1,2},{3,4,5},{6,7}}
[2,1,5,3,6,4,7]=>{{1,2},{3,4,5,6},{7}}
[2,1,5,3,6,7,4]=>{{1,2},{3,4,5,6,7}}
[2,1,5,3,7,4,6]=>{{1,2},{3,4,5,6,7}}
[2,1,5,3,7,6,4]=>{{1,2},{3,4,5,7},{6}}
[2,1,5,4,3,6,7]=>{{1,2},{3,5},{4},{6},{7}}
[2,1,5,4,3,7,6]=>{{1,2},{3,5},{4},{6,7}}
[2,1,5,4,6,3,7]=>{{1,2},{3,5,6},{4},{7}}
[2,1,5,4,6,7,3]=>{{1,2},{3,5,6,7},{4}}
[2,1,5,4,7,3,6]=>{{1,2},{3,5,6,7},{4}}
[2,1,5,4,7,6,3]=>{{1,2},{3,5,7},{4},{6}}
[2,1,5,6,3,4,7]=>{{1,2},{3,5},{4,6},{7}}
[2,1,5,6,3,7,4]=>{{1,2},{3,5},{4,6,7}}
[2,1,5,6,4,3,7]=>{{1,2},{3,4,5,6},{7}}
[2,1,5,6,4,7,3]=>{{1,2},{3,4,5,6,7}}
[2,1,5,6,7,3,4]=>{{1,2},{3,4,5,6,7}}
[2,1,5,6,7,4,3]=>{{1,2},{3,5,7},{4,6}}
[2,1,5,7,3,4,6]=>{{1,2},{3,5},{4,6,7}}
[2,1,5,7,3,6,4]=>{{1,2},{3,5},{4,7},{6}}
[2,1,5,7,4,3,6]=>{{1,2},{3,4,5,6,7}}
[2,1,5,7,4,6,3]=>{{1,2},{3,4,5,7},{6}}
[2,1,5,7,6,3,4]=>{{1,2},{3,5,6},{4,7}}
[2,1,5,7,6,4,3]=>{{1,2},{3,4,5,6,7}}
[2,1,6,3,4,5,7]=>{{1,2},{3,4,5,6},{7}}
[2,1,6,3,4,7,5]=>{{1,2},{3,4,5,6,7}}
[2,1,6,3,5,4,7]=>{{1,2},{3,4,6},{5},{7}}
[2,1,6,3,5,7,4]=>{{1,2},{3,4,6,7},{5}}
[2,1,6,3,7,4,5]=>{{1,2},{3,4,6},{5,7}}
[2,1,6,3,7,5,4]=>{{1,2},{3,4,5,6,7}}
[2,1,6,4,3,5,7]=>{{1,2},{3,5,6},{4},{7}}
[2,1,6,4,3,7,5]=>{{1,2},{3,5,6,7},{4}}
[2,1,6,4,5,3,7]=>{{1,2},{3,6},{4},{5},{7}}
[2,1,6,4,5,7,3]=>{{1,2},{3,6,7},{4},{5}}
[2,1,6,4,7,3,5]=>{{1,2},{3,6},{4},{5,7}}
[2,1,6,4,7,5,3]=>{{1,2},{3,5,6,7},{4}}
[2,1,6,5,3,4,7]=>{{1,2},{3,4,5,6},{7}}
[2,1,6,5,3,7,4]=>{{1,2},{3,4,5,6,7}}
[2,1,6,5,4,3,7]=>{{1,2},{3,6},{4,5},{7}}
[2,1,6,5,4,7,3]=>{{1,2},{3,6,7},{4,5}}
[2,1,6,5,7,3,4]=>{{1,2},{3,6},{4,5,7}}
[2,1,6,5,7,4,3]=>{{1,2},{3,4,5,6,7}}
[2,1,6,7,3,4,5]=>{{1,2},{3,4,5,6,7}}
[2,1,6,7,3,5,4]=>{{1,2},{3,5,6},{4,7}}
[2,1,6,7,4,3,5]=>{{1,2},{3,6},{4,5,7}}
[2,1,6,7,4,5,3]=>{{1,2},{3,4,5,6,7}}
[2,1,6,7,5,3,4]=>{{1,2},{3,6},{4,7},{5}}
[2,1,6,7,5,4,3]=>{{1,2},{3,4,6,7},{5}}
[2,1,7,3,4,5,6]=>{{1,2},{3,4,5,6,7}}
[2,1,7,3,4,6,5]=>{{1,2},{3,4,5,7},{6}}
[2,1,7,3,5,4,6]=>{{1,2},{3,4,6,7},{5}}
[2,1,7,3,5,6,4]=>{{1,2},{3,4,7},{5},{6}}
[2,1,7,3,6,4,5]=>{{1,2},{3,4,5,6,7}}
[2,1,7,3,6,5,4]=>{{1,2},{3,4,7},{5,6}}
[2,1,7,4,3,5,6]=>{{1,2},{3,5,6,7},{4}}
[2,1,7,4,3,6,5]=>{{1,2},{3,5,7},{4},{6}}
[2,1,7,4,5,3,6]=>{{1,2},{3,6,7},{4},{5}}
[2,1,7,4,5,6,3]=>{{1,2},{3,7},{4},{5},{6}}
[2,1,7,4,6,3,5]=>{{1,2},{3,5,6,7},{4}}
[2,1,7,4,6,5,3]=>{{1,2},{3,7},{4},{5,6}}
[2,1,7,5,3,4,6]=>{{1,2},{3,4,5,6,7}}
[2,1,7,5,3,6,4]=>{{1,2},{3,4,5,7},{6}}
[2,1,7,5,4,3,6]=>{{1,2},{3,6,7},{4,5}}
[2,1,7,5,4,6,3]=>{{1,2},{3,7},{4,5},{6}}
[2,1,7,5,6,3,4]=>{{1,2},{3,4,5,6,7}}
[2,1,7,5,6,4,3]=>{{1,2},{3,7},{4,5,6}}
[2,1,7,6,3,4,5]=>{{1,2},{3,5,7},{4,6}}
[2,1,7,6,3,5,4]=>{{1,2},{3,4,5,6,7}}
[2,1,7,6,4,3,5]=>{{1,2},{3,4,5,6,7}}
[2,1,7,6,4,5,3]=>{{1,2},{3,7},{4,5,6}}
[2,1,7,6,5,3,4]=>{{1,2},{3,4,6,7},{5}}
[2,1,7,6,5,4,3]=>{{1,2},{3,7},{4,6},{5}}
[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}
[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}
[2,3,1,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}
[2,3,1,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}
[2,3,1,4,7,5,6]=>{{1,2,3},{4},{5,6,7}}
[2,3,1,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}}
[2,3,1,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}
[2,3,1,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}
[2,3,1,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}
[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}}
[2,3,1,5,7,4,6]=>{{1,2,3},{4,5,6,7}}
[2,3,1,5,7,6,4]=>{{1,2,3},{4,5,7},{6}}
[2,3,1,6,4,5,7]=>{{1,2,3},{4,5,6},{7}}
[2,3,1,6,4,7,5]=>{{1,2,3},{4,5,6,7}}
[2,3,1,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}}
[2,3,1,6,5,7,4]=>{{1,2,3},{4,6,7},{5}}
[2,3,1,6,7,4,5]=>{{1,2,3},{4,6},{5,7}}
[2,3,1,6,7,5,4]=>{{1,2,3},{4,5,6,7}}
[2,3,1,7,4,5,6]=>{{1,2,3},{4,5,6,7}}
[2,3,1,7,4,6,5]=>{{1,2,3},{4,5,7},{6}}
[2,3,1,7,5,4,6]=>{{1,2,3},{4,6,7},{5}}
[2,3,1,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}}
[2,3,1,7,6,4,5]=>{{1,2,3},{4,5,6,7}}
[2,3,1,7,6,5,4]=>{{1,2,3},{4,7},{5,6}}
[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[2,3,4,1,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}}
[2,3,4,1,7,5,6]=>{{1,2,3,4},{5,6,7}}
[2,3,4,1,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}}
[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}}
[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}}
[2,3,4,6,1,5,7]=>{{1,2,3,4,5,6},{7}}
[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[2,3,4,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[2,3,4,6,5,7,1]=>{{1,2,3,4,6,7},{5}}
[2,3,4,6,7,1,5]=>{{1,2,3,4,6},{5,7}}
[2,3,4,6,7,5,1]=>{{1,2,3,4,5,6,7}}
[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[2,3,4,7,1,6,5]=>{{1,2,3,4,5,7},{6}}
[2,3,4,7,5,1,6]=>{{1,2,3,4,6,7},{5}}
[2,3,4,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[2,3,4,7,6,1,5]=>{{1,2,3,4,5,6,7}}
[2,3,4,7,6,5,1]=>{{1,2,3,4,7},{5,6}}
[2,3,5,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[2,3,5,1,4,7,6]=>{{1,2,3,4,5},{6,7}}
[2,3,5,1,6,4,7]=>{{1,2,3,4,5,6},{7}}
[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[2,3,5,1,7,6,4]=>{{1,2,3,4,5,7},{6}}
[2,3,5,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}}
[2,3,5,4,1,7,6]=>{{1,2,3,5},{4},{6,7}}
[2,3,5,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}
[2,3,5,4,6,7,1]=>{{1,2,3,5,6,7},{4}}
[2,3,5,4,7,1,6]=>{{1,2,3,5,6,7},{4}}
[2,3,5,4,7,6,1]=>{{1,2,3,5,7},{4},{6}}
[2,3,5,6,1,4,7]=>{{1,2,3,5},{4,6},{7}}
[2,3,5,6,1,7,4]=>{{1,2,3,5},{4,6,7}}
[2,3,5,6,4,1,7]=>{{1,2,3,4,5,6},{7}}
[2,3,5,6,4,7,1]=>{{1,2,3,4,5,6,7}}
[2,3,5,6,7,1,4]=>{{1,2,3,4,5,6,7}}
[2,3,5,6,7,4,1]=>{{1,2,3,5,7},{4,6}}
[2,3,5,7,1,4,6]=>{{1,2,3,5},{4,6,7}}
[2,3,5,7,1,6,4]=>{{1,2,3,5},{4,7},{6}}
[2,3,5,7,4,1,6]=>{{1,2,3,4,5,6,7}}
[2,3,5,7,4,6,1]=>{{1,2,3,4,5,7},{6}}
[2,3,5,7,6,1,4]=>{{1,2,3,5,6},{4,7}}
[2,3,5,7,6,4,1]=>{{1,2,3,4,5,6,7}}
[2,3,6,1,4,5,7]=>{{1,2,3,4,5,6},{7}}
[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}}
[2,3,6,1,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[2,3,6,1,5,7,4]=>{{1,2,3,4,6,7},{5}}
[2,3,6,1,7,4,5]=>{{1,2,3,4,6},{5,7}}
[2,3,6,1,7,5,4]=>{{1,2,3,4,5,6,7}}
[2,3,6,4,1,5,7]=>{{1,2,3,5,6},{4},{7}}
[2,3,6,4,1,7,5]=>{{1,2,3,5,6,7},{4}}
[2,3,6,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}
[2,3,6,4,5,7,1]=>{{1,2,3,6,7},{4},{5}}
[2,3,6,4,7,1,5]=>{{1,2,3,6},{4},{5,7}}
[2,3,6,4,7,5,1]=>{{1,2,3,5,6,7},{4}}
[2,3,6,5,1,4,7]=>{{1,2,3,4,5,6},{7}}
[2,3,6,5,1,7,4]=>{{1,2,3,4,5,6,7}}
[2,3,6,5,4,1,7]=>{{1,2,3,6},{4,5},{7}}
[2,3,6,5,4,7,1]=>{{1,2,3,6,7},{4,5}}
[2,3,6,5,7,1,4]=>{{1,2,3,6},{4,5,7}}
[2,3,6,5,7,4,1]=>{{1,2,3,4,5,6,7}}
[2,3,6,7,1,4,5]=>{{1,2,3,4,5,6,7}}
[2,3,6,7,1,5,4]=>{{1,2,3,5,6},{4,7}}
[2,3,6,7,4,1,5]=>{{1,2,3,6},{4,5,7}}
[2,3,6,7,4,5,1]=>{{1,2,3,4,5,6,7}}
[2,3,6,7,5,1,4]=>{{1,2,3,6},{4,7},{5}}
[2,3,6,7,5,4,1]=>{{1,2,3,4,6,7},{5}}
[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}}
[2,3,7,1,4,6,5]=>{{1,2,3,4,5,7},{6}}
[2,3,7,1,5,4,6]=>{{1,2,3,4,6,7},{5}}
[2,3,7,1,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[2,3,7,1,6,4,5]=>{{1,2,3,4,5,6,7}}
[2,3,7,1,6,5,4]=>{{1,2,3,4,7},{5,6}}
[2,3,7,4,1,5,6]=>{{1,2,3,5,6,7},{4}}
[2,3,7,4,1,6,5]=>{{1,2,3,5,7},{4},{6}}
[2,3,7,4,5,1,6]=>{{1,2,3,6,7},{4},{5}}
[2,3,7,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}}
[2,3,7,4,6,1,5]=>{{1,2,3,5,6,7},{4}}
[2,3,7,4,6,5,1]=>{{1,2,3,7},{4},{5,6}}
[2,3,7,5,1,4,6]=>{{1,2,3,4,5,6,7}}
[2,3,7,5,1,6,4]=>{{1,2,3,4,5,7},{6}}
[2,3,7,5,4,1,6]=>{{1,2,3,6,7},{4,5}}
[2,3,7,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}
[2,3,7,5,6,1,4]=>{{1,2,3,4,5,6,7}}
[2,3,7,5,6,4,1]=>{{1,2,3,7},{4,5,6}}
[2,3,7,6,1,4,5]=>{{1,2,3,5,7},{4,6}}
[2,3,7,6,1,5,4]=>{{1,2,3,4,5,6,7}}
[2,3,7,6,4,1,5]=>{{1,2,3,4,5,6,7}}
[2,3,7,6,4,5,1]=>{{1,2,3,7},{4,5,6}}
[2,3,7,6,5,1,4]=>{{1,2,3,4,6,7},{5}}
[2,3,7,6,5,4,1]=>{{1,2,3,7},{4,6},{5}}
[2,4,1,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[2,4,1,3,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[2,4,1,3,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[2,4,1,3,6,7,5]=>{{1,2,3,4},{5,6,7}}
[2,4,1,3,7,5,6]=>{{1,2,3,4},{5,6,7}}
[2,4,1,3,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[2,4,1,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[2,4,1,5,3,7,6]=>{{1,2,3,4,5},{6,7}}
[2,4,1,5,6,3,7]=>{{1,2,3,4,5,6},{7}}
[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[2,4,1,5,7,6,3]=>{{1,2,3,4,5,7},{6}}
[2,4,1,6,3,5,7]=>{{1,2,3,4,5,6},{7}}
[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[2,4,1,6,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[2,4,1,6,5,7,3]=>{{1,2,3,4,6,7},{5}}
[2,4,1,6,7,3,5]=>{{1,2,3,4,6},{5,7}}
[2,4,1,6,7,5,3]=>{{1,2,3,4,5,6,7}}
[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[2,4,1,7,3,6,5]=>{{1,2,3,4,5,7},{6}}
[2,4,1,7,5,3,6]=>{{1,2,3,4,6,7},{5}}
[2,4,1,7,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}}
[2,4,1,7,6,5,3]=>{{1,2,3,4,7},{5,6}}
[2,4,3,1,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}
[2,4,3,1,5,7,6]=>{{1,2,4},{3},{5},{6,7}}
[2,4,3,1,6,5,7]=>{{1,2,4},{3},{5,6},{7}}
[2,4,3,1,6,7,5]=>{{1,2,4},{3},{5,6,7}}
[2,4,3,1,7,5,6]=>{{1,2,4},{3},{5,6,7}}
[2,4,3,1,7,6,5]=>{{1,2,4},{3},{5,7},{6}}
[2,4,3,5,1,6,7]=>{{1,2,4,5},{3},{6},{7}}
[2,4,3,5,1,7,6]=>{{1,2,4,5},{3},{6,7}}
[2,4,3,5,6,1,7]=>{{1,2,4,5,6},{3},{7}}
[2,4,3,5,6,7,1]=>{{1,2,4,5,6,7},{3}}
[2,4,3,5,7,1,6]=>{{1,2,4,5,6,7},{3}}
[2,4,3,5,7,6,1]=>{{1,2,4,5,7},{3},{6}}
[2,4,3,6,1,5,7]=>{{1,2,4,5,6},{3},{7}}
[2,4,3,6,1,7,5]=>{{1,2,4,5,6,7},{3}}
[2,4,3,6,5,1,7]=>{{1,2,4,6},{3},{5},{7}}
[2,4,3,6,5,7,1]=>{{1,2,4,6,7},{3},{5}}
[2,4,3,6,7,1,5]=>{{1,2,4,6},{3},{5,7}}
[2,4,3,6,7,5,1]=>{{1,2,4,5,6,7},{3}}
[2,4,3,7,1,5,6]=>{{1,2,4,5,6,7},{3}}
[2,4,3,7,1,6,5]=>{{1,2,4,5,7},{3},{6}}
[2,4,3,7,5,1,6]=>{{1,2,4,6,7},{3},{5}}
[2,4,3,7,5,6,1]=>{{1,2,4,7},{3},{5},{6}}
[2,4,3,7,6,1,5]=>{{1,2,4,5,6,7},{3}}
[2,4,3,7,6,5,1]=>{{1,2,4,7},{3},{5,6}}
[2,4,5,1,3,6,7]=>{{1,2,4},{3,5},{6},{7}}
[2,4,5,1,3,7,6]=>{{1,2,4},{3,5},{6,7}}
[2,4,5,1,6,3,7]=>{{1,2,4},{3,5,6},{7}}
[2,4,5,1,6,7,3]=>{{1,2,4},{3,5,6,7}}
[2,4,5,1,7,3,6]=>{{1,2,4},{3,5,6,7}}
[2,4,5,1,7,6,3]=>{{1,2,4},{3,5,7},{6}}
[2,4,5,3,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[2,4,5,3,1,7,6]=>{{1,2,3,4,5},{6,7}}
[2,4,5,3,6,1,7]=>{{1,2,3,4,5,6},{7}}
[2,4,5,3,6,7,1]=>{{1,2,3,4,5,6,7}}
[2,4,5,3,7,1,6]=>{{1,2,3,4,5,6,7}}
[2,4,5,3,7,6,1]=>{{1,2,3,4,5,7},{6}}
[2,4,5,6,1,3,7]=>{{1,2,3,4,5,6},{7}}
[2,4,5,6,1,7,3]=>{{1,2,3,4,5,6,7}}
[2,4,5,6,3,1,7]=>{{1,2,4,6},{3,5},{7}}
[2,4,5,6,3,7,1]=>{{1,2,4,6,7},{3,5}}
[2,4,5,6,7,1,3]=>{{1,2,4,6},{3,5,7}}
[2,4,5,6,7,3,1]=>{{1,2,3,4,5,6,7}}
[2,4,5,7,1,3,6]=>{{1,2,3,4,5,6,7}}
[2,4,5,7,1,6,3]=>{{1,2,3,4,5,7},{6}}
[2,4,5,7,3,1,6]=>{{1,2,4,6,7},{3,5}}
[2,4,5,7,3,6,1]=>{{1,2,4,7},{3,5},{6}}
[2,4,5,7,6,1,3]=>{{1,2,3,4,5,6,7}}
[2,4,5,7,6,3,1]=>{{1,2,4,7},{3,5,6}}
[2,4,6,1,3,5,7]=>{{1,2,4},{3,5,6},{7}}
[2,4,6,1,3,7,5]=>{{1,2,4},{3,5,6,7}}
[2,4,6,1,5,3,7]=>{{1,2,4},{3,6},{5},{7}}
[2,4,6,1,5,7,3]=>{{1,2,4},{3,6,7},{5}}
[2,4,6,1,7,3,5]=>{{1,2,4},{3,6},{5,7}}
[2,4,6,1,7,5,3]=>{{1,2,4},{3,5,6,7}}
[2,4,6,3,1,5,7]=>{{1,2,3,4,5,6},{7}}
[2,4,6,3,1,7,5]=>{{1,2,3,4,5,6,7}}
[2,4,6,3,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[2,4,6,3,5,7,1]=>{{1,2,3,4,6,7},{5}}
[2,4,6,3,7,1,5]=>{{1,2,3,4,6},{5,7}}
[2,4,6,3,7,5,1]=>{{1,2,3,4,5,6,7}}
[2,4,6,5,1,3,7]=>{{1,2,4,5},{3,6},{7}}
[2,4,6,5,1,7,3]=>{{1,2,4,5},{3,6,7}}
[2,4,6,5,3,1,7]=>{{1,2,3,4,5,6},{7}}
[2,4,6,5,3,7,1]=>{{1,2,3,4,5,6,7}}
[2,4,6,5,7,1,3]=>{{1,2,3,4,5,6,7}}
[2,4,6,5,7,3,1]=>{{1,2,4,5,7},{3,6}}
[2,4,6,7,1,3,5]=>{{1,2,4,5,7},{3,6}}
[2,4,6,7,1,5,3]=>{{1,2,3,4,5,6,7}}
[2,4,6,7,3,1,5]=>{{1,2,3,4,5,6,7}}
[2,4,6,7,3,5,1]=>{{1,2,4,7},{3,5,6}}
[2,4,6,7,5,1,3]=>{{1,2,3,4,6,7},{5}}
[2,4,6,7,5,3,1]=>{{1,2,4,7},{3,6},{5}}
[2,4,7,1,3,5,6]=>{{1,2,4},{3,5,6,7}}
[2,4,7,1,3,6,5]=>{{1,2,4},{3,5,7},{6}}
[2,4,7,1,5,3,6]=>{{1,2,4},{3,6,7},{5}}
[2,4,7,1,5,6,3]=>{{1,2,4},{3,7},{5},{6}}
[2,4,7,1,6,3,5]=>{{1,2,4},{3,5,6,7}}
[2,4,7,1,6,5,3]=>{{1,2,4},{3,7},{5,6}}
[2,4,7,3,1,5,6]=>{{1,2,3,4,5,6,7}}
[2,4,7,3,1,6,5]=>{{1,2,3,4,5,7},{6}}
[2,4,7,3,5,1,6]=>{{1,2,3,4,6,7},{5}}
[2,4,7,3,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[2,4,7,3,6,1,5]=>{{1,2,3,4,5,6,7}}
[2,4,7,3,6,5,1]=>{{1,2,3,4,7},{5,6}}
[2,4,7,5,1,3,6]=>{{1,2,4,5},{3,6,7}}
[2,4,7,5,1,6,3]=>{{1,2,4,5},{3,7},{6}}
[2,4,7,5,3,1,6]=>{{1,2,3,4,5,6,7}}
[2,4,7,5,3,6,1]=>{{1,2,3,4,5,7},{6}}
[2,4,7,5,6,1,3]=>{{1,2,4,5,6},{3,7}}
[2,4,7,5,6,3,1]=>{{1,2,3,4,5,6,7}}
[2,4,7,6,1,3,5]=>{{1,2,3,4,5,6,7}}
[2,4,7,6,1,5,3]=>{{1,2,4,5,6},{3,7}}
[2,4,7,6,3,1,5]=>{{1,2,4,6},{3,5,7}}
[2,4,7,6,3,5,1]=>{{1,2,3,4,5,6,7}}
[2,4,7,6,5,1,3]=>{{1,2,4,6},{3,7},{5}}
[2,4,7,6,5,3,1]=>{{1,2,3,4,6,7},{5}}
[2,5,1,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[2,5,1,3,4,7,6]=>{{1,2,3,4,5},{6,7}}
[2,5,1,3,6,4,7]=>{{1,2,3,4,5,6},{7}}
[2,5,1,3,6,7,4]=>{{1,2,3,4,5,6,7}}
[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[2,5,1,3,7,6,4]=>{{1,2,3,4,5,7},{6}}
[2,5,1,4,3,6,7]=>{{1,2,3,5},{4},{6},{7}}
[2,5,1,4,3,7,6]=>{{1,2,3,5},{4},{6,7}}
[2,5,1,4,6,3,7]=>{{1,2,3,5,6},{4},{7}}
[2,5,1,4,6,7,3]=>{{1,2,3,5,6,7},{4}}
[2,5,1,4,7,3,6]=>{{1,2,3,5,6,7},{4}}
[2,5,1,4,7,6,3]=>{{1,2,3,5,7},{4},{6}}
[2,5,1,6,3,4,7]=>{{1,2,3,5},{4,6},{7}}
[2,5,1,6,3,7,4]=>{{1,2,3,5},{4,6,7}}
[2,5,1,6,4,3,7]=>{{1,2,3,4,5,6},{7}}
[2,5,1,6,4,7,3]=>{{1,2,3,4,5,6,7}}
[2,5,1,6,7,3,4]=>{{1,2,3,4,5,6,7}}
[2,5,1,6,7,4,3]=>{{1,2,3,5,7},{4,6}}
[2,5,1,7,3,4,6]=>{{1,2,3,5},{4,6,7}}
[2,5,1,7,3,6,4]=>{{1,2,3,5},{4,7},{6}}
[2,5,1,7,4,3,6]=>{{1,2,3,4,5,6,7}}
[2,5,1,7,4,6,3]=>{{1,2,3,4,5,7},{6}}
[2,5,1,7,6,3,4]=>{{1,2,3,5,6},{4,7}}
[2,5,1,7,6,4,3]=>{{1,2,3,4,5,6,7}}
[2,5,3,1,4,6,7]=>{{1,2,4,5},{3},{6},{7}}
[2,5,3,1,4,7,6]=>{{1,2,4,5},{3},{6,7}}
[2,5,3,1,6,4,7]=>{{1,2,4,5,6},{3},{7}}
[2,5,3,1,6,7,4]=>{{1,2,4,5,6,7},{3}}
[2,5,3,1,7,4,6]=>{{1,2,4,5,6,7},{3}}
[2,5,3,1,7,6,4]=>{{1,2,4,5,7},{3},{6}}
[2,5,3,4,1,6,7]=>{{1,2,5},{3},{4},{6},{7}}
[2,5,3,4,1,7,6]=>{{1,2,5},{3},{4},{6,7}}
[2,5,3,4,6,1,7]=>{{1,2,5,6},{3},{4},{7}}
[2,5,3,4,6,7,1]=>{{1,2,5,6,7},{3},{4}}
[2,5,3,4,7,1,6]=>{{1,2,5,6,7},{3},{4}}
[2,5,3,4,7,6,1]=>{{1,2,5,7},{3},{4},{6}}
[2,5,3,6,1,4,7]=>{{1,2,5},{3},{4,6},{7}}
[2,5,3,6,1,7,4]=>{{1,2,5},{3},{4,6,7}}
[2,5,3,6,4,1,7]=>{{1,2,4,5,6},{3},{7}}
[2,5,3,6,4,7,1]=>{{1,2,4,5,6,7},{3}}
[2,5,3,6,7,1,4]=>{{1,2,4,5,6,7},{3}}
[2,5,3,6,7,4,1]=>{{1,2,5,7},{3},{4,6}}
[2,5,3,7,1,4,6]=>{{1,2,5},{3},{4,6,7}}
[2,5,3,7,1,6,4]=>{{1,2,5},{3},{4,7},{6}}
[2,5,3,7,4,1,6]=>{{1,2,4,5,6,7},{3}}
[2,5,3,7,4,6,1]=>{{1,2,4,5,7},{3},{6}}
[2,5,3,7,6,1,4]=>{{1,2,5,6},{3},{4,7}}
[2,5,3,7,6,4,1]=>{{1,2,4,5,6,7},{3}}
[2,5,4,1,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[2,5,4,1,3,7,6]=>{{1,2,3,4,5},{6,7}}
[2,5,4,1,6,3,7]=>{{1,2,3,4,5,6},{7}}
[2,5,4,1,6,7,3]=>{{1,2,3,4,5,6,7}}
[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}}
[2,5,4,1,7,6,3]=>{{1,2,3,4,5,7},{6}}
[2,5,4,3,1,6,7]=>{{1,2,5},{3,4},{6},{7}}
[2,5,4,3,1,7,6]=>{{1,2,5},{3,4},{6,7}}
[2,5,4,3,6,1,7]=>{{1,2,5,6},{3,4},{7}}
[2,5,4,3,6,7,1]=>{{1,2,5,6,7},{3,4}}
[2,5,4,3,7,1,6]=>{{1,2,5,6,7},{3,4}}
[2,5,4,3,7,6,1]=>{{1,2,5,7},{3,4},{6}}
[2,5,4,6,1,3,7]=>{{1,2,5},{3,4,6},{7}}
[2,5,4,6,1,7,3]=>{{1,2,5},{3,4,6,7}}
[2,5,4,6,3,1,7]=>{{1,2,3,4,5,6},{7}}
[2,5,4,6,3,7,1]=>{{1,2,3,4,5,6,7}}
[2,5,4,6,7,1,3]=>{{1,2,3,4,5,6,7}}
[2,5,4,6,7,3,1]=>{{1,2,5,7},{3,4,6}}
[2,5,4,7,1,3,6]=>{{1,2,5},{3,4,6,7}}
[2,5,4,7,1,6,3]=>{{1,2,5},{3,4,7},{6}}
[2,5,4,7,3,1,6]=>{{1,2,3,4,5,6,7}}
[2,5,4,7,3,6,1]=>{{1,2,3,4,5,7},{6}}
[2,5,4,7,6,1,3]=>{{1,2,5,6},{3,4,7}}
[2,5,4,7,6,3,1]=>{{1,2,3,4,5,6,7}}
[2,5,6,1,3,4,7]=>{{1,2,3,4,5,6},{7}}
[2,5,6,1,3,7,4]=>{{1,2,3,4,5,6,7}}
[2,5,6,1,4,3,7]=>{{1,2,4,5},{3,6},{7}}
[2,5,6,1,4,7,3]=>{{1,2,4,5},{3,6,7}}
[2,5,6,1,7,3,4]=>{{1,2,4,5,7},{3,6}}
[2,5,6,1,7,4,3]=>{{1,2,3,4,5,6,7}}
[2,5,6,3,1,4,7]=>{{1,2,5},{3,4,6},{7}}
[2,5,6,3,1,7,4]=>{{1,2,5},{3,4,6,7}}
[2,5,6,3,4,1,7]=>{{1,2,3,4,5,6},{7}}
[2,5,6,3,4,7,1]=>{{1,2,3,4,5,6,7}}
[2,5,6,3,7,1,4]=>{{1,2,3,4,5,6,7}}
[2,5,6,3,7,4,1]=>{{1,2,5,7},{3,4,6}}
[2,5,6,4,1,3,7]=>{{1,2,5},{3,6},{4},{7}}
[2,5,6,4,1,7,3]=>{{1,2,5},{3,6,7},{4}}
[2,5,6,4,3,1,7]=>{{1,2,3,5,6},{4},{7}}
[2,5,6,4,3,7,1]=>{{1,2,3,5,6,7},{4}}
[2,5,6,4,7,1,3]=>{{1,2,3,5,6,7},{4}}
[2,5,6,4,7,3,1]=>{{1,2,5,7},{3,6},{4}}
[2,5,6,7,1,3,4]=>{{1,2,5},{3,6},{4,7}}
[2,5,6,7,1,4,3]=>{{1,2,5},{3,4,6,7}}
[2,5,6,7,3,1,4]=>{{1,2,3,5,6},{4,7}}
[2,5,6,7,3,4,1]=>{{1,2,3,4,5,6,7}}
[2,5,6,7,4,1,3]=>{{1,2,3,4,5,6,7}}
[2,5,6,7,4,3,1]=>{{1,2,4,5,7},{3,6}}
[2,5,7,1,3,4,6]=>{{1,2,3,4,5,6,7}}
[2,5,7,1,3,6,4]=>{{1,2,3,4,5,7},{6}}
[2,5,7,1,4,3,6]=>{{1,2,4,5},{3,6,7}}
[2,5,7,1,4,6,3]=>{{1,2,4,5},{3,7},{6}}
[2,5,7,1,6,3,4]=>{{1,2,3,4,5,6,7}}
[2,5,7,1,6,4,3]=>{{1,2,4,5,6},{3,7}}
[2,5,7,3,1,4,6]=>{{1,2,5},{3,4,6,7}}
[2,5,7,3,1,6,4]=>{{1,2,5},{3,4,7},{6}}
[2,5,7,3,4,1,6]=>{{1,2,3,4,5,6,7}}
[2,5,7,3,4,6,1]=>{{1,2,3,4,5,7},{6}}
[2,5,7,3,6,1,4]=>{{1,2,5,6},{3,4,7}}
[2,5,7,3,6,4,1]=>{{1,2,3,4,5,6,7}}
[2,5,7,4,1,3,6]=>{{1,2,5},{3,6,7},{4}}
[2,5,7,4,1,6,3]=>{{1,2,5},{3,7},{4},{6}}
[2,5,7,4,3,1,6]=>{{1,2,3,5,6,7},{4}}
[2,5,7,4,3,6,1]=>{{1,2,3,5,7},{4},{6}}
[2,5,7,4,6,1,3]=>{{1,2,5,6},{3,7},{4}}
[2,5,7,4,6,3,1]=>{{1,2,3,5,6,7},{4}}
[2,5,7,6,1,3,4]=>{{1,2,5},{3,4,6,7}}
[2,5,7,6,1,4,3]=>{{1,2,5},{3,7},{4,6}}
[2,5,7,6,3,1,4]=>{{1,2,3,4,5,6,7}}
[2,5,7,6,3,4,1]=>{{1,2,3,5,7},{4,6}}
[2,5,7,6,4,1,3]=>{{1,2,4,5,6},{3,7}}
[2,5,7,6,4,3,1]=>{{1,2,3,4,5,6,7}}
[2,6,1,3,4,5,7]=>{{1,2,3,4,5,6},{7}}
[2,6,1,3,4,7,5]=>{{1,2,3,4,5,6,7}}
[2,6,1,3,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[2,6,1,3,5,7,4]=>{{1,2,3,4,6,7},{5}}
[2,6,1,3,7,4,5]=>{{1,2,3,4,6},{5,7}}
[2,6,1,3,7,5,4]=>{{1,2,3,4,5,6,7}}
[2,6,1,4,3,5,7]=>{{1,2,3,5,6},{4},{7}}
[2,6,1,4,3,7,5]=>{{1,2,3,5,6,7},{4}}
[2,6,1,4,5,3,7]=>{{1,2,3,6},{4},{5},{7}}
[2,6,1,4,5,7,3]=>{{1,2,3,6,7},{4},{5}}
[2,6,1,4,7,3,5]=>{{1,2,3,6},{4},{5,7}}
[2,6,1,4,7,5,3]=>{{1,2,3,5,6,7},{4}}
[2,6,1,5,3,4,7]=>{{1,2,3,4,5,6},{7}}
[2,6,1,5,3,7,4]=>{{1,2,3,4,5,6,7}}
[2,6,1,5,4,3,7]=>{{1,2,3,6},{4,5},{7}}
[2,6,1,5,4,7,3]=>{{1,2,3,6,7},{4,5}}
[2,6,1,5,7,3,4]=>{{1,2,3,6},{4,5,7}}
[2,6,1,5,7,4,3]=>{{1,2,3,4,5,6,7}}
[2,6,1,7,3,4,5]=>{{1,2,3,4,5,6,7}}
[2,6,1,7,3,5,4]=>{{1,2,3,5,6},{4,7}}
[2,6,1,7,4,3,5]=>{{1,2,3,6},{4,5,7}}
[2,6,1,7,4,5,3]=>{{1,2,3,4,5,6,7}}
[2,6,1,7,5,3,4]=>{{1,2,3,6},{4,7},{5}}
[2,6,1,7,5,4,3]=>{{1,2,3,4,6,7},{5}}
[2,6,3,1,4,5,7]=>{{1,2,4,5,6},{3},{7}}
[2,6,3,1,4,7,5]=>{{1,2,4,5,6,7},{3}}
[2,6,3,1,5,4,7]=>{{1,2,4,6},{3},{5},{7}}
[2,6,3,1,5,7,4]=>{{1,2,4,6,7},{3},{5}}
[2,6,3,1,7,4,5]=>{{1,2,4,6},{3},{5,7}}
[2,6,3,1,7,5,4]=>{{1,2,4,5,6,7},{3}}
[2,6,3,4,1,5,7]=>{{1,2,5,6},{3},{4},{7}}
[2,6,3,4,1,7,5]=>{{1,2,5,6,7},{3},{4}}
[2,6,3,4,5,1,7]=>{{1,2,6},{3},{4},{5},{7}}
[2,6,3,4,5,7,1]=>{{1,2,6,7},{3},{4},{5}}
[2,6,3,4,7,1,5]=>{{1,2,6},{3},{4},{5,7}}
[2,6,3,4,7,5,1]=>{{1,2,5,6,7},{3},{4}}
[2,6,3,5,1,4,7]=>{{1,2,4,5,6},{3},{7}}
[2,6,3,5,1,7,4]=>{{1,2,4,5,6,7},{3}}
[2,6,3,5,4,1,7]=>{{1,2,6},{3},{4,5},{7}}
[2,6,3,5,4,7,1]=>{{1,2,6,7},{3},{4,5}}
[2,6,3,5,7,1,4]=>{{1,2,6},{3},{4,5,7}}
[2,6,3,5,7,4,1]=>{{1,2,4,5,6,7},{3}}
[2,6,3,7,1,4,5]=>{{1,2,4,5,6,7},{3}}
[2,6,3,7,1,5,4]=>{{1,2,5,6},{3},{4,7}}
[2,6,3,7,4,1,5]=>{{1,2,6},{3},{4,5,7}}
[2,6,3,7,4,5,1]=>{{1,2,4,5,6,7},{3}}
[2,6,3,7,5,1,4]=>{{1,2,6},{3},{4,7},{5}}
[2,6,3,7,5,4,1]=>{{1,2,4,6,7},{3},{5}}
[2,6,4,1,3,5,7]=>{{1,2,3,4,5,6},{7}}
[2,6,4,1,3,7,5]=>{{1,2,3,4,5,6,7}}
[2,6,4,1,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[2,6,4,1,5,7,3]=>{{1,2,3,4,6,7},{5}}
[2,6,4,1,7,3,5]=>{{1,2,3,4,6},{5,7}}
[2,6,4,1,7,5,3]=>{{1,2,3,4,5,6,7}}
[2,6,4,3,1,5,7]=>{{1,2,5,6},{3,4},{7}}
[2,6,4,3,1,7,5]=>{{1,2,5,6,7},{3,4}}
[2,6,4,3,5,1,7]=>{{1,2,6},{3,4},{5},{7}}
[2,6,4,3,5,7,1]=>{{1,2,6,7},{3,4},{5}}
[2,6,4,3,7,1,5]=>{{1,2,6},{3,4},{5,7}}
[2,6,4,3,7,5,1]=>{{1,2,5,6,7},{3,4}}
[2,6,4,5,1,3,7]=>{{1,2,3,4,5,6},{7}}
[2,6,4,5,1,7,3]=>{{1,2,3,4,5,6,7}}
[2,6,4,5,3,1,7]=>{{1,2,6},{3,4,5},{7}}
[2,6,4,5,3,7,1]=>{{1,2,6,7},{3,4,5}}
[2,6,4,5,7,1,3]=>{{1,2,6},{3,4,5,7}}
[2,6,4,5,7,3,1]=>{{1,2,3,4,5,6,7}}
[2,6,4,7,1,3,5]=>{{1,2,3,4,5,6,7}}
[2,6,4,7,1,5,3]=>{{1,2,5,6},{3,4,7}}
[2,6,4,7,3,1,5]=>{{1,2,6},{3,4,5,7}}
[2,6,4,7,3,5,1]=>{{1,2,3,4,5,6,7}}
[2,6,4,7,5,1,3]=>{{1,2,6},{3,4,7},{5}}
[2,6,4,7,5,3,1]=>{{1,2,3,4,6,7},{5}}
[2,6,5,1,3,4,7]=>{{1,2,4,6},{3,5},{7}}
[2,6,5,1,3,7,4]=>{{1,2,4,6,7},{3,5}}
[2,6,5,1,4,3,7]=>{{1,2,3,4,5,6},{7}}
[2,6,5,1,4,7,3]=>{{1,2,3,4,5,6,7}}
[2,6,5,1,7,3,4]=>{{1,2,3,4,5,6,7}}
[2,6,5,1,7,4,3]=>{{1,2,4,6},{3,5,7}}
[2,6,5,3,1,4,7]=>{{1,2,3,4,5,6},{7}}
[2,6,5,3,1,7,4]=>{{1,2,3,4,5,6,7}}
[2,6,5,3,4,1,7]=>{{1,2,6},{3,4,5},{7}}
[2,6,5,3,4,7,1]=>{{1,2,6,7},{3,4,5}}
[2,6,5,3,7,1,4]=>{{1,2,6},{3,4,5,7}}
[2,6,5,3,7,4,1]=>{{1,2,3,4,5,6,7}}
[2,6,5,4,1,3,7]=>{{1,2,3,5,6},{4},{7}}
[2,6,5,4,1,7,3]=>{{1,2,3,5,6,7},{4}}
[2,6,5,4,3,1,7]=>{{1,2,6},{3,5},{4},{7}}
[2,6,5,4,3,7,1]=>{{1,2,6,7},{3,5},{4}}
[2,6,5,4,7,1,3]=>{{1,2,6},{3,5,7},{4}}
[2,6,5,4,7,3,1]=>{{1,2,3,5,6,7},{4}}
[2,6,5,7,1,3,4]=>{{1,2,3,5,6},{4,7}}
[2,6,5,7,1,4,3]=>{{1,2,3,4,5,6,7}}
[2,6,5,7,3,1,4]=>{{1,2,6},{3,5},{4,7}}
[2,6,5,7,3,4,1]=>{{1,2,4,6,7},{3,5}}
[2,6,5,7,4,1,3]=>{{1,2,6},{3,4,5,7}}
[2,6,5,7,4,3,1]=>{{1,2,3,4,5,6,7}}
[2,6,7,1,3,4,5]=>{{1,2,4,6},{3,5,7}}
[2,6,7,1,3,5,4]=>{{1,2,3,4,5,6,7}}
[2,6,7,1,4,3,5]=>{{1,2,3,4,5,6,7}}
[2,6,7,1,4,5,3]=>{{1,2,4,5,6},{3,7}}
[2,6,7,1,5,3,4]=>{{1,2,3,4,6,7},{5}}
[2,6,7,1,5,4,3]=>{{1,2,4,6},{3,7},{5}}
[2,6,7,3,1,4,5]=>{{1,2,3,4,5,6,7}}
[2,6,7,3,1,5,4]=>{{1,2,5,6},{3,4,7}}
[2,6,7,3,4,1,5]=>{{1,2,6},{3,4,5,7}}
[2,6,7,3,4,5,1]=>{{1,2,3,4,5,6,7}}
[2,6,7,3,5,1,4]=>{{1,2,6},{3,4,7},{5}}
[2,6,7,3,5,4,1]=>{{1,2,3,4,6,7},{5}}
[2,6,7,4,1,3,5]=>{{1,2,3,5,6,7},{4}}
[2,6,7,4,1,5,3]=>{{1,2,5,6},{3,7},{4}}
[2,6,7,4,3,1,5]=>{{1,2,6},{3,5,7},{4}}
[2,6,7,4,3,5,1]=>{{1,2,3,5,6,7},{4}}
[2,6,7,4,5,1,3]=>{{1,2,6},{3,7},{4},{5}}
[2,6,7,4,5,3,1]=>{{1,2,3,6,7},{4},{5}}
[2,6,7,5,1,3,4]=>{{1,2,3,4,5,6,7}}
[2,6,7,5,1,4,3]=>{{1,2,4,5,6},{3,7}}
[2,6,7,5,3,1,4]=>{{1,2,6},{3,4,5,7}}
[2,6,7,5,3,4,1]=>{{1,2,3,4,5,6,7}}
[2,6,7,5,4,1,3]=>{{1,2,6},{3,7},{4,5}}
[2,6,7,5,4,3,1]=>{{1,2,3,6,7},{4,5}}
[2,7,1,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[2,7,1,3,4,6,5]=>{{1,2,3,4,5,7},{6}}
[2,7,1,3,5,4,6]=>{{1,2,3,4,6,7},{5}}
[2,7,1,3,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[2,7,1,3,6,4,5]=>{{1,2,3,4,5,6,7}}
[2,7,1,3,6,5,4]=>{{1,2,3,4,7},{5,6}}
[2,7,1,4,3,5,6]=>{{1,2,3,5,6,7},{4}}
[2,7,1,4,3,6,5]=>{{1,2,3,5,7},{4},{6}}
[2,7,1,4,5,3,6]=>{{1,2,3,6,7},{4},{5}}
[2,7,1,4,5,6,3]=>{{1,2,3,7},{4},{5},{6}}
[2,7,1,4,6,3,5]=>{{1,2,3,5,6,7},{4}}
[2,7,1,4,6,5,3]=>{{1,2,3,7},{4},{5,6}}
[2,7,1,5,3,4,6]=>{{1,2,3,4,5,6,7}}
[2,7,1,5,3,6,4]=>{{1,2,3,4,5,7},{6}}
[2,7,1,5,4,3,6]=>{{1,2,3,6,7},{4,5}}
[2,7,1,5,4,6,3]=>{{1,2,3,7},{4,5},{6}}
[2,7,1,5,6,3,4]=>{{1,2,3,4,5,6,7}}
[2,7,1,5,6,4,3]=>{{1,2,3,7},{4,5,6}}
[2,7,1,6,3,4,5]=>{{1,2,3,5,7},{4,6}}
[2,7,1,6,3,5,4]=>{{1,2,3,4,5,6,7}}
[2,7,1,6,4,3,5]=>{{1,2,3,4,5,6,7}}
[2,7,1,6,4,5,3]=>{{1,2,3,7},{4,5,6}}
[2,7,1,6,5,3,4]=>{{1,2,3,4,6,7},{5}}
[2,7,1,6,5,4,3]=>{{1,2,3,7},{4,6},{5}}
[2,7,3,1,4,5,6]=>{{1,2,4,5,6,7},{3}}
[2,7,3,1,4,6,5]=>{{1,2,4,5,7},{3},{6}}
[2,7,3,1,5,4,6]=>{{1,2,4,6,7},{3},{5}}
[2,7,3,1,5,6,4]=>{{1,2,4,7},{3},{5},{6}}
[2,7,3,1,6,4,5]=>{{1,2,4,5,6,7},{3}}
[2,7,3,1,6,5,4]=>{{1,2,4,7},{3},{5,6}}
[2,7,3,4,1,5,6]=>{{1,2,5,6,7},{3},{4}}
[2,7,3,4,1,6,5]=>{{1,2,5,7},{3},{4},{6}}
[2,7,3,4,5,1,6]=>{{1,2,6,7},{3},{4},{5}}
[2,7,3,4,5,6,1]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,3,4,6,1,5]=>{{1,2,5,6,7},{3},{4}}
[2,7,3,4,6,5,1]=>{{1,2,7},{3},{4},{5,6}}
[2,7,3,5,1,4,6]=>{{1,2,4,5,6,7},{3}}
[2,7,3,5,1,6,4]=>{{1,2,4,5,7},{3},{6}}
[2,7,3,5,4,1,6]=>{{1,2,6,7},{3},{4,5}}
[2,7,3,5,4,6,1]=>{{1,2,7},{3},{4,5},{6}}
[2,7,3,5,6,1,4]=>{{1,2,4,5,6,7},{3}}
[2,7,3,5,6,4,1]=>{{1,2,7},{3},{4,5,6}}
[2,7,3,6,1,4,5]=>{{1,2,5,7},{3},{4,6}}
[2,7,3,6,1,5,4]=>{{1,2,4,5,6,7},{3}}
[2,7,3,6,4,1,5]=>{{1,2,4,5,6,7},{3}}
[2,7,3,6,4,5,1]=>{{1,2,7},{3},{4,5,6}}
[2,7,3,6,5,1,4]=>{{1,2,4,6,7},{3},{5}}
[2,7,3,6,5,4,1]=>{{1,2,7},{3},{4,6},{5}}
[2,7,4,1,3,5,6]=>{{1,2,3,4,5,6,7}}
[2,7,4,1,3,6,5]=>{{1,2,3,4,5,7},{6}}
[2,7,4,1,5,3,6]=>{{1,2,3,4,6,7},{5}}
[2,7,4,1,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[2,7,4,1,6,3,5]=>{{1,2,3,4,5,6,7}}
[2,7,4,1,6,5,3]=>{{1,2,3,4,7},{5,6}}
[2,7,4,3,1,5,6]=>{{1,2,5,6,7},{3,4}}
[2,7,4,3,1,6,5]=>{{1,2,5,7},{3,4},{6}}
[2,7,4,3,5,1,6]=>{{1,2,6,7},{3,4},{5}}
[2,7,4,3,5,6,1]=>{{1,2,7},{3,4},{5},{6}}
[2,7,4,3,6,1,5]=>{{1,2,5,6,7},{3,4}}
[2,7,4,3,6,5,1]=>{{1,2,7},{3,4},{5,6}}
[2,7,4,5,1,3,6]=>{{1,2,3,4,5,6,7}}
[2,7,4,5,1,6,3]=>{{1,2,3,4,5,7},{6}}
[2,7,4,5,3,1,6]=>{{1,2,6,7},{3,4,5}}
[2,7,4,5,3,6,1]=>{{1,2,7},{3,4,5},{6}}
[2,7,4,5,6,1,3]=>{{1,2,3,4,5,6,7}}
[2,7,4,5,6,3,1]=>{{1,2,7},{3,4,5,6}}
[2,7,4,6,1,3,5]=>{{1,2,5,7},{3,4,6}}
[2,7,4,6,1,5,3]=>{{1,2,3,4,5,6,7}}
[2,7,4,6,3,1,5]=>{{1,2,3,4,5,6,7}}
[2,7,4,6,3,5,1]=>{{1,2,7},{3,4,5,6}}
[2,7,4,6,5,1,3]=>{{1,2,3,4,6,7},{5}}
[2,7,4,6,5,3,1]=>{{1,2,7},{3,4,6},{5}}
[2,7,5,1,3,4,6]=>{{1,2,4,6,7},{3,5}}
[2,7,5,1,3,6,4]=>{{1,2,4,7},{3,5},{6}}
[2,7,5,1,4,3,6]=>{{1,2,3,4,5,6,7}}
[2,7,5,1,4,6,3]=>{{1,2,3,4,5,7},{6}}
[2,7,5,1,6,3,4]=>{{1,2,4,7},{3,5,6}}
[2,7,5,1,6,4,3]=>{{1,2,3,4,5,6,7}}
[2,7,5,3,1,4,6]=>{{1,2,3,4,5,6,7}}
[2,7,5,3,1,6,4]=>{{1,2,3,4,5,7},{6}}
[2,7,5,3,4,1,6]=>{{1,2,6,7},{3,4,5}}
[2,7,5,3,4,6,1]=>{{1,2,7},{3,4,5},{6}}
[2,7,5,3,6,1,4]=>{{1,2,3,4,5,6,7}}
[2,7,5,3,6,4,1]=>{{1,2,7},{3,4,5,6}}
[2,7,5,4,1,3,6]=>{{1,2,3,5,6,7},{4}}
[2,7,5,4,1,6,3]=>{{1,2,3,5,7},{4},{6}}
[2,7,5,4,3,1,6]=>{{1,2,6,7},{3,5},{4}}
[2,7,5,4,3,6,1]=>{{1,2,7},{3,5},{4},{6}}
[2,7,5,4,6,1,3]=>{{1,2,3,5,6,7},{4}}
[2,7,5,4,6,3,1]=>{{1,2,7},{3,5,6},{4}}
[2,7,5,6,1,3,4]=>{{1,2,3,4,5,6,7}}
[2,7,5,6,1,4,3]=>{{1,2,3,5,7},{4,6}}
[2,7,5,6,3,1,4]=>{{1,2,4,6,7},{3,5}}
[2,7,5,6,3,4,1]=>{{1,2,7},{3,5},{4,6}}
[2,7,5,6,4,1,3]=>{{1,2,3,4,5,6,7}}
[2,7,5,6,4,3,1]=>{{1,2,7},{3,4,5,6}}
[2,7,6,1,3,4,5]=>{{1,2,3,4,5,6,7}}
[2,7,6,1,3,5,4]=>{{1,2,4,7},{3,5,6}}
[2,7,6,1,4,3,5]=>{{1,2,4,5,7},{3,6}}
[2,7,6,1,4,5,3]=>{{1,2,3,4,5,6,7}}
[2,7,6,1,5,3,4]=>{{1,2,4,7},{3,6},{5}}
[2,7,6,1,5,4,3]=>{{1,2,3,4,6,7},{5}}
[2,7,6,3,1,4,5]=>{{1,2,5,7},{3,4,6}}
[2,7,6,3,1,5,4]=>{{1,2,3,4,5,6,7}}
[2,7,6,3,4,1,5]=>{{1,2,3,4,5,6,7}}
[2,7,6,3,4,5,1]=>{{1,2,7},{3,4,5,6}}
[2,7,6,3,5,1,4]=>{{1,2,3,4,6,7},{5}}
[2,7,6,3,5,4,1]=>{{1,2,7},{3,4,6},{5}}
[2,7,6,4,1,3,5]=>{{1,2,5,7},{3,6},{4}}
[2,7,6,4,1,5,3]=>{{1,2,3,5,6,7},{4}}
[2,7,6,4,3,1,5]=>{{1,2,3,5,6,7},{4}}
[2,7,6,4,3,5,1]=>{{1,2,7},{3,5,6},{4}}
[2,7,6,4,5,1,3]=>{{1,2,3,6,7},{4},{5}}
[2,7,6,4,5,3,1]=>{{1,2,7},{3,6},{4},{5}}
[2,7,6,5,1,3,4]=>{{1,2,4,5,7},{3,6}}
[2,7,6,5,1,4,3]=>{{1,2,3,4,5,6,7}}
[2,7,6,5,3,1,4]=>{{1,2,3,4,5,6,7}}
[2,7,6,5,3,4,1]=>{{1,2,7},{3,4,5,6}}
[2,7,6,5,4,1,3]=>{{1,2,3,6,7},{4,5}}
[2,7,6,5,4,3,1]=>{{1,2,7},{3,6},{4,5}}
[3,1,2,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}
[3,1,2,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}
[3,1,2,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}
[3,1,2,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}
[3,1,2,4,7,5,6]=>{{1,2,3},{4},{5,6,7}}
[3,1,2,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}}
[3,1,2,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}
[3,1,2,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}
[3,1,2,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}
[3,1,2,5,6,7,4]=>{{1,2,3},{4,5,6,7}}
[3,1,2,5,7,4,6]=>{{1,2,3},{4,5,6,7}}
[3,1,2,5,7,6,4]=>{{1,2,3},{4,5,7},{6}}
[3,1,2,6,4,5,7]=>{{1,2,3},{4,5,6},{7}}
[3,1,2,6,4,7,5]=>{{1,2,3},{4,5,6,7}}
[3,1,2,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}}
[3,1,2,6,5,7,4]=>{{1,2,3},{4,6,7},{5}}
[3,1,2,6,7,4,5]=>{{1,2,3},{4,6},{5,7}}
[3,1,2,6,7,5,4]=>{{1,2,3},{4,5,6,7}}
[3,1,2,7,4,5,6]=>{{1,2,3},{4,5,6,7}}
[3,1,2,7,4,6,5]=>{{1,2,3},{4,5,7},{6}}
[3,1,2,7,5,4,6]=>{{1,2,3},{4,6,7},{5}}
[3,1,2,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}}
[3,1,2,7,6,4,5]=>{{1,2,3},{4,5,6,7}}
[3,1,2,7,6,5,4]=>{{1,2,3},{4,7},{5,6}}
[3,1,4,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[3,1,4,2,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[3,1,4,2,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[3,1,4,2,6,7,5]=>{{1,2,3,4},{5,6,7}}
[3,1,4,2,7,5,6]=>{{1,2,3,4},{5,6,7}}
[3,1,4,2,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[3,1,4,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[3,1,4,5,2,7,6]=>{{1,2,3,4,5},{6,7}}
[3,1,4,5,6,2,7]=>{{1,2,3,4,5,6},{7}}
[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}}
[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}}
[3,1,4,5,7,6,2]=>{{1,2,3,4,5,7},{6}}
[3,1,4,6,2,5,7]=>{{1,2,3,4,5,6},{7}}
[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}
[3,1,4,6,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[3,1,4,6,5,7,2]=>{{1,2,3,4,6,7},{5}}
[3,1,4,6,7,2,5]=>{{1,2,3,4,6},{5,7}}
[3,1,4,6,7,5,2]=>{{1,2,3,4,5,6,7}}
[3,1,4,7,2,5,6]=>{{1,2,3,4,5,6,7}}
[3,1,4,7,2,6,5]=>{{1,2,3,4,5,7},{6}}
[3,1,4,7,5,2,6]=>{{1,2,3,4,6,7},{5}}
[3,1,4,7,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[3,1,4,7,6,2,5]=>{{1,2,3,4,5,6,7}}
[3,1,4,7,6,5,2]=>{{1,2,3,4,7},{5,6}}
[3,1,5,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[3,1,5,2,4,7,6]=>{{1,2,3,4,5},{6,7}}
[3,1,5,2,6,4,7]=>{{1,2,3,4,5,6},{7}}
[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}}
[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}
[3,1,5,2,7,6,4]=>{{1,2,3,4,5,7},{6}}
[3,1,5,4,2,6,7]=>{{1,2,3,5},{4},{6},{7}}
[3,1,5,4,2,7,6]=>{{1,2,3,5},{4},{6,7}}
[3,1,5,4,6,2,7]=>{{1,2,3,5,6},{4},{7}}
[3,1,5,4,6,7,2]=>{{1,2,3,5,6,7},{4}}
[3,1,5,4,7,2,6]=>{{1,2,3,5,6,7},{4}}
[3,1,5,4,7,6,2]=>{{1,2,3,5,7},{4},{6}}
[3,1,5,6,2,4,7]=>{{1,2,3,5},{4,6},{7}}
[3,1,5,6,2,7,4]=>{{1,2,3,5},{4,6,7}}
[3,1,5,6,4,2,7]=>{{1,2,3,4,5,6},{7}}
[3,1,5,6,4,7,2]=>{{1,2,3,4,5,6,7}}
[3,1,5,6,7,2,4]=>{{1,2,3,4,5,6,7}}
[3,1,5,6,7,4,2]=>{{1,2,3,5,7},{4,6}}
[3,1,5,7,2,4,6]=>{{1,2,3,5},{4,6,7}}
[3,1,5,7,2,6,4]=>{{1,2,3,5},{4,7},{6}}
[3,1,5,7,4,2,6]=>{{1,2,3,4,5,6,7}}
[3,1,5,7,4,6,2]=>{{1,2,3,4,5,7},{6}}
[3,1,5,7,6,2,4]=>{{1,2,3,5,6},{4,7}}
[3,1,5,7,6,4,2]=>{{1,2,3,4,5,6,7}}
[3,1,6,2,4,5,7]=>{{1,2,3,4,5,6},{7}}
[3,1,6,2,4,7,5]=>{{1,2,3,4,5,6,7}}
[3,1,6,2,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[3,1,6,2,5,7,4]=>{{1,2,3,4,6,7},{5}}
[3,1,6,2,7,4,5]=>{{1,2,3,4,6},{5,7}}
[3,1,6,2,7,5,4]=>{{1,2,3,4,5,6,7}}
[3,1,6,4,2,5,7]=>{{1,2,3,5,6},{4},{7}}
[3,1,6,4,2,7,5]=>{{1,2,3,5,6,7},{4}}
[3,1,6,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}}
[3,1,6,4,5,7,2]=>{{1,2,3,6,7},{4},{5}}
[3,1,6,4,7,2,5]=>{{1,2,3,6},{4},{5,7}}
[3,1,6,4,7,5,2]=>{{1,2,3,5,6,7},{4}}
[3,1,6,5,2,4,7]=>{{1,2,3,4,5,6},{7}}
[3,1,6,5,2,7,4]=>{{1,2,3,4,5,6,7}}
[3,1,6,5,4,2,7]=>{{1,2,3,6},{4,5},{7}}
[3,1,6,5,4,7,2]=>{{1,2,3,6,7},{4,5}}
[3,1,6,5,7,2,4]=>{{1,2,3,6},{4,5,7}}
[3,1,6,5,7,4,2]=>{{1,2,3,4,5,6,7}}
[3,1,6,7,2,4,5]=>{{1,2,3,4,5,6,7}}
[3,1,6,7,2,5,4]=>{{1,2,3,5,6},{4,7}}
[3,1,6,7,4,2,5]=>{{1,2,3,6},{4,5,7}}
[3,1,6,7,4,5,2]=>{{1,2,3,4,5,6,7}}
[3,1,6,7,5,2,4]=>{{1,2,3,6},{4,7},{5}}
[3,1,6,7,5,4,2]=>{{1,2,3,4,6,7},{5}}
[3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7}}
[3,1,7,2,4,6,5]=>{{1,2,3,4,5,7},{6}}
[3,1,7,2,5,4,6]=>{{1,2,3,4,6,7},{5}}
[3,1,7,2,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[3,1,7,2,6,4,5]=>{{1,2,3,4,5,6,7}}
[3,1,7,2,6,5,4]=>{{1,2,3,4,7},{5,6}}
[3,1,7,4,2,5,6]=>{{1,2,3,5,6,7},{4}}
[3,1,7,4,2,6,5]=>{{1,2,3,5,7},{4},{6}}
[3,1,7,4,5,2,6]=>{{1,2,3,6,7},{4},{5}}
[3,1,7,4,5,6,2]=>{{1,2,3,7},{4},{5},{6}}
[3,1,7,4,6,2,5]=>{{1,2,3,5,6,7},{4}}
[3,1,7,4,6,5,2]=>{{1,2,3,7},{4},{5,6}}
[3,1,7,5,2,4,6]=>{{1,2,3,4,5,6,7}}
[3,1,7,5,2,6,4]=>{{1,2,3,4,5,7},{6}}
[3,1,7,5,4,2,6]=>{{1,2,3,6,7},{4,5}}
[3,1,7,5,4,6,2]=>{{1,2,3,7},{4,5},{6}}
[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}}
[3,1,7,5,6,4,2]=>{{1,2,3,7},{4,5,6}}
[3,1,7,6,2,4,5]=>{{1,2,3,5,7},{4,6}}
[3,1,7,6,2,5,4]=>{{1,2,3,4,5,6,7}}
[3,1,7,6,4,2,5]=>{{1,2,3,4,5,6,7}}
[3,1,7,6,4,5,2]=>{{1,2,3,7},{4,5,6}}
[3,1,7,6,5,2,4]=>{{1,2,3,4,6,7},{5}}
[3,1,7,6,5,4,2]=>{{1,2,3,7},{4,6},{5}}
[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}
[3,2,1,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}}
[3,2,1,4,6,5,7]=>{{1,3},{2},{4},{5,6},{7}}
[3,2,1,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}}
[3,2,1,4,7,5,6]=>{{1,3},{2},{4},{5,6,7}}
[3,2,1,4,7,6,5]=>{{1,3},{2},{4},{5,7},{6}}
[3,2,1,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}}
[3,2,1,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}}
[3,2,1,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}}
[3,2,1,5,6,7,4]=>{{1,3},{2},{4,5,6,7}}
[3,2,1,5,7,4,6]=>{{1,3},{2},{4,5,6,7}}
[3,2,1,5,7,6,4]=>{{1,3},{2},{4,5,7},{6}}
[3,2,1,6,4,5,7]=>{{1,3},{2},{4,5,6},{7}}
[3,2,1,6,4,7,5]=>{{1,3},{2},{4,5,6,7}}
[3,2,1,6,5,4,7]=>{{1,3},{2},{4,6},{5},{7}}
[3,2,1,6,5,7,4]=>{{1,3},{2},{4,6,7},{5}}
[3,2,1,6,7,4,5]=>{{1,3},{2},{4,6},{5,7}}
[3,2,1,6,7,5,4]=>{{1,3},{2},{4,5,6,7}}
[3,2,1,7,4,5,6]=>{{1,3},{2},{4,5,6,7}}
[3,2,1,7,4,6,5]=>{{1,3},{2},{4,5,7},{6}}
[3,2,1,7,5,4,6]=>{{1,3},{2},{4,6,7},{5}}
[3,2,1,7,5,6,4]=>{{1,3},{2},{4,7},{5},{6}}
[3,2,1,7,6,4,5]=>{{1,3},{2},{4,5,6,7}}
[3,2,1,7,6,5,4]=>{{1,3},{2},{4,7},{5,6}}
[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}
[3,2,4,1,5,7,6]=>{{1,3,4},{2},{5},{6,7}}
[3,2,4,1,6,5,7]=>{{1,3,4},{2},{5,6},{7}}
[3,2,4,1,6,7,5]=>{{1,3,4},{2},{5,6,7}}
[3,2,4,1,7,5,6]=>{{1,3,4},{2},{5,6,7}}
[3,2,4,1,7,6,5]=>{{1,3,4},{2},{5,7},{6}}
[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}}
[3,2,4,5,1,7,6]=>{{1,3,4,5},{2},{6,7}}
[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}}
[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}}
[3,2,4,5,7,1,6]=>{{1,3,4,5,6,7},{2}}
[3,2,4,5,7,6,1]=>{{1,3,4,5,7},{2},{6}}
[3,2,4,6,1,5,7]=>{{1,3,4,5,6},{2},{7}}
[3,2,4,6,1,7,5]=>{{1,3,4,5,6,7},{2}}
[3,2,4,6,5,1,7]=>{{1,3,4,6},{2},{5},{7}}
[3,2,4,6,5,7,1]=>{{1,3,4,6,7},{2},{5}}
[3,2,4,6,7,1,5]=>{{1,3,4,6},{2},{5,7}}
[3,2,4,6,7,5,1]=>{{1,3,4,5,6,7},{2}}
[3,2,4,7,1,5,6]=>{{1,3,4,5,6,7},{2}}
[3,2,4,7,1,6,5]=>{{1,3,4,5,7},{2},{6}}
[3,2,4,7,5,1,6]=>{{1,3,4,6,7},{2},{5}}
[3,2,4,7,5,6,1]=>{{1,3,4,7},{2},{5},{6}}
[3,2,4,7,6,1,5]=>{{1,3,4,5,6,7},{2}}
[3,2,4,7,6,5,1]=>{{1,3,4,7},{2},{5,6}}
[3,2,5,1,4,6,7]=>{{1,3,4,5},{2},{6},{7}}
[3,2,5,1,4,7,6]=>{{1,3,4,5},{2},{6,7}}
[3,2,5,1,6,4,7]=>{{1,3,4,5,6},{2},{7}}
[3,2,5,1,6,7,4]=>{{1,3,4,5,6,7},{2}}
[3,2,5,1,7,4,6]=>{{1,3,4,5,6,7},{2}}
[3,2,5,1,7,6,4]=>{{1,3,4,5,7},{2},{6}}
[3,2,5,4,1,6,7]=>{{1,3,5},{2},{4},{6},{7}}
[3,2,5,4,1,7,6]=>{{1,3,5},{2},{4},{6,7}}
[3,2,5,4,6,1,7]=>{{1,3,5,6},{2},{4},{7}}
[3,2,5,4,6,7,1]=>{{1,3,5,6,7},{2},{4}}
[3,2,5,4,7,1,6]=>{{1,3,5,6,7},{2},{4}}
[3,2,5,4,7,6,1]=>{{1,3,5,7},{2},{4},{6}}
[3,2,5,6,1,4,7]=>{{1,3,5},{2},{4,6},{7}}
[3,2,5,6,1,7,4]=>{{1,3,5},{2},{4,6,7}}
[3,2,5,6,4,1,7]=>{{1,3,4,5,6},{2},{7}}
[3,2,5,6,4,7,1]=>{{1,3,4,5,6,7},{2}}
[3,2,5,6,7,1,4]=>{{1,3,4,5,6,7},{2}}
[3,2,5,6,7,4,1]=>{{1,3,5,7},{2},{4,6}}
[3,2,5,7,1,4,6]=>{{1,3,5},{2},{4,6,7}}
[3,2,5,7,1,6,4]=>{{1,3,5},{2},{4,7},{6}}
[3,2,5,7,4,1,6]=>{{1,3,4,5,6,7},{2}}
[3,2,5,7,4,6,1]=>{{1,3,4,5,7},{2},{6}}
[3,2,5,7,6,1,4]=>{{1,3,5,6},{2},{4,7}}
[3,2,5,7,6,4,1]=>{{1,3,4,5,6,7},{2}}
[3,2,6,1,4,5,7]=>{{1,3,4,5,6},{2},{7}}
[3,2,6,1,4,7,5]=>{{1,3,4,5,6,7},{2}}
[3,2,6,1,5,4,7]=>{{1,3,4,6},{2},{5},{7}}
[3,2,6,1,5,7,4]=>{{1,3,4,6,7},{2},{5}}
[3,2,6,1,7,4,5]=>{{1,3,4,6},{2},{5,7}}
[3,2,6,1,7,5,4]=>{{1,3,4,5,6,7},{2}}
[3,2,6,4,1,5,7]=>{{1,3,5,6},{2},{4},{7}}
[3,2,6,4,1,7,5]=>{{1,3,5,6,7},{2},{4}}
[3,2,6,4,5,1,7]=>{{1,3,6},{2},{4},{5},{7}}
[3,2,6,4,5,7,1]=>{{1,3,6,7},{2},{4},{5}}
[3,2,6,4,7,1,5]=>{{1,3,6},{2},{4},{5,7}}
[3,2,6,4,7,5,1]=>{{1,3,5,6,7},{2},{4}}
[3,2,6,5,1,4,7]=>{{1,3,4,5,6},{2},{7}}
[3,2,6,5,1,7,4]=>{{1,3,4,5,6,7},{2}}
[3,2,6,5,4,1,7]=>{{1,3,6},{2},{4,5},{7}}
[3,2,6,5,4,7,1]=>{{1,3,6,7},{2},{4,5}}
[3,2,6,5,7,1,4]=>{{1,3,6},{2},{4,5,7}}
[3,2,6,5,7,4,1]=>{{1,3,4,5,6,7},{2}}
[3,2,6,7,1,4,5]=>{{1,3,4,5,6,7},{2}}
[3,2,6,7,1,5,4]=>{{1,3,5,6},{2},{4,7}}
[3,2,6,7,4,1,5]=>{{1,3,6},{2},{4,5,7}}
[3,2,6,7,4,5,1]=>{{1,3,4,5,6,7},{2}}
[3,2,6,7,5,1,4]=>{{1,3,6},{2},{4,7},{5}}
[3,2,6,7,5,4,1]=>{{1,3,4,6,7},{2},{5}}
[3,2,7,1,4,5,6]=>{{1,3,4,5,6,7},{2}}
[3,2,7,1,4,6,5]=>{{1,3,4,5,7},{2},{6}}
[3,2,7,1,5,4,6]=>{{1,3,4,6,7},{2},{5}}
[3,2,7,1,5,6,4]=>{{1,3,4,7},{2},{5},{6}}
[3,2,7,1,6,4,5]=>{{1,3,4,5,6,7},{2}}
[3,2,7,1,6,5,4]=>{{1,3,4,7},{2},{5,6}}
[3,2,7,4,1,5,6]=>{{1,3,5,6,7},{2},{4}}
[3,2,7,4,1,6,5]=>{{1,3,5,7},{2},{4},{6}}
[3,2,7,4,5,1,6]=>{{1,3,6,7},{2},{4},{5}}
[3,2,7,4,5,6,1]=>{{1,3,7},{2},{4},{5},{6}}
[3,2,7,4,6,1,5]=>{{1,3,5,6,7},{2},{4}}
[3,2,7,4,6,5,1]=>{{1,3,7},{2},{4},{5,6}}
[3,2,7,5,1,4,6]=>{{1,3,4,5,6,7},{2}}
[3,2,7,5,1,6,4]=>{{1,3,4,5,7},{2},{6}}
[3,2,7,5,4,1,6]=>{{1,3,6,7},{2},{4,5}}
[3,2,7,5,4,6,1]=>{{1,3,7},{2},{4,5},{6}}
[3,2,7,5,6,1,4]=>{{1,3,4,5,6,7},{2}}
[3,2,7,5,6,4,1]=>{{1,3,7},{2},{4,5,6}}
[3,2,7,6,1,4,5]=>{{1,3,5,7},{2},{4,6}}
[3,2,7,6,1,5,4]=>{{1,3,4,5,6,7},{2}}
[3,2,7,6,4,1,5]=>{{1,3,4,5,6,7},{2}}
[3,2,7,6,4,5,1]=>{{1,3,7},{2},{4,5,6}}
[3,2,7,6,5,1,4]=>{{1,3,4,6,7},{2},{5}}
[3,2,7,6,5,4,1]=>{{1,3,7},{2},{4,6},{5}}
[3,4,1,2,5,6,7]=>{{1,3},{2,4},{5},{6},{7}}
[3,4,1,2,5,7,6]=>{{1,3},{2,4},{5},{6,7}}
[3,4,1,2,6,5,7]=>{{1,3},{2,4},{5,6},{7}}
[3,4,1,2,6,7,5]=>{{1,3},{2,4},{5,6,7}}
[3,4,1,2,7,5,6]=>{{1,3},{2,4},{5,6,7}}
[3,4,1,2,7,6,5]=>{{1,3},{2,4},{5,7},{6}}
[3,4,1,5,2,6,7]=>{{1,3},{2,4,5},{6},{7}}
[3,4,1,5,2,7,6]=>{{1,3},{2,4,5},{6,7}}
[3,4,1,5,6,2,7]=>{{1,3},{2,4,5,6},{7}}
[3,4,1,5,6,7,2]=>{{1,3},{2,4,5,6,7}}
[3,4,1,5,7,2,6]=>{{1,3},{2,4,5,6,7}}
[3,4,1,5,7,6,2]=>{{1,3},{2,4,5,7},{6}}
[3,4,1,6,2,5,7]=>{{1,3},{2,4,5,6},{7}}
[3,4,1,6,2,7,5]=>{{1,3},{2,4,5,6,7}}
[3,4,1,6,5,2,7]=>{{1,3},{2,4,6},{5},{7}}
[3,4,1,6,5,7,2]=>{{1,3},{2,4,6,7},{5}}
[3,4,1,6,7,2,5]=>{{1,3},{2,4,6},{5,7}}
[3,4,1,6,7,5,2]=>{{1,3},{2,4,5,6,7}}
[3,4,1,7,2,5,6]=>{{1,3},{2,4,5,6,7}}
[3,4,1,7,2,6,5]=>{{1,3},{2,4,5,7},{6}}
[3,4,1,7,5,2,6]=>{{1,3},{2,4,6,7},{5}}
[3,4,1,7,5,6,2]=>{{1,3},{2,4,7},{5},{6}}
[3,4,1,7,6,2,5]=>{{1,3},{2,4,5,6,7}}
[3,4,1,7,6,5,2]=>{{1,3},{2,4,7},{5,6}}
[3,4,2,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[3,4,2,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[3,4,2,1,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[3,4,2,1,6,7,5]=>{{1,2,3,4},{5,6,7}}
[3,4,2,1,7,5,6]=>{{1,2,3,4},{5,6,7}}
[3,4,2,1,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[3,4,2,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[3,4,2,5,1,7,6]=>{{1,2,3,4,5},{6,7}}
[3,4,2,5,6,1,7]=>{{1,2,3,4,5,6},{7}}
[3,4,2,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[3,4,2,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[3,4,2,5,7,6,1]=>{{1,2,3,4,5,7},{6}}
[3,4,2,6,1,5,7]=>{{1,2,3,4,5,6},{7}}
[3,4,2,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[3,4,2,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[3,4,2,6,5,7,1]=>{{1,2,3,4,6,7},{5}}
[3,4,2,6,7,1,5]=>{{1,2,3,4,6},{5,7}}
[3,4,2,6,7,5,1]=>{{1,2,3,4,5,6,7}}
[3,4,2,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[3,4,2,7,1,6,5]=>{{1,2,3,4,5,7},{6}}
[3,4,2,7,5,1,6]=>{{1,2,3,4,6,7},{5}}
[3,4,2,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[3,4,2,7,6,1,5]=>{{1,2,3,4,5,6,7}}
[3,4,2,7,6,5,1]=>{{1,2,3,4,7},{5,6}}
[3,4,5,1,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[3,4,5,1,2,7,6]=>{{1,2,3,4,5},{6,7}}
[3,4,5,1,6,2,7]=>{{1,2,3,4,5,6},{7}}
[3,4,5,1,6,7,2]=>{{1,2,3,4,5,6,7}}
[3,4,5,1,7,2,6]=>{{1,2,3,4,5,6,7}}
[3,4,5,1,7,6,2]=>{{1,2,3,4,5,7},{6}}
[3,4,5,2,1,6,7]=>{{1,3,5},{2,4},{6},{7}}
[3,4,5,2,1,7,6]=>{{1,3,5},{2,4},{6,7}}
[3,4,5,2,6,1,7]=>{{1,3,5,6},{2,4},{7}}
[3,4,5,2,6,7,1]=>{{1,3,5,6,7},{2,4}}
[3,4,5,2,7,1,6]=>{{1,3,5,6,7},{2,4}}
[3,4,5,2,7,6,1]=>{{1,3,5,7},{2,4},{6}}
[3,4,5,6,1,2,7]=>{{1,3,5},{2,4,6},{7}}
[3,4,5,6,1,7,2]=>{{1,3,5},{2,4,6,7}}
[3,4,5,6,2,1,7]=>{{1,2,3,4,5,6},{7}}
[3,4,5,6,2,7,1]=>{{1,2,3,4,5,6,7}}
[3,4,5,6,7,1,2]=>{{1,2,3,4,5,6,7}}
[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}}
[3,4,5,7,1,2,6]=>{{1,3,5},{2,4,6,7}}
[3,4,5,7,1,6,2]=>{{1,3,5},{2,4,7},{6}}
[3,4,5,7,2,1,6]=>{{1,2,3,4,5,6,7}}
[3,4,5,7,2,6,1]=>{{1,2,3,4,5,7},{6}}
[3,4,5,7,6,1,2]=>{{1,3,5,6},{2,4,7}}
[3,4,5,7,6,2,1]=>{{1,2,3,4,5,6,7}}
[3,4,6,1,2,5,7]=>{{1,2,3,4,5,6},{7}}
[3,4,6,1,2,7,5]=>{{1,2,3,4,5,6,7}}
[3,4,6,1,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[3,4,6,1,5,7,2]=>{{1,2,3,4,6,7},{5}}
[3,4,6,1,7,2,5]=>{{1,2,3,4,6},{5,7}}
[3,4,6,1,7,5,2]=>{{1,2,3,4,5,6,7}}
[3,4,6,2,1,5,7]=>{{1,3,5,6},{2,4},{7}}
[3,4,6,2,1,7,5]=>{{1,3,5,6,7},{2,4}}
[3,4,6,2,5,1,7]=>{{1,3,6},{2,4},{5},{7}}
[3,4,6,2,5,7,1]=>{{1,3,6,7},{2,4},{5}}
[3,4,6,2,7,1,5]=>{{1,3,6},{2,4},{5,7}}
[3,4,6,2,7,5,1]=>{{1,3,5,6,7},{2,4}}
[3,4,6,5,1,2,7]=>{{1,2,3,4,5,6},{7}}
[3,4,6,5,1,7,2]=>{{1,2,3,4,5,6,7}}
[3,4,6,5,2,1,7]=>{{1,3,6},{2,4,5},{7}}
[3,4,6,5,2,7,1]=>{{1,3,6,7},{2,4,5}}
[3,4,6,5,7,1,2]=>{{1,3,6},{2,4,5,7}}
[3,4,6,5,7,2,1]=>{{1,2,3,4,5,6,7}}
[3,4,6,7,1,2,5]=>{{1,2,3,4,5,6,7}}
[3,4,6,7,1,5,2]=>{{1,3,5,6},{2,4,7}}
[3,4,6,7,2,1,5]=>{{1,3,6},{2,4,5,7}}
[3,4,6,7,2,5,1]=>{{1,2,3,4,5,6,7}}
[3,4,6,7,5,1,2]=>{{1,3,6},{2,4,7},{5}}
[3,4,6,7,5,2,1]=>{{1,2,3,4,6,7},{5}}
[3,4,7,1,2,5,6]=>{{1,2,3,4,5,6,7}}
[3,4,7,1,2,6,5]=>{{1,2,3,4,5,7},{6}}
[3,4,7,1,5,2,6]=>{{1,2,3,4,6,7},{5}}
[3,4,7,1,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[3,4,7,1,6,2,5]=>{{1,2,3,4,5,6,7}}
[3,4,7,1,6,5,2]=>{{1,2,3,4,7},{5,6}}
[3,4,7,2,1,5,6]=>{{1,3,5,6,7},{2,4}}
[3,4,7,2,1,6,5]=>{{1,3,5,7},{2,4},{6}}
[3,4,7,2,5,1,6]=>{{1,3,6,7},{2,4},{5}}
[3,4,7,2,5,6,1]=>{{1,3,7},{2,4},{5},{6}}
[3,4,7,2,6,1,5]=>{{1,3,5,6,7},{2,4}}
[3,4,7,2,6,5,1]=>{{1,3,7},{2,4},{5,6}}
[3,4,7,5,1,2,6]=>{{1,2,3,4,5,6,7}}
[3,4,7,5,1,6,2]=>{{1,2,3,4,5,7},{6}}
[3,4,7,5,2,1,6]=>{{1,3,6,7},{2,4,5}}
[3,4,7,5,2,6,1]=>{{1,3,7},{2,4,5},{6}}
[3,4,7,5,6,1,2]=>{{1,2,3,4,5,6,7}}
[3,4,7,5,6,2,1]=>{{1,3,7},{2,4,5,6}}
[3,4,7,6,1,2,5]=>{{1,3,5,7},{2,4,6}}
[3,4,7,6,1,5,2]=>{{1,2,3,4,5,6,7}}
[3,4,7,6,2,1,5]=>{{1,2,3,4,5,6,7}}
[3,4,7,6,2,5,1]=>{{1,3,7},{2,4,5,6}}
[3,4,7,6,5,1,2]=>{{1,2,3,4,6,7},{5}}
[3,4,7,6,5,2,1]=>{{1,3,7},{2,4,6},{5}}
[3,5,1,2,4,6,7]=>{{1,3},{2,4,5},{6},{7}}
[3,5,1,2,4,7,6]=>{{1,3},{2,4,5},{6,7}}
[3,5,1,2,6,4,7]=>{{1,3},{2,4,5,6},{7}}
[3,5,1,2,6,7,4]=>{{1,3},{2,4,5,6,7}}
[3,5,1,2,7,4,6]=>{{1,3},{2,4,5,6,7}}
[3,5,1,2,7,6,4]=>{{1,3},{2,4,5,7},{6}}
[3,5,1,4,2,6,7]=>{{1,3},{2,5},{4},{6},{7}}
[3,5,1,4,2,7,6]=>{{1,3},{2,5},{4},{6,7}}
[3,5,1,4,6,2,7]=>{{1,3},{2,5,6},{4},{7}}
[3,5,1,4,6,7,2]=>{{1,3},{2,5,6,7},{4}}
[3,5,1,4,7,2,6]=>{{1,3},{2,5,6,7},{4}}
[3,5,1,4,7,6,2]=>{{1,3},{2,5,7},{4},{6}}
[3,5,1,6,2,4,7]=>{{1,3},{2,5},{4,6},{7}}
[3,5,1,6,2,7,4]=>{{1,3},{2,5},{4,6,7}}
[3,5,1,6,4,2,7]=>{{1,3},{2,4,5,6},{7}}
[3,5,1,6,4,7,2]=>{{1,3},{2,4,5,6,7}}
[3,5,1,6,7,2,4]=>{{1,3},{2,4,5,6,7}}
[3,5,1,6,7,4,2]=>{{1,3},{2,5,7},{4,6}}
[3,5,1,7,2,4,6]=>{{1,3},{2,5},{4,6,7}}
[3,5,1,7,2,6,4]=>{{1,3},{2,5},{4,7},{6}}
[3,5,1,7,4,2,6]=>{{1,3},{2,4,5,6,7}}
[3,5,1,7,4,6,2]=>{{1,3},{2,4,5,7},{6}}
[3,5,1,7,6,2,4]=>{{1,3},{2,5,6},{4,7}}
[3,5,1,7,6,4,2]=>{{1,3},{2,4,5,6,7}}
[3,5,2,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[3,5,2,1,4,7,6]=>{{1,2,3,4,5},{6,7}}
[3,5,2,1,6,4,7]=>{{1,2,3,4,5,6},{7}}
[3,5,2,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[3,5,2,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[3,5,2,1,7,6,4]=>{{1,2,3,4,5,7},{6}}
[3,5,2,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}}
[3,5,2,4,1,7,6]=>{{1,2,3,5},{4},{6,7}}
[3,5,2,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}
[3,5,2,4,6,7,1]=>{{1,2,3,5,6,7},{4}}
[3,5,2,4,7,1,6]=>{{1,2,3,5,6,7},{4}}
[3,5,2,4,7,6,1]=>{{1,2,3,5,7},{4},{6}}
[3,5,2,6,1,4,7]=>{{1,2,3,5},{4,6},{7}}
[3,5,2,6,1,7,4]=>{{1,2,3,5},{4,6,7}}
[3,5,2,6,4,1,7]=>{{1,2,3,4,5,6},{7}}
[3,5,2,6,4,7,1]=>{{1,2,3,4,5,6,7}}
[3,5,2,6,7,1,4]=>{{1,2,3,4,5,6,7}}
[3,5,2,6,7,4,1]=>{{1,2,3,5,7},{4,6}}
[3,5,2,7,1,4,6]=>{{1,2,3,5},{4,6,7}}
[3,5,2,7,1,6,4]=>{{1,2,3,5},{4,7},{6}}
[3,5,2,7,4,1,6]=>{{1,2,3,4,5,6,7}}
[3,5,2,7,4,6,1]=>{{1,2,3,4,5,7},{6}}
[3,5,2,7,6,1,4]=>{{1,2,3,5,6},{4,7}}
[3,5,2,7,6,4,1]=>{{1,2,3,4,5,6,7}}
[3,5,4,1,2,6,7]=>{{1,3,4},{2,5},{6},{7}}
[3,5,4,1,2,7,6]=>{{1,3,4},{2,5},{6,7}}
[3,5,4,1,6,2,7]=>{{1,3,4},{2,5,6},{7}}
[3,5,4,1,6,7,2]=>{{1,3,4},{2,5,6,7}}
[3,5,4,1,7,2,6]=>{{1,3,4},{2,5,6,7}}
[3,5,4,1,7,6,2]=>{{1,3,4},{2,5,7},{6}}
[3,5,4,2,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[3,5,4,2,1,7,6]=>{{1,2,3,4,5},{6,7}}
[3,5,4,2,6,1,7]=>{{1,2,3,4,5,6},{7}}
[3,5,4,2,6,7,1]=>{{1,2,3,4,5,6,7}}
[3,5,4,2,7,1,6]=>{{1,2,3,4,5,6,7}}
[3,5,4,2,7,6,1]=>{{1,2,3,4,5,7},{6}}
[3,5,4,6,1,2,7]=>{{1,2,3,4,5,6},{7}}
[3,5,4,6,1,7,2]=>{{1,2,3,4,5,6,7}}
[3,5,4,6,2,1,7]=>{{1,3,4,6},{2,5},{7}}
[3,5,4,6,2,7,1]=>{{1,3,4,6,7},{2,5}}
[3,5,4,6,7,1,2]=>{{1,3,4,6},{2,5,7}}
[3,5,4,6,7,2,1]=>{{1,2,3,4,5,6,7}}
[3,5,4,7,1,2,6]=>{{1,2,3,4,5,6,7}}
[3,5,4,7,1,6,2]=>{{1,2,3,4,5,7},{6}}
[3,5,4,7,2,1,6]=>{{1,3,4,6,7},{2,5}}
[3,5,4,7,2,6,1]=>{{1,3,4,7},{2,5},{6}}
[3,5,4,7,6,1,2]=>{{1,2,3,4,5,6,7}}
[3,5,4,7,6,2,1]=>{{1,3,4,7},{2,5,6}}
[3,5,6,1,2,4,7]=>{{1,3,4,6},{2,5},{7}}
[3,5,6,1,2,7,4]=>{{1,3,4,6,7},{2,5}}
[3,5,6,1,4,2,7]=>{{1,2,3,4,5,6},{7}}
[3,5,6,1,4,7,2]=>{{1,2,3,4,5,6,7}}
[3,5,6,1,7,2,4]=>{{1,2,3,4,5,6,7}}
[3,5,6,1,7,4,2]=>{{1,3,4,6},{2,5,7}}
[3,5,6,2,1,4,7]=>{{1,2,3,4,5,6},{7}}
[3,5,6,2,1,7,4]=>{{1,2,3,4,5,6,7}}
[3,5,6,2,4,1,7]=>{{1,3,6},{2,4,5},{7}}
[3,5,6,2,4,7,1]=>{{1,3,6,7},{2,4,5}}
[3,5,6,2,7,1,4]=>{{1,3,6},{2,4,5,7}}
[3,5,6,2,7,4,1]=>{{1,2,3,4,5,6,7}}
[3,5,6,4,1,2,7]=>{{1,2,3,5,6},{4},{7}}
[3,5,6,4,1,7,2]=>{{1,2,3,5,6,7},{4}}
[3,5,6,4,2,1,7]=>{{1,3,6},{2,5},{4},{7}}
[3,5,6,4,2,7,1]=>{{1,3,6,7},{2,5},{4}}
[3,5,6,4,7,1,2]=>{{1,3,6},{2,5,7},{4}}
[3,5,6,4,7,2,1]=>{{1,2,3,5,6,7},{4}}
[3,5,6,7,1,2,4]=>{{1,2,3,5,6},{4,7}}
[3,5,6,7,1,4,2]=>{{1,2,3,4,5,6,7}}
[3,5,6,7,2,1,4]=>{{1,3,6},{2,5},{4,7}}
[3,5,6,7,2,4,1]=>{{1,3,4,6,7},{2,5}}
[3,5,6,7,4,1,2]=>{{1,3,6},{2,4,5,7}}
[3,5,6,7,4,2,1]=>{{1,2,3,4,5,6,7}}
[3,5,7,1,2,4,6]=>{{1,3,4,6,7},{2,5}}
[3,5,7,1,2,6,4]=>{{1,3,4,7},{2,5},{6}}
[3,5,7,1,4,2,6]=>{{1,2,3,4,5,6,7}}
[3,5,7,1,4,6,2]=>{{1,2,3,4,5,7},{6}}
[3,5,7,1,6,2,4]=>{{1,3,4,7},{2,5,6}}
[3,5,7,1,6,4,2]=>{{1,2,3,4,5,6,7}}
[3,5,7,2,1,4,6]=>{{1,2,3,4,5,6,7}}
[3,5,7,2,1,6,4]=>{{1,2,3,4,5,7},{6}}
[3,5,7,2,4,1,6]=>{{1,3,6,7},{2,4,5}}
[3,5,7,2,4,6,1]=>{{1,3,7},{2,4,5},{6}}
[3,5,7,2,6,1,4]=>{{1,2,3,4,5,6,7}}
[3,5,7,2,6,4,1]=>{{1,3,7},{2,4,5,6}}
[3,5,7,4,1,2,6]=>{{1,2,3,5,6,7},{4}}
[3,5,7,4,1,6,2]=>{{1,2,3,5,7},{4},{6}}
[3,5,7,4,2,1,6]=>{{1,3,6,7},{2,5},{4}}
[3,5,7,4,2,6,1]=>{{1,3,7},{2,5},{4},{6}}
[3,5,7,4,6,1,2]=>{{1,2,3,5,6,7},{4}}
[3,5,7,4,6,2,1]=>{{1,3,7},{2,5,6},{4}}
[3,5,7,6,1,2,4]=>{{1,2,3,4,5,6,7}}
[3,5,7,6,1,4,2]=>{{1,2,3,5,7},{4,6}}
[3,5,7,6,2,1,4]=>{{1,3,4,6,7},{2,5}}
[3,5,7,6,2,4,1]=>{{1,3,7},{2,5},{4,6}}
[3,5,7,6,4,1,2]=>{{1,2,3,4,5,6,7}}
[3,5,7,6,4,2,1]=>{{1,3,7},{2,4,5,6}}
[3,6,1,2,4,5,7]=>{{1,3},{2,4,5,6},{7}}
[3,6,1,2,4,7,5]=>{{1,3},{2,4,5,6,7}}
[3,6,1,2,5,4,7]=>{{1,3},{2,4,6},{5},{7}}
[3,6,1,2,5,7,4]=>{{1,3},{2,4,6,7},{5}}
[3,6,1,2,7,4,5]=>{{1,3},{2,4,6},{5,7}}
[3,6,1,2,7,5,4]=>{{1,3},{2,4,5,6,7}}
[3,6,1,4,2,5,7]=>{{1,3},{2,5,6},{4},{7}}
[3,6,1,4,2,7,5]=>{{1,3},{2,5,6,7},{4}}
[3,6,1,4,5,2,7]=>{{1,3},{2,6},{4},{5},{7}}
[3,6,1,4,5,7,2]=>{{1,3},{2,6,7},{4},{5}}
[3,6,1,4,7,2,5]=>{{1,3},{2,6},{4},{5,7}}
[3,6,1,4,7,5,2]=>{{1,3},{2,5,6,7},{4}}
[3,6,1,5,2,4,7]=>{{1,3},{2,4,5,6},{7}}
[3,6,1,5,2,7,4]=>{{1,3},{2,4,5,6,7}}
[3,6,1,5,4,2,7]=>{{1,3},{2,6},{4,5},{7}}
[3,6,1,5,4,7,2]=>{{1,3},{2,6,7},{4,5}}
[3,6,1,5,7,2,4]=>{{1,3},{2,6},{4,5,7}}
[3,6,1,5,7,4,2]=>{{1,3},{2,4,5,6,7}}
[3,6,1,7,2,4,5]=>{{1,3},{2,4,5,6,7}}
[3,6,1,7,2,5,4]=>{{1,3},{2,5,6},{4,7}}
[3,6,1,7,4,2,5]=>{{1,3},{2,6},{4,5,7}}
[3,6,1,7,4,5,2]=>{{1,3},{2,4,5,6,7}}
[3,6,1,7,5,2,4]=>{{1,3},{2,6},{4,7},{5}}
[3,6,1,7,5,4,2]=>{{1,3},{2,4,6,7},{5}}
[3,6,2,1,4,5,7]=>{{1,2,3,4,5,6},{7}}
[3,6,2,1,4,7,5]=>{{1,2,3,4,5,6,7}}
[3,6,2,1,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[3,6,2,1,5,7,4]=>{{1,2,3,4,6,7},{5}}
[3,6,2,1,7,4,5]=>{{1,2,3,4,6},{5,7}}
[3,6,2,1,7,5,4]=>{{1,2,3,4,5,6,7}}
[3,6,2,4,1,5,7]=>{{1,2,3,5,6},{4},{7}}
[3,6,2,4,1,7,5]=>{{1,2,3,5,6,7},{4}}
[3,6,2,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}
[3,6,2,4,5,7,1]=>{{1,2,3,6,7},{4},{5}}
[3,6,2,4,7,1,5]=>{{1,2,3,6},{4},{5,7}}
[3,6,2,4,7,5,1]=>{{1,2,3,5,6,7},{4}}
[3,6,2,5,1,4,7]=>{{1,2,3,4,5,6},{7}}
[3,6,2,5,1,7,4]=>{{1,2,3,4,5,6,7}}
[3,6,2,5,4,1,7]=>{{1,2,3,6},{4,5},{7}}
[3,6,2,5,4,7,1]=>{{1,2,3,6,7},{4,5}}
[3,6,2,5,7,1,4]=>{{1,2,3,6},{4,5,7}}
[3,6,2,5,7,4,1]=>{{1,2,3,4,5,6,7}}
[3,6,2,7,1,4,5]=>{{1,2,3,4,5,6,7}}
[3,6,2,7,1,5,4]=>{{1,2,3,5,6},{4,7}}
[3,6,2,7,4,1,5]=>{{1,2,3,6},{4,5,7}}
[3,6,2,7,4,5,1]=>{{1,2,3,4,5,6,7}}
[3,6,2,7,5,1,4]=>{{1,2,3,6},{4,7},{5}}
[3,6,2,7,5,4,1]=>{{1,2,3,4,6,7},{5}}
[3,6,4,1,2,5,7]=>{{1,3,4},{2,5,6},{7}}
[3,6,4,1,2,7,5]=>{{1,3,4},{2,5,6,7}}
[3,6,4,1,5,2,7]=>{{1,3,4},{2,6},{5},{7}}
[3,6,4,1,5,7,2]=>{{1,3,4},{2,6,7},{5}}
[3,6,4,1,7,2,5]=>{{1,3,4},{2,6},{5,7}}
[3,6,4,1,7,5,2]=>{{1,3,4},{2,5,6,7}}
[3,6,4,2,1,5,7]=>{{1,2,3,4,5,6},{7}}
[3,6,4,2,1,7,5]=>{{1,2,3,4,5,6,7}}
[3,6,4,2,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[3,6,4,2,5,7,1]=>{{1,2,3,4,6,7},{5}}
[3,6,4,2,7,1,5]=>{{1,2,3,4,6},{5,7}}
[3,6,4,2,7,5,1]=>{{1,2,3,4,5,6,7}}
[3,6,4,5,1,2,7]=>{{1,3,4,5},{2,6},{7}}
[3,6,4,5,1,7,2]=>{{1,3,4,5},{2,6,7}}
[3,6,4,5,2,1,7]=>{{1,2,3,4,5,6},{7}}
[3,6,4,5,2,7,1]=>{{1,2,3,4,5,6,7}}
[3,6,4,5,7,1,2]=>{{1,2,3,4,5,6,7}}
[3,6,4,5,7,2,1]=>{{1,3,4,5,7},{2,6}}
[3,6,4,7,1,2,5]=>{{1,3,4,5,7},{2,6}}
[3,6,4,7,1,5,2]=>{{1,2,3,4,5,6,7}}
[3,6,4,7,2,1,5]=>{{1,2,3,4,5,6,7}}
[3,6,4,7,2,5,1]=>{{1,3,4,7},{2,5,6}}
[3,6,4,7,5,1,2]=>{{1,2,3,4,6,7},{5}}
[3,6,4,7,5,2,1]=>{{1,3,4,7},{2,6},{5}}
[3,6,5,1,2,4,7]=>{{1,2,3,4,5,6},{7}}
[3,6,5,1,2,7,4]=>{{1,2,3,4,5,6,7}}
[3,6,5,1,4,2,7]=>{{1,3,4,5},{2,6},{7}}
[3,6,5,1,4,7,2]=>{{1,3,4,5},{2,6,7}}
[3,6,5,1,7,2,4]=>{{1,3,4,5,7},{2,6}}
[3,6,5,1,7,4,2]=>{{1,2,3,4,5,6,7}}
[3,6,5,2,1,4,7]=>{{1,3,5},{2,4,6},{7}}
[3,6,5,2,1,7,4]=>{{1,3,5},{2,4,6,7}}
[3,6,5,2,4,1,7]=>{{1,2,3,4,5,6},{7}}
[3,6,5,2,4,7,1]=>{{1,2,3,4,5,6,7}}
[3,6,5,2,7,1,4]=>{{1,2,3,4,5,6,7}}
[3,6,5,2,7,4,1]=>{{1,3,5,7},{2,4,6}}
[3,6,5,4,1,2,7]=>{{1,3,5},{2,6},{4},{7}}
[3,6,5,4,1,7,2]=>{{1,3,5},{2,6,7},{4}}
[3,6,5,4,2,1,7]=>{{1,2,3,5,6},{4},{7}}
[3,6,5,4,2,7,1]=>{{1,2,3,5,6,7},{4}}
[3,6,5,4,7,1,2]=>{{1,2,3,5,6,7},{4}}
[3,6,5,4,7,2,1]=>{{1,3,5,7},{2,6},{4}}
[3,6,5,7,1,2,4]=>{{1,3,5},{2,6},{4,7}}
[3,6,5,7,1,4,2]=>{{1,3,5},{2,4,6,7}}
[3,6,5,7,2,1,4]=>{{1,2,3,5,6},{4,7}}
[3,6,5,7,2,4,1]=>{{1,2,3,4,5,6,7}}
[3,6,5,7,4,1,2]=>{{1,2,3,4,5,6,7}}
[3,6,5,7,4,2,1]=>{{1,3,4,5,7},{2,6}}
[3,6,7,1,2,4,5]=>{{1,2,3,4,5,6,7}}
[3,6,7,1,2,5,4]=>{{1,3,4,7},{2,5,6}}
[3,6,7,1,4,2,5]=>{{1,3,4,5,7},{2,6}}
[3,6,7,1,4,5,2]=>{{1,2,3,4,5,6,7}}
[3,6,7,1,5,2,4]=>{{1,3,4,7},{2,6},{5}}
[3,6,7,1,5,4,2]=>{{1,2,3,4,6,7},{5}}
[3,6,7,2,1,4,5]=>{{1,3,5,7},{2,4,6}}
[3,6,7,2,1,5,4]=>{{1,2,3,4,5,6,7}}
[3,6,7,2,4,1,5]=>{{1,2,3,4,5,6,7}}
[3,6,7,2,4,5,1]=>{{1,3,7},{2,4,5,6}}
[3,6,7,2,5,1,4]=>{{1,2,3,4,6,7},{5}}
[3,6,7,2,5,4,1]=>{{1,3,7},{2,4,6},{5}}
[3,6,7,4,1,2,5]=>{{1,3,5,7},{2,6},{4}}
[3,6,7,4,1,5,2]=>{{1,2,3,5,6,7},{4}}
[3,6,7,4,2,1,5]=>{{1,2,3,5,6,7},{4}}
[3,6,7,4,2,5,1]=>{{1,3,7},{2,5,6},{4}}
[3,6,7,4,5,1,2]=>{{1,2,3,6,7},{4},{5}}
[3,6,7,4,5,2,1]=>{{1,3,7},{2,6},{4},{5}}
[3,6,7,5,1,2,4]=>{{1,3,4,5,7},{2,6}}
[3,6,7,5,1,4,2]=>{{1,2,3,4,5,6,7}}
[3,6,7,5,2,1,4]=>{{1,2,3,4,5,6,7}}
[3,6,7,5,2,4,1]=>{{1,3,7},{2,4,5,6}}
[3,6,7,5,4,1,2]=>{{1,2,3,6,7},{4,5}}
[3,6,7,5,4,2,1]=>{{1,3,7},{2,6},{4,5}}
[3,7,1,2,4,5,6]=>{{1,3},{2,4,5,6,7}}
[3,7,1,2,4,6,5]=>{{1,3},{2,4,5,7},{6}}
[3,7,1,2,5,4,6]=>{{1,3},{2,4,6,7},{5}}
[3,7,1,2,5,6,4]=>{{1,3},{2,4,7},{5},{6}}
[3,7,1,2,6,4,5]=>{{1,3},{2,4,5,6,7}}
[3,7,1,2,6,5,4]=>{{1,3},{2,4,7},{5,6}}
[3,7,1,4,2,5,6]=>{{1,3},{2,5,6,7},{4}}
[3,7,1,4,2,6,5]=>{{1,3},{2,5,7},{4},{6}}
[3,7,1,4,5,2,6]=>{{1,3},{2,6,7},{4},{5}}
[3,7,1,4,5,6,2]=>{{1,3},{2,7},{4},{5},{6}}
[3,7,1,4,6,2,5]=>{{1,3},{2,5,6,7},{4}}
[3,7,1,4,6,5,2]=>{{1,3},{2,7},{4},{5,6}}
[3,7,1,5,2,4,6]=>{{1,3},{2,4,5,6,7}}
[3,7,1,5,2,6,4]=>{{1,3},{2,4,5,7},{6}}
[3,7,1,5,4,2,6]=>{{1,3},{2,6,7},{4,5}}
[3,7,1,5,4,6,2]=>{{1,3},{2,7},{4,5},{6}}
[3,7,1,5,6,2,4]=>{{1,3},{2,4,5,6,7}}
[3,7,1,5,6,4,2]=>{{1,3},{2,7},{4,5,6}}
[3,7,1,6,2,4,5]=>{{1,3},{2,5,7},{4,6}}
[3,7,1,6,2,5,4]=>{{1,3},{2,4,5,6,7}}
[3,7,1,6,4,2,5]=>{{1,3},{2,4,5,6,7}}
[3,7,1,6,4,5,2]=>{{1,3},{2,7},{4,5,6}}
[3,7,1,6,5,2,4]=>{{1,3},{2,4,6,7},{5}}
[3,7,1,6,5,4,2]=>{{1,3},{2,7},{4,6},{5}}
[3,7,2,1,4,5,6]=>{{1,2,3,4,5,6,7}}
[3,7,2,1,4,6,5]=>{{1,2,3,4,5,7},{6}}
[3,7,2,1,5,4,6]=>{{1,2,3,4,6,7},{5}}
[3,7,2,1,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[3,7,2,1,6,4,5]=>{{1,2,3,4,5,6,7}}
[3,7,2,1,6,5,4]=>{{1,2,3,4,7},{5,6}}
[3,7,2,4,1,5,6]=>{{1,2,3,5,6,7},{4}}
[3,7,2,4,1,6,5]=>{{1,2,3,5,7},{4},{6}}
[3,7,2,4,5,1,6]=>{{1,2,3,6,7},{4},{5}}
[3,7,2,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}}
[3,7,2,4,6,1,5]=>{{1,2,3,5,6,7},{4}}
[3,7,2,4,6,5,1]=>{{1,2,3,7},{4},{5,6}}
[3,7,2,5,1,4,6]=>{{1,2,3,4,5,6,7}}
[3,7,2,5,1,6,4]=>{{1,2,3,4,5,7},{6}}
[3,7,2,5,4,1,6]=>{{1,2,3,6,7},{4,5}}
[3,7,2,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}
[3,7,2,5,6,1,4]=>{{1,2,3,4,5,6,7}}
[3,7,2,5,6,4,1]=>{{1,2,3,7},{4,5,6}}
[3,7,2,6,1,4,5]=>{{1,2,3,5,7},{4,6}}
[3,7,2,6,1,5,4]=>{{1,2,3,4,5,6,7}}
[3,7,2,6,4,1,5]=>{{1,2,3,4,5,6,7}}
[3,7,2,6,4,5,1]=>{{1,2,3,7},{4,5,6}}
[3,7,2,6,5,1,4]=>{{1,2,3,4,6,7},{5}}
[3,7,2,6,5,4,1]=>{{1,2,3,7},{4,6},{5}}
[3,7,4,1,2,5,6]=>{{1,3,4},{2,5,6,7}}
[3,7,4,1,2,6,5]=>{{1,3,4},{2,5,7},{6}}
[3,7,4,1,5,2,6]=>{{1,3,4},{2,6,7},{5}}
[3,7,4,1,5,6,2]=>{{1,3,4},{2,7},{5},{6}}
[3,7,4,1,6,2,5]=>{{1,3,4},{2,5,6,7}}
[3,7,4,1,6,5,2]=>{{1,3,4},{2,7},{5,6}}
[3,7,4,2,1,5,6]=>{{1,2,3,4,5,6,7}}
[3,7,4,2,1,6,5]=>{{1,2,3,4,5,7},{6}}
[3,7,4,2,5,1,6]=>{{1,2,3,4,6,7},{5}}
[3,7,4,2,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[3,7,4,2,6,1,5]=>{{1,2,3,4,5,6,7}}
[3,7,4,2,6,5,1]=>{{1,2,3,4,7},{5,6}}
[3,7,4,5,1,2,6]=>{{1,3,4,5},{2,6,7}}
[3,7,4,5,1,6,2]=>{{1,3,4,5},{2,7},{6}}
[3,7,4,5,2,1,6]=>{{1,2,3,4,5,6,7}}
[3,7,4,5,2,6,1]=>{{1,2,3,4,5,7},{6}}
[3,7,4,5,6,1,2]=>{{1,3,4,5,6},{2,7}}
[3,7,4,5,6,2,1]=>{{1,2,3,4,5,6,7}}
[3,7,4,6,1,2,5]=>{{1,2,3,4,5,6,7}}
[3,7,4,6,1,5,2]=>{{1,3,4,5,6},{2,7}}
[3,7,4,6,2,1,5]=>{{1,3,4,6},{2,5,7}}
[3,7,4,6,2,5,1]=>{{1,2,3,4,5,6,7}}
[3,7,4,6,5,1,2]=>{{1,3,4,6},{2,7},{5}}
[3,7,4,6,5,2,1]=>{{1,2,3,4,6,7},{5}}
[3,7,5,1,2,4,6]=>{{1,2,3,4,5,6,7}}
[3,7,5,1,2,6,4]=>{{1,2,3,4,5,7},{6}}
[3,7,5,1,4,2,6]=>{{1,3,4,5},{2,6,7}}
[3,7,5,1,4,6,2]=>{{1,3,4,5},{2,7},{6}}
[3,7,5,1,6,2,4]=>{{1,2,3,4,5,6,7}}
[3,7,5,1,6,4,2]=>{{1,3,4,5,6},{2,7}}
[3,7,5,2,1,4,6]=>{{1,3,5},{2,4,6,7}}
[3,7,5,2,1,6,4]=>{{1,3,5},{2,4,7},{6}}
[3,7,5,2,4,1,6]=>{{1,2,3,4,5,6,7}}
[3,7,5,2,4,6,1]=>{{1,2,3,4,5,7},{6}}
[3,7,5,2,6,1,4]=>{{1,3,5,6},{2,4,7}}
[3,7,5,2,6,4,1]=>{{1,2,3,4,5,6,7}}
[3,7,5,4,1,2,6]=>{{1,3,5},{2,6,7},{4}}
[3,7,5,4,1,6,2]=>{{1,3,5},{2,7},{4},{6}}
[3,7,5,4,2,1,6]=>{{1,2,3,5,6,7},{4}}
[3,7,5,4,2,6,1]=>{{1,2,3,5,7},{4},{6}}
[3,7,5,4,6,1,2]=>{{1,3,5,6},{2,7},{4}}
[3,7,5,4,6,2,1]=>{{1,2,3,5,6,7},{4}}
[3,7,5,6,1,2,4]=>{{1,3,5},{2,4,6,7}}
[3,7,5,6,1,4,2]=>{{1,3,5},{2,7},{4,6}}
[3,7,5,6,2,1,4]=>{{1,2,3,4,5,6,7}}
[3,7,5,6,2,4,1]=>{{1,2,3,5,7},{4,6}}
[3,7,5,6,4,1,2]=>{{1,3,4,5,6},{2,7}}
[3,7,5,6,4,2,1]=>{{1,2,3,4,5,6,7}}
[3,7,6,1,2,4,5]=>{{1,3,4,6},{2,5,7}}
[3,7,6,1,2,5,4]=>{{1,2,3,4,5,6,7}}
[3,7,6,1,4,2,5]=>{{1,2,3,4,5,6,7}}
[3,7,6,1,4,5,2]=>{{1,3,4,5,6},{2,7}}
[3,7,6,1,5,2,4]=>{{1,2,3,4,6,7},{5}}
[3,7,6,1,5,4,2]=>{{1,3,4,6},{2,7},{5}}
[3,7,6,2,1,4,5]=>{{1,2,3,4,5,6,7}}
[3,7,6,2,1,5,4]=>{{1,3,5,6},{2,4,7}}
[3,7,6,2,4,1,5]=>{{1,3,6},{2,4,5,7}}
[3,7,6,2,4,5,1]=>{{1,2,3,4,5,6,7}}
[3,7,6,2,5,1,4]=>{{1,3,6},{2,4,7},{5}}
[3,7,6,2,5,4,1]=>{{1,2,3,4,6,7},{5}}
[3,7,6,4,1,2,5]=>{{1,2,3,5,6,7},{4}}
[3,7,6,4,1,5,2]=>{{1,3,5,6},{2,7},{4}}
[3,7,6,4,2,1,5]=>{{1,3,6},{2,5,7},{4}}
[3,7,6,4,2,5,1]=>{{1,2,3,5,6,7},{4}}
[3,7,6,4,5,1,2]=>{{1,3,6},{2,7},{4},{5}}
[3,7,6,4,5,2,1]=>{{1,2,3,6,7},{4},{5}}
[3,7,6,5,1,2,4]=>{{1,2,3,4,5,6,7}}
[3,7,6,5,1,4,2]=>{{1,3,4,5,6},{2,7}}
[3,7,6,5,2,1,4]=>{{1,3,6},{2,4,5,7}}
[3,7,6,5,2,4,1]=>{{1,2,3,4,5,6,7}}
[3,7,6,5,4,1,2]=>{{1,3,6},{2,7},{4,5}}
[3,7,6,5,4,2,1]=>{{1,2,3,6,7},{4,5}}
[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[4,1,2,3,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[4,1,2,3,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[4,1,2,3,6,7,5]=>{{1,2,3,4},{5,6,7}}
[4,1,2,3,7,5,6]=>{{1,2,3,4},{5,6,7}}
[4,1,2,3,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[4,1,2,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[4,1,2,5,3,7,6]=>{{1,2,3,4,5},{6,7}}
[4,1,2,5,6,3,7]=>{{1,2,3,4,5,6},{7}}
[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[4,1,2,5,7,6,3]=>{{1,2,3,4,5,7},{6}}
[4,1,2,6,3,5,7]=>{{1,2,3,4,5,6},{7}}
[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[4,1,2,6,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[4,1,2,6,5,7,3]=>{{1,2,3,4,6,7},{5}}
[4,1,2,6,7,3,5]=>{{1,2,3,4,6},{5,7}}
[4,1,2,6,7,5,3]=>{{1,2,3,4,5,6,7}}
[4,1,2,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[4,1,2,7,3,6,5]=>{{1,2,3,4,5,7},{6}}
[4,1,2,7,5,3,6]=>{{1,2,3,4,6,7},{5}}
[4,1,2,7,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[4,1,2,7,6,3,5]=>{{1,2,3,4,5,6,7}}
[4,1,2,7,6,5,3]=>{{1,2,3,4,7},{5,6}}
[4,1,3,2,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}
[4,1,3,2,5,7,6]=>{{1,2,4},{3},{5},{6,7}}
[4,1,3,2,6,5,7]=>{{1,2,4},{3},{5,6},{7}}
[4,1,3,2,6,7,5]=>{{1,2,4},{3},{5,6,7}}
[4,1,3,2,7,5,6]=>{{1,2,4},{3},{5,6,7}}
[4,1,3,2,7,6,5]=>{{1,2,4},{3},{5,7},{6}}
[4,1,3,5,2,6,7]=>{{1,2,4,5},{3},{6},{7}}
[4,1,3,5,2,7,6]=>{{1,2,4,5},{3},{6,7}}
[4,1,3,5,6,2,7]=>{{1,2,4,5,6},{3},{7}}
[4,1,3,5,6,7,2]=>{{1,2,4,5,6,7},{3}}
[4,1,3,5,7,2,6]=>{{1,2,4,5,6,7},{3}}
[4,1,3,5,7,6,2]=>{{1,2,4,5,7},{3},{6}}
[4,1,3,6,2,5,7]=>{{1,2,4,5,6},{3},{7}}
[4,1,3,6,2,7,5]=>{{1,2,4,5,6,7},{3}}
[4,1,3,6,5,2,7]=>{{1,2,4,6},{3},{5},{7}}
[4,1,3,6,5,7,2]=>{{1,2,4,6,7},{3},{5}}
[4,1,3,6,7,2,5]=>{{1,2,4,6},{3},{5,7}}
[4,1,3,6,7,5,2]=>{{1,2,4,5,6,7},{3}}
[4,1,3,7,2,5,6]=>{{1,2,4,5,6,7},{3}}
[4,1,3,7,2,6,5]=>{{1,2,4,5,7},{3},{6}}
[4,1,3,7,5,2,6]=>{{1,2,4,6,7},{3},{5}}
[4,1,3,7,5,6,2]=>{{1,2,4,7},{3},{5},{6}}
[4,1,3,7,6,2,5]=>{{1,2,4,5,6,7},{3}}
[4,1,3,7,6,5,2]=>{{1,2,4,7},{3},{5,6}}
[4,1,5,2,3,6,7]=>{{1,2,4},{3,5},{6},{7}}
[4,1,5,2,3,7,6]=>{{1,2,4},{3,5},{6,7}}
[4,1,5,2,6,3,7]=>{{1,2,4},{3,5,6},{7}}
[4,1,5,2,6,7,3]=>{{1,2,4},{3,5,6,7}}
[4,1,5,2,7,3,6]=>{{1,2,4},{3,5,6,7}}
[4,1,5,2,7,6,3]=>{{1,2,4},{3,5,7},{6}}
[4,1,5,3,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[4,1,5,3,2,7,6]=>{{1,2,3,4,5},{6,7}}
[4,1,5,3,6,2,7]=>{{1,2,3,4,5,6},{7}}
[4,1,5,3,6,7,2]=>{{1,2,3,4,5,6,7}}
[4,1,5,3,7,2,6]=>{{1,2,3,4,5,6,7}}
[4,1,5,3,7,6,2]=>{{1,2,3,4,5,7},{6}}
[4,1,5,6,2,3,7]=>{{1,2,3,4,5,6},{7}}
[4,1,5,6,2,7,3]=>{{1,2,3,4,5,6,7}}
[4,1,5,6,3,2,7]=>{{1,2,4,6},{3,5},{7}}
[4,1,5,6,3,7,2]=>{{1,2,4,6,7},{3,5}}
[4,1,5,6,7,2,3]=>{{1,2,4,6},{3,5,7}}
[4,1,5,6,7,3,2]=>{{1,2,3,4,5,6,7}}
[4,1,5,7,2,3,6]=>{{1,2,3,4,5,6,7}}
[4,1,5,7,2,6,3]=>{{1,2,3,4,5,7},{6}}
[4,1,5,7,3,2,6]=>{{1,2,4,6,7},{3,5}}
[4,1,5,7,3,6,2]=>{{1,2,4,7},{3,5},{6}}
[4,1,5,7,6,2,3]=>{{1,2,3,4,5,6,7}}
[4,1,5,7,6,3,2]=>{{1,2,4,7},{3,5,6}}
[4,1,6,2,3,5,7]=>{{1,2,4},{3,5,6},{7}}
[4,1,6,2,3,7,5]=>{{1,2,4},{3,5,6,7}}
[4,1,6,2,5,3,7]=>{{1,2,4},{3,6},{5},{7}}
[4,1,6,2,5,7,3]=>{{1,2,4},{3,6,7},{5}}
[4,1,6,2,7,3,5]=>{{1,2,4},{3,6},{5,7}}
[4,1,6,2,7,5,3]=>{{1,2,4},{3,5,6,7}}
[4,1,6,3,2,5,7]=>{{1,2,3,4,5,6},{7}}
[4,1,6,3,2,7,5]=>{{1,2,3,4,5,6,7}}
[4,1,6,3,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[4,1,6,3,5,7,2]=>{{1,2,3,4,6,7},{5}}
[4,1,6,3,7,2,5]=>{{1,2,3,4,6},{5,7}}
[4,1,6,3,7,5,2]=>{{1,2,3,4,5,6,7}}
[4,1,6,5,2,3,7]=>{{1,2,4,5},{3,6},{7}}
[4,1,6,5,2,7,3]=>{{1,2,4,5},{3,6,7}}
[4,1,6,5,3,2,7]=>{{1,2,3,4,5,6},{7}}
[4,1,6,5,3,7,2]=>{{1,2,3,4,5,6,7}}
[4,1,6,5,7,2,3]=>{{1,2,3,4,5,6,7}}
[4,1,6,5,7,3,2]=>{{1,2,4,5,7},{3,6}}
[4,1,6,7,2,3,5]=>{{1,2,4,5,7},{3,6}}
[4,1,6,7,2,5,3]=>{{1,2,3,4,5,6,7}}
[4,1,6,7,3,2,5]=>{{1,2,3,4,5,6,7}}
[4,1,6,7,3,5,2]=>{{1,2,4,7},{3,5,6}}
[4,1,6,7,5,2,3]=>{{1,2,3,4,6,7},{5}}
[4,1,6,7,5,3,2]=>{{1,2,4,7},{3,6},{5}}
[4,1,7,2,3,5,6]=>{{1,2,4},{3,5,6,7}}
[4,1,7,2,3,6,5]=>{{1,2,4},{3,5,7},{6}}
[4,1,7,2,5,3,6]=>{{1,2,4},{3,6,7},{5}}
[4,1,7,2,5,6,3]=>{{1,2,4},{3,7},{5},{6}}
[4,1,7,2,6,3,5]=>{{1,2,4},{3,5,6,7}}
[4,1,7,2,6,5,3]=>{{1,2,4},{3,7},{5,6}}
[4,1,7,3,2,5,6]=>{{1,2,3,4,5,6,7}}
[4,1,7,3,2,6,5]=>{{1,2,3,4,5,7},{6}}
[4,1,7,3,5,2,6]=>{{1,2,3,4,6,7},{5}}
[4,1,7,3,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[4,1,7,3,6,2,5]=>{{1,2,3,4,5,6,7}}
[4,1,7,3,6,5,2]=>{{1,2,3,4,7},{5,6}}
[4,1,7,5,2,3,6]=>{{1,2,4,5},{3,6,7}}
[4,1,7,5,2,6,3]=>{{1,2,4,5},{3,7},{6}}
[4,1,7,5,3,2,6]=>{{1,2,3,4,5,6,7}}
[4,1,7,5,3,6,2]=>{{1,2,3,4,5,7},{6}}
[4,1,7,5,6,2,3]=>{{1,2,4,5,6},{3,7}}
[4,1,7,5,6,3,2]=>{{1,2,3,4,5,6,7}}
[4,1,7,6,2,3,5]=>{{1,2,3,4,5,6,7}}
[4,1,7,6,2,5,3]=>{{1,2,4,5,6},{3,7}}
[4,1,7,6,3,2,5]=>{{1,2,4,6},{3,5,7}}
[4,1,7,6,3,5,2]=>{{1,2,3,4,5,6,7}}
[4,1,7,6,5,2,3]=>{{1,2,4,6},{3,7},{5}}
[4,1,7,6,5,3,2]=>{{1,2,3,4,6,7},{5}}
[4,2,1,3,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}
[4,2,1,3,5,7,6]=>{{1,3,4},{2},{5},{6,7}}
[4,2,1,3,6,5,7]=>{{1,3,4},{2},{5,6},{7}}
[4,2,1,3,6,7,5]=>{{1,3,4},{2},{5,6,7}}
[4,2,1,3,7,5,6]=>{{1,3,4},{2},{5,6,7}}
[4,2,1,3,7,6,5]=>{{1,3,4},{2},{5,7},{6}}
[4,2,1,5,3,6,7]=>{{1,3,4,5},{2},{6},{7}}
[4,2,1,5,3,7,6]=>{{1,3,4,5},{2},{6,7}}
[4,2,1,5,6,3,7]=>{{1,3,4,5,6},{2},{7}}
[4,2,1,5,6,7,3]=>{{1,3,4,5,6,7},{2}}
[4,2,1,5,7,3,6]=>{{1,3,4,5,6,7},{2}}
[4,2,1,5,7,6,3]=>{{1,3,4,5,7},{2},{6}}
[4,2,1,6,3,5,7]=>{{1,3,4,5,6},{2},{7}}
[4,2,1,6,3,7,5]=>{{1,3,4,5,6,7},{2}}
[4,2,1,6,5,3,7]=>{{1,3,4,6},{2},{5},{7}}
[4,2,1,6,5,7,3]=>{{1,3,4,6,7},{2},{5}}
[4,2,1,6,7,3,5]=>{{1,3,4,6},{2},{5,7}}
[4,2,1,6,7,5,3]=>{{1,3,4,5,6,7},{2}}
[4,2,1,7,3,5,6]=>{{1,3,4,5,6,7},{2}}
[4,2,1,7,3,6,5]=>{{1,3,4,5,7},{2},{6}}
[4,2,1,7,5,3,6]=>{{1,3,4,6,7},{2},{5}}
[4,2,1,7,5,6,3]=>{{1,3,4,7},{2},{5},{6}}
[4,2,1,7,6,3,5]=>{{1,3,4,5,6,7},{2}}
[4,2,1,7,6,5,3]=>{{1,3,4,7},{2},{5,6}}
[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}
[4,2,3,1,5,7,6]=>{{1,4},{2},{3},{5},{6,7}}
[4,2,3,1,6,5,7]=>{{1,4},{2},{3},{5,6},{7}}
[4,2,3,1,6,7,5]=>{{1,4},{2},{3},{5,6,7}}
[4,2,3,1,7,5,6]=>{{1,4},{2},{3},{5,6,7}}
[4,2,3,1,7,6,5]=>{{1,4},{2},{3},{5,7},{6}}
[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[4,2,3,5,1,7,6]=>{{1,4,5},{2},{3},{6,7}}
[4,2,3,5,6,1,7]=>{{1,4,5,6},{2},{3},{7}}
[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}}
[4,2,3,5,7,1,6]=>{{1,4,5,6,7},{2},{3}}
[4,2,3,5,7,6,1]=>{{1,4,5,7},{2},{3},{6}}
[4,2,3,6,1,5,7]=>{{1,4,5,6},{2},{3},{7}}
[4,2,3,6,1,7,5]=>{{1,4,5,6,7},{2},{3}}
[4,2,3,6,5,1,7]=>{{1,4,6},{2},{3},{5},{7}}
[4,2,3,6,5,7,1]=>{{1,4,6,7},{2},{3},{5}}
[4,2,3,6,7,1,5]=>{{1,4,6},{2},{3},{5,7}}
[4,2,3,6,7,5,1]=>{{1,4,5,6,7},{2},{3}}
[4,2,3,7,1,5,6]=>{{1,4,5,6,7},{2},{3}}
[4,2,3,7,1,6,5]=>{{1,4,5,7},{2},{3},{6}}
[4,2,3,7,5,1,6]=>{{1,4,6,7},{2},{3},{5}}
[4,2,3,7,5,6,1]=>{{1,4,7},{2},{3},{5},{6}}
[4,2,3,7,6,1,5]=>{{1,4,5,6,7},{2},{3}}
[4,2,3,7,6,5,1]=>{{1,4,7},{2},{3},{5,6}}
[4,2,5,1,3,6,7]=>{{1,4},{2},{3,5},{6},{7}}
[4,2,5,1,3,7,6]=>{{1,4},{2},{3,5},{6,7}}
[4,2,5,1,6,3,7]=>{{1,4},{2},{3,5,6},{7}}
[4,2,5,1,6,7,3]=>{{1,4},{2},{3,5,6,7}}
[4,2,5,1,7,3,6]=>{{1,4},{2},{3,5,6,7}}
[4,2,5,1,7,6,3]=>{{1,4},{2},{3,5,7},{6}}
[4,2,5,3,1,6,7]=>{{1,3,4,5},{2},{6},{7}}
[4,2,5,3,1,7,6]=>{{1,3,4,5},{2},{6,7}}
[4,2,5,3,6,1,7]=>{{1,3,4,5,6},{2},{7}}
[4,2,5,3,6,7,1]=>{{1,3,4,5,6,7},{2}}
[4,2,5,3,7,1,6]=>{{1,3,4,5,6,7},{2}}
[4,2,5,3,7,6,1]=>{{1,3,4,5,7},{2},{6}}
[4,2,5,6,1,3,7]=>{{1,3,4,5,6},{2},{7}}
[4,2,5,6,1,7,3]=>{{1,3,4,5,6,7},{2}}
[4,2,5,6,3,1,7]=>{{1,4,6},{2},{3,5},{7}}
[4,2,5,6,3,7,1]=>{{1,4,6,7},{2},{3,5}}
[4,2,5,6,7,1,3]=>{{1,4,6},{2},{3,5,7}}
[4,2,5,6,7,3,1]=>{{1,3,4,5,6,7},{2}}
[4,2,5,7,1,3,6]=>{{1,3,4,5,6,7},{2}}
[4,2,5,7,1,6,3]=>{{1,3,4,5,7},{2},{6}}
[4,2,5,7,3,1,6]=>{{1,4,6,7},{2},{3,5}}
[4,2,5,7,3,6,1]=>{{1,4,7},{2},{3,5},{6}}
[4,2,5,7,6,1,3]=>{{1,3,4,5,6,7},{2}}
[4,2,5,7,6,3,1]=>{{1,4,7},{2},{3,5,6}}
[4,2,6,1,3,5,7]=>{{1,4},{2},{3,5,6},{7}}
[4,2,6,1,3,7,5]=>{{1,4},{2},{3,5,6,7}}
[4,2,6,1,5,3,7]=>{{1,4},{2},{3,6},{5},{7}}
[4,2,6,1,5,7,3]=>{{1,4},{2},{3,6,7},{5}}
[4,2,6,1,7,3,5]=>{{1,4},{2},{3,6},{5,7}}
[4,2,6,1,7,5,3]=>{{1,4},{2},{3,5,6,7}}
[4,2,6,3,1,5,7]=>{{1,3,4,5,6},{2},{7}}
[4,2,6,3,1,7,5]=>{{1,3,4,5,6,7},{2}}
[4,2,6,3,5,1,7]=>{{1,3,4,6},{2},{5},{7}}
[4,2,6,3,5,7,1]=>{{1,3,4,6,7},{2},{5}}
[4,2,6,3,7,1,5]=>{{1,3,4,6},{2},{5,7}}
[4,2,6,3,7,5,1]=>{{1,3,4,5,6,7},{2}}
[4,2,6,5,1,3,7]=>{{1,4,5},{2},{3,6},{7}}
[4,2,6,5,1,7,3]=>{{1,4,5},{2},{3,6,7}}
[4,2,6,5,3,1,7]=>{{1,3,4,5,6},{2},{7}}
[4,2,6,5,3,7,1]=>{{1,3,4,5,6,7},{2}}
[4,2,6,5,7,1,3]=>{{1,3,4,5,6,7},{2}}
[4,2,6,5,7,3,1]=>{{1,4,5,7},{2},{3,6}}
[4,2,6,7,1,3,5]=>{{1,4,5,7},{2},{3,6}}
[4,2,6,7,1,5,3]=>{{1,3,4,5,6,7},{2}}
[4,2,6,7,3,1,5]=>{{1,3,4,5,6,7},{2}}
[4,2,6,7,3,5,1]=>{{1,4,7},{2},{3,5,6}}
[4,2,6,7,5,1,3]=>{{1,3,4,6,7},{2},{5}}
[4,2,6,7,5,3,1]=>{{1,4,7},{2},{3,6},{5}}
[4,2,7,1,3,5,6]=>{{1,4},{2},{3,5,6,7}}
[4,2,7,1,3,6,5]=>{{1,4},{2},{3,5,7},{6}}
[4,2,7,1,5,3,6]=>{{1,4},{2},{3,6,7},{5}}
[4,2,7,1,5,6,3]=>{{1,4},{2},{3,7},{5},{6}}
[4,2,7,1,6,3,5]=>{{1,4},{2},{3,5,6,7}}
[4,2,7,1,6,5,3]=>{{1,4},{2},{3,7},{5,6}}
[4,2,7,3,1,5,6]=>{{1,3,4,5,6,7},{2}}
[4,2,7,3,1,6,5]=>{{1,3,4,5,7},{2},{6}}
[4,2,7,3,5,1,6]=>{{1,3,4,6,7},{2},{5}}
[4,2,7,3,5,6,1]=>{{1,3,4,7},{2},{5},{6}}
[4,2,7,3,6,1,5]=>{{1,3,4,5,6,7},{2}}
[4,2,7,3,6,5,1]=>{{1,3,4,7},{2},{5,6}}
[4,2,7,5,1,3,6]=>{{1,4,5},{2},{3,6,7}}
[4,2,7,5,1,6,3]=>{{1,4,5},{2},{3,7},{6}}
[4,2,7,5,3,1,6]=>{{1,3,4,5,6,7},{2}}
[4,2,7,5,3,6,1]=>{{1,3,4,5,7},{2},{6}}
[4,2,7,5,6,1,3]=>{{1,4,5,6},{2},{3,7}}
[4,2,7,5,6,3,1]=>{{1,3,4,5,6,7},{2}}
[4,2,7,6,1,3,5]=>{{1,3,4,5,6,7},{2}}
[4,2,7,6,1,5,3]=>{{1,4,5,6},{2},{3,7}}
[4,2,7,6,3,1,5]=>{{1,4,6},{2},{3,5,7}}
[4,2,7,6,3,5,1]=>{{1,3,4,5,6,7},{2}}
[4,2,7,6,5,1,3]=>{{1,4,6},{2},{3,7},{5}}
[4,2,7,6,5,3,1]=>{{1,3,4,6,7},{2},{5}}
[4,3,1,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[4,3,1,2,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[4,3,1,2,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[4,3,1,2,6,7,5]=>{{1,2,3,4},{5,6,7}}
[4,3,1,2,7,5,6]=>{{1,2,3,4},{5,6,7}}
[4,3,1,2,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[4,3,1,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[4,3,1,5,2,7,6]=>{{1,2,3,4,5},{6,7}}
[4,3,1,5,6,2,7]=>{{1,2,3,4,5,6},{7}}
[4,3,1,5,6,7,2]=>{{1,2,3,4,5,6,7}}
[4,3,1,5,7,2,6]=>{{1,2,3,4,5,6,7}}
[4,3,1,5,7,6,2]=>{{1,2,3,4,5,7},{6}}
[4,3,1,6,2,5,7]=>{{1,2,3,4,5,6},{7}}
[4,3,1,6,2,7,5]=>{{1,2,3,4,5,6,7}}
[4,3,1,6,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[4,3,1,6,5,7,2]=>{{1,2,3,4,6,7},{5}}
[4,3,1,6,7,2,5]=>{{1,2,3,4,6},{5,7}}
[4,3,1,6,7,5,2]=>{{1,2,3,4,5,6,7}}
[4,3,1,7,2,5,6]=>{{1,2,3,4,5,6,7}}
[4,3,1,7,2,6,5]=>{{1,2,3,4,5,7},{6}}
[4,3,1,7,5,2,6]=>{{1,2,3,4,6,7},{5}}
[4,3,1,7,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}}
[4,3,1,7,6,5,2]=>{{1,2,3,4,7},{5,6}}
[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}}
[4,3,2,1,5,7,6]=>{{1,4},{2,3},{5},{6,7}}
[4,3,2,1,6,5,7]=>{{1,4},{2,3},{5,6},{7}}
[4,3,2,1,6,7,5]=>{{1,4},{2,3},{5,6,7}}
[4,3,2,1,7,5,6]=>{{1,4},{2,3},{5,6,7}}
[4,3,2,1,7,6,5]=>{{1,4},{2,3},{5,7},{6}}
[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}}
[4,3,2,5,1,7,6]=>{{1,4,5},{2,3},{6,7}}
[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}}
[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}}
[4,3,2,5,7,1,6]=>{{1,4,5,6,7},{2,3}}
[4,3,2,5,7,6,1]=>{{1,4,5,7},{2,3},{6}}
[4,3,2,6,1,5,7]=>{{1,4,5,6},{2,3},{7}}
[4,3,2,6,1,7,5]=>{{1,4,5,6,7},{2,3}}
[4,3,2,6,5,1,7]=>{{1,4,6},{2,3},{5},{7}}
[4,3,2,6,5,7,1]=>{{1,4,6,7},{2,3},{5}}
[4,3,2,6,7,1,5]=>{{1,4,6},{2,3},{5,7}}
[4,3,2,6,7,5,1]=>{{1,4,5,6,7},{2,3}}
[4,3,2,7,1,5,6]=>{{1,4,5,6,7},{2,3}}
[4,3,2,7,1,6,5]=>{{1,4,5,7},{2,3},{6}}
[4,3,2,7,5,1,6]=>{{1,4,6,7},{2,3},{5}}
[4,3,2,7,5,6,1]=>{{1,4,7},{2,3},{5},{6}}
[4,3,2,7,6,1,5]=>{{1,4,5,6,7},{2,3}}
[4,3,2,7,6,5,1]=>{{1,4,7},{2,3},{5,6}}
[4,3,5,1,2,6,7]=>{{1,4},{2,3,5},{6},{7}}
[4,3,5,1,2,7,6]=>{{1,4},{2,3,5},{6,7}}
[4,3,5,1,6,2,7]=>{{1,4},{2,3,5,6},{7}}
[4,3,5,1,6,7,2]=>{{1,4},{2,3,5,6,7}}
[4,3,5,1,7,2,6]=>{{1,4},{2,3,5,6,7}}
[4,3,5,1,7,6,2]=>{{1,4},{2,3,5,7},{6}}
[4,3,5,2,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[4,3,5,2,1,7,6]=>{{1,2,3,4,5},{6,7}}
[4,3,5,2,6,1,7]=>{{1,2,3,4,5,6},{7}}
[4,3,5,2,6,7,1]=>{{1,2,3,4,5,6,7}}
[4,3,5,2,7,1,6]=>{{1,2,3,4,5,6,7}}
[4,3,5,2,7,6,1]=>{{1,2,3,4,5,7},{6}}
[4,3,5,6,1,2,7]=>{{1,2,3,4,5,6},{7}}
[4,3,5,6,1,7,2]=>{{1,2,3,4,5,6,7}}
[4,3,5,6,2,1,7]=>{{1,4,6},{2,3,5},{7}}
[4,3,5,6,2,7,1]=>{{1,4,6,7},{2,3,5}}
[4,3,5,6,7,1,2]=>{{1,4,6},{2,3,5,7}}
[4,3,5,6,7,2,1]=>{{1,2,3,4,5,6,7}}
[4,3,5,7,1,2,6]=>{{1,2,3,4,5,6,7}}
[4,3,5,7,1,6,2]=>{{1,2,3,4,5,7},{6}}
[4,3,5,7,2,1,6]=>{{1,4,6,7},{2,3,5}}
[4,3,5,7,2,6,1]=>{{1,4,7},{2,3,5},{6}}
[4,3,5,7,6,1,2]=>{{1,2,3,4,5,6,7}}
[4,3,5,7,6,2,1]=>{{1,4,7},{2,3,5,6}}
[4,3,6,1,2,5,7]=>{{1,4},{2,3,5,6},{7}}
[4,3,6,1,2,7,5]=>{{1,4},{2,3,5,6,7}}
[4,3,6,1,5,2,7]=>{{1,4},{2,3,6},{5},{7}}
[4,3,6,1,5,7,2]=>{{1,4},{2,3,6,7},{5}}
[4,3,6,1,7,2,5]=>{{1,4},{2,3,6},{5,7}}
[4,3,6,1,7,5,2]=>{{1,4},{2,3,5,6,7}}
[4,3,6,2,1,5,7]=>{{1,2,3,4,5,6},{7}}
[4,3,6,2,1,7,5]=>{{1,2,3,4,5,6,7}}
[4,3,6,2,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[4,3,6,2,5,7,1]=>{{1,2,3,4,6,7},{5}}
[4,3,6,2,7,1,5]=>{{1,2,3,4,6},{5,7}}
[4,3,6,2,7,5,1]=>{{1,2,3,4,5,6,7}}
[4,3,6,5,1,2,7]=>{{1,4,5},{2,3,6},{7}}
[4,3,6,5,1,7,2]=>{{1,4,5},{2,3,6,7}}
[4,3,6,5,2,1,7]=>{{1,2,3,4,5,6},{7}}
[4,3,6,5,2,7,1]=>{{1,2,3,4,5,6,7}}
[4,3,6,5,7,1,2]=>{{1,2,3,4,5,6,7}}
[4,3,6,5,7,2,1]=>{{1,4,5,7},{2,3,6}}
[4,3,6,7,1,2,5]=>{{1,4,5,7},{2,3,6}}
[4,3,6,7,1,5,2]=>{{1,2,3,4,5,6,7}}
[4,3,6,7,2,1,5]=>{{1,2,3,4,5,6,7}}
[4,3,6,7,2,5,1]=>{{1,4,7},{2,3,5,6}}
[4,3,6,7,5,1,2]=>{{1,2,3,4,6,7},{5}}
[4,3,6,7,5,2,1]=>{{1,4,7},{2,3,6},{5}}
[4,3,7,1,2,5,6]=>{{1,4},{2,3,5,6,7}}
[4,3,7,1,2,6,5]=>{{1,4},{2,3,5,7},{6}}
[4,3,7,1,5,2,6]=>{{1,4},{2,3,6,7},{5}}
[4,3,7,1,5,6,2]=>{{1,4},{2,3,7},{5},{6}}
[4,3,7,1,6,2,5]=>{{1,4},{2,3,5,6,7}}
[4,3,7,1,6,5,2]=>{{1,4},{2,3,7},{5,6}}
[4,3,7,2,1,5,6]=>{{1,2,3,4,5,6,7}}
[4,3,7,2,1,6,5]=>{{1,2,3,4,5,7},{6}}
[4,3,7,2,5,1,6]=>{{1,2,3,4,6,7},{5}}
[4,3,7,2,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[4,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7}}
[4,3,7,2,6,5,1]=>{{1,2,3,4,7},{5,6}}
[4,3,7,5,1,2,6]=>{{1,4,5},{2,3,6,7}}
[4,3,7,5,1,6,2]=>{{1,4,5},{2,3,7},{6}}
[4,3,7,5,2,1,6]=>{{1,2,3,4,5,6,7}}
[4,3,7,5,2,6,1]=>{{1,2,3,4,5,7},{6}}
[4,3,7,5,6,1,2]=>{{1,4,5,6},{2,3,7}}
[4,3,7,5,6,2,1]=>{{1,2,3,4,5,6,7}}
[4,3,7,6,1,2,5]=>{{1,2,3,4,5,6,7}}
[4,3,7,6,1,5,2]=>{{1,4,5,6},{2,3,7}}
[4,3,7,6,2,1,5]=>{{1,4,6},{2,3,5,7}}
[4,3,7,6,2,5,1]=>{{1,2,3,4,5,6,7}}
[4,3,7,6,5,1,2]=>{{1,4,6},{2,3,7},{5}}
[4,3,7,6,5,2,1]=>{{1,2,3,4,6,7},{5}}
[4,5,1,2,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[4,5,1,2,3,7,6]=>{{1,2,3,4,5},{6,7}}
[4,5,1,2,6,3,7]=>{{1,2,3,4,5,6},{7}}
[4,5,1,2,6,7,3]=>{{1,2,3,4,5,6,7}}
[4,5,1,2,7,3,6]=>{{1,2,3,4,5,6,7}}
[4,5,1,2,7,6,3]=>{{1,2,3,4,5,7},{6}}
[4,5,1,3,2,6,7]=>{{1,3,4},{2,5},{6},{7}}
[4,5,1,3,2,7,6]=>{{1,3,4},{2,5},{6,7}}
[4,5,1,3,6,2,7]=>{{1,3,4},{2,5,6},{7}}
[4,5,1,3,6,7,2]=>{{1,3,4},{2,5,6,7}}
[4,5,1,3,7,2,6]=>{{1,3,4},{2,5,6,7}}
[4,5,1,3,7,6,2]=>{{1,3,4},{2,5,7},{6}}
[4,5,1,6,2,3,7]=>{{1,3,4,6},{2,5},{7}}
[4,5,1,6,2,7,3]=>{{1,3,4,6,7},{2,5}}
[4,5,1,6,3,2,7]=>{{1,2,3,4,5,6},{7}}
[4,5,1,6,3,7,2]=>{{1,2,3,4,5,6,7}}
[4,5,1,6,7,2,3]=>{{1,2,3,4,5,6,7}}
[4,5,1,6,7,3,2]=>{{1,3,4,6},{2,5,7}}
[4,5,1,7,2,3,6]=>{{1,3,4,6,7},{2,5}}
[4,5,1,7,2,6,3]=>{{1,3,4,7},{2,5},{6}}
[4,5,1,7,3,2,6]=>{{1,2,3,4,5,6,7}}
[4,5,1,7,3,6,2]=>{{1,2,3,4,5,7},{6}}
[4,5,1,7,6,2,3]=>{{1,3,4,7},{2,5,6}}
[4,5,1,7,6,3,2]=>{{1,2,3,4,5,6,7}}
[4,5,2,1,3,6,7]=>{{1,4},{2,3,5},{6},{7}}
[4,5,2,1,3,7,6]=>{{1,4},{2,3,5},{6,7}}
[4,5,2,1,6,3,7]=>{{1,4},{2,3,5,6},{7}}
[4,5,2,1,6,7,3]=>{{1,4},{2,3,5,6,7}}
[4,5,2,1,7,3,6]=>{{1,4},{2,3,5,6,7}}
[4,5,2,1,7,6,3]=>{{1,4},{2,3,5,7},{6}}
[4,5,2,3,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[4,5,2,3,1,7,6]=>{{1,2,3,4,5},{6,7}}
[4,5,2,3,6,1,7]=>{{1,2,3,4,5,6},{7}}
[4,5,2,3,6,7,1]=>{{1,2,3,4,5,6,7}}
[4,5,2,3,7,1,6]=>{{1,2,3,4,5,6,7}}
[4,5,2,3,7,6,1]=>{{1,2,3,4,5,7},{6}}
[4,5,2,6,1,3,7]=>{{1,2,3,4,5,6},{7}}
[4,5,2,6,1,7,3]=>{{1,2,3,4,5,6,7}}
[4,5,2,6,3,1,7]=>{{1,4,6},{2,3,5},{7}}
[4,5,2,6,3,7,1]=>{{1,4,6,7},{2,3,5}}
[4,5,2,6,7,1,3]=>{{1,4,6},{2,3,5,7}}
[4,5,2,6,7,3,1]=>{{1,2,3,4,5,6,7}}
[4,5,2,7,1,3,6]=>{{1,2,3,4,5,6,7}}
[4,5,2,7,1,6,3]=>{{1,2,3,4,5,7},{6}}
[4,5,2,7,3,1,6]=>{{1,4,6,7},{2,3,5}}
[4,5,2,7,3,6,1]=>{{1,4,7},{2,3,5},{6}}
[4,5,2,7,6,1,3]=>{{1,2,3,4,5,6,7}}
[4,5,2,7,6,3,1]=>{{1,4,7},{2,3,5,6}}
[4,5,3,1,2,6,7]=>{{1,4},{2,5},{3},{6},{7}}
[4,5,3,1,2,7,6]=>{{1,4},{2,5},{3},{6,7}}
[4,5,3,1,6,2,7]=>{{1,4},{2,5,6},{3},{7}}
[4,5,3,1,6,7,2]=>{{1,4},{2,5,6,7},{3}}
[4,5,3,1,7,2,6]=>{{1,4},{2,5,6,7},{3}}
[4,5,3,1,7,6,2]=>{{1,4},{2,5,7},{3},{6}}
[4,5,3,2,1,6,7]=>{{1,2,4,5},{3},{6},{7}}
[4,5,3,2,1,7,6]=>{{1,2,4,5},{3},{6,7}}
[4,5,3,2,6,1,7]=>{{1,2,4,5,6},{3},{7}}
[4,5,3,2,6,7,1]=>{{1,2,4,5,6,7},{3}}
[4,5,3,2,7,1,6]=>{{1,2,4,5,6,7},{3}}
[4,5,3,2,7,6,1]=>{{1,2,4,5,7},{3},{6}}
[4,5,3,6,1,2,7]=>{{1,2,4,5,6},{3},{7}}
[4,5,3,6,1,7,2]=>{{1,2,4,5,6,7},{3}}
[4,5,3,6,2,1,7]=>{{1,4,6},{2,5},{3},{7}}
[4,5,3,6,2,7,1]=>{{1,4,6,7},{2,5},{3}}
[4,5,3,6,7,1,2]=>{{1,4,6},{2,5,7},{3}}
[4,5,3,6,7,2,1]=>{{1,2,4,5,6,7},{3}}
[4,5,3,7,1,2,6]=>{{1,2,4,5,6,7},{3}}
[4,5,3,7,1,6,2]=>{{1,2,4,5,7},{3},{6}}
[4,5,3,7,2,1,6]=>{{1,4,6,7},{2,5},{3}}
[4,5,3,7,2,6,1]=>{{1,4,7},{2,5},{3},{6}}
[4,5,3,7,6,1,2]=>{{1,2,4,5,6,7},{3}}
[4,5,3,7,6,2,1]=>{{1,4,7},{2,5,6},{3}}
[4,5,6,1,2,3,7]=>{{1,4},{2,5},{3,6},{7}}
[4,5,6,1,2,7,3]=>{{1,4},{2,5},{3,6,7}}
[4,5,6,1,3,2,7]=>{{1,4},{2,3,5,6},{7}}
[4,5,6,1,3,7,2]=>{{1,4},{2,3,5,6,7}}
[4,5,6,1,7,2,3]=>{{1,4},{2,3,5,6,7}}
[4,5,6,1,7,3,2]=>{{1,4},{2,5,7},{3,6}}
[4,5,6,2,1,3,7]=>{{1,2,4,5},{3,6},{7}}
[4,5,6,2,1,7,3]=>{{1,2,4,5},{3,6,7}}
[4,5,6,2,3,1,7]=>{{1,2,3,4,5,6},{7}}
[4,5,6,2,3,7,1]=>{{1,2,3,4,5,6,7}}
[4,5,6,2,7,1,3]=>{{1,2,3,4,5,6,7}}
[4,5,6,2,7,3,1]=>{{1,2,4,5,7},{3,6}}
[4,5,6,3,1,2,7]=>{{1,2,3,4,5,6},{7}}
[4,5,6,3,1,7,2]=>{{1,2,3,4,5,6,7}}
[4,5,6,3,2,1,7]=>{{1,3,4,6},{2,5},{7}}
[4,5,6,3,2,7,1]=>{{1,3,4,6,7},{2,5}}
[4,5,6,3,7,1,2]=>{{1,3,4,6},{2,5,7}}
[4,5,6,3,7,2,1]=>{{1,2,3,4,5,6,7}}
[4,5,6,7,1,2,3]=>{{1,2,3,4,5,6,7}}
[4,5,6,7,1,3,2]=>{{1,2,4,5,7},{3,6}}
[4,5,6,7,2,1,3]=>{{1,3,4,6,7},{2,5}}
[4,5,6,7,2,3,1]=>{{1,4,7},{2,5},{3,6}}
[4,5,6,7,3,1,2]=>{{1,2,3,4,5,6,7}}
[4,5,6,7,3,2,1]=>{{1,4,7},{2,3,5,6}}
[4,5,7,1,2,3,6]=>{{1,4},{2,5},{3,6,7}}
[4,5,7,1,2,6,3]=>{{1,4},{2,5},{3,7},{6}}
[4,5,7,1,3,2,6]=>{{1,4},{2,3,5,6,7}}
[4,5,7,1,3,6,2]=>{{1,4},{2,3,5,7},{6}}
[4,5,7,1,6,2,3]=>{{1,4},{2,5,6},{3,7}}
[4,5,7,1,6,3,2]=>{{1,4},{2,3,5,6,7}}
[4,5,7,2,1,3,6]=>{{1,2,4,5},{3,6,7}}
[4,5,7,2,1,6,3]=>{{1,2,4,5},{3,7},{6}}
[4,5,7,2,3,1,6]=>{{1,2,3,4,5,6,7}}
[4,5,7,2,3,6,1]=>{{1,2,3,4,5,7},{6}}
[4,5,7,2,6,1,3]=>{{1,2,4,5,6},{3,7}}
[4,5,7,2,6,3,1]=>{{1,2,3,4,5,6,7}}
[4,5,7,3,1,2,6]=>{{1,2,3,4,5,6,7}}
[4,5,7,3,1,6,2]=>{{1,2,3,4,5,7},{6}}
[4,5,7,3,2,1,6]=>{{1,3,4,6,7},{2,5}}
[4,5,7,3,2,6,1]=>{{1,3,4,7},{2,5},{6}}
[4,5,7,3,6,1,2]=>{{1,2,3,4,5,6,7}}
[4,5,7,3,6,2,1]=>{{1,3,4,7},{2,5,6}}
[4,5,7,6,1,2,3]=>{{1,2,4,5,6},{3,7}}
[4,5,7,6,1,3,2]=>{{1,2,3,4,5,6,7}}
[4,5,7,6,2,1,3]=>{{1,4,6},{2,5},{3,7}}
[4,5,7,6,2,3,1]=>{{1,3,4,6,7},{2,5}}
[4,5,7,6,3,1,2]=>{{1,4,6},{2,3,5,7}}
[4,5,7,6,3,2,1]=>{{1,2,3,4,5,6,7}}
[4,6,1,2,3,5,7]=>{{1,2,3,4,5,6},{7}}
[4,6,1,2,3,7,5]=>{{1,2,3,4,5,6,7}}
[4,6,1,2,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[4,6,1,2,5,7,3]=>{{1,2,3,4,6,7},{5}}
[4,6,1,2,7,3,5]=>{{1,2,3,4,6},{5,7}}
[4,6,1,2,7,5,3]=>{{1,2,3,4,5,6,7}}
[4,6,1,3,2,5,7]=>{{1,3,4},{2,5,6},{7}}
[4,6,1,3,2,7,5]=>{{1,3,4},{2,5,6,7}}
[4,6,1,3,5,2,7]=>{{1,3,4},{2,6},{5},{7}}
[4,6,1,3,5,7,2]=>{{1,3,4},{2,6,7},{5}}
[4,6,1,3,7,2,5]=>{{1,3,4},{2,6},{5,7}}
[4,6,1,3,7,5,2]=>{{1,3,4},{2,5,6,7}}
[4,6,1,5,2,3,7]=>{{1,2,3,4,5,6},{7}}
[4,6,1,5,2,7,3]=>{{1,2,3,4,5,6,7}}
[4,6,1,5,3,2,7]=>{{1,3,4,5},{2,6},{7}}
[4,6,1,5,3,7,2]=>{{1,3,4,5},{2,6,7}}
[4,6,1,5,7,2,3]=>{{1,3,4,5,7},{2,6}}
[4,6,1,5,7,3,2]=>{{1,2,3,4,5,6,7}}
[4,6,1,7,2,3,5]=>{{1,2,3,4,5,6,7}}
[4,6,1,7,2,5,3]=>{{1,3,4,7},{2,5,6}}
[4,6,1,7,3,2,5]=>{{1,3,4,5,7},{2,6}}
[4,6,1,7,3,5,2]=>{{1,2,3,4,5,6,7}}
[4,6,1,7,5,2,3]=>{{1,3,4,7},{2,6},{5}}
[4,6,1,7,5,3,2]=>{{1,2,3,4,6,7},{5}}
[4,6,2,1,3,5,7]=>{{1,4},{2,3,5,6},{7}}
[4,6,2,1,3,7,5]=>{{1,4},{2,3,5,6,7}}
[4,6,2,1,5,3,7]=>{{1,4},{2,3,6},{5},{7}}
[4,6,2,1,5,7,3]=>{{1,4},{2,3,6,7},{5}}
[4,6,2,1,7,3,5]=>{{1,4},{2,3,6},{5,7}}
[4,6,2,1,7,5,3]=>{{1,4},{2,3,5,6,7}}
[4,6,2,3,1,5,7]=>{{1,2,3,4,5,6},{7}}
[4,6,2,3,1,7,5]=>{{1,2,3,4,5,6,7}}
[4,6,2,3,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[4,6,2,3,5,7,1]=>{{1,2,3,4,6,7},{5}}
[4,6,2,3,7,1,5]=>{{1,2,3,4,6},{5,7}}
[4,6,2,3,7,5,1]=>{{1,2,3,4,5,6,7}}
[4,6,2,5,1,3,7]=>{{1,4,5},{2,3,6},{7}}
[4,6,2,5,1,7,3]=>{{1,4,5},{2,3,6,7}}
[4,6,2,5,3,1,7]=>{{1,2,3,4,5,6},{7}}
[4,6,2,5,3,7,1]=>{{1,2,3,4,5,6,7}}
[4,6,2,5,7,1,3]=>{{1,2,3,4,5,6,7}}
[4,6,2,5,7,3,1]=>{{1,4,5,7},{2,3,6}}
[4,6,2,7,1,3,5]=>{{1,4,5,7},{2,3,6}}
[4,6,2,7,1,5,3]=>{{1,2,3,4,5,6,7}}
[4,6,2,7,3,1,5]=>{{1,2,3,4,5,6,7}}
[4,6,2,7,3,5,1]=>{{1,4,7},{2,3,5,6}}
[4,6,2,7,5,1,3]=>{{1,2,3,4,6,7},{5}}
[4,6,2,7,5,3,1]=>{{1,4,7},{2,3,6},{5}}
[4,6,3,1,2,5,7]=>{{1,4},{2,5,6},{3},{7}}
[4,6,3,1,2,7,5]=>{{1,4},{2,5,6,7},{3}}
[4,6,3,1,5,2,7]=>{{1,4},{2,6},{3},{5},{7}}
[4,6,3,1,5,7,2]=>{{1,4},{2,6,7},{3},{5}}
[4,6,3,1,7,2,5]=>{{1,4},{2,6},{3},{5,7}}
[4,6,3,1,7,5,2]=>{{1,4},{2,5,6,7},{3}}
[4,6,3,2,1,5,7]=>{{1,2,4,5,6},{3},{7}}
[4,6,3,2,1,7,5]=>{{1,2,4,5,6,7},{3}}
[4,6,3,2,5,1,7]=>{{1,2,4,6},{3},{5},{7}}
[4,6,3,2,5,7,1]=>{{1,2,4,6,7},{3},{5}}
[4,6,3,2,7,1,5]=>{{1,2,4,6},{3},{5,7}}
[4,6,3,2,7,5,1]=>{{1,2,4,5,6,7},{3}}
[4,6,3,5,1,2,7]=>{{1,4,5},{2,6},{3},{7}}
[4,6,3,5,1,7,2]=>{{1,4,5},{2,6,7},{3}}
[4,6,3,5,2,1,7]=>{{1,2,4,5,6},{3},{7}}
[4,6,3,5,2,7,1]=>{{1,2,4,5,6,7},{3}}
[4,6,3,5,7,1,2]=>{{1,2,4,5,6,7},{3}}
[4,6,3,5,7,2,1]=>{{1,4,5,7},{2,6},{3}}
[4,6,3,7,1,2,5]=>{{1,4,5,7},{2,6},{3}}
[4,6,3,7,1,5,2]=>{{1,2,4,5,6,7},{3}}
[4,6,3,7,2,1,5]=>{{1,2,4,5,6,7},{3}}
[4,6,3,7,2,5,1]=>{{1,4,7},{2,5,6},{3}}
[4,6,3,7,5,1,2]=>{{1,2,4,6,7},{3},{5}}
[4,6,3,7,5,2,1]=>{{1,4,7},{2,6},{3},{5}}
[4,6,5,1,2,3,7]=>{{1,4},{2,3,5,6},{7}}
[4,6,5,1,2,7,3]=>{{1,4},{2,3,5,6,7}}
[4,6,5,1,3,2,7]=>{{1,4},{2,6},{3,5},{7}}
[4,6,5,1,3,7,2]=>{{1,4},{2,6,7},{3,5}}
[4,6,5,1,7,2,3]=>{{1,4},{2,6},{3,5,7}}
[4,6,5,1,7,3,2]=>{{1,4},{2,3,5,6,7}}
[4,6,5,2,1,3,7]=>{{1,2,3,4,5,6},{7}}
[4,6,5,2,1,7,3]=>{{1,2,3,4,5,6,7}}
[4,6,5,2,3,1,7]=>{{1,2,4,6},{3,5},{7}}
[4,6,5,2,3,7,1]=>{{1,2,4,6,7},{3,5}}
[4,6,5,2,7,1,3]=>{{1,2,4,6},{3,5,7}}
[4,6,5,2,7,3,1]=>{{1,2,3,4,5,6,7}}
[4,6,5,3,1,2,7]=>{{1,3,4,5},{2,6},{7}}
[4,6,5,3,1,7,2]=>{{1,3,4,5},{2,6,7}}
[4,6,5,3,2,1,7]=>{{1,2,3,4,5,6},{7}}
[4,6,5,3,2,7,1]=>{{1,2,3,4,5,6,7}}
[4,6,5,3,7,1,2]=>{{1,2,3,4,5,6,7}}
[4,6,5,3,7,2,1]=>{{1,3,4,5,7},{2,6}}
[4,6,5,7,1,2,3]=>{{1,3,4,5,7},{2,6}}
[4,6,5,7,1,3,2]=>{{1,2,3,4,5,6,7}}
[4,6,5,7,2,1,3]=>{{1,2,3,4,5,6,7}}
[4,6,5,7,2,3,1]=>{{1,4,7},{2,3,5,6}}
[4,6,5,7,3,1,2]=>{{1,2,4,6,7},{3,5}}
[4,6,5,7,3,2,1]=>{{1,4,7},{2,6},{3,5}}
[4,6,7,1,2,3,5]=>{{1,4},{2,3,5,6,7}}
[4,6,7,1,2,5,3]=>{{1,4},{2,5,6},{3,7}}
[4,6,7,1,3,2,5]=>{{1,4},{2,6},{3,5,7}}
[4,6,7,1,3,5,2]=>{{1,4},{2,3,5,6,7}}
[4,6,7,1,5,2,3]=>{{1,4},{2,6},{3,7},{5}}
[4,6,7,1,5,3,2]=>{{1,4},{2,3,6,7},{5}}
[4,6,7,2,1,3,5]=>{{1,2,3,4,5,6,7}}
[4,6,7,2,1,5,3]=>{{1,2,4,5,6},{3,7}}
[4,6,7,2,3,1,5]=>{{1,2,4,6},{3,5,7}}
[4,6,7,2,3,5,1]=>{{1,2,3,4,5,6,7}}
[4,6,7,2,5,1,3]=>{{1,2,4,6},{3,7},{5}}
[4,6,7,2,5,3,1]=>{{1,2,3,4,6,7},{5}}
[4,6,7,3,1,2,5]=>{{1,3,4,5,7},{2,6}}
[4,6,7,3,1,5,2]=>{{1,2,3,4,5,6,7}}
[4,6,7,3,2,1,5]=>{{1,2,3,4,5,6,7}}
[4,6,7,3,2,5,1]=>{{1,3,4,7},{2,5,6}}
[4,6,7,3,5,1,2]=>{{1,2,3,4,6,7},{5}}
[4,6,7,3,5,2,1]=>{{1,3,4,7},{2,6},{5}}
[4,6,7,5,1,2,3]=>{{1,4,5},{2,6},{3,7}}
[4,6,7,5,1,3,2]=>{{1,4,5},{2,3,6,7}}
[4,6,7,5,2,1,3]=>{{1,2,4,5,6},{3,7}}
[4,6,7,5,2,3,1]=>{{1,2,3,4,5,6,7}}
[4,6,7,5,3,1,2]=>{{1,2,3,4,5,6,7}}
[4,6,7,5,3,2,1]=>{{1,3,4,5,7},{2,6}}
[4,7,1,2,3,5,6]=>{{1,2,3,4,5,6,7}}
[4,7,1,2,3,6,5]=>{{1,2,3,4,5,7},{6}}
[4,7,1,2,5,3,6]=>{{1,2,3,4,6,7},{5}}
[4,7,1,2,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[4,7,1,2,6,3,5]=>{{1,2,3,4,5,6,7}}
[4,7,1,2,6,5,3]=>{{1,2,3,4,7},{5,6}}
[4,7,1,3,2,5,6]=>{{1,3,4},{2,5,6,7}}
[4,7,1,3,2,6,5]=>{{1,3,4},{2,5,7},{6}}
[4,7,1,3,5,2,6]=>{{1,3,4},{2,6,7},{5}}
[4,7,1,3,5,6,2]=>{{1,3,4},{2,7},{5},{6}}
[4,7,1,3,6,2,5]=>{{1,3,4},{2,5,6,7}}
[4,7,1,3,6,5,2]=>{{1,3,4},{2,7},{5,6}}
[4,7,1,5,2,3,6]=>{{1,2,3,4,5,6,7}}
[4,7,1,5,2,6,3]=>{{1,2,3,4,5,7},{6}}
[4,7,1,5,3,2,6]=>{{1,3,4,5},{2,6,7}}
[4,7,1,5,3,6,2]=>{{1,3,4,5},{2,7},{6}}
[4,7,1,5,6,2,3]=>{{1,2,3,4,5,6,7}}
[4,7,1,5,6,3,2]=>{{1,3,4,5,6},{2,7}}
[4,7,1,6,2,3,5]=>{{1,3,4,6},{2,5,7}}
[4,7,1,6,2,5,3]=>{{1,2,3,4,5,6,7}}
[4,7,1,6,3,2,5]=>{{1,2,3,4,5,6,7}}
[4,7,1,6,3,5,2]=>{{1,3,4,5,6},{2,7}}
[4,7,1,6,5,2,3]=>{{1,2,3,4,6,7},{5}}
[4,7,1,6,5,3,2]=>{{1,3,4,6},{2,7},{5}}
[4,7,2,1,3,5,6]=>{{1,4},{2,3,5,6,7}}
[4,7,2,1,3,6,5]=>{{1,4},{2,3,5,7},{6}}
[4,7,2,1,5,3,6]=>{{1,4},{2,3,6,7},{5}}
[4,7,2,1,5,6,3]=>{{1,4},{2,3,7},{5},{6}}
[4,7,2,1,6,3,5]=>{{1,4},{2,3,5,6,7}}
[4,7,2,1,6,5,3]=>{{1,4},{2,3,7},{5,6}}
[4,7,2,3,1,5,6]=>{{1,2,3,4,5,6,7}}
[4,7,2,3,1,6,5]=>{{1,2,3,4,5,7},{6}}
[4,7,2,3,5,1,6]=>{{1,2,3,4,6,7},{5}}
[4,7,2,3,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[4,7,2,3,6,1,5]=>{{1,2,3,4,5,6,7}}
[4,7,2,3,6,5,1]=>{{1,2,3,4,7},{5,6}}
[4,7,2,5,1,3,6]=>{{1,4,5},{2,3,6,7}}
[4,7,2,5,1,6,3]=>{{1,4,5},{2,3,7},{6}}
[4,7,2,5,3,1,6]=>{{1,2,3,4,5,6,7}}
[4,7,2,5,3,6,1]=>{{1,2,3,4,5,7},{6}}
[4,7,2,5,6,1,3]=>{{1,4,5,6},{2,3,7}}
[4,7,2,5,6,3,1]=>{{1,2,3,4,5,6,7}}
[4,7,2,6,1,3,5]=>{{1,2,3,4,5,6,7}}
[4,7,2,6,1,5,3]=>{{1,4,5,6},{2,3,7}}
[4,7,2,6,3,1,5]=>{{1,4,6},{2,3,5,7}}
[4,7,2,6,3,5,1]=>{{1,2,3,4,5,6,7}}
[4,7,2,6,5,1,3]=>{{1,4,6},{2,3,7},{5}}
[4,7,2,6,5,3,1]=>{{1,2,3,4,6,7},{5}}
[4,7,3,1,2,5,6]=>{{1,4},{2,5,6,7},{3}}
[4,7,3,1,2,6,5]=>{{1,4},{2,5,7},{3},{6}}
[4,7,3,1,5,2,6]=>{{1,4},{2,6,7},{3},{5}}
[4,7,3,1,5,6,2]=>{{1,4},{2,7},{3},{5},{6}}
[4,7,3,1,6,2,5]=>{{1,4},{2,5,6,7},{3}}
[4,7,3,1,6,5,2]=>{{1,4},{2,7},{3},{5,6}}
[4,7,3,2,1,5,6]=>{{1,2,4,5,6,7},{3}}
[4,7,3,2,1,6,5]=>{{1,2,4,5,7},{3},{6}}
[4,7,3,2,5,1,6]=>{{1,2,4,6,7},{3},{5}}
[4,7,3,2,5,6,1]=>{{1,2,4,7},{3},{5},{6}}
[4,7,3,2,6,1,5]=>{{1,2,4,5,6,7},{3}}
[4,7,3,2,6,5,1]=>{{1,2,4,7},{3},{5,6}}
[4,7,3,5,1,2,6]=>{{1,4,5},{2,6,7},{3}}
[4,7,3,5,1,6,2]=>{{1,4,5},{2,7},{3},{6}}
[4,7,3,5,2,1,6]=>{{1,2,4,5,6,7},{3}}
[4,7,3,5,2,6,1]=>{{1,2,4,5,7},{3},{6}}
[4,7,3,5,6,1,2]=>{{1,4,5,6},{2,7},{3}}
[4,7,3,5,6,2,1]=>{{1,2,4,5,6,7},{3}}
[4,7,3,6,1,2,5]=>{{1,2,4,5,6,7},{3}}
[4,7,3,6,1,5,2]=>{{1,4,5,6},{2,7},{3}}
[4,7,3,6,2,1,5]=>{{1,4,6},{2,5,7},{3}}
[4,7,3,6,2,5,1]=>{{1,2,4,5,6,7},{3}}
[4,7,3,6,5,1,2]=>{{1,4,6},{2,7},{3},{5}}
[4,7,3,6,5,2,1]=>{{1,2,4,6,7},{3},{5}}
[4,7,5,1,2,3,6]=>{{1,4},{2,3,5,6,7}}
[4,7,5,1,2,6,3]=>{{1,4},{2,3,5,7},{6}}
[4,7,5,1,3,2,6]=>{{1,4},{2,6,7},{3,5}}
[4,7,5,1,3,6,2]=>{{1,4},{2,7},{3,5},{6}}
[4,7,5,1,6,2,3]=>{{1,4},{2,3,5,6,7}}
[4,7,5,1,6,3,2]=>{{1,4},{2,7},{3,5,6}}
[4,7,5,2,1,3,6]=>{{1,2,3,4,5,6,7}}
[4,7,5,2,1,6,3]=>{{1,2,3,4,5,7},{6}}
[4,7,5,2,3,1,6]=>{{1,2,4,6,7},{3,5}}
[4,7,5,2,3,6,1]=>{{1,2,4,7},{3,5},{6}}
[4,7,5,2,6,1,3]=>{{1,2,3,4,5,6,7}}
[4,7,5,2,6,3,1]=>{{1,2,4,7},{3,5,6}}
[4,7,5,3,1,2,6]=>{{1,3,4,5},{2,6,7}}
[4,7,5,3,1,6,2]=>{{1,3,4,5},{2,7},{6}}
[4,7,5,3,2,1,6]=>{{1,2,3,4,5,6,7}}
[4,7,5,3,2,6,1]=>{{1,2,3,4,5,7},{6}}
[4,7,5,3,6,1,2]=>{{1,3,4,5,6},{2,7}}
[4,7,5,3,6,2,1]=>{{1,2,3,4,5,6,7}}
[4,7,5,6,1,2,3]=>{{1,2,3,4,5,6,7}}
[4,7,5,6,1,3,2]=>{{1,3,4,5,6},{2,7}}
[4,7,5,6,2,1,3]=>{{1,4,6},{2,3,5,7}}
[4,7,5,6,2,3,1]=>{{1,2,3,4,5,6,7}}
[4,7,5,6,3,1,2]=>{{1,4,6},{2,7},{3,5}}
[4,7,5,6,3,2,1]=>{{1,2,4,6,7},{3,5}}
[4,7,6,1,2,3,5]=>{{1,4},{2,5,7},{3,6}}
[4,7,6,1,2,5,3]=>{{1,4},{2,3,5,6,7}}
[4,7,6,1,3,2,5]=>{{1,4},{2,3,5,6,7}}
[4,7,6,1,3,5,2]=>{{1,4},{2,7},{3,5,6}}
[4,7,6,1,5,2,3]=>{{1,4},{2,3,6,7},{5}}
[4,7,6,1,5,3,2]=>{{1,4},{2,7},{3,6},{5}}
[4,7,6,2,1,3,5]=>{{1,2,4,5,7},{3,6}}
[4,7,6,2,1,5,3]=>{{1,2,3,4,5,6,7}}
[4,7,6,2,3,1,5]=>{{1,2,3,4,5,6,7}}
[4,7,6,2,3,5,1]=>{{1,2,4,7},{3,5,6}}
[4,7,6,2,5,1,3]=>{{1,2,3,4,6,7},{5}}
[4,7,6,2,5,3,1]=>{{1,2,4,7},{3,6},{5}}
[4,7,6,3,1,2,5]=>{{1,2,3,4,5,6,7}}
[4,7,6,3,1,5,2]=>{{1,3,4,5,6},{2,7}}
[4,7,6,3,2,1,5]=>{{1,3,4,6},{2,5,7}}
[4,7,6,3,2,5,1]=>{{1,2,3,4,5,6,7}}
[4,7,6,3,5,1,2]=>{{1,3,4,6},{2,7},{5}}
[4,7,6,3,5,2,1]=>{{1,2,3,4,6,7},{5}}
[4,7,6,5,1,2,3]=>{{1,4,5},{2,3,6,7}}
[4,7,6,5,1,3,2]=>{{1,4,5},{2,7},{3,6}}
[4,7,6,5,2,1,3]=>{{1,2,3,4,5,6,7}}
[4,7,6,5,2,3,1]=>{{1,2,4,5,7},{3,6}}
[4,7,6,5,3,1,2]=>{{1,3,4,5,6},{2,7}}
[4,7,6,5,3,2,1]=>{{1,2,3,4,5,6,7}}
[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[5,1,2,3,4,7,6]=>{{1,2,3,4,5},{6,7}}
[5,1,2,3,6,4,7]=>{{1,2,3,4,5,6},{7}}
[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}}
[5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[5,1,2,3,7,6,4]=>{{1,2,3,4,5,7},{6}}
[5,1,2,4,3,6,7]=>{{1,2,3,5},{4},{6},{7}}
[5,1,2,4,3,7,6]=>{{1,2,3,5},{4},{6,7}}
[5,1,2,4,6,3,7]=>{{1,2,3,5,6},{4},{7}}
[5,1,2,4,6,7,3]=>{{1,2,3,5,6,7},{4}}
[5,1,2,4,7,3,6]=>{{1,2,3,5,6,7},{4}}
[5,1,2,4,7,6,3]=>{{1,2,3,5,7},{4},{6}}
[5,1,2,6,3,4,7]=>{{1,2,3,5},{4,6},{7}}
[5,1,2,6,3,7,4]=>{{1,2,3,5},{4,6,7}}
[5,1,2,6,4,3,7]=>{{1,2,3,4,5,6},{7}}
[5,1,2,6,4,7,3]=>{{1,2,3,4,5,6,7}}
[5,1,2,6,7,3,4]=>{{1,2,3,4,5,6,7}}
[5,1,2,6,7,4,3]=>{{1,2,3,5,7},{4,6}}
[5,1,2,7,3,4,6]=>{{1,2,3,5},{4,6,7}}
[5,1,2,7,3,6,4]=>{{1,2,3,5},{4,7},{6}}
[5,1,2,7,4,3,6]=>{{1,2,3,4,5,6,7}}
[5,1,2,7,4,6,3]=>{{1,2,3,4,5,7},{6}}
[5,1,2,7,6,3,4]=>{{1,2,3,5,6},{4,7}}
[5,1,2,7,6,4,3]=>{{1,2,3,4,5,6,7}}
[5,1,3,2,4,6,7]=>{{1,2,4,5},{3},{6},{7}}
[5,1,3,2,4,7,6]=>{{1,2,4,5},{3},{6,7}}
[5,1,3,2,6,4,7]=>{{1,2,4,5,6},{3},{7}}
[5,1,3,2,6,7,4]=>{{1,2,4,5,6,7},{3}}
[5,1,3,2,7,4,6]=>{{1,2,4,5,6,7},{3}}
[5,1,3,2,7,6,4]=>{{1,2,4,5,7},{3},{6}}
[5,1,3,4,2,6,7]=>{{1,2,5},{3},{4},{6},{7}}
[5,1,3,4,2,7,6]=>{{1,2,5},{3},{4},{6,7}}
[5,1,3,4,6,2,7]=>{{1,2,5,6},{3},{4},{7}}
[5,1,3,4,6,7,2]=>{{1,2,5,6,7},{3},{4}}
[5,1,3,4,7,2,6]=>{{1,2,5,6,7},{3},{4}}
[5,1,3,4,7,6,2]=>{{1,2,5,7},{3},{4},{6}}
[5,1,3,6,2,4,7]=>{{1,2,5},{3},{4,6},{7}}
[5,1,3,6,2,7,4]=>{{1,2,5},{3},{4,6,7}}
[5,1,3,6,4,2,7]=>{{1,2,4,5,6},{3},{7}}
[5,1,3,6,4,7,2]=>{{1,2,4,5,6,7},{3}}
[5,1,3,6,7,2,4]=>{{1,2,4,5,6,7},{3}}
[5,1,3,6,7,4,2]=>{{1,2,5,7},{3},{4,6}}
[5,1,3,7,2,4,6]=>{{1,2,5},{3},{4,6,7}}
[5,1,3,7,2,6,4]=>{{1,2,5},{3},{4,7},{6}}
[5,1,3,7,4,2,6]=>{{1,2,4,5,6,7},{3}}
[5,1,3,7,4,6,2]=>{{1,2,4,5,7},{3},{6}}
[5,1,3,7,6,2,4]=>{{1,2,5,6},{3},{4,7}}
[5,1,3,7,6,4,2]=>{{1,2,4,5,6,7},{3}}
[5,1,4,2,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[5,1,4,2,3,7,6]=>{{1,2,3,4,5},{6,7}}
[5,1,4,2,6,3,7]=>{{1,2,3,4,5,6},{7}}
[5,1,4,2,6,7,3]=>{{1,2,3,4,5,6,7}}
[5,1,4,2,7,3,6]=>{{1,2,3,4,5,6,7}}
[5,1,4,2,7,6,3]=>{{1,2,3,4,5,7},{6}}
[5,1,4,3,2,6,7]=>{{1,2,5},{3,4},{6},{7}}
[5,1,4,3,2,7,6]=>{{1,2,5},{3,4},{6,7}}
[5,1,4,3,6,2,7]=>{{1,2,5,6},{3,4},{7}}
[5,1,4,3,6,7,2]=>{{1,2,5,6,7},{3,4}}
[5,1,4,3,7,2,6]=>{{1,2,5,6,7},{3,4}}
[5,1,4,3,7,6,2]=>{{1,2,5,7},{3,4},{6}}
[5,1,4,6,2,3,7]=>{{1,2,5},{3,4,6},{7}}
[5,1,4,6,2,7,3]=>{{1,2,5},{3,4,6,7}}
[5,1,4,6,3,2,7]=>{{1,2,3,4,5,6},{7}}
[5,1,4,6,3,7,2]=>{{1,2,3,4,5,6,7}}
[5,1,4,6,7,2,3]=>{{1,2,3,4,5,6,7}}
[5,1,4,6,7,3,2]=>{{1,2,5,7},{3,4,6}}
[5,1,4,7,2,3,6]=>{{1,2,5},{3,4,6,7}}
[5,1,4,7,2,6,3]=>{{1,2,5},{3,4,7},{6}}
[5,1,4,7,3,2,6]=>{{1,2,3,4,5,6,7}}
[5,1,4,7,3,6,2]=>{{1,2,3,4,5,7},{6}}
[5,1,4,7,6,2,3]=>{{1,2,5,6},{3,4,7}}
[5,1,4,7,6,3,2]=>{{1,2,3,4,5,6,7}}
[5,1,6,2,3,4,7]=>{{1,2,3,4,5,6},{7}}
[5,1,6,2,3,7,4]=>{{1,2,3,4,5,6,7}}
[5,1,6,2,4,3,7]=>{{1,2,4,5},{3,6},{7}}
[5,1,6,2,4,7,3]=>{{1,2,4,5},{3,6,7}}
[5,1,6,2,7,3,4]=>{{1,2,4,5,7},{3,6}}
[5,1,6,2,7,4,3]=>{{1,2,3,4,5,6,7}}
[5,1,6,3,2,4,7]=>{{1,2,5},{3,4,6},{7}}
[5,1,6,3,2,7,4]=>{{1,2,5},{3,4,6,7}}
[5,1,6,3,4,2,7]=>{{1,2,3,4,5,6},{7}}
[5,1,6,3,4,7,2]=>{{1,2,3,4,5,6,7}}
[5,1,6,3,7,2,4]=>{{1,2,3,4,5,6,7}}
[5,1,6,3,7,4,2]=>{{1,2,5,7},{3,4,6}}
[5,1,6,4,2,3,7]=>{{1,2,5},{3,6},{4},{7}}
[5,1,6,4,2,7,3]=>{{1,2,5},{3,6,7},{4}}
[5,1,6,4,3,2,7]=>{{1,2,3,5,6},{4},{7}}
[5,1,6,4,3,7,2]=>{{1,2,3,5,6,7},{4}}
[5,1,6,4,7,2,3]=>{{1,2,3,5,6,7},{4}}
[5,1,6,4,7,3,2]=>{{1,2,5,7},{3,6},{4}}
[5,1,6,7,2,3,4]=>{{1,2,5},{3,6},{4,7}}
[5,1,6,7,2,4,3]=>{{1,2,5},{3,4,6,7}}
[5,1,6,7,3,2,4]=>{{1,2,3,5,6},{4,7}}
[5,1,6,7,3,4,2]=>{{1,2,3,4,5,6,7}}
[5,1,6,7,4,2,3]=>{{1,2,3,4,5,6,7}}
[5,1,6,7,4,3,2]=>{{1,2,4,5,7},{3,6}}
[5,1,7,2,3,4,6]=>{{1,2,3,4,5,6,7}}
[5,1,7,2,3,6,4]=>{{1,2,3,4,5,7},{6}}
[5,1,7,2,4,3,6]=>{{1,2,4,5},{3,6,7}}
[5,1,7,2,4,6,3]=>{{1,2,4,5},{3,7},{6}}
[5,1,7,2,6,3,4]=>{{1,2,3,4,5,6,7}}
[5,1,7,2,6,4,3]=>{{1,2,4,5,6},{3,7}}
[5,1,7,3,2,4,6]=>{{1,2,5},{3,4,6,7}}
[5,1,7,3,2,6,4]=>{{1,2,5},{3,4,7},{6}}
[5,1,7,3,4,2,6]=>{{1,2,3,4,5,6,7}}
[5,1,7,3,4,6,2]=>{{1,2,3,4,5,7},{6}}
[5,1,7,3,6,2,4]=>{{1,2,5,6},{3,4,7}}
[5,1,7,3,6,4,2]=>{{1,2,3,4,5,6,7}}
[5,1,7,4,2,3,6]=>{{1,2,5},{3,6,7},{4}}
[5,1,7,4,2,6,3]=>{{1,2,5},{3,7},{4},{6}}
[5,1,7,4,3,2,6]=>{{1,2,3,5,6,7},{4}}
[5,1,7,4,3,6,2]=>{{1,2,3,5,7},{4},{6}}
[5,1,7,4,6,2,3]=>{{1,2,5,6},{3,7},{4}}
[5,1,7,4,6,3,2]=>{{1,2,3,5,6,7},{4}}
[5,1,7,6,2,3,4]=>{{1,2,5},{3,4,6,7}}
[5,1,7,6,2,4,3]=>{{1,2,5},{3,7},{4,6}}
[5,1,7,6,3,2,4]=>{{1,2,3,4,5,6,7}}
[5,1,7,6,3,4,2]=>{{1,2,3,5,7},{4,6}}
[5,1,7,6,4,2,3]=>{{1,2,4,5,6},{3,7}}
[5,1,7,6,4,3,2]=>{{1,2,3,4,5,6,7}}
[5,2,1,3,4,6,7]=>{{1,3,4,5},{2},{6},{7}}
[5,2,1,3,4,7,6]=>{{1,3,4,5},{2},{6,7}}
[5,2,1,3,6,4,7]=>{{1,3,4,5,6},{2},{7}}
[5,2,1,3,6,7,4]=>{{1,3,4,5,6,7},{2}}
[5,2,1,3,7,4,6]=>{{1,3,4,5,6,7},{2}}
[5,2,1,3,7,6,4]=>{{1,3,4,5,7},{2},{6}}
[5,2,1,4,3,6,7]=>{{1,3,5},{2},{4},{6},{7}}
[5,2,1,4,3,7,6]=>{{1,3,5},{2},{4},{6,7}}
[5,2,1,4,6,3,7]=>{{1,3,5,6},{2},{4},{7}}
[5,2,1,4,6,7,3]=>{{1,3,5,6,7},{2},{4}}
[5,2,1,4,7,3,6]=>{{1,3,5,6,7},{2},{4}}
[5,2,1,4,7,6,3]=>{{1,3,5,7},{2},{4},{6}}
[5,2,1,6,3,4,7]=>{{1,3,5},{2},{4,6},{7}}
[5,2,1,6,3,7,4]=>{{1,3,5},{2},{4,6,7}}
[5,2,1,6,4,3,7]=>{{1,3,4,5,6},{2},{7}}
[5,2,1,6,4,7,3]=>{{1,3,4,5,6,7},{2}}
[5,2,1,6,7,3,4]=>{{1,3,4,5,6,7},{2}}
[5,2,1,6,7,4,3]=>{{1,3,5,7},{2},{4,6}}
[5,2,1,7,3,4,6]=>{{1,3,5},{2},{4,6,7}}
[5,2,1,7,3,6,4]=>{{1,3,5},{2},{4,7},{6}}
[5,2,1,7,4,3,6]=>{{1,3,4,5,6,7},{2}}
[5,2,1,7,4,6,3]=>{{1,3,4,5,7},{2},{6}}
[5,2,1,7,6,3,4]=>{{1,3,5,6},{2},{4,7}}
[5,2,1,7,6,4,3]=>{{1,3,4,5,6,7},{2}}
[5,2,3,1,4,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[5,2,3,1,4,7,6]=>{{1,4,5},{2},{3},{6,7}}
[5,2,3,1,6,4,7]=>{{1,4,5,6},{2},{3},{7}}
[5,2,3,1,6,7,4]=>{{1,4,5,6,7},{2},{3}}
[5,2,3,1,7,4,6]=>{{1,4,5,6,7},{2},{3}}
[5,2,3,1,7,6,4]=>{{1,4,5,7},{2},{3},{6}}
[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[5,2,3,4,1,7,6]=>{{1,5},{2},{3},{4},{6,7}}
[5,2,3,4,6,1,7]=>{{1,5,6},{2},{3},{4},{7}}
[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}}
[5,2,3,4,7,1,6]=>{{1,5,6,7},{2},{3},{4}}
[5,2,3,4,7,6,1]=>{{1,5,7},{2},{3},{4},{6}}
[5,2,3,6,1,4,7]=>{{1,5},{2},{3},{4,6},{7}}
[5,2,3,6,1,7,4]=>{{1,5},{2},{3},{4,6,7}}
[5,2,3,6,4,1,7]=>{{1,4,5,6},{2},{3},{7}}
[5,2,3,6,4,7,1]=>{{1,4,5,6,7},{2},{3}}
[5,2,3,6,7,1,4]=>{{1,4,5,6,7},{2},{3}}
[5,2,3,6,7,4,1]=>{{1,5,7},{2},{3},{4,6}}
[5,2,3,7,1,4,6]=>{{1,5},{2},{3},{4,6,7}}
[5,2,3,7,1,6,4]=>{{1,5},{2},{3},{4,7},{6}}
[5,2,3,7,4,1,6]=>{{1,4,5,6,7},{2},{3}}
[5,2,3,7,4,6,1]=>{{1,4,5,7},{2},{3},{6}}
[5,2,3,7,6,1,4]=>{{1,5,6},{2},{3},{4,7}}
[5,2,3,7,6,4,1]=>{{1,4,5,6,7},{2},{3}}
[5,2,4,1,3,6,7]=>{{1,3,4,5},{2},{6},{7}}
[5,2,4,1,3,7,6]=>{{1,3,4,5},{2},{6,7}}
[5,2,4,1,6,3,7]=>{{1,3,4,5,6},{2},{7}}
[5,2,4,1,6,7,3]=>{{1,3,4,5,6,7},{2}}
[5,2,4,1,7,3,6]=>{{1,3,4,5,6,7},{2}}
[5,2,4,1,7,6,3]=>{{1,3,4,5,7},{2},{6}}
[5,2,4,3,1,6,7]=>{{1,5},{2},{3,4},{6},{7}}
[5,2,4,3,1,7,6]=>{{1,5},{2},{3,4},{6,7}}
[5,2,4,3,6,1,7]=>{{1,5,6},{2},{3,4},{7}}
[5,2,4,3,6,7,1]=>{{1,5,6,7},{2},{3,4}}
[5,2,4,3,7,1,6]=>{{1,5,6,7},{2},{3,4}}
[5,2,4,3,7,6,1]=>{{1,5,7},{2},{3,4},{6}}
[5,2,4,6,1,3,7]=>{{1,5},{2},{3,4,6},{7}}
[5,2,4,6,1,7,3]=>{{1,5},{2},{3,4,6,7}}
[5,2,4,6,3,1,7]=>{{1,3,4,5,6},{2},{7}}
[5,2,4,6,3,7,1]=>{{1,3,4,5,6,7},{2}}
[5,2,4,6,7,1,3]=>{{1,3,4,5,6,7},{2}}
[5,2,4,6,7,3,1]=>{{1,5,7},{2},{3,4,6}}
[5,2,4,7,1,3,6]=>{{1,5},{2},{3,4,6,7}}
[5,2,4,7,1,6,3]=>{{1,5},{2},{3,4,7},{6}}
[5,2,4,7,3,1,6]=>{{1,3,4,5,6,7},{2}}
[5,2,4,7,3,6,1]=>{{1,3,4,5,7},{2},{6}}
[5,2,4,7,6,1,3]=>{{1,5,6},{2},{3,4,7}}
[5,2,4,7,6,3,1]=>{{1,3,4,5,6,7},{2}}
[5,2,6,1,3,4,7]=>{{1,3,4,5,6},{2},{7}}
[5,2,6,1,3,7,4]=>{{1,3,4,5,6,7},{2}}
[5,2,6,1,4,3,7]=>{{1,4,5},{2},{3,6},{7}}
[5,2,6,1,4,7,3]=>{{1,4,5},{2},{3,6,7}}
[5,2,6,1,7,3,4]=>{{1,4,5,7},{2},{3,6}}
[5,2,6,1,7,4,3]=>{{1,3,4,5,6,7},{2}}
[5,2,6,3,1,4,7]=>{{1,5},{2},{3,4,6},{7}}
[5,2,6,3,1,7,4]=>{{1,5},{2},{3,4,6,7}}
[5,2,6,3,4,1,7]=>{{1,3,4,5,6},{2},{7}}
[5,2,6,3,4,7,1]=>{{1,3,4,5,6,7},{2}}
[5,2,6,3,7,1,4]=>{{1,3,4,5,6,7},{2}}
[5,2,6,3,7,4,1]=>{{1,5,7},{2},{3,4,6}}
[5,2,6,4,1,3,7]=>{{1,5},{2},{3,6},{4},{7}}
[5,2,6,4,1,7,3]=>{{1,5},{2},{3,6,7},{4}}
[5,2,6,4,3,1,7]=>{{1,3,5,6},{2},{4},{7}}
[5,2,6,4,3,7,1]=>{{1,3,5,6,7},{2},{4}}
[5,2,6,4,7,1,3]=>{{1,3,5,6,7},{2},{4}}
[5,2,6,4,7,3,1]=>{{1,5,7},{2},{3,6},{4}}
[5,2,6,7,1,3,4]=>{{1,5},{2},{3,6},{4,7}}
[5,2,6,7,1,4,3]=>{{1,5},{2},{3,4,6,7}}
[5,2,6,7,3,1,4]=>{{1,3,5,6},{2},{4,7}}
[5,2,6,7,3,4,1]=>{{1,3,4,5,6,7},{2}}
[5,2,6,7,4,1,3]=>{{1,3,4,5,6,7},{2}}
[5,2,6,7,4,3,1]=>{{1,4,5,7},{2},{3,6}}
[5,2,7,1,3,4,6]=>{{1,3,4,5,6,7},{2}}
[5,2,7,1,3,6,4]=>{{1,3,4,5,7},{2},{6}}
[5,2,7,1,4,3,6]=>{{1,4,5},{2},{3,6,7}}
[5,2,7,1,4,6,3]=>{{1,4,5},{2},{3,7},{6}}
[5,2,7,1,6,3,4]=>{{1,3,4,5,6,7},{2}}
[5,2,7,1,6,4,3]=>{{1,4,5,6},{2},{3,7}}
[5,2,7,3,1,4,6]=>{{1,5},{2},{3,4,6,7}}
[5,2,7,3,1,6,4]=>{{1,5},{2},{3,4,7},{6}}
[5,2,7,3,4,1,6]=>{{1,3,4,5,6,7},{2}}
[5,2,7,3,4,6,1]=>{{1,3,4,5,7},{2},{6}}
[5,2,7,3,6,1,4]=>{{1,5,6},{2},{3,4,7}}
[5,2,7,3,6,4,1]=>{{1,3,4,5,6,7},{2}}
[5,2,7,4,1,3,6]=>{{1,5},{2},{3,6,7},{4}}
[5,2,7,4,1,6,3]=>{{1,5},{2},{3,7},{4},{6}}
[5,2,7,4,3,1,6]=>{{1,3,5,6,7},{2},{4}}
[5,2,7,4,3,6,1]=>{{1,3,5,7},{2},{4},{6}}
[5,2,7,4,6,1,3]=>{{1,5,6},{2},{3,7},{4}}
[5,2,7,4,6,3,1]=>{{1,3,5,6,7},{2},{4}}
[5,2,7,6,1,3,4]=>{{1,5},{2},{3,4,6,7}}
[5,2,7,6,1,4,3]=>{{1,5},{2},{3,7},{4,6}}
[5,2,7,6,3,1,4]=>{{1,3,4,5,6,7},{2}}
[5,2,7,6,3,4,1]=>{{1,3,5,7},{2},{4,6}}
[5,2,7,6,4,1,3]=>{{1,4,5,6},{2},{3,7}}
[5,2,7,6,4,3,1]=>{{1,3,4,5,6,7},{2}}
[5,3,1,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[5,3,1,2,4,7,6]=>{{1,2,3,4,5},{6,7}}
[5,3,1,2,6,4,7]=>{{1,2,3,4,5,6},{7}}
[5,3,1,2,6,7,4]=>{{1,2,3,4,5,6,7}}
[5,3,1,2,7,4,6]=>{{1,2,3,4,5,6,7}}
[5,3,1,2,7,6,4]=>{{1,2,3,4,5,7},{6}}
[5,3,1,4,2,6,7]=>{{1,2,3,5},{4},{6},{7}}
[5,3,1,4,2,7,6]=>{{1,2,3,5},{4},{6,7}}
[5,3,1,4,6,2,7]=>{{1,2,3,5,6},{4},{7}}
[5,3,1,4,6,7,2]=>{{1,2,3,5,6,7},{4}}
[5,3,1,4,7,2,6]=>{{1,2,3,5,6,7},{4}}
[5,3,1,4,7,6,2]=>{{1,2,3,5,7},{4},{6}}
[5,3,1,6,2,4,7]=>{{1,2,3,5},{4,6},{7}}
[5,3,1,6,2,7,4]=>{{1,2,3,5},{4,6,7}}
[5,3,1,6,4,2,7]=>{{1,2,3,4,5,6},{7}}
[5,3,1,6,4,7,2]=>{{1,2,3,4,5,6,7}}
[5,3,1,6,7,2,4]=>{{1,2,3,4,5,6,7}}
[5,3,1,6,7,4,2]=>{{1,2,3,5,7},{4,6}}
[5,3,1,7,2,4,6]=>{{1,2,3,5},{4,6,7}}
[5,3,1,7,2,6,4]=>{{1,2,3,5},{4,7},{6}}
[5,3,1,7,4,2,6]=>{{1,2,3,4,5,6,7}}
[5,3,1,7,4,6,2]=>{{1,2,3,4,5,7},{6}}
[5,3,1,7,6,2,4]=>{{1,2,3,5,6},{4,7}}
[5,3,1,7,6,4,2]=>{{1,2,3,4,5,6,7}}
[5,3,2,1,4,6,7]=>{{1,4,5},{2,3},{6},{7}}
[5,3,2,1,4,7,6]=>{{1,4,5},{2,3},{6,7}}
[5,3,2,1,6,4,7]=>{{1,4,5,6},{2,3},{7}}
[5,3,2,1,6,7,4]=>{{1,4,5,6,7},{2,3}}
[5,3,2,1,7,4,6]=>{{1,4,5,6,7},{2,3}}
[5,3,2,1,7,6,4]=>{{1,4,5,7},{2,3},{6}}
[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}}
[5,3,2,4,1,7,6]=>{{1,5},{2,3},{4},{6,7}}
[5,3,2,4,6,1,7]=>{{1,5,6},{2,3},{4},{7}}
[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}}
[5,3,2,4,7,1,6]=>{{1,5,6,7},{2,3},{4}}
[5,3,2,4,7,6,1]=>{{1,5,7},{2,3},{4},{6}}
[5,3,2,6,1,4,7]=>{{1,5},{2,3},{4,6},{7}}
[5,3,2,6,1,7,4]=>{{1,5},{2,3},{4,6,7}}
[5,3,2,6,4,1,7]=>{{1,4,5,6},{2,3},{7}}
[5,3,2,6,4,7,1]=>{{1,4,5,6,7},{2,3}}
[5,3,2,6,7,1,4]=>{{1,4,5,6,7},{2,3}}
[5,3,2,6,7,4,1]=>{{1,5,7},{2,3},{4,6}}
[5,3,2,7,1,4,6]=>{{1,5},{2,3},{4,6,7}}
[5,3,2,7,1,6,4]=>{{1,5},{2,3},{4,7},{6}}
[5,3,2,7,4,1,6]=>{{1,4,5,6,7},{2,3}}
[5,3,2,7,4,6,1]=>{{1,4,5,7},{2,3},{6}}
[5,3,2,7,6,1,4]=>{{1,5,6},{2,3},{4,7}}
[5,3,2,7,6,4,1]=>{{1,4,5,6,7},{2,3}}
[5,3,4,1,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[5,3,4,1,2,7,6]=>{{1,2,3,4,5},{6,7}}
[5,3,4,1,6,2,7]=>{{1,2,3,4,5,6},{7}}
[5,3,4,1,6,7,2]=>{{1,2,3,4,5,6,7}}
[5,3,4,1,7,2,6]=>{{1,2,3,4,5,6,7}}
[5,3,4,1,7,6,2]=>{{1,2,3,4,5,7},{6}}
[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}}
[5,3,4,2,1,7,6]=>{{1,5},{2,3,4},{6,7}}
[5,3,4,2,6,1,7]=>{{1,5,6},{2,3,4},{7}}
[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}}
[5,3,4,2,7,1,6]=>{{1,5,6,7},{2,3,4}}
[5,3,4,2,7,6,1]=>{{1,5,7},{2,3,4},{6}}
[5,3,4,6,1,2,7]=>{{1,5},{2,3,4,6},{7}}
[5,3,4,6,1,7,2]=>{{1,5},{2,3,4,6,7}}
[5,3,4,6,2,1,7]=>{{1,2,3,4,5,6},{7}}
[5,3,4,6,2,7,1]=>{{1,2,3,4,5,6,7}}
[5,3,4,6,7,1,2]=>{{1,2,3,4,5,6,7}}
[5,3,4,6,7,2,1]=>{{1,5,7},{2,3,4,6}}
[5,3,4,7,1,2,6]=>{{1,5},{2,3,4,6,7}}
[5,3,4,7,1,6,2]=>{{1,5},{2,3,4,7},{6}}
[5,3,4,7,2,1,6]=>{{1,2,3,4,5,6,7}}
[5,3,4,7,2,6,1]=>{{1,2,3,4,5,7},{6}}
[5,3,4,7,6,1,2]=>{{1,5,6},{2,3,4,7}}
[5,3,4,7,6,2,1]=>{{1,2,3,4,5,6,7}}
[5,3,6,1,2,4,7]=>{{1,2,3,4,5,6},{7}}
[5,3,6,1,2,7,4]=>{{1,2,3,4,5,6,7}}
[5,3,6,1,4,2,7]=>{{1,4,5},{2,3,6},{7}}
[5,3,6,1,4,7,2]=>{{1,4,5},{2,3,6,7}}
[5,3,6,1,7,2,4]=>{{1,4,5,7},{2,3,6}}
[5,3,6,1,7,4,2]=>{{1,2,3,4,5,6,7}}
[5,3,6,2,1,4,7]=>{{1,5},{2,3,4,6},{7}}
[5,3,6,2,1,7,4]=>{{1,5},{2,3,4,6,7}}
[5,3,6,2,4,1,7]=>{{1,2,3,4,5,6},{7}}
[5,3,6,2,4,7,1]=>{{1,2,3,4,5,6,7}}
[5,3,6,2,7,1,4]=>{{1,2,3,4,5,6,7}}
[5,3,6,2,7,4,1]=>{{1,5,7},{2,3,4,6}}
[5,3,6,4,1,2,7]=>{{1,5},{2,3,6},{4},{7}}
[5,3,6,4,1,7,2]=>{{1,5},{2,3,6,7},{4}}
[5,3,6,4,2,1,7]=>{{1,2,3,5,6},{4},{7}}
[5,3,6,4,2,7,1]=>{{1,2,3,5,6,7},{4}}
[5,3,6,4,7,1,2]=>{{1,2,3,5,6,7},{4}}
[5,3,6,4,7,2,1]=>{{1,5,7},{2,3,6},{4}}
[5,3,6,7,1,2,4]=>{{1,5},{2,3,6},{4,7}}
[5,3,6,7,1,4,2]=>{{1,5},{2,3,4,6,7}}
[5,3,6,7,2,1,4]=>{{1,2,3,5,6},{4,7}}
[5,3,6,7,2,4,1]=>{{1,2,3,4,5,6,7}}
[5,3,6,7,4,1,2]=>{{1,2,3,4,5,6,7}}
[5,3,6,7,4,2,1]=>{{1,4,5,7},{2,3,6}}
[5,3,7,1,2,4,6]=>{{1,2,3,4,5,6,7}}
[5,3,7,1,2,6,4]=>{{1,2,3,4,5,7},{6}}
[5,3,7,1,4,2,6]=>{{1,4,5},{2,3,6,7}}
[5,3,7,1,4,6,2]=>{{1,4,5},{2,3,7},{6}}
[5,3,7,1,6,2,4]=>{{1,2,3,4,5,6,7}}
[5,3,7,1,6,4,2]=>{{1,4,5,6},{2,3,7}}
[5,3,7,2,1,4,6]=>{{1,5},{2,3,4,6,7}}
[5,3,7,2,1,6,4]=>{{1,5},{2,3,4,7},{6}}
[5,3,7,2,4,1,6]=>{{1,2,3,4,5,6,7}}
[5,3,7,2,4,6,1]=>{{1,2,3,4,5,7},{6}}
[5,3,7,2,6,1,4]=>{{1,5,6},{2,3,4,7}}
[5,3,7,2,6,4,1]=>{{1,2,3,4,5,6,7}}
[5,3,7,4,1,2,6]=>{{1,5},{2,3,6,7},{4}}
[5,3,7,4,1,6,2]=>{{1,5},{2,3,7},{4},{6}}
[5,3,7,4,2,1,6]=>{{1,2,3,5,6,7},{4}}
[5,3,7,4,2,6,1]=>{{1,2,3,5,7},{4},{6}}
[5,3,7,4,6,1,2]=>{{1,5,6},{2,3,7},{4}}
[5,3,7,4,6,2,1]=>{{1,2,3,5,6,7},{4}}
[5,3,7,6,1,2,4]=>{{1,5},{2,3,4,6,7}}
[5,3,7,6,1,4,2]=>{{1,5},{2,3,7},{4,6}}
[5,3,7,6,2,1,4]=>{{1,2,3,4,5,6,7}}
[5,3,7,6,2,4,1]=>{{1,2,3,5,7},{4,6}}
[5,3,7,6,4,1,2]=>{{1,4,5,6},{2,3,7}}
[5,3,7,6,4,2,1]=>{{1,2,3,4,5,6,7}}
[5,4,1,2,3,6,7]=>{{1,3,5},{2,4},{6},{7}}
[5,4,1,2,3,7,6]=>{{1,3,5},{2,4},{6,7}}
[5,4,1,2,6,3,7]=>{{1,3,5,6},{2,4},{7}}
[5,4,1,2,6,7,3]=>{{1,3,5,6,7},{2,4}}
[5,4,1,2,7,3,6]=>{{1,3,5,6,7},{2,4}}
[5,4,1,2,7,6,3]=>{{1,3,5,7},{2,4},{6}}
[5,4,1,3,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[5,4,1,3,2,7,6]=>{{1,2,3,4,5},{6,7}}
[5,4,1,3,6,2,7]=>{{1,2,3,4,5,6},{7}}
[5,4,1,3,6,7,2]=>{{1,2,3,4,5,6,7}}
[5,4,1,3,7,2,6]=>{{1,2,3,4,5,6,7}}
[5,4,1,3,7,6,2]=>{{1,2,3,4,5,7},{6}}
[5,4,1,6,2,3,7]=>{{1,2,3,4,5,6},{7}}
[5,4,1,6,2,7,3]=>{{1,2,3,4,5,6,7}}
[5,4,1,6,3,2,7]=>{{1,3,5},{2,4,6},{7}}
[5,4,1,6,3,7,2]=>{{1,3,5},{2,4,6,7}}
[5,4,1,6,7,2,3]=>{{1,3,5,7},{2,4,6}}
[5,4,1,6,7,3,2]=>{{1,2,3,4,5,6,7}}
[5,4,1,7,2,3,6]=>{{1,2,3,4,5,6,7}}
[5,4,1,7,2,6,3]=>{{1,2,3,4,5,7},{6}}
[5,4,1,7,3,2,6]=>{{1,3,5},{2,4,6,7}}
[5,4,1,7,3,6,2]=>{{1,3,5},{2,4,7},{6}}
[5,4,1,7,6,2,3]=>{{1,2,3,4,5,6,7}}
[5,4,1,7,6,3,2]=>{{1,3,5,6},{2,4,7}}
[5,4,2,1,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[5,4,2,1,3,7,6]=>{{1,2,3,4,5},{6,7}}
[5,4,2,1,6,3,7]=>{{1,2,3,4,5,6},{7}}
[5,4,2,1,6,7,3]=>{{1,2,3,4,5,6,7}}
[5,4,2,1,7,3,6]=>{{1,2,3,4,5,6,7}}
[5,4,2,1,7,6,3]=>{{1,2,3,4,5,7},{6}}
[5,4,2,3,1,6,7]=>{{1,5},{2,3,4},{6},{7}}
[5,4,2,3,1,7,6]=>{{1,5},{2,3,4},{6,7}}
[5,4,2,3,6,1,7]=>{{1,5,6},{2,3,4},{7}}
[5,4,2,3,6,7,1]=>{{1,5,6,7},{2,3,4}}
[5,4,2,3,7,1,6]=>{{1,5,6,7},{2,3,4}}
[5,4,2,3,7,6,1]=>{{1,5,7},{2,3,4},{6}}
[5,4,2,6,1,3,7]=>{{1,5},{2,3,4,6},{7}}
[5,4,2,6,1,7,3]=>{{1,5},{2,3,4,6,7}}
[5,4,2,6,3,1,7]=>{{1,2,3,4,5,6},{7}}
[5,4,2,6,3,7,1]=>{{1,2,3,4,5,6,7}}
[5,4,2,6,7,1,3]=>{{1,2,3,4,5,6,7}}
[5,4,2,6,7,3,1]=>{{1,5,7},{2,3,4,6}}
[5,4,2,7,1,3,6]=>{{1,5},{2,3,4,6,7}}
[5,4,2,7,1,6,3]=>{{1,5},{2,3,4,7},{6}}
[5,4,2,7,3,1,6]=>{{1,2,3,4,5,6,7}}
[5,4,2,7,3,6,1]=>{{1,2,3,4,5,7},{6}}
[5,4,2,7,6,1,3]=>{{1,5,6},{2,3,4,7}}
[5,4,2,7,6,3,1]=>{{1,2,3,4,5,6,7}}
[5,4,3,1,2,6,7]=>{{1,2,4,5},{3},{6},{7}}
[5,4,3,1,2,7,6]=>{{1,2,4,5},{3},{6,7}}
[5,4,3,1,6,2,7]=>{{1,2,4,5,6},{3},{7}}
[5,4,3,1,6,7,2]=>{{1,2,4,5,6,7},{3}}
[5,4,3,1,7,2,6]=>{{1,2,4,5,6,7},{3}}
[5,4,3,1,7,6,2]=>{{1,2,4,5,7},{3},{6}}
[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}}
[5,4,3,2,1,7,6]=>{{1,5},{2,4},{3},{6,7}}
[5,4,3,2,6,1,7]=>{{1,5,6},{2,4},{3},{7}}
[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}}
[5,4,3,2,7,1,6]=>{{1,5,6,7},{2,4},{3}}
[5,4,3,2,7,6,1]=>{{1,5,7},{2,4},{3},{6}}
[5,4,3,6,1,2,7]=>{{1,5},{2,4,6},{3},{7}}
[5,4,3,6,1,7,2]=>{{1,5},{2,4,6,7},{3}}
[5,4,3,6,2,1,7]=>{{1,2,4,5,6},{3},{7}}
[5,4,3,6,2,7,1]=>{{1,2,4,5,6,7},{3}}
[5,4,3,6,7,1,2]=>{{1,2,4,5,6,7},{3}}
[5,4,3,6,7,2,1]=>{{1,5,7},{2,4,6},{3}}
[5,4,3,7,1,2,6]=>{{1,5},{2,4,6,7},{3}}
[5,4,3,7,1,6,2]=>{{1,5},{2,4,7},{3},{6}}
[5,4,3,7,2,1,6]=>{{1,2,4,5,6,7},{3}}
[5,4,3,7,2,6,1]=>{{1,2,4,5,7},{3},{6}}
[5,4,3,7,6,1,2]=>{{1,5,6},{2,4,7},{3}}
[5,4,3,7,6,2,1]=>{{1,2,4,5,6,7},{3}}
[5,4,6,1,2,3,7]=>{{1,2,4,5},{3,6},{7}}
[5,4,6,1,2,7,3]=>{{1,2,4,5},{3,6,7}}
[5,4,6,1,3,2,7]=>{{1,2,3,4,5,6},{7}}
[5,4,6,1,3,7,2]=>{{1,2,3,4,5,6,7}}
[5,4,6,1,7,2,3]=>{{1,2,3,4,5,6,7}}
[5,4,6,1,7,3,2]=>{{1,2,4,5,7},{3,6}}
[5,4,6,2,1,3,7]=>{{1,5},{2,4},{3,6},{7}}
[5,4,6,2,1,7,3]=>{{1,5},{2,4},{3,6,7}}
[5,4,6,2,3,1,7]=>{{1,3,5,6},{2,4},{7}}
[5,4,6,2,3,7,1]=>{{1,3,5,6,7},{2,4}}
[5,4,6,2,7,1,3]=>{{1,3,5,6,7},{2,4}}
[5,4,6,2,7,3,1]=>{{1,5,7},{2,4},{3,6}}
[5,4,6,3,1,2,7]=>{{1,5},{2,3,4,6},{7}}
[5,4,6,3,1,7,2]=>{{1,5},{2,3,4,6,7}}
[5,4,6,3,2,1,7]=>{{1,2,3,4,5,6},{7}}
[5,4,6,3,2,7,1]=>{{1,2,3,4,5,6,7}}
[5,4,6,3,7,1,2]=>{{1,2,3,4,5,6,7}}
[5,4,6,3,7,2,1]=>{{1,5,7},{2,3,4,6}}
[5,4,6,7,1,2,3]=>{{1,5},{2,3,4,6,7}}
[5,4,6,7,1,3,2]=>{{1,5},{2,4,7},{3,6}}
[5,4,6,7,2,1,3]=>{{1,2,3,4,5,6,7}}
[5,4,6,7,2,3,1]=>{{1,2,4,5,7},{3,6}}
[5,4,6,7,3,1,2]=>{{1,3,5,6},{2,4,7}}
[5,4,6,7,3,2,1]=>{{1,2,3,4,5,6,7}}
[5,4,7,1,2,3,6]=>{{1,2,4,5},{3,6,7}}
[5,4,7,1,2,6,3]=>{{1,2,4,5},{3,7},{6}}
[5,4,7,1,3,2,6]=>{{1,2,3,4,5,6,7}}
[5,4,7,1,3,6,2]=>{{1,2,3,4,5,7},{6}}
[5,4,7,1,6,2,3]=>{{1,2,4,5,6},{3,7}}
[5,4,7,1,6,3,2]=>{{1,2,3,4,5,6,7}}
[5,4,7,2,1,3,6]=>{{1,5},{2,4},{3,6,7}}
[5,4,7,2,1,6,3]=>{{1,5},{2,4},{3,7},{6}}
[5,4,7,2,3,1,6]=>{{1,3,5,6,7},{2,4}}
[5,4,7,2,3,6,1]=>{{1,3,5,7},{2,4},{6}}
[5,4,7,2,6,1,3]=>{{1,5,6},{2,4},{3,7}}
[5,4,7,2,6,3,1]=>{{1,3,5,6,7},{2,4}}
[5,4,7,3,1,2,6]=>{{1,5},{2,3,4,6,7}}
[5,4,7,3,1,6,2]=>{{1,5},{2,3,4,7},{6}}
[5,4,7,3,2,1,6]=>{{1,2,3,4,5,6,7}}
[5,4,7,3,2,6,1]=>{{1,2,3,4,5,7},{6}}
[5,4,7,3,6,1,2]=>{{1,5,6},{2,3,4,7}}
[5,4,7,3,6,2,1]=>{{1,2,3,4,5,6,7}}
[5,4,7,6,1,2,3]=>{{1,5},{2,4,6},{3,7}}
[5,4,7,6,1,3,2]=>{{1,5},{2,3,4,6,7}}
[5,4,7,6,2,1,3]=>{{1,2,4,5,6},{3,7}}
[5,4,7,6,2,3,1]=>{{1,2,3,4,5,6,7}}
[5,4,7,6,3,1,2]=>{{1,2,3,4,5,6,7}}
[5,4,7,6,3,2,1]=>{{1,3,5,7},{2,4,6}}
[5,6,1,2,3,4,7]=>{{1,3,5},{2,4,6},{7}}
[5,6,1,2,3,7,4]=>{{1,3,5},{2,4,6,7}}
[5,6,1,2,4,3,7]=>{{1,2,3,4,5,6},{7}}
[5,6,1,2,4,7,3]=>{{1,2,3,4,5,6,7}}
[5,6,1,2,7,3,4]=>{{1,2,3,4,5,6,7}}
[5,6,1,2,7,4,3]=>{{1,3,5,7},{2,4,6}}
[5,6,1,3,2,4,7]=>{{1,2,3,4,5,6},{7}}
[5,6,1,3,2,7,4]=>{{1,2,3,4,5,6,7}}
[5,6,1,3,4,2,7]=>{{1,3,4,5},{2,6},{7}}
[5,6,1,3,4,7,2]=>{{1,3,4,5},{2,6,7}}
[5,6,1,3,7,2,4]=>{{1,3,4,5,7},{2,6}}
[5,6,1,3,7,4,2]=>{{1,2,3,4,5,6,7}}
[5,6,1,4,2,3,7]=>{{1,2,3,5,6},{4},{7}}
[5,6,1,4,2,7,3]=>{{1,2,3,5,6,7},{4}}
[5,6,1,4,3,2,7]=>{{1,3,5},{2,6},{4},{7}}
[5,6,1,4,3,7,2]=>{{1,3,5},{2,6,7},{4}}
[5,6,1,4,7,2,3]=>{{1,3,5,7},{2,6},{4}}
[5,6,1,4,7,3,2]=>{{1,2,3,5,6,7},{4}}
[5,6,1,7,2,3,4]=>{{1,2,3,5,6},{4,7}}
[5,6,1,7,2,4,3]=>{{1,2,3,4,5,6,7}}
[5,6,1,7,3,2,4]=>{{1,3,5},{2,6},{4,7}}
[5,6,1,7,3,4,2]=>{{1,3,5},{2,4,6,7}}
[5,6,1,7,4,2,3]=>{{1,3,4,5,7},{2,6}}
[5,6,1,7,4,3,2]=>{{1,2,3,4,5,6,7}}
[5,6,2,1,3,4,7]=>{{1,2,3,4,5,6},{7}}
[5,6,2,1,3,7,4]=>{{1,2,3,4,5,6,7}}
[5,6,2,1,4,3,7]=>{{1,4,5},{2,3,6},{7}}
[5,6,2,1,4,7,3]=>{{1,4,5},{2,3,6,7}}
[5,6,2,1,7,3,4]=>{{1,4,5,7},{2,3,6}}
[5,6,2,1,7,4,3]=>{{1,2,3,4,5,6,7}}
[5,6,2,3,1,4,7]=>{{1,5},{2,3,4,6},{7}}
[5,6,2,3,1,7,4]=>{{1,5},{2,3,4,6,7}}
[5,6,2,3,4,1,7]=>{{1,2,3,4,5,6},{7}}
[5,6,2,3,4,7,1]=>{{1,2,3,4,5,6,7}}
[5,6,2,3,7,1,4]=>{{1,2,3,4,5,6,7}}
[5,6,2,3,7,4,1]=>{{1,5,7},{2,3,4,6}}
[5,6,2,4,1,3,7]=>{{1,5},{2,3,6},{4},{7}}
[5,6,2,4,1,7,3]=>{{1,5},{2,3,6,7},{4}}
[5,6,2,4,3,1,7]=>{{1,2,3,5,6},{4},{7}}
[5,6,2,4,3,7,1]=>{{1,2,3,5,6,7},{4}}
[5,6,2,4,7,1,3]=>{{1,2,3,5,6,7},{4}}
[5,6,2,4,7,3,1]=>{{1,5,7},{2,3,6},{4}}
[5,6,2,7,1,3,4]=>{{1,5},{2,3,6},{4,7}}
[5,6,2,7,1,4,3]=>{{1,5},{2,3,4,6,7}}
[5,6,2,7,3,1,4]=>{{1,2,3,5,6},{4,7}}
[5,6,2,7,3,4,1]=>{{1,2,3,4,5,6,7}}
[5,6,2,7,4,1,3]=>{{1,2,3,4,5,6,7}}
[5,6,2,7,4,3,1]=>{{1,4,5,7},{2,3,6}}
[5,6,3,1,2,4,7]=>{{1,2,4,5,6},{3},{7}}
[5,6,3,1,2,7,4]=>{{1,2,4,5,6,7},{3}}
[5,6,3,1,4,2,7]=>{{1,4,5},{2,6},{3},{7}}
[5,6,3,1,4,7,2]=>{{1,4,5},{2,6,7},{3}}
[5,6,3,1,7,2,4]=>{{1,4,5,7},{2,6},{3}}
[5,6,3,1,7,4,2]=>{{1,2,4,5,6,7},{3}}
[5,6,3,2,1,4,7]=>{{1,5},{2,4,6},{3},{7}}
[5,6,3,2,1,7,4]=>{{1,5},{2,4,6,7},{3}}
[5,6,3,2,4,1,7]=>{{1,2,4,5,6},{3},{7}}
[5,6,3,2,4,7,1]=>{{1,2,4,5,6,7},{3}}
[5,6,3,2,7,1,4]=>{{1,2,4,5,6,7},{3}}
[5,6,3,2,7,4,1]=>{{1,5,7},{2,4,6},{3}}
[5,6,3,4,1,2,7]=>{{1,5},{2,6},{3},{4},{7}}
[5,6,3,4,1,7,2]=>{{1,5},{2,6,7},{3},{4}}
[5,6,3,4,2,1,7]=>{{1,2,5,6},{3},{4},{7}}
[5,6,3,4,2,7,1]=>{{1,2,5,6,7},{3},{4}}
[5,6,3,4,7,1,2]=>{{1,2,5,6,7},{3},{4}}
[5,6,3,4,7,2,1]=>{{1,5,7},{2,6},{3},{4}}
[5,6,3,7,1,2,4]=>{{1,5},{2,6},{3},{4,7}}
[5,6,3,7,1,4,2]=>{{1,5},{2,4,6,7},{3}}
[5,6,3,7,2,1,4]=>{{1,2,5,6},{3},{4,7}}
[5,6,3,7,2,4,1]=>{{1,2,4,5,6,7},{3}}
[5,6,3,7,4,1,2]=>{{1,2,4,5,6,7},{3}}
[5,6,3,7,4,2,1]=>{{1,4,5,7},{2,6},{3}}
[5,6,4,1,2,3,7]=>{{1,2,3,4,5,6},{7}}
[5,6,4,1,2,7,3]=>{{1,2,3,4,5,6,7}}
[5,6,4,1,3,2,7]=>{{1,3,4,5},{2,6},{7}}
[5,6,4,1,3,7,2]=>{{1,3,4,5},{2,6,7}}
[5,6,4,1,7,2,3]=>{{1,3,4,5,7},{2,6}}
[5,6,4,1,7,3,2]=>{{1,2,3,4,5,6,7}}
[5,6,4,2,1,3,7]=>{{1,5},{2,3,4,6},{7}}
[5,6,4,2,1,7,3]=>{{1,5},{2,3,4,6,7}}
[5,6,4,2,3,1,7]=>{{1,2,3,4,5,6},{7}}
[5,6,4,2,3,7,1]=>{{1,2,3,4,5,6,7}}
[5,6,4,2,7,1,3]=>{{1,2,3,4,5,6,7}}
[5,6,4,2,7,3,1]=>{{1,5,7},{2,3,4,6}}
[5,6,4,3,1,2,7]=>{{1,5},{2,6},{3,4},{7}}
[5,6,4,3,1,7,2]=>{{1,5},{2,6,7},{3,4}}
[5,6,4,3,2,1,7]=>{{1,2,5,6},{3,4},{7}}
[5,6,4,3,2,7,1]=>{{1,2,5,6,7},{3,4}}
[5,6,4,3,7,1,2]=>{{1,2,5,6,7},{3,4}}
[5,6,4,3,7,2,1]=>{{1,5,7},{2,6},{3,4}}
[5,6,4,7,1,2,3]=>{{1,5},{2,6},{3,4,7}}
[5,6,4,7,1,3,2]=>{{1,5},{2,3,4,6,7}}
[5,6,4,7,2,1,3]=>{{1,2,5,6},{3,4,7}}
[5,6,4,7,2,3,1]=>{{1,2,3,4,5,6,7}}
[5,6,4,7,3,1,2]=>{{1,2,3,4,5,6,7}}
[5,6,4,7,3,2,1]=>{{1,3,4,5,7},{2,6}}
[5,6,7,1,2,3,4]=>{{1,2,3,4,5,6,7}}
[5,6,7,1,2,4,3]=>{{1,2,4,5,6},{3,7}}
[5,6,7,1,3,2,4]=>{{1,3,4,5,7},{2,6}}
[5,6,7,1,3,4,2]=>{{1,2,3,4,5,6,7}}
[5,6,7,1,4,2,3]=>{{1,4,5},{2,6},{3,7}}
[5,6,7,1,4,3,2]=>{{1,4,5},{2,3,6,7}}
[5,6,7,2,1,3,4]=>{{1,5},{2,3,4,6,7}}
[5,6,7,2,1,4,3]=>{{1,5},{2,4,6},{3,7}}
[5,6,7,2,3,1,4]=>{{1,2,3,4,5,6,7}}
[5,6,7,2,3,4,1]=>{{1,3,5,7},{2,4,6}}
[5,6,7,2,4,1,3]=>{{1,2,4,5,6},{3,7}}
[5,6,7,2,4,3,1]=>{{1,2,3,4,5,6,7}}
[5,6,7,3,1,2,4]=>{{1,5},{2,6},{3,4,7}}
[5,6,7,3,1,4,2]=>{{1,5},{2,3,4,6,7}}
[5,6,7,3,2,1,4]=>{{1,2,5,6},{3,4,7}}
[5,6,7,3,2,4,1]=>{{1,2,3,4,5,6,7}}
[5,6,7,3,4,1,2]=>{{1,2,3,4,5,6,7}}
[5,6,7,3,4,2,1]=>{{1,3,4,5,7},{2,6}}
[5,6,7,4,1,2,3]=>{{1,5},{2,6},{3,7},{4}}
[5,6,7,4,1,3,2]=>{{1,5},{2,3,6,7},{4}}
[5,6,7,4,2,1,3]=>{{1,2,5,6},{3,7},{4}}
[5,6,7,4,2,3,1]=>{{1,2,3,5,6,7},{4}}
[5,6,7,4,3,1,2]=>{{1,2,3,5,6,7},{4}}
[5,6,7,4,3,2,1]=>{{1,3,5,7},{2,6},{4}}
[5,7,1,2,3,4,6]=>{{1,3,5},{2,4,6,7}}
[5,7,1,2,3,6,4]=>{{1,3,5},{2,4,7},{6}}
[5,7,1,2,4,3,6]=>{{1,2,3,4,5,6,7}}
[5,7,1,2,4,6,3]=>{{1,2,3,4,5,7},{6}}
[5,7,1,2,6,3,4]=>{{1,3,5,6},{2,4,7}}
[5,7,1,2,6,4,3]=>{{1,2,3,4,5,6,7}}
[5,7,1,3,2,4,6]=>{{1,2,3,4,5,6,7}}
[5,7,1,3,2,6,4]=>{{1,2,3,4,5,7},{6}}
[5,7,1,3,4,2,6]=>{{1,3,4,5},{2,6,7}}
[5,7,1,3,4,6,2]=>{{1,3,4,5},{2,7},{6}}
[5,7,1,3,6,2,4]=>{{1,2,3,4,5,6,7}}
[5,7,1,3,6,4,2]=>{{1,3,4,5,6},{2,7}}
[5,7,1,4,2,3,6]=>{{1,2,3,5,6,7},{4}}
[5,7,1,4,2,6,3]=>{{1,2,3,5,7},{4},{6}}
[5,7,1,4,3,2,6]=>{{1,3,5},{2,6,7},{4}}
[5,7,1,4,3,6,2]=>{{1,3,5},{2,7},{4},{6}}
[5,7,1,4,6,2,3]=>{{1,2,3,5,6,7},{4}}
[5,7,1,4,6,3,2]=>{{1,3,5,6},{2,7},{4}}
[5,7,1,6,2,3,4]=>{{1,2,3,4,5,6,7}}
[5,7,1,6,2,4,3]=>{{1,2,3,5,7},{4,6}}
[5,7,1,6,3,2,4]=>{{1,3,5},{2,4,6,7}}
[5,7,1,6,3,4,2]=>{{1,3,5},{2,7},{4,6}}
[5,7,1,6,4,2,3]=>{{1,2,3,4,5,6,7}}
[5,7,1,6,4,3,2]=>{{1,3,4,5,6},{2,7}}
[5,7,2,1,3,4,6]=>{{1,2,3,4,5,6,7}}
[5,7,2,1,3,6,4]=>{{1,2,3,4,5,7},{6}}
[5,7,2,1,4,3,6]=>{{1,4,5},{2,3,6,7}}
[5,7,2,1,4,6,3]=>{{1,4,5},{2,3,7},{6}}
[5,7,2,1,6,3,4]=>{{1,2,3,4,5,6,7}}
[5,7,2,1,6,4,3]=>{{1,4,5,6},{2,3,7}}
[5,7,2,3,1,4,6]=>{{1,5},{2,3,4,6,7}}
[5,7,2,3,1,6,4]=>{{1,5},{2,3,4,7},{6}}
[5,7,2,3,4,1,6]=>{{1,2,3,4,5,6,7}}
[5,7,2,3,4,6,1]=>{{1,2,3,4,5,7},{6}}
[5,7,2,3,6,1,4]=>{{1,5,6},{2,3,4,7}}
[5,7,2,3,6,4,1]=>{{1,2,3,4,5,6,7}}
[5,7,2,4,1,3,6]=>{{1,5},{2,3,6,7},{4}}
[5,7,2,4,1,6,3]=>{{1,5},{2,3,7},{4},{6}}
[5,7,2,4,3,1,6]=>{{1,2,3,5,6,7},{4}}
[5,7,2,4,3,6,1]=>{{1,2,3,5,7},{4},{6}}
[5,7,2,4,6,1,3]=>{{1,5,6},{2,3,7},{4}}
[5,7,2,4,6,3,1]=>{{1,2,3,5,6,7},{4}}
[5,7,2,6,1,3,4]=>{{1,5},{2,3,4,6,7}}
[5,7,2,6,1,4,3]=>{{1,5},{2,3,7},{4,6}}
[5,7,2,6,3,1,4]=>{{1,2,3,4,5,6,7}}
[5,7,2,6,3,4,1]=>{{1,2,3,5,7},{4,6}}
[5,7,2,6,4,1,3]=>{{1,4,5,6},{2,3,7}}
[5,7,2,6,4,3,1]=>{{1,2,3,4,5,6,7}}
[5,7,3,1,2,4,6]=>{{1,2,4,5,6,7},{3}}
[5,7,3,1,2,6,4]=>{{1,2,4,5,7},{3},{6}}
[5,7,3,1,4,2,6]=>{{1,4,5},{2,6,7},{3}}
[5,7,3,1,4,6,2]=>{{1,4,5},{2,7},{3},{6}}
[5,7,3,1,6,2,4]=>{{1,2,4,5,6,7},{3}}
[5,7,3,1,6,4,2]=>{{1,4,5,6},{2,7},{3}}
[5,7,3,2,1,4,6]=>{{1,5},{2,4,6,7},{3}}
[5,7,3,2,1,6,4]=>{{1,5},{2,4,7},{3},{6}}
[5,7,3,2,4,1,6]=>{{1,2,4,5,6,7},{3}}
[5,7,3,2,4,6,1]=>{{1,2,4,5,7},{3},{6}}
[5,7,3,2,6,1,4]=>{{1,5,6},{2,4,7},{3}}
[5,7,3,2,6,4,1]=>{{1,2,4,5,6,7},{3}}
[5,7,3,4,1,2,6]=>{{1,5},{2,6,7},{3},{4}}
[5,7,3,4,1,6,2]=>{{1,5},{2,7},{3},{4},{6}}
[5,7,3,4,2,1,6]=>{{1,2,5,6,7},{3},{4}}
[5,7,3,4,2,6,1]=>{{1,2,5,7},{3},{4},{6}}
[5,7,3,4,6,1,2]=>{{1,5,6},{2,7},{3},{4}}
[5,7,3,4,6,2,1]=>{{1,2,5,6,7},{3},{4}}
[5,7,3,6,1,2,4]=>{{1,5},{2,4,6,7},{3}}
[5,7,3,6,1,4,2]=>{{1,5},{2,7},{3},{4,6}}
[5,7,3,6,2,1,4]=>{{1,2,4,5,6,7},{3}}
[5,7,3,6,2,4,1]=>{{1,2,5,7},{3},{4,6}}
[5,7,3,6,4,1,2]=>{{1,4,5,6},{2,7},{3}}
[5,7,3,6,4,2,1]=>{{1,2,4,5,6,7},{3}}
[5,7,4,1,2,3,6]=>{{1,2,3,4,5,6,7}}
[5,7,4,1,2,6,3]=>{{1,2,3,4,5,7},{6}}
[5,7,4,1,3,2,6]=>{{1,3,4,5},{2,6,7}}
[5,7,4,1,3,6,2]=>{{1,3,4,5},{2,7},{6}}
[5,7,4,1,6,2,3]=>{{1,2,3,4,5,6,7}}
[5,7,4,1,6,3,2]=>{{1,3,4,5,6},{2,7}}
[5,7,4,2,1,3,6]=>{{1,5},{2,3,4,6,7}}
[5,7,4,2,1,6,3]=>{{1,5},{2,3,4,7},{6}}
[5,7,4,2,3,1,6]=>{{1,2,3,4,5,6,7}}
[5,7,4,2,3,6,1]=>{{1,2,3,4,5,7},{6}}
[5,7,4,2,6,1,3]=>{{1,5,6},{2,3,4,7}}
[5,7,4,2,6,3,1]=>{{1,2,3,4,5,6,7}}
[5,7,4,3,1,2,6]=>{{1,5},{2,6,7},{3,4}}
[5,7,4,3,1,6,2]=>{{1,5},{2,7},{3,4},{6}}
[5,7,4,3,2,1,6]=>{{1,2,5,6,7},{3,4}}
[5,7,4,3,2,6,1]=>{{1,2,5,7},{3,4},{6}}
[5,7,4,3,6,1,2]=>{{1,5,6},{2,7},{3,4}}
[5,7,4,3,6,2,1]=>{{1,2,5,6,7},{3,4}}
[5,7,4,6,1,2,3]=>{{1,5},{2,3,4,6,7}}
[5,7,4,6,1,3,2]=>{{1,5},{2,7},{3,4,6}}
[5,7,4,6,2,1,3]=>{{1,2,3,4,5,6,7}}
[5,7,4,6,2,3,1]=>{{1,2,5,7},{3,4,6}}
[5,7,4,6,3,1,2]=>{{1,3,4,5,6},{2,7}}
[5,7,4,6,3,2,1]=>{{1,2,3,4,5,6,7}}
[5,7,6,1,2,3,4]=>{{1,2,4,5,7},{3,6}}
[5,7,6,1,2,4,3]=>{{1,2,3,4,5,6,7}}
[5,7,6,1,3,2,4]=>{{1,2,3,4,5,6,7}}
[5,7,6,1,3,4,2]=>{{1,3,4,5,6},{2,7}}
[5,7,6,1,4,2,3]=>{{1,4,5},{2,3,6,7}}
[5,7,6,1,4,3,2]=>{{1,4,5},{2,7},{3,6}}
[5,7,6,2,1,3,4]=>{{1,5},{2,4,7},{3,6}}
[5,7,6,2,1,4,3]=>{{1,5},{2,3,4,6,7}}
[5,7,6,2,3,1,4]=>{{1,3,5,6},{2,4,7}}
[5,7,6,2,3,4,1]=>{{1,2,3,4,5,6,7}}
[5,7,6,2,4,1,3]=>{{1,2,3,4,5,6,7}}
[5,7,6,2,4,3,1]=>{{1,2,4,5,7},{3,6}}
[5,7,6,3,1,2,4]=>{{1,5},{2,3,4,6,7}}
[5,7,6,3,1,4,2]=>{{1,5},{2,7},{3,4,6}}
[5,7,6,3,2,1,4]=>{{1,2,3,4,5,6,7}}
[5,7,6,3,2,4,1]=>{{1,2,5,7},{3,4,6}}
[5,7,6,3,4,1,2]=>{{1,3,4,5,6},{2,7}}
[5,7,6,3,4,2,1]=>{{1,2,3,4,5,6,7}}
[5,7,6,4,1,2,3]=>{{1,5},{2,3,6,7},{4}}
[5,7,6,4,1,3,2]=>{{1,5},{2,7},{3,6},{4}}
[5,7,6,4,2,1,3]=>{{1,2,3,5,6,7},{4}}
[5,7,6,4,2,3,1]=>{{1,2,5,7},{3,6},{4}}
[5,7,6,4,3,1,2]=>{{1,3,5,6},{2,7},{4}}
[5,7,6,4,3,2,1]=>{{1,2,3,5,6,7},{4}}
[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}}
[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}}
[6,1,2,3,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[6,1,2,3,5,7,4]=>{{1,2,3,4,6,7},{5}}
[6,1,2,3,7,4,5]=>{{1,2,3,4,6},{5,7}}
[6,1,2,3,7,5,4]=>{{1,2,3,4,5,6,7}}
[6,1,2,4,3,5,7]=>{{1,2,3,5,6},{4},{7}}
[6,1,2,4,3,7,5]=>{{1,2,3,5,6,7},{4}}
[6,1,2,4,5,3,7]=>{{1,2,3,6},{4},{5},{7}}
[6,1,2,4,5,7,3]=>{{1,2,3,6,7},{4},{5}}
[6,1,2,4,7,3,5]=>{{1,2,3,6},{4},{5,7}}
[6,1,2,4,7,5,3]=>{{1,2,3,5,6,7},{4}}
[6,1,2,5,3,4,7]=>{{1,2,3,4,5,6},{7}}
[6,1,2,5,3,7,4]=>{{1,2,3,4,5,6,7}}
[6,1,2,5,4,3,7]=>{{1,2,3,6},{4,5},{7}}
[6,1,2,5,4,7,3]=>{{1,2,3,6,7},{4,5}}
[6,1,2,5,7,3,4]=>{{1,2,3,6},{4,5,7}}
[6,1,2,5,7,4,3]=>{{1,2,3,4,5,6,7}}
[6,1,2,7,3,4,5]=>{{1,2,3,4,5,6,7}}
[6,1,2,7,3,5,4]=>{{1,2,3,5,6},{4,7}}
[6,1,2,7,4,3,5]=>{{1,2,3,6},{4,5,7}}
[6,1,2,7,4,5,3]=>{{1,2,3,4,5,6,7}}
[6,1,2,7,5,3,4]=>{{1,2,3,6},{4,7},{5}}
[6,1,2,7,5,4,3]=>{{1,2,3,4,6,7},{5}}
[6,1,3,2,4,5,7]=>{{1,2,4,5,6},{3},{7}}
[6,1,3,2,4,7,5]=>{{1,2,4,5,6,7},{3}}
[6,1,3,2,5,4,7]=>{{1,2,4,6},{3},{5},{7}}
[6,1,3,2,5,7,4]=>{{1,2,4,6,7},{3},{5}}
[6,1,3,2,7,4,5]=>{{1,2,4,6},{3},{5,7}}
[6,1,3,2,7,5,4]=>{{1,2,4,5,6,7},{3}}
[6,1,3,4,2,5,7]=>{{1,2,5,6},{3},{4},{7}}
[6,1,3,4,2,7,5]=>{{1,2,5,6,7},{3},{4}}
[6,1,3,4,5,2,7]=>{{1,2,6},{3},{4},{5},{7}}
[6,1,3,4,5,7,2]=>{{1,2,6,7},{3},{4},{5}}
[6,1,3,4,7,2,5]=>{{1,2,6},{3},{4},{5,7}}
[6,1,3,4,7,5,2]=>{{1,2,5,6,7},{3},{4}}
[6,1,3,5,2,4,7]=>{{1,2,4,5,6},{3},{7}}
[6,1,3,5,2,7,4]=>{{1,2,4,5,6,7},{3}}
[6,1,3,5,4,2,7]=>{{1,2,6},{3},{4,5},{7}}
[6,1,3,5,4,7,2]=>{{1,2,6,7},{3},{4,5}}
[6,1,3,5,7,2,4]=>{{1,2,6},{3},{4,5,7}}
[6,1,3,5,7,4,2]=>{{1,2,4,5,6,7},{3}}
[6,1,3,7,2,4,5]=>{{1,2,4,5,6,7},{3}}
[6,1,3,7,2,5,4]=>{{1,2,5,6},{3},{4,7}}
[6,1,3,7,4,2,5]=>{{1,2,6},{3},{4,5,7}}
[6,1,3,7,4,5,2]=>{{1,2,4,5,6,7},{3}}
[6,1,3,7,5,2,4]=>{{1,2,6},{3},{4,7},{5}}
[6,1,3,7,5,4,2]=>{{1,2,4,6,7},{3},{5}}
[6,1,4,2,3,5,7]=>{{1,2,3,4,5,6},{7}}
[6,1,4,2,3,7,5]=>{{1,2,3,4,5,6,7}}
[6,1,4,2,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[6,1,4,2,5,7,3]=>{{1,2,3,4,6,7},{5}}
[6,1,4,2,7,3,5]=>{{1,2,3,4,6},{5,7}}
[6,1,4,2,7,5,3]=>{{1,2,3,4,5,6,7}}
[6,1,4,3,2,5,7]=>{{1,2,5,6},{3,4},{7}}
[6,1,4,3,2,7,5]=>{{1,2,5,6,7},{3,4}}
[6,1,4,3,5,2,7]=>{{1,2,6},{3,4},{5},{7}}
[6,1,4,3,5,7,2]=>{{1,2,6,7},{3,4},{5}}
[6,1,4,3,7,2,5]=>{{1,2,6},{3,4},{5,7}}
[6,1,4,3,7,5,2]=>{{1,2,5,6,7},{3,4}}
[6,1,4,5,2,3,7]=>{{1,2,3,4,5,6},{7}}
[6,1,4,5,2,7,3]=>{{1,2,3,4,5,6,7}}
[6,1,4,5,3,2,7]=>{{1,2,6},{3,4,5},{7}}
[6,1,4,5,3,7,2]=>{{1,2,6,7},{3,4,5}}
[6,1,4,5,7,2,3]=>{{1,2,6},{3,4,5,7}}
[6,1,4,5,7,3,2]=>{{1,2,3,4,5,6,7}}
[6,1,4,7,2,3,5]=>{{1,2,3,4,5,6,7}}
[6,1,4,7,2,5,3]=>{{1,2,5,6},{3,4,7}}
[6,1,4,7,3,2,5]=>{{1,2,6},{3,4,5,7}}
[6,1,4,7,3,5,2]=>{{1,2,3,4,5,6,7}}
[6,1,4,7,5,2,3]=>{{1,2,6},{3,4,7},{5}}
[6,1,4,7,5,3,2]=>{{1,2,3,4,6,7},{5}}
[6,1,5,2,3,4,7]=>{{1,2,4,6},{3,5},{7}}
[6,1,5,2,3,7,4]=>{{1,2,4,6,7},{3,5}}
[6,1,5,2,4,3,7]=>{{1,2,3,4,5,6},{7}}
[6,1,5,2,4,7,3]=>{{1,2,3,4,5,6,7}}
[6,1,5,2,7,3,4]=>{{1,2,3,4,5,6,7}}
[6,1,5,2,7,4,3]=>{{1,2,4,6},{3,5,7}}
[6,1,5,3,2,4,7]=>{{1,2,3,4,5,6},{7}}
[6,1,5,3,2,7,4]=>{{1,2,3,4,5,6,7}}
[6,1,5,3,4,2,7]=>{{1,2,6},{3,4,5},{7}}
[6,1,5,3,4,7,2]=>{{1,2,6,7},{3,4,5}}
[6,1,5,3,7,2,4]=>{{1,2,6},{3,4,5,7}}
[6,1,5,3,7,4,2]=>{{1,2,3,4,5,6,7}}
[6,1,5,4,2,3,7]=>{{1,2,3,5,6},{4},{7}}
[6,1,5,4,2,7,3]=>{{1,2,3,5,6,7},{4}}
[6,1,5,4,3,2,7]=>{{1,2,6},{3,5},{4},{7}}
[6,1,5,4,3,7,2]=>{{1,2,6,7},{3,5},{4}}
[6,1,5,4,7,2,3]=>{{1,2,6},{3,5,7},{4}}
[6,1,5,4,7,3,2]=>{{1,2,3,5,6,7},{4}}
[6,1,5,7,2,3,4]=>{{1,2,3,5,6},{4,7}}
[6,1,5,7,2,4,3]=>{{1,2,3,4,5,6,7}}
[6,1,5,7,3,2,4]=>{{1,2,6},{3,5},{4,7}}
[6,1,5,7,3,4,2]=>{{1,2,4,6,7},{3,5}}
[6,1,5,7,4,2,3]=>{{1,2,6},{3,4,5,7}}
[6,1,5,7,4,3,2]=>{{1,2,3,4,5,6,7}}
[6,1,7,2,3,4,5]=>{{1,2,4,6},{3,5,7}}
[6,1,7,2,3,5,4]=>{{1,2,3,4,5,6,7}}
[6,1,7,2,4,3,5]=>{{1,2,3,4,5,6,7}}
[6,1,7,2,4,5,3]=>{{1,2,4,5,6},{3,7}}
[6,1,7,2,5,3,4]=>{{1,2,3,4,6,7},{5}}
[6,1,7,2,5,4,3]=>{{1,2,4,6},{3,7},{5}}
[6,1,7,3,2,4,5]=>{{1,2,3,4,5,6,7}}
[6,1,7,3,2,5,4]=>{{1,2,5,6},{3,4,7}}
[6,1,7,3,4,2,5]=>{{1,2,6},{3,4,5,7}}
[6,1,7,3,4,5,2]=>{{1,2,3,4,5,6,7}}
[6,1,7,3,5,2,4]=>{{1,2,6},{3,4,7},{5}}
[6,1,7,3,5,4,2]=>{{1,2,3,4,6,7},{5}}
[6,1,7,4,2,3,5]=>{{1,2,3,5,6,7},{4}}
[6,1,7,4,2,5,3]=>{{1,2,5,6},{3,7},{4}}
[6,1,7,4,3,2,5]=>{{1,2,6},{3,5,7},{4}}
[6,1,7,4,3,5,2]=>{{1,2,3,5,6,7},{4}}
[6,1,7,4,5,2,3]=>{{1,2,6},{3,7},{4},{5}}
[6,1,7,4,5,3,2]=>{{1,2,3,6,7},{4},{5}}
[6,1,7,5,2,3,4]=>{{1,2,3,4,5,6,7}}
[6,1,7,5,2,4,3]=>{{1,2,4,5,6},{3,7}}
[6,1,7,5,3,2,4]=>{{1,2,6},{3,4,5,7}}
[6,1,7,5,3,4,2]=>{{1,2,3,4,5,6,7}}
[6,1,7,5,4,2,3]=>{{1,2,6},{3,7},{4,5}}
[6,1,7,5,4,3,2]=>{{1,2,3,6,7},{4,5}}
[6,2,1,3,4,5,7]=>{{1,3,4,5,6},{2},{7}}
[6,2,1,3,4,7,5]=>{{1,3,4,5,6,7},{2}}
[6,2,1,3,5,4,7]=>{{1,3,4,6},{2},{5},{7}}
[6,2,1,3,5,7,4]=>{{1,3,4,6,7},{2},{5}}
[6,2,1,3,7,4,5]=>{{1,3,4,6},{2},{5,7}}
[6,2,1,3,7,5,4]=>{{1,3,4,5,6,7},{2}}
[6,2,1,4,3,5,7]=>{{1,3,5,6},{2},{4},{7}}
[6,2,1,4,3,7,5]=>{{1,3,5,6,7},{2},{4}}
[6,2,1,4,5,3,7]=>{{1,3,6},{2},{4},{5},{7}}
[6,2,1,4,5,7,3]=>{{1,3,6,7},{2},{4},{5}}
[6,2,1,4,7,3,5]=>{{1,3,6},{2},{4},{5,7}}
[6,2,1,4,7,5,3]=>{{1,3,5,6,7},{2},{4}}
[6,2,1,5,3,4,7]=>{{1,3,4,5,6},{2},{7}}
[6,2,1,5,3,7,4]=>{{1,3,4,5,6,7},{2}}
[6,2,1,5,4,3,7]=>{{1,3,6},{2},{4,5},{7}}
[6,2,1,5,4,7,3]=>{{1,3,6,7},{2},{4,5}}
[6,2,1,5,7,3,4]=>{{1,3,6},{2},{4,5,7}}
[6,2,1,5,7,4,3]=>{{1,3,4,5,6,7},{2}}
[6,2,1,7,3,4,5]=>{{1,3,4,5,6,7},{2}}
[6,2,1,7,3,5,4]=>{{1,3,5,6},{2},{4,7}}
[6,2,1,7,4,3,5]=>{{1,3,6},{2},{4,5,7}}
[6,2,1,7,4,5,3]=>{{1,3,4,5,6,7},{2}}
[6,2,1,7,5,3,4]=>{{1,3,6},{2},{4,7},{5}}
[6,2,1,7,5,4,3]=>{{1,3,4,6,7},{2},{5}}
[6,2,3,1,4,5,7]=>{{1,4,5,6},{2},{3},{7}}
[6,2,3,1,4,7,5]=>{{1,4,5,6,7},{2},{3}}
[6,2,3,1,5,4,7]=>{{1,4,6},{2},{3},{5},{7}}
[6,2,3,1,5,7,4]=>{{1,4,6,7},{2},{3},{5}}
[6,2,3,1,7,4,5]=>{{1,4,6},{2},{3},{5,7}}
[6,2,3,1,7,5,4]=>{{1,4,5,6,7},{2},{3}}
[6,2,3,4,1,5,7]=>{{1,5,6},{2},{3},{4},{7}}
[6,2,3,4,1,7,5]=>{{1,5,6,7},{2},{3},{4}}
[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}}
[6,2,3,4,7,1,5]=>{{1,6},{2},{3},{4},{5,7}}
[6,2,3,4,7,5,1]=>{{1,5,6,7},{2},{3},{4}}
[6,2,3,5,1,4,7]=>{{1,4,5,6},{2},{3},{7}}
[6,2,3,5,1,7,4]=>{{1,4,5,6,7},{2},{3}}
[6,2,3,5,4,1,7]=>{{1,6},{2},{3},{4,5},{7}}
[6,2,3,5,4,7,1]=>{{1,6,7},{2},{3},{4,5}}
[6,2,3,5,7,1,4]=>{{1,6},{2},{3},{4,5,7}}
[6,2,3,5,7,4,1]=>{{1,4,5,6,7},{2},{3}}
[6,2,3,7,1,4,5]=>{{1,4,5,6,7},{2},{3}}
[6,2,3,7,1,5,4]=>{{1,5,6},{2},{3},{4,7}}
[6,2,3,7,4,1,5]=>{{1,6},{2},{3},{4,5,7}}
[6,2,3,7,4,5,1]=>{{1,4,5,6,7},{2},{3}}
[6,2,3,7,5,1,4]=>{{1,6},{2},{3},{4,7},{5}}
[6,2,3,7,5,4,1]=>{{1,4,6,7},{2},{3},{5}}
[6,2,4,1,3,5,7]=>{{1,3,4,5,6},{2},{7}}
[6,2,4,1,3,7,5]=>{{1,3,4,5,6,7},{2}}
[6,2,4,1,5,3,7]=>{{1,3,4,6},{2},{5},{7}}
[6,2,4,1,5,7,3]=>{{1,3,4,6,7},{2},{5}}
[6,2,4,1,7,3,5]=>{{1,3,4,6},{2},{5,7}}
[6,2,4,1,7,5,3]=>{{1,3,4,5,6,7},{2}}
[6,2,4,3,1,5,7]=>{{1,5,6},{2},{3,4},{7}}
[6,2,4,3,1,7,5]=>{{1,5,6,7},{2},{3,4}}
[6,2,4,3,5,1,7]=>{{1,6},{2},{3,4},{5},{7}}
[6,2,4,3,5,7,1]=>{{1,6,7},{2},{3,4},{5}}
[6,2,4,3,7,1,5]=>{{1,6},{2},{3,4},{5,7}}
[6,2,4,3,7,5,1]=>{{1,5,6,7},{2},{3,4}}
[6,2,4,5,1,3,7]=>{{1,3,4,5,6},{2},{7}}
[6,2,4,5,1,7,3]=>{{1,3,4,5,6,7},{2}}
[6,2,4,5,3,1,7]=>{{1,6},{2},{3,4,5},{7}}
[6,2,4,5,3,7,1]=>{{1,6,7},{2},{3,4,5}}
[6,2,4,5,7,1,3]=>{{1,6},{2},{3,4,5,7}}
[6,2,4,5,7,3,1]=>{{1,3,4,5,6,7},{2}}
[6,2,4,7,1,3,5]=>{{1,3,4,5,6,7},{2}}
[6,2,4,7,1,5,3]=>{{1,5,6},{2},{3,4,7}}
[6,2,4,7,3,1,5]=>{{1,6},{2},{3,4,5,7}}
[6,2,4,7,3,5,1]=>{{1,3,4,5,6,7},{2}}
[6,2,4,7,5,1,3]=>{{1,6},{2},{3,4,7},{5}}
[6,2,4,7,5,3,1]=>{{1,3,4,6,7},{2},{5}}
[6,2,5,1,3,4,7]=>{{1,4,6},{2},{3,5},{7}}
[6,2,5,1,3,7,4]=>{{1,4,6,7},{2},{3,5}}
[6,2,5,1,4,3,7]=>{{1,3,4,5,6},{2},{7}}
[6,2,5,1,4,7,3]=>{{1,3,4,5,6,7},{2}}
[6,2,5,1,7,3,4]=>{{1,3,4,5,6,7},{2}}
[6,2,5,1,7,4,3]=>{{1,4,6},{2},{3,5,7}}
[6,2,5,3,1,4,7]=>{{1,3,4,5,6},{2},{7}}
[6,2,5,3,1,7,4]=>{{1,3,4,5,6,7},{2}}
[6,2,5,3,4,1,7]=>{{1,6},{2},{3,4,5},{7}}
[6,2,5,3,4,7,1]=>{{1,6,7},{2},{3,4,5}}
[6,2,5,3,7,1,4]=>{{1,6},{2},{3,4,5,7}}
[6,2,5,3,7,4,1]=>{{1,3,4,5,6,7},{2}}
[6,2,5,4,1,3,7]=>{{1,3,5,6},{2},{4},{7}}
[6,2,5,4,1,7,3]=>{{1,3,5,6,7},{2},{4}}
[6,2,5,4,3,1,7]=>{{1,6},{2},{3,5},{4},{7}}
[6,2,5,4,3,7,1]=>{{1,6,7},{2},{3,5},{4}}
[6,2,5,4,7,1,3]=>{{1,6},{2},{3,5,7},{4}}
[6,2,5,4,7,3,1]=>{{1,3,5,6,7},{2},{4}}
[6,2,5,7,1,3,4]=>{{1,3,5,6},{2},{4,7}}
[6,2,5,7,1,4,3]=>{{1,3,4,5,6,7},{2}}
[6,2,5,7,3,1,4]=>{{1,6},{2},{3,5},{4,7}}
[6,2,5,7,3,4,1]=>{{1,4,6,7},{2},{3,5}}
[6,2,5,7,4,1,3]=>{{1,6},{2},{3,4,5,7}}
[6,2,5,7,4,3,1]=>{{1,3,4,5,6,7},{2}}
[6,2,7,1,3,4,5]=>{{1,4,6},{2},{3,5,7}}
[6,2,7,1,3,5,4]=>{{1,3,4,5,6,7},{2}}
[6,2,7,1,4,3,5]=>{{1,3,4,5,6,7},{2}}
[6,2,7,1,4,5,3]=>{{1,4,5,6},{2},{3,7}}
[6,2,7,1,5,3,4]=>{{1,3,4,6,7},{2},{5}}
[6,2,7,1,5,4,3]=>{{1,4,6},{2},{3,7},{5}}
[6,2,7,3,1,4,5]=>{{1,3,4,5,6,7},{2}}
[6,2,7,3,1,5,4]=>{{1,5,6},{2},{3,4,7}}
[6,2,7,3,4,1,5]=>{{1,6},{2},{3,4,5,7}}
[6,2,7,3,4,5,1]=>{{1,3,4,5,6,7},{2}}
[6,2,7,3,5,1,4]=>{{1,6},{2},{3,4,7},{5}}
[6,2,7,3,5,4,1]=>{{1,3,4,6,7},{2},{5}}
[6,2,7,4,1,3,5]=>{{1,3,5,6,7},{2},{4}}
[6,2,7,4,1,5,3]=>{{1,5,6},{2},{3,7},{4}}
[6,2,7,4,3,1,5]=>{{1,6},{2},{3,5,7},{4}}
[6,2,7,4,3,5,1]=>{{1,3,5,6,7},{2},{4}}
[6,2,7,4,5,1,3]=>{{1,6},{2},{3,7},{4},{5}}
[6,2,7,4,5,3,1]=>{{1,3,6,7},{2},{4},{5}}
[6,2,7,5,1,3,4]=>{{1,3,4,5,6,7},{2}}
[6,2,7,5,1,4,3]=>{{1,4,5,6},{2},{3,7}}
[6,2,7,5,3,1,4]=>{{1,6},{2},{3,4,5,7}}
[6,2,7,5,3,4,1]=>{{1,3,4,5,6,7},{2}}
[6,2,7,5,4,1,3]=>{{1,6},{2},{3,7},{4,5}}
[6,2,7,5,4,3,1]=>{{1,3,6,7},{2},{4,5}}
[6,3,1,2,4,5,7]=>{{1,2,3,4,5,6},{7}}
[6,3,1,2,4,7,5]=>{{1,2,3,4,5,6,7}}
[6,3,1,2,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[6,3,1,2,5,7,4]=>{{1,2,3,4,6,7},{5}}
[6,3,1,2,7,4,5]=>{{1,2,3,4,6},{5,7}}
[6,3,1,2,7,5,4]=>{{1,2,3,4,5,6,7}}
[6,3,1,4,2,5,7]=>{{1,2,3,5,6},{4},{7}}
[6,3,1,4,2,7,5]=>{{1,2,3,5,6,7},{4}}
[6,3,1,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}}
[6,3,1,4,5,7,2]=>{{1,2,3,6,7},{4},{5}}
[6,3,1,4,7,2,5]=>{{1,2,3,6},{4},{5,7}}
[6,3,1,4,7,5,2]=>{{1,2,3,5,6,7},{4}}
[6,3,1,5,2,4,7]=>{{1,2,3,4,5,6},{7}}
[6,3,1,5,2,7,4]=>{{1,2,3,4,5,6,7}}
[6,3,1,5,4,2,7]=>{{1,2,3,6},{4,5},{7}}
[6,3,1,5,4,7,2]=>{{1,2,3,6,7},{4,5}}
[6,3,1,5,7,2,4]=>{{1,2,3,6},{4,5,7}}
[6,3,1,5,7,4,2]=>{{1,2,3,4,5,6,7}}
[6,3,1,7,2,4,5]=>{{1,2,3,4,5,6,7}}
[6,3,1,7,2,5,4]=>{{1,2,3,5,6},{4,7}}
[6,3,1,7,4,2,5]=>{{1,2,3,6},{4,5,7}}
[6,3,1,7,4,5,2]=>{{1,2,3,4,5,6,7}}
[6,3,1,7,5,2,4]=>{{1,2,3,6},{4,7},{5}}
[6,3,1,7,5,4,2]=>{{1,2,3,4,6,7},{5}}
[6,3,2,1,4,5,7]=>{{1,4,5,6},{2,3},{7}}
[6,3,2,1,4,7,5]=>{{1,4,5,6,7},{2,3}}
[6,3,2,1,5,4,7]=>{{1,4,6},{2,3},{5},{7}}
[6,3,2,1,5,7,4]=>{{1,4,6,7},{2,3},{5}}
[6,3,2,1,7,4,5]=>{{1,4,6},{2,3},{5,7}}
[6,3,2,1,7,5,4]=>{{1,4,5,6,7},{2,3}}
[6,3,2,4,1,5,7]=>{{1,5,6},{2,3},{4},{7}}
[6,3,2,4,1,7,5]=>{{1,5,6,7},{2,3},{4}}
[6,3,2,4,5,1,7]=>{{1,6},{2,3},{4},{5},{7}}
[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}}
[6,3,2,4,7,1,5]=>{{1,6},{2,3},{4},{5,7}}
[6,3,2,4,7,5,1]=>{{1,5,6,7},{2,3},{4}}
[6,3,2,5,1,4,7]=>{{1,4,5,6},{2,3},{7}}
[6,3,2,5,1,7,4]=>{{1,4,5,6,7},{2,3}}
[6,3,2,5,4,1,7]=>{{1,6},{2,3},{4,5},{7}}
[6,3,2,5,4,7,1]=>{{1,6,7},{2,3},{4,5}}
[6,3,2,5,7,1,4]=>{{1,6},{2,3},{4,5,7}}
[6,3,2,5,7,4,1]=>{{1,4,5,6,7},{2,3}}
[6,3,2,7,1,4,5]=>{{1,4,5,6,7},{2,3}}
[6,3,2,7,1,5,4]=>{{1,5,6},{2,3},{4,7}}
[6,3,2,7,4,1,5]=>{{1,6},{2,3},{4,5,7}}
[6,3,2,7,4,5,1]=>{{1,4,5,6,7},{2,3}}
[6,3,2,7,5,1,4]=>{{1,6},{2,3},{4,7},{5}}
[6,3,2,7,5,4,1]=>{{1,4,6,7},{2,3},{5}}
[6,3,4,1,2,5,7]=>{{1,2,3,4,5,6},{7}}
[6,3,4,1,2,7,5]=>{{1,2,3,4,5,6,7}}
[6,3,4,1,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[6,3,4,1,5,7,2]=>{{1,2,3,4,6,7},{5}}
[6,3,4,1,7,2,5]=>{{1,2,3,4,6},{5,7}}
[6,3,4,1,7,5,2]=>{{1,2,3,4,5,6,7}}
[6,3,4,2,1,5,7]=>{{1,5,6},{2,3,4},{7}}
[6,3,4,2,1,7,5]=>{{1,5,6,7},{2,3,4}}
[6,3,4,2,5,1,7]=>{{1,6},{2,3,4},{5},{7}}
[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}}
[6,3,4,2,7,1,5]=>{{1,6},{2,3,4},{5,7}}
[6,3,4,2,7,5,1]=>{{1,5,6,7},{2,3,4}}
[6,3,4,5,1,2,7]=>{{1,2,3,4,5,6},{7}}
[6,3,4,5,1,7,2]=>{{1,2,3,4,5,6,7}}
[6,3,4,5,2,1,7]=>{{1,6},{2,3,4,5},{7}}
[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}}
[6,3,4,5,7,1,2]=>{{1,6},{2,3,4,5,7}}
[6,3,4,5,7,2,1]=>{{1,2,3,4,5,6,7}}
[6,3,4,7,1,2,5]=>{{1,2,3,4,5,6,7}}
[6,3,4,7,1,5,2]=>{{1,5,6},{2,3,4,7}}
[6,3,4,7,2,1,5]=>{{1,6},{2,3,4,5,7}}
[6,3,4,7,2,5,1]=>{{1,2,3,4,5,6,7}}
[6,3,4,7,5,1,2]=>{{1,6},{2,3,4,7},{5}}
[6,3,4,7,5,2,1]=>{{1,2,3,4,6,7},{5}}
[6,3,5,1,2,4,7]=>{{1,4,6},{2,3,5},{7}}
[6,3,5,1,2,7,4]=>{{1,4,6,7},{2,3,5}}
[6,3,5,1,4,2,7]=>{{1,2,3,4,5,6},{7}}
[6,3,5,1,4,7,2]=>{{1,2,3,4,5,6,7}}
[6,3,5,1,7,2,4]=>{{1,2,3,4,5,6,7}}
[6,3,5,1,7,4,2]=>{{1,4,6},{2,3,5,7}}
[6,3,5,2,1,4,7]=>{{1,2,3,4,5,6},{7}}
[6,3,5,2,1,7,4]=>{{1,2,3,4,5,6,7}}
[6,3,5,2,4,1,7]=>{{1,6},{2,3,4,5},{7}}
[6,3,5,2,4,7,1]=>{{1,6,7},{2,3,4,5}}
[6,3,5,2,7,1,4]=>{{1,6},{2,3,4,5,7}}
[6,3,5,2,7,4,1]=>{{1,2,3,4,5,6,7}}
[6,3,5,4,1,2,7]=>{{1,2,3,5,6},{4},{7}}
[6,3,5,4,1,7,2]=>{{1,2,3,5,6,7},{4}}
[6,3,5,4,2,1,7]=>{{1,6},{2,3,5},{4},{7}}
[6,3,5,4,2,7,1]=>{{1,6,7},{2,3,5},{4}}
[6,3,5,4,7,1,2]=>{{1,6},{2,3,5,7},{4}}
[6,3,5,4,7,2,1]=>{{1,2,3,5,6,7},{4}}
[6,3,5,7,1,2,4]=>{{1,2,3,5,6},{4,7}}
[6,3,5,7,1,4,2]=>{{1,2,3,4,5,6,7}}
[6,3,5,7,2,1,4]=>{{1,6},{2,3,5},{4,7}}
[6,3,5,7,2,4,1]=>{{1,4,6,7},{2,3,5}}
[6,3,5,7,4,1,2]=>{{1,6},{2,3,4,5,7}}
[6,3,5,7,4,2,1]=>{{1,2,3,4,5,6,7}}
[6,3,7,1,2,4,5]=>{{1,4,6},{2,3,5,7}}
[6,3,7,1,2,5,4]=>{{1,2,3,4,5,6,7}}
[6,3,7,1,4,2,5]=>{{1,2,3,4,5,6,7}}
[6,3,7,1,4,5,2]=>{{1,4,5,6},{2,3,7}}
[6,3,7,1,5,2,4]=>{{1,2,3,4,6,7},{5}}
[6,3,7,1,5,4,2]=>{{1,4,6},{2,3,7},{5}}
[6,3,7,2,1,4,5]=>{{1,2,3,4,5,6,7}}
[6,3,7,2,1,5,4]=>{{1,5,6},{2,3,4,7}}
[6,3,7,2,4,1,5]=>{{1,6},{2,3,4,5,7}}
[6,3,7,2,4,5,1]=>{{1,2,3,4,5,6,7}}
[6,3,7,2,5,1,4]=>{{1,6},{2,3,4,7},{5}}
[6,3,7,2,5,4,1]=>{{1,2,3,4,6,7},{5}}
[6,3,7,4,1,2,5]=>{{1,2,3,5,6,7},{4}}
[6,3,7,4,1,5,2]=>{{1,5,6},{2,3,7},{4}}
[6,3,7,4,2,1,5]=>{{1,6},{2,3,5,7},{4}}
[6,3,7,4,2,5,1]=>{{1,2,3,5,6,7},{4}}
[6,3,7,4,5,1,2]=>{{1,6},{2,3,7},{4},{5}}
[6,3,7,4,5,2,1]=>{{1,2,3,6,7},{4},{5}}
[6,3,7,5,1,2,4]=>{{1,2,3,4,5,6,7}}
[6,3,7,5,1,4,2]=>{{1,4,5,6},{2,3,7}}
[6,3,7,5,2,1,4]=>{{1,6},{2,3,4,5,7}}
[6,3,7,5,2,4,1]=>{{1,2,3,4,5,6,7}}
[6,3,7,5,4,1,2]=>{{1,6},{2,3,7},{4,5}}
[6,3,7,5,4,2,1]=>{{1,2,3,6,7},{4,5}}
[6,4,1,2,3,5,7]=>{{1,3,5,6},{2,4},{7}}
[6,4,1,2,3,7,5]=>{{1,3,5,6,7},{2,4}}
[6,4,1,2,5,3,7]=>{{1,3,6},{2,4},{5},{7}}
[6,4,1,2,5,7,3]=>{{1,3,6,7},{2,4},{5}}
[6,4,1,2,7,3,5]=>{{1,3,6},{2,4},{5,7}}
[6,4,1,2,7,5,3]=>{{1,3,5,6,7},{2,4}}
[6,4,1,3,2,5,7]=>{{1,2,3,4,5,6},{7}}
[6,4,1,3,2,7,5]=>{{1,2,3,4,5,6,7}}
[6,4,1,3,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[6,4,1,3,5,7,2]=>{{1,2,3,4,6,7},{5}}
[6,4,1,3,7,2,5]=>{{1,2,3,4,6},{5,7}}
[6,4,1,3,7,5,2]=>{{1,2,3,4,5,6,7}}
[6,4,1,5,2,3,7]=>{{1,3,6},{2,4,5},{7}}
[6,4,1,5,2,7,3]=>{{1,3,6,7},{2,4,5}}
[6,4,1,5,3,2,7]=>{{1,2,3,4,5,6},{7}}
[6,4,1,5,3,7,2]=>{{1,2,3,4,5,6,7}}
[6,4,1,5,7,2,3]=>{{1,2,3,4,5,6,7}}
[6,4,1,5,7,3,2]=>{{1,3,6},{2,4,5,7}}
[6,4,1,7,2,3,5]=>{{1,3,6},{2,4,5,7}}
[6,4,1,7,2,5,3]=>{{1,2,3,4,5,6,7}}
[6,4,1,7,3,2,5]=>{{1,2,3,4,5,6,7}}
[6,4,1,7,3,5,2]=>{{1,3,5,6},{2,4,7}}
[6,4,1,7,5,2,3]=>{{1,2,3,4,6,7},{5}}
[6,4,1,7,5,3,2]=>{{1,3,6},{2,4,7},{5}}
[6,4,2,1,3,5,7]=>{{1,2,3,4,5,6},{7}}
[6,4,2,1,3,7,5]=>{{1,2,3,4,5,6,7}}
[6,4,2,1,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[6,4,2,1,5,7,3]=>{{1,2,3,4,6,7},{5}}
[6,4,2,1,7,3,5]=>{{1,2,3,4,6},{5,7}}
[6,4,2,1,7,5,3]=>{{1,2,3,4,5,6,7}}
[6,4,2,3,1,5,7]=>{{1,5,6},{2,3,4},{7}}
[6,4,2,3,1,7,5]=>{{1,5,6,7},{2,3,4}}
[6,4,2,3,5,1,7]=>{{1,6},{2,3,4},{5},{7}}
[6,4,2,3,5,7,1]=>{{1,6,7},{2,3,4},{5}}
[6,4,2,3,7,1,5]=>{{1,6},{2,3,4},{5,7}}
[6,4,2,3,7,5,1]=>{{1,5,6,7},{2,3,4}}
[6,4,2,5,1,3,7]=>{{1,2,3,4,5,6},{7}}
[6,4,2,5,1,7,3]=>{{1,2,3,4,5,6,7}}
[6,4,2,5,3,1,7]=>{{1,6},{2,3,4,5},{7}}
[6,4,2,5,3,7,1]=>{{1,6,7},{2,3,4,5}}
[6,4,2,5,7,1,3]=>{{1,6},{2,3,4,5,7}}
[6,4,2,5,7,3,1]=>{{1,2,3,4,5,6,7}}
[6,4,2,7,1,3,5]=>{{1,2,3,4,5,6,7}}
[6,4,2,7,1,5,3]=>{{1,5,6},{2,3,4,7}}
[6,4,2,7,3,1,5]=>{{1,6},{2,3,4,5,7}}
[6,4,2,7,3,5,1]=>{{1,2,3,4,5,6,7}}
[6,4,2,7,5,1,3]=>{{1,6},{2,3,4,7},{5}}
[6,4,2,7,5,3,1]=>{{1,2,3,4,6,7},{5}}
[6,4,3,1,2,5,7]=>{{1,2,4,5,6},{3},{7}}
[6,4,3,1,2,7,5]=>{{1,2,4,5,6,7},{3}}
[6,4,3,1,5,2,7]=>{{1,2,4,6},{3},{5},{7}}
[6,4,3,1,5,7,2]=>{{1,2,4,6,7},{3},{5}}
[6,4,3,1,7,2,5]=>{{1,2,4,6},{3},{5,7}}
[6,4,3,1,7,5,2]=>{{1,2,4,5,6,7},{3}}
[6,4,3,2,1,5,7]=>{{1,5,6},{2,4},{3},{7}}
[6,4,3,2,1,7,5]=>{{1,5,6,7},{2,4},{3}}
[6,4,3,2,5,1,7]=>{{1,6},{2,4},{3},{5},{7}}
[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}}
[6,4,3,2,7,1,5]=>{{1,6},{2,4},{3},{5,7}}
[6,4,3,2,7,5,1]=>{{1,5,6,7},{2,4},{3}}
[6,4,3,5,1,2,7]=>{{1,2,4,5,6},{3},{7}}
[6,4,3,5,1,7,2]=>{{1,2,4,5,6,7},{3}}
[6,4,3,5,2,1,7]=>{{1,6},{2,4,5},{3},{7}}
[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}}
[6,4,3,5,7,1,2]=>{{1,6},{2,4,5,7},{3}}
[6,4,3,5,7,2,1]=>{{1,2,4,5,6,7},{3}}
[6,4,3,7,1,2,5]=>{{1,2,4,5,6,7},{3}}
[6,4,3,7,1,5,2]=>{{1,5,6},{2,4,7},{3}}
[6,4,3,7,2,1,5]=>{{1,6},{2,4,5,7},{3}}
[6,4,3,7,2,5,1]=>{{1,2,4,5,6,7},{3}}
[6,4,3,7,5,1,2]=>{{1,6},{2,4,7},{3},{5}}
[6,4,3,7,5,2,1]=>{{1,2,4,6,7},{3},{5}}
[6,4,5,1,2,3,7]=>{{1,2,3,4,5,6},{7}}
[6,4,5,1,2,7,3]=>{{1,2,3,4,5,6,7}}
[6,4,5,1,3,2,7]=>{{1,2,4,6},{3,5},{7}}
[6,4,5,1,3,7,2]=>{{1,2,4,6,7},{3,5}}
[6,4,5,1,7,2,3]=>{{1,2,4,6},{3,5,7}}
[6,4,5,1,7,3,2]=>{{1,2,3,4,5,6,7}}
[6,4,5,2,1,3,7]=>{{1,3,5,6},{2,4},{7}}
[6,4,5,2,1,7,3]=>{{1,3,5,6,7},{2,4}}
[6,4,5,2,3,1,7]=>{{1,6},{2,4},{3,5},{7}}
[6,4,5,2,3,7,1]=>{{1,6,7},{2,4},{3,5}}
[6,4,5,2,7,1,3]=>{{1,6},{2,4},{3,5,7}}
[6,4,5,2,7,3,1]=>{{1,3,5,6,7},{2,4}}
[6,4,5,3,1,2,7]=>{{1,2,3,4,5,6},{7}}
[6,4,5,3,1,7,2]=>{{1,2,3,4,5,6,7}}
[6,4,5,3,2,1,7]=>{{1,6},{2,3,4,5},{7}}
[6,4,5,3,2,7,1]=>{{1,6,7},{2,3,4,5}}
[6,4,5,3,7,1,2]=>{{1,6},{2,3,4,5,7}}
[6,4,5,3,7,2,1]=>{{1,2,3,4,5,6,7}}
[6,4,5,7,1,2,3]=>{{1,2,3,4,5,6,7}}
[6,4,5,7,1,3,2]=>{{1,3,5,6},{2,4,7}}
[6,4,5,7,2,1,3]=>{{1,6},{2,3,4,5,7}}
[6,4,5,7,2,3,1]=>{{1,2,3,4,5,6,7}}
[6,4,5,7,3,1,2]=>{{1,6},{2,4,7},{3,5}}
[6,4,5,7,3,2,1]=>{{1,2,4,6,7},{3,5}}
[6,4,7,1,2,3,5]=>{{1,2,3,4,5,6,7}}
[6,4,7,1,2,5,3]=>{{1,2,4,5,6},{3,7}}
[6,4,7,1,3,2,5]=>{{1,2,4,6},{3,5,7}}
[6,4,7,1,3,5,2]=>{{1,2,3,4,5,6,7}}
[6,4,7,1,5,2,3]=>{{1,2,4,6},{3,7},{5}}
[6,4,7,1,5,3,2]=>{{1,2,3,4,6,7},{5}}
[6,4,7,2,1,3,5]=>{{1,3,5,6,7},{2,4}}
[6,4,7,2,1,5,3]=>{{1,5,6},{2,4},{3,7}}
[6,4,7,2,3,1,5]=>{{1,6},{2,4},{3,5,7}}
[6,4,7,2,3,5,1]=>{{1,3,5,6,7},{2,4}}
[6,4,7,2,5,1,3]=>{{1,6},{2,4},{3,7},{5}}
[6,4,7,2,5,3,1]=>{{1,3,6,7},{2,4},{5}}
[6,4,7,3,1,2,5]=>{{1,2,3,4,5,6,7}}
[6,4,7,3,1,5,2]=>{{1,5,6},{2,3,4,7}}
[6,4,7,3,2,1,5]=>{{1,6},{2,3,4,5,7}}
[6,4,7,3,2,5,1]=>{{1,2,3,4,5,6,7}}
[6,4,7,3,5,1,2]=>{{1,6},{2,3,4,7},{5}}
[6,4,7,3,5,2,1]=>{{1,2,3,4,6,7},{5}}
[6,4,7,5,1,2,3]=>{{1,2,4,5,6},{3,7}}
[6,4,7,5,1,3,2]=>{{1,2,3,4,5,6,7}}
[6,4,7,5,2,1,3]=>{{1,6},{2,4,5},{3,7}}
[6,4,7,5,2,3,1]=>{{1,3,6,7},{2,4,5}}
[6,4,7,5,3,1,2]=>{{1,6},{2,3,4,5,7}}
[6,4,7,5,3,2,1]=>{{1,2,3,4,5,6,7}}
[6,5,1,2,3,4,7]=>{{1,2,3,4,5,6},{7}}
[6,5,1,2,3,7,4]=>{{1,2,3,4,5,6,7}}
[6,5,1,2,4,3,7]=>{{1,3,6},{2,4,5},{7}}
[6,5,1,2,4,7,3]=>{{1,3,6,7},{2,4,5}}
[6,5,1,2,7,3,4]=>{{1,3,6},{2,4,5,7}}
[6,5,1,2,7,4,3]=>{{1,2,3,4,5,6,7}}
[6,5,1,3,2,4,7]=>{{1,3,4,6},{2,5},{7}}
[6,5,1,3,2,7,4]=>{{1,3,4,6,7},{2,5}}
[6,5,1,3,4,2,7]=>{{1,2,3,4,5,6},{7}}
[6,5,1,3,4,7,2]=>{{1,2,3,4,5,6,7}}
[6,5,1,3,7,2,4]=>{{1,2,3,4,5,6,7}}
[6,5,1,3,7,4,2]=>{{1,3,4,6},{2,5,7}}
[6,5,1,4,2,3,7]=>{{1,3,6},{2,5},{4},{7}}
[6,5,1,4,2,7,3]=>{{1,3,6,7},{2,5},{4}}
[6,5,1,4,3,2,7]=>{{1,2,3,5,6},{4},{7}}
[6,5,1,4,3,7,2]=>{{1,2,3,5,6,7},{4}}
[6,5,1,4,7,2,3]=>{{1,2,3,5,6,7},{4}}
[6,5,1,4,7,3,2]=>{{1,3,6},{2,5,7},{4}}
[6,5,1,7,2,3,4]=>{{1,3,6},{2,5},{4,7}}
[6,5,1,7,2,4,3]=>{{1,3,4,6,7},{2,5}}
[6,5,1,7,3,2,4]=>{{1,2,3,5,6},{4,7}}
[6,5,1,7,3,4,2]=>{{1,2,3,4,5,6,7}}
[6,5,1,7,4,2,3]=>{{1,2,3,4,5,6,7}}
[6,5,1,7,4,3,2]=>{{1,3,6},{2,4,5,7}}
[6,5,2,1,3,4,7]=>{{1,4,6},{2,3,5},{7}}
[6,5,2,1,3,7,4]=>{{1,4,6,7},{2,3,5}}
[6,5,2,1,4,3,7]=>{{1,2,3,4,5,6},{7}}
[6,5,2,1,4,7,3]=>{{1,2,3,4,5,6,7}}
[6,5,2,1,7,3,4]=>{{1,2,3,4,5,6,7}}
[6,5,2,1,7,4,3]=>{{1,4,6},{2,3,5,7}}
[6,5,2,3,1,4,7]=>{{1,2,3,4,5,6},{7}}
[6,5,2,3,1,7,4]=>{{1,2,3,4,5,6,7}}
[6,5,2,3,4,1,7]=>{{1,6},{2,3,4,5},{7}}
[6,5,2,3,4,7,1]=>{{1,6,7},{2,3,4,5}}
[6,5,2,3,7,1,4]=>{{1,6},{2,3,4,5,7}}
[6,5,2,3,7,4,1]=>{{1,2,3,4,5,6,7}}
[6,5,2,4,1,3,7]=>{{1,2,3,5,6},{4},{7}}
[6,5,2,4,1,7,3]=>{{1,2,3,5,6,7},{4}}
[6,5,2,4,3,1,7]=>{{1,6},{2,3,5},{4},{7}}
[6,5,2,4,3,7,1]=>{{1,6,7},{2,3,5},{4}}
[6,5,2,4,7,1,3]=>{{1,6},{2,3,5,7},{4}}
[6,5,2,4,7,3,1]=>{{1,2,3,5,6,7},{4}}
[6,5,2,7,1,3,4]=>{{1,2,3,5,6},{4,7}}
[6,5,2,7,1,4,3]=>{{1,2,3,4,5,6,7}}
[6,5,2,7,3,1,4]=>{{1,6},{2,3,5},{4,7}}
[6,5,2,7,3,4,1]=>{{1,4,6,7},{2,3,5}}
[6,5,2,7,4,1,3]=>{{1,6},{2,3,4,5,7}}
[6,5,2,7,4,3,1]=>{{1,2,3,4,5,6,7}}
[6,5,3,1,2,4,7]=>{{1,4,6},{2,5},{3},{7}}
[6,5,3,1,2,7,4]=>{{1,4,6,7},{2,5},{3}}
[6,5,3,1,4,2,7]=>{{1,2,4,5,6},{3},{7}}
[6,5,3,1,4,7,2]=>{{1,2,4,5,6,7},{3}}
[6,5,3,1,7,2,4]=>{{1,2,4,5,6,7},{3}}
[6,5,3,1,7,4,2]=>{{1,4,6},{2,5,7},{3}}
[6,5,3,2,1,4,7]=>{{1,2,4,5,6},{3},{7}}
[6,5,3,2,1,7,4]=>{{1,2,4,5,6,7},{3}}
[6,5,3,2,4,1,7]=>{{1,6},{2,4,5},{3},{7}}
[6,5,3,2,4,7,1]=>{{1,6,7},{2,4,5},{3}}
[6,5,3,2,7,1,4]=>{{1,6},{2,4,5,7},{3}}
[6,5,3,2,7,4,1]=>{{1,2,4,5,6,7},{3}}
[6,5,3,4,1,2,7]=>{{1,2,5,6},{3},{4},{7}}
[6,5,3,4,1,7,2]=>{{1,2,5,6,7},{3},{4}}
[6,5,3,4,2,1,7]=>{{1,6},{2,5},{3},{4},{7}}
[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}}
[6,5,3,4,7,1,2]=>{{1,6},{2,5,7},{3},{4}}
[6,5,3,4,7,2,1]=>{{1,2,5,6,7},{3},{4}}
[6,5,3,7,1,2,4]=>{{1,2,5,6},{3},{4,7}}
[6,5,3,7,1,4,2]=>{{1,2,4,5,6,7},{3}}
[6,5,3,7,2,1,4]=>{{1,6},{2,5},{3},{4,7}}
[6,5,3,7,2,4,1]=>{{1,4,6,7},{2,5},{3}}
[6,5,3,7,4,1,2]=>{{1,6},{2,4,5,7},{3}}
[6,5,3,7,4,2,1]=>{{1,2,4,5,6,7},{3}}
[6,5,4,1,2,3,7]=>{{1,3,4,6},{2,5},{7}}
[6,5,4,1,2,7,3]=>{{1,3,4,6,7},{2,5}}
[6,5,4,1,3,2,7]=>{{1,2,3,4,5,6},{7}}
[6,5,4,1,3,7,2]=>{{1,2,3,4,5,6,7}}
[6,5,4,1,7,2,3]=>{{1,2,3,4,5,6,7}}
[6,5,4,1,7,3,2]=>{{1,3,4,6},{2,5,7}}
[6,5,4,2,1,3,7]=>{{1,2,3,4,5,6},{7}}
[6,5,4,2,1,7,3]=>{{1,2,3,4,5,6,7}}
[6,5,4,2,3,1,7]=>{{1,6},{2,3,4,5},{7}}
[6,5,4,2,3,7,1]=>{{1,6,7},{2,3,4,5}}
[6,5,4,2,7,1,3]=>{{1,6},{2,3,4,5,7}}
[6,5,4,2,7,3,1]=>{{1,2,3,4,5,6,7}}
[6,5,4,3,1,2,7]=>{{1,2,5,6},{3,4},{7}}
[6,5,4,3,1,7,2]=>{{1,2,5,6,7},{3,4}}
[6,5,4,3,2,1,7]=>{{1,6},{2,5},{3,4},{7}}
[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}}
[6,5,4,3,7,1,2]=>{{1,6},{2,5,7},{3,4}}
[6,5,4,3,7,2,1]=>{{1,2,5,6,7},{3,4}}
[6,5,4,7,1,2,3]=>{{1,2,5,6},{3,4,7}}
[6,5,4,7,1,3,2]=>{{1,2,3,4,5,6,7}}
[6,5,4,7,2,1,3]=>{{1,6},{2,5},{3,4,7}}
[6,5,4,7,2,3,1]=>{{1,3,4,6,7},{2,5}}
[6,5,4,7,3,1,2]=>{{1,6},{2,3,4,5,7}}
[6,5,4,7,3,2,1]=>{{1,2,3,4,5,6,7}}
[6,5,7,1,2,3,4]=>{{1,3,4,6,7},{2,5}}
[6,5,7,1,2,4,3]=>{{1,4,6},{2,5},{3,7}}
[6,5,7,1,3,2,4]=>{{1,2,3,4,5,6,7}}
[6,5,7,1,3,4,2]=>{{1,4,6},{2,3,5,7}}
[6,5,7,1,4,2,3]=>{{1,2,4,5,6},{3,7}}
[6,5,7,1,4,3,2]=>{{1,2,3,4,5,6,7}}
[6,5,7,2,1,3,4]=>{{1,2,3,4,5,6,7}}
[6,5,7,2,1,4,3]=>{{1,2,4,5,6},{3,7}}
[6,5,7,2,3,1,4]=>{{1,6},{2,3,4,5,7}}
[6,5,7,2,3,4,1]=>{{1,2,3,4,5,6,7}}
[6,5,7,2,4,1,3]=>{{1,6},{2,4,5},{3,7}}
[6,5,7,2,4,3,1]=>{{1,3,6,7},{2,4,5}}
[6,5,7,3,1,2,4]=>{{1,2,5,6},{3,4,7}}
[6,5,7,3,1,4,2]=>{{1,2,3,4,5,6,7}}
[6,5,7,3,2,1,4]=>{{1,6},{2,5},{3,4,7}}
[6,5,7,3,2,4,1]=>{{1,3,4,6,7},{2,5}}
[6,5,7,3,4,1,2]=>{{1,6},{2,3,4,5,7}}
[6,5,7,3,4,2,1]=>{{1,2,3,4,5,6,7}}
[6,5,7,4,1,2,3]=>{{1,2,5,6},{3,7},{4}}
[6,5,7,4,1,3,2]=>{{1,2,3,5,6,7},{4}}
[6,5,7,4,2,1,3]=>{{1,6},{2,5},{3,7},{4}}
[6,5,7,4,2,3,1]=>{{1,3,6,7},{2,5},{4}}
[6,5,7,4,3,1,2]=>{{1,6},{2,3,5,7},{4}}
[6,5,7,4,3,2,1]=>{{1,2,3,5,6,7},{4}}
[6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7}}
[6,7,1,2,3,5,4]=>{{1,3,5,6},{2,4,7}}
[6,7,1,2,4,3,5]=>{{1,3,6},{2,4,5,7}}
[6,7,1,2,4,5,3]=>{{1,2,3,4,5,6,7}}
[6,7,1,2,5,3,4]=>{{1,3,6},{2,4,7},{5}}
[6,7,1,2,5,4,3]=>{{1,2,3,4,6,7},{5}}
[6,7,1,3,2,4,5]=>{{1,3,4,6},{2,5,7}}
[6,7,1,3,2,5,4]=>{{1,2,3,4,5,6,7}}
[6,7,1,3,4,2,5]=>{{1,2,3,4,5,6,7}}
[6,7,1,3,4,5,2]=>{{1,3,4,5,6},{2,7}}
[6,7,1,3,5,2,4]=>{{1,2,3,4,6,7},{5}}
[6,7,1,3,5,4,2]=>{{1,3,4,6},{2,7},{5}}
[6,7,1,4,2,3,5]=>{{1,3,6},{2,5,7},{4}}
[6,7,1,4,2,5,3]=>{{1,2,3,5,6,7},{4}}
[6,7,1,4,3,2,5]=>{{1,2,3,5,6,7},{4}}
[6,7,1,4,3,5,2]=>{{1,3,5,6},{2,7},{4}}
[6,7,1,4,5,2,3]=>{{1,2,3,6,7},{4},{5}}
[6,7,1,4,5,3,2]=>{{1,3,6},{2,7},{4},{5}}
[6,7,1,5,2,3,4]=>{{1,3,6},{2,4,5,7}}
[6,7,1,5,2,4,3]=>{{1,2,3,4,5,6,7}}
[6,7,1,5,3,2,4]=>{{1,2,3,4,5,6,7}}
[6,7,1,5,3,4,2]=>{{1,3,4,5,6},{2,7}}
[6,7,1,5,4,2,3]=>{{1,2,3,6,7},{4,5}}
[6,7,1,5,4,3,2]=>{{1,3,6},{2,7},{4,5}}
[6,7,2,1,3,4,5]=>{{1,4,6},{2,3,5,7}}
[6,7,2,1,3,5,4]=>{{1,2,3,4,5,6,7}}
[6,7,2,1,4,3,5]=>{{1,2,3,4,5,6,7}}
[6,7,2,1,4,5,3]=>{{1,4,5,6},{2,3,7}}
[6,7,2,1,5,3,4]=>{{1,2,3,4,6,7},{5}}
[6,7,2,1,5,4,3]=>{{1,4,6},{2,3,7},{5}}
[6,7,2,3,1,4,5]=>{{1,2,3,4,5,6,7}}
[6,7,2,3,1,5,4]=>{{1,5,6},{2,3,4,7}}
[6,7,2,3,4,1,5]=>{{1,6},{2,3,4,5,7}}
[6,7,2,3,4,5,1]=>{{1,2,3,4,5,6,7}}
[6,7,2,3,5,1,4]=>{{1,6},{2,3,4,7},{5}}
[6,7,2,3,5,4,1]=>{{1,2,3,4,6,7},{5}}
[6,7,2,4,1,3,5]=>{{1,2,3,5,6,7},{4}}
[6,7,2,4,1,5,3]=>{{1,5,6},{2,3,7},{4}}
[6,7,2,4,3,1,5]=>{{1,6},{2,3,5,7},{4}}
[6,7,2,4,3,5,1]=>{{1,2,3,5,6,7},{4}}
[6,7,2,4,5,1,3]=>{{1,6},{2,3,7},{4},{5}}
[6,7,2,4,5,3,1]=>{{1,2,3,6,7},{4},{5}}
[6,7,2,5,1,3,4]=>{{1,2,3,4,5,6,7}}
[6,7,2,5,1,4,3]=>{{1,4,5,6},{2,3,7}}
[6,7,2,5,3,1,4]=>{{1,6},{2,3,4,5,7}}
[6,7,2,5,3,4,1]=>{{1,2,3,4,5,6,7}}
[6,7,2,5,4,1,3]=>{{1,6},{2,3,7},{4,5}}
[6,7,2,5,4,3,1]=>{{1,2,3,6,7},{4,5}}
[6,7,3,1,2,4,5]=>{{1,4,6},{2,5,7},{3}}
[6,7,3,1,2,5,4]=>{{1,2,4,5,6,7},{3}}
[6,7,3,1,4,2,5]=>{{1,2,4,5,6,7},{3}}
[6,7,3,1,4,5,2]=>{{1,4,5,6},{2,7},{3}}
[6,7,3,1,5,2,4]=>{{1,2,4,6,7},{3},{5}}
[6,7,3,1,5,4,2]=>{{1,4,6},{2,7},{3},{5}}
[6,7,3,2,1,4,5]=>{{1,2,4,5,6,7},{3}}
[6,7,3,2,1,5,4]=>{{1,5,6},{2,4,7},{3}}
[6,7,3,2,4,1,5]=>{{1,6},{2,4,5,7},{3}}
[6,7,3,2,4,5,1]=>{{1,2,4,5,6,7},{3}}
[6,7,3,2,5,1,4]=>{{1,6},{2,4,7},{3},{5}}
[6,7,3,2,5,4,1]=>{{1,2,4,6,7},{3},{5}}
[6,7,3,4,1,2,5]=>{{1,2,5,6,7},{3},{4}}
[6,7,3,4,1,5,2]=>{{1,5,6},{2,7},{3},{4}}
[6,7,3,4,2,1,5]=>{{1,6},{2,5,7},{3},{4}}
[6,7,3,4,2,5,1]=>{{1,2,5,6,7},{3},{4}}
[6,7,3,4,5,1,2]=>{{1,6},{2,7},{3},{4},{5}}
[6,7,3,4,5,2,1]=>{{1,2,6,7},{3},{4},{5}}
[6,7,3,5,1,2,4]=>{{1,2,4,5,6,7},{3}}
[6,7,3,5,1,4,2]=>{{1,4,5,6},{2,7},{3}}
[6,7,3,5,2,1,4]=>{{1,6},{2,4,5,7},{3}}
[6,7,3,5,2,4,1]=>{{1,2,4,5,6,7},{3}}
[6,7,3,5,4,1,2]=>{{1,6},{2,7},{3},{4,5}}
[6,7,3,5,4,2,1]=>{{1,2,6,7},{3},{4,5}}
[6,7,4,1,2,3,5]=>{{1,3,4,6},{2,5,7}}
[6,7,4,1,2,5,3]=>{{1,2,3,4,5,6,7}}
[6,7,4,1,3,2,5]=>{{1,2,3,4,5,6,7}}
[6,7,4,1,3,5,2]=>{{1,3,4,5,6},{2,7}}
[6,7,4,1,5,2,3]=>{{1,2,3,4,6,7},{5}}
[6,7,4,1,5,3,2]=>{{1,3,4,6},{2,7},{5}}
[6,7,4,2,1,3,5]=>{{1,2,3,4,5,6,7}}
[6,7,4,2,1,5,3]=>{{1,5,6},{2,3,4,7}}
[6,7,4,2,3,1,5]=>{{1,6},{2,3,4,5,7}}
[6,7,4,2,3,5,1]=>{{1,2,3,4,5,6,7}}
[6,7,4,2,5,1,3]=>{{1,6},{2,3,4,7},{5}}
[6,7,4,2,5,3,1]=>{{1,2,3,4,6,7},{5}}
[6,7,4,3,1,2,5]=>{{1,2,5,6,7},{3,4}}
[6,7,4,3,1,5,2]=>{{1,5,6},{2,7},{3,4}}
[6,7,4,3,2,1,5]=>{{1,6},{2,5,7},{3,4}}
[6,7,4,3,2,5,1]=>{{1,2,5,6,7},{3,4}}
[6,7,4,3,5,1,2]=>{{1,6},{2,7},{3,4},{5}}
[6,7,4,3,5,2,1]=>{{1,2,6,7},{3,4},{5}}
[6,7,4,5,1,2,3]=>{{1,2,3,4,5,6,7}}
[6,7,4,5,1,3,2]=>{{1,3,4,5,6},{2,7}}
[6,7,4,5,2,1,3]=>{{1,6},{2,3,4,5,7}}
[6,7,4,5,2,3,1]=>{{1,2,3,4,5,6,7}}
[6,7,4,5,3,1,2]=>{{1,6},{2,7},{3,4,5}}
[6,7,4,5,3,2,1]=>{{1,2,6,7},{3,4,5}}
[6,7,5,1,2,3,4]=>{{1,2,3,4,5,6,7}}
[6,7,5,1,2,4,3]=>{{1,4,6},{2,3,5,7}}
[6,7,5,1,3,2,4]=>{{1,2,4,6,7},{3,5}}
[6,7,5,1,3,4,2]=>{{1,4,6},{2,7},{3,5}}
[6,7,5,1,4,2,3]=>{{1,2,3,4,5,6,7}}
[6,7,5,1,4,3,2]=>{{1,3,4,5,6},{2,7}}
[6,7,5,2,1,3,4]=>{{1,3,5,6},{2,4,7}}
[6,7,5,2,1,4,3]=>{{1,2,3,4,5,6,7}}
[6,7,5,2,3,1,4]=>{{1,6},{2,4,7},{3,5}}
[6,7,5,2,3,4,1]=>{{1,2,4,6,7},{3,5}}
[6,7,5,2,4,1,3]=>{{1,6},{2,3,4,5,7}}
[6,7,5,2,4,3,1]=>{{1,2,3,4,5,6,7}}
[6,7,5,3,1,2,4]=>{{1,2,3,4,5,6,7}}
[6,7,5,3,1,4,2]=>{{1,3,4,5,6},{2,7}}
[6,7,5,3,2,1,4]=>{{1,6},{2,3,4,5,7}}
[6,7,5,3,2,4,1]=>{{1,2,3,4,5,6,7}}
[6,7,5,3,4,1,2]=>{{1,6},{2,7},{3,4,5}}
[6,7,5,3,4,2,1]=>{{1,2,6,7},{3,4,5}}
[6,7,5,4,1,2,3]=>{{1,2,3,5,6,7},{4}}
[6,7,5,4,1,3,2]=>{{1,3,5,6},{2,7},{4}}
[6,7,5,4,2,1,3]=>{{1,6},{2,3,5,7},{4}}
[6,7,5,4,2,3,1]=>{{1,2,3,5,6,7},{4}}
[6,7,5,4,3,1,2]=>{{1,6},{2,7},{3,5},{4}}
[6,7,5,4,3,2,1]=>{{1,2,6,7},{3,5},{4}}
[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[7,1,2,3,4,6,5]=>{{1,2,3,4,5,7},{6}}
[7,1,2,3,5,4,6]=>{{1,2,3,4,6,7},{5}}
[7,1,2,3,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[7,1,2,3,6,4,5]=>{{1,2,3,4,5,6,7}}
[7,1,2,3,6,5,4]=>{{1,2,3,4,7},{5,6}}
[7,1,2,4,3,5,6]=>{{1,2,3,5,6,7},{4}}
[7,1,2,4,3,6,5]=>{{1,2,3,5,7},{4},{6}}
[7,1,2,4,5,3,6]=>{{1,2,3,6,7},{4},{5}}
[7,1,2,4,5,6,3]=>{{1,2,3,7},{4},{5},{6}}
[7,1,2,4,6,3,5]=>{{1,2,3,5,6,7},{4}}
[7,1,2,4,6,5,3]=>{{1,2,3,7},{4},{5,6}}
[7,1,2,5,3,4,6]=>{{1,2,3,4,5,6,7}}
[7,1,2,5,3,6,4]=>{{1,2,3,4,5,7},{6}}
[7,1,2,5,4,3,6]=>{{1,2,3,6,7},{4,5}}
[7,1,2,5,4,6,3]=>{{1,2,3,7},{4,5},{6}}
[7,1,2,5,6,3,4]=>{{1,2,3,4,5,6,7}}
[7,1,2,5,6,4,3]=>{{1,2,3,7},{4,5,6}}
[7,1,2,6,3,4,5]=>{{1,2,3,5,7},{4,6}}
[7,1,2,6,3,5,4]=>{{1,2,3,4,5,6,7}}
[7,1,2,6,4,3,5]=>{{1,2,3,4,5,6,7}}
[7,1,2,6,4,5,3]=>{{1,2,3,7},{4,5,6}}
[7,1,2,6,5,3,4]=>{{1,2,3,4,6,7},{5}}
[7,1,2,6,5,4,3]=>{{1,2,3,7},{4,6},{5}}
[7,1,3,2,4,5,6]=>{{1,2,4,5,6,7},{3}}
[7,1,3,2,4,6,5]=>{{1,2,4,5,7},{3},{6}}
[7,1,3,2,5,4,6]=>{{1,2,4,6,7},{3},{5}}
[7,1,3,2,5,6,4]=>{{1,2,4,7},{3},{5},{6}}
[7,1,3,2,6,4,5]=>{{1,2,4,5,6,7},{3}}
[7,1,3,2,6,5,4]=>{{1,2,4,7},{3},{5,6}}
[7,1,3,4,2,5,6]=>{{1,2,5,6,7},{3},{4}}
[7,1,3,4,2,6,5]=>{{1,2,5,7},{3},{4},{6}}
[7,1,3,4,5,2,6]=>{{1,2,6,7},{3},{4},{5}}
[7,1,3,4,5,6,2]=>{{1,2,7},{3},{4},{5},{6}}
[7,1,3,4,6,2,5]=>{{1,2,5,6,7},{3},{4}}
[7,1,3,4,6,5,2]=>{{1,2,7},{3},{4},{5,6}}
[7,1,3,5,2,4,6]=>{{1,2,4,5,6,7},{3}}
[7,1,3,5,2,6,4]=>{{1,2,4,5,7},{3},{6}}
[7,1,3,5,4,2,6]=>{{1,2,6,7},{3},{4,5}}
[7,1,3,5,4,6,2]=>{{1,2,7},{3},{4,5},{6}}
[7,1,3,5,6,2,4]=>{{1,2,4,5,6,7},{3}}
[7,1,3,5,6,4,2]=>{{1,2,7},{3},{4,5,6}}
[7,1,3,6,2,4,5]=>{{1,2,5,7},{3},{4,6}}
[7,1,3,6,2,5,4]=>{{1,2,4,5,6,7},{3}}
[7,1,3,6,4,2,5]=>{{1,2,4,5,6,7},{3}}
[7,1,3,6,4,5,2]=>{{1,2,7},{3},{4,5,6}}
[7,1,3,6,5,2,4]=>{{1,2,4,6,7},{3},{5}}
[7,1,3,6,5,4,2]=>{{1,2,7},{3},{4,6},{5}}
[7,1,4,2,3,5,6]=>{{1,2,3,4,5,6,7}}
[7,1,4,2,3,6,5]=>{{1,2,3,4,5,7},{6}}
[7,1,4,2,5,3,6]=>{{1,2,3,4,6,7},{5}}
[7,1,4,2,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[7,1,4,2,6,3,5]=>{{1,2,3,4,5,6,7}}
[7,1,4,2,6,5,3]=>{{1,2,3,4,7},{5,6}}
[7,1,4,3,2,5,6]=>{{1,2,5,6,7},{3,4}}
[7,1,4,3,2,6,5]=>{{1,2,5,7},{3,4},{6}}
[7,1,4,3,5,2,6]=>{{1,2,6,7},{3,4},{5}}
[7,1,4,3,5,6,2]=>{{1,2,7},{3,4},{5},{6}}
[7,1,4,3,6,2,5]=>{{1,2,5,6,7},{3,4}}
[7,1,4,3,6,5,2]=>{{1,2,7},{3,4},{5,6}}
[7,1,4,5,2,3,6]=>{{1,2,3,4,5,6,7}}
[7,1,4,5,2,6,3]=>{{1,2,3,4,5,7},{6}}
[7,1,4,5,3,2,6]=>{{1,2,6,7},{3,4,5}}
[7,1,4,5,3,6,2]=>{{1,2,7},{3,4,5},{6}}
[7,1,4,5,6,2,3]=>{{1,2,3,4,5,6,7}}
[7,1,4,5,6,3,2]=>{{1,2,7},{3,4,5,6}}
[7,1,4,6,2,3,5]=>{{1,2,5,7},{3,4,6}}
[7,1,4,6,2,5,3]=>{{1,2,3,4,5,6,7}}
[7,1,4,6,3,2,5]=>{{1,2,3,4,5,6,7}}
[7,1,4,6,3,5,2]=>{{1,2,7},{3,4,5,6}}
[7,1,4,6,5,2,3]=>{{1,2,3,4,6,7},{5}}
[7,1,4,6,5,3,2]=>{{1,2,7},{3,4,6},{5}}
[7,1,5,2,3,4,6]=>{{1,2,4,6,7},{3,5}}
[7,1,5,2,3,6,4]=>{{1,2,4,7},{3,5},{6}}
[7,1,5,2,4,3,6]=>{{1,2,3,4,5,6,7}}
[7,1,5,2,4,6,3]=>{{1,2,3,4,5,7},{6}}
[7,1,5,2,6,3,4]=>{{1,2,4,7},{3,5,6}}
[7,1,5,2,6,4,3]=>{{1,2,3,4,5,6,7}}
[7,1,5,3,2,4,6]=>{{1,2,3,4,5,6,7}}
[7,1,5,3,2,6,4]=>{{1,2,3,4,5,7},{6}}
[7,1,5,3,4,2,6]=>{{1,2,6,7},{3,4,5}}
[7,1,5,3,4,6,2]=>{{1,2,7},{3,4,5},{6}}
[7,1,5,3,6,2,4]=>{{1,2,3,4,5,6,7}}
[7,1,5,3,6,4,2]=>{{1,2,7},{3,4,5,6}}
[7,1,5,4,2,3,6]=>{{1,2,3,5,6,7},{4}}
[7,1,5,4,2,6,3]=>{{1,2,3,5,7},{4},{6}}
[7,1,5,4,3,2,6]=>{{1,2,6,7},{3,5},{4}}
[7,1,5,4,3,6,2]=>{{1,2,7},{3,5},{4},{6}}
[7,1,5,4,6,2,3]=>{{1,2,3,5,6,7},{4}}
[7,1,5,4,6,3,2]=>{{1,2,7},{3,5,6},{4}}
[7,1,5,6,2,3,4]=>{{1,2,3,4,5,6,7}}
[7,1,5,6,2,4,3]=>{{1,2,3,5,7},{4,6}}
[7,1,5,6,3,2,4]=>{{1,2,4,6,7},{3,5}}
[7,1,5,6,3,4,2]=>{{1,2,7},{3,5},{4,6}}
[7,1,5,6,4,2,3]=>{{1,2,3,4,5,6,7}}
[7,1,5,6,4,3,2]=>{{1,2,7},{3,4,5,6}}
[7,1,6,2,3,4,5]=>{{1,2,3,4,5,6,7}}
[7,1,6,2,3,5,4]=>{{1,2,4,7},{3,5,6}}
[7,1,6,2,4,3,5]=>{{1,2,4,5,7},{3,6}}
[7,1,6,2,4,5,3]=>{{1,2,3,4,5,6,7}}
[7,1,6,2,5,3,4]=>{{1,2,4,7},{3,6},{5}}
[7,1,6,2,5,4,3]=>{{1,2,3,4,6,7},{5}}
[7,1,6,3,2,4,5]=>{{1,2,5,7},{3,4,6}}
[7,1,6,3,2,5,4]=>{{1,2,3,4,5,6,7}}
[7,1,6,3,4,2,5]=>{{1,2,3,4,5,6,7}}
[7,1,6,3,4,5,2]=>{{1,2,7},{3,4,5,6}}
[7,1,6,3,5,2,4]=>{{1,2,3,4,6,7},{5}}
[7,1,6,3,5,4,2]=>{{1,2,7},{3,4,6},{5}}
[7,1,6,4,2,3,5]=>{{1,2,5,7},{3,6},{4}}
[7,1,6,4,2,5,3]=>{{1,2,3,5,6,7},{4}}
[7,1,6,4,3,2,5]=>{{1,2,3,5,6,7},{4}}
[7,1,6,4,3,5,2]=>{{1,2,7},{3,5,6},{4}}
[7,1,6,4,5,2,3]=>{{1,2,3,6,7},{4},{5}}
[7,1,6,4,5,3,2]=>{{1,2,7},{3,6},{4},{5}}
[7,1,6,5,2,3,4]=>{{1,2,4,5,7},{3,6}}
[7,1,6,5,2,4,3]=>{{1,2,3,4,5,6,7}}
[7,1,6,5,3,2,4]=>{{1,2,3,4,5,6,7}}
[7,1,6,5,3,4,2]=>{{1,2,7},{3,4,5,6}}
[7,1,6,5,4,2,3]=>{{1,2,3,6,7},{4,5}}
[7,1,6,5,4,3,2]=>{{1,2,7},{3,6},{4,5}}
[7,2,1,3,4,5,6]=>{{1,3,4,5,6,7},{2}}
[7,2,1,3,4,6,5]=>{{1,3,4,5,7},{2},{6}}
[7,2,1,3,5,4,6]=>{{1,3,4,6,7},{2},{5}}
[7,2,1,3,5,6,4]=>{{1,3,4,7},{2},{5},{6}}
[7,2,1,3,6,4,5]=>{{1,3,4,5,6,7},{2}}
[7,2,1,3,6,5,4]=>{{1,3,4,7},{2},{5,6}}
[7,2,1,4,3,5,6]=>{{1,3,5,6,7},{2},{4}}
[7,2,1,4,3,6,5]=>{{1,3,5,7},{2},{4},{6}}
[7,2,1,4,5,3,6]=>{{1,3,6,7},{2},{4},{5}}
[7,2,1,4,5,6,3]=>{{1,3,7},{2},{4},{5},{6}}
[7,2,1,4,6,3,5]=>{{1,3,5,6,7},{2},{4}}
[7,2,1,4,6,5,3]=>{{1,3,7},{2},{4},{5,6}}
[7,2,1,5,3,4,6]=>{{1,3,4,5,6,7},{2}}
[7,2,1,5,3,6,4]=>{{1,3,4,5,7},{2},{6}}
[7,2,1,5,4,3,6]=>{{1,3,6,7},{2},{4,5}}
[7,2,1,5,4,6,3]=>{{1,3,7},{2},{4,5},{6}}
[7,2,1,5,6,3,4]=>{{1,3,4,5,6,7},{2}}
[7,2,1,5,6,4,3]=>{{1,3,7},{2},{4,5,6}}
[7,2,1,6,3,4,5]=>{{1,3,5,7},{2},{4,6}}
[7,2,1,6,3,5,4]=>{{1,3,4,5,6,7},{2}}
[7,2,1,6,4,3,5]=>{{1,3,4,5,6,7},{2}}
[7,2,1,6,4,5,3]=>{{1,3,7},{2},{4,5,6}}
[7,2,1,6,5,3,4]=>{{1,3,4,6,7},{2},{5}}
[7,2,1,6,5,4,3]=>{{1,3,7},{2},{4,6},{5}}
[7,2,3,1,4,5,6]=>{{1,4,5,6,7},{2},{3}}
[7,2,3,1,4,6,5]=>{{1,4,5,7},{2},{3},{6}}
[7,2,3,1,5,4,6]=>{{1,4,6,7},{2},{3},{5}}
[7,2,3,1,5,6,4]=>{{1,4,7},{2},{3},{5},{6}}
[7,2,3,1,6,4,5]=>{{1,4,5,6,7},{2},{3}}
[7,2,3,1,6,5,4]=>{{1,4,7},{2},{3},{5,6}}
[7,2,3,4,1,5,6]=>{{1,5,6,7},{2},{3},{4}}
[7,2,3,4,1,6,5]=>{{1,5,7},{2},{3},{4},{6}}
[7,2,3,4,5,1,6]=>{{1,6,7},{2},{3},{4},{5}}
[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}}
[7,2,3,4,6,1,5]=>{{1,5,6,7},{2},{3},{4}}
[7,2,3,4,6,5,1]=>{{1,7},{2},{3},{4},{5,6}}
[7,2,3,5,1,4,6]=>{{1,4,5,6,7},{2},{3}}
[7,2,3,5,1,6,4]=>{{1,4,5,7},{2},{3},{6}}
[7,2,3,5,4,1,6]=>{{1,6,7},{2},{3},{4,5}}
[7,2,3,5,4,6,1]=>{{1,7},{2},{3},{4,5},{6}}
[7,2,3,5,6,1,4]=>{{1,4,5,6,7},{2},{3}}
[7,2,3,5,6,4,1]=>{{1,7},{2},{3},{4,5,6}}
[7,2,3,6,1,4,5]=>{{1,5,7},{2},{3},{4,6}}
[7,2,3,6,1,5,4]=>{{1,4,5,6,7},{2},{3}}
[7,2,3,6,4,1,5]=>{{1,4,5,6,7},{2},{3}}
[7,2,3,6,4,5,1]=>{{1,7},{2},{3},{4,5,6}}
[7,2,3,6,5,1,4]=>{{1,4,6,7},{2},{3},{5}}
[7,2,3,6,5,4,1]=>{{1,7},{2},{3},{4,6},{5}}
[7,2,4,1,3,5,6]=>{{1,3,4,5,6,7},{2}}
[7,2,4,1,3,6,5]=>{{1,3,4,5,7},{2},{6}}
[7,2,4,1,5,3,6]=>{{1,3,4,6,7},{2},{5}}
[7,2,4,1,5,6,3]=>{{1,3,4,7},{2},{5},{6}}
[7,2,4,1,6,3,5]=>{{1,3,4,5,6,7},{2}}
[7,2,4,1,6,5,3]=>{{1,3,4,7},{2},{5,6}}
[7,2,4,3,1,5,6]=>{{1,5,6,7},{2},{3,4}}
[7,2,4,3,1,6,5]=>{{1,5,7},{2},{3,4},{6}}
[7,2,4,3,5,1,6]=>{{1,6,7},{2},{3,4},{5}}
[7,2,4,3,5,6,1]=>{{1,7},{2},{3,4},{5},{6}}
[7,2,4,3,6,1,5]=>{{1,5,6,7},{2},{3,4}}
[7,2,4,3,6,5,1]=>{{1,7},{2},{3,4},{5,6}}
[7,2,4,5,1,3,6]=>{{1,3,4,5,6,7},{2}}
[7,2,4,5,1,6,3]=>{{1,3,4,5,7},{2},{6}}
[7,2,4,5,3,1,6]=>{{1,6,7},{2},{3,4,5}}
[7,2,4,5,3,6,1]=>{{1,7},{2},{3,4,5},{6}}
[7,2,4,5,6,1,3]=>{{1,3,4,5,6,7},{2}}
[7,2,4,5,6,3,1]=>{{1,7},{2},{3,4,5,6}}
[7,2,4,6,1,3,5]=>{{1,5,7},{2},{3,4,6}}
[7,2,4,6,1,5,3]=>{{1,3,4,5,6,7},{2}}
[7,2,4,6,3,1,5]=>{{1,3,4,5,6,7},{2}}
[7,2,4,6,3,5,1]=>{{1,7},{2},{3,4,5,6}}
[7,2,4,6,5,1,3]=>{{1,3,4,6,7},{2},{5}}
[7,2,4,6,5,3,1]=>{{1,7},{2},{3,4,6},{5}}
[7,2,5,1,3,4,6]=>{{1,4,6,7},{2},{3,5}}
[7,2,5,1,3,6,4]=>{{1,4,7},{2},{3,5},{6}}
[7,2,5,1,4,3,6]=>{{1,3,4,5,6,7},{2}}
[7,2,5,1,4,6,3]=>{{1,3,4,5,7},{2},{6}}
[7,2,5,1,6,3,4]=>{{1,4,7},{2},{3,5,6}}
[7,2,5,1,6,4,3]=>{{1,3,4,5,6,7},{2}}
[7,2,5,3,1,4,6]=>{{1,3,4,5,6,7},{2}}
[7,2,5,3,1,6,4]=>{{1,3,4,5,7},{2},{6}}
[7,2,5,3,4,1,6]=>{{1,6,7},{2},{3,4,5}}
[7,2,5,3,4,6,1]=>{{1,7},{2},{3,4,5},{6}}
[7,2,5,3,6,1,4]=>{{1,3,4,5,6,7},{2}}
[7,2,5,3,6,4,1]=>{{1,7},{2},{3,4,5,6}}
[7,2,5,4,1,3,6]=>{{1,3,5,6,7},{2},{4}}
[7,2,5,4,1,6,3]=>{{1,3,5,7},{2},{4},{6}}
[7,2,5,4,3,1,6]=>{{1,6,7},{2},{3,5},{4}}
[7,2,5,4,3,6,1]=>{{1,7},{2},{3,5},{4},{6}}
[7,2,5,4,6,1,3]=>{{1,3,5,6,7},{2},{4}}
[7,2,5,4,6,3,1]=>{{1,7},{2},{3,5,6},{4}}
[7,2,5,6,1,3,4]=>{{1,3,4,5,6,7},{2}}
[7,2,5,6,1,4,3]=>{{1,3,5,7},{2},{4,6}}
[7,2,5,6,3,1,4]=>{{1,4,6,7},{2},{3,5}}
[7,2,5,6,3,4,1]=>{{1,7},{2},{3,5},{4,6}}
[7,2,5,6,4,1,3]=>{{1,3,4,5,6,7},{2}}
[7,2,5,6,4,3,1]=>{{1,7},{2},{3,4,5,6}}
[7,2,6,1,3,4,5]=>{{1,3,4,5,6,7},{2}}
[7,2,6,1,3,5,4]=>{{1,4,7},{2},{3,5,6}}
[7,2,6,1,4,3,5]=>{{1,4,5,7},{2},{3,6}}
[7,2,6,1,4,5,3]=>{{1,3,4,5,6,7},{2}}
[7,2,6,1,5,3,4]=>{{1,4,7},{2},{3,6},{5}}
[7,2,6,1,5,4,3]=>{{1,3,4,6,7},{2},{5}}
[7,2,6,3,1,4,5]=>{{1,5,7},{2},{3,4,6}}
[7,2,6,3,1,5,4]=>{{1,3,4,5,6,7},{2}}
[7,2,6,3,4,1,5]=>{{1,3,4,5,6,7},{2}}
[7,2,6,3,4,5,1]=>{{1,7},{2},{3,4,5,6}}
[7,2,6,3,5,1,4]=>{{1,3,4,6,7},{2},{5}}
[7,2,6,3,5,4,1]=>{{1,7},{2},{3,4,6},{5}}
[7,2,6,4,1,3,5]=>{{1,5,7},{2},{3,6},{4}}
[7,2,6,4,1,5,3]=>{{1,3,5,6,7},{2},{4}}
[7,2,6,4,3,1,5]=>{{1,3,5,6,7},{2},{4}}
[7,2,6,4,3,5,1]=>{{1,7},{2},{3,5,6},{4}}
[7,2,6,4,5,1,3]=>{{1,3,6,7},{2},{4},{5}}
[7,2,6,4,5,3,1]=>{{1,7},{2},{3,6},{4},{5}}
[7,2,6,5,1,3,4]=>{{1,4,5,7},{2},{3,6}}
[7,2,6,5,1,4,3]=>{{1,3,4,5,6,7},{2}}
[7,2,6,5,3,1,4]=>{{1,3,4,5,6,7},{2}}
[7,2,6,5,3,4,1]=>{{1,7},{2},{3,4,5,6}}
[7,2,6,5,4,1,3]=>{{1,3,6,7},{2},{4,5}}
[7,2,6,5,4,3,1]=>{{1,7},{2},{3,6},{4,5}}
[7,3,1,2,4,5,6]=>{{1,2,3,4,5,6,7}}
[7,3,1,2,4,6,5]=>{{1,2,3,4,5,7},{6}}
[7,3,1,2,5,4,6]=>{{1,2,3,4,6,7},{5}}
[7,3,1,2,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[7,3,1,2,6,4,5]=>{{1,2,3,4,5,6,7}}
[7,3,1,2,6,5,4]=>{{1,2,3,4,7},{5,6}}
[7,3,1,4,2,5,6]=>{{1,2,3,5,6,7},{4}}
[7,3,1,4,2,6,5]=>{{1,2,3,5,7},{4},{6}}
[7,3,1,4,5,2,6]=>{{1,2,3,6,7},{4},{5}}
[7,3,1,4,5,6,2]=>{{1,2,3,7},{4},{5},{6}}
[7,3,1,4,6,2,5]=>{{1,2,3,5,6,7},{4}}
[7,3,1,4,6,5,2]=>{{1,2,3,7},{4},{5,6}}
[7,3,1,5,2,4,6]=>{{1,2,3,4,5,6,7}}
[7,3,1,5,2,6,4]=>{{1,2,3,4,5,7},{6}}
[7,3,1,5,4,2,6]=>{{1,2,3,6,7},{4,5}}
[7,3,1,5,4,6,2]=>{{1,2,3,7},{4,5},{6}}
[7,3,1,5,6,2,4]=>{{1,2,3,4,5,6,7}}
[7,3,1,5,6,4,2]=>{{1,2,3,7},{4,5,6}}
[7,3,1,6,2,4,5]=>{{1,2,3,5,7},{4,6}}
[7,3,1,6,2,5,4]=>{{1,2,3,4,5,6,7}}
[7,3,1,6,4,2,5]=>{{1,2,3,4,5,6,7}}
[7,3,1,6,4,5,2]=>{{1,2,3,7},{4,5,6}}
[7,3,1,6,5,2,4]=>{{1,2,3,4,6,7},{5}}
[7,3,1,6,5,4,2]=>{{1,2,3,7},{4,6},{5}}
[7,3,2,1,4,5,6]=>{{1,4,5,6,7},{2,3}}
[7,3,2,1,4,6,5]=>{{1,4,5,7},{2,3},{6}}
[7,3,2,1,5,4,6]=>{{1,4,6,7},{2,3},{5}}
[7,3,2,1,5,6,4]=>{{1,4,7},{2,3},{5},{6}}
[7,3,2,1,6,4,5]=>{{1,4,5,6,7},{2,3}}
[7,3,2,1,6,5,4]=>{{1,4,7},{2,3},{5,6}}
[7,3,2,4,1,5,6]=>{{1,5,6,7},{2,3},{4}}
[7,3,2,4,1,6,5]=>{{1,5,7},{2,3},{4},{6}}
[7,3,2,4,5,1,6]=>{{1,6,7},{2,3},{4},{5}}
[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}}
[7,3,2,4,6,1,5]=>{{1,5,6,7},{2,3},{4}}
[7,3,2,4,6,5,1]=>{{1,7},{2,3},{4},{5,6}}
[7,3,2,5,1,4,6]=>{{1,4,5,6,7},{2,3}}
[7,3,2,5,1,6,4]=>{{1,4,5,7},{2,3},{6}}
[7,3,2,5,4,1,6]=>{{1,6,7},{2,3},{4,5}}
[7,3,2,5,4,6,1]=>{{1,7},{2,3},{4,5},{6}}
[7,3,2,5,6,1,4]=>{{1,4,5,6,7},{2,3}}
[7,3,2,5,6,4,1]=>{{1,7},{2,3},{4,5,6}}
[7,3,2,6,1,4,5]=>{{1,5,7},{2,3},{4,6}}
[7,3,2,6,1,5,4]=>{{1,4,5,6,7},{2,3}}
[7,3,2,6,4,1,5]=>{{1,4,5,6,7},{2,3}}
[7,3,2,6,4,5,1]=>{{1,7},{2,3},{4,5,6}}
[7,3,2,6,5,1,4]=>{{1,4,6,7},{2,3},{5}}
[7,3,2,6,5,4,1]=>{{1,7},{2,3},{4,6},{5}}
[7,3,4,1,2,5,6]=>{{1,2,3,4,5,6,7}}
[7,3,4,1,2,6,5]=>{{1,2,3,4,5,7},{6}}
[7,3,4,1,5,2,6]=>{{1,2,3,4,6,7},{5}}
[7,3,4,1,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[7,3,4,1,6,2,5]=>{{1,2,3,4,5,6,7}}
[7,3,4,1,6,5,2]=>{{1,2,3,4,7},{5,6}}
[7,3,4,2,1,5,6]=>{{1,5,6,7},{2,3,4}}
[7,3,4,2,1,6,5]=>{{1,5,7},{2,3,4},{6}}
[7,3,4,2,5,1,6]=>{{1,6,7},{2,3,4},{5}}
[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}}
[7,3,4,2,6,1,5]=>{{1,5,6,7},{2,3,4}}
[7,3,4,2,6,5,1]=>{{1,7},{2,3,4},{5,6}}
[7,3,4,5,1,2,6]=>{{1,2,3,4,5,6,7}}
[7,3,4,5,1,6,2]=>{{1,2,3,4,5,7},{6}}
[7,3,4,5,2,1,6]=>{{1,6,7},{2,3,4,5}}
[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}}
[7,3,4,5,6,1,2]=>{{1,2,3,4,5,6,7}}
[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}}
[7,3,4,6,1,2,5]=>{{1,5,7},{2,3,4,6}}
[7,3,4,6,1,5,2]=>{{1,2,3,4,5,6,7}}
[7,3,4,6,2,1,5]=>{{1,2,3,4,5,6,7}}
[7,3,4,6,2,5,1]=>{{1,7},{2,3,4,5,6}}
[7,3,4,6,5,1,2]=>{{1,2,3,4,6,7},{5}}
[7,3,4,6,5,2,1]=>{{1,7},{2,3,4,6},{5}}
[7,3,5,1,2,4,6]=>{{1,4,6,7},{2,3,5}}
[7,3,5,1,2,6,4]=>{{1,4,7},{2,3,5},{6}}
[7,3,5,1,4,2,6]=>{{1,2,3,4,5,6,7}}
[7,3,5,1,4,6,2]=>{{1,2,3,4,5,7},{6}}
[7,3,5,1,6,2,4]=>{{1,4,7},{2,3,5,6}}
[7,3,5,1,6,4,2]=>{{1,2,3,4,5,6,7}}
[7,3,5,2,1,4,6]=>{{1,2,3,4,5,6,7}}
[7,3,5,2,1,6,4]=>{{1,2,3,4,5,7},{6}}
[7,3,5,2,4,1,6]=>{{1,6,7},{2,3,4,5}}
[7,3,5,2,4,6,1]=>{{1,7},{2,3,4,5},{6}}
[7,3,5,2,6,1,4]=>{{1,2,3,4,5,6,7}}
[7,3,5,2,6,4,1]=>{{1,7},{2,3,4,5,6}}
[7,3,5,4,1,2,6]=>{{1,2,3,5,6,7},{4}}
[7,3,5,4,1,6,2]=>{{1,2,3,5,7},{4},{6}}
[7,3,5,4,2,1,6]=>{{1,6,7},{2,3,5},{4}}
[7,3,5,4,2,6,1]=>{{1,7},{2,3,5},{4},{6}}
[7,3,5,4,6,1,2]=>{{1,2,3,5,6,7},{4}}
[7,3,5,4,6,2,1]=>{{1,7},{2,3,5,6},{4}}
[7,3,5,6,1,2,4]=>{{1,2,3,4,5,6,7}}
[7,3,5,6,1,4,2]=>{{1,2,3,5,7},{4,6}}
[7,3,5,6,2,1,4]=>{{1,4,6,7},{2,3,5}}
[7,3,5,6,2,4,1]=>{{1,7},{2,3,5},{4,6}}
[7,3,5,6,4,1,2]=>{{1,2,3,4,5,6,7}}
[7,3,5,6,4,2,1]=>{{1,7},{2,3,4,5,6}}
[7,3,6,1,2,4,5]=>{{1,2,3,4,5,6,7}}
[7,3,6,1,2,5,4]=>{{1,4,7},{2,3,5,6}}
[7,3,6,1,4,2,5]=>{{1,4,5,7},{2,3,6}}
[7,3,6,1,4,5,2]=>{{1,2,3,4,5,6,7}}
[7,3,6,1,5,2,4]=>{{1,4,7},{2,3,6},{5}}
[7,3,6,1,5,4,2]=>{{1,2,3,4,6,7},{5}}
[7,3,6,2,1,4,5]=>{{1,5,7},{2,3,4,6}}
[7,3,6,2,1,5,4]=>{{1,2,3,4,5,6,7}}
[7,3,6,2,4,1,5]=>{{1,2,3,4,5,6,7}}
[7,3,6,2,4,5,1]=>{{1,7},{2,3,4,5,6}}
[7,3,6,2,5,1,4]=>{{1,2,3,4,6,7},{5}}
[7,3,6,2,5,4,1]=>{{1,7},{2,3,4,6},{5}}
[7,3,6,4,1,2,5]=>{{1,5,7},{2,3,6},{4}}
[7,3,6,4,1,5,2]=>{{1,2,3,5,6,7},{4}}
[7,3,6,4,2,1,5]=>{{1,2,3,5,6,7},{4}}
[7,3,6,4,2,5,1]=>{{1,7},{2,3,5,6},{4}}
[7,3,6,4,5,1,2]=>{{1,2,3,6,7},{4},{5}}
[7,3,6,4,5,2,1]=>{{1,7},{2,3,6},{4},{5}}
[7,3,6,5,1,2,4]=>{{1,4,5,7},{2,3,6}}
[7,3,6,5,1,4,2]=>{{1,2,3,4,5,6,7}}
[7,3,6,5,2,1,4]=>{{1,2,3,4,5,6,7}}
[7,3,6,5,2,4,1]=>{{1,7},{2,3,4,5,6}}
[7,3,6,5,4,1,2]=>{{1,2,3,6,7},{4,5}}
[7,3,6,5,4,2,1]=>{{1,7},{2,3,6},{4,5}}
[7,4,1,2,3,5,6]=>{{1,3,5,6,7},{2,4}}
[7,4,1,2,3,6,5]=>{{1,3,5,7},{2,4},{6}}
[7,4,1,2,5,3,6]=>{{1,3,6,7},{2,4},{5}}
[7,4,1,2,5,6,3]=>{{1,3,7},{2,4},{5},{6}}
[7,4,1,2,6,3,5]=>{{1,3,5,6,7},{2,4}}
[7,4,1,2,6,5,3]=>{{1,3,7},{2,4},{5,6}}
[7,4,1,3,2,5,6]=>{{1,2,3,4,5,6,7}}
[7,4,1,3,2,6,5]=>{{1,2,3,4,5,7},{6}}
[7,4,1,3,5,2,6]=>{{1,2,3,4,6,7},{5}}
[7,4,1,3,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[7,4,1,3,6,2,5]=>{{1,2,3,4,5,6,7}}
[7,4,1,3,6,5,2]=>{{1,2,3,4,7},{5,6}}
[7,4,1,5,2,3,6]=>{{1,3,6,7},{2,4,5}}
[7,4,1,5,2,6,3]=>{{1,3,7},{2,4,5},{6}}
[7,4,1,5,3,2,6]=>{{1,2,3,4,5,6,7}}
[7,4,1,5,3,6,2]=>{{1,2,3,4,5,7},{6}}
[7,4,1,5,6,2,3]=>{{1,3,7},{2,4,5,6}}
[7,4,1,5,6,3,2]=>{{1,2,3,4,5,6,7}}
[7,4,1,6,2,3,5]=>{{1,2,3,4,5,6,7}}
[7,4,1,6,2,5,3]=>{{1,3,7},{2,4,5,6}}
[7,4,1,6,3,2,5]=>{{1,3,5,7},{2,4,6}}
[7,4,1,6,3,5,2]=>{{1,2,3,4,5,6,7}}
[7,4,1,6,5,2,3]=>{{1,3,7},{2,4,6},{5}}
[7,4,1,6,5,3,2]=>{{1,2,3,4,6,7},{5}}
[7,4,2,1,3,5,6]=>{{1,2,3,4,5,6,7}}
[7,4,2,1,3,6,5]=>{{1,2,3,4,5,7},{6}}
[7,4,2,1,5,3,6]=>{{1,2,3,4,6,7},{5}}
[7,4,2,1,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[7,4,2,1,6,3,5]=>{{1,2,3,4,5,6,7}}
[7,4,2,1,6,5,3]=>{{1,2,3,4,7},{5,6}}
[7,4,2,3,1,5,6]=>{{1,5,6,7},{2,3,4}}
[7,4,2,3,1,6,5]=>{{1,5,7},{2,3,4},{6}}
[7,4,2,3,5,1,6]=>{{1,6,7},{2,3,4},{5}}
[7,4,2,3,5,6,1]=>{{1,7},{2,3,4},{5},{6}}
[7,4,2,3,6,1,5]=>{{1,5,6,7},{2,3,4}}
[7,4,2,3,6,5,1]=>{{1,7},{2,3,4},{5,6}}
[7,4,2,5,1,3,6]=>{{1,2,3,4,5,6,7}}
[7,4,2,5,1,6,3]=>{{1,2,3,4,5,7},{6}}
[7,4,2,5,3,1,6]=>{{1,6,7},{2,3,4,5}}
[7,4,2,5,3,6,1]=>{{1,7},{2,3,4,5},{6}}
[7,4,2,5,6,1,3]=>{{1,2,3,4,5,6,7}}
[7,4,2,5,6,3,1]=>{{1,7},{2,3,4,5,6}}
[7,4,2,6,1,3,5]=>{{1,5,7},{2,3,4,6}}
[7,4,2,6,1,5,3]=>{{1,2,3,4,5,6,7}}
[7,4,2,6,3,1,5]=>{{1,2,3,4,5,6,7}}
[7,4,2,6,3,5,1]=>{{1,7},{2,3,4,5,6}}
[7,4,2,6,5,1,3]=>{{1,2,3,4,6,7},{5}}
[7,4,2,6,5,3,1]=>{{1,7},{2,3,4,6},{5}}
[7,4,3,1,2,5,6]=>{{1,2,4,5,6,7},{3}}
[7,4,3,1,2,6,5]=>{{1,2,4,5,7},{3},{6}}
[7,4,3,1,5,2,6]=>{{1,2,4,6,7},{3},{5}}
[7,4,3,1,5,6,2]=>{{1,2,4,7},{3},{5},{6}}
[7,4,3,1,6,2,5]=>{{1,2,4,5,6,7},{3}}
[7,4,3,1,6,5,2]=>{{1,2,4,7},{3},{5,6}}
[7,4,3,2,1,5,6]=>{{1,5,6,7},{2,4},{3}}
[7,4,3,2,1,6,5]=>{{1,5,7},{2,4},{3},{6}}
[7,4,3,2,5,1,6]=>{{1,6,7},{2,4},{3},{5}}
[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}}
[7,4,3,2,6,1,5]=>{{1,5,6,7},{2,4},{3}}
[7,4,3,2,6,5,1]=>{{1,7},{2,4},{3},{5,6}}
[7,4,3,5,1,2,6]=>{{1,2,4,5,6,7},{3}}
[7,4,3,5,1,6,2]=>{{1,2,4,5,7},{3},{6}}
[7,4,3,5,2,1,6]=>{{1,6,7},{2,4,5},{3}}
[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{6}}
[7,4,3,5,6,1,2]=>{{1,2,4,5,6,7},{3}}
[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}}
[7,4,3,6,1,2,5]=>{{1,5,7},{2,4,6},{3}}
[7,4,3,6,1,5,2]=>{{1,2,4,5,6,7},{3}}
[7,4,3,6,2,1,5]=>{{1,2,4,5,6,7},{3}}
[7,4,3,6,2,5,1]=>{{1,7},{2,4,5,6},{3}}
[7,4,3,6,5,1,2]=>{{1,2,4,6,7},{3},{5}}
[7,4,3,6,5,2,1]=>{{1,7},{2,4,6},{3},{5}}
[7,4,5,1,2,3,6]=>{{1,2,3,4,5,6,7}}
[7,4,5,1,2,6,3]=>{{1,2,3,4,5,7},{6}}
[7,4,5,1,3,2,6]=>{{1,2,4,6,7},{3,5}}
[7,4,5,1,3,6,2]=>{{1,2,4,7},{3,5},{6}}
[7,4,5,1,6,2,3]=>{{1,2,3,4,5,6,7}}
[7,4,5,1,6,3,2]=>{{1,2,4,7},{3,5,6}}
[7,4,5,2,1,3,6]=>{{1,3,5,6,7},{2,4}}
[7,4,5,2,1,6,3]=>{{1,3,5,7},{2,4},{6}}
[7,4,5,2,3,1,6]=>{{1,6,7},{2,4},{3,5}}
[7,4,5,2,3,6,1]=>{{1,7},{2,4},{3,5},{6}}
[7,4,5,2,6,1,3]=>{{1,3,5,6,7},{2,4}}
[7,4,5,2,6,3,1]=>{{1,7},{2,4},{3,5,6}}
[7,4,5,3,1,2,6]=>{{1,2,3,4,5,6,7}}
[7,4,5,3,1,6,2]=>{{1,2,3,4,5,7},{6}}
[7,4,5,3,2,1,6]=>{{1,6,7},{2,3,4,5}}
[7,4,5,3,2,6,1]=>{{1,7},{2,3,4,5},{6}}
[7,4,5,3,6,1,2]=>{{1,2,3,4,5,6,7}}
[7,4,5,3,6,2,1]=>{{1,7},{2,3,4,5,6}}
[7,4,5,6,1,2,3]=>{{1,3,5,7},{2,4,6}}
[7,4,5,6,1,3,2]=>{{1,2,3,4,5,6,7}}
[7,4,5,6,2,1,3]=>{{1,2,3,4,5,6,7}}
[7,4,5,6,2,3,1]=>{{1,7},{2,3,4,5,6}}
[7,4,5,6,3,1,2]=>{{1,2,4,6,7},{3,5}}
[7,4,5,6,3,2,1]=>{{1,7},{2,4,6},{3,5}}
[7,4,6,1,2,3,5]=>{{1,2,4,5,7},{3,6}}
[7,4,6,1,2,5,3]=>{{1,2,3,4,5,6,7}}
[7,4,6,1,3,2,5]=>{{1,2,3,4,5,6,7}}
[7,4,6,1,3,5,2]=>{{1,2,4,7},{3,5,6}}
[7,4,6,1,5,2,3]=>{{1,2,3,4,6,7},{5}}
[7,4,6,1,5,3,2]=>{{1,2,4,7},{3,6},{5}}
[7,4,6,2,1,3,5]=>{{1,5,7},{2,4},{3,6}}
[7,4,6,2,1,5,3]=>{{1,3,5,6,7},{2,4}}
[7,4,6,2,3,1,5]=>{{1,3,5,6,7},{2,4}}
[7,4,6,2,3,5,1]=>{{1,7},{2,4},{3,5,6}}
[7,4,6,2,5,1,3]=>{{1,3,6,7},{2,4},{5}}
[7,4,6,2,5,3,1]=>{{1,7},{2,4},{3,6},{5}}
[7,4,6,3,1,2,5]=>{{1,5,7},{2,3,4,6}}
[7,4,6,3,1,5,2]=>{{1,2,3,4,5,6,7}}
[7,4,6,3,2,1,5]=>{{1,2,3,4,5,6,7}}
[7,4,6,3,2,5,1]=>{{1,7},{2,3,4,5,6}}
[7,4,6,3,5,1,2]=>{{1,2,3,4,6,7},{5}}
[7,4,6,3,5,2,1]=>{{1,7},{2,3,4,6},{5}}
[7,4,6,5,1,2,3]=>{{1,2,3,4,5,6,7}}
[7,4,6,5,1,3,2]=>{{1,2,4,5,7},{3,6}}
[7,4,6,5,2,1,3]=>{{1,3,6,7},{2,4,5}}
[7,4,6,5,2,3,1]=>{{1,7},{2,4,5},{3,6}}
[7,4,6,5,3,1,2]=>{{1,2,3,4,5,6,7}}
[7,4,6,5,3,2,1]=>{{1,7},{2,3,4,5,6}}
[7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7}}
[7,5,1,2,3,6,4]=>{{1,2,3,4,5,7},{6}}
[7,5,1,2,4,3,6]=>{{1,3,6,7},{2,4,5}}
[7,5,1,2,4,6,3]=>{{1,3,7},{2,4,5},{6}}
[7,5,1,2,6,3,4]=>{{1,2,3,4,5,6,7}}
[7,5,1,2,6,4,3]=>{{1,3,7},{2,4,5,6}}
[7,5,1,3,2,4,6]=>{{1,3,4,6,7},{2,5}}
[7,5,1,3,2,6,4]=>{{1,3,4,7},{2,5},{6}}
[7,5,1,3,4,2,6]=>{{1,2,3,4,5,6,7}}
[7,5,1,3,4,6,2]=>{{1,2,3,4,5,7},{6}}
[7,5,1,3,6,2,4]=>{{1,3,4,7},{2,5,6}}
[7,5,1,3,6,4,2]=>{{1,2,3,4,5,6,7}}
[7,5,1,4,2,3,6]=>{{1,3,6,7},{2,5},{4}}
[7,5,1,4,2,6,3]=>{{1,3,7},{2,5},{4},{6}}
[7,5,1,4,3,2,6]=>{{1,2,3,5,6,7},{4}}
[7,5,1,4,3,6,2]=>{{1,2,3,5,7},{4},{6}}
[7,5,1,4,6,2,3]=>{{1,3,7},{2,5,6},{4}}
[7,5,1,4,6,3,2]=>{{1,2,3,5,6,7},{4}}
[7,5,1,6,2,3,4]=>{{1,3,4,6,7},{2,5}}
[7,5,1,6,2,4,3]=>{{1,3,7},{2,5},{4,6}}
[7,5,1,6,3,2,4]=>{{1,2,3,4,5,6,7}}
[7,5,1,6,3,4,2]=>{{1,2,3,5,7},{4,6}}
[7,5,1,6,4,2,3]=>{{1,3,7},{2,4,5,6}}
[7,5,1,6,4,3,2]=>{{1,2,3,4,5,6,7}}
[7,5,2,1,3,4,6]=>{{1,4,6,7},{2,3,5}}
[7,5,2,1,3,6,4]=>{{1,4,7},{2,3,5},{6}}
[7,5,2,1,4,3,6]=>{{1,2,3,4,5,6,7}}
[7,5,2,1,4,6,3]=>{{1,2,3,4,5,7},{6}}
[7,5,2,1,6,3,4]=>{{1,4,7},{2,3,5,6}}
[7,5,2,1,6,4,3]=>{{1,2,3,4,5,6,7}}
[7,5,2,3,1,4,6]=>{{1,2,3,4,5,6,7}}
[7,5,2,3,1,6,4]=>{{1,2,3,4,5,7},{6}}
[7,5,2,3,4,1,6]=>{{1,6,7},{2,3,4,5}}
[7,5,2,3,4,6,1]=>{{1,7},{2,3,4,5},{6}}
[7,5,2,3,6,1,4]=>{{1,2,3,4,5,6,7}}
[7,5,2,3,6,4,1]=>{{1,7},{2,3,4,5,6}}
[7,5,2,4,1,3,6]=>{{1,2,3,5,6,7},{4}}
[7,5,2,4,1,6,3]=>{{1,2,3,5,7},{4},{6}}
[7,5,2,4,3,1,6]=>{{1,6,7},{2,3,5},{4}}
[7,5,2,4,3,6,1]=>{{1,7},{2,3,5},{4},{6}}
[7,5,2,4,6,1,3]=>{{1,2,3,5,6,7},{4}}
[7,5,2,4,6,3,1]=>{{1,7},{2,3,5,6},{4}}
[7,5,2,6,1,3,4]=>{{1,2,3,4,5,6,7}}
[7,5,2,6,1,4,3]=>{{1,2,3,5,7},{4,6}}
[7,5,2,6,3,1,4]=>{{1,4,6,7},{2,3,5}}
[7,5,2,6,3,4,1]=>{{1,7},{2,3,5},{4,6}}
[7,5,2,6,4,1,3]=>{{1,2,3,4,5,6,7}}
[7,5,2,6,4,3,1]=>{{1,7},{2,3,4,5,6}}
[7,5,3,1,2,4,6]=>{{1,4,6,7},{2,5},{3}}
[7,5,3,1,2,6,4]=>{{1,4,7},{2,5},{3},{6}}
[7,5,3,1,4,2,6]=>{{1,2,4,5,6,7},{3}}
[7,5,3,1,4,6,2]=>{{1,2,4,5,7},{3},{6}}
[7,5,3,1,6,2,4]=>{{1,4,7},{2,5,6},{3}}
[7,5,3,1,6,4,2]=>{{1,2,4,5,6,7},{3}}
[7,5,3,2,1,4,6]=>{{1,2,4,5,6,7},{3}}
[7,5,3,2,1,6,4]=>{{1,2,4,5,7},{3},{6}}
[7,5,3,2,4,1,6]=>{{1,6,7},{2,4,5},{3}}
[7,5,3,2,4,6,1]=>{{1,7},{2,4,5},{3},{6}}
[7,5,3,2,6,1,4]=>{{1,2,4,5,6,7},{3}}
[7,5,3,2,6,4,1]=>{{1,7},{2,4,5,6},{3}}
[7,5,3,4,1,2,6]=>{{1,2,5,6,7},{3},{4}}
[7,5,3,4,1,6,2]=>{{1,2,5,7},{3},{4},{6}}
[7,5,3,4,2,1,6]=>{{1,6,7},{2,5},{3},{4}}
[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}}
[7,5,3,4,6,1,2]=>{{1,2,5,6,7},{3},{4}}
[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}}
[7,5,3,6,1,2,4]=>{{1,2,4,5,6,7},{3}}
[7,5,3,6,1,4,2]=>{{1,2,5,7},{3},{4,6}}
[7,5,3,6,2,1,4]=>{{1,4,6,7},{2,5},{3}}
[7,5,3,6,2,4,1]=>{{1,7},{2,5},{3},{4,6}}
[7,5,3,6,4,1,2]=>{{1,2,4,5,6,7},{3}}
[7,5,3,6,4,2,1]=>{{1,7},{2,4,5,6},{3}}
[7,5,4,1,2,3,6]=>{{1,3,4,6,7},{2,5}}
[7,5,4,1,2,6,3]=>{{1,3,4,7},{2,5},{6}}
[7,5,4,1,3,2,6]=>{{1,2,3,4,5,6,7}}
[7,5,4,1,3,6,2]=>{{1,2,3,4,5,7},{6}}
[7,5,4,1,6,2,3]=>{{1,3,4,7},{2,5,6}}
[7,5,4,1,6,3,2]=>{{1,2,3,4,5,6,7}}
[7,5,4,2,1,3,6]=>{{1,2,3,4,5,6,7}}
[7,5,4,2,1,6,3]=>{{1,2,3,4,5,7},{6}}
[7,5,4,2,3,1,6]=>{{1,6,7},{2,3,4,5}}
[7,5,4,2,3,6,1]=>{{1,7},{2,3,4,5},{6}}
[7,5,4,2,6,1,3]=>{{1,2,3,4,5,6,7}}
[7,5,4,2,6,3,1]=>{{1,7},{2,3,4,5,6}}
[7,5,4,3,1,2,6]=>{{1,2,5,6,7},{3,4}}
[7,5,4,3,1,6,2]=>{{1,2,5,7},{3,4},{6}}
[7,5,4,3,2,1,6]=>{{1,6,7},{2,5},{3,4}}
[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}}
[7,5,4,3,6,1,2]=>{{1,2,5,6,7},{3,4}}
[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}}
[7,5,4,6,1,2,3]=>{{1,2,3,4,5,6,7}}
[7,5,4,6,1,3,2]=>{{1,2,5,7},{3,4,6}}
[7,5,4,6,2,1,3]=>{{1,3,4,6,7},{2,5}}
[7,5,4,6,2,3,1]=>{{1,7},{2,5},{3,4,6}}
[7,5,4,6,3,1,2]=>{{1,2,3,4,5,6,7}}
[7,5,4,6,3,2,1]=>{{1,7},{2,3,4,5,6}}
[7,5,6,1,2,3,4]=>{{1,4,7},{2,5},{3,6}}
[7,5,6,1,2,4,3]=>{{1,3,4,6,7},{2,5}}
[7,5,6,1,3,2,4]=>{{1,4,7},{2,3,5,6}}
[7,5,6,1,3,4,2]=>{{1,2,3,4,5,6,7}}
[7,5,6,1,4,2,3]=>{{1,2,3,4,5,6,7}}
[7,5,6,1,4,3,2]=>{{1,2,4,5,7},{3,6}}
[7,5,6,2,1,3,4]=>{{1,2,4,5,7},{3,6}}
[7,5,6,2,1,4,3]=>{{1,2,3,4,5,6,7}}
[7,5,6,2,3,1,4]=>{{1,2,3,4,5,6,7}}
[7,5,6,2,3,4,1]=>{{1,7},{2,3,4,5,6}}
[7,5,6,2,4,1,3]=>{{1,3,6,7},{2,4,5}}
[7,5,6,2,4,3,1]=>{{1,7},{2,4,5},{3,6}}
[7,5,6,3,1,2,4]=>{{1,2,3,4,5,6,7}}
[7,5,6,3,1,4,2]=>{{1,2,5,7},{3,4,6}}
[7,5,6,3,2,1,4]=>{{1,3,4,6,7},{2,5}}
[7,5,6,3,2,4,1]=>{{1,7},{2,5},{3,4,6}}
[7,5,6,3,4,1,2]=>{{1,2,3,4,5,6,7}}
[7,5,6,3,4,2,1]=>{{1,7},{2,3,4,5,6}}
[7,5,6,4,1,2,3]=>{{1,2,3,5,6,7},{4}}
[7,5,6,4,1,3,2]=>{{1,2,5,7},{3,6},{4}}
[7,5,6,4,2,1,3]=>{{1,3,6,7},{2,5},{4}}
[7,5,6,4,2,3,1]=>{{1,7},{2,5},{3,6},{4}}
[7,5,6,4,3,1,2]=>{{1,2,3,5,6,7},{4}}
[7,5,6,4,3,2,1]=>{{1,7},{2,3,5,6},{4}}
[7,6,1,2,3,4,5]=>{{1,3,5,7},{2,4,6}}
[7,6,1,2,3,5,4]=>{{1,2,3,4,5,6,7}}
[7,6,1,2,4,3,5]=>{{1,2,3,4,5,6,7}}
[7,6,1,2,4,5,3]=>{{1,3,7},{2,4,5,6}}
[7,6,1,2,5,3,4]=>{{1,2,3,4,6,7},{5}}
[7,6,1,2,5,4,3]=>{{1,3,7},{2,4,6},{5}}
[7,6,1,3,2,4,5]=>{{1,2,3,4,5,6,7}}
[7,6,1,3,2,5,4]=>{{1,3,4,7},{2,5,6}}
[7,6,1,3,4,2,5]=>{{1,3,4,5,7},{2,6}}
[7,6,1,3,4,5,2]=>{{1,2,3,4,5,6,7}}
[7,6,1,3,5,2,4]=>{{1,3,4,7},{2,6},{5}}
[7,6,1,3,5,4,2]=>{{1,2,3,4,6,7},{5}}
[7,6,1,4,2,3,5]=>{{1,2,3,5,6,7},{4}}
[7,6,1,4,2,5,3]=>{{1,3,7},{2,5,6},{4}}
[7,6,1,4,3,2,5]=>{{1,3,5,7},{2,6},{4}}
[7,6,1,4,3,5,2]=>{{1,2,3,5,6,7},{4}}
[7,6,1,4,5,2,3]=>{{1,3,7},{2,6},{4},{5}}
[7,6,1,4,5,3,2]=>{{1,2,3,6,7},{4},{5}}
[7,6,1,5,2,3,4]=>{{1,2,3,4,5,6,7}}
[7,6,1,5,2,4,3]=>{{1,3,7},{2,4,5,6}}
[7,6,1,5,3,2,4]=>{{1,3,4,5,7},{2,6}}
[7,6,1,5,3,4,2]=>{{1,2,3,4,5,6,7}}
[7,6,1,5,4,2,3]=>{{1,3,7},{2,6},{4,5}}
[7,6,1,5,4,3,2]=>{{1,2,3,6,7},{4,5}}
[7,6,2,1,3,4,5]=>{{1,2,3,4,5,6,7}}
[7,6,2,1,3,5,4]=>{{1,4,7},{2,3,5,6}}
[7,6,2,1,4,3,5]=>{{1,4,5,7},{2,3,6}}
[7,6,2,1,4,5,3]=>{{1,2,3,4,5,6,7}}
[7,6,2,1,5,3,4]=>{{1,4,7},{2,3,6},{5}}
[7,6,2,1,5,4,3]=>{{1,2,3,4,6,7},{5}}
[7,6,2,3,1,4,5]=>{{1,5,7},{2,3,4,6}}
[7,6,2,3,1,5,4]=>{{1,2,3,4,5,6,7}}
[7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7}}
[7,6,2,3,4,5,1]=>{{1,7},{2,3,4,5,6}}
[7,6,2,3,5,1,4]=>{{1,2,3,4,6,7},{5}}
[7,6,2,3,5,4,1]=>{{1,7},{2,3,4,6},{5}}
[7,6,2,4,1,3,5]=>{{1,5,7},{2,3,6},{4}}
[7,6,2,4,1,5,3]=>{{1,2,3,5,6,7},{4}}
[7,6,2,4,3,1,5]=>{{1,2,3,5,6,7},{4}}
[7,6,2,4,3,5,1]=>{{1,7},{2,3,5,6},{4}}
[7,6,2,4,5,1,3]=>{{1,2,3,6,7},{4},{5}}
[7,6,2,4,5,3,1]=>{{1,7},{2,3,6},{4},{5}}
[7,6,2,5,1,3,4]=>{{1,4,5,7},{2,3,6}}
[7,6,2,5,1,4,3]=>{{1,2,3,4,5,6,7}}
[7,6,2,5,3,1,4]=>{{1,2,3,4,5,6,7}}
[7,6,2,5,3,4,1]=>{{1,7},{2,3,4,5,6}}
[7,6,2,5,4,1,3]=>{{1,2,3,6,7},{4,5}}
[7,6,2,5,4,3,1]=>{{1,7},{2,3,6},{4,5}}
[7,6,3,1,2,4,5]=>{{1,2,4,5,6,7},{3}}
[7,6,3,1,2,5,4]=>{{1,4,7},{2,5,6},{3}}
[7,6,3,1,4,2,5]=>{{1,4,5,7},{2,6},{3}}
[7,6,3,1,4,5,2]=>{{1,2,4,5,6,7},{3}}
[7,6,3,1,5,2,4]=>{{1,4,7},{2,6},{3},{5}}
[7,6,3,1,5,4,2]=>{{1,2,4,6,7},{3},{5}}
[7,6,3,2,1,4,5]=>{{1,5,7},{2,4,6},{3}}
[7,6,3,2,1,5,4]=>{{1,2,4,5,6,7},{3}}
[7,6,3,2,4,1,5]=>{{1,2,4,5,6,7},{3}}
[7,6,3,2,4,5,1]=>{{1,7},{2,4,5,6},{3}}
[7,6,3,2,5,1,4]=>{{1,2,4,6,7},{3},{5}}
[7,6,3,2,5,4,1]=>{{1,7},{2,4,6},{3},{5}}
[7,6,3,4,1,2,5]=>{{1,5,7},{2,6},{3},{4}}
[7,6,3,4,1,5,2]=>{{1,2,5,6,7},{3},{4}}
[7,6,3,4,2,1,5]=>{{1,2,5,6,7},{3},{4}}
[7,6,3,4,2,5,1]=>{{1,7},{2,5,6},{3},{4}}
[7,6,3,4,5,1,2]=>{{1,2,6,7},{3},{4},{5}}
[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}}
[7,6,3,5,1,2,4]=>{{1,4,5,7},{2,6},{3}}
[7,6,3,5,1,4,2]=>{{1,2,4,5,6,7},{3}}
[7,6,3,5,2,1,4]=>{{1,2,4,5,6,7},{3}}
[7,6,3,5,2,4,1]=>{{1,7},{2,4,5,6},{3}}
[7,6,3,5,4,1,2]=>{{1,2,6,7},{3},{4,5}}
[7,6,3,5,4,2,1]=>{{1,7},{2,6},{3},{4,5}}
[7,6,4,1,2,3,5]=>{{1,2,3,4,5,6,7}}
[7,6,4,1,2,5,3]=>{{1,3,4,7},{2,5,6}}
[7,6,4,1,3,2,5]=>{{1,3,4,5,7},{2,6}}
[7,6,4,1,3,5,2]=>{{1,2,3,4,5,6,7}}
[7,6,4,1,5,2,3]=>{{1,3,4,7},{2,6},{5}}
[7,6,4,1,5,3,2]=>{{1,2,3,4,6,7},{5}}
[7,6,4,2,1,3,5]=>{{1,5,7},{2,3,4,6}}
[7,6,4,2,1,5,3]=>{{1,2,3,4,5,6,7}}
[7,6,4,2,3,1,5]=>{{1,2,3,4,5,6,7}}
[7,6,4,2,3,5,1]=>{{1,7},{2,3,4,5,6}}
[7,6,4,2,5,1,3]=>{{1,2,3,4,6,7},{5}}
[7,6,4,2,5,3,1]=>{{1,7},{2,3,4,6},{5}}
[7,6,4,3,1,2,5]=>{{1,5,7},{2,6},{3,4}}
[7,6,4,3,1,5,2]=>{{1,2,5,6,7},{3,4}}
[7,6,4,3,2,1,5]=>{{1,2,5,6,7},{3,4}}
[7,6,4,3,2,5,1]=>{{1,7},{2,5,6},{3,4}}
[7,6,4,3,5,1,2]=>{{1,2,6,7},{3,4},{5}}
[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}}
[7,6,4,5,1,2,3]=>{{1,3,4,5,7},{2,6}}
[7,6,4,5,1,3,2]=>{{1,2,3,4,5,6,7}}
[7,6,4,5,2,1,3]=>{{1,2,3,4,5,6,7}}
[7,6,4,5,2,3,1]=>{{1,7},{2,3,4,5,6}}
[7,6,4,5,3,1,2]=>{{1,2,6,7},{3,4,5}}
[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}}
[7,6,5,1,2,3,4]=>{{1,4,7},{2,3,5,6}}
[7,6,5,1,2,4,3]=>{{1,2,3,4,5,6,7}}
[7,6,5,1,3,2,4]=>{{1,4,7},{2,6},{3,5}}
[7,6,5,1,3,4,2]=>{{1,2,4,6,7},{3,5}}
[7,6,5,1,4,2,3]=>{{1,3,4,5,7},{2,6}}
[7,6,5,1,4,3,2]=>{{1,2,3,4,5,6,7}}
[7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7}}
[7,6,5,2,1,4,3]=>{{1,3,5,7},{2,4,6}}
[7,6,5,2,3,1,4]=>{{1,2,4,6,7},{3,5}}
[7,6,5,2,3,4,1]=>{{1,7},{2,4,6},{3,5}}
[7,6,5,2,4,1,3]=>{{1,2,3,4,5,6,7}}
[7,6,5,2,4,3,1]=>{{1,7},{2,3,4,5,6}}
[7,6,5,3,1,2,4]=>{{1,3,4,5,7},{2,6}}
[7,6,5,3,1,4,2]=>{{1,2,3,4,5,6,7}}
[7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7}}
[7,6,5,3,2,4,1]=>{{1,7},{2,3,4,5,6}}
[7,6,5,3,4,1,2]=>{{1,2,6,7},{3,4,5}}
[7,6,5,3,4,2,1]=>{{1,7},{2,6},{3,4,5}}
[7,6,5,4,1,2,3]=>{{1,3,5,7},{2,6},{4}}
[7,6,5,4,1,3,2]=>{{1,2,3,5,6,7},{4}}
[7,6,5,4,2,1,3]=>{{1,2,3,5,6,7},{4}}
[7,6,5,4,2,3,1]=>{{1,7},{2,3,5,6},{4}}
[7,6,5,4,3,1,2]=>{{1,2,6,7},{3,5},{4}}
[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}}
[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}}
[7,8,6,5,4,3,2,1]=>{{1,2,7,8},{3,6},{4,5}}
[8,6,7,5,4,3,2,1]=>{{1,8},{2,3,6,7},{4,5}}
[7,6,8,5,4,3,2,1]=>{{1,2,3,6,7,8},{4,5}}
[6,7,8,5,4,3,2,1]=>{{1,3,6,8},{2,7},{4,5}}
[8,7,5,6,4,3,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[7,8,5,6,4,3,2,1]=>{{1,2,7,8},{3,4,5,6}}
[8,6,5,7,4,3,2,1]=>{{1,8},{2,3,4,5,6,7}}
[8,5,6,7,4,3,2,1]=>{{1,8},{2,4,5,7},{3,6}}
[7,6,5,8,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,5,8,4,3,2,1]=>{{1,3,4,5,6,8},{2,7}}
[7,5,6,8,4,3,2,1]=>{{1,2,4,5,7,8},{3,6}}
[6,5,7,8,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,8,4,3,2,1]=>{{1,4,5,8},{2,3,6,7}}
[8,7,6,4,5,3,2,1]=>{{1,8},{2,7},{3,6},{4},{5}}
[7,8,6,4,5,3,2,1]=>{{1,2,7,8},{3,6},{4},{5}}
[8,6,7,4,5,3,2,1]=>{{1,8},{2,3,6,7},{4},{5}}
[7,6,8,4,5,3,2,1]=>{{1,2,3,6,7,8},{4},{5}}
[8,7,5,4,6,3,2,1]=>{{1,8},{2,7},{3,5,6},{4}}
[8,7,4,5,6,3,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[8,6,5,4,7,3,2,1]=>{{1,8},{2,3,5,6,7},{4}}
[8,5,6,4,7,3,2,1]=>{{1,8},{2,5,7},{3,6},{4}}
[8,6,4,5,7,3,2,1]=>{{1,8},{2,3,4,5,6,7}}
[8,4,5,6,7,3,2,1]=>{{1,8},{2,3,4,5,6,7}}
[7,6,5,4,8,3,2,1]=>{{1,2,3,5,6,7,8},{4}}
[6,7,5,4,8,3,2,1]=>{{1,3,5,6,8},{2,7},{4}}
[7,5,6,4,8,3,2,1]=>{{1,2,5,7,8},{3,6},{4}}
[6,5,7,4,8,3,2,1]=>{{1,2,3,5,6,7,8},{4}}
[5,6,7,4,8,3,2,1]=>{{1,5,8},{2,3,6,7},{4}}
[7,6,4,5,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,5,8,3,2,1]=>{{1,3,4,5,6,8},{2,7}}
[7,5,4,6,8,3,2,1]=>{{1,2,5,7,8},{3,4,6}}
[7,4,5,6,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,7,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,6,4,7,8,3,2,1]=>{{1,5,8},{2,3,4,6,7}}
[6,4,5,7,8,3,2,1]=>{{1,3,5,6,8},{2,4,7}}
[5,4,6,7,8,3,2,1]=>{{1,5,8},{2,4,7},{3,6}}
[4,5,6,7,8,3,2,1]=>{{1,2,4,5,7,8},{3,6}}
[8,7,6,5,3,4,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[7,8,6,5,3,4,2,1]=>{{1,2,7,8},{3,4,5,6}}
[8,6,7,5,3,4,2,1]=>{{1,8},{2,3,4,5,6,7}}
[7,6,8,5,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,6,3,4,2,1]=>{{1,8},{2,7},{3,5},{4,6}}
[7,8,5,6,3,4,2,1]=>{{1,2,7,8},{3,5},{4,6}}
[8,5,6,7,3,4,2,1]=>{{1,8},{2,3,4,5,6,7}}
[7,6,5,8,3,4,2,1]=>{{1,2,4,6,7,8},{3,5}}
[6,7,5,8,3,4,2,1]=>{{1,4,6,8},{2,7},{3,5}}
[6,5,7,8,3,4,2,1]=>{{1,4,6,8},{2,3,5,7}}
[5,6,7,8,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,4,3,5,2,1]=>{{1,8},{2,7},{3,5,6},{4}}
[7,8,6,4,3,5,2,1]=>{{1,2,7,8},{3,5,6},{4}}
[8,6,7,4,3,5,2,1]=>{{1,8},{2,3,5,6,7},{4}}
[7,6,8,4,3,5,2,1]=>{{1,2,3,5,6,7,8},{4}}
[6,7,8,4,3,5,2,1]=>{{1,3,5,6,8},{2,7},{4}}
[8,7,6,3,4,5,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[7,8,6,3,4,5,2,1]=>{{1,2,7,8},{3,4,5,6}}
[8,6,7,3,4,5,2,1]=>{{1,8},{2,3,4,5,6,7}}
[7,6,8,3,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,3,4,5,2,1]=>{{1,3,4,5,6,8},{2,7}}
[8,7,5,4,3,6,2,1]=>{{1,8},{2,7},{3,5},{4},{6}}
[7,8,5,4,3,6,2,1]=>{{1,2,7,8},{3,5},{4},{6}}
[8,7,4,5,3,6,2,1]=>{{1,8},{2,7},{3,4,5},{6}}
[8,7,5,3,4,6,2,1]=>{{1,8},{2,7},{3,4,5},{6}}
[7,8,5,3,4,6,2,1]=>{{1,2,7,8},{3,4,5},{6}}
[8,7,4,3,5,6,2,1]=>{{1,8},{2,7},{3,4},{5},{6}}
[8,7,3,4,5,6,2,1]=>{{1,8},{2,7},{3},{4},{5},{6}}
[7,8,3,4,5,6,2,1]=>{{1,2,7,8},{3},{4},{5},{6}}
[8,6,5,4,3,7,2,1]=>{{1,8},{2,6,7},{3,5},{4}}
[8,6,4,3,5,7,2,1]=>{{1,8},{2,6,7},{3,4},{5}}
[8,5,4,3,6,7,2,1]=>{{1,8},{2,5,6,7},{3,4}}
[8,5,3,4,6,7,2,1]=>{{1,8},{2,5,6,7},{3},{4}}
[8,4,3,5,6,7,2,1]=>{{1,8},{2,4,5,6,7},{3}}
[8,3,4,5,6,7,2,1]=>{{1,8},{2,3,4,5,6,7}}
[7,6,5,4,3,8,2,1]=>{{1,2,6,7,8},{3,5},{4}}
[6,7,5,4,3,8,2,1]=>{{1,6,8},{2,7},{3,5},{4}}
[7,5,6,4,3,8,2,1]=>{{1,2,3,5,6,7,8},{4}}
[6,5,7,4,3,8,2,1]=>{{1,6,8},{2,3,5,7},{4}}
[5,6,7,4,3,8,2,1]=>{{1,2,3,5,6,7,8},{4}}
[6,7,4,5,3,8,2,1]=>{{1,6,8},{2,7},{3,4,5}}
[7,5,4,6,3,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,6,3,8,2,1]=>{{1,2,4,6,7,8},{3,5}}
[6,5,4,7,3,8,2,1]=>{{1,6,8},{2,3,4,5,7}}
[6,4,5,7,3,8,2,1]=>{{1,6,8},{2,4,7},{3,5}}
[5,4,6,7,3,8,2,1]=>{{1,3,5,6,8},{2,4,7}}
[4,5,6,7,3,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,3,4,8,2,1]=>{{1,2,6,7,8},{3,4,5}}
[7,6,4,3,5,8,2,1]=>{{1,2,6,7,8},{3,4},{5}}
[7,6,3,4,5,8,2,1]=>{{1,2,6,7,8},{3},{4},{5}}
[7,5,4,3,6,8,2,1]=>{{1,2,5,6,7,8},{3,4}}
[7,5,3,4,6,8,2,1]=>{{1,2,5,6,7,8},{3},{4}}
[7,3,4,5,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,3,7,8,2,1]=>{{1,6,8},{2,5,7},{3,4}}
[6,3,4,5,7,8,2,1]=>{{1,6,8},{2,3,4,5,7}}
[5,4,3,6,7,8,2,1]=>{{1,2,4,5,6,7,8},{3}}
[5,3,4,6,7,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,5,6,7,8,2,1]=>{{1,4,6,8},{2,3,5,7}}
[3,4,5,6,7,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,5,4,2,3,1]=>{{1,8},{2,3,6,7},{4,5}}
[7,8,6,5,4,2,3,1]=>{{1,2,3,6,7,8},{4,5}}
[8,6,7,5,4,2,3,1]=>{{1,8},{2,6},{3,7},{4,5}}
[7,6,8,5,4,2,3,1]=>{{1,3,7,8},{2,6},{4,5}}
[8,7,5,6,4,2,3,1]=>{{1,8},{2,3,4,5,6,7}}
[8,6,5,7,4,2,3,1]=>{{1,8},{2,6},{3,4,5,7}}
[7,6,5,8,4,2,3,1]=>{{1,3,4,5,7,8},{2,6}}
[6,7,5,8,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[7,5,6,8,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,8,4,2,3,1]=>{{1,4,5,8},{2,6},{3,7}}
[8,7,6,4,5,2,3,1]=>{{1,8},{2,3,6,7},{4},{5}}
[8,6,7,4,5,2,3,1]=>{{1,8},{2,6},{3,7},{4},{5}}
[7,6,8,4,5,2,3,1]=>{{1,3,7,8},{2,6},{4},{5}}
[6,7,8,4,5,2,3,1]=>{{1,2,3,6,7,8},{4},{5}}
[8,7,5,4,6,2,3,1]=>{{1,8},{2,3,5,6,7},{4}}
[8,7,4,5,6,2,3,1]=>{{1,8},{2,3,4,5,6,7}}
[7,8,4,5,6,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,4,7,2,3,1]=>{{1,8},{2,6},{3,5,7},{4}}
[8,5,6,4,7,2,3,1]=>{{1,8},{2,3,5,6,7},{4}}
[8,6,4,5,7,2,3,1]=>{{1,8},{2,6},{3,4,5,7}}
[8,4,5,6,7,2,3,1]=>{{1,8},{2,4,6},{3,5,7}}
[7,6,5,4,8,2,3,1]=>{{1,3,5,7,8},{2,6},{4}}
[7,5,6,4,8,2,3,1]=>{{1,2,3,5,6,7,8},{4}}
[6,5,7,4,8,2,3,1]=>{{1,2,5,6,8},{3,7},{4}}
[6,7,4,5,8,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,7,8,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,5,3,2,4,1]=>{{1,8},{2,3,4,5,6,7}}
[7,8,6,5,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,5,3,2,4,1]=>{{1,8},{2,6},{3,4,5,7}}
[7,6,8,5,3,2,4,1]=>{{1,3,4,5,7,8},{2,6}}
[6,7,8,5,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,6,3,2,4,1]=>{{1,8},{2,4,6,7},{3,5}}
[8,6,5,7,3,2,4,1]=>{{1,8},{2,6},{3,5},{4,7}}
[8,5,6,7,3,2,4,1]=>{{1,8},{2,3,5,6},{4,7}}
[7,6,5,8,3,2,4,1]=>{{1,4,7,8},{2,6},{3,5}}
[6,7,5,8,3,2,4,1]=>{{1,2,4,6,7,8},{3,5}}
[5,6,7,8,3,2,4,1]=>{{1,3,4,5,7,8},{2,6}}
[8,7,6,5,2,3,4,1]=>{{1,8},{2,4,5,7},{3,6}}
[8,6,7,5,2,3,4,1]=>{{1,8},{2,3,4,5,6,7}}
[7,6,8,5,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,5,2,3,4,1]=>{{1,3,6,8},{2,4,5,7}}
[8,7,5,6,2,3,4,1]=>{{1,8},{2,3,4,5,6,7}}
[7,8,5,6,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,7,2,3,4,1]=>{{1,8},{2,3,5,6},{4,7}}
[8,5,6,7,2,3,4,1]=>{{1,8},{2,5},{3,6},{4,7}}
[7,6,5,8,2,3,4,1]=>{{1,4,7,8},{2,3,5,6}}
[6,7,5,8,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,7,8,2,3,4,1]=>{{1,3,4,6,7,8},{2,5}}
[5,6,7,8,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,4,3,2,5,1]=>{{1,8},{2,3,5,6,7},{4}}
[7,8,6,4,3,2,5,1]=>{{1,2,3,5,6,7,8},{4}}
[8,6,7,4,3,2,5,1]=>{{1,8},{2,6},{3,5,7},{4}}
[7,6,8,4,3,2,5,1]=>{{1,3,5,7,8},{2,6},{4}}
[6,7,8,4,3,2,5,1]=>{{1,2,3,5,6,7,8},{4}}
[8,7,6,3,4,2,5,1]=>{{1,8},{2,3,4,5,6,7}}
[7,8,6,3,4,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,3,4,2,5,1]=>{{1,8},{2,6},{3,4,5,7}}
[7,6,8,3,4,2,5,1]=>{{1,3,4,5,7,8},{2,6}}
[6,7,8,3,4,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,4,2,3,5,1]=>{{1,2,3,5,6,7,8},{4}}
[6,7,8,4,2,3,5,1]=>{{1,3,6,8},{2,5,7},{4}}
[8,7,6,3,2,4,5,1]=>{{1,8},{2,5,7},{3,4,6}}
[7,8,6,3,2,4,5,1]=>{{1,2,5,7,8},{3,4,6}}
[8,6,7,3,2,4,5,1]=>{{1,8},{2,3,4,5,6,7}}
[6,7,8,3,2,4,5,1]=>{{1,3,4,6,8},{2,5,7}}
[8,7,6,2,3,4,5,1]=>{{1,8},{2,3,4,5,6,7}}
[7,8,6,2,3,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,2,3,4,5,1]=>{{1,8},{2,4,6},{3,5,7}}
[7,6,8,2,3,4,5,1]=>{{1,3,5,7,8},{2,4,6}}
[6,7,8,2,3,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,4,3,2,6,1]=>{{1,8},{2,6,7},{3,5},{4}}
[7,8,5,4,3,2,6,1]=>{{1,2,6,7,8},{3,5},{4}}
[8,7,5,3,4,2,6,1]=>{{1,8},{2,6,7},{3,4,5}}
[7,8,5,3,4,2,6,1]=>{{1,2,6,7,8},{3,4,5}}
[8,7,4,3,5,2,6,1]=>{{1,8},{2,6,7},{3,4},{5}}
[7,8,4,3,5,2,6,1]=>{{1,2,6,7,8},{3,4},{5}}
[8,7,5,4,2,3,6,1]=>{{1,8},{2,3,5,6,7},{4}}
[8,7,5,3,2,4,6,1]=>{{1,8},{2,3,4,5,6,7}}
[8,7,4,3,2,5,6,1]=>{{1,8},{2,5,6,7},{3,4}}
[7,8,4,3,2,5,6,1]=>{{1,2,5,6,7,8},{3,4}}
[7,8,3,4,2,5,6,1]=>{{1,2,5,6,7,8},{3},{4}}
[7,8,4,2,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,8,3,2,4,5,6,1]=>{{1,2,4,5,6,7,8},{3}}
[8,7,2,3,4,5,6,1]=>{{1,8},{2,3,4,5,6,7}}
[7,8,2,3,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,4,3,2,7,1]=>{{1,8},{2,6},{3,5},{4},{7}}
[8,5,6,4,3,2,7,1]=>{{1,8},{2,3,5,6},{4},{7}}
[8,6,4,5,3,2,7,1]=>{{1,8},{2,6},{3,4,5},{7}}
[8,5,4,6,3,2,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[8,6,5,3,4,2,7,1]=>{{1,8},{2,6},{3,4,5},{7}}
[8,5,6,3,4,2,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[8,6,4,3,5,2,7,1]=>{{1,8},{2,6},{3,4},{5},{7}}
[8,6,3,4,5,2,7,1]=>{{1,8},{2,6},{3},{4},{5},{7}}
[8,5,4,3,6,2,7,1]=>{{1,8},{2,5,6},{3,4},{7}}
[8,4,5,3,6,2,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[8,4,3,5,6,2,7,1]=>{{1,8},{2,4,5,6},{3},{7}}
[8,3,4,5,6,2,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[8,6,5,4,2,3,7,1]=>{{1,8},{2,3,5,6},{4},{7}}
[8,5,6,4,2,3,7,1]=>{{1,8},{2,5},{3,6},{4},{7}}
[8,6,5,3,2,4,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[8,6,4,3,2,5,7,1]=>{{1,8},{2,5,6},{3,4},{7}}
[8,6,4,2,3,5,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[8,6,2,3,4,5,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[8,5,4,3,2,6,7,1]=>{{1,8},{2,5},{3,4},{6},{7}}
[8,4,5,3,2,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}}
[8,5,3,4,2,6,7,1]=>{{1,8},{2,5},{3},{4},{6},{7}}
[8,3,4,5,2,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}}
[8,5,4,2,3,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}}
[8,4,5,2,3,6,7,1]=>{{1,8},{2,4},{3,5},{6},{7}}
[8,4,3,2,5,6,7,1]=>{{1,8},{2,4},{3},{5},{6},{7}}
[8,3,4,2,5,6,7,1]=>{{1,8},{2,3,4},{5},{6},{7}}
[8,4,2,3,5,6,7,1]=>{{1,8},{2,3,4},{5},{6},{7}}
[8,3,2,4,5,6,7,1]=>{{1,8},{2,3},{4},{5},{6},{7}}
[8,2,3,4,5,6,7,1]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[7,6,5,4,3,2,8,1]=>{{1,7,8},{2,6},{3,5},{4}}
[6,7,5,4,3,2,8,1]=>{{1,2,6,7,8},{3,5},{4}}
[7,5,6,4,3,2,8,1]=>{{1,7,8},{2,3,5,6},{4}}
[6,5,7,4,3,2,8,1]=>{{1,2,3,5,6,7,8},{4}}
[5,6,7,4,3,2,8,1]=>{{1,3,5,7,8},{2,6},{4}}
[7,6,4,5,3,2,8,1]=>{{1,7,8},{2,6},{3,4,5}}
[6,7,4,5,3,2,8,1]=>{{1,2,6,7,8},{3,4,5}}
[7,4,5,6,3,2,8,1]=>{{1,7,8},{2,4,6},{3,5}}
[6,5,4,7,3,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,5,7,3,2,8,1]=>{{1,2,4,6,7,8},{3,5}}
[4,5,6,7,3,2,8,1]=>{{1,4,7,8},{2,3,5,6}}
[7,6,5,3,4,2,8,1]=>{{1,7,8},{2,6},{3,4,5}}
[7,5,6,3,4,2,8,1]=>{{1,7,8},{2,3,4,5,6}}
[6,5,7,3,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,4,3,5,2,8,1]=>{{1,7,8},{2,6},{3,4},{5}}
[7,6,3,4,5,2,8,1]=>{{1,7,8},{2,6},{3},{4},{5}}
[7,5,4,3,6,2,8,1]=>{{1,7,8},{2,5,6},{3,4}}
[7,4,5,3,6,2,8,1]=>{{1,7,8},{2,3,4,5,6}}
[7,3,4,5,6,2,8,1]=>{{1,7,8},{2,3,4,5,6}}
[6,5,4,3,7,2,8,1]=>{{1,2,5,6,7,8},{3,4}}
[6,4,5,3,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,6,3,7,2,8,1]=>{{1,5,7,8},{2,3,4,6}}
[4,5,6,3,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,3,4,7,2,8,1]=>{{1,2,5,6,7,8},{3},{4}}
[5,6,3,4,7,2,8,1]=>{{1,5,7,8},{2,6},{3},{4}}
[6,4,3,5,7,2,8,1]=>{{1,2,4,5,6,7,8},{3}}
[6,3,4,5,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,6,7,2,8,1]=>{{1,5,7,8},{2,4,6},{3}}
[4,5,3,6,7,2,8,1]=>{{1,2,4,5,6,7,8},{3}}
[4,3,5,6,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[3,4,5,6,7,2,8,1]=>{{1,3,5,7,8},{2,4,6}}
[7,6,5,4,2,3,8,1]=>{{1,7,8},{2,3,5,6},{4}}
[6,7,5,4,2,3,8,1]=>{{1,2,3,5,6,7,8},{4}}
[7,5,6,4,2,3,8,1]=>{{1,7,8},{2,5},{3,6},{4}}
[6,5,7,4,2,3,8,1]=>{{1,3,6,7,8},{2,5},{4}}
[5,6,7,4,2,3,8,1]=>{{1,2,3,5,6,7,8},{4}}
[7,6,4,5,2,3,8,1]=>{{1,7,8},{2,3,4,5,6}}
[6,7,4,5,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[7,5,4,6,2,3,8,1]=>{{1,7,8},{2,5},{3,4,6}}
[7,4,5,6,2,3,8,1]=>{{1,7,8},{2,3,4,5,6}}
[6,5,4,7,2,3,8,1]=>{{1,3,4,6,7,8},{2,5}}
[5,6,4,7,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,6,7,2,3,8,1]=>{{1,2,4,5,7,8},{3,6}}
[4,5,6,7,2,3,8,1]=>{{1,4,7,8},{2,5},{3,6}}
[7,6,5,3,2,4,8,1]=>{{1,7,8},{2,3,4,5,6}}
[6,7,5,3,2,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,7,3,2,4,8,1]=>{{1,3,4,6,7,8},{2,5}}
[7,6,5,2,3,4,8,1]=>{{1,7,8},{2,4,6},{3,5}}
[7,5,6,2,3,4,8,1]=>{{1,7,8},{2,3,4,5,6}}
[5,6,7,2,3,4,8,1]=>{{1,3,5,7,8},{2,4,6}}
[6,7,4,3,2,5,8,1]=>{{1,2,5,6,7,8},{3,4}}
[7,6,4,2,3,5,8,1]=>{{1,7,8},{2,3,4,5,6}}
[7,6,3,2,4,5,8,1]=>{{1,7,8},{2,4,5,6},{3}}
[6,7,3,2,4,5,8,1]=>{{1,2,4,5,6,7,8},{3}}
[7,6,2,3,4,5,8,1]=>{{1,7,8},{2,3,4,5,6}}
[6,7,2,3,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[7,5,4,3,2,6,8,1]=>{{1,7,8},{2,5},{3,4},{6}}
[7,4,3,5,2,6,8,1]=>{{1,7,8},{2,4,5},{3},{6}}
[7,5,4,2,3,6,8,1]=>{{1,7,8},{2,3,4,5},{6}}
[7,4,5,2,3,6,8,1]=>{{1,7,8},{2,4},{3,5},{6}}
[7,5,3,2,4,6,8,1]=>{{1,7,8},{2,4,5},{3},{6}}
[7,5,2,3,4,6,8,1]=>{{1,7,8},{2,3,4,5},{6}}
[7,4,3,2,5,6,8,1]=>{{1,7,8},{2,4},{3},{5},{6}}
[7,3,2,4,5,6,8,1]=>{{1,7,8},{2,3},{4},{5},{6}}
[7,2,3,4,5,6,8,1]=>{{1,7,8},{2},{3},{4},{5},{6}}
[6,5,4,3,2,7,8,1]=>{{1,6,7,8},{2,5},{3,4}}
[5,4,6,3,2,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,3,2,7,8,1]=>{{1,3,4,6,7,8},{2,5}}
[6,3,4,5,2,7,8,1]=>{{1,6,7,8},{2,3,4,5}}
[5,4,3,6,2,7,8,1]=>{{1,2,4,5,6,7,8},{3}}
[4,3,5,6,2,7,8,1]=>{{1,4,6,7,8},{2,3,5}}
[3,4,5,6,2,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,2,3,7,8,1]=>{{1,6,7,8},{2,3,4,5}}
[5,6,4,2,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,5,2,3,7,8,1]=>{{1,6,7,8},{2,4},{3,5}}
[5,4,6,2,3,7,8,1]=>{{1,3,5,6,7,8},{2,4}}
[4,5,6,2,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,3,2,4,7,8,1]=>{{1,6,7,8},{2,4,5},{3}}
[6,5,2,3,4,7,8,1]=>{{1,6,7,8},{2,3,4,5}}
[6,2,3,4,5,7,8,1]=>{{1,6,7,8},{2},{3},{4},{5}}
[5,4,3,2,6,7,8,1]=>{{1,5,6,7,8},{2,4},{3}}
[4,5,3,2,6,7,8,1]=>{{1,2,4,5,6,7,8},{3}}
[5,3,4,2,6,7,8,1]=>{{1,5,6,7,8},{2,3,4}}
[4,3,5,2,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[3,4,5,2,6,7,8,1]=>{{1,3,5,6,7,8},{2,4}}
[5,4,2,3,6,7,8,1]=>{{1,5,6,7,8},{2,3,4}}
[4,5,2,3,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,3,2,4,6,7,8,1]=>{{1,5,6,7,8},{2,3},{4}}
[5,2,3,4,6,7,8,1]=>{{1,5,6,7,8},{2},{3},{4}}
[4,3,2,5,6,7,8,1]=>{{1,4,5,6,7,8},{2,3}}
[3,4,2,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,2,3,5,6,7,8,1]=>{{1,4,5,6,7,8},{2},{3}}
[3,2,4,5,6,7,8,1]=>{{1,3,4,5,6,7,8},{2}}
[2,3,4,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,5,4,3,1,2]=>{{1,2,7,8},{3,6},{4,5}}
[7,8,6,5,4,3,1,2]=>{{1,7},{2,8},{3,6},{4,5}}
[8,6,7,5,4,3,1,2]=>{{1,2,3,6,7,8},{4,5}}
[7,6,8,5,4,3,1,2]=>{{1,7},{2,3,6,8},{4,5}}
[6,7,8,5,4,3,1,2]=>{{1,2,3,6,7,8},{4,5}}
[8,7,5,6,4,3,1,2]=>{{1,2,7,8},{3,4,5,6}}
[7,8,5,6,4,3,1,2]=>{{1,7},{2,8},{3,4,5,6}}
[8,6,5,7,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,8,4,3,1,2]=>{{1,7},{2,3,4,5,6,8}}
[6,7,5,8,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,7,8,4,3,1,2]=>{{1,3,6,7},{2,4,5,8}}
[5,6,7,8,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,4,5,3,1,2]=>{{1,2,7,8},{3,6},{4},{5}}
[7,8,6,4,5,3,1,2]=>{{1,7},{2,8},{3,6},{4},{5}}
[8,6,7,4,5,3,1,2]=>{{1,2,3,6,7,8},{4},{5}}
[6,7,8,4,5,3,1,2]=>{{1,2,3,6,7,8},{4},{5}}
[8,7,5,4,6,3,1,2]=>{{1,2,7,8},{3,5,6},{4}}
[7,8,4,5,6,3,1,2]=>{{1,7},{2,8},{3,4,5,6}}
[8,5,6,4,7,3,1,2]=>{{1,2,5,7,8},{3,6},{4}}
[8,6,4,5,7,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,6,7,3,1,2]=>{{1,2,5,7,8},{3,4,6}}
[7,6,5,4,8,3,1,2]=>{{1,7},{2,3,5,6,8},{4}}
[7,5,6,4,8,3,1,2]=>{{1,7},{2,5,8},{3,6},{4}}
[6,5,7,4,8,3,1,2]=>{{1,3,6,7},{2,5,8},{4}}
[7,6,4,5,8,3,1,2]=>{{1,7},{2,3,4,5,6,8}}
[6,7,4,5,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,7,8,3,1,2]=>{{1,3,4,6,7},{2,5,8}}
[5,6,4,7,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,6,7,8,3,1,2]=>{{1,2,4,5,7,8},{3,6}}
[4,5,6,7,8,3,1,2]=>{{1,4,7},{2,5,8},{3,6}}
[8,7,6,5,3,4,1,2]=>{{1,2,7,8},{3,4,5,6}}
[7,8,6,5,3,4,1,2]=>{{1,7},{2,8},{3,4,5,6}}
[7,6,8,5,3,4,1,2]=>{{1,7},{2,3,4,5,6,8}}
[6,7,8,5,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,6,3,4,1,2]=>{{1,2,7,8},{3,5},{4,6}}
[7,8,5,6,3,4,1,2]=>{{1,7},{2,8},{3,5},{4,6}}
[8,6,5,7,3,4,1,2]=>{{1,2,4,6,7,8},{3,5}}
[8,5,6,7,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,8,3,4,1,2]=>{{1,7},{2,4,6,8},{3,5}}
[6,7,5,8,3,4,1,2]=>{{1,2,4,6,7,8},{3,5}}
[7,5,6,8,3,4,1,2]=>{{1,7},{2,3,4,5,6,8}}
[6,5,7,8,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,8,3,4,1,2]=>{{1,3,5,7},{2,4,6,8}}
[6,7,8,4,3,5,1,2]=>{{1,2,3,5,6,7,8},{4}}
[8,7,6,3,4,5,1,2]=>{{1,2,7,8},{3,4,5,6}}
[7,8,6,3,4,5,1,2]=>{{1,7},{2,8},{3,4,5,6}}
[8,6,7,3,4,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,4,3,6,1,2]=>{{1,7},{2,8},{3,5},{4},{6}}
[8,7,4,5,3,6,1,2]=>{{1,2,7,8},{3,4,5},{6}}
[7,8,4,5,3,6,1,2]=>{{1,7},{2,8},{3,4,5},{6}}
[7,8,5,3,4,6,1,2]=>{{1,7},{2,8},{3,4,5},{6}}
[8,7,4,3,5,6,1,2]=>{{1,2,7,8},{3,4},{5},{6}}
[7,8,4,3,5,6,1,2]=>{{1,7},{2,8},{3,4},{5},{6}}
[8,7,3,4,5,6,1,2]=>{{1,2,7,8},{3},{4},{5},{6}}
[7,8,3,4,5,6,1,2]=>{{1,7},{2,8},{3},{4},{5},{6}}
[8,6,5,4,3,7,1,2]=>{{1,2,6,7,8},{3,5},{4}}
[8,5,4,6,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,3,6,7,1,2]=>{{1,2,5,6,7,8},{3,4}}
[8,5,3,4,6,7,1,2]=>{{1,2,5,6,7,8},{3},{4}}
[8,4,3,5,6,7,1,2]=>{{1,2,4,5,6,7,8},{3}}
[8,3,4,5,6,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,4,3,8,1,2]=>{{1,7},{2,6,8},{3,5},{4}}
[7,5,6,4,3,8,1,2]=>{{1,7},{2,3,5,6,8},{4}}
[5,6,7,4,3,8,1,2]=>{{1,3,5,7},{2,6,8},{4}}
[6,7,4,5,3,8,1,2]=>{{1,2,6,7,8},{3,4,5}}
[7,5,4,6,3,8,1,2]=>{{1,7},{2,3,4,5,6,8}}
[6,5,4,7,3,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,4,7,3,8,1,2]=>{{1,3,4,5,7},{2,6,8}}
[4,5,6,7,3,8,1,2]=>{{1,4,7},{2,3,5,6,8}}
[7,6,5,3,4,8,1,2]=>{{1,7},{2,6,8},{3,4,5}}
[7,6,3,4,5,8,1,2]=>{{1,7},{2,6,8},{3},{4},{5}}
[7,5,4,3,6,8,1,2]=>{{1,7},{2,5,6,8},{3,4}}
[7,4,5,3,6,8,1,2]=>{{1,7},{2,3,4,5,6,8}}
[7,5,3,4,6,8,1,2]=>{{1,7},{2,5,6,8},{3},{4}}
[7,3,4,5,6,8,1,2]=>{{1,7},{2,3,4,5,6,8}}
[6,5,4,3,7,8,1,2]=>{{1,2,5,6,7,8},{3,4}}
[5,6,4,3,7,8,1,2]=>{{1,5,7},{2,6,8},{3,4}}
[5,4,6,3,7,8,1,2]=>{{1,5,7},{2,3,4,6,8}}
[4,5,6,3,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,3,4,7,8,1,2]=>{{1,5,7},{2,6,8},{3},{4}}
[6,4,3,5,7,8,1,2]=>{{1,2,4,5,6,7,8},{3}}
[6,3,4,5,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,6,7,8,1,2]=>{{1,5,7},{2,4,6,8},{3}}
[4,5,3,6,7,8,1,2]=>{{1,2,4,5,6,7,8},{3}}
[5,3,4,6,7,8,1,2]=>{{1,5,7},{2,3,4,6,8}}
[4,3,5,6,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[3,4,5,6,7,8,1,2]=>{{1,3,5,7},{2,4,6,8}}
[8,7,6,5,4,2,1,3]=>{{1,2,3,6,7,8},{4,5}}
[7,8,6,5,4,2,1,3]=>{{1,7},{2,3,6,8},{4,5}}
[8,6,7,5,4,2,1,3]=>{{1,3,7,8},{2,6},{4,5}}
[7,6,8,5,4,2,1,3]=>{{1,7},{2,6},{3,8},{4,5}}
[6,7,8,5,4,2,1,3]=>{{1,2,6,7},{3,8},{4,5}}
[8,7,5,6,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,6,4,2,1,3]=>{{1,7},{2,3,4,5,6,8}}
[7,6,5,8,4,2,1,3]=>{{1,7},{2,6},{3,4,5,8}}
[6,7,5,8,4,2,1,3]=>{{1,2,6,7},{3,4,5,8}}
[7,5,6,8,4,2,1,3]=>{{1,7},{2,3,4,5,6,8}}
[6,5,7,8,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,8,4,2,1,3]=>{{1,3,4,5,7,8},{2,6}}
[8,7,6,4,5,2,1,3]=>{{1,2,3,6,7,8},{4},{5}}
[7,6,8,4,5,2,1,3]=>{{1,7},{2,6},{3,8},{4},{5}}
[8,4,5,6,7,2,1,3]=>{{1,3,5,7,8},{2,4,6}}
[6,7,5,4,8,2,1,3]=>{{1,2,6,7},{3,5,8},{4}}
[6,5,7,4,8,2,1,3]=>{{1,2,3,5,6,7,8},{4}}
[5,6,7,4,8,2,1,3]=>{{1,3,5,7,8},{2,6},{4}}
[7,6,4,5,8,2,1,3]=>{{1,7},{2,6},{3,4,5,8}}
[7,4,5,6,8,2,1,3]=>{{1,7},{2,4,6},{3,5,8}}
[5,4,6,7,8,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,7,8,2,1,3]=>{{1,4,7},{2,3,5,6,8}}
[8,7,6,5,4,1,2,3]=>{{1,3,6,8},{2,7},{4,5}}
[7,8,6,5,4,1,2,3]=>{{1,2,3,6,7,8},{4,5}}
[7,6,8,5,4,1,2,3]=>{{1,2,6,7},{3,8},{4,5}}
[6,7,8,5,4,1,2,3]=>{{1,6},{2,7},{3,8},{4,5}}
[7,8,5,6,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,7,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,7,4,1,2,3]=>{{1,3,6,8},{2,4,5,7}}
[7,6,5,8,4,1,2,3]=>{{1,2,6,7},{3,4,5,8}}
[6,7,5,8,4,1,2,3]=>{{1,6},{2,7},{3,4,5,8}}
[7,5,6,8,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,7,8,4,1,2,3]=>{{1,6},{2,3,4,5,7,8}}
[5,6,7,8,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,4,5,1,2,3]=>{{1,3,6,8},{2,7},{4},{5}}
[8,6,7,4,5,1,2,3]=>{{1,2,3,6,7,8},{4},{5}}
[6,7,8,4,5,1,2,3]=>{{1,6},{2,7},{3,8},{4},{5}}
[8,7,5,4,6,1,2,3]=>{{1,3,5,6,8},{2,7},{4}}
[7,8,5,4,6,1,2,3]=>{{1,2,3,5,6,7,8},{4}}
[8,7,4,5,6,1,2,3]=>{{1,3,4,5,6,8},{2,7}}
[7,8,4,5,6,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,4,7,1,2,3]=>{{1,2,3,5,6,7,8},{4}}
[8,5,6,4,7,1,2,3]=>{{1,3,6,8},{2,5,7},{4}}
[8,6,4,5,7,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,6,7,1,2,3]=>{{1,3,4,6,8},{2,5,7}}
[8,4,5,6,7,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,4,8,1,2,3]=>{{1,2,6,7},{3,5,8},{4}}
[6,5,7,4,8,1,2,3]=>{{1,6},{2,3,5,7,8},{4}}
[5,6,7,4,8,1,2,3]=>{{1,2,3,5,6,7,8},{4}}
[6,7,4,5,8,1,2,3]=>{{1,6},{2,7},{3,4,5,8}}
[7,5,4,6,8,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,7,8,1,2,3]=>{{1,6},{2,3,4,5,7,8}}
[5,6,4,7,8,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,4,6,7,8,1,2,3]=>{{1,3,5,6,8},{2,4,7}}
[4,5,6,7,8,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,6,5,3,2,1,4]=>{{1,7},{2,3,4,5,6,8}}
[8,6,7,5,3,2,1,4]=>{{1,3,4,5,7,8},{2,6}}
[7,6,8,5,3,2,1,4]=>{{1,7},{2,6},{3,4,5,8}}
[6,7,8,5,3,2,1,4]=>{{1,2,6,7},{3,4,5,8}}
[8,7,5,6,3,2,1,4]=>{{1,2,4,6,7,8},{3,5}}
[7,8,5,6,3,2,1,4]=>{{1,7},{2,4,6,8},{3,5}}
[8,6,5,7,3,2,1,4]=>{{1,4,7,8},{2,6},{3,5}}
[8,5,6,7,3,2,1,4]=>{{1,4,7,8},{2,3,5,6}}
[7,6,5,8,3,2,1,4]=>{{1,7},{2,6},{3,5},{4,8}}
[6,7,5,8,3,2,1,4]=>{{1,2,6,7},{3,5},{4,8}}
[7,5,6,8,3,2,1,4]=>{{1,7},{2,3,5,6},{4,8}}
[6,5,7,8,3,2,1,4]=>{{1,2,3,5,6,7},{4,8}}
[5,6,7,8,3,2,1,4]=>{{1,3,5,7},{2,6},{4,8}}
[8,7,6,5,2,3,1,4]=>{{1,2,4,5,7,8},{3,6}}
[7,8,6,5,2,3,1,4]=>{{1,7},{2,4,5,8},{3,6}}
[8,6,7,5,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,5,2,3,1,4]=>{{1,7},{2,3,4,5,6,8}}
[6,7,8,5,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,6,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,6,2,3,1,4]=>{{1,7},{2,3,4,5,6,8}}
[8,6,5,7,2,3,1,4]=>{{1,4,7,8},{2,3,5,6}}
[8,5,6,7,2,3,1,4]=>{{1,4,7,8},{2,5},{3,6}}
[7,6,5,8,2,3,1,4]=>{{1,7},{2,3,5,6},{4,8}}
[6,7,5,8,2,3,1,4]=>{{1,2,3,5,6,7},{4,8}}
[7,5,6,8,2,3,1,4]=>{{1,7},{2,5},{3,6},{4,8}}
[6,5,7,8,2,3,1,4]=>{{1,3,6,7},{2,5},{4,8}}
[5,6,7,8,2,3,1,4]=>{{1,2,3,5,6,7},{4,8}}
[8,7,6,5,3,1,2,4]=>{{1,3,4,5,6,8},{2,7}}
[7,8,6,5,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,5,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,5,3,1,2,4]=>{{1,2,6,7},{3,4,5,8}}
[8,7,5,6,3,1,2,4]=>{{1,4,6,8},{2,7},{3,5}}
[7,8,5,6,3,1,2,4]=>{{1,2,4,6,7,8},{3,5}}
[8,6,5,7,3,1,2,4]=>{{1,2,4,6,7,8},{3,5}}
[7,6,5,8,3,1,2,4]=>{{1,2,6,7},{3,5},{4,8}}
[6,7,5,8,3,1,2,4]=>{{1,6},{2,7},{3,5},{4,8}}
[7,5,6,8,3,1,2,4]=>{{1,2,3,5,6,7},{4,8}}
[6,5,7,8,3,1,2,4]=>{{1,6},{2,3,5,7},{4,8}}
[5,6,7,8,3,1,2,4]=>{{1,2,3,5,6,7},{4,8}}
[8,7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,6,5,2,1,3,4]=>{{1,3,6,7},{2,4,5,8}}
[7,6,8,5,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,5,2,1,3,4]=>{{1,6},{2,3,4,5,7,8}}
[8,7,5,6,2,1,3,4]=>{{1,4,6,8},{2,3,5,7}}
[7,8,5,6,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,7,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,7,2,1,3,4]=>{{1,3,4,6,7,8},{2,5}}
[7,6,5,8,2,1,3,4]=>{{1,2,3,5,6,7},{4,8}}
[6,7,5,8,2,1,3,4]=>{{1,6},{2,3,5,7},{4,8}}
[7,5,6,8,2,1,3,4]=>{{1,3,6,7},{2,5},{4,8}}
[6,5,7,8,2,1,3,4]=>{{1,6},{2,5},{3,7},{4,8}}
[5,6,7,8,2,1,3,4]=>{{1,2,5,6},{3,7},{4,8}}
[8,7,6,5,1,2,3,4]=>{{1,4,5,8},{2,3,6,7}}
[7,8,6,5,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,5,1,2,3,4]=>{{1,4,5,8},{2,6},{3,7}}
[7,6,8,5,1,2,3,4]=>{{1,3,4,5,7,8},{2,6}}
[6,7,8,5,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,6,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,6,1,2,3,4]=>{{1,3,5,7},{2,4,6,8}}
[8,6,5,7,1,2,3,4]=>{{1,3,4,5,7,8},{2,6}}
[8,5,6,7,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,8,1,2,3,4]=>{{1,3,5,7},{2,6},{4,8}}
[6,7,5,8,1,2,3,4]=>{{1,2,3,5,6,7},{4,8}}
[7,5,6,8,1,2,3,4]=>{{1,2,3,5,6,7},{4,8}}
[6,5,7,8,1,2,3,4]=>{{1,2,5,6},{3,7},{4,8}}
[5,6,7,8,1,2,3,4]=>{{1,5},{2,6},{3,7},{4,8}}
[8,7,6,4,3,2,1,5]=>{{1,2,3,5,6,7,8},{4}}
[7,8,6,4,3,2,1,5]=>{{1,7},{2,3,5,6,8},{4}}
[8,6,7,4,3,2,1,5]=>{{1,3,5,7,8},{2,6},{4}}
[7,6,8,4,3,2,1,5]=>{{1,7},{2,6},{3,5,8},{4}}
[6,7,8,4,3,2,1,5]=>{{1,2,6,7},{3,5,8},{4}}
[8,7,6,3,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,6,3,4,2,1,5]=>{{1,7},{2,3,4,5,6,8}}
[6,7,8,3,4,2,1,5]=>{{1,2,6,7},{3,4,5,8}}
[8,7,6,4,2,3,1,5]=>{{1,2,5,7,8},{3,6},{4}}
[7,6,8,4,2,3,1,5]=>{{1,7},{2,3,5,6,8},{4}}
[6,7,8,4,2,3,1,5]=>{{1,2,3,5,6,7,8},{4}}
[8,7,6,3,2,4,1,5]=>{{1,2,5,7,8},{3,4,6}}
[8,6,7,3,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,3,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,2,3,4,1,5]=>{{1,3,5,7,8},{2,4,6}}
[7,6,8,2,3,4,1,5]=>{{1,7},{2,4,6},{3,5,8}}
[6,7,8,2,3,4,1,5]=>{{1,2,4,6,7},{3,5,8}}
[8,7,6,4,3,1,2,5]=>{{1,3,5,6,8},{2,7},{4}}
[6,7,8,4,3,1,2,5]=>{{1,6},{2,7},{3,5,8},{4}}
[8,7,6,3,4,1,2,5]=>{{1,3,4,5,6,8},{2,7}}
[7,8,6,3,4,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,3,4,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,3,4,1,2,5]=>{{1,6},{2,7},{3,4,5,8}}
[8,7,6,4,2,1,3,5]=>{{1,2,3,5,6,7,8},{4}}
[7,8,6,4,2,1,3,5]=>{{1,3,6,7},{2,5,8},{4}}
[8,6,7,4,2,1,3,5]=>{{1,2,5,6,8},{3,7},{4}}
[6,7,8,4,2,1,3,5]=>{{1,6},{2,3,5,7,8},{4}}
[8,7,6,4,1,2,3,5]=>{{1,5,8},{2,3,6,7},{4}}
[7,8,6,4,1,2,3,5]=>{{1,2,3,5,6,7,8},{4}}
[7,6,8,4,1,2,3,5]=>{{1,3,5,7,8},{2,6},{4}}
[6,7,8,4,1,2,3,5]=>{{1,2,3,5,6,7,8},{4}}
[8,7,6,3,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,6,3,2,1,4,5]=>{{1,3,4,6,7},{2,5,8}}
[8,6,7,3,2,1,4,5]=>{{1,2,5,6,8},{3,4,7}}
[7,6,8,3,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,3,2,1,4,5]=>{{1,6},{2,3,4,5,7,8}}
[8,7,6,2,3,1,4,5]=>{{1,3,5,6,8},{2,4,7}}
[7,8,6,2,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,2,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,2,3,1,4,5]=>{{1,2,4,6,7},{3,5,8}}
[6,7,8,2,3,1,4,5]=>{{1,6},{2,4,7},{3,5,8}}
[8,7,6,3,1,2,4,5]=>{{1,5,8},{2,3,4,6,7}}
[7,8,6,3,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,3,1,2,4,5]=>{{1,5,8},{2,6},{3,4,7}}
[7,6,8,3,1,2,4,5]=>{{1,3,4,5,7,8},{2,6}}
[6,7,8,3,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,2,1,3,4,5]=>{{1,5,8},{2,4,7},{3,6}}
[7,8,6,2,1,3,4,5]=>{{1,2,4,5,7,8},{3,6}}
[8,6,7,2,1,3,4,5]=>{{1,5,8},{2,3,4,6,7}}
[6,7,8,2,1,3,4,5]=>{{1,3,5,6,8},{2,4,7}}
[8,7,6,1,2,3,4,5]=>{{1,2,4,5,7,8},{3,6}}
[7,8,6,1,2,3,4,5]=>{{1,4,7},{2,5,8},{3,6}}
[8,6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,1,2,3,4,5]=>{{1,4,7},{2,3,5,6,8}}
[6,7,8,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,4,3,2,1,6]=>{{1,2,6,7,8},{3,5},{4}}
[7,8,5,4,3,2,1,6]=>{{1,7},{2,6,8},{3,5},{4}}
[8,7,4,5,3,2,1,6]=>{{1,2,6,7,8},{3,4,5}}
[7,8,4,5,3,2,1,6]=>{{1,7},{2,6,8},{3,4,5}}
[8,7,5,3,4,2,1,6]=>{{1,2,6,7,8},{3,4,5}}
[8,7,3,4,5,2,1,6]=>{{1,2,6,7,8},{3},{4},{5}}
[7,8,3,4,5,2,1,6]=>{{1,7},{2,6,8},{3},{4},{5}}
[8,7,4,5,2,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,5,2,3,1,6]=>{{1,7},{2,3,4,5,6,8}}
[8,7,5,3,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,2,3,4,1,6]=>{{1,7},{2,4,6,8},{3,5}}
[8,7,4,3,2,5,1,6]=>{{1,2,5,6,7,8},{3,4}}
[7,8,4,3,2,5,1,6]=>{{1,7},{2,5,6,8},{3,4}}
[8,7,3,4,2,5,1,6]=>{{1,2,5,6,7,8},{3},{4}}
[7,8,3,4,2,5,1,6]=>{{1,7},{2,5,6,8},{3},{4}}
[8,7,2,3,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,2,3,4,5,1,6]=>{{1,7},{2,3,4,5,6,8}}
[8,7,5,4,3,1,2,6]=>{{1,6,8},{2,7},{3,5},{4}}
[7,8,5,4,3,1,2,6]=>{{1,2,6,7,8},{3,5},{4}}
[8,7,5,3,4,1,2,6]=>{{1,6,8},{2,7},{3,4,5}}
[8,7,3,4,5,1,2,6]=>{{1,6,8},{2,7},{3},{4},{5}}
[7,8,3,4,5,1,2,6]=>{{1,2,6,7,8},{3},{4},{5}}
[7,8,5,4,2,1,3,6]=>{{1,2,3,5,6,7,8},{4}}
[8,7,5,4,1,2,3,6]=>{{1,2,3,5,6,7,8},{4}}
[7,8,5,4,1,2,3,6]=>{{1,3,5,7},{2,6,8},{4}}
[8,7,4,5,1,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,5,1,2,3,6]=>{{1,3,4,5,7},{2,6,8}}
[8,7,5,3,2,1,4,6]=>{{1,6,8},{2,3,4,5,7}}
[7,8,5,3,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,3,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,3,1,2,4,6]=>{{1,3,4,5,7},{2,6,8}}
[8,7,5,2,1,3,4,6]=>{{1,3,5,6,8},{2,4,7}}
[7,8,5,2,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,1,2,3,4,6]=>{{1,4,7},{2,3,5,6,8}}
[8,7,4,3,2,1,5,6]=>{{1,6,8},{2,5,7},{3,4}}
[7,8,4,3,2,1,5,6]=>{{1,2,5,6,7,8},{3,4}}
[8,7,3,4,2,1,5,6]=>{{1,6,8},{2,5,7},{3},{4}}
[7,8,3,4,2,1,5,6]=>{{1,2,5,6,7,8},{3},{4}}
[7,8,4,2,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,2,4,1,5,6]=>{{1,6,8},{2,4,5,7},{3}}
[7,8,3,2,4,1,5,6]=>{{1,2,4,5,6,7,8},{3}}
[8,7,2,3,4,1,5,6]=>{{1,6,8},{2,3,4,5,7}}
[7,8,2,3,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,3,1,2,5,6]=>{{1,5,7},{2,6,8},{3,4}}
[8,7,3,4,1,2,5,6]=>{{1,2,5,6,7,8},{3},{4}}
[7,8,3,4,1,2,5,6]=>{{1,5,7},{2,6,8},{3},{4}}
[8,7,4,2,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,2,1,3,5,6]=>{{1,5,7},{2,3,4,6,8}}
[8,7,4,1,2,3,5,6]=>{{1,3,4,6,8},{2,5,7}}
[7,8,4,1,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,2,1,4,5,6]=>{{1,2,4,5,6,7,8},{3}}
[7,8,3,2,1,4,5,6]=>{{1,5,7},{2,4,6,8},{3}}
[8,7,2,3,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,2,3,1,4,5,6]=>{{1,5,7},{2,3,4,6,8}}
[7,8,3,1,2,4,5,6]=>{{1,2,4,5,6,7,8},{3}}
[8,7,2,1,3,4,5,6]=>{{1,4,6,8},{2,3,5,7}}
[7,8,2,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,2,3,4,5,6]=>{{1,3,5,7},{2,4,6,8}}
[8,6,5,4,3,2,1,7]=>{{1,7,8},{2,6},{3,5},{4}}
[8,5,6,4,3,2,1,7]=>{{1,7,8},{2,3,5,6},{4}}
[8,6,4,5,3,2,1,7]=>{{1,7,8},{2,6},{3,4,5}}
[8,4,5,6,3,2,1,7]=>{{1,7,8},{2,4,6},{3,5}}
[8,6,5,3,4,2,1,7]=>{{1,7,8},{2,6},{3,4,5}}
[8,5,6,3,4,2,1,7]=>{{1,7,8},{2,3,4,5,6}}
[8,4,5,3,6,2,1,7]=>{{1,7,8},{2,3,4,5,6}}
[8,4,3,5,6,2,1,7]=>{{1,7,8},{2,4,5,6},{3}}
[8,3,4,5,6,2,1,7]=>{{1,7,8},{2,3,4,5,6}}
[8,6,5,4,2,3,1,7]=>{{1,7,8},{2,3,5,6},{4}}
[8,5,6,4,2,3,1,7]=>{{1,7,8},{2,5},{3,6},{4}}
[8,4,5,6,2,3,1,7]=>{{1,7,8},{2,3,4,5,6}}
[8,6,5,3,2,4,1,7]=>{{1,7,8},{2,3,4,5,6}}
[8,6,5,2,3,4,1,7]=>{{1,7,8},{2,4,6},{3,5}}
[8,5,6,2,3,4,1,7]=>{{1,7,8},{2,3,4,5,6}}
[8,6,4,2,3,5,1,7]=>{{1,7,8},{2,3,4,5,6}}
[8,6,3,2,4,5,1,7]=>{{1,7,8},{2,4,5,6},{3}}
[8,5,4,3,2,6,1,7]=>{{1,7,8},{2,5},{3,4},{6}}
[8,4,3,5,2,6,1,7]=>{{1,7,8},{2,4,5},{3},{6}}
[8,5,4,2,3,6,1,7]=>{{1,7,8},{2,3,4,5},{6}}
[8,4,5,2,3,6,1,7]=>{{1,7,8},{2,4},{3,5},{6}}
[8,5,3,2,4,6,1,7]=>{{1,7,8},{2,4,5},{3},{6}}
[8,5,2,3,4,6,1,7]=>{{1,7,8},{2,3,4,5},{6}}
[8,3,4,2,5,6,1,7]=>{{1,7,8},{2,3,4},{5},{6}}
[8,3,2,4,5,6,1,7]=>{{1,7,8},{2,3},{4},{5},{6}}
[8,2,3,4,5,6,1,7]=>{{1,7,8},{2},{3},{4},{5},{6}}
[8,6,5,4,3,1,2,7]=>{{1,2,6,7,8},{3,5},{4}}
[8,6,4,5,3,1,2,7]=>{{1,2,6,7,8},{3,4,5}}
[8,6,5,3,4,1,2,7]=>{{1,2,6,7,8},{3,4,5}}
[8,5,6,3,4,1,2,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,3,4,5,1,2,7]=>{{1,2,6,7,8},{3},{4},{5}}
[8,5,4,3,6,1,2,7]=>{{1,2,5,6,7,8},{3,4}}
[8,4,5,3,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,4,6,1,2,7]=>{{1,2,5,6,7,8},{3},{4}}
[8,4,3,5,6,1,2,7]=>{{1,2,4,5,6,7,8},{3}}
[8,3,4,5,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,4,2,1,3,7]=>{{1,2,3,5,6,7,8},{4}}
[8,5,6,4,2,1,3,7]=>{{1,3,6,7,8},{2,5},{4}}
[8,4,5,6,2,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,4,1,2,3,7]=>{{1,3,5,7,8},{2,6},{4}}
[8,5,6,4,1,2,3,7]=>{{1,2,3,5,6,7,8},{4}}
[8,6,4,5,1,2,3,7]=>{{1,3,4,5,7,8},{2,6}}
[8,4,5,6,1,2,3,7]=>{{1,3,5,7,8},{2,4,6}}
[8,6,5,3,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,3,2,1,4,7]=>{{1,3,4,6,7,8},{2,5}}
[8,6,5,2,3,1,4,7]=>{{1,2,4,6,7,8},{3,5}}
[8,5,6,2,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,3,1,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,2,1,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,2,1,3,4,7]=>{{1,2,4,5,7,8},{3,6}}
[8,6,5,1,2,3,4,7]=>{{1,4,7,8},{2,3,5,6}}
[8,5,6,1,2,3,4,7]=>{{1,4,7,8},{2,5},{3,6}}
[8,6,4,3,2,1,5,7]=>{{1,2,5,6,7,8},{3,4}}
[8,6,3,4,2,1,5,7]=>{{1,2,5,6,7,8},{3},{4}}
[8,6,4,2,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,3,2,4,1,5,7]=>{{1,2,4,5,6,7,8},{3}}
[8,6,2,3,4,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,4,3,1,2,5,7]=>{{1,5,7,8},{2,6},{3,4}}
[8,6,3,4,1,2,5,7]=>{{1,5,7,8},{2,6},{3},{4}}
[8,6,4,2,1,3,5,7]=>{{1,5,7,8},{2,3,4,6}}
[8,6,4,1,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,3,2,1,4,5,7]=>{{1,5,7,8},{2,4,6},{3}}
[8,6,1,2,3,4,5,7]=>{{1,3,5,7,8},{2,4,6}}
[8,5,4,3,2,1,6,7]=>{{1,6,7,8},{2,5},{3,4}}
[8,4,5,3,2,1,6,7]=>{{1,6,7,8},{2,3,4,5}}
[8,4,3,5,2,1,6,7]=>{{1,6,7,8},{2,4,5},{3}}
[8,3,4,5,2,1,6,7]=>{{1,6,7,8},{2,3,4,5}}
[8,4,5,2,3,1,6,7]=>{{1,6,7,8},{2,4},{3,5}}
[8,5,2,3,4,1,6,7]=>{{1,6,7,8},{2,3,4,5}}
[8,4,2,3,5,1,6,7]=>{{1,6,7,8},{2,3,4},{5}}
[8,2,3,4,5,1,6,7]=>{{1,6,7,8},{2},{3},{4},{5}}
[8,5,3,4,1,2,6,7]=>{{1,2,5,6,7,8},{3},{4}}
[8,3,4,5,1,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,2,1,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,1,2,3,6,7]=>{{1,3,4,6,7,8},{2,5}}
[8,4,5,1,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,2,1,4,6,7]=>{{1,2,4,5,6,7,8},{3}}
[8,5,3,1,2,4,6,7]=>{{1,4,6,7,8},{2,5},{3}}
[8,5,2,1,3,4,6,7]=>{{1,4,6,7,8},{2,3,5}}
[8,5,1,2,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,3,2,1,5,6,7]=>{{1,5,6,7,8},{2,4},{3}}
[8,3,4,2,1,5,6,7]=>{{1,5,6,7,8},{2,3,4}}
[8,4,2,3,1,5,6,7]=>{{1,5,6,7,8},{2,3,4}}
[8,2,3,4,1,5,6,7]=>{{1,5,6,7,8},{2},{3},{4}}
[8,3,4,1,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,1,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,2,3,5,6,7]=>{{1,3,5,6,7,8},{2,4}}
[8,3,2,1,4,5,6,7]=>{{1,4,5,6,7,8},{2,3}}
[8,2,3,1,4,5,6,7]=>{{1,4,5,6,7,8},{2},{3}}
[8,3,1,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,3,4,5,6,7]=>{{1,3,4,5,6,7,8},{2}}
[8,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,4,3,2,1,8]=>{{1,7},{2,6},{3,5},{4},{8}}
[6,7,5,4,3,2,1,8]=>{{1,2,6,7},{3,5},{4},{8}}
[7,5,6,4,3,2,1,8]=>{{1,7},{2,3,5,6},{4},{8}}
[6,5,7,4,3,2,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[5,6,7,4,3,2,1,8]=>{{1,3,5,7},{2,6},{4},{8}}
[7,6,4,5,3,2,1,8]=>{{1,7},{2,6},{3,4,5},{8}}
[6,7,4,5,3,2,1,8]=>{{1,2,6,7},{3,4,5},{8}}
[7,5,4,6,3,2,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[6,5,4,7,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,4,7,3,2,1,8]=>{{1,3,4,5,7},{2,6},{8}}
[5,4,6,7,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,6,7,3,2,1,8]=>{{1,4,7},{2,3,5,6},{8}}
[7,6,5,3,4,2,1,8]=>{{1,7},{2,6},{3,4,5},{8}}
[6,7,5,3,4,2,1,8]=>{{1,2,6,7},{3,4,5},{8}}
[7,5,6,3,4,2,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[6,5,7,3,4,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,7,3,4,2,1,8]=>{{1,3,4,5,7},{2,6},{8}}
[7,6,4,3,5,2,1,8]=>{{1,7},{2,6},{3,4},{5},{8}}
[6,7,4,3,5,2,1,8]=>{{1,2,6,7},{3,4},{5},{8}}
[7,6,3,4,5,2,1,8]=>{{1,7},{2,6},{3},{4},{5},{8}}
[7,5,4,3,6,2,1,8]=>{{1,7},{2,5,6},{3,4},{8}}
[7,3,4,5,6,2,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[6,5,4,3,7,2,1,8]=>{{1,2,5,6,7},{3,4},{8}}
[5,6,4,3,7,2,1,8]=>{{1,5,7},{2,6},{3,4},{8}}
[5,4,6,3,7,2,1,8]=>{{1,5,7},{2,3,4,6},{8}}
[5,4,3,6,7,2,1,8]=>{{1,5,7},{2,4,6},{3},{8}}
[3,4,5,6,7,2,1,8]=>{{1,3,5,7},{2,4,6},{8}}
[7,6,5,4,2,3,1,8]=>{{1,7},{2,3,5,6},{4},{8}}
[6,7,5,4,2,3,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,5,6,4,2,3,1,8]=>{{1,7},{2,5},{3,6},{4},{8}}
[5,6,7,4,2,3,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,6,4,5,2,3,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[6,7,4,5,2,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,4,6,2,3,1,8]=>{{1,7},{2,5},{3,4,6},{8}}
[6,5,4,7,2,3,1,8]=>{{1,3,4,6,7},{2,5},{8}}
[5,6,4,7,2,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,6,7,2,3,1,8]=>{{1,2,4,5,7},{3,6},{8}}
[4,5,6,7,2,3,1,8]=>{{1,4,7},{2,5},{3,6},{8}}
[7,6,5,3,2,4,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[6,5,7,3,2,4,1,8]=>{{1,3,4,6,7},{2,5},{8}}
[5,6,7,3,2,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,5,2,3,4,1,8]=>{{1,7},{2,4,6},{3,5},{8}}
[6,7,5,2,3,4,1,8]=>{{1,2,4,6,7},{3,5},{8}}
[7,5,6,2,3,4,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[6,5,7,2,3,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,7,2,3,4,1,8]=>{{1,3,5,7},{2,4,6},{8}}
[7,6,4,3,2,5,1,8]=>{{1,7},{2,5,6},{3,4},{8}}
[6,7,4,3,2,5,1,8]=>{{1,2,5,6,7},{3,4},{8}}
[6,7,3,4,2,5,1,8]=>{{1,2,5,6,7},{3},{4},{8}}
[7,6,4,2,3,5,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[6,7,4,2,3,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,3,2,4,5,1,8]=>{{1,7},{2,4,5,6},{3},{8}}
[6,7,3,2,4,5,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,6,2,3,4,5,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[6,7,2,3,4,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,4,3,2,6,1,8]=>{{1,7},{2,5},{3,4},{6},{8}}
[7,4,5,3,2,6,1,8]=>{{1,7},{2,3,4,5},{6},{8}}
[7,5,3,4,2,6,1,8]=>{{1,7},{2,5},{3},{4},{6},{8}}
[7,4,3,5,2,6,1,8]=>{{1,7},{2,4,5},{3},{6},{8}}
[7,4,5,2,3,6,1,8]=>{{1,7},{2,4},{3,5},{6},{8}}
[7,5,3,2,4,6,1,8]=>{{1,7},{2,4,5},{3},{6},{8}}
[7,4,2,3,5,6,1,8]=>{{1,7},{2,3,4},{5},{6},{8}}
[7,2,3,4,5,6,1,8]=>{{1,7},{2},{3},{4},{5},{6},{8}}
[6,5,4,3,2,7,1,8]=>{{1,6,7},{2,5},{3,4},{8}}
[5,6,4,3,2,7,1,8]=>{{1,2,5,6,7},{3,4},{8}}
[5,4,6,3,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,3,4,2,7,1,8]=>{{1,2,5,6,7},{3},{4},{8}}
[6,3,4,5,2,7,1,8]=>{{1,6,7},{2,3,4,5},{8}}
[5,4,3,6,2,7,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[4,5,3,6,2,7,1,8]=>{{1,4,6,7},{2,5},{3},{8}}
[5,3,4,6,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,3,5,6,2,7,1,8]=>{{1,4,6,7},{2,3,5},{8}}
[3,4,5,6,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,6,2,3,7,1,8]=>{{1,3,5,6,7},{2,4},{8}}
[6,5,3,2,4,7,1,8]=>{{1,6,7},{2,4,5},{3},{8}}
[6,4,2,3,5,7,1,8]=>{{1,6,7},{2,3,4},{5},{8}}
[6,3,2,4,5,7,1,8]=>{{1,6,7},{2,3},{4},{5},{8}}
[6,2,3,4,5,7,1,8]=>{{1,6,7},{2},{3},{4},{5},{8}}
[5,4,3,2,6,7,1,8]=>{{1,5,6,7},{2,4},{3},{8}}
[3,4,5,2,6,7,1,8]=>{{1,3,5,6,7},{2,4},{8}}
[5,4,2,3,6,7,1,8]=>{{1,5,6,7},{2,3,4},{8}}
[4,5,2,3,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,2,3,4,6,7,1,8]=>{{1,5,6,7},{2},{3},{4},{8}}
[4,3,2,5,6,7,1,8]=>{{1,4,5,6,7},{2,3},{8}}
[3,4,2,5,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,2,3,5,6,7,1,8]=>{{1,4,5,6,7},{2},{3},{8}}
[3,2,4,5,6,7,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[2,3,4,5,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,5,4,3,1,2,8]=>{{1,2,6,7},{3,5},{4},{8}}
[6,7,5,4,3,1,2,8]=>{{1,6},{2,7},{3,5},{4},{8}}
[7,5,6,4,3,1,2,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,6,4,5,3,1,2,8]=>{{1,2,6,7},{3,4,5},{8}}
[5,4,6,7,3,1,2,8]=>{{1,3,5,6},{2,4,7},{8}}
[4,5,6,7,3,1,2,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,5,3,4,1,2,8]=>{{1,2,6,7},{3,4,5},{8}}
[6,5,7,3,4,1,2,8]=>{{1,6},{2,3,4,5,7},{8}}
[6,7,3,4,5,1,2,8]=>{{1,6},{2,7},{3},{4},{5},{8}}
[6,5,4,3,7,1,2,8]=>{{1,6},{2,5,7},{3,4},{8}}
[6,4,5,3,7,1,2,8]=>{{1,6},{2,3,4,5,7},{8}}
[5,6,3,4,7,1,2,8]=>{{1,2,5,6,7},{3},{4},{8}}
[6,3,4,5,7,1,2,8]=>{{1,6},{2,3,4,5,7},{8}}
[4,3,5,6,7,1,2,8]=>{{1,4,6},{2,3,5,7},{8}}
[3,4,5,6,7,1,2,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,5,4,2,1,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[6,5,7,4,2,1,3,8]=>{{1,6},{2,5},{3,7},{4},{8}}
[7,6,4,5,2,1,3,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,4,6,2,1,3,8]=>{{1,3,4,6,7},{2,5},{8}}
[5,4,6,7,2,1,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,6,7,2,1,3,8]=>{{1,3,4,6,7},{2,5},{8}}
[7,6,5,4,1,2,3,8]=>{{1,3,5,7},{2,6},{4},{8}}
[5,6,7,4,1,2,3,8]=>{{1,5},{2,6},{3,7},{4},{8}}
[7,4,5,6,1,2,3,8]=>{{1,3,5,7},{2,4,6},{8}}
[5,6,4,7,1,2,3,8]=>{{1,5},{2,6},{3,4,7},{8}}
[5,4,6,7,1,2,3,8]=>{{1,5},{2,3,4,6,7},{8}}
[4,5,6,7,1,2,3,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,5,3,2,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,5,2,3,1,4,8]=>{{1,2,4,6,7},{3,5},{8}}
[6,7,5,2,3,1,4,8]=>{{1,6},{2,4,7},{3,5},{8}}
[7,5,6,2,3,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,5,7,2,3,1,4,8]=>{{1,6},{2,3,4,5,7},{8}}
[5,6,7,2,3,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,7,3,1,2,4,8]=>{{1,5},{2,6},{3,4,7},{8}}
[7,6,5,2,1,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,7,5,2,1,3,4,8]=>{{1,3,5,6},{2,4,7},{8}}
[7,5,6,2,1,3,4,8]=>{{1,2,4,5,7},{3,6},{8}}
[5,6,7,2,1,3,4,8]=>{{1,5},{2,3,4,6,7},{8}}
[7,6,5,1,2,3,4,8]=>{{1,4,7},{2,3,5,6},{8}}
[6,7,5,1,2,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,6,1,2,3,4,8]=>{{1,4,7},{2,5},{3,6},{8}}
[6,5,7,1,2,3,4,8]=>{{1,3,4,6,7},{2,5},{8}}
[5,6,7,1,2,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,4,3,2,1,5,8]=>{{1,2,5,6,7},{3,4},{8}}
[6,7,4,3,2,1,5,8]=>{{1,6},{2,5,7},{3,4},{8}}
[7,6,3,4,2,1,5,8]=>{{1,2,5,6,7},{3},{4},{8}}
[6,7,3,4,2,1,5,8]=>{{1,6},{2,5,7},{3},{4},{8}}
[7,6,4,2,3,1,5,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,3,2,4,1,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[6,7,3,2,4,1,5,8]=>{{1,6},{2,4,5,7},{3},{8}}
[7,6,2,3,4,1,5,8]=>{{1,2,3,4,5,6,7},{8}}
[6,7,2,3,4,1,5,8]=>{{1,6},{2,3,4,5,7},{8}}
[7,6,4,3,1,2,5,8]=>{{1,5,7},{2,6},{3,4},{8}}
[6,7,3,4,1,2,5,8]=>{{1,2,5,6,7},{3},{4},{8}}
[7,6,4,2,1,3,5,8]=>{{1,5,7},{2,3,4,6},{8}}
[7,6,3,2,1,4,5,8]=>{{1,5,7},{2,4,6},{3},{8}}
[6,7,3,2,1,4,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,6,2,3,1,4,5,8]=>{{1,5,7},{2,3,4,6},{8}}
[6,7,2,3,1,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[6,7,3,1,2,4,5,8]=>{{1,4,6},{2,5,7},{3},{8}}
[7,6,1,2,3,4,5,8]=>{{1,3,5,7},{2,4,6},{8}}
[6,7,1,2,3,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,4,3,2,1,6,8]=>{{1,6,7},{2,5},{3,4},{8}}
[7,4,5,3,2,1,6,8]=>{{1,6,7},{2,3,4,5},{8}}
[7,4,3,5,2,1,6,8]=>{{1,6,7},{2,4,5},{3},{8}}
[7,3,4,5,2,1,6,8]=>{{1,6,7},{2,3,4,5},{8}}
[7,5,4,2,3,1,6,8]=>{{1,6,7},{2,3,4,5},{8}}
[7,5,3,2,4,1,6,8]=>{{1,6,7},{2,4,5},{3},{8}}
[7,5,2,3,4,1,6,8]=>{{1,6,7},{2,3,4,5},{8}}
[7,4,2,3,5,1,6,8]=>{{1,6,7},{2,3,4},{5},{8}}
[7,2,3,4,5,1,6,8]=>{{1,6,7},{2},{3},{4},{5},{8}}
[7,5,4,3,1,2,6,8]=>{{1,2,5,6,7},{3,4},{8}}
[7,4,5,2,1,3,6,8]=>{{1,3,5,6,7},{2,4},{8}}
[7,4,5,1,2,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,3,2,1,4,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,5,2,3,1,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,3,1,2,4,6,8]=>{{1,4,6,7},{2,5},{3},{8}}
[7,5,1,2,3,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[7,4,3,2,1,5,6,8]=>{{1,5,6,7},{2,4},{3},{8}}
[7,2,3,4,1,5,6,8]=>{{1,5,6,7},{2},{3},{4},{8}}
[7,4,3,1,2,5,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,3,4,1,2,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[7,4,1,2,3,5,6,8]=>{{1,3,5,6,7},{2,4},{8}}
[7,3,2,1,4,5,6,8]=>{{1,4,5,6,7},{2,3},{8}}
[7,2,3,1,4,5,6,8]=>{{1,4,5,6,7},{2},{3},{8}}
[7,3,1,2,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[7,2,1,3,4,5,6,8]=>{{1,3,4,5,6,7},{2},{8}}
[7,1,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[6,5,4,3,2,1,7,8]=>{{1,6},{2,5},{3,4},{7},{8}}
[5,6,4,3,2,1,7,8]=>{{1,2,5,6},{3,4},{7},{8}}
[5,4,6,3,2,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[4,5,6,3,2,1,7,8]=>{{1,3,4,6},{2,5},{7},{8}}
[6,5,3,4,2,1,7,8]=>{{1,6},{2,5},{3},{4},{7},{8}}
[5,6,3,4,2,1,7,8]=>{{1,2,5,6},{3},{4},{7},{8}}
[5,4,3,6,2,1,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[3,4,5,6,2,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,4,6,2,3,1,7,8]=>{{1,3,5,6},{2,4},{7},{8}}
[5,6,3,2,4,1,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[6,5,2,3,4,1,7,8]=>{{1,6},{2,3,4,5},{7},{8}}
[5,6,2,3,4,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[6,4,3,2,5,1,7,8]=>{{1,6},{2,4},{3},{5},{7},{8}}
[6,2,3,4,5,1,7,8]=>{{1,6},{2},{3},{4},{5},{7},{8}}
[5,4,3,2,6,1,7,8]=>{{1,5,6},{2,4},{3},{7},{8}}
[4,5,3,2,6,1,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[4,3,5,2,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[3,4,5,2,6,1,7,8]=>{{1,3,5,6},{2,4},{7},{8}}
[5,3,2,4,6,1,7,8]=>{{1,5,6},{2,3},{4},{7},{8}}
[5,2,3,4,6,1,7,8]=>{{1,5,6},{2},{3},{4},{7},{8}}
[4,3,2,5,6,1,7,8]=>{{1,4,5,6},{2,3},{7},{8}}
[3,4,2,5,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[4,2,3,5,6,1,7,8]=>{{1,4,5,6},{2},{3},{7},{8}}
[3,2,4,5,6,1,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[2,3,4,5,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[6,5,4,3,1,2,7,8]=>{{1,2,5,6},{3,4},{7},{8}}
[5,6,4,3,1,2,7,8]=>{{1,5},{2,6},{3,4},{7},{8}}
[6,4,5,3,1,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,4,6,3,1,2,7,8]=>{{1,5},{2,3,4,6},{7},{8}}
[5,6,3,4,1,2,7,8]=>{{1,5},{2,6},{3},{4},{7},{8}}
[6,4,3,5,1,2,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[5,4,3,6,1,2,7,8]=>{{1,5},{2,4,6},{3},{7},{8}}
[4,3,5,6,1,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[3,4,5,6,1,2,7,8]=>{{1,3,5},{2,4,6},{7},{8}}
[6,5,4,2,1,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,6,4,2,1,3,7,8]=>{{1,5},{2,3,4,6},{7},{8}}
[6,4,5,2,1,3,7,8]=>{{1,3,5,6},{2,4},{7},{8}}
[5,4,6,2,1,3,7,8]=>{{1,5},{2,4},{3,6},{7},{8}}
[4,5,6,2,1,3,7,8]=>{{1,2,4,5},{3,6},{7},{8}}
[6,5,4,1,2,3,7,8]=>{{1,3,4,6},{2,5},{7},{8}}
[4,5,6,1,2,3,7,8]=>{{1,4},{2,5},{3,6},{7},{8}}
[6,5,3,2,1,4,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[5,6,3,2,1,4,7,8]=>{{1,5},{2,4,6},{3},{7},{8}}
[5,6,2,1,3,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[6,4,3,2,1,5,7,8]=>{{1,5,6},{2,4},{3},{7},{8}}
[6,3,4,2,1,5,7,8]=>{{1,5,6},{2,3,4},{7},{8}}
[6,4,3,1,2,5,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[6,4,2,1,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[6,4,1,2,3,5,7,8]=>{{1,3,5,6},{2,4},{7},{8}}
[6,2,3,1,4,5,7,8]=>{{1,4,5,6},{2},{3},{7},{8}}
[6,3,1,2,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[6,1,2,3,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,4,3,2,1,6,7,8]=>{{1,5},{2,4},{3},{6},{7},{8}}
[4,5,3,2,1,6,7,8]=>{{1,2,4,5},{3},{6},{7},{8}}
[5,3,4,2,1,6,7,8]=>{{1,5},{2,3,4},{6},{7},{8}}
[4,3,5,2,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[3,4,5,2,1,6,7,8]=>{{1,3,5},{2,4},{6},{7},{8}}
[5,4,2,3,1,6,7,8]=>{{1,5},{2,3,4},{6},{7},{8}}
[4,5,2,3,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[5,3,2,4,1,6,7,8]=>{{1,5},{2,3},{4},{6},{7},{8}}
[5,2,3,4,1,6,7,8]=>{{1,5},{2},{3},{4},{6},{7},{8}}
[4,3,2,5,1,6,7,8]=>{{1,4,5},{2,3},{6},{7},{8}}
[3,4,2,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[4,2,3,5,1,6,7,8]=>{{1,4,5},{2},{3},{6},{7},{8}}
[3,2,4,5,1,6,7,8]=>{{1,3,4,5},{2},{6},{7},{8}}
[2,3,4,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[5,4,3,1,2,6,7,8]=>{{1,2,4,5},{3},{6},{7},{8}}
[5,3,4,1,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[4,3,5,1,2,6,7,8]=>{{1,4},{2,3,5},{6},{7},{8}}
[3,4,5,1,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[5,4,2,1,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[4,5,2,1,3,6,7,8]=>{{1,4},{2,3,5},{6},{7},{8}}
[5,4,1,2,3,6,7,8]=>{{1,3,5},{2,4},{6},{7},{8}}
[4,5,1,2,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[5,3,2,1,4,6,7,8]=>{{1,4,5},{2,3},{6},{7},{8}}
[5,2,3,1,4,6,7,8]=>{{1,4,5},{2},{3},{6},{7},{8}}
[5,3,1,2,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[5,2,1,3,4,6,7,8]=>{{1,3,4,5},{2},{6},{7},{8}}
[5,1,2,3,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[4,3,2,1,5,6,7,8]=>{{1,4},{2,3},{5},{6},{7},{8}}
[3,4,2,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[4,2,3,1,5,6,7,8]=>{{1,4},{2},{3},{5},{6},{7},{8}}
[3,2,4,1,5,6,7,8]=>{{1,3,4},{2},{5},{6},{7},{8}}
[2,3,4,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[4,3,1,2,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[3,4,1,2,5,6,7,8]=>{{1,3},{2,4},{5},{6},{7},{8}}
[4,2,1,3,5,6,7,8]=>{{1,3,4},{2},{5},{6},{7},{8}}
[4,1,2,3,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[3,2,1,4,5,6,7,8]=>{{1,3},{2},{4},{5},{6},{7},{8}}
[2,3,1,4,5,6,7,8]=>{{1,2,3},{4},{5},{6},{7},{8}}
[3,1,2,4,5,6,7,8]=>{{1,2,3},{4},{5},{6},{7},{8}}
[2,1,3,4,5,6,7,8]=>{{1,2},{3},{4},{5},{6},{7},{8}}
[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[6,8,7,5,4,3,2,1]=>{{1,2,3,6,7,8},{4,5}}
[5,8,7,6,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,6,4,3,2,1]=>{{1,3,4,5,6,8},{2,7}}
[6,5,8,7,4,3,2,1]=>{{1,3,6,8},{2,4,5,7}}
[5,6,8,7,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,8,4,3,2,1]=>{{1,4,5,8},{2,7},{3,6}}
[4,8,7,6,5,3,2,1]=>{{1,2,3,4,6,7,8},{5}}
[4,7,8,6,5,3,2,1]=>{{1,3,4,6,8},{2,7},{5}}
[4,6,8,7,5,3,2,1]=>{{1,2,3,4,6,7,8},{5}}
[4,7,6,8,5,3,2,1]=>{{1,4,8},{2,7},{3,6},{5}}
[4,6,7,8,5,3,2,1]=>{{1,4,8},{2,3,6,7},{5}}
[5,4,7,8,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,8,7,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,7,8,6,3,2,1]=>{{1,4,8},{2,3,5,6,7}}
[5,6,4,8,7,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,8,7,3,2,1]=>{{1,4,8},{2,3,5,6,7}}
[4,5,6,8,7,3,2,1]=>{{1,4,8},{2,5,7},{3,6}}
[5,7,6,4,8,3,2,1]=>{{1,5,8},{2,7},{3,6},{4}}
[4,7,6,5,8,3,2,1]=>{{1,4,5,8},{2,7},{3,6}}
[4,6,7,5,8,3,2,1]=>{{1,4,5,8},{2,3,6,7}}
[5,4,7,6,8,3,2,1]=>{{1,5,8},{2,3,4,6,7}}
[4,5,7,6,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,7,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,6,5,4,2,1]=>{{1,2,3,7,8},{4,6},{5}}
[3,7,8,6,5,4,2,1]=>{{1,3,8},{2,7},{4,6},{5}}
[3,6,8,7,5,4,2,1]=>{{1,3,8},{2,4,6,7},{5}}
[3,7,6,8,5,4,2,1]=>{{1,3,4,6,8},{2,7},{5}}
[3,5,8,7,6,4,2,1]=>{{1,3,8},{2,4,5,6,7}}
[3,5,7,8,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,8,7,4,2,1]=>{{1,3,4,6,8},{2,5,7}}
[3,7,6,5,8,4,2,1]=>{{1,3,4,5,6,8},{2,7}}
[3,5,7,6,8,4,2,1]=>{{1,2,3,5,7,8},{4,6}}
[3,5,6,7,8,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,7,6,5,2,1]=>{{1,2,3,4,7,8},{5,6}}
[4,3,7,8,6,5,2,1]=>{{1,4,8},{2,3,7},{5,6}}
[4,3,6,7,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,4,8,7,6,5,2,1]=>{{1,3,8},{2,4,7},{5,6}}
[3,4,6,7,8,5,2,1]=>{{1,3,5,6,8},{2,4,7}}
[5,4,3,8,7,6,2,1]=>{{1,2,4,5,7,8},{3},{6}}
[5,4,3,7,8,6,2,1]=>{{1,5,8},{2,4,7},{3},{6}}
[4,5,3,7,8,6,2,1]=>{{1,2,4,5,7,8},{3},{6}}
[3,5,4,7,8,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[4,3,5,7,8,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[3,4,5,8,7,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[3,4,5,7,8,6,2,1]=>{{1,3,5,8},{2,4,7},{6}}
[6,5,4,3,8,7,2,1]=>{{1,2,5,6,7,8},{3,4}}
[5,6,4,3,8,7,2,1]=>{{1,5,8},{2,6,7},{3,4}}
[4,5,6,3,8,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,6,5,4,8,7,2,1]=>{{1,3,5,8},{2,6,7},{4}}
[4,3,6,5,8,7,2,1]=>{{1,4,5,8},{2,3,6,7}}
[5,4,3,6,8,7,2,1]=>{{1,5,8},{2,4,6,7},{3}}
[4,5,3,6,8,7,2,1]=>{{1,2,4,5,6,7,8},{3}}
[4,3,5,6,8,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,4,5,6,8,7,2,1]=>{{1,3,5,8},{2,4,6,7}}
[5,7,6,4,3,8,2,1]=>{{1,3,5,6,8},{2,7},{4}}
[4,7,6,5,3,8,2,1]=>{{1,3,4,5,6,8},{2,7}}
[5,4,7,6,3,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,5,4,8,2,1]=>{{1,3,6,8},{2,7},{4,5}}
[3,5,7,6,4,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,7,4,8,2,1]=>{{1,3,6,8},{2,4,5,7}}
[4,3,7,6,5,8,2,1]=>{{1,4,6,8},{2,3,7},{5}}
[3,4,7,6,5,8,2,1]=>{{1,2,3,4,6,7,8},{5}}
[3,4,6,7,5,8,2,1]=>{{1,3,6,8},{2,4,7},{5}}
[4,5,3,7,6,8,2,1]=>{{1,2,4,5,6,7,8},{3}}
[3,5,4,7,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,5,7,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,4,5,7,6,8,2,1]=>{{1,3,5,6,8},{2,4,7}}
[3,6,5,4,7,8,2,1]=>{{1,2,3,5,6,7,8},{4}}
[3,5,6,4,7,8,2,1]=>{{1,3,6,8},{2,5,7},{4}}
[4,3,6,5,7,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,4,6,5,7,8,2,1]=>{{1,3,6,8},{2,4,5,7}}
[3,5,4,6,7,8,2,1]=>{{1,3,4,6,8},{2,5,7}}
[2,8,7,6,5,4,3,1]=>{{1,2,8},{3,7},{4,6},{5}}
[2,7,8,6,5,4,3,1]=>{{1,2,3,7,8},{4,6},{5}}
[2,6,8,7,5,4,3,1]=>{{1,2,3,4,6,7,8},{5}}
[2,7,6,8,5,4,3,1]=>{{1,2,3,4,6,7,8},{5}}
[2,6,7,8,5,4,3,1]=>{{1,2,4,6,8},{3,7},{5}}
[2,5,8,7,6,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,6,7,5,8,4,3,1]=>{{1,2,4,5,6,8},{3,7}}
[2,5,6,7,8,4,3,1]=>{{1,2,5,8},{3,4,6,7}}
[2,4,8,7,6,5,3,1]=>{{1,2,3,4,7,8},{5,6}}
[2,4,7,8,6,5,3,1]=>{{1,2,4,8},{3,7},{5,6}}
[2,4,6,8,7,5,3,1]=>{{1,2,4,8},{3,5,6,7}}
[2,4,6,7,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,8,7,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[2,5,4,7,8,6,3,1]=>{{1,2,5,8},{3,4,7},{6}}
[2,4,5,7,8,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[2,6,5,4,8,7,3,1]=>{{1,2,3,5,6,7,8},{4}}
[2,5,6,4,8,7,3,1]=>{{1,2,5,8},{3,6,7},{4}}
[2,4,6,5,8,7,3,1]=>{{1,2,4,5,8},{3,6,7}}
[2,4,5,6,8,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,5,4,8,3,1]=>{{1,2,3,6,7,8},{4,5}}
[2,5,6,7,4,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,4,7,6,5,8,3,1]=>{{1,2,4,6,8},{3,7},{5}}
[2,4,6,7,5,8,3,1]=>{{1,2,3,4,6,7,8},{5}}
[2,5,4,7,6,8,3,1]=>{{1,2,5,6,8},{3,4,7}}
[2,6,5,4,7,8,3,1]=>{{1,2,6,8},{3,5,7},{4}}
[2,5,6,4,7,8,3,1]=>{{1,2,3,5,6,7,8},{4}}
[2,4,6,5,7,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,6,7,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,6,7,8,3,1]=>{{1,2,4,6,8},{3,5,7}}
[3,2,8,7,6,5,4,1]=>{{1,3,8},{2},{4,7},{5,6}}
[3,2,7,8,6,5,4,1]=>{{1,3,4,7,8},{2},{5,6}}
[3,2,6,8,7,5,4,1]=>{{1,3,4,5,6,7,8},{2}}
[3,2,5,7,8,6,4,1]=>{{1,3,5,8},{2},{4,7},{6}}
[3,2,5,7,6,8,4,1]=>{{1,3,5,6,8},{2},{4,7}}
[3,2,5,6,7,8,4,1]=>{{1,3,4,5,6,7,8},{2}}
[2,3,8,7,6,5,4,1]=>{{1,2,3,8},{4,7},{5,6}}
[2,3,6,7,8,5,4,1]=>{{1,2,3,5,6,8},{4,7}}
[2,3,5,8,7,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[2,3,5,7,8,6,4,1]=>{{1,2,3,5,8},{4,7},{6}}
[2,3,6,5,8,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,6,8,7,4,1]=>{{1,2,3,5,8},{4,6,7}}
[2,3,7,6,5,8,4,1]=>{{1,2,3,4,6,7,8},{5}}
[2,3,5,7,6,8,4,1]=>{{1,2,3,5,6,8},{4,7}}
[2,3,5,6,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,2,8,7,6,5,1]=>{{1,4,8},{2,3},{5,7},{6}}
[4,3,2,7,8,6,5,1]=>{{1,4,5,7,8},{2,3},{6}}
[4,3,2,6,8,7,5,1]=>{{1,4,5,6,7,8},{2,3}}
[3,4,2,8,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}
[3,4,2,7,8,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[2,4,3,8,7,6,5,1]=>{{1,2,4,8},{3},{5,7},{6}}
[2,4,3,6,8,7,5,1]=>{{1,2,4,5,6,7,8},{3}}
[2,4,3,6,7,8,5,1]=>{{1,2,4,6,8},{3},{5,7}}
[3,2,4,8,7,6,5,1]=>{{1,3,4,8},{2},{5,7},{6}}
[2,3,4,8,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}
[2,3,4,7,8,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[2,3,4,6,8,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,7,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,6,7,8,5,1]=>{{1,2,3,4,6,8},{5,7}}
[5,4,3,2,8,7,6,1]=>{{1,5,8},{2,4},{3},{6,7}}
[5,4,3,2,7,8,6,1]=>{{1,5,6,7,8},{2,4},{3}}
[4,5,3,2,8,7,6,1]=>{{1,2,4,5,8},{3},{6,7}}
[3,5,4,2,7,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,5,2,8,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[3,4,5,2,7,8,6,1]=>{{1,3,5,6,7,8},{2,4}}
[2,5,4,3,8,7,6,1]=>{{1,2,5,8},{3,4},{6,7}}
[2,5,4,3,7,8,6,1]=>{{1,2,5,6,7,8},{3,4}}
[2,4,5,3,8,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[2,4,5,3,7,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,2,5,4,7,8,6,1]=>{{1,3,5,6,7,8},{2},{4}}
[2,3,5,4,8,7,6,1]=>{{1,2,3,5,8},{4},{6,7}}
[2,3,5,4,7,8,6,1]=>{{1,2,3,5,6,7,8},{4}}
[4,3,2,5,8,7,6,1]=>{{1,4,5,8},{2,3},{6,7}}
[4,3,2,5,7,8,6,1]=>{{1,4,5,6,7,8},{2,3}}
[3,4,2,5,8,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[3,4,2,5,7,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,2,4,5,7,8,6,1]=>{{1,3,4,5,6,7,8},{2}}
[2,3,4,5,8,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[2,3,4,5,7,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,3,2,8,7,1]=>{{1,6,8},{2,5},{3,4},{7}}
[4,6,5,3,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,4,6,3,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,5,6,3,2,8,7,1]=>{{1,3,4,6,8},{2,5},{7}}
[3,6,5,4,2,8,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[3,5,6,4,2,8,7,1]=>{{1,3,6,8},{2,5},{4},{7}}
[4,3,6,5,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,4,3,6,2,8,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[4,5,3,6,2,8,7,1]=>{{1,4,6,8},{2,5},{3},{7}}
[3,4,5,6,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,6,5,4,3,8,7,1]=>{{1,2,6,8},{3,5},{4},{7}}
[2,4,6,5,3,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,4,5,6,3,8,7,1]=>{{1,2,4,6,8},{3,5},{7}}
[3,2,6,5,4,8,7,1]=>{{1,3,6,8},{2},{4,5},{7}}
[2,3,5,6,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,3,2,6,5,8,7,1]=>{{1,4,6,8},{2,3},{5},{7}}
[3,4,2,6,5,8,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[2,4,3,6,5,8,7,1]=>{{1,2,4,6,8},{3},{5},{7}}
[3,2,4,6,5,8,7,1]=>{{1,3,4,6,8},{2},{5},{7}}
[2,3,4,6,5,8,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[5,4,3,2,6,8,7,1]=>{{1,5,6,8},{2,4},{3},{7}}
[2,5,4,3,6,8,7,1]=>{{1,2,5,6,8},{3,4},{7}}
[2,4,5,3,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[3,2,5,4,6,8,7,1]=>{{1,3,5,6,8},{2},{4},{7}}
[4,3,2,5,6,8,7,1]=>{{1,4,5,6,8},{2,3},{7}}
[3,4,2,5,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,4,3,5,6,8,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[3,2,4,5,6,8,7,1]=>{{1,3,4,5,6,8},{2},{7}}
[2,3,4,5,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,7,6,4,3,2,8,1]=>{{1,2,3,5,6,7,8},{4}}
[4,7,6,5,3,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,5,3,2,8,1]=>{{1,3,4,5,7,8},{2,6}}
[4,6,5,7,3,2,8,1]=>{{1,4,7,8},{2,6},{3,5}}
[3,5,7,6,4,2,8,1]=>{{1,3,7,8},{2,4,5,6}}
[3,5,6,7,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,6,5,2,8,1]=>{{1,2,3,4,6,7,8},{5}}
[4,3,6,7,5,2,8,1]=>{{1,4,7,8},{2,3,6},{5}}
[3,4,7,6,5,2,8,1]=>{{1,3,7,8},{2,4,6},{5}}
[3,4,6,7,5,2,8,1]=>{{1,2,3,4,6,7,8},{5}}
[5,4,3,7,6,2,8,1]=>{{1,2,4,5,6,7,8},{3}}
[3,5,4,7,6,2,8,1]=>{{1,3,4,7,8},{2,5,6}}
[3,4,5,7,6,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,3,7,2,8,1]=>{{1,3,4,5,7,8},{2,6}}
[3,6,5,4,7,2,8,1]=>{{1,3,5,7,8},{2,6},{4}}
[3,5,6,4,7,2,8,1]=>{{1,2,3,5,6,7,8},{4}}
[4,3,6,5,7,2,8,1]=>{{1,4,5,7,8},{2,3,6}}
[3,4,6,5,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,4,6,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,5,4,3,8,1]=>{{1,2,7,8},{3,6},{4,5}}
[2,6,5,7,4,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,7,4,3,8,1]=>{{1,2,4,5,7,8},{3,6}}
[2,4,6,7,5,3,8,1]=>{{1,2,4,7,8},{3,6},{5}}
[2,5,4,7,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,5,7,3,8,1]=>{{1,2,4,5,7,8},{3,6}}
[2,5,4,6,7,3,8,1]=>{{1,2,5,7,8},{3,4,6}}
[2,4,5,6,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[3,2,7,6,5,4,8,1]=>{{1,3,7,8},{2},{4,6},{5}}
[3,2,6,7,5,4,8,1]=>{{1,3,4,6,7,8},{2},{5}}
[3,2,5,7,6,4,8,1]=>{{1,3,4,5,6,7,8},{2}}
[3,2,6,5,7,4,8,1]=>{{1,3,4,5,6,7,8},{2}}
[3,2,5,6,7,4,8,1]=>{{1,3,5,7,8},{2},{4,6}}
[2,3,7,6,5,4,8,1]=>{{1,2,3,7,8},{4,6},{5}}
[2,3,5,7,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,6,7,4,8,1]=>{{1,2,3,5,7,8},{4,6}}
[4,3,2,7,6,5,8,1]=>{{1,4,7,8},{2,3},{5,6}}
[4,3,2,6,7,5,8,1]=>{{1,4,5,6,7,8},{2,3}}
[3,4,2,7,6,5,8,1]=>{{1,2,3,4,7,8},{5,6}}
[3,4,2,6,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,4,3,7,6,5,8,1]=>{{1,2,4,7,8},{3},{5,6}}
[2,4,3,6,7,5,8,1]=>{{1,2,4,5,6,7,8},{3}}
[3,2,4,7,6,5,8,1]=>{{1,3,4,7,8},{2},{5,6}}
[2,3,4,7,6,5,8,1]=>{{1,2,3,4,7,8},{5,6}}
[2,3,4,6,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,2,7,6,8,1]=>{{1,5,7,8},{2,4},{3},{6}}
[3,5,4,2,7,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[4,3,5,2,7,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[3,4,5,2,7,6,8,1]=>{{1,3,5,7,8},{2,4},{6}}
[2,5,4,3,7,6,8,1]=>{{1,2,5,7,8},{3,4},{6}}
[3,2,5,4,7,6,8,1]=>{{1,3,5,7,8},{2},{4},{6}}
[2,3,5,4,7,6,8,1]=>{{1,2,3,5,7,8},{4},{6}}
[4,3,2,5,7,6,8,1]=>{{1,4,5,7,8},{2,3},{6}}
[3,4,2,5,7,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[2,4,3,5,7,6,8,1]=>{{1,2,4,5,7,8},{3},{6}}
[3,2,4,5,7,6,8,1]=>{{1,3,4,5,7,8},{2},{6}}
[2,3,4,5,7,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[3,6,5,4,2,7,8,1]=>{{1,2,3,5,6,7,8},{4}}
[3,5,6,4,2,7,8,1]=>{{1,3,6,7,8},{2,5},{4}}
[3,4,6,5,2,7,8,1]=>{{1,3,6,7,8},{2,4,5}}
[3,5,4,6,2,7,8,1]=>{{1,3,4,6,7,8},{2,5}}
[2,6,5,4,3,7,8,1]=>{{1,2,6,7,8},{3,5},{4}}
[2,5,6,4,3,7,8,1]=>{{1,2,3,5,6,7,8},{4}}
[2,4,6,5,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,6,3,7,8,1]=>{{1,2,4,6,7,8},{3,5}}
[3,2,5,6,4,7,8,1]=>{{1,3,4,5,6,7,8},{2}}
[2,3,6,5,4,7,8,1]=>{{1,2,3,6,7,8},{4,5}}
[2,3,5,6,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,2,6,5,7,8,1]=>{{1,4,6,7,8},{2,3},{5}}
[3,4,2,6,5,7,8,1]=>{{1,2,3,4,6,7,8},{5}}
[2,4,3,6,5,7,8,1]=>{{1,2,4,6,7,8},{3},{5}}
[2,3,4,6,5,7,8,1]=>{{1,2,3,4,6,7,8},{5}}
[3,5,4,2,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,3,6,7,8,1]=>{{1,2,5,6,7,8},{3,4}}
[2,4,5,3,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[3,2,5,4,6,7,8,1]=>{{1,3,5,6,7,8},{2},{4}}
[2,3,5,4,6,7,8,1]=>{{1,2,3,5,6,7,8},{4}}
[2,4,3,5,6,7,8,1]=>{{1,2,4,5,6,7,8},{3}}
[1,8,7,6,5,4,3,2]=>{{1},{2,8},{3,7},{4,6},{5}}
[1,7,8,6,5,4,3,2]=>{{1},{2,3,7,8},{4,6},{5}}
[1,6,8,7,5,4,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,7,6,8,5,4,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,6,7,8,5,4,3,2]=>{{1},{2,4,6,8},{3,7},{5}}
[1,5,8,7,6,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,5,8,7,4,3,2]=>{{1},{2,4,6,8},{3,5,7}}
[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,7,5,8,4,3,2]=>{{1},{2,4,5,6,8},{3,7}}
[1,5,7,6,8,4,3,2]=>{{1},{2,5,8},{3,7},{4,6}}
[1,6,5,7,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,6,7,8,4,3,2]=>{{1},{2,5,8},{3,4,6,7}}
[1,4,8,7,6,5,3,2]=>{{1},{2,3,4,7,8},{5,6}}
[1,4,7,8,6,5,3,2]=>{{1},{2,4,8},{3,7},{5,6}}
[1,4,6,8,7,5,3,2]=>{{1},{2,4,8},{3,5,6,7}}
[1,4,6,7,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,4,7,8,6,3,2]=>{{1},{2,5,8},{3,4,7},{6}}
[1,4,6,5,8,7,3,2]=>{{1},{2,4,5,8},{3,6,7}}
[1,7,6,5,4,8,3,2]=>{{1},{2,3,6,7,8},{4,5}}
[1,4,7,6,5,8,3,2]=>{{1},{2,4,6,8},{3,7},{5}}
[1,4,6,7,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,6,5,4,7,8,3,2]=>{{1},{2,6,8},{3,5,7},{4}}
[1,5,6,4,7,8,3,2]=>{{1},{2,3,5,6,7,8},{4}}
[1,5,4,6,7,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,4,5,6,7,8,3,2]=>{{1},{2,4,6,8},{3,5,7}}
[1,3,8,7,6,5,4,2]=>{{1},{2,3,8},{4,7},{5,6}}
[1,3,7,8,6,5,4,2]=>{{1},{2,3,4,7,8},{5,6}}
[1,3,6,8,7,5,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,3,6,7,8,5,4,2]=>{{1},{2,3,5,6,8},{4,7}}
[1,3,5,8,7,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,3,5,7,8,6,4,2]=>{{1},{2,3,5,8},{4,7},{6}}
[1,3,5,6,8,7,4,2]=>{{1},{2,3,5,8},{4,6,7}}
[1,3,6,7,5,8,4,2]=>{{1},{2,3,6,8},{4,7},{5}}
[1,3,6,5,7,8,4,2]=>{{1},{2,3,6,8},{4,5,7}}
[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,4,3,8,7,6,5,2]=>{{1},{2,4,8},{3},{5,7},{6}}
[1,4,3,7,8,6,5,2]=>{{1},{2,4,5,7,8},{3},{6}}
[1,4,3,6,8,7,5,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,4,3,7,6,8,5,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,4,3,6,7,8,5,2]=>{{1},{2,4,6,8},{3},{5,7}}
[1,3,4,8,7,6,5,2]=>{{1},{2,3,4,8},{5,7},{6}}
[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,3,4,6,7,8,5,2]=>{{1},{2,3,4,6,8},{5,7}}
[1,5,4,3,8,7,6,2]=>{{1},{2,5,8},{3,4},{6,7}}
[1,4,5,3,8,7,6,2]=>{{1},{2,3,4,5,8},{6,7}}
[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,3,5,4,8,7,6,2]=>{{1},{2,3,5,8},{4},{6,7}}
[1,4,3,5,8,7,6,2]=>{{1},{2,4,5,8},{3},{6,7}}
[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,3,4,5,8,7,6,2]=>{{1},{2,3,4,5,8},{6,7}}
[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,5,4,3,8,7,2]=>{{1},{2,6,8},{3,5},{4},{7}}
[1,5,6,4,3,8,7,2]=>{{1},{2,3,5,6,8},{4},{7}}
[1,4,6,5,3,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[1,4,5,6,3,8,7,2]=>{{1},{2,4,6,8},{3,5},{7}}
[1,3,6,5,4,8,7,2]=>{{1},{2,3,6,8},{4,5},{7}}
[1,4,3,6,5,8,7,2]=>{{1},{2,4,6,8},{3},{5},{7}}
[1,5,4,3,6,8,7,2]=>{{1},{2,5,6,8},{3,4},{7}}
[1,4,5,3,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[1,7,6,5,4,3,8,2]=>{{1},{2,7,8},{3,6},{4,5}}
[1,6,7,5,4,3,8,2]=>{{1},{2,3,6,7,8},{4,5}}
[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,6,7,4,3,8,2]=>{{1},{2,4,5,7,8},{3,6}}
[1,4,6,7,5,3,8,2]=>{{1},{2,4,7,8},{3,6},{5}}
[1,5,6,4,7,3,8,2]=>{{1},{2,5,7,8},{3,6},{4}}
[1,4,6,5,7,3,8,2]=>{{1},{2,4,5,7,8},{3,6}}
[1,5,4,6,7,3,8,2]=>{{1},{2,5,7,8},{3,4,6}}
[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,3,5,6,7,4,8,2]=>{{1},{2,3,5,7,8},{4,6}}
[1,3,4,7,6,5,8,2]=>{{1},{2,3,4,7,8},{5,6}}
[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,3,5,4,7,6,8,2]=>{{1},{2,3,5,7,8},{4},{6}}
[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,5,4,3,6,7,8,2]=>{{1},{2,5,6,7,8},{3,4}}
[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,8,7,6,5,4,3]=>{{1,2},{3,8},{4,7},{5,6}}
[2,1,7,8,6,5,4,3]=>{{1,2},{3,4,7,8},{5,6}}
[2,1,6,8,7,5,4,3]=>{{1,2},{3,4,5,6,7,8}}
[2,1,7,6,8,5,4,3]=>{{1,2},{3,4,5,6,7,8}}
[2,1,6,7,8,5,4,3]=>{{1,2},{3,5,6,8},{4,7}}
[2,1,5,8,7,6,4,3]=>{{1,2},{3,4,5,7,8},{6}}
[2,1,5,7,8,6,4,3]=>{{1,2},{3,5,8},{4,7},{6}}
[2,1,6,5,8,7,4,3]=>{{1,2},{3,4,5,6,7,8}}
[2,1,5,6,8,7,4,3]=>{{1,2},{3,5,8},{4,6,7}}
[2,1,7,6,5,8,4,3]=>{{1,2},{3,4,6,7,8},{5}}
[2,1,6,7,5,8,4,3]=>{{1,2},{3,6,8},{4,7},{5}}
[2,1,5,7,6,8,4,3]=>{{1,2},{3,5,6,8},{4,7}}
[2,1,6,5,7,8,4,3]=>{{1,2},{3,6,8},{4,5,7}}
[2,1,5,6,7,8,4,3]=>{{1,2},{3,4,5,6,7,8}}
[2,1,4,8,7,6,5,3]=>{{1,2},{3,4,8},{5,7},{6}}
[2,1,4,7,8,6,5,3]=>{{1,2},{3,4,5,7,8},{6}}
[2,1,4,6,8,7,5,3]=>{{1,2},{3,4,5,6,7,8}}
[2,1,4,6,7,8,5,3]=>{{1,2},{3,4,6,8},{5,7}}
[2,1,5,4,8,7,6,3]=>{{1,2},{3,5,8},{4},{6,7}}
[2,1,5,4,7,8,6,3]=>{{1,2},{3,5,6,7,8},{4}}
[2,1,4,5,8,7,6,3]=>{{1,2},{3,4,5,8},{6,7}}
[2,1,4,5,7,8,6,3]=>{{1,2},{3,4,5,6,7,8}}
[2,1,5,6,4,8,7,3]=>{{1,2},{3,4,5,6,8},{7}}
[2,1,4,6,5,8,7,3]=>{{1,2},{3,4,6,8},{5},{7}}
[2,1,4,5,6,8,7,3]=>{{1,2},{3,4,5,6,8},{7}}
[2,1,7,6,5,4,8,3]=>{{1,2},{3,7,8},{4,6},{5}}
[2,1,6,7,5,4,8,3]=>{{1,2},{3,4,6,7,8},{5}}
[2,1,5,7,6,4,8,3]=>{{1,2},{3,4,5,6,7,8}}
[2,1,6,5,7,4,8,3]=>{{1,2},{3,4,5,6,7,8}}
[2,1,5,6,7,4,8,3]=>{{1,2},{3,5,7,8},{4,6}}
[2,1,4,7,6,5,8,3]=>{{1,2},{3,4,7,8},{5,6}}
[2,1,4,6,7,5,8,3]=>{{1,2},{3,4,5,6,7,8}}
[2,1,5,4,7,6,8,3]=>{{1,2},{3,5,7,8},{4},{6}}
[2,1,5,6,4,7,8,3]=>{{1,2},{3,4,5,6,7,8}}
[2,1,5,4,6,7,8,3]=>{{1,2},{3,5,6,7,8},{4}}
[2,1,4,5,6,7,8,3]=>{{1,2},{3,4,5,6,7,8}}
[1,2,8,7,6,5,4,3]=>{{1},{2},{3,8},{4,7},{5,6}}
[1,2,7,8,6,5,4,3]=>{{1},{2},{3,4,7,8},{5,6}}
[1,2,7,6,8,5,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,6,7,8,5,4,3]=>{{1},{2},{3,5,6,8},{4,7}}
[1,2,5,8,7,6,4,3]=>{{1},{2},{3,4,5,7,8},{6}}
[1,2,6,5,8,7,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,5,6,8,7,4,3]=>{{1},{2},{3,5,8},{4,6,7}}
[1,2,7,6,5,8,4,3]=>{{1},{2},{3,4,6,7,8},{5}}
[1,2,5,7,6,8,4,3]=>{{1},{2},{3,5,6,8},{4,7}}
[1,2,6,5,7,8,4,3]=>{{1},{2},{3,6,8},{4,5,7}}
[1,2,5,6,7,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,4,8,7,6,5,3]=>{{1},{2},{3,4,8},{5,7},{6}}
[1,2,4,7,8,6,5,3]=>{{1},{2},{3,4,5,7,8},{6}}
[1,2,4,6,8,7,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,4,6,7,8,5,3]=>{{1},{2},{3,4,6,8},{5,7}}
[1,2,5,4,8,7,6,3]=>{{1},{2},{3,5,8},{4},{6,7}}
[1,2,5,4,7,8,6,3]=>{{1},{2},{3,5,6,7,8},{4}}
[1,2,4,5,8,7,6,3]=>{{1},{2},{3,4,5,8},{6,7}}
[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,6,5,4,8,7,3]=>{{1},{2},{3,6,8},{4,5},{7}}
[1,2,4,6,5,8,7,3]=>{{1},{2},{3,4,6,8},{5},{7}}
[1,2,5,4,6,8,7,3]=>{{1},{2},{3,5,6,8},{4},{7}}
[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[1,2,7,6,5,4,8,3]=>{{1},{2},{3,7,8},{4,6},{5}}
[1,2,5,7,6,4,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,5,6,7,4,8,3]=>{{1},{2},{3,5,7,8},{4,6}}
[1,2,4,7,6,5,8,3]=>{{1},{2},{3,4,7,8},{5,6}}
[1,2,5,4,7,6,8,3]=>{{1},{2},{3,5,7,8},{4},{6}}
[1,2,6,5,4,7,8,3]=>{{1},{2},{3,6,7,8},{4,5}}
[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,2,1,8,7,6,5,4]=>{{1,3},{2},{4,8},{5,7},{6}}
[3,2,1,7,8,6,5,4]=>{{1,3},{2},{4,5,7,8},{6}}
[3,2,1,6,8,7,5,4]=>{{1,3},{2},{4,5,6,7,8}}
[3,2,1,7,6,8,5,4]=>{{1,3},{2},{4,5,6,7,8}}
[3,2,1,6,7,8,5,4]=>{{1,3},{2},{4,6,8},{5,7}}
[3,2,1,5,8,7,6,4]=>{{1,3},{2},{4,5,8},{6,7}}
[3,2,1,5,7,8,6,4]=>{{1,3},{2},{4,5,6,7,8}}
[3,2,1,6,5,8,7,4]=>{{1,3},{2},{4,6,8},{5},{7}}
[3,2,1,5,6,8,7,4]=>{{1,3},{2},{4,5,6,8},{7}}
[3,2,1,7,6,5,8,4]=>{{1,3},{2},{4,7,8},{5,6}}
[3,2,1,6,7,5,8,4]=>{{1,3},{2},{4,5,6,7,8}}
[3,2,1,5,7,6,8,4]=>{{1,3},{2},{4,5,7,8},{6}}
[3,2,1,6,5,7,8,4]=>{{1,3},{2},{4,6,7,8},{5}}
[3,2,1,5,6,7,8,4]=>{{1,3},{2},{4,5,6,7,8}}
[2,3,1,8,7,6,5,4]=>{{1,2,3},{4,8},{5,7},{6}}
[2,3,1,7,8,6,5,4]=>{{1,2,3},{4,5,7,8},{6}}
[2,3,1,6,8,7,5,4]=>{{1,2,3},{4,5,6,7,8}}
[2,3,1,7,6,8,5,4]=>{{1,2,3},{4,5,6,7,8}}
[2,3,1,6,7,8,5,4]=>{{1,2,3},{4,6,8},{5,7}}
[2,3,1,5,7,8,6,4]=>{{1,2,3},{4,5,6,7,8}}
[2,3,1,6,5,8,7,4]=>{{1,2,3},{4,6,8},{5},{7}}
[2,3,1,7,6,5,8,4]=>{{1,2,3},{4,7,8},{5,6}}
[2,3,1,6,7,5,8,4]=>{{1,2,3},{4,5,6,7,8}}
[2,3,1,5,7,6,8,4]=>{{1,2,3},{4,5,7,8},{6}}
[2,3,1,5,6,7,8,4]=>{{1,2,3},{4,5,6,7,8}}
[1,3,2,8,7,6,5,4]=>{{1},{2,3},{4,8},{5,7},{6}}
[1,3,2,6,8,7,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,3,2,6,7,8,5,4]=>{{1},{2,3},{4,6,8},{5,7}}
[1,3,2,5,8,7,6,4]=>{{1},{2,3},{4,5,8},{6,7}}
[1,3,2,5,7,8,6,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,3,2,6,5,8,7,4]=>{{1},{2,3},{4,6,8},{5},{7}}
[1,3,2,7,6,5,8,4]=>{{1},{2,3},{4,7,8},{5,6}}
[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,3,2,6,5,7,8,4]=>{{1},{2,3},{4,6,7,8},{5}}
[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[2,1,3,8,7,6,5,4]=>{{1,2},{3},{4,8},{5,7},{6}}
[2,1,3,7,8,6,5,4]=>{{1,2},{3},{4,5,7,8},{6}}
[2,1,3,6,8,7,5,4]=>{{1,2},{3},{4,5,6,7,8}}
[2,1,3,6,7,8,5,4]=>{{1,2},{3},{4,6,8},{5,7}}
[2,1,3,6,5,8,7,4]=>{{1,2},{3},{4,6,8},{5},{7}}
[2,1,3,5,6,7,8,4]=>{{1,2},{3},{4,5,6,7,8}}
[1,2,3,8,7,6,5,4]=>{{1},{2},{3},{4,8},{5,7},{6}}
[1,2,3,7,8,6,5,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,6,7,8,5,4]=>{{1},{2},{3},{4,6,8},{5,7}}
[1,2,3,5,8,7,6,4]=>{{1},{2},{3},{4,5,8},{6,7}}
[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}}
[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[1,2,3,7,6,5,8,4]=>{{1},{2},{3},{4,7,8},{5,6}}
[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,3,2,1,8,7,6,5]=>{{1,4},{2,3},{5,8},{6,7}}
[4,3,2,1,7,8,6,5]=>{{1,4},{2,3},{5,6,7,8}}
[4,3,2,1,6,8,7,5]=>{{1,4},{2,3},{5,6,8},{7}}
[4,3,2,1,7,6,8,5]=>{{1,4},{2,3},{5,7,8},{6}}
[4,3,2,1,6,7,8,5]=>{{1,4},{2,3},{5,6,7,8}}
[3,4,2,1,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}
[3,4,2,1,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}
[3,4,2,1,6,8,7,5]=>{{1,2,3,4},{5,6,8},{7}}
[3,4,2,1,7,6,8,5]=>{{1,2,3,4},{5,7,8},{6}}
[3,4,2,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}
[2,4,3,1,8,7,6,5]=>{{1,2,4},{3},{5,8},{6,7}}
[2,4,3,1,7,8,6,5]=>{{1,2,4},{3},{5,6,7,8}}
[2,4,3,1,6,8,7,5]=>{{1,2,4},{3},{5,6,8},{7}}
[2,4,3,1,7,6,8,5]=>{{1,2,4},{3},{5,7,8},{6}}
[2,4,3,1,6,7,8,5]=>{{1,2,4},{3},{5,6,7,8}}
[3,2,4,1,8,7,6,5]=>{{1,3,4},{2},{5,8},{6,7}}
[3,2,4,1,7,8,6,5]=>{{1,3,4},{2},{5,6,7,8}}
[3,2,4,1,6,8,7,5]=>{{1,3,4},{2},{5,6,8},{7}}
[3,2,4,1,7,6,8,5]=>{{1,3,4},{2},{5,7,8},{6}}
[3,2,4,1,6,7,8,5]=>{{1,3,4},{2},{5,6,7,8}}
[2,3,4,1,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}
[2,3,4,1,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}
[2,3,4,1,6,8,7,5]=>{{1,2,3,4},{5,6,8},{7}}
[2,3,4,1,7,6,8,5]=>{{1,2,3,4},{5,7,8},{6}}
[2,3,4,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}
[1,4,3,2,8,7,6,5]=>{{1},{2,4},{3},{5,8},{6,7}}
[1,4,3,2,6,8,7,5]=>{{1},{2,4},{3},{5,6,8},{7}}
[1,4,3,2,7,6,8,5]=>{{1},{2,4},{3},{5,7,8},{6}}
[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}}
[1,3,4,2,8,7,6,5]=>{{1},{2,3,4},{5,8},{6,7}}
[1,3,4,2,7,8,6,5]=>{{1},{2,3,4},{5,6,7,8}}
[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[1,3,4,2,7,6,8,5]=>{{1},{2,3,4},{5,7,8},{6}}
[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[2,1,4,3,8,7,6,5]=>{{1,2},{3,4},{5,8},{6,7}}
[2,1,4,3,7,8,6,5]=>{{1,2},{3,4},{5,6,7,8}}
[2,1,4,3,6,8,7,5]=>{{1,2},{3,4},{5,6,8},{7}}
[2,1,4,3,7,6,8,5]=>{{1,2},{3,4},{5,7,8},{6}}
[2,1,4,3,6,7,8,5]=>{{1,2},{3,4},{5,6,7,8}}
[1,2,4,3,8,7,6,5]=>{{1},{2},{3,4},{5,8},{6,7}}
[1,2,4,3,7,8,6,5]=>{{1},{2},{3,4},{5,6,7,8}}
[1,2,4,3,6,8,7,5]=>{{1},{2},{3,4},{5,6,8},{7}}
[1,2,4,3,7,6,8,5]=>{{1},{2},{3,4},{5,7,8},{6}}
[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[3,2,1,4,8,7,6,5]=>{{1,3},{2},{4},{5,8},{6,7}}
[3,2,1,4,7,8,6,5]=>{{1,3},{2},{4},{5,6,7,8}}
[3,2,1,4,6,8,7,5]=>{{1,3},{2},{4},{5,6,8},{7}}
[3,2,1,4,7,6,8,5]=>{{1,3},{2},{4},{5,7,8},{6}}
[3,2,1,4,6,7,8,5]=>{{1,3},{2},{4},{5,6,7,8}}
[2,3,1,4,8,7,6,5]=>{{1,2,3},{4},{5,8},{6,7}}
[2,3,1,4,7,8,6,5]=>{{1,2,3},{4},{5,6,7,8}}
[2,3,1,4,7,6,8,5]=>{{1,2,3},{4},{5,7,8},{6}}
[2,3,1,4,6,7,8,5]=>{{1,2,3},{4},{5,6,7,8}}
[1,3,2,4,8,7,6,5]=>{{1},{2,3},{4},{5,8},{6,7}}
[1,3,2,4,6,8,7,5]=>{{1},{2,3},{4},{5,6,8},{7}}
[1,3,2,4,7,6,8,5]=>{{1},{2,3},{4},{5,7,8},{6}}
[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}}
[2,1,3,4,8,7,6,5]=>{{1,2},{3},{4},{5,8},{6,7}}
[2,1,3,4,7,8,6,5]=>{{1,2},{3},{4},{5,6,7,8}}
[2,1,3,4,7,6,8,5]=>{{1,2},{3},{4},{5,7,8},{6}}
[2,1,3,4,6,7,8,5]=>{{1,2},{3},{4},{5,6,7,8}}
[1,2,3,4,8,7,6,5]=>{{1},{2},{3},{4},{5,8},{6,7}}
[1,2,3,4,7,8,6,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[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},{5,7,8},{6}}
[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[5,4,3,2,1,8,7,6]=>{{1,5},{2,4},{3},{6,8},{7}}
[5,4,3,2,1,7,8,6]=>{{1,5},{2,4},{3},{6,7,8}}
[4,5,3,2,1,8,7,6]=>{{1,2,4,5},{3},{6,8},{7}}
[3,5,4,2,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[3,5,4,2,1,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[4,3,5,2,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[3,4,5,2,1,8,7,6]=>{{1,3,5},{2,4},{6,8},{7}}
[2,5,4,3,1,8,7,6]=>{{1,2,5},{3,4},{6,8},{7}}
[2,5,4,3,1,7,8,6]=>{{1,2,5},{3,4},{6,7,8}}
[2,4,5,3,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[2,4,5,3,1,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[3,2,5,4,1,8,7,6]=>{{1,3,5},{2},{4},{6,8},{7}}
[3,2,5,4,1,7,8,6]=>{{1,3,5},{2},{4},{6,7,8}}
[2,3,5,4,1,8,7,6]=>{{1,2,3,5},{4},{6,8},{7}}
[4,3,2,5,1,8,7,6]=>{{1,4,5},{2,3},{6,8},{7}}
[4,3,2,5,1,7,8,6]=>{{1,4,5},{2,3},{6,7,8}}
[3,4,2,5,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[3,4,2,5,1,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[2,4,3,5,1,8,7,6]=>{{1,2,4,5},{3},{6,8},{7}}
[2,4,3,5,1,7,8,6]=>{{1,2,4,5},{3},{6,7,8}}
[3,2,4,5,1,8,7,6]=>{{1,3,4,5},{2},{6,8},{7}}
[2,3,4,5,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[2,3,4,5,1,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[1,5,4,3,2,8,7,6]=>{{1},{2,5},{3,4},{6,8},{7}}
[1,5,4,3,2,7,8,6]=>{{1},{2,5},{3,4},{6,7,8}}
[1,4,5,3,2,8,7,6]=>{{1},{2,3,4,5},{6,8},{7}}
[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[1,3,5,4,2,7,8,6]=>{{1},{2,3,5},{4},{6,7,8}}
[1,3,4,5,2,8,7,6]=>{{1},{2,3,4,5},{6,8},{7}}
[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[2,1,5,4,3,8,7,6]=>{{1,2},{3,5},{4},{6,8},{7}}
[2,1,4,5,3,8,7,6]=>{{1,2},{3,4,5},{6,8},{7}}
[1,2,5,4,3,8,7,6]=>{{1},{2},{3,5},{4},{6,8},{7}}
[1,2,5,4,3,7,8,6]=>{{1},{2},{3,5},{4},{6,7,8}}
[1,2,4,5,3,8,7,6]=>{{1},{2},{3,4,5},{6,8},{7}}
[1,2,4,5,3,7,8,6]=>{{1},{2},{3,4,5},{6,7,8}}
[1,3,2,5,4,8,7,6]=>{{1},{2,3},{4,5},{6,8},{7}}
[1,3,2,5,4,7,8,6]=>{{1},{2,3},{4,5},{6,7,8}}
[2,1,3,5,4,8,7,6]=>{{1,2},{3},{4,5},{6,8},{7}}
[2,1,3,5,4,7,8,6]=>{{1,2},{3},{4,5},{6,7,8}}
[1,2,3,5,4,8,7,6]=>{{1},{2},{3},{4,5},{6,8},{7}}
[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}}
[4,3,2,1,5,8,7,6]=>{{1,4},{2,3},{5},{6,8},{7}}
[4,3,2,1,5,7,8,6]=>{{1,4},{2,3},{5},{6,7,8}}
[2,4,3,1,5,8,7,6]=>{{1,2,4},{3},{5},{6,8},{7}}
[3,2,4,1,5,8,7,6]=>{{1,3,4},{2},{5},{6,8},{7}}
[3,2,4,1,5,7,8,6]=>{{1,3,4},{2},{5},{6,7,8}}
[2,3,4,1,5,8,7,6]=>{{1,2,3,4},{5},{6,8},{7}}
[2,3,4,1,5,7,8,6]=>{{1,2,3,4},{5},{6,7,8}}
[1,4,3,2,5,8,7,6]=>{{1},{2,4},{3},{5},{6,8},{7}}
[1,4,3,2,5,7,8,6]=>{{1},{2,4},{3},{5},{6,7,8}}
[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[2,1,4,3,5,8,7,6]=>{{1,2},{3,4},{5},{6,8},{7}}
[2,1,4,3,5,7,8,6]=>{{1,2},{3,4},{5},{6,7,8}}
[1,2,4,3,5,8,7,6]=>{{1},{2},{3,4},{5},{6,8},{7}}
[1,2,4,3,5,7,8,6]=>{{1},{2},{3,4},{5},{6,7,8}}
[3,2,1,4,5,8,7,6]=>{{1,3},{2},{4},{5},{6,8},{7}}
[3,2,1,4,5,7,8,6]=>{{1,3},{2},{4},{5},{6,7,8}}
[2,3,1,4,5,7,8,6]=>{{1,2,3},{4},{5},{6,7,8}}
[1,3,2,4,5,8,7,6]=>{{1},{2,3},{4},{5},{6,8},{7}}
[1,3,2,4,5,7,8,6]=>{{1},{2,3},{4},{5},{6,7,8}}
[2,1,3,4,5,8,7,6]=>{{1,2},{3},{4},{5},{6,8},{7}}
[2,1,3,4,5,7,8,6]=>{{1,2},{3},{4},{5},{6,7,8}}
[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[6,5,4,3,2,1,8,7]=>{{1,6},{2,5},{3,4},{7,8}}
[5,6,4,3,2,1,8,7]=>{{1,2,5,6},{3,4},{7,8}}
[4,6,5,3,2,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[5,4,6,3,2,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,5,6,3,2,1,8,7]=>{{1,3,4,6},{2,5},{7,8}}
[3,6,5,4,2,1,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[3,5,6,4,2,1,8,7]=>{{1,3,6},{2,5},{4},{7,8}}
[4,3,6,5,2,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,4,6,5,2,1,8,7]=>{{1,3,6},{2,4,5},{7,8}}
[5,4,3,6,2,1,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[4,5,3,6,2,1,8,7]=>{{1,4,6},{2,5},{3},{7,8}}
[4,3,5,6,2,1,8,7]=>{{1,4,6},{2,3,5},{7,8}}
[3,4,5,6,2,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,6,5,4,3,1,8,7]=>{{1,2,6},{3,5},{4},{7,8}}
[2,5,6,4,3,1,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[2,4,6,5,3,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,2,5,6,4,1,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[2,3,6,5,4,1,8,7]=>{{1,2,3,6},{4,5},{7,8}}
[2,3,5,6,4,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,3,2,6,5,1,8,7]=>{{1,4,6},{2,3},{5},{7,8}}
[3,4,2,6,5,1,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[2,4,3,6,5,1,8,7]=>{{1,2,4,6},{3},{5},{7,8}}
[5,4,3,2,6,1,8,7]=>{{1,5,6},{2,4},{3},{7,8}}
[4,5,3,2,6,1,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[3,5,4,2,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,3,5,2,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,4,5,2,6,1,8,7]=>{{1,3,5,6},{2,4},{7,8}}
[2,5,4,3,6,1,8,7]=>{{1,2,5,6},{3,4},{7,8}}
[2,4,5,3,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,2,5,4,6,1,8,7]=>{{1,3,5,6},{2},{4},{7,8}}
[4,3,2,5,6,1,8,7]=>{{1,4,5,6},{2,3},{7,8}}
[3,4,2,5,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,4,3,5,6,1,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[2,3,4,5,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[1,6,5,4,3,2,8,7]=>{{1},{2,6},{3,5},{4},{7,8}}
[1,5,6,4,3,2,8,7]=>{{1},{2,3,5,6},{4},{7,8}}
[1,5,4,6,3,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[1,3,6,5,4,2,8,7]=>{{1},{2,3,6},{4,5},{7,8}}
[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[2,1,6,5,4,3,8,7]=>{{1,2},{3,6},{4,5},{7,8}}
[2,1,5,6,4,3,8,7]=>{{1,2},{3,4,5,6},{7,8}}
[2,1,4,6,5,3,8,7]=>{{1,2},{3,4,6},{5},{7,8}}
[2,1,5,4,6,3,8,7]=>{{1,2},{3,5,6},{4},{7,8}}
[2,1,4,5,6,3,8,7]=>{{1,2},{3,4,5,6},{7,8}}
[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[3,2,1,6,5,4,8,7]=>{{1,3},{2},{4,6},{5},{7,8}}
[2,3,1,6,5,4,8,7]=>{{1,2,3},{4,6},{5},{7,8}}
[1,3,2,6,5,4,8,7]=>{{1},{2,3},{4,6},{5},{7,8}}
[1,3,2,5,6,4,8,7]=>{{1},{2,3},{4,5,6},{7,8}}
[2,1,3,6,5,4,8,7]=>{{1,2},{3},{4,6},{5},{7,8}}
[2,1,3,5,6,4,8,7]=>{{1,2},{3},{4,5,6},{7,8}}
[1,2,3,6,5,4,8,7]=>{{1},{2},{3},{4,6},{5},{7,8}}
[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[4,3,2,1,6,5,8,7]=>{{1,4},{2,3},{5,6},{7,8}}
[3,4,2,1,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}
[2,4,3,1,6,5,8,7]=>{{1,2,4},{3},{5,6},{7,8}}
[3,2,4,1,6,5,8,7]=>{{1,3,4},{2},{5,6},{7,8}}
[2,3,4,1,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}
[1,3,4,2,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}}
[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}}
[1,2,4,3,6,5,8,7]=>{{1},{2},{3,4},{5,6},{7,8}}
[2,3,1,4,6,5,8,7]=>{{1,2,3},{4},{5,6},{7,8}}
[1,3,2,4,6,5,8,7]=>{{1},{2,3},{4},{5,6},{7,8}}
[2,1,3,4,6,5,8,7]=>{{1,2},{3},{4},{5,6},{7,8}}
[1,2,3,4,6,5,8,7]=>{{1},{2},{3},{4},{5,6},{7,8}}
[5,4,3,2,1,6,8,7]=>{{1,5},{2,4},{3},{6},{7,8}}
[4,5,3,2,1,6,8,7]=>{{1,2,4,5},{3},{6},{7,8}}
[3,5,4,2,1,6,8,7]=>{{1,2,3,4,5},{6},{7,8}}
[4,3,5,2,1,6,8,7]=>{{1,2,3,4,5},{6},{7,8}}
[3,4,5,2,1,6,8,7]=>{{1,3,5},{2,4},{6},{7,8}}
[2,5,4,3,1,6,8,7]=>{{1,2,5},{3,4},{6},{7,8}}
[2,4,5,3,1,6,8,7]=>{{1,2,3,4,5},{6},{7,8}}
[3,2,5,4,1,6,8,7]=>{{1,3,5},{2},{4},{6},{7,8}}
[2,3,5,4,1,6,8,7]=>{{1,2,3,5},{4},{6},{7,8}}
[2,4,3,5,1,6,8,7]=>{{1,2,4,5},{3},{6},{7,8}}
[2,3,4,5,1,6,8,7]=>{{1,2,3,4,5},{6},{7,8}}
[1,4,5,3,2,6,8,7]=>{{1},{2,3,4,5},{6},{7,8}}
[1,3,5,4,2,6,8,7]=>{{1},{2,3,5},{4},{6},{7,8}}
[2,1,5,4,3,6,8,7]=>{{1,2},{3,5},{4},{6},{7,8}}
[2,1,4,5,3,6,8,7]=>{{1,2},{3,4,5},{6},{7,8}}
[1,2,5,4,3,6,8,7]=>{{1},{2},{3,5},{4},{6},{7,8}}
[2,1,3,5,4,6,8,7]=>{{1,2},{3},{4,5},{6},{7,8}}
[1,2,3,5,4,6,8,7]=>{{1},{2},{3},{4,5},{6},{7,8}}
[4,3,2,1,5,6,8,7]=>{{1,4},{2,3},{5},{6},{7,8}}
[3,2,4,1,5,6,8,7]=>{{1,3,4},{2},{5},{6},{7,8}}
[2,3,4,1,5,6,8,7]=>{{1,2,3,4},{5},{6},{7,8}}
[1,4,3,2,5,6,8,7]=>{{1},{2,4},{3},{5},{6},{7,8}}
[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[2,1,4,3,5,6,8,7]=>{{1,2},{3,4},{5},{6},{7,8}}
[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}}
[3,2,1,4,5,6,8,7]=>{{1,3},{2},{4},{5},{6},{7,8}}
[2,3,1,4,5,6,8,7]=>{{1,2,3},{4},{5},{6},{7,8}}
[1,3,2,4,5,6,8,7]=>{{1},{2,3},{4},{5},{6},{7,8}}
[2,1,3,4,5,6,8,7]=>{{1,2},{3},{4},{5},{6},{7,8}}
[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[5,7,6,4,3,2,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[4,7,6,5,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,7,5,3,2,1,8]=>{{1,3,4,5,7},{2,6},{8}}
[5,4,7,6,3,2,1,8]=>{{1,3,5,7},{2,4,6},{8}}
[4,5,7,6,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,5,7,3,2,1,8]=>{{1,4,7},{2,6},{3,5},{8}}
[3,5,7,6,4,2,1,8]=>{{1,3,7},{2,4,5,6},{8}}
[3,5,6,7,4,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,3,7,6,5,2,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[3,4,7,6,5,2,1,8]=>{{1,3,7},{2,4,6},{5},{8}}
[5,4,3,7,6,2,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[4,5,3,7,6,2,1,8]=>{{1,4,7},{2,5,6},{3},{8}}
[3,5,4,7,6,2,1,8]=>{{1,3,4,7},{2,5,6},{8}}
[4,3,5,7,6,2,1,8]=>{{1,4,7},{2,3,5,6},{8}}
[3,5,6,4,7,2,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[4,3,6,5,7,2,1,8]=>{{1,4,5,7},{2,3,6},{8}}
[2,7,6,5,4,3,1,8]=>{{1,2,7},{3,6},{4,5},{8}}
[2,6,7,5,4,3,1,8]=>{{1,2,3,6,7},{4,5},{8}}
[2,5,7,6,4,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[2,5,6,7,4,3,1,8]=>{{1,2,4,5,7},{3,6},{8}}
[2,4,6,7,5,3,1,8]=>{{1,2,4,7},{3,6},{5},{8}}
[2,5,4,7,6,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[2,5,6,4,7,3,1,8]=>{{1,2,5,7},{3,6},{4},{8}}
[2,5,4,6,7,3,1,8]=>{{1,2,5,7},{3,4,6},{8}}
[2,4,5,6,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[3,2,7,6,5,4,1,8]=>{{1,3,7},{2},{4,6},{5},{8}}
[3,2,6,7,5,4,1,8]=>{{1,3,4,6,7},{2},{5},{8}}
[3,2,5,7,6,4,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,2,6,5,7,4,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,2,5,6,7,4,1,8]=>{{1,3,5,7},{2},{4,6},{8}}
[2,3,7,6,5,4,1,8]=>{{1,2,3,7},{4,6},{5},{8}}
[2,3,6,7,5,4,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,3,5,7,6,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[2,3,6,5,7,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[2,3,5,6,7,4,1,8]=>{{1,2,3,5,7},{4,6},{8}}
[4,3,2,6,7,5,1,8]=>{{1,4,5,6,7},{2,3},{8}}
[3,4,2,7,6,5,1,8]=>{{1,2,3,4,7},{5,6},{8}}
[3,4,2,6,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[3,2,4,6,7,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[2,3,4,7,6,5,1,8]=>{{1,2,3,4,7},{5,6},{8}}
[2,3,4,6,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,3,2,7,6,1,8]=>{{1,5,7},{2,4},{3},{6},{8}}
[4,5,3,2,7,6,1,8]=>{{1,2,4,5,7},{3},{6},{8}}
[3,5,4,2,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,3,5,2,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[3,4,5,2,7,6,1,8]=>{{1,3,5,7},{2,4},{6},{8}}
[3,2,5,4,7,6,1,8]=>{{1,3,5,7},{2},{4},{6},{8}}
[4,3,2,5,7,6,1,8]=>{{1,4,5,7},{2,3},{6},{8}}
[3,4,2,5,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[2,3,4,5,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[3,6,5,4,2,7,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[3,5,6,4,2,7,1,8]=>{{1,3,6,7},{2,5},{4},{8}}
[3,4,6,5,2,7,1,8]=>{{1,3,6,7},{2,4,5},{8}}
[3,5,4,6,2,7,1,8]=>{{1,3,4,6,7},{2,5},{8}}
[2,5,4,6,3,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[3,2,6,5,4,7,1,8]=>{{1,3,6,7},{2},{4,5},{8}}
[4,3,2,6,5,7,1,8]=>{{1,4,6,7},{2,3},{5},{8}}
[3,4,2,6,5,7,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,4,3,6,5,7,1,8]=>{{1,2,4,6,7},{3},{5},{8}}
[2,3,4,6,5,7,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[3,5,4,2,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[2,5,4,3,6,7,1,8]=>{{1,2,5,6,7},{3,4},{8}}
[2,3,5,4,6,7,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[1,7,6,5,4,3,2,8]=>{{1},{2,7},{3,6},{4,5},{8}}
[1,6,7,5,4,3,2,8]=>{{1},{2,3,6,7},{4,5},{8}}
[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,5,6,7,4,3,2,8]=>{{1},{2,4,5,7},{3,6},{8}}
[1,4,7,6,5,3,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[1,4,6,7,5,3,2,8]=>{{1},{2,4,7},{3,6},{5},{8}}
[1,5,6,4,7,3,2,8]=>{{1},{2,5,7},{3,6},{4},{8}}
[1,4,6,5,7,3,2,8]=>{{1},{2,4,5,7},{3,6},{8}}
[1,5,4,6,7,3,2,8]=>{{1},{2,5,7},{3,4,6},{8}}
[1,4,5,6,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,6,7,5,4,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[1,3,5,7,6,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,5,6,7,4,2,8]=>{{1},{2,3,5,7},{4,6},{8}}
[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,5,4,7,6,2,8]=>{{1},{2,3,5,7},{4},{6},{8}}
[1,4,3,5,7,6,2,8]=>{{1},{2,4,5,7},{3},{6},{8}}
[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,6,5,4,7,2,8]=>{{1},{2,3,6,7},{4,5},{8}}
[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,4,3,6,5,7,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[1,5,4,3,6,7,2,8]=>{{1},{2,5,6,7},{3,4},{8}}
[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,1,7,6,5,4,3,8]=>{{1,2},{3,7},{4,6},{5},{8}}
[2,1,6,7,5,4,3,8]=>{{1,2},{3,4,6,7},{5},{8}}
[2,1,5,6,7,4,3,8]=>{{1,2},{3,5,7},{4,6},{8}}
[2,1,5,4,6,7,3,8]=>{{1,2},{3,5,6,7},{4},{8}}
[2,1,4,5,6,7,3,8]=>{{1,2},{3,4,5,6,7},{8}}
[1,2,7,6,5,4,3,8]=>{{1},{2},{3,7},{4,6},{5},{8}}
[1,2,6,7,5,4,3,8]=>{{1},{2},{3,4,6,7},{5},{8}}
[1,2,5,7,6,4,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,5,6,7,4,3,8]=>{{1},{2},{3,5,7},{4,6},{8}}
[1,2,4,6,7,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,5,4,6,7,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[3,2,1,7,6,5,4,8]=>{{1,3},{2},{4,7},{5,6},{8}}
[3,2,1,5,7,6,4,8]=>{{1,3},{2},{4,5,7},{6},{8}}
[3,2,1,6,5,7,4,8]=>{{1,3},{2},{4,6,7},{5},{8}}
[2,3,1,6,7,5,4,8]=>{{1,2,3},{4,5,6,7},{8}}
[2,3,1,6,5,7,4,8]=>{{1,2,3},{4,6,7},{5},{8}}
[2,3,1,5,6,7,4,8]=>{{1,2,3},{4,5,6,7},{8}}
[1,3,2,7,6,5,4,8]=>{{1},{2,3},{4,7},{5,6},{8}}
[1,3,2,6,7,5,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[1,3,2,5,7,6,4,8]=>{{1},{2,3},{4,5,7},{6},{8}}
[1,3,2,6,5,7,4,8]=>{{1},{2,3},{4,6,7},{5},{8}}
[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[2,1,3,6,7,5,4,8]=>{{1,2},{3},{4,5,6,7},{8}}
[1,2,3,7,6,5,4,8]=>{{1},{2},{3},{4,7},{5,6},{8}}
[1,2,3,6,7,5,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[1,2,3,5,7,6,4,8]=>{{1},{2},{3},{4,5,7},{6},{8}}
[1,2,3,6,5,7,4,8]=>{{1},{2},{3},{4,6,7},{5},{8}}
[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[4,3,2,1,7,6,5,8]=>{{1,4},{2,3},{5,7},{6},{8}}
[4,3,2,1,6,7,5,8]=>{{1,4},{2,3},{5,6,7},{8}}
[3,2,4,1,7,6,5,8]=>{{1,3,4},{2},{5,7},{6},{8}}
[3,2,4,1,6,7,5,8]=>{{1,3,4},{2},{5,6,7},{8}}
[2,3,4,1,7,6,5,8]=>{{1,2,3,4},{5,7},{6},{8}}
[2,3,4,1,6,7,5,8]=>{{1,2,3,4},{5,6,7},{8}}
[1,4,3,2,7,6,5,8]=>{{1},{2,4},{3},{5,7},{6},{8}}
[1,4,3,2,6,7,5,8]=>{{1},{2,4},{3},{5,6,7},{8}}
[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[2,1,4,3,6,7,5,8]=>{{1,2},{3,4},{5,6,7},{8}}
[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[3,2,1,4,7,6,5,8]=>{{1,3},{2},{4},{5,7},{6},{8}}
[2,3,1,4,6,7,5,8]=>{{1,2,3},{4},{5,6,7},{8}}
[1,3,2,4,7,6,5,8]=>{{1},{2,3},{4},{5,7},{6},{8}}
[1,2,3,4,7,6,5,8]=>{{1},{2},{3},{4},{5,7},{6},{8}}
[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[5,4,3,2,1,7,6,8]=>{{1,5},{2,4},{3},{6,7},{8}}
[4,5,3,2,1,7,6,8]=>{{1,2,4,5},{3},{6,7},{8}}
[3,5,4,2,1,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[3,4,5,2,1,7,6,8]=>{{1,3,5},{2,4},{6,7},{8}}
[2,5,4,3,1,7,6,8]=>{{1,2,5},{3,4},{6,7},{8}}
[2,4,5,3,1,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[3,2,5,4,1,7,6,8]=>{{1,3,5},{2},{4},{6,7},{8}}
[2,3,5,4,1,7,6,8]=>{{1,2,3,5},{4},{6,7},{8}}
[3,4,2,5,1,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[2,4,3,5,1,7,6,8]=>{{1,2,4,5},{3},{6,7},{8}}
[2,3,4,5,1,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[1,5,4,3,2,7,6,8]=>{{1},{2,5},{3,4},{6,7},{8}}
[1,4,5,3,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[1,3,5,4,2,7,6,8]=>{{1},{2,3,5},{4},{6,7},{8}}
[1,4,3,5,2,7,6,8]=>{{1},{2,4,5},{3},{6,7},{8}}
[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[2,1,5,4,3,7,6,8]=>{{1,2},{3,5},{4},{6,7},{8}}
[1,2,4,5,3,7,6,8]=>{{1},{2},{3,4,5},{6,7},{8}}
[3,2,1,5,4,7,6,8]=>{{1,3},{2},{4,5},{6,7},{8}}
[2,3,1,5,4,7,6,8]=>{{1,2,3},{4,5},{6,7},{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},{4,5},{6,7},{8}}
[4,3,2,1,5,7,6,8]=>{{1,4},{2,3},{5},{6,7},{8}}
[3,2,4,1,5,7,6,8]=>{{1,3,4},{2},{5},{6,7},{8}}
[2,3,4,1,5,7,6,8]=>{{1,2,3,4},{5},{6,7},{8}}
[1,4,3,2,5,7,6,8]=>{{1},{2,4},{3},{5},{6,7},{8}}
[1,3,4,2,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}}
[1,2,4,3,5,7,6,8]=>{{1},{2},{3,4},{5},{6,7},{8}}
[3,2,1,4,5,7,6,8]=>{{1,3},{2},{4},{5},{6,7},{8}}
[2,3,1,4,5,7,6,8]=>{{1,2,3},{4},{5},{6,7},{8}}
[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}
[2,1,3,4,5,7,6,8]=>{{1,2},{3},{4},{5},{6,7},{8}}
[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[3,6,5,4,2,1,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[4,3,6,5,2,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,4,6,5,3,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,4,5,6,3,1,7,8]=>{{1,2,4,6},{3,5},{7},{8}}
[2,3,6,5,4,1,7,8]=>{{1,2,3,6},{4,5},{7},{8}}
[2,3,5,6,4,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[4,3,2,6,5,1,7,8]=>{{1,4,6},{2,3},{5},{7},{8}}
[2,4,3,6,5,1,7,8]=>{{1,2,4,6},{3},{5},{7},{8}}
[2,3,4,6,5,1,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[3,5,4,2,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,3,5,4,6,1,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[1,6,5,4,3,2,7,8]=>{{1},{2,6},{3,5},{4},{7},{8}}
[1,5,6,4,3,2,7,8]=>{{1},{2,3,5,6},{4},{7},{8}}
[1,4,6,5,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,4,5,6,3,2,7,8]=>{{1},{2,4,6},{3,5},{7},{8}}
[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,4,3,6,5,2,7,8]=>{{1},{2,4,6},{3},{5},{7},{8}}
[1,5,4,3,6,2,7,8]=>{{1},{2,5,6},{3,4},{7},{8}}
[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,1,5,6,4,3,7,8]=>{{1,2},{3,4,5,6},{7},{8}}
[2,1,4,6,5,3,7,8]=>{{1,2},{3,4,6},{5},{7},{8}}
[1,2,6,5,4,3,7,8]=>{{1},{2},{3,6},{4,5},{7},{8}}
[1,2,5,6,4,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[1,2,4,6,5,3,7,8]=>{{1},{2},{3,4,6},{5},{7},{8}}
[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[3,2,1,6,5,4,7,8]=>{{1,3},{2},{4,6},{5},{7},{8}}
[3,2,1,5,6,4,7,8]=>{{1,3},{2},{4,5,6},{7},{8}}
[2,3,1,6,5,4,7,8]=>{{1,2,3},{4,6},{5},{7},{8}}
[2,3,1,5,6,4,7,8]=>{{1,2,3},{4,5,6},{7},{8}}
[1,3,2,6,5,4,7,8]=>{{1},{2,3},{4,6},{5},{7},{8}}
[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[1,2,3,6,5,4,7,8]=>{{1},{2},{3},{4,6},{5},{7},{8}}
[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[4,3,2,1,6,5,7,8]=>{{1,4},{2,3},{5,6},{7},{8}}
[2,4,3,1,6,5,7,8]=>{{1,2,4},{3},{5,6},{7},{8}}
[3,2,4,1,6,5,7,8]=>{{1,3,4},{2},{5,6},{7},{8}}
[2,3,4,1,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}}
[2,1,4,3,6,5,7,8]=>{{1,2},{3,4},{5,6},{7},{8}}
[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}}
[1,3,2,4,6,5,7,8]=>{{1},{2,3},{4},{5,6},{7},{8}}
[2,1,3,4,6,5,7,8]=>{{1,2},{3},{4},{5,6},{7},{8}}
[1,2,3,4,6,5,7,8]=>{{1},{2},{3},{4},{5,6},{7},{8}}
[3,5,4,2,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[2,5,4,3,1,6,7,8]=>{{1,2,5},{3,4},{6},{7},{8}}
[2,4,5,3,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[3,2,5,4,1,6,7,8]=>{{1,3,5},{2},{4},{6},{7},{8}}
[2,3,5,4,1,6,7,8]=>{{1,2,3,5},{4},{6},{7},{8}}
[2,4,3,5,1,6,7,8]=>{{1,2,4,5},{3},{6},{7},{8}}
[1,5,4,3,2,6,7,8]=>{{1},{2,5},{3,4},{6},{7},{8}}
[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[2,1,5,4,3,6,7,8]=>{{1,2},{3,5},{4},{6},{7},{8}}
[2,1,4,5,3,6,7,8]=>{{1,2},{3,4,5},{6},{7},{8}}
[1,2,5,4,3,6,7,8]=>{{1},{2},{3,5},{4},{6},{7},{8}}
[3,2,1,5,4,6,7,8]=>{{1,3},{2},{4,5},{6},{7},{8}}
[2,3,1,5,4,6,7,8]=>{{1,2,3},{4,5},{6},{7},{8}}
[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[2,1,3,5,4,6,7,8]=>{{1,2},{3},{4,5},{6},{7},{8}}
[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[2,4,3,1,5,6,7,8]=>{{1,2,4},{3},{5},{6},{7},{8}}
[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[2,1,4,3,5,6,7,8]=>{{1,2},{3,4},{5},{6},{7},{8}}
[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{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},{5,8},{6},{7}}
[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}}
[1,2,3,7,5,6,4,8]=>{{1},{2},{3},{4,7},{5},{6},{8}}
[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[1,2,3,8,5,7,6,4]=>{{1},{2},{3},{4,8},{5},{6,7}}
[1,2,3,8,6,5,7,4]=>{{1},{2},{3},{4,8},{5,6},{7}}
[1,2,3,8,6,7,5,4]=>{{1},{2},{3},{4,8},{5,6,7}}
[1,2,4,3,8,6,7,5]=>{{1},{2},{3,4},{5,8},{6},{7}}
[1,2,4,5,8,6,7,3]=>{{1},{2},{3,4,5,8},{6},{7}}
[1,2,4,7,5,6,8,3]=>{{1},{2},{3,4,7,8},{5},{6}}
[1,2,4,8,5,6,7,3]=>{{1},{2},{3,4,8},{5},{6},{7}}
[1,2,4,8,6,5,7,3]=>{{1},{2},{3,4,8},{5,6},{7}}
[1,2,5,4,8,6,7,3]=>{{1},{2},{3,5,8},{4},{6},{7}}
[1,2,6,4,5,3,7,8]=>{{1},{2},{3,6},{4},{5},{7},{8}}
[1,2,6,4,5,7,8,3]=>{{1},{2},{3,6,7,8},{4},{5}}
[1,2,7,4,5,6,8,3]=>{{1},{2},{3,7,8},{4},{5},{6}}
[1,2,8,4,5,6,7,3]=>{{1},{2},{3,8},{4},{5},{6},{7}}
[1,2,8,4,6,7,5,3]=>{{1},{2},{3,8},{4},{5,6,7}}
[1,2,8,4,7,6,5,3]=>{{1},{2},{3,8},{4},{5,7},{6}}
[1,2,7,5,4,6,3,8]=>{{1},{2},{3,7},{4,5},{6},{8}}
[1,2,7,5,4,6,8,3]=>{{1},{2},{3,7,8},{4,5},{6}}
[1,2,8,5,4,6,7,3]=>{{1},{2},{3,8},{4,5},{6},{7}}
[1,2,8,5,4,7,6,3]=>{{1},{2},{3,8},{4,5},{6,7}}
[1,2,8,5,6,4,7,3]=>{{1},{2},{3,8},{4,5,6},{7}}
[1,2,8,5,6,7,4,3]=>{{1},{2},{3,8},{4,5,6,7}}
[1,2,8,6,5,4,7,3]=>{{1},{2},{3,8},{4,6},{5},{7}}
[1,2,8,6,5,7,4,3]=>{{1},{2},{3,8},{4,6,7},{5}}
[1,2,8,7,5,6,4,3]=>{{1},{2},{3,8},{4,7},{5},{6}}
[1,3,2,4,8,6,7,5]=>{{1},{2,3},{4},{5,8},{6},{7}}
[1,3,2,7,5,6,8,4]=>{{1},{2,3},{4,7,8},{5},{6}}
[1,3,2,8,5,7,6,4]=>{{1},{2,3},{4,8},{5},{6,7}}
[1,3,2,8,6,5,7,4]=>{{1},{2,3},{4,8},{5,6},{7}}
[1,3,2,8,6,7,5,4]=>{{1},{2,3},{4,8},{5,6,7}}
[1,3,4,2,8,6,7,5]=>{{1},{2,3,4},{5,8},{6},{7}}
[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[1,3,6,4,5,2,8,7]=>{{1},{2,3,6},{4},{5},{7,8}}
[1,3,6,4,5,7,2,8]=>{{1},{2,3,6,7},{4},{5},{8}}
[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[1,3,6,4,5,8,7,2]=>{{1},{2,3,6,8},{4},{5},{7}}
[1,3,7,4,5,6,2,8]=>{{1},{2,3,7},{4},{5},{6},{8}}
[1,3,7,4,5,6,8,2]=>{{1},{2,3,7,8},{4},{5},{6}}
[1,3,8,4,5,6,7,2]=>{{1},{2,3,8},{4},{5},{6},{7}}
[1,3,8,4,6,5,7,2]=>{{1},{2,3,8},{4},{5,6},{7}}
[1,3,8,4,6,7,5,2]=>{{1},{2,3,8},{4},{5,6,7}}
[1,3,8,5,4,6,7,2]=>{{1},{2,3,8},{4,5},{6},{7}}
[1,3,8,5,4,7,6,2]=>{{1},{2,3,8},{4,5},{6,7}}
[1,3,8,5,6,7,4,2]=>{{1},{2,3,8},{4,5,6,7}}
[1,3,8,5,7,6,4,2]=>{{1},{2,3,8},{4,5,7},{6}}
[1,3,8,6,5,7,4,2]=>{{1},{2,3,8},{4,6,7},{5}}
[1,3,8,7,5,6,4,2]=>{{1},{2,3,8},{4,7},{5},{6}}
[1,4,3,2,8,6,7,5]=>{{1},{2,4},{3},{5,8},{6},{7}}
[1,4,3,5,8,6,7,2]=>{{1},{2,4,5,8},{3},{6},{7}}
[1,4,3,8,5,6,7,2]=>{{1},{2,4,8},{3},{5},{6},{7}}
[1,4,3,8,5,7,6,2]=>{{1},{2,4,8},{3},{5},{6,7}}
[1,4,3,8,6,5,7,2]=>{{1},{2,4,8},{3},{5,6},{7}}
[1,4,3,8,6,7,5,2]=>{{1},{2,4,8},{3},{5,6,7}}
[1,5,3,4,2,6,7,8]=>{{1},{2,5},{3},{4},{6},{7},{8}}
[1,5,3,4,2,7,8,6]=>{{1},{2,5},{3},{4},{6,7,8}}
[1,5,3,4,2,8,7,6]=>{{1},{2,5},{3},{4},{6,8},{7}}
[1,5,3,4,6,2,8,7]=>{{1},{2,5,6},{3},{4},{7,8}}
[1,5,3,4,6,7,2,8]=>{{1},{2,5,6,7},{3},{4},{8}}
[1,5,3,4,6,7,8,2]=>{{1},{2,5,6,7,8},{3},{4}}
[1,5,3,4,8,6,7,2]=>{{1},{2,5,8},{3},{4},{6},{7}}
[1,6,3,4,5,2,7,8]=>{{1},{2,6},{3},{4},{5},{7},{8}}
[1,6,3,4,5,8,7,2]=>{{1},{2,6,8},{3},{4},{5},{7}}
[1,7,3,4,5,6,2,8]=>{{1},{2,7},{3},{4},{5},{6},{8}}
[1,7,3,4,5,6,8,2]=>{{1},{2,7,8},{3},{4},{5},{6}}
[1,8,3,4,5,6,7,2]=>{{1},{2,8},{3},{4},{5},{6},{7}}
[1,8,3,4,6,7,5,2]=>{{1},{2,8},{3},{4},{5,6,7}}
[1,8,3,4,7,6,5,2]=>{{1},{2,8},{3},{4},{5,7},{6}}
[1,6,3,5,4,2,7,8]=>{{1},{2,6},{3},{4,5},{7},{8}}
[1,6,3,5,4,8,7,2]=>{{1},{2,6,8},{3},{4,5},{7}}
[1,7,3,5,4,6,2,8]=>{{1},{2,7},{3},{4,5},{6},{8}}
[1,8,3,5,4,6,7,2]=>{{1},{2,8},{3},{4,5},{6},{7}}
[1,8,3,5,4,7,6,2]=>{{1},{2,8},{3},{4,5},{6,7}}
[1,8,3,5,6,4,7,2]=>{{1},{2,8},{3},{4,5,6},{7}}
[1,8,3,5,6,7,4,2]=>{{1},{2,8},{3},{4,5,6,7}}
[1,8,3,5,7,6,4,2]=>{{1},{2,8},{3},{4,5,7},{6}}
[1,7,3,6,5,4,2,8]=>{{1},{2,7},{3},{4,6},{5},{8}}
[1,7,3,6,5,4,8,2]=>{{1},{2,7,8},{3},{4,6},{5}}
[1,8,3,6,5,4,7,2]=>{{1},{2,8},{3},{4,6},{5},{7}}
[1,8,3,7,5,6,4,2]=>{{1},{2,8},{3},{4,7},{5},{6}}
[1,8,3,7,6,5,4,2]=>{{1},{2,8},{3},{4,7},{5,6}}
[1,6,4,3,5,2,7,8]=>{{1},{2,6},{3,4},{5},{7},{8}}
[1,6,4,3,5,8,7,2]=>{{1},{2,6,8},{3,4},{5},{7}}
[1,8,4,3,5,6,7,2]=>{{1},{2,8},{3,4},{5},{6},{7}}
[1,8,4,3,5,7,6,2]=>{{1},{2,8},{3,4},{5},{6,7}}
[1,7,4,3,6,5,8,2]=>{{1},{2,7,8},{3,4},{5,6}}
[1,8,4,3,6,5,7,2]=>{{1},{2,8},{3,4},{5,6},{7}}
[1,6,4,5,3,2,7,8]=>{{1},{2,6},{3,4,5},{7},{8}}
[1,6,4,5,3,2,8,7]=>{{1},{2,6},{3,4,5},{7,8}}
[1,6,4,5,3,8,7,2]=>{{1},{2,6,8},{3,4,5},{7}}
[1,7,4,5,3,6,8,2]=>{{1},{2,7,8},{3,4,5},{6}}
[1,8,4,5,3,6,7,2]=>{{1},{2,8},{3,4,5},{6},{7}}
[1,7,4,5,6,3,8,2]=>{{1},{2,7,8},{3,4,5,6}}
[1,8,4,5,6,3,7,2]=>{{1},{2,8},{3,4,5,6},{7}}
[1,8,4,5,6,7,3,2]=>{{1},{2,8},{3,4,5,6,7}}
[1,7,4,6,5,3,2,8]=>{{1},{2,7},{3,4,6},{5},{8}}
[1,8,4,6,5,3,7,2]=>{{1},{2,8},{3,4,6},{5},{7}}
[1,8,4,6,5,7,3,2]=>{{1},{2,8},{3,4,6,7},{5}}
[1,8,4,7,6,5,3,2]=>{{1},{2,8},{3,4,7},{5,6}}
[1,7,5,4,3,6,2,8]=>{{1},{2,7},{3,5},{4},{6},{8}}
[1,7,5,4,3,6,8,2]=>{{1},{2,7,8},{3,5},{4},{6}}
[1,8,5,4,3,6,7,2]=>{{1},{2,8},{3,5},{4},{6},{7}}
[1,8,5,4,3,7,6,2]=>{{1},{2,8},{3,5},{4},{6,7}}
[1,8,5,4,6,3,7,2]=>{{1},{2,8},{3,5,6},{4},{7}}
[1,8,5,4,6,7,3,2]=>{{1},{2,8},{3,5,6,7},{4}}
[1,8,5,4,7,6,3,2]=>{{1},{2,8},{3,5,7},{4},{6}}
[1,7,6,4,5,3,2,8]=>{{1},{2,7},{3,6},{4},{5},{8}}
[1,8,6,4,5,3,7,2]=>{{1},{2,8},{3,6},{4},{5},{7}}
[1,8,6,4,5,7,3,2]=>{{1},{2,8},{3,6,7},{4},{5}}
[1,8,7,4,5,6,3,2]=>{{1},{2,8},{3,7},{4},{5},{6}}
[1,8,7,4,6,5,3,2]=>{{1},{2,8},{3,7},{4},{5,6}}
[1,8,6,5,4,3,7,2]=>{{1},{2,8},{3,6},{4,5},{7}}
[1,8,6,5,4,7,3,2]=>{{1},{2,8},{3,6,7},{4,5}}
[1,8,7,5,4,6,3,2]=>{{1},{2,8},{3,7},{4,5},{6}}
[1,8,7,5,6,4,3,2]=>{{1},{2,8},{3,7},{4,5,6}}
[2,1,3,4,8,6,7,5]=>{{1,2},{3},{4},{5,8},{6},{7}}
[2,1,3,5,8,6,7,4]=>{{1,2},{3},{4,5,8},{6},{7}}
[2,1,3,8,5,6,7,4]=>{{1,2},{3},{4,8},{5},{6},{7}}
[2,1,3,8,5,7,6,4]=>{{1,2},{3},{4,8},{5},{6,7}}
[2,1,3,8,6,5,7,4]=>{{1,2},{3},{4,8},{5,6},{7}}
[2,1,3,8,6,7,5,4]=>{{1,2},{3},{4,8},{5,6,7}}
[2,1,4,3,8,6,7,5]=>{{1,2},{3,4},{5,8},{6},{7}}
[2,1,4,5,8,6,7,3]=>{{1,2},{3,4,5,8},{6},{7}}
[2,1,4,8,5,6,7,3]=>{{1,2},{3,4,8},{5},{6},{7}}
[2,1,4,8,5,7,6,3]=>{{1,2},{3,4,8},{5},{6,7}}
[2,1,4,8,6,5,7,3]=>{{1,2},{3,4,8},{5,6},{7}}
[2,1,4,8,6,7,5,3]=>{{1,2},{3,4,8},{5,6,7}}
[2,1,5,4,8,6,7,3]=>{{1,2},{3,5,8},{4},{6},{7}}
[2,1,6,4,5,3,8,7]=>{{1,2},{3,6},{4},{5},{7,8}}
[2,1,6,4,5,7,8,3]=>{{1,2},{3,6,7,8},{4},{5}}
[2,1,6,4,5,8,7,3]=>{{1,2},{3,6,8},{4},{5},{7}}
[2,1,8,4,5,6,7,3]=>{{1,2},{3,8},{4},{5},{6},{7}}
[2,1,8,4,5,7,6,3]=>{{1,2},{3,8},{4},{5},{6,7}}
[2,1,7,4,6,5,8,3]=>{{1,2},{3,7,8},{4},{5,6}}
[2,1,8,4,6,5,7,3]=>{{1,2},{3,8},{4},{5,6},{7}}
[2,1,8,4,6,7,5,3]=>{{1,2},{3,8},{4},{5,6,7}}
[2,1,8,4,7,6,5,3]=>{{1,2},{3,8},{4},{5,7},{6}}
[2,1,8,5,4,6,7,3]=>{{1,2},{3,8},{4,5},{6},{7}}
[2,1,8,5,4,7,6,3]=>{{1,2},{3,8},{4,5},{6,7}}
[2,1,7,5,6,4,8,3]=>{{1,2},{3,7,8},{4,5,6}}
[2,1,8,5,6,4,7,3]=>{{1,2},{3,8},{4,5,6},{7}}
[2,1,8,5,6,7,4,3]=>{{1,2},{3,8},{4,5,6,7}}
[2,1,8,5,7,6,4,3]=>{{1,2},{3,8},{4,5,7},{6}}
[2,1,8,6,5,4,7,3]=>{{1,2},{3,8},{4,6},{5},{7}}
[2,1,8,6,5,7,4,3]=>{{1,2},{3,8},{4,6,7},{5}}
[2,1,8,7,5,6,4,3]=>{{1,2},{3,8},{4,7},{5},{6}}
[2,3,1,7,5,6,4,8]=>{{1,2,3},{4,7},{5},{6},{8}}
[2,3,1,8,5,6,7,4]=>{{1,2,3},{4,8},{5},{6},{7}}
[2,3,1,8,6,7,5,4]=>{{1,2,3},{4,8},{5,6,7}}
[2,3,4,1,8,6,7,5]=>{{1,2,3,4},{5,8},{6},{7}}
[2,3,4,5,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[2,3,4,7,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}
[2,3,4,7,5,6,8,1]=>{{1,2,3,4,7,8},{5},{6}}
[2,3,4,8,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[2,3,4,8,5,7,6,1]=>{{1,2,3,4,8},{5},{6,7}}
[2,3,4,8,6,5,7,1]=>{{1,2,3,4,8},{5,6},{7}}
[2,3,4,8,6,7,5,1]=>{{1,2,3,4,8},{5,6,7}}
[2,3,5,4,8,6,7,1]=>{{1,2,3,5,8},{4},{6},{7}}
[2,3,6,4,5,1,7,8]=>{{1,2,3,6},{4},{5},{7},{8}}
[2,3,6,4,5,1,8,7]=>{{1,2,3,6},{4},{5},{7,8}}
[2,3,6,4,5,7,8,1]=>{{1,2,3,6,7,8},{4},{5}}
[2,3,6,4,5,8,7,1]=>{{1,2,3,6,8},{4},{5},{7}}
[2,3,7,4,5,6,8,1]=>{{1,2,3,7,8},{4},{5},{6}}
[2,3,8,4,5,6,7,1]=>{{1,2,3,8},{4},{5},{6},{7}}
[2,3,7,4,6,5,8,1]=>{{1,2,3,7,8},{4},{5,6}}
[2,3,8,4,6,7,5,1]=>{{1,2,3,8},{4},{5,6,7}}
[2,3,7,5,4,6,1,8]=>{{1,2,3,7},{4,5},{6},{8}}
[2,3,7,5,4,6,8,1]=>{{1,2,3,7,8},{4,5},{6}}
[2,3,8,5,4,6,7,1]=>{{1,2,3,8},{4,5},{6},{7}}
[2,3,7,5,6,4,1,8]=>{{1,2,3,7},{4,5,6},{8}}
[2,3,7,5,6,4,8,1]=>{{1,2,3,7,8},{4,5,6}}
[2,3,8,5,6,4,7,1]=>{{1,2,3,8},{4,5,6},{7}}
[2,3,8,5,6,7,4,1]=>{{1,2,3,8},{4,5,6,7}}
[2,3,8,5,7,6,4,1]=>{{1,2,3,8},{4,5,7},{6}}
[2,3,8,6,5,4,7,1]=>{{1,2,3,8},{4,6},{5},{7}}
[2,4,3,5,8,6,7,1]=>{{1,2,4,5,8},{3},{6},{7}}
[2,4,3,7,5,6,8,1]=>{{1,2,4,7,8},{3},{5},{6}}
[2,4,3,8,5,6,7,1]=>{{1,2,4,8},{3},{5},{6},{7}}
[2,4,3,8,6,5,7,1]=>{{1,2,4,8},{3},{5,6},{7}}
[2,5,3,4,1,6,7,8]=>{{1,2,5},{3},{4},{6},{7},{8}}
[2,5,3,4,1,8,7,6]=>{{1,2,5},{3},{4},{6,8},{7}}
[2,5,3,4,6,7,1,8]=>{{1,2,5,6,7},{3},{4},{8}}
[2,5,3,4,6,7,8,1]=>{{1,2,5,6,7,8},{3},{4}}
[2,5,3,4,6,8,7,1]=>{{1,2,5,6,8},{3},{4},{7}}
[2,5,3,4,7,6,8,1]=>{{1,2,5,7,8},{3},{4},{6}}
[2,5,3,4,8,6,7,1]=>{{1,2,5,8},{3},{4},{6},{7}}
[2,5,3,4,8,7,6,1]=>{{1,2,5,8},{3},{4},{6,7}}
[2,6,3,4,5,1,7,8]=>{{1,2,6},{3},{4},{5},{7},{8}}
[2,6,3,4,5,7,8,1]=>{{1,2,6,7,8},{3},{4},{5}}
[2,6,3,4,5,8,7,1]=>{{1,2,6,8},{3},{4},{5},{7}}
[2,7,3,4,5,6,1,8]=>{{1,2,7},{3},{4},{5},{6},{8}}
[2,8,3,4,5,6,7,1]=>{{1,2,8},{3},{4},{5},{6},{7}}
[2,8,3,4,5,7,6,1]=>{{1,2,8},{3},{4},{5},{6,7}}
[2,6,3,5,4,1,8,7]=>{{1,2,6},{3},{4,5},{7,8}}
[2,6,3,5,4,7,8,1]=>{{1,2,6,7,8},{3},{4,5}}
[2,7,3,5,4,6,8,1]=>{{1,2,7,8},{3},{4,5},{6}}
[2,8,3,5,4,7,6,1]=>{{1,2,8},{3},{4,5},{6,7}}
[2,7,3,5,6,4,8,1]=>{{1,2,7,8},{3},{4,5,6}}
[2,8,3,5,6,7,4,1]=>{{1,2,8},{3},{4,5,6,7}}
[2,8,3,5,7,6,4,1]=>{{1,2,8},{3},{4,5,7},{6}}
[2,7,3,6,5,4,1,8]=>{{1,2,7},{3},{4,6},{5},{8}}
[2,8,3,7,5,6,4,1]=>{{1,2,8},{3},{4,7},{5},{6}}
[2,8,3,7,6,5,4,1]=>{{1,2,8},{3},{4,7},{5,6}}
[2,5,4,3,8,6,7,1]=>{{1,2,5,8},{3,4},{6},{7}}
[2,6,4,3,5,1,8,7]=>{{1,2,6},{3,4},{5},{7,8}}
[2,6,4,3,5,7,8,1]=>{{1,2,6,7,8},{3,4},{5}}
[2,6,4,3,5,8,7,1]=>{{1,2,6,8},{3,4},{5},{7}}
[2,7,4,3,5,6,8,1]=>{{1,2,7,8},{3,4},{5},{6}}
[2,8,4,3,5,6,7,1]=>{{1,2,8},{3,4},{5},{6},{7}}
[2,8,4,3,5,7,6,1]=>{{1,2,8},{3,4},{5},{6,7}}
[2,7,4,3,6,5,8,1]=>{{1,2,7,8},{3,4},{5,6}}
[2,8,4,3,6,5,7,1]=>{{1,2,8},{3,4},{5,6},{7}}
[2,8,4,3,6,7,5,1]=>{{1,2,8},{3,4},{5,6,7}}
[2,8,4,3,7,6,5,1]=>{{1,2,8},{3,4},{5,7},{6}}
[2,6,4,5,3,1,7,8]=>{{1,2,6},{3,4,5},{7},{8}}
[2,6,4,5,3,7,8,1]=>{{1,2,6,7,8},{3,4,5}}
[2,8,4,5,3,6,7,1]=>{{1,2,8},{3,4,5},{6},{7}}
[2,7,4,5,6,3,1,8]=>{{1,2,7},{3,4,5,6},{8}}
[2,7,4,5,6,3,8,1]=>{{1,2,7,8},{3,4,5,6}}
[2,8,4,5,6,3,7,1]=>{{1,2,8},{3,4,5,6},{7}}
[2,8,4,5,6,7,3,1]=>{{1,2,8},{3,4,5,6,7}}
[2,7,4,6,5,3,1,8]=>{{1,2,7},{3,4,6},{5},{8}}
[2,7,4,6,5,3,8,1]=>{{1,2,7,8},{3,4,6},{5}}
[2,8,4,6,5,3,7,1]=>{{1,2,8},{3,4,6},{5},{7}}
[2,8,4,7,6,5,3,1]=>{{1,2,8},{3,4,7},{5,6}}
[2,7,5,4,3,6,8,1]=>{{1,2,7,8},{3,5},{4},{6}}
[2,8,5,4,3,6,7,1]=>{{1,2,8},{3,5},{4},{6},{7}}
[2,8,5,4,3,7,6,1]=>{{1,2,8},{3,5},{4},{6,7}}
[2,7,5,4,6,3,8,1]=>{{1,2,7,8},{3,5,6},{4}}
[2,8,5,4,6,7,3,1]=>{{1,2,8},{3,5,6,7},{4}}
[2,8,5,4,7,6,3,1]=>{{1,2,8},{3,5,7},{4},{6}}
[2,7,6,4,5,3,8,1]=>{{1,2,7,8},{3,6},{4},{5}}
[2,8,7,4,5,6,3,1]=>{{1,2,8},{3,7},{4},{5},{6}}
[2,8,7,4,6,5,3,1]=>{{1,2,8},{3,7},{4},{5,6}}
[2,8,7,5,4,6,3,1]=>{{1,2,8},{3,7},{4,5},{6}}
[2,8,7,5,6,4,3,1]=>{{1,2,8},{3,7},{4,5,6}}
[3,2,1,4,8,6,7,5]=>{{1,3},{2},{4},{5,8},{6},{7}}
[3,2,1,5,8,6,7,4]=>{{1,3},{2},{4,5,8},{6},{7}}
[3,2,1,7,5,6,4,8]=>{{1,3},{2},{4,7},{5},{6},{8}}
[3,2,1,7,5,6,8,4]=>{{1,3},{2},{4,7,8},{5},{6}}
[3,2,1,8,5,6,7,4]=>{{1,3},{2},{4,8},{5},{6},{7}}
[3,2,1,8,5,7,6,4]=>{{1,3},{2},{4,8},{5},{6,7}}
[3,2,1,8,6,5,7,4]=>{{1,3},{2},{4,8},{5,6},{7}}
[3,2,1,8,6,7,5,4]=>{{1,3},{2},{4,8},{5,6,7}}
[3,2,4,1,8,6,7,5]=>{{1,3,4},{2},{5,8},{6},{7}}
[3,2,4,5,8,6,7,1]=>{{1,3,4,5,8},{2},{6},{7}}
[3,2,4,7,5,6,8,1]=>{{1,3,4,7,8},{2},{5},{6}}
[3,2,4,8,5,6,7,1]=>{{1,3,4,8},{2},{5},{6},{7}}
[3,2,4,8,6,7,5,1]=>{{1,3,4,8},{2},{5,6,7}}
[3,2,5,4,8,6,7,1]=>{{1,3,5,8},{2},{4},{6},{7}}
[3,2,6,4,5,1,8,7]=>{{1,3,6},{2},{4},{5},{7,8}}
[3,2,7,4,5,6,1,8]=>{{1,3,7},{2},{4},{5},{6},{8}}
[3,2,8,4,5,6,7,1]=>{{1,3,8},{2},{4},{5},{6},{7}}
[3,2,7,4,6,5,1,8]=>{{1,3,7},{2},{4},{5,6},{8}}
[3,2,7,4,6,5,8,1]=>{{1,3,7,8},{2},{4},{5,6}}
[3,2,8,4,6,5,7,1]=>{{1,3,8},{2},{4},{5,6},{7}}
[3,2,7,5,4,6,1,8]=>{{1,3,7},{2},{4,5},{6},{8}}
[3,2,8,5,4,6,7,1]=>{{1,3,8},{2},{4,5},{6},{7}}
[3,2,8,5,4,7,6,1]=>{{1,3,8},{2},{4,5},{6,7}}
[3,2,7,5,6,4,1,8]=>{{1,3,7},{2},{4,5,6},{8}}
[3,2,7,5,6,4,8,1]=>{{1,3,7,8},{2},{4,5,6}}
[3,2,8,5,6,4,7,1]=>{{1,3,8},{2},{4,5,6},{7}}
[3,2,8,5,7,6,4,1]=>{{1,3,8},{2},{4,5,7},{6}}
[3,2,8,7,5,6,4,1]=>{{1,3,8},{2},{4,7},{5},{6}}
[4,2,3,1,5,7,6,8]=>{{1,4},{2},{3},{5},{6,7},{8}}
[4,2,3,1,5,7,8,6]=>{{1,4},{2},{3},{5},{6,7,8}}
[4,2,3,1,5,8,7,6]=>{{1,4},{2},{3},{5},{6,8},{7}}
[4,2,3,1,6,5,7,8]=>{{1,4},{2},{3},{5,6},{7},{8}}
[4,2,3,1,6,5,8,7]=>{{1,4},{2},{3},{5,6},{7,8}}
[4,2,3,1,6,7,8,5]=>{{1,4},{2},{3},{5,6,7,8}}
[4,2,3,1,6,8,7,5]=>{{1,4},{2},{3},{5,6,8},{7}}
[4,2,3,1,7,6,5,8]=>{{1,4},{2},{3},{5,7},{6},{8}}
[4,2,3,1,7,6,8,5]=>{{1,4},{2},{3},{5,7,8},{6}}
[4,2,3,1,8,6,7,5]=>{{1,4},{2},{3},{5,8},{6},{7}}
[4,2,3,1,8,7,6,5]=>{{1,4},{2},{3},{5,8},{6,7}}
[4,2,3,5,1,6,8,7]=>{{1,4,5},{2},{3},{6},{7,8}}
[4,2,3,5,1,7,8,6]=>{{1,4,5},{2},{3},{6,7,8}}
[4,2,3,5,1,8,7,6]=>{{1,4,5},{2},{3},{6,8},{7}}
[4,2,3,5,6,1,8,7]=>{{1,4,5,6},{2},{3},{7,8}}
[4,2,3,5,6,8,7,1]=>{{1,4,5,6,8},{2},{3},{7}}
[4,2,3,6,5,8,7,1]=>{{1,4,6,8},{2},{3},{5},{7}}
[4,2,3,7,5,6,1,8]=>{{1,4,7},{2},{3},{5},{6},{8}}
[4,2,3,7,5,6,8,1]=>{{1,4,7,8},{2},{3},{5},{6}}
[4,2,3,8,5,6,7,1]=>{{1,4,8},{2},{3},{5},{6},{7}}
[4,2,3,8,5,7,6,1]=>{{1,4,8},{2},{3},{5},{6,7}}
[4,2,3,7,6,5,8,1]=>{{1,4,7,8},{2},{3},{5,6}}
[4,2,3,8,7,6,5,1]=>{{1,4,8},{2},{3},{5,7},{6}}
[5,2,3,4,1,6,8,7]=>{{1,5},{2},{3},{4},{6},{7,8}}
[5,2,3,4,1,7,8,6]=>{{1,5},{2},{3},{4},{6,7,8}}
[5,2,3,4,1,8,7,6]=>{{1,5},{2},{3},{4},{6,8},{7}}
[5,2,3,4,6,1,8,7]=>{{1,5,6},{2},{3},{4},{7,8}}
[5,2,3,4,7,6,1,8]=>{{1,5,7},{2},{3},{4},{6},{8}}
[5,2,3,4,8,6,7,1]=>{{1,5,8},{2},{3},{4},{6},{7}}
[5,2,3,4,8,7,6,1]=>{{1,5,8},{2},{3},{4},{6,7}}
[6,2,3,4,5,1,8,7]=>{{1,6},{2},{3},{4},{5},{7,8}}
[6,2,3,4,5,8,7,1]=>{{1,6,8},{2},{3},{4},{5},{7}}
[8,2,3,4,5,7,6,1]=>{{1,8},{2},{3},{4},{5},{6,7}}
[7,2,3,4,6,5,1,8]=>{{1,7},{2},{3},{4},{5,6},{8}}
[8,2,3,4,7,6,5,1]=>{{1,8},{2},{3},{4},{5,7},{6}}
[6,2,3,5,4,1,7,8]=>{{1,6},{2},{3},{4,5},{7},{8}}
[6,2,3,5,4,1,8,7]=>{{1,6},{2},{3},{4,5},{7,8}}
[6,2,3,5,4,7,1,8]=>{{1,6,7},{2},{3},{4,5},{8}}
[7,2,3,5,4,6,1,8]=>{{1,7},{2},{3},{4,5},{6},{8}}
[8,2,3,5,4,6,7,1]=>{{1,8},{2},{3},{4,5},{6},{7}}
[8,2,3,5,4,7,6,1]=>{{1,8},{2},{3},{4,5},{6,7}}
[7,2,3,5,6,4,1,8]=>{{1,7},{2},{3},{4,5,6},{8}}
[8,2,3,5,6,7,4,1]=>{{1,8},{2},{3},{4,5,6,7}}
[8,2,3,5,7,6,4,1]=>{{1,8},{2},{3},{4,5,7},{6}}
[7,2,3,6,5,4,1,8]=>{{1,7},{2},{3},{4,6},{5},{8}}
[8,2,3,6,5,4,7,1]=>{{1,8},{2},{3},{4,6},{5},{7}}
[8,2,3,7,5,6,4,1]=>{{1,8},{2},{3},{4,7},{5},{6}}
[8,2,3,7,6,5,4,1]=>{{1,8},{2},{3},{4,7},{5,6}}
[5,2,4,3,1,6,7,8]=>{{1,5},{2},{3,4},{6},{7},{8}}
[5,2,4,3,1,6,8,7]=>{{1,5},{2},{3,4},{6},{7,8}}
[5,2,4,3,1,7,6,8]=>{{1,5},{2},{3,4},{6,7},{8}}
[5,2,4,3,1,8,7,6]=>{{1,5},{2},{3,4},{6,8},{7}}
[5,2,4,3,6,1,7,8]=>{{1,5,6},{2},{3,4},{7},{8}}
[5,2,4,3,6,1,8,7]=>{{1,5,6},{2},{3,4},{7,8}}
[5,2,4,3,6,7,1,8]=>{{1,5,6,7},{2},{3,4},{8}}
[5,2,4,3,7,6,1,8]=>{{1,5,7},{2},{3,4},{6},{8}}
[5,2,4,3,7,6,8,1]=>{{1,5,7,8},{2},{3,4},{6}}
[6,2,4,3,5,1,8,7]=>{{1,6},{2},{3,4},{5},{7,8}}
[7,2,4,3,6,5,1,8]=>{{1,7},{2},{3,4},{5,6},{8}}
[7,2,4,3,6,5,8,1]=>{{1,7,8},{2},{3,4},{5,6}}
[8,2,4,3,6,5,7,1]=>{{1,8},{2},{3,4},{5,6},{7}}
[8,2,4,3,6,7,5,1]=>{{1,8},{2},{3,4},{5,6,7}}
[8,2,4,3,7,6,5,1]=>{{1,8},{2},{3,4},{5,7},{6}}
[6,2,4,5,3,1,7,8]=>{{1,6},{2},{3,4,5},{7},{8}}
[7,2,4,5,3,6,1,8]=>{{1,7},{2},{3,4,5},{6},{8}}
[7,2,4,5,3,6,8,1]=>{{1,7,8},{2},{3,4,5},{6}}
[8,2,4,5,3,7,6,1]=>{{1,8},{2},{3,4,5},{6,7}}
[8,2,4,5,6,7,3,1]=>{{1,8},{2},{3,4,5,6,7}}
[8,2,4,5,7,6,3,1]=>{{1,8},{2},{3,4,5,7},{6}}
[7,2,4,6,5,3,1,8]=>{{1,7},{2},{3,4,6},{5},{8}}
[7,2,4,6,5,3,8,1]=>{{1,7,8},{2},{3,4,6},{5}}
[8,2,4,7,5,6,3,1]=>{{1,8},{2},{3,4,7},{5},{6}}
[8,2,4,7,6,5,3,1]=>{{1,8},{2},{3,4,7},{5,6}}
[6,2,5,4,3,1,7,8]=>{{1,6},{2},{3,5},{4},{7},{8}}
[6,2,5,4,3,1,8,7]=>{{1,6},{2},{3,5},{4},{7,8}}
[6,2,5,4,3,7,1,8]=>{{1,6,7},{2},{3,5},{4},{8}}
[7,2,5,4,3,6,1,8]=>{{1,7},{2},{3,5},{4},{6},{8}}
[8,2,5,4,3,6,7,1]=>{{1,8},{2},{3,5},{4},{6},{7}}
[8,2,5,4,3,7,6,1]=>{{1,8},{2},{3,5},{4},{6,7}}
[8,2,5,4,7,6,3,1]=>{{1,8},{2},{3,5,7},{4},{6}}
[7,2,6,4,5,3,1,8]=>{{1,7},{2},{3,6},{4},{5},{8}}
[7,2,6,4,5,3,8,1]=>{{1,7,8},{2},{3,6},{4},{5}}
[8,2,6,4,5,3,7,1]=>{{1,8},{2},{3,6},{4},{5},{7}}
[8,2,6,4,5,7,3,1]=>{{1,8},{2},{3,6,7},{4},{5}}
[8,2,7,4,5,6,3,1]=>{{1,8},{2},{3,7},{4},{5},{6}}
[8,2,7,4,6,5,3,1]=>{{1,8},{2},{3,7},{4},{5,6}}
[7,2,6,5,4,3,1,8]=>{{1,7},{2},{3,6},{4,5},{8}}
[8,2,6,5,4,3,7,1]=>{{1,8},{2},{3,6},{4,5},{7}}
[8,2,6,5,4,7,3,1]=>{{1,8},{2},{3,6,7},{4,5}}
[8,2,7,5,4,6,3,1]=>{{1,8},{2},{3,7},{4,5},{6}}
[8,2,7,5,6,4,3,1]=>{{1,8},{2},{3,7},{4,5,6}}
[8,2,7,6,5,4,3,1]=>{{1,8},{2},{3,7},{4,6},{5}}
[4,3,2,1,8,6,7,5]=>{{1,4},{2,3},{5,8},{6},{7}}
[4,3,2,7,5,6,8,1]=>{{1,4,7,8},{2,3},{5},{6}}
[4,3,2,8,5,6,7,1]=>{{1,4,8},{2,3},{5},{6},{7}}
[4,3,2,8,5,7,6,1]=>{{1,4,8},{2,3},{5},{6,7}}
[4,3,2,8,6,7,5,1]=>{{1,4,8},{2,3},{5,6,7}}
[5,3,2,4,1,6,8,7]=>{{1,5},{2,3},{4},{6},{7,8}}
[5,3,2,4,1,7,6,8]=>{{1,5},{2,3},{4},{6,7},{8}}
[5,3,2,4,1,8,7,6]=>{{1,5},{2,3},{4},{6,8},{7}}
[5,3,2,4,6,1,8,7]=>{{1,5,6},{2,3},{4},{7,8}}
[5,3,2,4,7,6,1,8]=>{{1,5,7},{2,3},{4},{6},{8}}
[8,3,2,4,6,5,7,1]=>{{1,8},{2,3},{4},{5,6},{7}}
[8,3,2,4,6,7,5,1]=>{{1,8},{2,3},{4},{5,6,7}}
[8,3,2,4,7,6,5,1]=>{{1,8},{2,3},{4},{5,7},{6}}
[6,3,2,5,4,1,7,8]=>{{1,6},{2,3},{4,5},{7},{8}}
[6,3,2,5,4,1,8,7]=>{{1,6},{2,3},{4,5},{7,8}}
[6,3,2,5,4,7,1,8]=>{{1,6,7},{2,3},{4,5},{8}}
[6,3,2,5,4,7,8,1]=>{{1,6,7,8},{2,3},{4,5}}
[7,3,2,5,4,6,1,8]=>{{1,7},{2,3},{4,5},{6},{8}}
[8,3,2,5,4,7,6,1]=>{{1,8},{2,3},{4,5},{6,7}}
[7,3,2,5,6,4,8,1]=>{{1,7,8},{2,3},{4,5,6}}
[8,3,2,5,6,4,7,1]=>{{1,8},{2,3},{4,5,6},{7}}
[8,3,2,5,6,7,4,1]=>{{1,8},{2,3},{4,5,6,7}}
[8,3,2,5,7,6,4,1]=>{{1,8},{2,3},{4,5,7},{6}}
[8,3,2,6,5,7,4,1]=>{{1,8},{2,3},{4,6,7},{5}}
[8,3,2,7,5,6,4,1]=>{{1,8},{2,3},{4,7},{5},{6}}
[8,3,2,7,6,5,4,1]=>{{1,8},{2,3},{4,7},{5,6}}
[5,3,4,2,1,6,8,7]=>{{1,5},{2,3,4},{6},{7,8}}
[5,3,4,2,1,7,8,6]=>{{1,5},{2,3,4},{6,7,8}}
[5,3,4,2,1,8,7,6]=>{{1,5},{2,3,4},{6,8},{7}}
[5,3,4,2,6,1,8,7]=>{{1,5,6},{2,3,4},{7,8}}
[5,3,4,2,7,6,1,8]=>{{1,5,7},{2,3,4},{6},{8}}
[5,3,4,2,7,6,8,1]=>{{1,5,7,8},{2,3,4},{6}}
[5,3,4,2,8,6,7,1]=>{{1,5,8},{2,3,4},{6},{7}}
[6,3,4,2,5,1,8,7]=>{{1,6},{2,3,4},{5},{7,8}}
[7,3,4,2,6,5,1,8]=>{{1,7},{2,3,4},{5,6},{8}}
[7,3,4,2,6,5,8,1]=>{{1,7,8},{2,3,4},{5,6}}
[8,3,4,2,6,5,7,1]=>{{1,8},{2,3,4},{5,6},{7}}
[6,3,4,5,2,1,8,7]=>{{1,6},{2,3,4,5},{7,8}}
[6,3,4,5,2,8,7,1]=>{{1,6,8},{2,3,4,5},{7}}
[8,3,4,5,2,7,6,1]=>{{1,8},{2,3,4,5},{6,7}}
[8,3,4,5,7,6,2,1]=>{{1,8},{2,3,4,5,7},{6}}
[7,3,4,6,5,2,1,8]=>{{1,7},{2,3,4,6},{5},{8}}
[8,3,4,7,6,5,2,1]=>{{1,8},{2,3,4,7},{5,6}}
[6,3,5,4,2,1,8,7]=>{{1,6},{2,3,5},{4},{7,8}}
[6,3,5,4,2,7,1,8]=>{{1,6,7},{2,3,5},{4},{8}}
[6,3,5,4,2,7,8,1]=>{{1,6,7,8},{2,3,5},{4}}
[7,3,5,4,2,6,1,8]=>{{1,7},{2,3,5},{4},{6},{8}}
[8,3,5,4,2,6,7,1]=>{{1,8},{2,3,5},{4},{6},{7}}
[7,3,5,4,6,2,1,8]=>{{1,7},{2,3,5,6},{4},{8}}
[7,3,5,4,6,2,8,1]=>{{1,7,8},{2,3,5,6},{4}}
[8,3,5,4,6,7,2,1]=>{{1,8},{2,3,5,6,7},{4}}
[8,3,5,4,7,6,2,1]=>{{1,8},{2,3,5,7},{4},{6}}
[7,3,6,4,5,2,1,8]=>{{1,7},{2,3,6},{4},{5},{8}}
[7,3,6,4,5,2,8,1]=>{{1,7,8},{2,3,6},{4},{5}}
[8,3,6,4,5,2,7,1]=>{{1,8},{2,3,6},{4},{5},{7}}
[8,3,7,4,5,6,2,1]=>{{1,8},{2,3,7},{4},{5},{6}}
[8,3,7,4,6,5,2,1]=>{{1,8},{2,3,7},{4},{5,6}}
[7,3,6,5,4,2,1,8]=>{{1,7},{2,3,6},{4,5},{8}}
[7,3,6,5,4,2,8,1]=>{{1,7,8},{2,3,6},{4,5}}
[8,3,6,5,4,2,7,1]=>{{1,8},{2,3,6},{4,5},{7}}
[8,3,6,5,4,7,2,1]=>{{1,8},{2,3,6,7},{4,5}}
[8,3,7,5,6,4,2,1]=>{{1,8},{2,3,7},{4,5,6}}
[8,3,7,6,5,4,2,1]=>{{1,8},{2,3,7},{4,6},{5}}
[5,4,3,2,8,6,7,1]=>{{1,5,8},{2,4},{3},{6},{7}}
[6,4,3,2,5,1,8,7]=>{{1,6},{2,4},{3},{5},{7,8}}
[6,4,3,2,5,8,7,1]=>{{1,6,8},{2,4},{3},{5},{7}}
[8,4,3,2,5,7,6,1]=>{{1,8},{2,4},{3},{5},{6,7}}
[7,4,3,2,6,5,1,8]=>{{1,7},{2,4},{3},{5,6},{8}}
[7,4,3,2,6,5,8,1]=>{{1,7,8},{2,4},{3},{5,6}}
[8,4,3,2,6,5,7,1]=>{{1,8},{2,4},{3},{5,6},{7}}
[8,4,3,2,6,7,5,1]=>{{1,8},{2,4},{3},{5,6,7}}
[8,4,3,2,7,6,5,1]=>{{1,8},{2,4},{3},{5,7},{6}}
[6,4,3,5,2,1,8,7]=>{{1,6},{2,4,5},{3},{7,8}}
[8,4,3,5,7,6,2,1]=>{{1,8},{2,4,5,7},{3},{6}}
[7,4,3,6,5,2,1,8]=>{{1,7},{2,4,6},{3},{5},{8}}
[7,4,3,6,5,2,8,1]=>{{1,7,8},{2,4,6},{3},{5}}
[8,4,3,7,5,6,2,1]=>{{1,8},{2,4,7},{3},{5},{6}}
[6,5,3,4,2,1,8,7]=>{{1,6},{2,5},{3},{4},{7,8}}
[8,5,3,4,2,7,6,1]=>{{1,8},{2,5},{3},{4},{6,7}}
[8,5,3,4,7,6,2,1]=>{{1,8},{2,5,7},{3},{4},{6}}
[8,7,3,4,6,5,2,1]=>{{1,8},{2,7},{3},{4},{5,6}}
[7,6,3,5,4,2,1,8]=>{{1,7},{2,6},{3},{4,5},{8}}
[7,6,3,5,4,2,8,1]=>{{1,7,8},{2,6},{3},{4,5}}
[8,6,3,5,4,2,7,1]=>{{1,8},{2,6},{3},{4,5},{7}}
[8,7,3,5,4,6,2,1]=>{{1,8},{2,7},{3},{4,5},{6}}
[8,7,3,5,6,4,2,1]=>{{1,8},{2,7},{3},{4,5,6}}
[8,7,3,6,5,4,2,1]=>{{1,8},{2,7},{3},{4,6},{5}}
[8,5,4,3,2,7,6,1]=>{{1,8},{2,5},{3,4},{6,7}}
[8,5,4,3,7,6,2,1]=>{{1,8},{2,5,7},{3,4},{6}}
[8,7,4,3,6,5,2,1]=>{{1,8},{2,7},{3,4},{5,6}}
[8,7,4,6,5,3,2,1]=>{{1,8},{2,7},{3,4,6},{5}}
[2,4,1,3,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}
[2,1,4,6,3,5,8,7]=>{{1,2},{3,4,5,6},{7,8}}
[2,4,1,6,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,4,6,1,3,5,8,7]=>{{1,2,4},{3,5,6},{7,8}}
[2,1,4,3,6,8,5,7]=>{{1,2},{3,4},{5,6,7,8}}
[2,4,1,3,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}
[2,1,4,6,3,8,5,7]=>{{1,2},{3,4,5,6,7,8}}
[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,1,3,8,5,7]=>{{1,2,4},{3,5,6,7,8}}
[2,1,4,6,8,3,5,7]=>{{1,2},{3,4,6},{5,7,8}}
[2,4,1,6,8,3,5,7]=>{{1,2,3,4,6},{5,7,8}}
[2,4,6,1,8,3,5,7]=>{{1,2,4},{3,6},{5,7,8}}
[2,4,6,8,1,3,5,7]=>{{1,2,4,5,7,8},{3,6}}
[2,4,1,3,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}}
[2,1,4,6,3,5,7,8]=>{{1,2},{3,4,5,6},{7},{8}}
[2,4,1,6,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,4,6,1,3,5,7,8]=>{{1,2,4},{3,5,6},{7},{8}}
[2,1,4,6,3,7,5,8]=>{{1,2},{3,4,5,6,7},{8}}
[2,4,1,6,3,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[2,4,6,1,3,7,5,8]=>{{1,2,4},{3,5,6,7},{8}}
[2,4,6,7,1,3,5,8]=>{{1,2,4,5,7},{3,6},{8}}
[2,4,1,3,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}
[2,1,4,6,3,7,8,5]=>{{1,2},{3,4,5,6,7,8}}
[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,1,4,6,7,3,8,5]=>{{1,2},{3,4,6},{5,7,8}}
[2,4,1,6,7,3,8,5]=>{{1,2,3,4,6},{5,7,8}}
[2,4,6,1,7,3,8,5]=>{{1,2,4},{3,6},{5,7,8}}
[2,4,6,7,1,3,8,5]=>{{1,2,4,5,7,8},{3,6}}
[2,1,4,6,7,8,3,5]=>{{1,2},{3,4,5,6,7,8}}
[2,4,1,6,7,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,7,8,1,3,5]=>{{1,2,3,4,6,7},{5,8}}
[2,1,4,3,7,5,8,6]=>{{1,2},{3,4},{5,6,7,8}}
[2,4,1,3,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}
[2,1,4,7,3,5,8,6]=>{{1,2},{3,4,5,6,7,8}}
[2,4,1,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,4,7,1,3,5,8,6]=>{{1,2,4},{3,5,6,7,8}}
[2,1,4,3,7,8,5,6]=>{{1,2},{3,4},{5,7},{6,8}}
[2,4,1,3,7,8,5,6]=>{{1,2,3,4},{5,7},{6,8}}
[2,4,1,7,3,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[2,1,4,7,8,3,5,6]=>{{1,2},{3,4,5,6,7,8}}
[2,4,1,7,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,4,7,1,8,3,5,6]=>{{1,2,4},{3,5,6,7,8}}
[2,4,7,8,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,4,1,5,3,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[2,4,5,1,3,7,6,8]=>{{1,2,4},{3,5},{6,7},{8}}
[2,4,5,1,7,3,6,8]=>{{1,2,4},{3,5,6,7},{8}}
[2,4,1,3,5,7,8,6]=>{{1,2,3,4},{5},{6,7,8}}
[2,4,1,5,3,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[2,4,5,1,3,7,8,6]=>{{1,2,4},{3,5},{6,7,8}}
[2,1,4,5,7,3,8,6]=>{{1,2},{3,4,5,6,7,8}}
[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,1,7,3,8,6]=>{{1,2,4},{3,5,6,7,8}}
[2,1,4,5,7,8,3,6]=>{{1,2},{3,4,5,7},{6,8}}
[2,4,5,1,7,8,3,6]=>{{1,2,4},{3,5,7},{6,8}}
[2,4,5,7,1,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[2,4,5,7,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,4,3,8,5,6,7]=>{{1,2},{3,4},{5,6,7,8}}
[2,4,1,3,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}
[2,1,4,8,3,5,6,7]=>{{1,2},{3,4,5,6,7,8}}
[2,4,1,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,1,3,5,6,7]=>{{1,2,4},{3,5,6,7,8}}
[2,1,4,3,5,8,6,7]=>{{1,2},{3,4},{5},{6,7,8}}
[2,4,1,5,3,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[2,1,4,5,8,3,6,7]=>{{1,2},{3,4,5,6,7,8}}
[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,1,8,3,6,7]=>{{1,2,4},{3,5,6,7,8}}
[2,4,1,5,3,6,8,7]=>{{1,2,3,4,5},{6},{7,8}}
[2,4,1,5,6,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,4,5,1,6,3,8,7]=>{{1,2,4},{3,5,6},{7,8}}
[2,4,5,6,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,1,4,5,6,8,3,7]=>{{1,2},{3,4,5,6,7,8}}
[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,1,6,8,3,7]=>{{1,2,4},{3,5,6,7,8}}
[2,4,5,6,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,6,8,1,3,7]=>{{1,2,4,6},{3,5,7,8}}
[2,4,1,3,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[2,4,1,5,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[2,4,5,1,3,6,7,8]=>{{1,2,4},{3,5},{6},{7},{8}}
[2,4,1,5,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,4,5,1,6,3,7,8]=>{{1,2,4},{3,5,6},{7},{8}}
[2,4,5,6,1,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,4,1,5,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[2,4,5,6,1,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[2,4,5,6,7,1,3,8]=>{{1,2,4,6},{3,5,7},{8}}
[2,4,1,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,1,6,7,8,3]=>{{1,2,4},{3,5,6,7,8}}
[2,4,5,6,1,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,6,7,1,8,3]=>{{1,2,4,6},{3,5,7,8}}
[2,4,5,6,7,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,3,6,4,8,7]=>{{1,2},{3,4,5,6},{7,8}}
[2,5,1,3,6,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,1,5,6,3,4,8,7]=>{{1,2},{3,5},{4,6},{7,8}}
[2,5,1,6,3,4,8,7]=>{{1,2,3,5},{4,6},{7,8}}
[2,5,6,1,3,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,1,5,3,6,8,4,7]=>{{1,2},{3,4,5,6,7,8}}
[2,5,1,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,1,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,6,8,3,4,7]=>{{1,2},{3,4,5,6,7,8}}
[2,5,1,6,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,8,1,3,4,7]=>{{1,2,5},{3,6},{4,7,8}}
[2,5,1,3,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,1,5,6,3,4,7,8]=>{{1,2},{3,5},{4,6},{7},{8}}
[2,5,1,6,3,4,7,8]=>{{1,2,3,5},{4,6},{7},{8}}
[2,1,5,3,6,7,4,8]=>{{1,2},{3,4,5,6,7},{8}}
[2,1,5,6,3,7,4,8]=>{{1,2},{3,5},{4,6,7},{8}}
[2,5,1,6,3,7,4,8]=>{{1,2,3,5},{4,6,7},{8}}
[2,5,6,1,3,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,1,5,6,7,3,4,8]=>{{1,2},{3,4,5,6,7},{8}}
[2,5,1,6,7,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,5,6,1,7,3,4,8]=>{{1,2,4,5,7},{3,6},{8}}
[2,1,5,3,6,7,8,4]=>{{1,2},{3,4,5,6,7,8}}
[2,5,1,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,6,3,7,8,4]=>{{1,2},{3,5},{4,6,7,8}}
[2,5,1,6,3,7,8,4]=>{{1,2,3,5},{4,6,7,8}}
[2,5,6,1,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,6,7,3,8,4]=>{{1,2},{3,4,5,6,7,8}}
[2,5,1,6,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,7,1,3,8,4]=>{{1,2,5},{3,6},{4,7,8}}
[2,1,5,6,7,8,3,4]=>{{1,2},{3,5,7},{4,6,8}}
[2,5,1,6,7,8,3,4]=>{{1,2,3,5,7},{4,6,8}}
[2,5,6,1,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,7,1,8,3,4]=>{{1,2,5},{3,4,6,7,8}}
[2,5,6,7,8,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,3,7,4,8,6]=>{{1,2},{3,4,5,6,7,8}}
[2,5,1,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,7,3,4,8,6]=>{{1,2},{3,5},{4,6,7,8}}
[2,5,1,7,3,4,8,6]=>{{1,2,3,5},{4,6,7,8}}
[2,5,7,1,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,3,7,8,4,6]=>{{1,2},{3,4,5,7},{6,8}}
[2,5,1,3,7,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[2,1,5,7,3,8,4,6]=>{{1,2},{3,5},{4,7},{6,8}}
[2,1,5,7,8,3,4,6]=>{{1,2},{3,5,6,8},{4,7}}
[2,5,1,7,8,3,4,6]=>{{1,2,3,5,6,8},{4,7}}
[2,5,7,1,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,8,1,3,4,6]=>{{1,2,5},{3,4,6,7,8}}
[2,5,1,3,7,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[2,1,5,7,3,4,6,8]=>{{1,2},{3,5},{4,6,7},{8}}
[2,3,5,1,4,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[2,3,5,7,1,4,6,8]=>{{1,2,3,5},{4,6,7},{8}}
[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,7,1,4,8,6]=>{{1,2,3,5},{4,6,7,8}}
[2,3,1,5,7,8,4,6]=>{{1,2,3},{4,5,7},{6,8}}
[2,3,5,7,1,8,4,6]=>{{1,2,3,5},{4,7},{6,8}}
[2,3,5,7,8,1,4,6]=>{{1,2,3,5,6,8},{4,7}}
[2,1,5,3,8,4,6,7]=>{{1,2},{3,4,5,6,7,8}}
[2,5,1,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,8,3,4,6,7]=>{{1,2},{3,5},{4,6,7,8}}
[2,5,1,8,3,4,6,7]=>{{1,2,3,5},{4,6,7,8}}
[2,5,8,1,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,1,4,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[2,1,3,5,8,4,6,7]=>{{1,2},{3},{4,5,6,7,8}}
[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,8,1,4,6,7]=>{{1,2,3,5},{4,6,7,8}}
[2,1,5,3,4,6,8,7]=>{{1,2},{3,4,5},{6},{7,8}}
[2,3,5,1,6,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,3,5,6,1,4,8,7]=>{{1,2,3,5},{4,6},{7,8}}
[2,1,3,5,6,8,4,7]=>{{1,2},{3},{4,5,6,7,8}}
[2,3,1,5,6,8,4,7]=>{{1,2,3},{4,5,6,7,8}}
[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,6,1,8,4,7]=>{{1,2,3,5},{4,6,7,8}}
[2,3,5,6,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,3,4,6,7,8]=>{{1,2},{3,4,5},{6},{7},{8}}
[2,5,1,3,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[2,3,5,1,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[2,3,5,1,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,3,5,6,1,4,7,8]=>{{1,2,3,5},{4,6},{7},{8}}
[2,3,5,6,7,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,6,1,7,8,4]=>{{1,2,3,5},{4,6,7,8}}
[2,3,5,6,7,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,6,7,8,1,4]=>{{1,2,3,5,7},{4,6,8}}
[2,1,6,3,7,4,8,5]=>{{1,2},{3,4,6},{5,7,8}}
[2,6,1,3,7,4,8,5]=>{{1,2,3,4,6},{5,7,8}}
[2,1,6,7,3,4,8,5]=>{{1,2},{3,4,5,6,7,8}}
[2,6,1,7,3,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,6,7,1,3,4,8,5]=>{{1,2,4,6},{3,5,7,8}}
[2,1,6,3,7,8,4,5]=>{{1,2},{3,4,5,6,7,8}}
[2,6,1,3,7,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,6,1,7,3,8,4,5]=>{{1,2,3,5,6,8},{4,7}}
[2,6,7,1,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,1,6,7,8,3,4,5]=>{{1,2},{3,6},{4,7},{5,8}}
[2,6,1,7,8,3,4,5]=>{{1,2,3,6},{4,7},{5,8}}
[2,6,7,1,8,3,4,5]=>{{1,2,3,4,6,7},{5,8}}
[2,6,7,8,1,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,1,6,3,7,4,5,8]=>{{1,2},{3,4,6},{5,7},{8}}
[2,6,1,7,3,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[2,6,7,1,3,4,5,8]=>{{1,2,4,6},{3,5,7},{8}}
[2,6,1,3,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[2,3,1,6,4,7,5,8]=>{{1,2,3},{4,5,6,7},{8}}
[2,3,6,1,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[2,1,6,3,4,7,8,5]=>{{1,2},{3,4,5,6,7,8}}
[2,6,1,3,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,3,6,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,1,3,6,7,4,8,5]=>{{1,2},{3},{4,6},{5,7,8}}
[2,1,3,6,7,8,4,5]=>{{1,2},{3},{4,5,6,7,8}}
[2,3,1,6,7,8,4,5]=>{{1,2,3},{4,5,6,7,8}}
[2,3,6,1,7,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,3,6,7,1,8,4,5]=>{{1,2,3,5,6,8},{4,7}}
[2,3,6,7,8,1,4,5]=>{{1,2,3,6},{4,7},{5,8}}
[2,1,6,3,8,4,5,7]=>{{1,2},{3,4,6},{5,7,8}}
[2,6,1,3,8,4,5,7]=>{{1,2,3,4,6},{5,7,8}}
[2,1,6,8,3,4,5,7]=>{{1,2},{3,4,5,6,7,8}}
[2,6,1,8,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,6,8,1,3,4,5,7]=>{{1,2,4,6},{3,5,7,8}}
[2,1,6,3,4,8,5,7]=>{{1,2},{3,4,5,6,7,8}}
[2,6,1,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,1,6,4,8,5,7]=>{{1,2,3},{4,5,6,7,8}}
[2,3,6,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,1,6,8,4,5,7]=>{{1,2,3},{4,6},{5,7,8}}
[2,3,6,1,8,4,5,7]=>{{1,2,3,4,6},{5,7,8}}
[2,1,6,3,4,5,8,7]=>{{1,2},{3,4,5,6},{7,8}}
[2,6,1,3,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,1,3,6,4,5,8,7]=>{{1,2},{3},{4,5,6},{7,8}}
[2,3,6,1,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,3,4,1,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}
[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,6,8,1,5,7]=>{{1,2,3,4,6},{5,7,8}}
[2,6,1,3,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,1,3,6,4,5,7,8]=>{{1,2},{3},{4,5,6},{7},{8}}
[2,3,1,6,4,5,7,8]=>{{1,2,3},{4,5,6},{7},{8}}
[2,3,6,1,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,3,4,6,1,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,3,4,6,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[2,3,4,6,7,1,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,6,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,3,8,4,5,6]=>{{1,2},{3,4,5,6,7,8}}
[2,7,1,3,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,8,3,4,5,6]=>{{1,2},{3,5,7},{4,6,8}}
[2,7,1,8,3,4,5,6]=>{{1,2,3,5,7},{4,6,8}}
[2,7,8,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,3,4,8,5,6]=>{{1,2},{3,4,5,7},{6,8}}
[2,1,3,7,4,8,5,6]=>{{1,2},{3},{4,5,7},{6,8}}
[2,3,1,7,4,8,5,6]=>{{1,2,3},{4,5,7},{6,8}}
[2,3,7,1,4,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[2,1,3,7,8,4,5,6]=>{{1,2},{3},{4,5,6,7,8}}
[2,3,1,7,8,4,5,6]=>{{1,2,3},{4,5,6,7,8}}
[2,3,7,8,1,4,5,6]=>{{1,2,3,5,7},{4,6,8}}
[2,1,7,3,4,5,8,6]=>{{1,2},{3,4,5,6,7,8}}
[2,7,1,3,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,1,7,4,5,8,6]=>{{1,2,3},{4,5,6,7,8}}
[2,3,7,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,3,4,7,5,8,6]=>{{1,2},{3},{4},{5,6,7,8}}
[2,3,4,1,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}
[2,3,4,7,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,3,4,7,8,5,6]=>{{1,2},{3},{4},{5,7},{6,8}}
[2,3,1,4,7,8,5,6]=>{{1,2,3},{4},{5,7},{6,8}}
[2,3,4,1,7,8,5,6]=>{{1,2,3,4},{5,7},{6,8}}
[2,3,4,7,1,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[2,3,4,7,8,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,3,4,5,6,8]=>{{1,2},{3,4,5,6,7},{8}}
[2,7,1,3,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[2,3,7,1,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[2,1,3,4,7,5,6,8]=>{{1,2},{3},{4},{5,6,7},{8}}
[2,3,1,4,7,5,6,8]=>{{1,2,3},{4},{5,6,7},{8}}
[2,3,4,1,7,5,6,8]=>{{1,2,3,4},{5,6,7},{8}}
[2,3,4,7,1,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[2,3,4,5,7,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,5,7,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[2,1,8,3,4,5,6,7]=>{{1,2},{3,4,5,6,7,8}}
[2,8,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,1,3,8,4,5,6,7]=>{{1,2},{3},{4,5,6,7,8}}
[2,3,1,8,4,5,6,7]=>{{1,2,3},{4,5,6,7,8}}
[2,3,8,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,1,3,4,8,5,6,7]=>{{1,2},{3},{4},{5,6,7,8}}
[2,3,1,4,8,5,6,7]=>{{1,2,3},{4},{5,6,7,8}}
[2,3,4,1,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}
[2,3,4,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,1,3,4,5,8,6,7]=>{{1,2},{3},{4},{5},{6,7,8}}
[2,3,1,4,5,8,6,7]=>{{1,2,3},{4},{5},{6,7,8}}
[2,3,4,1,5,8,6,7]=>{{1,2,3,4},{5},{6,7,8}}
[2,3,4,5,1,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,2,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}
[3,4,1,2,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}
[3,1,4,6,2,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,4,1,6,2,5,8,7]=>{{1,3},{2,4,5,6},{7,8}}
[3,4,6,1,2,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,1,4,2,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}
[3,4,1,2,6,8,5,7]=>{{1,3},{2,4},{5,6,7,8}}
[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,6,2,8,5,7]=>{{1,3},{2,4,5,6,7,8}}
[3,1,4,6,8,2,5,7]=>{{1,2,3,4,6},{5,7,8}}
[3,4,1,6,8,2,5,7]=>{{1,3},{2,4,6},{5,7,8}}
[3,4,6,8,1,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,2,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}}
[3,4,1,2,6,5,7,8]=>{{1,3},{2,4},{5,6},{7},{8}}
[3,1,4,2,6,7,5,8]=>{{1,2,3,4},{5,6,7},{8}}
[3,4,1,2,6,7,5,8]=>{{1,3},{2,4},{5,6,7},{8}}
[3,4,1,6,2,7,5,8]=>{{1,3},{2,4,5,6,7},{8}}
[3,4,6,1,2,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,4,1,6,7,2,5,8]=>{{1,3},{2,4,6},{5,7},{8}}
[3,4,6,7,1,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,1,4,2,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}
[3,4,1,2,6,7,8,5]=>{{1,3},{2,4},{5,6,7,8}}
[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,6,2,7,8,5]=>{{1,3},{2,4,5,6,7,8}}
[3,4,6,1,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,6,7,2,8,5]=>{{1,2,3,4,6},{5,7,8}}
[3,4,1,6,7,2,8,5]=>{{1,3},{2,4,6},{5,7,8}}
[3,4,6,1,7,2,8,5]=>{{1,2,3,4,6},{5,7,8}}
[3,4,6,7,1,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,6,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,6,7,8,2,5]=>{{1,3},{2,4,5,6,7,8}}
[3,4,6,1,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,4,6,7,1,8,2,5]=>{{1,3,5,6,8},{2,4,7}}
[3,4,6,7,8,1,2,5]=>{{1,3,6},{2,4,7},{5,8}}
[3,1,4,2,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}
[3,4,1,2,7,5,8,6]=>{{1,3},{2,4},{5,6,7,8}}
[3,1,4,7,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,1,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,2,7,8,5,6]=>{{1,2,3,4},{5,7},{6,8}}
[3,4,1,2,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}}
[3,4,7,1,8,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,8,1,2,5,6]=>{{1,3,5,7},{2,4,6,8}}
[3,1,4,2,7,5,6,8]=>{{1,2,3,4},{5,6,7},{8}}
[3,4,1,2,7,5,6,8]=>{{1,3},{2,4},{5,6,7},{8}}
[3,4,1,2,5,7,6,8]=>{{1,3},{2,4},{5},{6,7},{8}}
[3,1,4,5,2,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[3,4,1,5,2,7,6,8]=>{{1,3},{2,4,5},{6,7},{8}}
[3,4,1,5,7,2,6,8]=>{{1,3},{2,4,5,6,7},{8}}
[3,4,5,7,1,2,6,8]=>{{1,3,5},{2,4,6,7},{8}}
[3,1,4,2,5,7,8,6]=>{{1,2,3,4},{5},{6,7,8}}
[3,4,1,2,5,7,8,6]=>{{1,3},{2,4},{5},{6,7,8}}
[3,1,4,5,2,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[3,4,5,1,2,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,5,7,2,8,6]=>{{1,3},{2,4,5,6,7,8}}
[3,4,5,7,1,2,8,6]=>{{1,3,5},{2,4,6,7,8}}
[3,1,4,5,7,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[3,4,1,5,7,8,2,6]=>{{1,3},{2,4,5,7},{6,8}}
[3,4,5,1,7,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[3,4,5,7,1,8,2,6]=>{{1,3,5},{2,4,7},{6,8}}
[3,4,5,7,8,1,2,6]=>{{1,3,5,6,8},{2,4,7}}
[3,1,4,2,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}
[3,4,1,2,8,5,6,7]=>{{1,3},{2,4},{5,6,7,8}}
[3,1,4,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,8,2,5,6,7]=>{{1,3},{2,4,5,6,7,8}}
[3,4,8,1,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,2,5,8,6,7]=>{{1,2,3,4},{5},{6,7,8}}
[3,4,1,2,5,8,6,7]=>{{1,3},{2,4},{5},{6,7,8}}
[3,4,1,5,2,8,6,7]=>{{1,3},{2,4,5},{6,7,8}}
[3,4,5,1,2,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[3,1,4,5,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,5,8,2,6,7]=>{{1,3},{2,4,5,6,7,8}}
[3,4,5,8,1,2,6,7]=>{{1,3,5},{2,4,6,7,8}}
[3,4,1,2,5,6,8,7]=>{{1,3},{2,4},{5},{6},{7,8}}
[3,4,5,1,2,6,8,7]=>{{1,2,3,4,5},{6},{7,8}}
[3,1,4,5,6,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,4,1,5,6,2,8,7]=>{{1,3},{2,4,5,6},{7,8}}
[3,4,5,1,6,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,4,5,6,1,2,8,7]=>{{1,3,5},{2,4,6},{7,8}}
[3,1,4,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,5,6,8,2,7]=>{{1,3},{2,4,5,6,7,8}}
[3,4,5,6,1,8,2,7]=>{{1,3,5},{2,4,6,7,8}}
[3,4,5,6,8,1,2,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,2,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[3,1,4,5,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[3,4,1,5,2,6,7,8]=>{{1,3},{2,4,5},{6},{7},{8}}
[3,4,1,5,6,2,7,8]=>{{1,3},{2,4,5,6},{7},{8}}
[3,4,5,1,6,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[3,1,4,5,6,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[3,4,1,5,6,7,2,8]=>{{1,3},{2,4,5,6,7},{8}}
[3,4,5,1,6,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[3,4,5,6,1,7,2,8]=>{{1,3,5},{2,4,6,7},{8}}
[3,1,4,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,5,6,7,8,2]=>{{1,3},{2,4,5,6,7,8}}
[3,4,5,1,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,4,5,6,1,7,8,2]=>{{1,3,5},{2,4,6,7,8}}
[3,4,5,6,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,1,5,2,6,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,5,1,2,6,4,8,7]=>{{1,3},{2,4,5,6},{7,8}}
[3,1,5,6,2,4,8,7]=>{{1,2,3,5},{4,6},{7,8}}
[3,5,1,6,2,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}}
[3,5,6,1,2,4,8,7]=>{{1,3,4,6},{2,5},{7,8}}
[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,2,6,8,4,7]=>{{1,3},{2,4,5,6,7,8}}
[3,1,5,6,2,8,4,7]=>{{1,2,3,5},{4,6,7,8}}
[3,5,6,1,2,8,4,7]=>{{1,3,4,6,7,8},{2,5}}
[3,1,5,6,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,6,8,2,4,7]=>{{1,3},{2,4,5,6,7,8}}
[3,5,6,1,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,8,1,2,4,7]=>{{1,2,3,5,6},{4,7,8}}
[3,1,5,6,2,4,7,8]=>{{1,2,3,5},{4,6},{7},{8}}
[3,5,1,6,2,4,7,8]=>{{1,3},{2,5},{4,6},{7},{8}}
[3,5,6,1,2,4,7,8]=>{{1,3,4,6},{2,5},{7},{8}}
[3,5,1,2,6,7,4,8]=>{{1,3},{2,4,5,6,7},{8}}
[3,5,1,6,2,7,4,8]=>{{1,3},{2,5},{4,6,7},{8}}
[3,5,6,1,2,7,4,8]=>{{1,3,4,6,7},{2,5},{8}}
[3,5,1,6,7,2,4,8]=>{{1,3},{2,4,5,6,7},{8}}
[3,5,6,1,7,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,6,7,1,2,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[3,1,5,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,2,6,7,8,4]=>{{1,3},{2,4,5,6,7,8}}
[3,1,5,6,2,7,8,4]=>{{1,2,3,5},{4,6,7,8}}
[3,5,1,6,2,7,8,4]=>{{1,3},{2,5},{4,6,7,8}}
[3,5,6,1,2,7,8,4]=>{{1,3,4,6,7,8},{2,5}}
[3,1,5,6,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,6,7,2,8,4]=>{{1,3},{2,4,5,6,7,8}}
[3,5,6,1,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,7,1,2,8,4]=>{{1,2,3,5,6},{4,7,8}}
[3,1,5,6,7,8,2,4]=>{{1,2,3,5,7},{4,6,8}}
[3,5,1,6,7,8,2,4]=>{{1,3},{2,5,7},{4,6,8}}
[3,5,6,1,7,8,2,4]=>{{1,3,4,6,8},{2,5,7}}
[3,5,6,7,1,8,2,4]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,7,8,1,2,4]=>{{1,3,6},{2,4,5,7,8}}
[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,2,7,4,8,6]=>{{1,3},{2,4,5,6,7,8}}
[3,1,5,7,2,4,8,6]=>{{1,2,3,5},{4,6,7,8}}
[3,5,1,7,2,4,8,6]=>{{1,3},{2,5},{4,6,7,8}}
[3,5,7,1,2,4,8,6]=>{{1,3,4,6,7,8},{2,5}}
[3,1,5,2,7,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[3,5,1,2,7,8,4,6]=>{{1,3},{2,4,5,7},{6,8}}
[3,1,5,7,2,8,4,6]=>{{1,2,3,5},{4,7},{6,8}}
[3,5,1,7,2,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}}
[3,1,5,7,8,2,4,6]=>{{1,2,3,5,6,8},{4,7}}
[3,5,1,7,8,2,4,6]=>{{1,3},{2,5,6,8},{4,7}}
[3,5,7,8,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,1,5,2,7,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,1,2,7,4,6,8]=>{{1,3},{2,4,5,6,7},{8}}
[3,1,5,7,2,4,6,8]=>{{1,2,3,5},{4,6,7},{8}}
[3,5,1,7,2,4,6,8]=>{{1,3},{2,5},{4,6,7},{8}}
[3,5,7,1,2,4,6,8]=>{{1,3,4,6,7},{2,5},{8}}
[3,1,5,2,4,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[3,5,1,2,4,7,6,8]=>{{1,3},{2,4,5},{6,7},{8}}
[3,1,2,5,4,7,6,8]=>{{1,2,3},{4,5},{6,7},{8}}
[1,3,5,2,4,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[3,1,2,5,7,4,6,8]=>{{1,2,3},{4,5,6,7},{8}}
[1,3,2,5,7,4,6,8]=>{{1},{2,3},{4,5,6,7},{8}}
[1,3,5,2,7,4,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,5,7,2,4,6,8]=>{{1},{2,3,5},{4,6,7},{8}}
[3,5,1,2,4,7,8,6]=>{{1,3},{2,4,5},{6,7,8}}
[3,1,2,5,7,4,8,6]=>{{1,2,3},{4,5,6,7,8}}
[1,3,5,2,7,4,8,6]=>{{1},{2,3,4,5,6,7,8}}
[1,3,5,7,2,4,8,6]=>{{1},{2,3,5},{4,6,7,8}}
[1,3,2,5,7,8,4,6]=>{{1},{2,3},{4,5,7},{6,8}}
[1,3,5,2,7,8,4,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,3,5,7,2,8,4,6]=>{{1},{2,3,5},{4,7},{6,8}}
[1,3,5,7,8,2,4,6]=>{{1},{2,3,5,6,8},{4,7}}
[3,1,5,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,2,8,4,6,7]=>{{1,3},{2,4,5,6,7,8}}
[3,1,5,8,2,4,6,7]=>{{1,2,3,5},{4,6,7,8}}
[3,5,1,8,2,4,6,7]=>{{1,3},{2,5},{4,6,7,8}}
[3,1,5,2,4,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[3,5,1,2,4,8,6,7]=>{{1,3},{2,4,5},{6,7,8}}
[1,3,2,5,4,8,6,7]=>{{1},{2,3},{4,5},{6,7,8}}
[1,3,5,2,4,8,6,7]=>{{1},{2,3,4,5},{6,7,8}}
[3,1,2,5,8,4,6,7]=>{{1,2,3},{4,5,6,7,8}}
[1,3,2,5,8,4,6,7]=>{{1},{2,3},{4,5,6,7,8}}
[1,3,5,2,8,4,6,7]=>{{1},{2,3,4,5,6,7,8}}
[1,3,5,8,2,4,6,7]=>{{1},{2,3,5},{4,6,7,8}}
[3,5,1,2,4,6,8,7]=>{{1,3},{2,4,5},{6},{7,8}}
[3,1,2,5,4,6,8,7]=>{{1,2,3},{4,5},{6},{7,8}}
[1,3,5,2,4,6,8,7]=>{{1},{2,3,4,5},{6},{7,8}}
[1,3,5,2,6,4,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[1,3,5,6,2,4,8,7]=>{{1},{2,3,5},{4,6},{7,8}}
[3,1,2,5,6,8,4,7]=>{{1,2,3},{4,5,6,7,8}}
[1,3,5,2,6,8,4,7]=>{{1},{2,3,4,5,6,7,8}}
[1,3,5,6,2,8,4,7]=>{{1},{2,3,5},{4,6,7,8}}
[1,3,5,6,8,2,4,7]=>{{1},{2,3,4,5,6,7,8}}
[3,5,1,2,4,6,7,8]=>{{1,3},{2,4,5},{6},{7},{8}}
[1,3,5,2,4,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[1,3,5,6,2,4,7,8]=>{{1},{2,3,5},{4,6},{7},{8}}
[3,1,2,5,6,7,4,8]=>{{1,2,3},{4,5,6,7},{8}}
[1,3,5,2,6,7,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[1,3,5,6,7,2,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,1,2,5,6,7,8,4]=>{{1,2,3},{4,5,6,7,8}}
[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[3,1,6,2,7,4,8,5]=>{{1,2,3,4,6},{5,7,8}}
[3,6,1,2,7,4,8,5]=>{{1,3},{2,4,6},{5,7,8}}
[3,6,1,7,2,4,8,5]=>{{1,3},{2,4,5,6,7,8}}
[3,6,7,1,2,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,2,7,8,4,5]=>{{1,3},{2,4,5,6,7,8}}
[3,1,6,7,2,8,4,5]=>{{1,2,3,5,6,8},{4,7}}
[3,6,1,7,2,8,4,5]=>{{1,3},{2,5,6,8},{4,7}}
[3,6,7,1,2,8,4,5]=>{{1,3,4,7},{2,5,6,8}}
[3,6,1,7,8,2,4,5]=>{{1,3},{2,6},{4,7},{5,8}}
[3,6,7,8,1,2,4,5]=>{{1,3,4,5,7,8},{2,6}}
[3,1,6,2,7,4,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[3,1,6,7,2,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,6,7,1,2,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,1,6,2,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,6,1,2,4,7,5,8]=>{{1,3},{2,4,5,6,7},{8}}
[3,1,2,6,4,7,5,8]=>{{1,2,3},{4,5,6,7},{8}}
[1,3,2,6,4,7,5,8]=>{{1},{2,3},{4,5,6,7},{8}}
[1,3,6,2,4,7,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,2,6,7,4,5,8]=>{{1},{2,3},{4,6},{5,7},{8}}
[1,3,6,2,7,4,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[3,1,6,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,2,4,7,8,5]=>{{1,3},{2,4,5,6,7,8}}
[3,1,2,6,4,7,8,5]=>{{1,2,3},{4,5,6,7,8}}
[1,3,6,2,4,7,8,5]=>{{1},{2,3,4,5,6,7,8}}
[3,1,2,6,7,4,8,5]=>{{1,2,3},{4,6},{5,7,8}}
[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[1,3,6,2,7,4,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[1,3,6,7,2,4,8,5]=>{{1},{2,3,4,5,6,7,8}}
[3,1,2,6,7,8,4,5]=>{{1,2,3},{4,5,6,7,8}}
[1,3,2,6,7,8,4,5]=>{{1},{2,3},{4,5,6,7,8}}
[1,3,6,2,7,8,4,5]=>{{1},{2,3,4,5,6,7,8}}
[1,3,6,7,8,2,4,5]=>{{1},{2,3,6},{4,7},{5,8}}
[3,1,6,2,8,4,5,7]=>{{1,2,3,4,6},{5,7,8}}
[3,6,1,2,8,4,5,7]=>{{1,3},{2,4,6},{5,7,8}}
[3,1,6,8,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,8,2,4,5,7]=>{{1,3},{2,4,5,6,7,8}}
[3,6,8,1,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,6,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,2,4,8,5,7]=>{{1,3},{2,4,5,6,7,8}}
[1,3,2,6,4,8,5,7]=>{{1},{2,3},{4,5,6,7,8}}
[1,3,6,2,4,8,5,7]=>{{1},{2,3,4,5,6,7,8}}
[3,1,2,6,8,4,5,7]=>{{1,2,3},{4,6},{5,7,8}}
[1,3,2,6,8,4,5,7]=>{{1},{2,3},{4,6},{5,7,8}}
[3,1,6,2,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,6,1,2,4,5,8,7]=>{{1,3},{2,4,5,6},{7,8}}
[3,1,2,6,4,5,8,7]=>{{1,2,3},{4,5,6},{7,8}}
[1,3,6,2,4,5,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[3,1,2,4,6,5,8,7]=>{{1,2,3},{4},{5,6},{7,8}}
[1,3,4,6,2,5,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[3,1,2,4,6,8,5,7]=>{{1,2,3},{4},{5,6,7,8}}
[1,3,2,4,6,8,5,7]=>{{1},{2,3},{4},{5,6,7,8}}
[1,3,4,6,8,2,5,7]=>{{1},{2,3,4,6},{5,7,8}}
[3,1,6,2,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[3,6,1,2,4,5,7,8]=>{{1,3},{2,4,5,6},{7},{8}}
[1,3,2,6,4,5,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[1,3,6,2,4,5,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,3,4,6,2,5,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,1,2,4,6,7,5,8]=>{{1,2,3},{4},{5,6,7},{8}}
[1,3,4,6,2,7,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[3,1,2,4,6,7,8,5]=>{{1,2,3},{4},{5,6,7,8}}
[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[3,1,7,2,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,1,2,8,4,5,6]=>{{1,3},{2,4,5,6,7,8}}
[3,1,7,8,2,4,5,6]=>{{1,2,3,5,7},{4,6,8}}
[3,7,1,8,2,4,5,6]=>{{1,3},{2,5,7},{4,6,8}}
[3,7,8,1,2,4,5,6]=>{{1,3,4,6,8},{2,5,7}}
[3,7,1,2,4,8,5,6]=>{{1,3},{2,4,5,7},{6,8}}
[3,1,2,7,4,8,5,6]=>{{1,2,3},{4,5,7},{6,8}}
[1,3,2,7,4,8,5,6]=>{{1},{2,3},{4,5,7},{6,8}}
[1,3,7,2,4,8,5,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,1,2,7,8,4,5,6]=>{{1,2,3},{4,5,6,7,8}}
[1,3,7,2,8,4,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,3,7,8,2,4,5,6]=>{{1},{2,3,5,7},{4,6,8}}
[3,1,7,2,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,1,2,4,5,8,6]=>{{1,3},{2,4,5,6,7,8}}
[1,3,7,2,4,5,8,6]=>{{1},{2,3,4,5,6,7,8}}
[3,1,2,4,7,5,8,6]=>{{1,2,3},{4},{5,6,7,8}}
[1,3,2,4,7,5,8,6]=>{{1},{2,3},{4},{5,6,7,8}}
[1,3,4,2,7,5,8,6]=>{{1},{2,3,4},{5,6,7,8}}
[1,3,4,7,2,5,8,6]=>{{1},{2,3,4,5,6,7,8}}
[3,1,2,4,7,8,5,6]=>{{1,2,3},{4},{5,7},{6,8}}
[1,3,2,4,7,8,5,6]=>{{1},{2,3},{4},{5,7},{6,8}}
[1,3,4,2,7,8,5,6]=>{{1},{2,3,4},{5,7},{6,8}}
[1,3,4,7,8,2,5,6]=>{{1},{2,3,4,5,6,7,8}}
[3,1,7,2,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[3,7,1,2,4,5,6,8]=>{{1,3},{2,4,5,6,7},{8}}
[3,1,2,7,4,5,6,8]=>{{1,2,3},{4,5,6,7},{8}}
[1,3,2,7,4,5,6,8]=>{{1},{2,3},{4,5,6,7},{8}}
[1,3,7,2,4,5,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,1,2,4,7,5,6,8]=>{{1,2,3},{4},{5,6,7},{8}}
[1,3,4,7,2,5,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,1,2,4,5,7,6,8]=>{{1,2,3},{4},{5},{6,7},{8}}
[1,3,4,5,7,2,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,1,2,4,5,7,8,6]=>{{1,2,3},{4},{5},{6,7,8}}
[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,1,8,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,8,1,2,4,5,6,7]=>{{1,3},{2,4,5,6,7,8}}
[3,1,2,8,4,5,6,7]=>{{1,2,3},{4,5,6,7,8}}
[1,3,2,8,4,5,6,7]=>{{1},{2,3},{4,5,6,7,8}}
[1,3,8,2,4,5,6,7]=>{{1},{2,3,4,5,6,7,8}}
[3,1,2,4,8,5,6,7]=>{{1,2,3},{4},{5,6,7,8}}
[1,3,2,4,8,5,6,7]=>{{1},{2,3},{4},{5,6,7,8}}
[1,3,4,2,8,5,6,7]=>{{1},{2,3,4},{5,6,7,8}}
[1,3,4,8,2,5,6,7]=>{{1},{2,3,4,5,6,7,8}}
[3,1,2,4,5,8,6,7]=>{{1,2,3},{4},{5},{6,7,8}}
[1,3,2,4,5,8,6,7]=>{{1},{2,3},{4},{5},{6,7,8}}
[1,3,4,2,5,8,6,7]=>{{1},{2,3,4},{5},{6,7,8}}
[1,3,4,5,2,8,6,7]=>{{1},{2,3,4,5},{6,7,8}}
[1,3,4,5,8,2,6,7]=>{{1},{2,3,4,5,6,7,8}}
[3,1,2,4,5,6,8,7]=>{{1,2,3},{4},{5},{6},{7,8}}
[1,3,4,5,6,8,2,7]=>{{1},{2,3,4,5,6,7,8}}
[4,1,5,2,6,3,8,7]=>{{1,2,4},{3,5,6},{7,8}}
[4,5,1,2,6,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,1,5,6,2,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,5,1,6,2,3,8,7]=>{{1,3,4,6},{2,5},{7,8}}
[4,5,6,1,2,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}}
[4,1,5,2,6,8,3,7]=>{{1,2,4},{3,5,6,7,8}}
[4,5,1,2,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,5,6,2,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,6,2,8,3,7]=>{{1,3,4,6,7,8},{2,5}}
[4,5,6,1,2,8,3,7]=>{{1,4},{2,5},{3,6,7,8}}
[4,1,5,6,8,2,3,7]=>{{1,2,4,6},{3,5,7,8}}
[4,5,1,6,8,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,1,8,2,3,7]=>{{1,4},{2,3,5,6,7,8}}
[4,5,6,8,1,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,5,2,6,3,7,8]=>{{1,2,4},{3,5,6},{7},{8}}
[4,1,5,6,2,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[4,5,1,6,2,3,7,8]=>{{1,3,4,6},{2,5},{7},{8}}
[4,5,1,2,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,1,6,2,7,3,8]=>{{1,3,4,6,7},{2,5},{8}}
[4,5,6,1,2,7,3,8]=>{{1,4},{2,5},{3,6,7},{8}}
[4,1,5,6,7,2,3,8]=>{{1,2,4,6},{3,5,7},{8}}
[4,5,1,6,7,2,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,6,1,7,2,3,8]=>{{1,4},{2,3,5,6,7},{8}}
[4,1,5,2,6,7,8,3]=>{{1,2,4},{3,5,6,7,8}}
[4,5,1,2,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,6,2,7,8,3]=>{{1,3,4,6,7,8},{2,5}}
[4,5,6,1,2,7,8,3]=>{{1,4},{2,5},{3,6,7,8}}
[4,1,5,6,7,2,8,3]=>{{1,2,4,6},{3,5,7,8}}
[4,5,1,6,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,1,7,2,8,3]=>{{1,4},{2,3,5,6,7,8}}
[4,5,6,7,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[4,1,5,6,7,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,6,7,8,2,3]=>{{1,3,4,6,8},{2,5,7}}
[4,5,6,1,7,8,2,3]=>{{1,4},{2,5,7},{3,6,8}}
[4,5,6,7,1,8,2,3]=>{{1,2,4,5,7},{3,6,8}}
[4,1,5,2,7,3,8,6]=>{{1,2,4},{3,5,6,7,8}}
[4,5,1,2,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,7,2,3,8,6]=>{{1,3,4,6,7,8},{2,5}}
[4,1,5,2,7,8,3,6]=>{{1,2,4},{3,5,7},{6,8}}
[4,5,1,2,7,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[4,1,5,7,2,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[4,5,1,7,2,8,3,6]=>{{1,3,4,7},{2,5},{6,8}}
[4,5,7,1,2,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}}
[4,5,1,7,8,2,3,6]=>{{1,3,4,7},{2,5,6,8}}
[4,5,7,8,1,2,3,6]=>{{1,2,4,5,6,8},{3,7}}
[4,1,5,2,7,3,6,8]=>{{1,2,4},{3,5,6,7},{8}}
[4,5,1,2,7,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[4,1,5,2,3,7,6,8]=>{{1,2,4},{3,5},{6,7},{8}}
[4,5,1,2,3,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[4,1,2,5,3,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[1,4,2,5,3,7,6,8]=>{{1},{2,3,4,5},{6,7},{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]=>{{1,2,3,4,5,6,7},{8}}
[1,4,2,5,7,3,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,4,5,2,7,3,6,8]=>{{1},{2,4},{3,5,6,7},{8}}
[1,4,5,7,2,3,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,1,5,2,3,7,8,6]=>{{1,2,4},{3,5},{6,7,8}}
[4,1,2,5,3,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}
[4,1,2,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,4,2,5,7,3,8,6]=>{{1},{2,3,4,5,6,7,8}}
[1,4,5,2,7,3,8,6]=>{{1},{2,4},{3,5,6,7,8}}
[1,4,5,7,2,3,8,6]=>{{1},{2,3,4,5,6,7,8}}
[4,1,2,5,7,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[1,4,2,5,7,8,3,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,4,5,2,7,8,3,6]=>{{1},{2,4},{3,5,7},{6,8}}
[1,4,5,7,8,2,3,6]=>{{1},{2,3,4,5,6,7,8}}
[4,1,5,2,8,3,6,7]=>{{1,2,4},{3,5,6,7,8}}
[4,5,1,2,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,8,2,3,6,7]=>{{1,3,4,6,7,8},{2,5}}
[4,5,8,1,2,3,6,7]=>{{1,4},{2,5},{3,6,7,8}}
[4,1,5,2,3,8,6,7]=>{{1,2,4},{3,5},{6,7,8}}
[4,5,1,2,3,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[4,1,2,5,3,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[1,4,2,5,3,8,6,7]=>{{1},{2,3,4,5},{6,7,8}}
[1,4,5,2,3,8,6,7]=>{{1},{2,4},{3,5},{6,7,8}}
[4,1,2,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,4,2,5,8,3,6,7]=>{{1},{2,3,4,5,6,7,8}}
[1,4,5,2,8,3,6,7]=>{{1},{2,4},{3,5,6,7,8}}
[1,4,2,5,3,6,8,7]=>{{1},{2,3,4,5},{6},{7,8}}
[4,1,2,5,6,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[1,4,5,2,6,3,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[4,1,2,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,4,2,5,6,8,3,7]=>{{1},{2,3,4,5,6,7,8}}
[1,4,5,2,6,8,3,7]=>{{1},{2,4},{3,5,6,7,8}}
[1,4,5,6,8,2,3,7]=>{{1},{2,4,6},{3,5,7,8}}
[4,1,5,2,3,6,7,8]=>{{1,2,4},{3,5},{6},{7},{8}}
[4,1,2,5,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[1,4,2,5,3,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[1,4,5,2,3,6,7,8]=>{{1},{2,4},{3,5},{6},{7},{8}}
[4,1,2,5,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[1,4,5,6,2,3,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[4,1,2,5,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[1,4,2,5,6,7,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[1,4,5,6,2,7,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,4,5,6,7,2,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[4,1,2,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[1,4,2,5,6,7,8,3]=>{{1},{2,3,4,5,6,7,8}}
[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,4,5,6,2,7,8,3]=>{{1},{2,3,4,5,6,7,8}}
[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[1,4,5,6,7,8,2,3]=>{{1},{2,3,4,5,6,7,8}}
[4,1,6,2,7,3,8,5]=>{{1,2,4},{3,6},{5,7,8}}
[4,1,6,7,2,3,8,5]=>{{1,2,4,5,7,8},{3,6}}
[4,6,7,1,2,3,8,5]=>{{1,4},{2,3,5,6,7,8}}
[4,6,1,2,7,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,1,7,2,8,3,5]=>{{1,3,4,7},{2,5,6,8}}
[4,6,7,1,2,8,3,5]=>{{1,4},{2,5,6,8},{3,7}}
[4,1,6,7,8,2,3,5]=>{{1,2,3,4,6,7},{5,8}}
[4,6,1,7,8,2,3,5]=>{{1,3,4,7},{2,6},{5,8}}
[4,6,7,1,8,2,3,5]=>{{1,4},{2,6},{3,7},{5,8}}
[4,6,7,8,1,2,3,5]=>{{1,4,5,8},{2,6},{3,7}}
[4,1,6,2,7,3,5,8]=>{{1,2,4},{3,6},{5,7},{8}}
[4,6,1,2,7,3,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[4,1,6,7,2,3,5,8]=>{{1,2,4,5,7},{3,6},{8}}
[4,6,1,7,2,3,5,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,7,1,2,3,5,8]=>{{1,4},{2,3,5,6,7},{8}}
[4,1,6,2,3,7,5,8]=>{{1,2,4},{3,5,6,7},{8}}
[4,6,1,2,3,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[4,1,2,6,3,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[1,4,2,6,3,7,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,1,2,6,7,3,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[1,4,2,6,7,3,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[1,4,6,7,2,3,5,8]=>{{1},{2,4,5,7},{3,6},{8}}
[4,1,6,2,3,7,8,5]=>{{1,2,4},{3,5,6,7,8}}
[4,1,2,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,4,6,2,3,7,8,5]=>{{1},{2,4},{3,5,6,7,8}}
[4,1,2,6,7,3,8,5]=>{{1,2,3,4,6},{5,7,8}}
[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[1,4,2,6,7,8,3,5]=>{{1},{2,3,4,5,6,7,8}}
[1,4,6,2,7,8,3,5]=>{{1},{2,4},{3,5,6,7,8}}
[1,4,6,7,2,8,3,5]=>{{1},{2,3,4,5,6,7,8}}
[1,4,6,7,8,2,3,5]=>{{1},{2,3,4,6,7},{5,8}}
[4,1,6,2,8,3,5,7]=>{{1,2,4},{3,6},{5,7,8}}
[4,6,1,2,8,3,5,7]=>{{1,2,3,4,6},{5,7,8}}
[4,1,6,8,2,3,5,7]=>{{1,2,4,5,7,8},{3,6}}
[4,6,1,8,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,6,8,1,2,3,5,7]=>{{1,4},{2,3,5,6,7,8}}
[4,1,6,2,3,8,5,7]=>{{1,2,4},{3,5,6,7,8}}
[4,6,1,2,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,4,2,6,3,8,5,7]=>{{1},{2,3,4,5,6,7,8}}
[1,4,6,2,3,8,5,7]=>{{1},{2,4},{3,5,6,7,8}}
[1,4,2,6,8,3,5,7]=>{{1},{2,3,4,6},{5,7,8}}
[1,4,6,2,8,3,5,7]=>{{1},{2,4},{3,6},{5,7,8}}
[1,4,6,8,2,3,5,7]=>{{1},{2,4,5,7,8},{3,6}}
[4,1,6,2,3,5,8,7]=>{{1,2,4},{3,5,6},{7,8}}
[4,6,1,2,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,1,2,6,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[1,4,2,6,3,5,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[1,4,6,2,3,5,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[4,1,2,3,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}
[1,4,2,3,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}}
[1,2,4,6,3,5,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[4,1,2,3,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}
[1,2,4,3,6,8,5,7]=>{{1},{2},{3,4},{5,6,7,8}}
[1,2,4,6,3,8,5,7]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,4,6,8,3,5,7]=>{{1},{2},{3,4,6},{5,7,8}}
[4,1,6,2,3,5,7,8]=>{{1,2,4},{3,5,6},{7},{8}}
[4,6,1,2,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[1,4,2,6,3,5,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,4,6,2,3,5,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[4,1,2,3,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}}
[1,4,2,3,6,5,7,8]=>{{1},{2,3,4},{5,6},{7},{8}}
[1,2,4,6,3,5,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[4,1,2,3,6,7,5,8]=>{{1,2,3,4},{5,6,7},{8}}
[1,4,2,3,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[4,1,2,3,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}
[1,4,2,3,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[1,2,4,6,7,8,3,5]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,7,2,8,3,5,6]=>{{1,2,4},{3,5,6,7,8}}
[4,7,1,2,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,1,7,8,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,7,1,8,2,3,5,6]=>{{1,3,4,6,8},{2,5,7}}
[4,7,8,1,2,3,5,6]=>{{1,4},{2,5,7},{3,6,8}}
[4,1,7,2,3,8,5,6]=>{{1,2,4},{3,5,7},{6,8}}
[4,7,1,2,3,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[1,4,2,7,3,8,5,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,4,7,2,3,8,5,6]=>{{1},{2,4},{3,5,7},{6,8}}
[4,1,2,7,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[1,4,2,7,8,3,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,4,7,2,8,3,5,6]=>{{1},{2,4},{3,5,6,7,8}}
[1,4,7,8,2,3,5,6]=>{{1},{2,3,4,5,6,7,8}}
[4,1,7,2,3,5,8,6]=>{{1,2,4},{3,5,6,7,8}}
[4,7,1,2,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,4,2,7,3,5,8,6]=>{{1},{2,3,4,5,6,7,8}}
[1,4,7,2,3,5,8,6]=>{{1},{2,4},{3,5,6,7,8}}
[4,1,2,3,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}
[1,4,2,3,7,5,8,6]=>{{1},{2,3,4},{5,6,7,8}}
[1,2,4,3,7,5,8,6]=>{{1},{2},{3,4},{5,6,7,8}}
[1,2,4,7,3,5,8,6]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,2,3,7,8,5,6]=>{{1,2,3,4},{5,7},{6,8}}
[1,4,2,3,7,8,5,6]=>{{1},{2,3,4},{5,7},{6,8}}
[1,2,4,3,7,8,5,6]=>{{1},{2},{3,4},{5,7},{6,8}}
[1,2,4,7,3,8,5,6]=>{{1},{2},{3,4,5,7},{6,8}}
[1,2,4,7,8,3,5,6]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,7,2,3,5,6,8]=>{{1,2,4},{3,5,6,7},{8}}
[4,7,1,2,3,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[4,1,2,7,3,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[1,4,2,7,3,5,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,4,7,2,3,5,6,8]=>{{1},{2,4},{3,5,6,7},{8}}
[4,1,2,3,7,5,6,8]=>{{1,2,3,4},{5,6,7},{8}}
[1,4,2,3,7,5,6,8]=>{{1},{2,3,4},{5,6,7},{8}}
[1,2,4,3,7,5,6,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[1,2,4,7,3,5,6,8]=>{{1},{2},{3,4,5,6,7},{8}}
[4,1,2,3,5,7,6,8]=>{{1,2,3,4},{5},{6,7},{8}}
[1,4,2,3,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}}
[1,2,4,5,7,3,6,8]=>{{1},{2},{3,4,5,6,7},{8}}
[4,1,2,3,5,7,8,6]=>{{1,2,3,4},{5},{6,7,8}}
[1,4,2,3,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[1,2,4,5,7,3,8,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[4,1,8,2,3,5,6,7]=>{{1,2,4},{3,5,6,7,8}}
[4,8,1,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,4,2,8,3,5,6,7]=>{{1},{2,3,4,5,6,7,8}}
[1,4,8,2,3,5,6,7]=>{{1},{2,4},{3,5,6,7,8}}
[4,1,2,3,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}
[1,4,2,3,8,5,6,7]=>{{1},{2,3,4},{5,6,7,8}}
[1,2,4,3,8,5,6,7]=>{{1},{2},{3,4},{5,6,7,8}}
[1,2,4,8,3,5,6,7]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,2,3,5,8,6,7]=>{{1,2,3,4},{5},{6,7,8}}
[1,4,2,3,5,8,6,7]=>{{1},{2,3,4},{5},{6,7,8}}
[1,2,4,3,5,8,6,7]=>{{1},{2},{3,4},{5},{6,7,8}}
[1,2,4,5,3,8,6,7]=>{{1},{2},{3,4,5},{6,7,8}}
[1,2,4,5,8,3,6,7]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,2,3,5,6,8,7]=>{{1,2,3,4},{5},{6},{7,8}}
[1,4,2,3,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[1,2,4,5,6,8,3,7]=>{{1},{2},{3,4,5,6,7,8}}
[1,4,2,3,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[5,1,6,2,7,3,8,4]=>{{1,2,4,5,7,8},{3,6}}
[5,6,1,2,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,7,2,3,8,4]=>{{1,2,5},{3,6},{4,7,8}}
[5,6,1,7,2,3,8,4]=>{{1,2,3,5,6},{4,7,8}}
[5,6,7,1,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,6,1,2,7,8,3,4]=>{{1,3,5,7},{2,4,6,8}}
[5,1,6,7,2,8,3,4]=>{{1,2,5},{3,4,6,7,8}}
[5,6,7,1,2,8,3,4]=>{{1,2,4,5,6,8},{3,7}}
[5,1,6,7,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,6,1,7,8,2,3,4]=>{{1,3,4,5,7,8},{2,6}}
[5,6,7,1,8,2,3,4]=>{{1,4,5,8},{2,6},{3,7}}
[5,1,6,2,7,3,4,8]=>{{1,2,4,5,7},{3,6},{8}}
[5,6,1,7,2,3,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[5,1,6,2,3,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[5,1,2,6,3,7,4,8]=>{{1,2,3,5},{4,6,7},{8}}
[1,5,2,6,3,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[5,1,2,6,7,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[1,5,2,6,7,3,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[5,1,6,2,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,6,1,2,3,7,8,4]=>{{1,3,5},{2,4,6,7,8}}
[5,1,2,6,3,7,8,4]=>{{1,2,3,5},{4,6,7,8}}
[1,5,2,6,3,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[1,5,6,2,3,7,8,4]=>{{1},{2,3,4,5,6,7,8}}
[5,1,2,6,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[5,1,2,6,7,8,3,4]=>{{1,2,3,5,7},{4,6,8}}
[1,5,2,6,7,8,3,4]=>{{1},{2,3,5,7},{4,6,8}}
[1,5,6,2,7,8,3,4]=>{{1},{2,3,4,5,6,7,8}}
[1,5,6,7,2,8,3,4]=>{{1},{2,5},{3,4,6,7,8}}
[1,5,6,7,8,2,3,4]=>{{1},{2,3,4,5,6,7,8}}
[5,1,6,2,8,3,4,7]=>{{1,2,4,5,7,8},{3,6}}
[5,6,1,2,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,1,8,2,3,4,7]=>{{1,2,3,5,6},{4,7,8}}
[5,6,8,1,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,2,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,1,2,3,8,4,7]=>{{1,3,5},{2,4,6,7,8}}
[5,1,2,6,3,8,4,7]=>{{1,2,3,5},{4,6,7,8}}
[1,5,2,6,3,8,4,7]=>{{1},{2,3,5},{4,6,7,8}}
[1,5,6,2,3,8,4,7]=>{{1},{2,3,4,5,6,7,8}}
[5,1,2,6,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,5,2,6,8,3,4,7]=>{{1},{2,3,4,5,6,7,8}}
[1,5,6,2,8,3,4,7]=>{{1},{2,4,5,7,8},{3,6}}
[1,5,6,8,2,3,4,7]=>{{1},{2,5},{3,6},{4,7,8}}
[5,1,6,2,3,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[5,6,1,2,3,4,8,7]=>{{1,3,5},{2,4,6},{7,8}}
[5,1,2,6,3,4,8,7]=>{{1,2,3,5},{4,6},{7,8}}
[1,5,2,6,3,4,8,7]=>{{1},{2,3,5},{4,6},{7,8}}
[1,5,6,2,3,4,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[1,5,2,3,6,4,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[1,2,5,3,6,4,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[1,2,5,6,3,4,8,7]=>{{1},{2},{3,5},{4,6},{7,8}}
[5,1,2,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,5,2,3,6,8,4,7]=>{{1},{2,3,4,5,6,7,8}}
[1,2,5,6,3,8,4,7]=>{{1},{2},{3,5},{4,6,7,8}}
[1,2,5,6,8,3,4,7]=>{{1},{2},{3,4,5,6,7,8}}
[5,1,6,2,3,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,1,2,6,3,4,7,8]=>{{1,2,3,5},{4,6},{7},{8}}
[1,5,2,6,3,4,7,8]=>{{1},{2,3,5},{4,6},{7},{8}}
[1,5,6,2,3,4,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,1,2,3,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[1,5,2,3,6,4,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,2,5,3,6,4,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[1,2,5,6,3,4,7,8]=>{{1},{2},{3,5},{4,6},{7},{8}}
[5,1,2,3,6,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[1,5,2,3,6,7,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,2,5,3,6,7,4,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,5,6,3,7,4,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[5,1,2,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,5,2,3,6,7,8,4]=>{{1},{2,3,4,5,6,7,8}}
[1,2,5,3,6,7,8,4]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[1,2,5,6,7,3,8,4]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,5,6,7,8,3,4]=>{{1},{2},{3,5,7},{4,6,8}}
[5,1,7,2,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[5,7,1,2,8,3,4,6]=>{{1,3,5,6,8},{2,4,7}}
[5,1,7,8,2,3,4,6]=>{{1,2,5},{3,4,6,7,8}}
[5,7,1,8,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,1,2,3,4,6]=>{{1,2,4,5,7},{3,6,8}}
[5,1,7,2,3,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[5,7,1,2,3,8,4,6]=>{{1,3,5},{2,4,7},{6,8}}
[5,1,2,7,3,8,4,6]=>{{1,2,3,5},{4,7},{6,8}}
[1,5,2,7,3,8,4,6]=>{{1},{2,3,5},{4,7},{6,8}}
[1,5,7,2,3,8,4,6]=>{{1},{2,3,4,5,7},{6,8}}
[5,1,2,7,8,3,4,6]=>{{1,2,3,5,6,8},{4,7}}
[1,5,2,7,8,3,4,6]=>{{1},{2,3,5,6,8},{4,7}}
[1,5,7,2,8,3,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,5,7,8,2,3,4,6]=>{{1},{2,5},{3,4,6,7,8}}
[5,1,7,2,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[5,7,1,2,3,4,8,6]=>{{1,3,5},{2,4,6,7,8}}
[5,1,2,7,3,4,8,6]=>{{1,2,3,5},{4,6,7,8}}
[1,5,2,7,3,4,8,6]=>{{1},{2,3,5},{4,6,7,8}}
[1,5,7,2,3,4,8,6]=>{{1},{2,3,4,5,6,7,8}}
[5,1,2,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,5,2,3,7,4,8,6]=>{{1},{2,3,4,5,6,7,8}}
[1,2,5,3,7,4,8,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,5,7,3,4,8,6]=>{{1},{2},{3,5},{4,6,7,8}}
[5,1,2,3,7,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[1,5,2,3,7,8,4,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,2,5,3,7,8,4,6]=>{{1},{2},{3,4,5,7},{6,8}}
[1,2,5,7,3,8,4,6]=>{{1},{2},{3,5},{4,7},{6,8}}
[1,2,5,7,8,3,4,6]=>{{1},{2},{3,5,6,8},{4,7}}
[5,1,7,2,3,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[5,7,1,2,3,4,6,8]=>{{1,3,5},{2,4,6,7},{8}}
[5,1,2,7,3,4,6,8]=>{{1,2,3,5},{4,6,7},{8}}
[1,5,2,7,3,4,6,8]=>{{1},{2,3,5},{4,6,7},{8}}
[1,5,2,3,7,4,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,2,5,3,7,4,6,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,5,7,3,4,6,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[1,5,2,3,4,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[1,2,5,3,4,7,6,8]=>{{1},{2},{3,4,5},{6,7},{8}}
[1,2,3,5,7,4,6,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[5,1,2,3,4,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[1,5,2,3,4,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[1,2,5,3,4,7,8,6]=>{{1},{2},{3,4,5},{6,7,8}}
[1,2,3,5,7,4,8,6]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[5,1,8,2,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,2,3,4,6,7]=>{{1,3,5},{2,4,6,7,8}}
[5,1,2,8,3,4,6,7]=>{{1,2,3,5},{4,6,7,8}}
[1,5,2,8,3,4,6,7]=>{{1},{2,3,5},{4,6,7,8}}
[1,5,8,2,3,4,6,7]=>{{1},{2,3,4,5,6,7,8}}
[5,1,2,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,5,2,3,8,4,6,7]=>{{1},{2,3,4,5,6,7,8}}
[1,2,5,3,8,4,6,7]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,5,8,3,4,6,7]=>{{1},{2},{3,5},{4,6,7,8}}
[5,1,2,3,4,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[1,5,2,3,4,8,6,7]=>{{1},{2,3,4,5},{6,7,8}}
[1,2,5,3,4,8,6,7]=>{{1},{2},{3,4,5},{6,7,8}}
[1,2,3,5,4,8,6,7]=>{{1},{2},{3},{4,5},{6,7,8}}
[1,2,3,5,8,4,6,7]=>{{1},{2},{3},{4,5,6,7,8}}
[5,1,2,3,4,6,8,7]=>{{1,2,3,4,5},{6},{7,8}}
[1,5,2,3,4,6,8,7]=>{{1},{2,3,4,5},{6},{7,8}}
[1,2,5,3,4,6,8,7]=>{{1},{2},{3,4,5},{6},{7,8}}
[1,2,3,5,6,8,4,7]=>{{1},{2},{3},{4,5,6,7,8}}
[1,5,2,3,4,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[1,2,5,3,4,6,7,8]=>{{1},{2},{3,4,5},{6},{7},{8}}
[6,1,7,2,8,3,4,5]=>{{1,2,3,4,6,7},{5,8}}
[6,7,1,2,8,3,4,5]=>{{1,3,6},{2,4,7},{5,8}}
[6,1,7,8,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,8,2,3,4,5]=>{{1,3,6},{2,4,5,7,8}}
[6,1,7,2,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,2,3,8,4,5]=>{{1,3,5,6,8},{2,4,7}}
[6,1,2,7,3,8,4,5]=>{{1,2,3,5,6,8},{4,7}}
[1,6,2,7,3,8,4,5]=>{{1},{2,3,5,6,8},{4,7}}
[1,6,7,2,3,8,4,5]=>{{1},{2,3,4,5,6,7,8}}
[6,1,2,7,8,3,4,5]=>{{1,2,3,6},{4,7},{5,8}}
[1,6,2,7,8,3,4,5]=>{{1},{2,3,6},{4,7},{5,8}}
[1,6,7,2,8,3,4,5]=>{{1},{2,3,4,6,7},{5,8}}
[1,6,7,8,2,3,4,5]=>{{1},{2,3,4,5,6,7,8}}
[6,1,7,2,3,4,8,5]=>{{1,2,4,6},{3,5,7,8}}
[6,7,1,2,3,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,1,2,7,3,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,6,2,7,3,4,8,5]=>{{1},{2,3,4,5,6,7,8}}
[1,6,7,2,3,4,8,5]=>{{1},{2,4,6},{3,5,7,8}}
[6,1,2,3,7,4,8,5]=>{{1,2,3,4,6},{5,7,8}}
[1,6,2,3,7,4,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[1,2,6,3,7,4,8,5]=>{{1},{2},{3,4,6},{5,7,8}}
[1,2,6,7,3,4,8,5]=>{{1},{2},{3,4,5,6,7,8}}
[6,1,2,3,7,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[1,6,2,3,7,8,4,5]=>{{1},{2,3,4,5,6,7,8}}
[1,2,6,3,7,8,4,5]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,6,7,3,8,4,5]=>{{1},{2},{3,5,6,8},{4,7}}
[1,2,6,7,8,3,4,5]=>{{1},{2},{3,6},{4,7},{5,8}}
[6,1,7,2,3,4,5,8]=>{{1,2,4,6},{3,5,7},{8}}
[6,1,2,7,3,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[1,6,2,7,3,4,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,7,2,3,4,5,8]=>{{1},{2,4,6},{3,5,7},{8}}
[6,1,2,3,7,4,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[1,6,2,3,7,4,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[1,2,6,3,7,4,5,8]=>{{1},{2},{3,4,6},{5,7},{8}}
[1,2,6,7,3,4,5,8]=>{{1},{2},{3,4,5,6,7},{8}}
[6,1,2,3,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[1,6,2,3,4,7,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,2,6,3,4,7,5,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,3,6,4,7,5,8]=>{{1},{2},{3},{4,5,6,7},{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]=>{{1,2,3,4,5,6,7,8}}
[1,6,2,3,4,7,8,5]=>{{1},{2,3,4,5,6,7,8}}
[1,2,6,3,4,7,8,5]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,3,6,4,7,8,5]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[1,2,3,6,7,8,4,5]=>{{1},{2},{3},{4,5,6,7,8}}
[6,1,8,2,3,4,5,7]=>{{1,2,4,6},{3,5,7,8}}
[6,8,1,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[6,1,2,8,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,2,8,3,4,5,7]=>{{1},{2,3,4,5,6,7,8}}
[1,6,8,2,3,4,5,7]=>{{1},{2,4,6},{3,5,7,8}}
[6,1,2,3,8,4,5,7]=>{{1,2,3,4,6},{5,7,8}}
[1,6,2,3,8,4,5,7]=>{{1},{2,3,4,6},{5,7,8}}
[1,2,6,3,8,4,5,7]=>{{1},{2},{3,4,6},{5,7,8}}
[1,2,6,8,3,4,5,7]=>{{1},{2},{3,4,5,6,7,8}}
[6,1,2,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,2,3,4,8,5,7]=>{{1},{2,3,4,5,6,7,8}}
[1,2,6,3,4,8,5,7]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,3,6,4,8,5,7]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,6,8,4,5,7]=>{{1},{2},{3},{4,6},{5,7,8}}
[6,1,2,3,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[1,6,2,3,4,5,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[1,2,6,3,4,5,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[1,2,3,6,4,5,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[1,2,3,4,6,8,5,7]=>{{1},{2},{3},{4},{5,6,7,8}}
[1,6,2,3,4,5,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,2,6,3,4,5,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[1,2,3,6,4,5,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[7,1,8,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,1,2,8,3,4,5,6]=>{{1,2,3,5,7},{4,6,8}}
[1,7,2,8,3,4,5,6]=>{{1},{2,3,5,7},{4,6,8}}
[1,7,8,2,3,4,5,6]=>{{1},{2,3,4,5,6,7,8}}
[7,1,2,3,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[1,7,2,3,8,4,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,2,7,3,8,4,5,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,7,8,3,4,5,6]=>{{1},{2},{3,5,7},{4,6,8}}
[7,1,2,3,4,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[1,7,2,3,4,8,5,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,2,7,3,4,8,5,6]=>{{1},{2},{3,4,5,7},{6,8}}
[1,2,3,7,4,8,5,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[1,2,3,7,8,4,5,6]=>{{1},{2},{3},{4,5,6,7,8}}
[7,1,2,3,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,7,2,3,4,5,8,6]=>{{1},{2,3,4,5,6,7,8}}
[1,2,7,3,4,5,8,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,3,7,4,5,8,6]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,4,7,5,8,6]=>{{1},{2},{3},{4},{5,6,7,8}}
[1,2,3,4,7,8,5,6]=>{{1},{2},{3},{4},{5,7},{6,8}}
[1,7,2,3,4,5,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,2,7,3,4,5,6,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,3,7,4,5,6,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[1,2,3,4,7,5,6,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[1,8,2,3,4,5,6,7]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,3,4,5,6,7]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,3,8,4,5,6,7]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,4,8,5,6,7]=>{{1},{2},{3},{4},{5,6,7,8}}
[1,2,3,4,5,8,6,7]=>{{1},{2},{3},{4},{5},{6,7,8}}
[5,3,2,6,1,4,8,7]=>{{1,5},{2,3},{4,6},{7,8}}
[7,3,2,5,4,8,1,6]=>{{1,7},{2,3},{4,5},{6,8}}
[8,4,5,2,3,7,6,1]=>{{1,8},{2,4},{3,5},{6,7}}
[7,4,5,2,3,8,1,6]=>{{1,7},{2,4},{3,5},{6,8}}
[6,4,5,2,3,1,8,7]=>{{1,6},{2,4},{3,5},{7,8}}
[5,4,6,2,1,3,8,7]=>{{1,5},{2,4},{3,6},{7,8}}
[3,6,1,5,4,2,8,7]=>{{1,3},{2,6},{4,5},{7,8}}
[4,6,5,1,3,2,8,7]=>{{1,4},{2,6},{3,5},{7,8}}
[5,6,4,3,1,2,8,7]=>{{1,5},{2,6},{3,4},{7,8}}
[7,5,4,3,2,8,1,6]=>{{1,7},{2,5},{3,4},{6,8}}
[8,6,4,3,7,2,5,1]=>{{1,8},{2,6},{3,4},{5,7}}
[7,6,4,3,8,2,1,5]=>{{1,7},{2,6},{3,4},{5,8}}
[6,7,4,3,8,1,2,5]=>{{1,6},{2,7},{3,4},{5,8}}
[5,7,4,3,1,8,2,6]=>{{1,5},{2,7},{3,4},{6,8}}
[4,7,5,1,3,8,2,6]=>{{1,4},{2,7},{3,5},{6,8}}
[3,7,1,5,4,8,2,6]=>{{1,3},{2,7},{4,5},{6,8}}
[2,1,7,5,4,8,3,6]=>{{1,2},{3,7},{4,5},{6,8}}
[3,8,1,5,4,7,6,2]=>{{1,3},{2,8},{4,5},{6,7}}
[4,8,5,1,3,7,6,2]=>{{1,4},{2,8},{3,5},{6,7}}
[5,8,4,3,1,7,6,2]=>{{1,5},{2,8},{3,4},{6,7}}
[6,8,4,3,7,1,5,2]=>{{1,6},{2,8},{3,4},{5,7}}
[7,8,4,3,6,5,1,2]=>{{1,7},{2,8},{3,4},{5,6}}
[6,8,5,7,3,1,4,2]=>{{1,6},{2,8},{3,5},{4,7}}
[5,8,6,7,1,3,4,2]=>{{1,5},{2,8},{3,6},{4,7}}
[4,8,6,1,7,3,5,2]=>{{1,4},{2,8},{3,6},{5,7}}
[3,8,1,6,7,4,5,2]=>{{1,3},{2,8},{4,6},{5,7}}
[2,1,8,6,7,4,5,3]=>{{1,2},{3,8},{4,6},{5,7}}
[2,1,7,6,8,4,3,5]=>{{1,2},{3,7},{4,6},{5,8}}
[3,7,1,6,8,4,2,5]=>{{1,3},{2,7},{4,6},{5,8}}
[4,7,6,1,8,3,2,5]=>{{1,4},{2,7},{3,6},{5,8}}
[5,7,6,8,1,3,2,4]=>{{1,5},{2,7},{3,6},{4,8}}
[5,4,7,2,1,8,3,6]=>{{1,5},{2,4},{3,7},{6,8}}
[6,4,7,2,8,1,3,5]=>{{1,6},{2,4},{3,7},{5,8}}
[7,4,6,2,8,3,1,5]=>{{1,7},{2,4},{3,6},{5,8}}
[8,4,6,2,7,3,5,1]=>{{1,8},{2,4},{3,6},{5,7}}
[8,3,2,6,7,4,5,1]=>{{1,8},{2,3},{4,6},{5,7}}
[7,3,2,6,8,4,1,5]=>{{1,7},{2,3},{4,6},{5,8}}
[6,3,2,7,8,1,4,5]=>{{1,6},{2,3},{4,7},{5,8}}
[5,3,2,7,1,8,4,6]=>{{1,5},{2,3},{4,7},{6,8}}
[4,3,2,1,7,8,5,6]=>{{1,4},{2,3},{5,7},{6,8}}
[3,4,1,2,8,7,6,5]=>{{1,3},{2,4},{5,8},{6,7}}
[5,3,2,8,1,7,6,4]=>{{1,5},{2,3},{4,8},{6,7}}
[6,3,2,8,7,1,5,4]=>{{1,6},{2,3},{4,8},{5,7}}
[7,3,2,8,6,5,1,4]=>{{1,7},{2,3},{4,8},{5,6}}
[8,4,7,2,6,5,3,1]=>{{1,8},{2,4},{3,7},{5,6}}
[7,4,8,2,6,5,1,3]=>{{1,7},{2,4},{3,8},{5,6}}
[6,4,8,2,7,1,5,3]=>{{1,6},{2,4},{3,8},{5,7}}
[5,4,8,2,1,7,6,3]=>{{1,5},{2,4},{3,8},{6,7}}
[4,5,8,1,2,7,6,3]=>{{1,4},{2,5},{3,8},{6,7}}
[3,5,1,8,2,7,6,4]=>{{1,3},{2,5},{4,8},{6,7}}
[2,1,5,8,3,7,6,4]=>{{1,2},{3,5},{4,8},{6,7}}
[2,1,6,8,7,3,5,4]=>{{1,2},{3,6},{4,8},{5,7}}
[3,6,1,8,7,2,5,4]=>{{1,3},{2,6},{4,8},{5,7}}
[4,6,8,1,7,2,5,3]=>{{1,4},{2,6},{3,8},{5,7}}
[5,6,8,7,1,2,4,3]=>{{1,5},{2,6},{3,8},{4,7}}
[6,5,8,7,2,1,4,3]=>{{1,6},{2,5},{3,8},{4,7}}
[7,5,8,6,2,4,1,3]=>{{1,7},{2,5},{3,8},{4,6}}
[8,5,7,6,2,4,3,1]=>{{1,8},{2,5},{3,7},{4,6}}
[5,7,8,6,1,4,2,3]=>{{1,5},{2,7},{3,8},{4,6}}
[4,7,8,1,6,5,2,3]=>{{1,4},{2,7},{3,8},{5,6}}
[3,7,1,8,6,5,2,4]=>{{1,3},{2,7},{4,8},{5,6}}
[2,1,7,8,6,5,3,4]=>{{1,2},{3,7},{4,8},{5,6}}
[3,8,1,7,6,5,4,2]=>{{1,3},{2,8},{4,7},{5,6}}
[4,8,7,1,6,5,3,2]=>{{1,4},{2,8},{3,7},{5,6}}
[5,8,7,6,1,4,3,2]=>{{1,5},{2,8},{3,7},{4,6}}
[6,8,7,5,4,1,3,2]=>{{1,6},{2,8},{3,7},{4,5}}
[3,2,5,1,4,6,7,8]=>{{1,3,4,5},{2},{6},{7},{8}}
[4,2,5,1,3,6,7,8]=>{{1,4},{2},{3,5},{6},{7},{8}}
[5,2,4,1,3,6,7,8]=>{{1,3,4,5},{2},{6},{7},{8}}
[3,2,6,1,4,5,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[4,2,6,1,3,5,7,8]=>{{1,4},{2},{3,5,6},{7},{8}}
[5,3,6,1,2,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[6,2,4,1,3,5,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[6,3,5,1,2,4,7,8]=>{{1,4,6},{2,3,5},{7},{8}}
[5,3,7,1,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,7,1,2,3,6,8]=>{{1,2,4,5},{3,6,7},{8}}
[6,2,7,1,3,4,5,8]=>{{1,4,6},{2},{3,5,7},{8}}
[6,3,7,1,2,4,5,8]=>{{1,4,6},{2,3,5,7},{8}}
[6,4,7,1,2,3,5,8]=>{{1,2,3,4,5,6,7},{8}}
[7,3,5,1,2,4,6,8]=>{{1,4,6,7},{2,3,5},{8}}
[7,3,6,1,2,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[7,4,6,1,2,3,5,8]=>{{1,2,4,5,7},{3,6},{8}}
[3,2,8,1,4,5,6,7]=>{{1,3,4,5,6,7,8},{2}}
[4,2,8,1,3,5,6,7]=>{{1,4},{2},{3,5,6,7,8}}
[5,4,8,1,2,3,6,7]=>{{1,2,4,5},{3,6,7,8}}
[6,2,8,1,3,4,5,7]=>{{1,4,6},{2},{3,5,7,8}}
[6,3,8,1,2,4,5,7]=>{{1,4,6},{2,3,5,7,8}}
[6,4,8,1,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,1,2,3,4,7]=>{{1,3,4,6,7,8},{2,5}}
[7,2,8,1,3,4,5,6]=>{{1,3,4,5,6,7,8},{2}}
[7,3,8,1,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,8,1,2,3,5,6]=>{{1,2,4,5,7},{3,6,8}}
[7,5,8,1,2,3,4,6]=>{{1,4,7},{2,5},{3,6,8}}
[8,2,4,1,3,5,6,7]=>{{1,3,4,5,6,7,8},{2}}
[8,3,5,1,2,4,6,7]=>{{1,4,6,7,8},{2,3,5}}
[8,3,6,1,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,1,2,4,5,6]=>{{1,4,6,8},{2,3,5,7}}
[8,4,7,1,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,1,2,3,4,6]=>{{1,3,4,6,7,8},{2,5}}
[3,2,5,7,1,4,6,8]=>{{1,3,5},{2},{4,6,7},{8}}
[4,2,5,7,1,3,6,8]=>{{1,3,4,5,6,7},{2},{8}}
[5,2,4,7,1,3,6,8]=>{{1,5},{2},{3,4,6,7},{8}}
[4,2,6,7,1,3,5,8]=>{{1,4,5,7},{2},{3,6},{8}}
[5,2,6,7,1,3,4,8]=>{{1,5},{2},{3,6},{4,7},{8}}
[5,3,6,7,1,2,4,8]=>{{1,5},{2,3,6},{4,7},{8}}
[6,2,5,7,1,3,4,8]=>{{1,3,5,6},{2},{4,7},{8}}
[6,3,5,7,1,2,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[3,2,5,8,1,4,6,7]=>{{1,3,5},{2},{4,6,7,8}}
[4,2,5,8,1,3,6,7]=>{{1,3,4,5,6,7,8},{2}}
[4,3,5,8,1,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,2,4,8,1,3,6,7]=>{{1,5},{2},{3,4,6,7,8}}
[3,2,6,8,1,4,5,7]=>{{1,3,4,5,6,7,8},{2}}
[4,2,6,8,1,3,5,7]=>{{1,4,5,7,8},{2},{3,6}}
[5,2,6,8,1,3,4,7]=>{{1,5},{2},{3,6},{4,7,8}}
[6,2,4,8,1,3,5,7]=>{{1,3,4,5,6,7,8},{2}}
[6,3,4,8,1,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[6,2,5,8,1,3,4,7]=>{{1,3,5,6},{2},{4,7,8}}
[6,3,5,8,1,2,4,7]=>{{1,2,3,5,6},{4,7,8}}
[6,4,5,8,1,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[3,2,7,8,1,4,5,6]=>{{1,3,5,7},{2},{4,6,8}}
[4,3,7,8,1,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,8,1,2,4,6]=>{{1,5},{2,3,4,6,7,8}}
[5,4,7,8,1,2,3,6]=>{{1,5},{2,4,6,8},{3,7}}
[6,2,7,8,1,3,4,5]=>{{1,3,4,5,6,7,8},{2}}
[6,3,7,8,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,8,1,2,3,5]=>{{1,2,4,5,6,8},{3,7}}
[7,2,4,8,1,3,5,6]=>{{1,5,7},{2},{3,4,6,8}}
[7,3,4,8,1,2,5,6]=>{{1,5,7},{2,3,4,6,8}}
[7,3,5,8,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,8,1,2,3,6]=>{{1,3,5,7},{2,4,6,8}}
[7,4,6,8,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,6,1,2,5,7]=>{{1,5,7,8},{2,3,4,6}}
[8,3,5,6,1,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,2,4,7,1,3,5,6]=>{{1,3,4,5,6,7,8},{2}}
[8,2,5,7,1,3,4,6]=>{{1,3,5,6,8},{2},{4,7}}
[8,3,5,7,1,2,4,6]=>{{1,2,3,5,6,8},{4,7}}
[8,2,6,7,1,3,4,5]=>{{1,5,8},{2},{3,6},{4,7}}
[8,4,6,7,1,2,3,5]=>{{1,5,8},{2,3,4,6,7}}
[3,6,2,5,1,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[4,6,2,5,1,3,7,8]=>{{1,4,5},{2,3,6},{7},{8}}
[4,6,3,5,1,2,7,8]=>{{1,4,5},{2,6},{3},{7},{8}}
[5,6,2,4,1,3,7,8]=>{{1,5},{2,3,6},{4},{7},{8}}
[3,7,2,5,1,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[4,7,3,5,1,2,6,8]=>{{1,4,5},{2,6,7},{3},{8}}
[5,7,2,4,1,3,6,8]=>{{1,5},{2,3,6,7},{4},{8}}
[3,7,2,6,1,4,5,8]=>{{1,2,3,5,7},{4,6},{8}}
[4,7,3,6,1,2,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,7,2,6,1,3,4,8]=>{{1,5},{2,3,4,6,7},{8}}
[6,7,2,5,1,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[4,8,2,5,1,3,6,7]=>{{1,4,5},{2,3,6,7,8}}
[5,8,2,4,1,3,6,7]=>{{1,5},{2,3,6,7,8},{4}}
[5,8,3,4,1,2,6,7]=>{{1,5},{2,6,7,8},{3},{4}}
[3,8,2,6,1,4,5,7]=>{{1,2,3,5,7,8},{4,6}}
[5,8,3,6,1,2,4,7]=>{{1,5},{2,4,6,7,8},{3}}
[5,8,4,6,1,2,3,7]=>{{1,5},{2,3,4,6,7,8}}
[6,8,3,5,1,2,4,7]=>{{1,2,4,5,6,7,8},{3}}
[3,8,2,7,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,2,7,1,3,5,6]=>{{1,4,5,7},{2,3,6,8}}
[4,8,3,7,1,2,5,6]=>{{1,4,5,7},{2,6,8},{3}}
[5,8,2,7,1,3,4,6]=>{{1,5},{2,3,6,8},{4,7}}
[5,8,3,7,1,2,4,6]=>{{1,5},{2,6,8},{3},{4,7}}
[5,8,4,7,1,2,3,6]=>{{1,5},{2,6,8},{3,4,7}}
[6,8,2,7,1,3,4,5]=>{{1,2,3,5,6,8},{4,7}}
[6,8,3,7,1,2,4,5]=>{{1,2,5,6,8},{3},{4,7}}
[6,8,5,7,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,2,4,1,3,5,6]=>{{1,5,7},{2,3,6,8},{4}}
[7,8,2,5,1,3,4,6]=>{{1,4,5,7},{2,3,6,8}}
[7,8,3,5,1,2,4,6]=>{{1,4,5,7},{2,6,8},{3}}
[7,8,4,6,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[4,3,2,6,1,5,7,8]=>{{1,4,5,6},{2,3},{7},{8}}
[5,3,2,6,1,4,7,8]=>{{1,5},{2,3},{4,6},{7},{8}}
[5,4,2,6,1,3,7,8]=>{{1,5},{2,3,4,6},{7},{8}}
[6,3,2,5,1,4,7,8]=>{{1,4,5,6},{2,3},{7},{8}}
[6,5,2,4,1,3,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[4,3,2,7,1,5,6,8]=>{{1,4,5,6,7},{2,3},{8}}
[5,3,2,7,1,4,6,8]=>{{1,5},{2,3},{4,6,7},{8}}
[5,4,3,7,1,2,6,8]=>{{1,5},{2,4,6,7},{3},{8}}
[6,3,2,7,1,4,5,8]=>{{1,4,5,6,7},{2,3},{8}}
[6,4,2,7,1,3,5,8]=>{{1,2,3,4,5,6,7},{8}}
[6,4,3,7,1,2,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[6,5,2,7,1,3,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[6,5,3,7,1,2,4,8]=>{{1,2,5,6},{3},{4,7},{8}}
[7,3,2,5,1,4,6,8]=>{{1,4,5,6,7},{2,3},{8}}
[7,4,2,5,1,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[7,3,2,6,1,4,5,8]=>{{1,5,7},{2,3},{4,6},{8}}
[7,4,2,6,1,3,5,8]=>{{1,5,7},{2,3,4,6},{8}}
[7,4,3,6,1,2,5,8]=>{{1,5,7},{2,4,6},{3},{8}}
[7,5,2,6,1,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,3,6,1,2,4,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,6,3,5,1,2,4,8]=>{{1,4,5,7},{2,6},{3},{8}}
[4,3,2,8,1,5,6,7]=>{{1,4,5,6,7,8},{2,3}}
[5,3,2,8,1,4,6,7]=>{{1,5},{2,3},{4,6,7,8}}
[5,4,3,8,1,2,6,7]=>{{1,5},{2,4,6,7,8},{3}}
[6,3,2,8,1,4,5,7]=>{{1,4,5,6,7,8},{2,3}}
[6,4,2,8,1,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[6,4,3,8,1,2,5,7]=>{{1,2,4,5,6,7,8},{3}}
[6,5,2,8,1,3,4,7]=>{{1,2,3,5,6},{4,7,8}}
[6,5,3,8,1,2,4,7]=>{{1,2,5,6},{3},{4,7,8}}
[7,3,2,8,1,4,5,6]=>{{1,5,7},{2,3},{4,6,8}}
[7,4,2,8,1,3,5,6]=>{{1,5,7},{2,3,4,6,8}}
[7,4,3,8,1,2,5,6]=>{{1,5,7},{2,4,6,8},{3}}
[7,5,3,8,1,2,4,6]=>{{1,2,4,5,6,7,8},{3}}
[7,5,4,8,1,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,6,2,8,1,3,4,5]=>{{1,4,5,7,8},{2,3,6}}
[8,3,2,5,1,4,6,7]=>{{1,4,5,6,7,8},{2,3}}
[8,4,2,5,1,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,2,6,1,4,5,7]=>{{1,5,7,8},{2,3},{4,6}}
[8,4,2,6,1,3,5,7]=>{{1,5,7,8},{2,3,4,6}}
[8,5,3,6,1,2,4,7]=>{{1,2,4,5,6,7,8},{3}}
[8,6,2,4,1,3,5,7]=>{{1,5,7,8},{2,3,6},{4}}
[8,6,2,5,1,3,4,7]=>{{1,4,5,7,8},{2,3,6}}
[8,3,2,7,1,4,5,6]=>{{1,4,5,6,7,8},{2,3}}
[8,4,2,7,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,4,3,7,1,2,5,6]=>{{1,2,4,5,6,7,8},{3}}
[8,5,2,7,1,3,4,6]=>{{1,2,3,5,6,8},{4,7}}
[8,5,3,7,1,2,4,6]=>{{1,2,5,6,8},{3},{4,7}}
[8,6,3,7,1,2,4,5]=>{{1,5,8},{2,6},{3},{4,7}}
[8,7,2,4,1,3,5,6]=>{{1,2,3,5,6,7,8},{4}}
[8,7,2,5,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,5,1,2,4,6]=>{{1,2,4,5,6,7,8},{3}}
[8,7,2,6,1,3,4,5]=>{{1,5,8},{2,3,4,6,7}}
[8,7,3,6,1,2,4,5]=>{{1,5,8},{2,4,6,7},{3}}
[8,7,4,6,1,2,3,5]=>{{1,5,8},{2,3,4,6,7}}
[3,6,2,5,8,1,4,7]=>{{1,2,3,6},{4,5,7,8}}
[4,6,3,5,8,1,2,7]=>{{1,2,4,5,6,7,8},{3}}
[5,6,2,4,8,1,3,7]=>{{1,2,3,5,6,7,8},{4}}
[4,7,2,5,8,1,3,6]=>{{1,4,5,6,8},{2,3,7}}
[4,7,3,5,8,1,2,6]=>{{1,4,5,6,8},{2,7},{3}}
[5,7,2,4,8,1,3,6]=>{{1,5,6,8},{2,3,7},{4}}
[5,7,3,4,8,1,2,6]=>{{1,5,6,8},{2,7},{3},{4}}
[4,7,3,6,8,1,2,5]=>{{1,4,6},{2,7},{3},{5,8}}
[5,7,2,6,8,1,3,4]=>{{1,4,5,6,8},{2,3,7}}
[5,7,4,6,8,1,2,3]=>{{1,3,4,5,6,8},{2,7}}
[6,7,3,4,8,1,2,5]=>{{1,6},{2,7},{3},{4},{5,8}}
[6,7,3,5,8,1,2,4]=>{{1,6},{2,7},{3},{4,5,8}}
[3,8,2,5,7,1,4,6]=>{{1,2,3,6,8},{4,5,7}}
[4,8,3,5,7,1,2,6]=>{{1,2,4,5,6,7,8},{3}}
[5,8,2,4,7,1,3,6]=>{{1,2,3,5,6,7,8},{4}}
[3,8,2,6,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[5,8,2,6,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,3,6,7,1,2,4]=>{{1,2,4,5,6,7,8},{3}}
[6,8,2,5,7,1,3,4]=>{{1,6},{2,3,4,5,7,8}}
[6,8,4,5,7,1,2,3]=>{{1,6},{2,3,4,5,7,8}}
[7,8,2,4,6,1,3,5]=>{{1,2,3,5,6,7,8},{4}}
[7,8,3,4,6,1,2,5]=>{{1,2,5,6,7,8},{3},{4}}
[7,8,2,5,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,3,5,6,1,2,4]=>{{1,2,4,5,6,7,8},{3}}
[4,3,2,6,8,1,5,7]=>{{1,4,6},{2,3},{5,7,8}}
[5,3,2,6,8,1,4,7]=>{{1,4,5,6,7,8},{2,3}}
[5,4,2,6,8,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,6,8,1,2,7]=>{{1,2,4,5,6,7,8},{3}}
[6,3,2,5,8,1,4,7]=>{{1,6},{2,3},{4,5,7,8}}
[6,4,3,5,8,1,2,7]=>{{1,6},{2,4,5,7,8},{3}}
[6,5,2,4,8,1,3,7]=>{{1,6},{2,3,5,7,8},{4}}
[4,3,2,7,8,1,5,6]=>{{1,4,5,6,7,8},{2,3}}
[5,4,2,7,8,1,3,6]=>{{1,5,6,8},{2,3,4,7}}
[5,4,3,7,8,1,2,6]=>{{1,5,6,8},{2,4,7},{3}}
[6,4,2,7,8,1,3,5]=>{{1,6},{2,3,4,7},{5,8}}
[6,4,3,7,8,1,2,5]=>{{1,6},{2,4,7},{3},{5,8}}
[6,5,2,7,8,1,3,4]=>{{1,6},{2,3,4,5,7,8}}
[7,4,2,5,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,3,5,8,1,2,6]=>{{1,2,4,5,6,7,8},{3}}
[7,5,2,6,8,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,3,6,8,1,2,4]=>{{1,2,4,5,6,7,8},{3}}
[7,6,2,4,8,1,3,5]=>{{1,2,3,6,7},{4},{5,8}}
[7,6,3,5,8,1,2,4]=>{{1,2,6,7},{3},{4,5,8}}
[8,3,2,5,7,1,4,6]=>{{1,6,8},{2,3},{4,5,7}}
[8,4,2,5,7,1,3,6]=>{{1,6,8},{2,3,4,5,7}}
[8,5,2,4,7,1,3,6]=>{{1,6,8},{2,3,5,7},{4}}
[8,3,2,6,7,1,4,5]=>{{1,4,5,6,7,8},{2,3}}
[8,5,2,6,7,1,3,4]=>{{1,4,6,8},{2,3,5,7}}
[8,5,3,6,7,1,2,4]=>{{1,4,6,8},{2,5,7},{3}}
[8,6,2,4,7,1,3,5]=>{{1,2,3,5,6,7,8},{4}}
[8,6,2,5,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,6,3,5,7,1,2,4]=>{{1,2,4,5,6,7,8},{3}}
[8,7,2,4,6,1,3,5]=>{{1,5,6,8},{2,3,7},{4}}
[8,7,3,4,6,1,2,5]=>{{1,5,6,8},{2,7},{3},{4}}
[8,7,2,5,6,1,3,4]=>{{1,4,5,6,8},{2,3,7}}
[4,3,7,2,6,1,5,8]=>{{1,2,3,4,5,6,7},{8}}
[5,3,7,2,6,1,4,8]=>{{1,5,6},{2,3,4,7},{8}}
[5,4,7,2,6,1,3,8]=>{{1,5,6},{2,4},{3,7},{8}}
[6,3,7,2,5,1,4,8]=>{{1,6},{2,3,4,7},{5},{8}}
[6,4,7,2,5,1,3,8]=>{{1,6},{2,4},{3,7},{5},{8}}
[6,4,7,3,5,1,2,8]=>{{1,6},{2,3,4,7},{5},{8}}
[7,3,6,2,5,1,4,8]=>{{1,2,3,4,6,7},{5},{8}}
[4,3,8,2,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,2,6,1,4,7]=>{{1,5,6},{2,3,4,7,8}}
[5,4,8,2,6,1,3,7]=>{{1,5,6},{2,4},{3,7,8}}
[5,4,8,3,6,1,2,7]=>{{1,5,6},{2,3,4,7,8}}
[6,3,8,2,5,1,4,7]=>{{1,6},{2,3,4,7,8},{5}}
[6,4,8,2,5,1,3,7]=>{{1,6},{2,4},{3,7,8},{5}}
[6,4,8,3,5,1,2,7]=>{{1,6},{2,3,4,7,8},{5}}
[6,5,8,2,4,1,3,7]=>{{1,6},{2,4,5},{3,7,8}}
[6,5,8,3,4,1,2,7]=>{{1,6},{2,3,4,5,7,8}}
[4,3,8,2,7,1,5,6]=>{{1,2,3,4,6,8},{5,7}}
[5,3,8,2,7,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,2,7,1,3,6]=>{{1,3,5,6,7,8},{2,4}}
[5,4,8,3,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[6,3,8,2,7,1,4,5]=>{{1,6},{2,3,4,5,7,8}}
[6,4,8,2,7,1,3,5]=>{{1,6},{2,4},{3,5,7,8}}
[7,3,8,2,5,1,4,6]=>{{1,2,3,4,6,7,8},{5}}
[7,4,8,3,5,1,2,6]=>{{1,2,3,4,6,7,8},{5}}
[7,5,8,2,4,1,3,6]=>{{1,3,6,7,8},{2,4,5}}
[7,5,8,2,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,4,6,1,2,3]=>{{1,2,5,6,7},{3,8},{4}}
[7,6,8,2,5,1,3,4]=>{{1,2,3,4,6,7,8},{5}}
[7,6,8,3,5,1,2,4]=>{{1,2,6,7},{3,4,8},{5}}
[8,3,6,2,5,1,4,7]=>{{1,2,3,4,6,7,8},{5}}
[8,4,6,2,5,1,3,7]=>{{1,3,6,7,8},{2,4},{5}}
[8,5,6,2,4,1,3,7]=>{{1,3,6,7,8},{2,4,5}}
[8,3,7,2,5,1,4,6]=>{{1,6,8},{2,3,4,7},{5}}
[8,4,7,3,5,1,2,6]=>{{1,6,8},{2,3,4,7},{5}}
[8,5,7,2,4,1,3,6]=>{{1,6,8},{2,4,5},{3,7}}
[8,3,7,2,6,1,4,5]=>{{1,5,6,8},{2,3,4,7}}
[8,4,7,2,6,1,3,5]=>{{1,5,6,8},{2,4},{3,7}}
[8,4,7,3,6,1,2,5]=>{{1,5,6,8},{2,3,4,7}}
[8,5,7,2,6,1,3,4]=>{{1,2,4,5,6,8},{3,7}}
[8,6,7,2,4,1,3,5]=>{{1,2,4,5,6,8},{3,7}}
[8,6,7,2,5,1,3,4]=>{{1,2,4,6,8},{3,7},{5}}
[8,6,7,3,5,1,2,4]=>{{1,2,3,4,6,7,8},{5}}
[5,4,3,2,7,1,6,8]=>{{1,5,6,7},{2,4},{3},{8}}
[6,4,3,2,7,1,5,8]=>{{1,6},{2,4},{3},{5,7},{8}}
[6,5,3,2,7,1,4,8]=>{{1,6},{2,4,5,7},{3},{8}}
[6,5,4,2,7,1,3,8]=>{{1,6},{2,3,4,5,7},{8}}
[7,5,3,2,6,1,4,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,5,4,2,6,1,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,3,2,8,1,6,7]=>{{1,5,6,7,8},{2,4},{3}}
[6,5,3,2,8,1,4,7]=>{{1,6},{2,4,5,7,8},{3}}
[6,5,4,2,8,1,3,7]=>{{1,6},{2,3,4,5,7,8}}
[6,5,4,3,8,1,2,7]=>{{1,6},{2,5,7,8},{3,4}}
[7,5,3,2,8,1,4,6]=>{{1,2,4,5,6,7,8},{3}}
[7,5,4,2,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,6,3,2,8,1,4,5]=>{{1,2,4,6,7},{3},{5,8}}
[7,6,4,3,8,1,2,5]=>{{1,2,6,7},{3,4},{5,8}}
[7,6,5,2,8,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,2,6,1,4,7]=>{{1,2,4,5,6,7,8},{3}}
[8,5,4,2,6,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,2,4,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,2,7,1,4,6]=>{{1,6,8},{2,4,5,7},{3}}
[8,6,3,2,7,1,4,5]=>{{1,2,4,5,6,7,8},{3}}
[8,6,4,3,7,1,2,5]=>{{1,2,5,6,7,8},{3,4}}
[8,7,3,2,6,1,4,5]=>{{1,5,6,8},{2,4,7},{3}}
[8,7,4,2,6,1,3,5]=>{{1,5,6,8},{2,3,4,7}}
[8,7,4,3,6,1,2,5]=>{{1,5,6,8},{2,7},{3,4}}
[8,7,5,2,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,3,6,1,2,4]=>{{1,3,4,5,6,8},{2,7}}
[8,7,6,2,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,2,5,1,3,4]=>{{1,2,3,4,6,7,8},{5}}
[8,7,6,3,5,1,2,4]=>{{1,3,4,6,8},{2,7},{5}}
[4,8,3,7,2,6,1,5]=>{{1,4,7},{2,5,8},{3},{6}}
[5,8,3,7,2,6,1,4]=>{{1,2,4,5,7,8},{3},{6}}
[5,8,4,7,2,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[5,8,4,7,3,6,1,2]=>{{1,3,4,5,7},{2,8},{6}}
[6,8,3,7,2,5,1,4]=>{{1,2,4,5,6,7,8},{3}}
[6,8,4,7,2,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,7,3,5,1,2]=>{{1,3,4,5,6,7},{2,8}}
[6,8,5,7,2,4,1,3]=>{{1,4,6,7},{2,3,5,8}}
[6,8,5,7,3,4,1,2]=>{{1,4,6,7},{2,8},{3,5}}
[7,8,3,6,2,5,1,4]=>{{1,7},{2,4,5,6,8},{3}}
[7,8,4,6,2,5,1,3]=>{{1,7},{2,3,4,5,6,8}}
[7,8,4,6,3,5,1,2]=>{{1,7},{2,8},{3,4,5,6}}
[7,8,5,6,2,4,1,3]=>{{1,7},{2,3,5,8},{4,6}}
[5,4,3,8,2,7,1,6]=>{{1,2,4,5,6,7,8},{3}}
[6,4,3,8,2,7,1,5]=>{{1,6,7},{2,4,5,8},{3}}
[6,5,3,8,2,7,1,4]=>{{1,6,7},{2,5},{3},{4,8}}
[6,5,4,8,3,7,1,2]=>{{1,6,7},{2,3,4,5,8}}
[7,4,3,8,2,6,1,5]=>{{1,7},{2,4,5,8},{3},{6}}
[7,5,3,8,2,6,1,4]=>{{1,7},{2,5},{3},{4,8},{6}}
[7,5,4,8,2,6,1,3]=>{{1,7},{2,5},{3,4,8},{6}}
[7,6,3,8,2,5,1,4]=>{{1,7},{2,5,6},{3},{4,8}}
[7,6,4,8,2,5,1,3]=>{{1,7},{2,5,6},{3,4,8}}
[7,6,5,8,2,4,1,3]=>{{1,7},{2,3,4,5,6,8}}
[8,4,3,7,2,6,1,5]=>{{1,2,4,5,7,8},{3},{6}}
[8,5,3,7,2,6,1,4]=>{{1,4,7,8},{2,5},{3},{6}}
[8,5,4,7,2,6,1,3]=>{{1,3,4,7,8},{2,5},{6}}
[8,5,4,7,3,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[8,6,3,7,2,5,1,4]=>{{1,4,7,8},{2,5,6},{3}}
[8,6,4,7,2,5,1,3]=>{{1,3,4,7,8},{2,5,6}}
[8,6,4,7,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,7,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,6,2,5,1,4]=>{{1,2,4,5,6,7,8},{3}}
[8,7,4,6,2,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,6,3,5,1,2]=>{{1,2,7,8},{3,4,5,6}}
[8,7,5,6,2,4,1,3]=>{{1,2,3,5,7,8},{4,6}}
[6,5,4,3,2,8,1,7]=>{{1,6,7,8},{2,5},{3,4}}
[7,6,5,4,2,8,1,3]=>{{1,7},{2,3,5,6,8},{4}}
[8,5,4,3,2,7,1,6]=>{{1,6,7,8},{2,5},{3,4}}
[8,6,5,3,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,3,2,6,1,5]=>{{1,2,5,7,8},{3,4},{6}}
[8,7,5,3,2,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[8,7,5,4,2,6,1,3]=>{{1,2,3,5,7,8},{4},{6}}
[8,7,6,3,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,4,2,5,1,3]=>{{1,2,3,5,6,7,8},{4}}
[8,7,6,5,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,3,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,3,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,3,7,4,5,6]=>{{1,2,3,4,6,8},{5,7}}
[7,1,2,3,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,1,2,3,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,3,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,8,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,5,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[7,1,2,5,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,6,3,4,5,7]=>{{1,2,3,5,7,8},{4,6}}
[7,1,2,6,3,4,8,5]=>{{1,2,3,5,7,8},{4,6}}
[6,1,2,5,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,5,3,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,6,3,7,4,5]=>{{1,2,3,5,8},{4,6,7}}
[6,1,2,5,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,8,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,8,7,3,5,6]=>{{1,2,3,4,6,8},{5,7}}
[4,1,2,7,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,5,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,5,7,3,4,6]=>{{1,2,3,6,8},{4,5,7}}
[8,1,2,7,6,3,4,5]=>{{1,2,3,5,6,8},{4,7}}
[7,1,2,5,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,5,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,8,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,5,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,2,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,2,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,2,7,4,5,6]=>{{1,2,3,4,6,8},{5,7}}
[3,1,7,2,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,5,2,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,2,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[7,1,4,2,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[6,1,4,2,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,2,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[6,1,4,2,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,5,2,3,4,6,7]=>{{1,2,4,6,7,8},{3,5}}
[7,1,5,2,3,4,8,6]=>{{1,2,4,6,7,8},{3,5}}
[8,1,7,2,3,4,5,6]=>{{1,2,4,6,8},{3,5,7}}
[6,1,5,2,3,8,4,7]=>{{1,2,4,6,7,8},{3,5}}
[8,1,5,2,3,7,4,6]=>{{1,2,4,6,7,8},{3,5}}
[6,1,8,2,3,7,4,5]=>{{1,2,4,6,7},{3,5,8}}
[6,1,5,2,3,7,8,4]=>{{1,2,4,6,7,8},{3,5}}
[5,1,4,2,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,1,4,2,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,2,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,2,7,3,5,6]=>{{1,2,3,4,6,8},{5,7}}
[7,1,4,2,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,5,2,6,3,4,7]=>{{1,2,4,7,8},{3,5,6}}
[8,1,5,2,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,2,6,3,4,5]=>{{1,2,4,7},{3,5,6,8}}
[7,1,5,2,6,3,8,4]=>{{1,2,4,7,8},{3,5,6}}
[5,1,4,2,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[5,1,4,2,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,2,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,5,2,6,7,3,4]=>{{1,2,4,8},{3,5,6,7}}
[5,1,4,2,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,8,2,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,5,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,5,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,6,2,4,5,7]=>{{1,2,3,5,7,8},{4,6}}
[3,1,7,6,2,4,8,5]=>{{1,2,3,5,7,8},{4,6}}
[3,1,6,5,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,5,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,6,2,7,4,5]=>{{1,2,3,5,8},{4,6,7}}
[3,1,6,5,2,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,5,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[7,1,4,5,2,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,6,2,3,5,7]=>{{1,2,5,7,8},{3,4,6}}
[7,1,4,8,2,3,5,6]=>{{1,2,5,7},{3,4,6,8}}
[7,1,4,6,2,3,8,5]=>{{1,2,5,7,8},{3,4,6}}
[8,1,6,5,2,3,4,7]=>{{1,2,4,5,7,8},{3,6}}
[7,1,8,5,2,3,4,6]=>{{1,2,4,5,7},{3,6,8}}
[7,1,8,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,5,2,3,8,4]=>{{1,2,4,5,7,8},{3,6}}
[6,1,4,5,2,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,5,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,6,2,7,3,5]=>{{1,2,5,8},{3,4,6,7}}
[8,1,6,5,2,7,3,4]=>{{1,2,4,5,8},{3,6,7}}
[6,1,4,5,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,8,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,8,7,2,5,6]=>{{1,2,3,4,6,8},{5,7}}
[3,1,4,7,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,5,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,5,7,2,4,6]=>{{1,2,3,6,8},{4,5,7}}
[3,1,8,7,6,2,4,5]=>{{1,2,3,5,6,8},{4,7}}
[3,1,7,5,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,5,6,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,5,7,2,3,6]=>{{1,2,6,8},{3,4,5,7}}
[8,1,4,7,6,2,3,5]=>{{1,2,5,6,8},{3,4,7}}
[8,1,7,5,6,2,3,4]=>{{1,2,4,5,6,8},{3,7}}
[7,1,4,5,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,5,8,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,8,6,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,5,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,5,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,3,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,3,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,3,7,4,5,6]=>{{1,2,3,4,6,8},{5,7}}
[2,7,1,3,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,5,1,3,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,3,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,4,1,8,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,5,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,7,1,5,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,6,3,4,5,7]=>{{1,2,3,5,7,8},{4,6}}
[2,7,1,6,3,4,8,5]=>{{1,2,3,5,7,8},{4,6}}
[2,6,1,5,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,5,3,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[2,6,1,5,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,4,1,8,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,1,8,7,3,5,6]=>{{1,2,3,4,6,8},{5,7}}
[2,4,1,7,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,5,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,5,7,3,4,6]=>{{1,2,3,6,8},{4,5,7}}
[2,8,1,7,6,3,4,5]=>{{1,2,3,5,6,8},{4,7}}
[2,7,1,5,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,4,1,5,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,4,1,8,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,5,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,3,1,2,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,2,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,2,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,2,7,4,5,6]=>{{1,2,3,4,6,8},{5,7}}
[7,3,1,2,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,2,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,2,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,2,3,5,8,6]=>{{1,3,5,6,7,8},{2,4}}
[6,4,1,2,3,8,5,7]=>{{1,3,5,6,7,8},{2,4}}
[8,4,1,2,3,7,5,6]=>{{1,3,5,6,7,8},{2,4}}
[6,4,1,2,3,7,8,5]=>{{1,3,5,6,7,8},{2,4}}
[7,6,1,2,3,4,8,5]=>{{1,3,5,7,8},{2,4,6}}
[5,8,1,2,3,7,4,6]=>{{1,3,5},{2,4,6,7,8}}
[8,6,1,2,3,7,4,5]=>{{1,3,5,8},{2,4,6,7}}
[5,4,1,2,8,3,6,7]=>{{1,3,5,6,7,8},{2,4}}
[5,4,1,2,7,3,8,6]=>{{1,3,5,6,7,8},{2,4}}
[8,4,1,2,6,3,5,7]=>{{1,3,5,6,7,8},{2,4}}
[8,4,1,2,7,3,5,6]=>{{1,3,6,8},{2,4},{5,7}}
[7,4,1,2,6,3,8,5]=>{{1,3,5,6,7,8},{2,4}}
[5,8,1,2,6,3,4,7]=>{{1,3,5,6},{2,4,7,8}}
[5,8,1,2,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,1,2,6,3,4,5]=>{{1,3,5,6,8},{2,4,7}}
[5,7,1,2,6,3,8,4]=>{{1,3,5,6},{2,4,7,8}}
[5,4,1,2,6,8,3,7]=>{{1,3,5,6,7,8},{2,4}}
[5,4,1,2,8,7,3,6]=>{{1,3,5,6,7,8},{2,4}}
[8,4,1,2,6,7,3,5]=>{{1,3,5,6,7,8},{2,4}}
[5,8,1,2,6,7,3,4]=>{{1,3,5,6,7},{2,4,8}}
[5,4,1,2,6,7,8,3]=>{{1,3,5,6,7,8},{2,4}}
[4,3,1,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,7,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,8,2,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,5,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[7,3,1,5,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,6,2,4,5,7]=>{{1,2,3,5,7,8},{4,6}}
[7,3,1,8,2,4,5,6]=>{{1,2,3,5,7},{4,6,8}}
[7,3,1,6,2,4,8,5]=>{{1,2,3,5,7,8},{4,6}}
[6,3,1,5,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,6,2,7,4,5]=>{{1,2,3,5,8},{4,6,7}}
[6,3,1,5,2,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,5,2,3,6,7]=>{{1,3,6,7,8},{2,4,5}}
[7,4,1,5,2,3,8,6]=>{{1,3,6,7,8},{2,4,5}}
[8,4,1,6,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,8,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,6,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,8,1,5,2,3,4,7]=>{{1,3,6},{2,4,5,7,8}}
[8,7,1,5,2,3,4,6]=>{{1,3,6,8},{2,4,5,7}}
[8,7,1,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,5,2,3,8,4]=>{{1,3,6},{2,4,5,7,8}}
[6,4,1,5,2,8,3,7]=>{{1,3,6,7,8},{2,4,5}}
[8,4,1,5,2,7,3,6]=>{{1,3,6,7,8},{2,4,5}}
[8,4,1,6,2,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,8,1,5,2,7,3,4]=>{{1,3,6,7},{2,4,5,8}}
[6,4,1,5,2,7,8,3]=>{{1,3,6,7,8},{2,4,5}}
[4,3,1,5,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,8,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,8,7,2,5,6]=>{{1,2,3,4,6,8},{5,7}}
[4,3,1,7,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,5,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,5,7,2,4,6]=>{{1,2,3,6,8},{4,5,7}}
[8,3,1,7,6,2,4,5]=>{{1,2,3,5,6,8},{4,7}}
[7,3,1,5,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,5,6,2,3,7]=>{{1,3,7,8},{2,4,5,6}}
[8,4,1,5,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,7,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,5,6,2,3,4]=>{{1,3,7},{2,4,5,6,8}}
[7,4,1,5,6,2,8,3]=>{{1,3,7,8},{2,4,5,6}}
[4,3,1,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,5,8,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,8,6,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,5,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,5,6,7,2,3]=>{{1,3,8},{2,4,5,6,7}}
[4,3,1,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,1,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,1,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,1,7,4,5,6]=>{{1,2,3,4,6,8},{5,7}}
[2,3,7,1,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,1,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,1,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,1,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,7,4,1,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,6,4,1,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,1,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,6,4,1,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,8,5,1,3,4,6,7]=>{{1,2,4,6,7,8},{3,5}}
[2,7,5,1,3,4,8,6]=>{{1,2,4,6,7,8},{3,5}}
[2,8,7,1,3,4,5,6]=>{{1,2,4,6,8},{3,5,7}}
[2,6,5,1,3,8,4,7]=>{{1,2,4,6,7,8},{3,5}}
[2,8,5,1,3,7,4,6]=>{{1,2,4,6,7,8},{3,5}}
[2,6,8,1,3,7,4,5]=>{{1,2,4,6,7},{3,5,8}}
[2,6,5,1,3,7,8,4]=>{{1,2,4,6,7,8},{3,5}}
[2,5,4,1,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,1,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,1,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,1,7,3,5,6]=>{{1,2,3,4,6,8},{5,7}}
[2,7,4,1,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,8,5,1,6,3,4,7]=>{{1,2,4,7,8},{3,5,6}}
[2,8,5,1,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,1,6,3,4,5]=>{{1,2,4,7},{3,5,6,8}}
[2,7,5,1,6,3,8,4]=>{{1,2,4,7,8},{3,5,6}}
[2,5,4,1,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,1,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,1,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[2,8,5,1,6,7,3,4]=>{{1,2,4,8},{3,5,6,7}}
[2,5,4,1,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,3,4,1,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[6,3,4,1,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,1,2,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[6,3,4,1,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[7,3,5,1,2,4,8,6]=>{{1,4,6,7,8},{2,3,5}}
[6,3,7,1,2,4,8,5]=>{{1,4,6},{2,3,5,7,8}}
[6,3,5,1,2,8,4,7]=>{{1,4,6,7,8},{2,3,5}}
[8,3,5,1,2,7,4,6]=>{{1,4,6,7,8},{2,3,5}}
[6,3,8,1,2,7,4,5]=>{{1,4,6,7},{2,3,5,8}}
[6,3,5,1,2,7,8,4]=>{{1,4,6,7,8},{2,3,5}}
[7,5,4,1,2,3,8,6]=>{{1,3,4,6,7,8},{2,5}}
[6,8,4,1,2,3,5,7]=>{{1,3,4,6},{2,5,7,8}}
[6,7,4,1,2,3,8,5]=>{{1,3,4,6},{2,5,7,8}}
[6,8,5,1,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[6,7,5,1,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,1,2,8,3,7]=>{{1,3,4,6,7,8},{2,5}}
[8,5,4,1,2,7,3,6]=>{{1,3,4,6,7,8},{2,5}}
[6,8,4,1,2,7,3,5]=>{{1,3,4,6,7},{2,5,8}}
[6,8,5,1,2,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,1,2,7,8,3]=>{{1,3,4,6,7,8},{2,5}}
[5,3,4,1,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,4,1,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,1,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,1,7,2,5,6]=>{{1,2,3,4,6,8},{5,7}}
[7,3,4,1,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,5,1,6,2,4,7]=>{{1,4,7,8},{2,3,5,6}}
[8,3,5,1,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,1,6,2,4,5]=>{{1,4,7},{2,3,5,6,8}}
[7,3,5,1,6,2,8,4]=>{{1,4,7,8},{2,3,5,6}}
[8,5,4,1,6,2,3,7]=>{{1,3,4,7,8},{2,5,6}}
[8,5,4,1,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,1,6,2,3,5]=>{{1,3,4,7},{2,5,6,8}}
[7,8,5,1,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,4,1,6,2,8,3]=>{{1,3,4,7,8},{2,5,6}}
[5,3,4,1,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,4,1,8,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,1,6,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,5,1,6,7,2,4]=>{{1,4,8},{2,3,5,6,7}}
[8,5,4,1,6,7,2,3]=>{{1,3,4,8},{2,5,6,7}}
[5,3,4,1,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,8,1,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,5,1,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,7,5,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,6,1,4,5,7]=>{{1,2,3,5,7,8},{4,6}}
[2,3,7,6,1,4,8,5]=>{{1,2,3,5,7,8},{4,6}}
[2,3,6,5,1,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,5,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,6,1,7,4,5]=>{{1,2,3,5,8},{4,6,7}}
[2,3,6,5,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,5,1,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,7,4,5,1,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,6,1,3,5,7]=>{{1,2,5,7,8},{3,4,6}}
[2,7,4,8,1,3,5,6]=>{{1,2,5,7},{3,4,6,8}}
[2,7,4,6,1,3,8,5]=>{{1,2,5,7,8},{3,4,6}}
[2,8,6,5,1,3,4,7]=>{{1,2,4,5,7,8},{3,6}}
[2,7,8,5,1,3,4,6]=>{{1,2,4,5,7},{3,6,8}}
[2,7,8,6,1,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,5,1,3,8,4]=>{{1,2,4,5,7,8},{3,6}}
[2,6,4,5,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,5,1,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,6,1,7,3,5]=>{{1,2,5,8},{3,4,6,7}}
[2,8,6,5,1,7,3,4]=>{{1,2,4,5,8},{3,6,7}}
[2,6,4,5,1,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,3,4,5,1,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[7,3,4,6,1,2,8,5]=>{{1,5,7,8},{2,3,4,6}}
[8,3,6,5,1,2,4,7]=>{{1,4,5,7,8},{2,3,6}}
[7,3,8,5,1,2,4,6]=>{{1,4,5,7},{2,3,6,8}}
[7,3,8,6,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,3,6,5,1,2,8,4]=>{{1,4,5,7,8},{2,3,6}}
[7,6,4,5,1,2,8,3]=>{{1,3,4,5,7,8},{2,6}}
[6,3,4,5,1,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,5,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,6,1,7,2,5]=>{{1,5,8},{2,3,4,6,7}}
[8,3,6,5,1,7,2,4]=>{{1,4,5,8},{2,3,6,7}}
[8,6,4,5,1,7,2,3]=>{{1,3,4,5,8},{2,6,7}}
[6,3,4,5,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,8,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,8,7,1,5,6]=>{{1,2,3,4,6,8},{5,7}}
[2,3,4,7,6,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,5,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,5,7,1,4,6]=>{{1,2,3,6,8},{4,5,7}}
[2,3,8,7,6,1,4,5]=>{{1,2,3,5,6,8},{4,7}}
[2,3,7,5,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,5,6,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,5,7,1,3,6]=>{{1,2,6,8},{3,4,5,7}}
[2,8,4,7,6,1,3,5]=>{{1,2,5,6,8},{3,4,7}}
[2,8,7,5,6,1,3,4]=>{{1,2,4,5,6,8},{3,7}}
[2,7,4,5,6,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,5,7,1,2,6]=>{{1,6,8},{2,3,4,5,7}}
[8,3,4,7,6,1,2,5]=>{{1,5,6,8},{2,3,4,7}}
[8,3,7,5,6,1,2,4]=>{{1,4,5,6,8},{2,3,7}}
[7,3,4,5,6,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,5,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,8,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,5,6,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,5,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,6,1,4,8,7]=>{{1,2,3,5},{4,6},{7,8}}
[3,5,2,6,4,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,5,2,7,4,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[3,5,2,7,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,7,2,3,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,7,2,3,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[4,5,6,2,3,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,5,6,2,1,3,8,7]=>{{1,2,4,5},{3,6},{7,8}}
[3,5,1,6,4,2,8,7]=>{{1,3},{2,4,5,6},{7,8}}
[4,5,6,1,3,2,8,7]=>{{1,4},{2,3,5,6},{7,8}}
[4,5,6,3,1,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,5,7,3,2,8,1,6]=>{{1,3,4,7},{2,5},{6,8}}
[4,5,7,3,2,8,6,1]=>{{1,3,4,6,7,8},{2,5}}
[4,6,7,3,8,2,5,1]=>{{1,3,4,5,7,8},{2,6}}
[4,6,7,3,8,2,1,5]=>{{1,3,4,7},{2,6},{5,8}}
[4,6,7,3,8,1,2,5]=>{{1,2,3,4,6,7},{5,8}}
[4,5,7,3,1,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[4,5,7,1,3,8,2,6]=>{{1,4},{2,3,5,7},{6,8}}
[3,5,1,7,4,8,2,6]=>{{1,3},{2,4,5,7},{6,8}}
[2,1,5,7,4,8,3,6]=>{{1,2},{3,4,5,7},{6,8}}
[2,1,5,7,4,8,6,3]=>{{1,2},{3,4,5,6,7,8}}
[3,5,1,7,4,8,6,2]=>{{1,3},{2,4,5,6,7,8}}
[4,5,7,1,3,8,6,2]=>{{1,4},{2,3,5,6,7,8}}
[4,5,7,3,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,3,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,3,8,5,1,2]=>{{1,3,4,7},{2,5,6,8}}
[4,6,7,3,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,8,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,8,1,3,4,2]=>{{1,5},{2,3,4,6,7,8}}
[4,6,7,1,8,3,5,2]=>{{1,4},{2,3,5,6,7,8}}
[3,6,1,7,8,4,5,2]=>{{1,3},{2,4,5,6,7,8}}
[2,1,6,7,8,4,5,3]=>{{1,2},{3,4,5,6,7,8}}
[2,1,6,7,8,4,3,5]=>{{1,2},{3,4,6,7},{5,8}}
[3,6,1,7,8,4,2,5]=>{{1,3},{2,4,6,7},{5,8}}
[4,6,7,1,8,3,2,5]=>{{1,4},{2,3,6,7},{5,8}}
[5,6,7,8,1,3,2,4]=>{{1,5},{2,3,6,7},{4,8}}
[4,5,7,2,1,8,3,6]=>{{1,2,4,5},{3,7},{6,8}}
[4,6,7,2,8,1,3,5]=>{{1,2,4,6},{3,7},{5,8}}
[4,6,7,2,8,3,1,5]=>{{1,2,3,4,6,7},{5,8}}
[4,6,7,2,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,6,2,7,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,6,2,7,8,4,1,5]=>{{1,2,3,4,6,7},{5,8}}
[3,6,2,7,8,1,4,5]=>{{1,2,3,6},{4,7},{5,8}}
[3,5,2,7,1,8,4,6]=>{{1,2,3,5},{4,7},{6,8}}
[3,4,2,1,7,8,5,6]=>{{1,2,3,4},{5,7},{6,8}}
[3,4,1,2,7,8,6,5]=>{{1,3},{2,4},{5,6,7,8}}
[3,5,2,7,1,8,6,4]=>{{1,2,3,5},{4,6,7,8}}
[3,6,2,7,8,1,5,4]=>{{1,2,3,6},{4,5,7,8}}
[3,6,2,7,8,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[3,6,2,7,8,5,4,1]=>{{1,2,3,5,6,8},{4,7}}
[4,6,7,2,8,5,3,1]=>{{1,2,4,5,6,8},{3,7}}
[4,6,7,2,8,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,2,8,1,5,3]=>{{1,2,4,6},{3,5,7,8}}
[4,5,7,2,1,8,6,3]=>{{1,2,4,5},{3,6,7,8}}
[4,5,7,1,2,8,6,3]=>{{1,4},{2,5},{3,6,7,8}}
[3,5,1,7,2,8,6,4]=>{{1,3},{2,5},{4,6,7,8}}
[2,1,5,7,3,8,6,4]=>{{1,2},{3,5},{4,6,7,8}}
[2,1,6,7,8,3,5,4]=>{{1,2},{3,6},{4,5,7,8}}
[3,6,1,7,8,2,5,4]=>{{1,3},{2,6},{4,5,7,8}}
[4,6,7,1,8,2,5,3]=>{{1,4},{2,6},{3,5,7,8}}
[5,6,7,8,1,2,4,3]=>{{1,5},{2,6},{3,4,7,8}}
[5,6,7,8,2,1,4,3]=>{{1,2,5,6},{3,4,7,8}}
[5,6,7,8,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,8,2,4,3,1]=>{{1,2,4,5,6,8},{3,7}}
[5,6,7,8,1,4,2,3]=>{{1,5},{2,3,4,6,7,8}}
[4,6,7,1,8,5,2,3]=>{{1,4},{2,3,5,6,7,8}}
[3,6,1,7,8,5,2,4]=>{{1,3},{2,4,5,6,7,8}}
[2,1,6,7,8,5,3,4]=>{{1,2},{3,4,5,6,7,8}}
[3,6,1,7,8,5,4,2]=>{{1,3},{2,5,6,8},{4,7}}
[4,6,7,1,8,5,3,2]=>{{1,4},{2,5,6,8},{3,7}}
[5,6,7,8,1,4,3,2]=>{{1,5},{2,4,6,8},{3,7}}
[5,6,7,8,4,1,3,2]=>{{1,2,4,5,6,8},{3,7}}
[6,5,8,7,3,4,1,2]=>{{1,4,6,7},{2,3,5,8}}
[3,6,7,4,5,8,1,2]=>{{1,3,7},{2,6,8},{4},{5}}
[2,6,7,4,5,1,8,3]=>{{1,2,6},{3,7,8},{4},{5}}
[1,6,7,4,5,2,3,8]=>{{1},{2,6},{3,7},{4},{5},{8}}
[1,5,4,7,6,2,3,8]=>{{1},{2,5,6},{3,4,7},{8}}
[2,5,4,7,6,1,8,3]=>{{1,2,5,6},{3,4,7,8}}
[3,5,4,7,6,8,1,2]=>{{1,3,4,7},{2,5,6,8}}
[4,5,3,7,8,6,1,2]=>{{1,4,7},{2,5,8},{3},{6}}
[5,4,3,8,7,6,1,2]=>{{1,5,7},{2,4,8},{3},{6}}
[6,4,8,3,7,5,1,2]=>{{1,5,6,7},{2,3,4,8}}
[6,3,8,4,5,7,1,2]=>{{1,6,7},{2,3,8},{4},{5}}
[5,3,4,8,6,7,1,2]=>{{1,5,6,7},{2,3,4,8}}
[4,3,5,6,8,7,1,2]=>{{1,4,6,7},{2,3,5,8}}
[3,2,5,6,1,8,7,4]=>{{1,3,5},{2},{4,6,8},{7}}
[4,2,5,6,8,1,7,3]=>{{1,4,6},{2},{3,5,8},{7}}
[5,2,4,8,6,1,7,3]=>{{1,5,6},{2},{3,4,8},{7}}
[6,2,8,4,5,1,7,3]=>{{1,6},{2},{3,8},{4},{5},{7}}
[7,8,2,4,5,1,6,3]=>{{1,6,7},{2,3,8},{4},{5}}
[7,8,1,4,5,2,3,6]=>{{1,3,7},{2,6,8},{4},{5}}
[6,1,8,4,5,2,3,7]=>{{1,2,6},{3,7,8},{4},{5}}
[5,1,4,8,6,2,3,7]=>{{1,2,5,6},{3,4,7,8}}
[4,1,3,2,8,6,5,7]=>{{1,2,4},{3},{5,7,8},{6}}
[5,1,3,8,2,6,4,7]=>{{1,2,5},{3},{4,7,8},{6}}
[6,1,8,3,2,5,4,7]=>{{1,2,5,6},{3,4,7,8}}
[7,8,1,3,2,5,4,6]=>{{1,3,4,7},{2,5,6,8}}
[7,8,2,3,1,5,6,4]=>{{1,5,6,7},{2,3,4,8}}
[6,2,8,3,1,5,7,4]=>{{1,5,6},{2},{3,4,8},{7}}
[5,2,3,8,1,6,7,4]=>{{1,5},{2},{3},{4,8},{6},{7}}
[6,3,8,2,1,7,5,4]=>{{1,5,6,7},{2,3,4,8}}
[7,8,3,2,1,6,5,4]=>{{1,5,7},{2,4,8},{3},{6}}
[7,8,4,2,6,1,5,3]=>{{1,5,6,7},{2,3,4,8}}
[5,4,2,8,7,1,6,3]=>{{1,5,6,7},{2,3,4,8}}
[4,5,2,7,8,1,6,3]=>{{1,4,6,7},{2,3,5,8}}
[2,5,3,7,1,6,8,4]=>{{1,2,5},{3},{4,7,8},{6}}
[1,5,3,7,2,6,4,8]=>{{1},{2,5},{3},{4,7},{6},{8}}
[1,6,7,3,2,5,4,8]=>{{1},{2,5,6},{3,4,7},{8}}
[2,6,7,3,1,5,8,4]=>{{1,2,5,6},{3,4,7,8}}
[3,6,7,2,1,8,5,4]=>{{1,3,5,7},{2,4,6,8}}
[7,8,5,6,2,1,4,3]=>{{1,4,6,7},{2,3,5,8}}
[6,5,8,7,1,2,3,4]=>{{1,2,5,6},{3,4,7,8}}
[5,4,1,8,7,2,3,6]=>{{1,3,5,7},{2,4,6,8}}
[6,4,8,1,7,2,3,5]=>{{1,2,4,6},{3,5,7,8}}
[7,8,3,1,2,6,4,5]=>{{1,4,7},{2,5,8},{3},{6}}
[5,3,1,8,2,7,4,6]=>{{1,2,3,5},{4,6,7,8}}
[4,3,1,2,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}
[4,2,1,3,8,5,7,6]=>{{1,3,4},{2},{5,6,8},{7}}
[5,2,1,8,3,4,7,6]=>{{1,3,5},{2},{4,6,8},{7}}
[6,2,8,1,3,4,7,5]=>{{1,4,6},{2},{3,5,8},{7}}
[7,8,2,1,3,4,6,5]=>{{1,4,6,7},{2,3,5,8}}
[4,3,1,2,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}
[5,3,1,6,2,4,8,7]=>{{1,2,3,5},{4,6},{7,8}}
[6,3,1,5,2,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[7,3,1,5,2,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[8,4,5,1,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,1,2,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[6,4,5,1,2,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[5,4,6,1,2,3,8,7]=>{{1,2,4,5},{3,6},{7,8}}
[2,1,6,5,3,4,8,7]=>{{1,2},{3,4,5,6},{7,8}}
[3,6,1,5,2,4,8,7]=>{{1,3},{2,4,5,6},{7,8}}
[4,6,5,1,2,3,8,7]=>{{1,4},{2,3,5,6},{7,8}}
[5,6,4,1,2,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[6,5,4,1,2,3,8,7]=>{{1,3,4,6},{2,5},{7,8}}
[7,5,4,1,2,8,3,6]=>{{1,3,4,7},{2,5},{6,8}}
[8,6,4,1,7,2,3,5]=>{{1,3,4,5,7,8},{2,6}}
[7,6,4,1,8,2,3,5]=>{{1,3,4,7},{2,6},{5,8}}
[6,7,4,1,8,2,3,5]=>{{1,2,3,4,6,7},{5,8}}
[5,7,4,1,2,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[4,7,5,1,2,8,3,6]=>{{1,4},{2,3,5,7},{6,8}}
[3,7,1,5,2,8,4,6]=>{{1,3},{2,4,5,7},{6,8}}
[2,1,7,5,3,8,4,6]=>{{1,2},{3,4,5,7},{6,8}}
[2,1,8,5,3,7,4,6]=>{{1,2},{3,4,5,6,7,8}}
[3,8,1,5,2,7,4,6]=>{{1,3},{2,4,5,6,7,8}}
[4,8,5,1,2,7,3,6]=>{{1,4},{2,3,5,6,7,8}}
[5,8,4,1,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,1,7,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,1,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,7,1,2,3,4]=>{{1,5},{2,3,4,6,7,8}}
[4,8,6,1,7,2,3,5]=>{{1,4},{2,3,5,6,7,8}}
[3,8,1,6,7,2,4,5]=>{{1,3},{2,4,5,6,7,8}}
[2,1,8,6,7,3,4,5]=>{{1,2},{3,4,5,6,7,8}}
[2,1,7,6,8,3,4,5]=>{{1,2},{3,4,6,7},{5,8}}
[3,7,1,6,8,2,4,5]=>{{1,3},{2,4,6,7},{5,8}}
[4,7,6,1,8,2,3,5]=>{{1,4},{2,3,6,7},{5,8}}
[5,7,6,8,1,2,3,4]=>{{1,5},{2,3,6,7},{4,8}}
[5,4,7,1,2,8,3,6]=>{{1,2,4,5},{3,7},{6,8}}
[6,4,7,1,8,2,3,5]=>{{1,2,4,6},{3,7},{5,8}}
[7,4,6,1,8,2,3,5]=>{{1,2,3,4,6,7},{5,8}}
[8,4,6,1,7,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,6,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,3,1,6,8,2,4,5]=>{{1,2,3,4,6,7},{5,8}}
[6,3,1,7,8,2,4,5]=>{{1,2,3,6},{4,7},{5,8}}
[5,3,1,7,2,8,4,6]=>{{1,2,3,5},{4,7},{6,8}}
[4,3,1,2,7,8,5,6]=>{{1,2,3,4},{5,7},{6,8}}
[2,1,4,3,8,7,5,6]=>{{1,2},{3,4},{5,6,7,8}}
[3,4,1,2,8,7,5,6]=>{{1,3},{2,4},{5,6,7,8}}
[6,3,1,8,7,2,4,5]=>{{1,2,3,6},{4,5,7,8}}
[7,3,1,8,6,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,1,6,2,3,5]=>{{1,2,4,5,6,8},{3,7}}
[7,4,8,1,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,1,2,7,3,6]=>{{1,2,4,5},{3,6,7,8}}
[4,5,8,1,2,7,3,6]=>{{1,4},{2,5},{3,6,7,8}}
[3,5,1,8,2,7,4,6]=>{{1,3},{2,5},{4,6,7,8}}
[2,1,5,8,3,7,4,6]=>{{1,2},{3,5},{4,6,7,8}}
[2,1,6,8,7,3,4,5]=>{{1,2},{3,6},{4,5,7,8}}
[3,6,1,8,7,2,4,5]=>{{1,3},{2,6},{4,5,7,8}}
[4,6,8,1,7,2,3,5]=>{{1,4},{2,6},{3,5,7,8}}
[5,6,8,7,1,2,3,4]=>{{1,5},{2,6},{3,4,7,8}}
[7,5,8,6,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,6,1,2,3,4]=>{{1,2,4,5,6,8},{3,7}}
[5,7,8,6,1,2,3,4]=>{{1,5},{2,3,4,6,7,8}}
[4,7,8,1,6,2,3,5]=>{{1,4},{2,3,5,6,7,8}}
[3,7,1,8,6,2,4,5]=>{{1,3},{2,4,5,6,7,8}}
[2,1,7,8,6,3,4,5]=>{{1,2},{3,4,5,6,7,8}}
[2,1,8,7,6,3,4,5]=>{{1,2},{3,5,6,8},{4,7}}
[3,8,1,7,6,2,4,5]=>{{1,3},{2,5,6,8},{4,7}}
[4,8,7,1,6,2,3,5]=>{{1,4},{2,5,6,8},{3,7}}
[5,8,7,6,1,2,3,4]=>{{1,5},{2,4,6,8},{3,7}}
[6,8,7,5,1,2,3,4]=>{{1,2,4,5,6,8},{3,7}}
[6,4,7,3,8,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,3,5,8,1,2]=>{{1,2,3,4,6,7,8},{5}}
[6,4,7,2,5,1,8,3]=>{{1,6},{2,4},{3,7,8},{5}}
[5,4,2,7,6,1,3,8]=>{{1,5,6},{2,3,4,7},{8}}
[5,4,2,7,6,1,8,3]=>{{1,5,6},{2,3,4,7,8}}
[5,4,3,7,6,8,1,2]=>{{1,2,4,5,6,7,8},{3}}
[5,4,3,7,8,6,1,2]=>{{1,2,4,5,7,8},{3},{6}}
[6,4,8,3,5,7,1,2]=>{{1,6,7},{2,3,4,8},{5}}
[5,4,3,8,6,7,1,2]=>{{1,5,6,7},{2,4,8},{3}}
[5,4,3,6,8,7,1,2]=>{{1,2,4,5,6,7,8},{3}}
[5,4,2,6,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[5,4,2,6,7,1,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,3,2,6,1,7,4,8]=>{{1,5},{2,3},{4,6,7},{8}}
[5,3,2,6,1,7,8,4]=>{{1,5},{2,3},{4,6,7,8}}
[5,3,2,6,1,8,7,4]=>{{1,5},{2,3},{4,6,8},{7}}
[5,4,2,6,8,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[5,4,2,8,6,1,7,3]=>{{1,5,6},{2,3,4,8},{7}}
[6,4,8,2,5,1,7,3]=>{{1,6},{2,4},{3,8},{5},{7}}
[7,8,4,2,5,1,6,3]=>{{1,6,7},{2,3,4,8},{5}}
[7,8,4,2,5,1,3,6]=>{{1,2,3,4,6,7,8},{5}}
[5,4,2,8,6,1,3,7]=>{{1,5,6},{2,3,4,7,8}}
[5,3,2,6,1,8,4,7]=>{{1,5},{2,3},{4,6,7,8}}
[4,3,2,1,6,8,5,7]=>{{1,4},{2,3},{5,6,7,8}}
[4,3,2,1,8,6,5,7]=>{{1,4},{2,3},{5,7,8},{6}}
[5,3,2,8,1,6,4,7]=>{{1,5},{2,3},{4,7,8},{6}}
[6,3,8,2,1,5,4,7]=>{{1,5,6},{2,3,4,7,8}}
[7,8,3,2,1,5,4,6]=>{{1,2,4,5,6,7,8},{3}}
[7,8,3,2,1,5,6,4]=>{{1,5,6,7},{2,4,8},{3}}
[6,3,8,2,1,5,7,4]=>{{1,5,6},{2,3,4,8},{7}}
[5,3,2,8,1,6,7,4]=>{{1,5},{2,3},{4,8},{6},{7}}
[5,4,2,7,8,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[5,3,2,7,1,8,6,4]=>{{1,5},{2,3},{4,6,7,8}}
[5,3,2,7,1,6,8,4]=>{{1,5},{2,3},{4,7,8},{6}}
[5,3,2,7,1,6,4,8]=>{{1,5},{2,3},{4,7},{6},{8}}
[6,3,7,2,1,5,4,8]=>{{1,5,6},{2,3,4,7},{8}}
[6,3,7,2,1,5,8,4]=>{{1,5,6},{2,3,4,7,8}}
[6,3,7,2,1,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,2,8,1,5,3]=>{{1,6},{2,4},{3,5,7,8}}
[6,5,7,8,2,1,4,3]=>{{1,6},{2,5},{3,4,7,8}}
[6,5,8,7,2,1,3,4]=>{{1,6},{2,5},{3,4,7,8}}
[6,3,7,2,1,8,4,5]=>{{1,5,6,8},{2,3,4,7}}
[6,3,7,2,1,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,2,1,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[5,3,2,7,1,4,8,6]=>{{1,5},{2,3},{4,6,7,8}}
[5,4,2,8,7,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,2,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,3,2,1,6,4,5]=>{{1,2,4,5,7,8},{3},{6}}
[6,3,8,2,1,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,2,8,1,7,4,6]=>{{1,5},{2,3},{4,6,7,8}}
[4,3,2,1,8,7,5,6]=>{{1,4},{2,3},{5,6,7,8}}
[4,3,2,1,7,5,8,6]=>{{1,4},{2,3},{5,6,7,8}}
[4,3,2,1,7,5,6,8]=>{{1,4},{2,3},{5,6,7},{8}}
[4,3,2,1,8,5,7,6]=>{{1,4},{2,3},{5,6,8},{7}}
[5,3,2,8,1,4,7,6]=>{{1,5},{2,3},{4,6,8},{7}}
[6,3,8,2,1,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[7,8,3,2,1,4,6,5]=>{{1,2,4,5,6,7,8},{3}}
[6,3,8,2,1,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,2,1,8,5,6,7]=>{{1,4},{2,3},{5,6,7,8}}
[4,3,2,1,5,8,6,7]=>{{1,4},{2,3},{5},{6,7,8}}
[7,8,5,6,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,1,6,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,4,6,2,5,3]=>{{1,2,3,5,6,7,8},{4}}
[6,1,8,4,7,2,5,3]=>{{1,2,6},{3,8},{4},{5,7}}
[1,6,8,4,7,2,5,3]=>{{1},{2,6},{3,8},{4},{5,7}}
[1,6,8,3,2,7,5,4]=>{{1},{2,5,6,7},{3,4,8}}
[6,1,8,3,2,7,5,4]=>{{1,2,5,6,7},{3,4,8}}
[7,8,1,3,2,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[7,8,3,1,2,6,5,4]=>{{1,2,4,5,7,8},{3},{6}}
[7,8,3,4,6,5,1,2]=>{{1,7},{2,8},{3},{4},{5,6}}
[7,8,2,4,6,1,5,3]=>{{1,5,6,7},{2,3,8},{4}}
[7,8,2,3,1,6,5,4]=>{{1,5,7},{2,3,4,8},{6}}
[7,8,2,1,3,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[7,8,1,2,3,6,5,4]=>{{1,3,5,7},{2,4,8},{6}}
[6,1,8,2,3,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[1,6,8,2,3,7,5,4]=>{{1},{2,3,4,5,6,7,8}}
[1,5,2,8,3,7,6,4]=>{{1},{2,3,5},{4,8},{6,7}}
[5,1,2,8,3,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}
[5,2,1,8,3,7,6,4]=>{{1,3,5},{2},{4,8},{6,7}}
[6,2,8,1,3,7,5,4]=>{{1,3,4,5,6,7,8},{2}}
[6,2,8,3,1,7,5,4]=>{{1,5,6,7},{2},{3,4,8}}
[6,2,8,4,7,1,5,3]=>{{1,6},{2},{3,8},{4},{5,7}}
[6,3,8,4,7,5,1,2]=>{{1,5,6,7},{2,3,8},{4}}
[3,6,8,4,7,5,1,2]=>{{1,2,3,5,6,7,8},{4}}
[2,6,8,4,7,1,5,3]=>{{1,2,6},{3,8},{4},{5,7}}
[2,6,8,3,1,7,5,4]=>{{1,2,5,6,7},{3,4,8}}
[2,6,8,1,3,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,1,8,3,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}
[1,2,5,8,3,7,6,4]=>{{1},{2},{3,5},{4,8},{6,7}}
[2,4,1,3,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}
[2,5,3,8,1,7,6,4]=>{{1,2,5},{3},{4,8},{6,7}}
[2,5,4,8,7,1,6,3]=>{{1,2,5,6,7},{3,4,8}}
[3,5,4,8,7,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[5,3,4,8,7,6,1,2]=>{{1,5,7},{2,3,4,8},{6}}
[5,2,4,8,7,1,6,3]=>{{1,5,6,7},{2},{3,4,8}}
[5,2,3,8,1,7,6,4]=>{{1,5},{2},{3},{4,8},{6,7}}
[4,2,1,3,8,7,6,5]=>{{1,3,4},{2},{5,8},{6,7}}
[4,1,2,3,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}
[1,4,2,3,8,7,6,5]=>{{1},{2,3,4},{5,8},{6,7}}
[4,1,3,2,8,7,6,5]=>{{1,2,4},{3},{5,8},{6,7}}
[4,3,1,2,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}
[6,3,8,1,2,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,8,2,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}
[5,1,3,8,2,7,6,4]=>{{1,2,5},{3},{4,8},{6,7}}
[1,5,3,8,2,7,6,4]=>{{1},{2,5},{3},{4,8},{6,7}}
[1,5,4,8,7,2,6,3]=>{{1},{2,5,6,7},{3,4,8}}
[5,1,4,8,7,2,6,3]=>{{1,2,5,6,7},{3,4,8}}
[5,4,1,8,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,1,7,2,5,3]=>{{1,2,4,6},{3,8},{5,7}}
[6,5,8,7,1,2,4,3]=>{{1,2,5,6},{3,8},{4,7}}
[5,6,8,7,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,8,7,2,1,4,3]=>{{1,2,5,6},{3,8},{4,7}}
[4,5,1,8,7,2,6,3]=>{{1,3,4,8},{2,5,6,7}}
[4,1,5,8,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[1,4,5,8,7,2,6,3]=>{{1},{2,3,4,5,6,7,8}}
[1,3,5,8,2,7,6,4]=>{{1},{2,3,5},{4,8},{6,7}}
[3,1,5,8,2,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}
[3,6,8,1,2,7,5,4]=>{{1,3,4,8},{2,5,6,7}}
[3,6,8,2,1,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[4,6,8,2,7,1,5,3]=>{{1,2,4,6},{3,8},{5,7}}
[4,6,8,3,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[4,5,3,8,7,6,1,2]=>{{1,2,4,5,7,8},{3},{6}}
[4,5,2,8,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,8,1,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}
[3,1,4,2,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}
[3,1,2,4,8,7,6,5]=>{{1,2,3},{4},{5,8},{6,7}}
[3,2,5,8,1,7,6,4]=>{{1,3,5},{2},{4,8},{6,7}}
[4,2,5,8,7,1,6,3]=>{{1,3,4,5,6,7,8},{2}}
[4,3,5,8,7,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[3,4,5,8,7,6,1,2]=>{{1,3,5,7},{2,4,8},{6}}
[2,4,5,8,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,8,1,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}
[4,1,3,2,6,5,8,7]=>{{1,2,4},{3},{5,6},{7,8}}
[5,1,3,2,6,4,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[6,1,3,2,5,4,8,7]=>{{1,2,4,6},{3},{5},{7,8}}
[7,1,3,2,5,4,8,6]=>{{1,2,4,6,7,8},{3},{5}}
[8,1,3,2,5,4,7,6]=>{{1,2,4,6,8},{3},{5},{7}}
[8,1,4,2,5,3,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[7,1,4,2,5,3,8,6]=>{{1,2,3,4,6,7,8},{5}}
[6,1,4,2,5,3,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[5,1,4,2,6,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,1,6,3,5,4,8,7]=>{{1,2},{3,4,6},{5},{7,8}}
[3,1,6,2,5,4,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[4,1,6,2,5,3,8,7]=>{{1,2,4},{3,6},{5},{7,8}}
[6,2,5,1,4,3,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[5,2,6,1,4,3,8,7]=>{{1,4,5},{2},{3,6},{7,8}}
[5,2,7,1,4,3,8,6]=>{{1,4,5},{2},{3,6,7,8}}
[5,2,8,1,4,3,7,6]=>{{1,4,5},{2},{3,6,8},{7}}
[6,2,8,1,4,3,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[6,2,7,1,4,3,8,5]=>{{1,3,4,5,6,7,8},{2}}
[7,2,6,1,4,3,8,5]=>{{1,4,5,7,8},{2},{3,6}}
[7,2,5,1,4,3,8,6]=>{{1,3,4,5,6,7,8},{2}}
[4,1,7,2,5,3,8,6]=>{{1,2,4},{3,6,7,8},{5}}
[3,1,7,2,5,4,8,6]=>{{1,2,3,4,6,7,8},{5}}
[2,1,7,3,5,4,8,6]=>{{1,2},{3,4,6,7,8},{5}}
[2,1,8,3,5,4,7,6]=>{{1,2},{3,4,6,8},{5},{7}}
[3,1,8,2,5,4,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[4,1,8,2,5,3,7,6]=>{{1,2,4},{3,6,8},{5},{7}}
[8,2,5,1,4,3,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[8,2,6,1,4,3,7,5]=>{{1,4,5,8},{2},{3,6},{7}}
[7,1,4,3,8,2,6,5]=>{{1,2,6,7},{3,4},{5,8}}
[8,1,4,3,7,2,6,5]=>{{1,2,5,6,7,8},{3,4}}
[8,1,5,3,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,5,3,8,2,6,4]=>{{1,2,6,7},{3,4,5,8}}
[8,2,6,1,5,3,7,4]=>{{1,4,8},{2},{3,6},{5},{7}}
[5,1,8,2,6,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[4,1,8,2,6,3,7,5]=>{{1,2,4},{3,5,6,8},{7}}
[3,1,8,2,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,1,8,3,6,4,7,5]=>{{1,2},{3,4,5,6,8},{7}}
[2,1,7,3,6,4,8,5]=>{{1,2},{3,4,5,6,7,8}}
[4,1,7,2,6,3,8,5]=>{{1,2,4},{3,5,6,7,8}}
[5,1,7,2,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[7,2,6,1,5,3,8,4]=>{{1,4,7,8},{2},{3,6},{5}}
[6,2,7,1,5,3,8,4]=>{{1,3,4,6,7,8},{2},{5}}
[6,2,8,1,5,3,7,4]=>{{1,3,4,6,8},{2},{5},{7}}
[8,1,5,2,6,3,7,4]=>{{1,2,4,8},{3,5,6},{7}}
[6,1,5,2,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[6,1,4,2,7,3,8,5]=>{{1,2,3,4,6},{5,7,8}}
[8,1,4,2,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[8,1,3,2,6,4,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[7,1,3,2,6,4,8,5]=>{{1,2,4,5,6,7,8},{3}}
[6,1,3,2,7,4,8,5]=>{{1,2,4,6},{3},{5,7,8}}
[5,1,3,2,7,4,8,6]=>{{1,2,4,5,6,7,8},{3}}
[4,1,3,2,7,5,8,6]=>{{1,2,4},{3},{5,6,7,8}}
[2,1,4,3,8,5,7,6]=>{{1,2},{3,4},{5,6,8},{7}}
[3,1,4,2,8,5,7,6]=>{{1,2,3,4},{5,6,8},{7}}
[4,1,3,2,8,5,7,6]=>{{1,2,4},{3},{5,6,8},{7}}
[5,1,3,2,8,4,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[6,1,3,2,8,4,7,5]=>{{1,2,4,6},{3},{5,8},{7}}
[8,4,7,1,3,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[7,4,8,1,3,2,6,5]=>{{1,2,4,6,7},{3,5,8}}
[7,3,8,1,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,1,4,2,6,5]=>{{1,4,5,8},{2,3,6,7}}
[6,1,4,2,8,3,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[5,1,4,2,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,1,5,2,8,3,7,6]=>{{1,2,4},{3,5,6,8},{7}}
[3,1,5,2,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,1,5,3,8,4,7,6]=>{{1,2},{3,4,5,6,8},{7}}
[2,1,6,3,8,4,7,5]=>{{1,2},{3,4,6},{5,8},{7}}
[3,1,6,2,8,4,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[4,1,6,2,8,3,7,5]=>{{1,2,4},{3,6},{5,8},{7}}
[5,1,6,2,8,3,7,4]=>{{1,2,4,5,8},{3,6},{7}}
[6,1,5,2,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[8,3,7,1,5,2,6,4]=>{{1,4,8},{2,3,6,7},{5}}
[7,3,8,1,5,2,6,4]=>{{1,2,3,4,6,7,8},{5}}
[6,2,7,3,8,1,5,4]=>{{1,6},{2},{3,4,5,7,8}}
[6,2,8,3,7,1,5,4]=>{{1,6},{2},{3,4,8},{5,7}}
[8,3,7,2,6,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,3,7,2,6,4]=>{{1,2,5,6,7},{3,4,8}}
[4,1,8,3,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,4,7,2,6,5]=>{{1,2,3,5,6,7,8},{4}}
[2,1,8,4,7,3,6,5]=>{{1,2},{3,5,6,7,8},{4}}
[2,1,7,4,8,3,6,5]=>{{1,2},{3,6,7},{4},{5,8}}
[3,1,7,4,8,2,6,5]=>{{1,2,3,6,7},{4},{5,8}}
[4,1,7,3,8,2,6,5]=>{{1,2,3,4,6,7},{5,8}}
[5,1,7,3,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,2,6,1,5,4]=>{{1,5,6,7},{2,3,4,8}}
[8,2,6,3,7,1,5,4]=>{{1,3,4,6,8},{2},{5,7}}
[7,2,6,3,8,1,5,4]=>{{1,3,4,5,6,7,8},{2}}
[3,4,2,6,8,1,5,7]=>{{1,2,3,4,6},{5,7,8}}
[5,3,6,2,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,2,4,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,7,3,8,2,4,1,6]=>{{1,2,5,7},{3},{4,6,8}}
[5,7,3,8,2,4,6,1]=>{{1,2,4,5,6,7,8},{3}}
[7,4,2,5,8,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,5,8,3,1,6]=>{{1,7},{2,3,4,5,6,8}}
[4,5,2,6,3,8,1,7]=>{{1,4,6,7,8},{2,3,5}}
[4,5,2,1,6,8,3,7]=>{{1,4},{2,3,5,6,7,8}}
[5,3,1,6,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,2,8,1,3,4,7]=>{{1,5},{2,3,6},{4,7,8}}
[3,5,6,1,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,5,6,3,8,2,7]=>{{1,2,4,6,7,8},{3,5}}
[4,5,1,6,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,3,2,8,1,7]=>{{1,3,4,6,7,8},{2,5}}
[7,4,5,3,8,2,1,6]=>{{1,7},{2,3,4,5,6,8}}
[7,4,5,3,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,8,3,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,8,3,2,1,5]=>{{1,2,6,7},{3,4,5,8}}
[6,7,4,1,8,3,2,5]=>{{1,3,4,6},{2,7},{5,8}}
[7,4,5,3,1,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[4,7,1,5,8,3,2,6]=>{{1,3,4,5,6,8},{2,7}}
[5,3,7,8,1,4,2,6]=>{{1,5},{2,3,7},{4,6,8}}
[7,5,8,2,4,6,1,3]=>{{1,7},{2,4,5},{3,8},{6}}
[7,3,5,8,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,7,8,3,6,2]=>{{1,3,4,6,7},{2,5,8}}
[7,4,1,5,8,3,6,2]=>{{1,3,6,7},{2,4,5,8}}
[6,7,4,3,8,1,5,2]=>{{1,6},{2,5,7,8},{3,4}}
[6,7,4,8,3,1,5,2]=>{{1,6},{2,3,4,5,7,8}}
[6,7,4,8,3,5,2,1]=>{{1,3,4,5,6,8},{2,7}}
[5,6,7,3,8,4,2,1]=>{{1,5,8},{2,3,4,6,7}}
[5,6,7,3,1,8,4,2]=>{{1,5},{2,6,8},{3,4,7}}
[5,6,1,7,3,8,4,2]=>{{1,3,5},{2,6,8},{4,7}}
[5,1,6,7,3,8,4,2]=>{{1,2,3,5,6,8},{4,7}}
[6,4,7,1,8,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,3,1,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,8,4,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,8,4,1,3,5]=>{{1,6},{2,3,7},{4,5,8}}
[6,1,7,4,8,3,2,5]=>{{1,2,3,6,7},{4},{5,8}}
[5,1,6,7,3,2,8,4]=>{{1,2,3,5,6},{4,7,8}}
[5,6,1,7,3,2,8,4]=>{{1,3,5},{2,6},{4,7,8}}
[5,6,7,3,2,1,8,4]=>{{1,2,5,6},{3,4,7,8}}
[5,6,7,3,2,8,4,1]=>{{1,2,5,6,8},{3,4,7}}
[5,6,2,7,3,8,4,1]=>{{1,2,3,5,6,8},{4,7}}
[5,6,2,7,3,1,8,4]=>{{1,2,3,5,6},{4,7,8}}
[5,6,2,1,7,3,8,4]=>{{1,4,5,7,8},{2,3,6}}
[6,1,7,4,2,8,3,5]=>{{1,2,5,6,8},{3,7},{4}}
[6,7,2,1,8,3,4,5]=>{{1,2,3,4,6,7},{5,8}}
[7,5,8,2,1,3,4,6]=>{{1,2,4,5,7},{3,6,8}}
[5,7,3,1,8,2,4,6]=>{{1,2,4,5,6,7,8},{3}}
[4,7,1,5,2,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[7,4,2,5,1,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[6,7,4,2,1,8,3,5]=>{{1,5,6,8},{2,3,4,7}}
[6,7,4,2,8,3,1,5]=>{{1,2,3,4,6,7},{5,8}}
[6,7,4,2,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,2,8,4,5,1]=>{{1,3,5,7,8},{2,4,6}}
[3,6,7,2,8,4,1,5]=>{{1,3,7},{2,4,6},{5,8}}
[3,6,7,2,1,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[5,7,3,8,2,1,4,6]=>{{1,2,4,5,6,7,8},{3}}
[3,4,7,8,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,1,4,6,2,5]=>{{1,3,4,5,8},{2,7},{6}}
[3,4,7,8,2,6,1,5]=>{{1,3,7},{2,4,5,8},{6}}
[5,7,3,8,2,6,1,4]=>{{1,2,5,7},{3},{4,8},{6}}
[3,6,7,2,8,5,1,4]=>{{1,3,7},{2,4,5,6,8}}
[3,6,7,8,5,2,1,4]=>{{1,3,7},{2,6},{4,8},{5}}
[3,6,7,8,5,2,4,1]=>{{1,3,4,7,8},{2,6},{5}}
[6,4,7,8,2,5,3,1]=>{{1,2,4,5,6,8},{3,7}}
[6,4,7,8,2,1,5,3]=>{{1,6},{2,3,4,5,7,8}}
[4,1,5,7,8,2,6,3]=>{{1,2,4,6,7},{3,5,8}}
[5,3,7,8,1,6,2,4]=>{{1,5},{2,3,7},{4,8},{6}}
[6,7,2,8,5,1,3,4]=>{{1,6},{2,3,7},{4,8},{5}}
[6,4,1,7,8,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,2,7,8,4,3]=>{{1,2,4,5,7},{3,6,8}}
[5,6,2,1,7,8,4,3]=>{{1,4,5,7},{2,3,6,8}}
[5,6,2,7,1,8,4,3]=>{{1,5},{2,3,6,8},{4,7}}
[5,6,2,7,8,4,3,1]=>{{1,5,8},{2,3,4,6,7}}
[5,6,7,2,8,4,3,1]=>{{1,5,8},{2,4,6},{3,7}}
[5,6,7,2,1,8,4,3]=>{{1,5},{2,3,4,6,7,8}}
[5,6,1,7,2,8,4,3]=>{{1,2,3,5,6,8},{4,7}}
[5,1,6,7,2,8,4,3]=>{{1,2,5},{3,6,8},{4,7}}
[6,4,7,1,8,2,5,3]=>{{1,2,4,6},{3,5,7,8}}
[3,6,7,1,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,5,2,4,1,3]=>{{1,2,4,5,6,7},{3,8}}
[6,7,8,3,5,1,4,2]=>{{1,6},{2,3,4,7,8},{5}}
[4,6,7,8,1,5,3,2]=>{{1,2,4,5,6,8},{3,7}}
[5,1,6,7,8,4,3,2]=>{{1,2,5,8},{3,4,6,7}}
[5,6,1,7,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,1,8,4,3,2]=>{{1,2,4,5,6,8},{3,7}}
[8,6,1,3,4,2,5,7]=>{{1,3,4,5,7,8},{2,6}}
[8,3,2,5,1,6,4,7]=>{{1,4,5,7,8},{2,3},{6}}
[8,5,3,6,2,4,1,7]=>{{1,7,8},{2,5},{3},{4,6}}
[5,3,2,7,4,1,8,6]=>{{1,4,5,6,7,8},{2,3}}
[7,5,3,8,2,4,6,1]=>{{1,4,6,7,8},{2,5},{3}}
[7,2,4,5,8,3,6,1]=>{{1,3,4,5,6,7,8},{2}}
[2,4,5,3,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,2,4,5,6,3,1,7]=>{{1,7,8},{2},{3,4,5,6}}
[8,2,4,5,6,1,3,7]=>{{1,3,4,5,6,7,8},{2}}
[8,1,2,4,5,6,3,7]=>{{1,2,3,7,8},{4},{5},{6}}
[8,2,5,1,3,6,4,7]=>{{1,4,7,8},{2},{3,5},{6}}
[8,5,6,2,1,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,6,4,1,2,7]=>{{1,2,4,5,6,7,8},{3}}
[8,4,1,5,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,5,6,3,2,7]=>{{1,2,7,8},{3,4,5,6}}
[4,5,3,7,2,1,8,6]=>{{1,4,6,7,8},{2,5},{3}}
[7,4,5,8,3,2,6,1]=>{{1,2,4,6,7,8},{3,5}}
[4,3,6,7,2,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,6,7,2,8,1,5]=>{{1,4,7},{2,3,5,6,8}}
[1,4,3,6,7,2,8,5]=>{{1},{2,4,6},{3},{5,7,8}}
[4,5,3,7,1,8,2,6]=>{{1,2,4,5,7},{3},{6,8}}
[4,1,5,3,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[5,3,4,7,1,2,8,6]=>{{1,5},{2,3,4,6,7,8}}
[7,5,8,2,1,4,6,3]=>{{1,2,4,5,6,7},{3,8}}
[7,5,3,8,4,1,6,2]=>{{1,6,7},{2,4,5,8},{3}}
[7,4,5,8,3,6,1,2]=>{{1,7},{2,4,8},{3,5},{6}}
[4,3,6,7,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,7,8,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,7,8,4,1,2]=>{{1,3,4,6,7},{2,5,8}}
[3,1,5,6,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[4,6,1,7,8,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,1,4,8,5,2]=>{{1,3,4,5,7},{2,6,8}}
[6,2,4,1,7,8,5,3]=>{{1,3,4,6,8},{2},{5,7}}
[2,6,7,1,4,8,3,5]=>{{1,2,4,5,6,8},{3,7}}
[4,3,6,7,8,1,2,5]=>{{1,2,3,4,6,7},{5,8}}
[1,5,3,6,7,8,2,4]=>{{1},{2,5,7},{3},{4,6,8}}
[3,5,6,7,8,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,7,8,2,4,1]=>{{1,2,3,5,6,8},{4,7}}
[5,2,7,1,3,8,4,6]=>{{1,3,4,5,7},{2},{6,8}}
[5,3,1,7,8,2,4,6]=>{{1,2,3,5,6,8},{4,7}}
[4,5,2,7,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[4,2,6,7,8,3,1,5]=>{{1,4,7},{2},{3,6},{5,8}}
[4,2,6,7,8,3,5,1]=>{{1,4,5,7,8},{2},{3,6}}
[3,6,2,7,4,8,5,1]=>{{1,2,3,6,8},{4,5,7}}
[3,6,2,7,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,2,1,6,4,7,8,5]=>{{1,3},{2},{4,5,6,7,8}}
[3,7,4,2,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,7,3,4,2,5,8,6]=>{{1},{2,5,6,7,8},{3},{4}}
[4,7,2,1,3,5,8,6]=>{{1,4},{2,3,5,6,7,8}}
[7,8,4,2,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,3,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,3,4,2,1,6,5]=>{{1,6,7},{2,5,8},{3},{4}}
[6,3,2,7,1,8,5,4]=>{{1,4,5,6,7,8},{2,3}}
[3,6,2,7,1,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,3,8,2,5,4,1]=>{{1,2,4,5,6,7,8},{3}}
[6,4,7,8,5,2,3,1]=>{{1,2,4,6,8},{3,7},{5}}
[2,6,4,7,8,1,5,3]=>{{1,2,6},{3,4,5,7,8}}
[4,6,2,7,8,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,8,6,2,1,3]=>{{1,7},{2,3,4,5,6,8}}
[7,4,1,5,8,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[7,5,3,8,6,1,2,4]=>{{1,2,5,6,7},{3},{4,8}}
[7,5,8,2,1,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[6,2,7,1,3,8,5,4]=>{{1,4,6,8},{2},{3,5,7}}
[6,3,1,7,8,2,5,4]=>{{1,2,3,6},{4,5,7,8}}
[4,6,1,7,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,1,2,6,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,2,6,7,8,4,1,3]=>{{1,3,4,5,6,7,8},{2}}
[5,2,6,7,8,4,3,1]=>{{1,5,8},{2},{3,4,6,7}}
[2,5,6,7,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[1,5,2,6,7,8,4,3]=>{{1},{2,3,4,5,6,7,8}}
[1,6,4,7,8,5,2,3]=>{{1},{2,3,4,5,6,7,8}}
[2,6,7,1,3,8,5,4]=>{{1,2,4,6,8},{3,5,7}}
[6,7,8,2,1,5,4,3]=>{{1,5,6},{2,4,7},{3,8}}
[6,7,3,8,5,1,4,2]=>{{1,6},{2,4,7,8},{3},{5}}
[6,4,7,8,5,3,1,2]=>{{1,3,6,7},{2,4,8},{5}}
[4,5,2,3,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[6,4,3,7,2,5,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[8,4,3,6,5,1,2,7]=>{{1,2,4,6,7,8},{3},{5}}
[1,5,6,3,4,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[4,6,2,7,3,5,1,8]=>{{1,4,7},{2,3,5,6},{8}}
[3,2,6,7,4,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[4,7,2,6,5,3,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[5,7,6,2,4,3,1,8]=>{{1,2,4,5,7},{3,6},{8}}
[1,7,5,4,8,3,6,2]=>{{1},{2,3,5,6,7,8},{4}}
[8,7,5,4,1,3,2,6]=>{{1,3,5,6,8},{2,7},{4}}
[6,8,5,4,2,1,3,7]=>{{1,6},{2,3,5,7,8},{4}}
[5,8,6,2,4,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[4,8,2,6,5,1,3,7]=>{{1,4,6},{2,3,7,8},{5}}
[3,2,8,6,5,1,4,7]=>{{1,3,4,6,7,8},{2},{5}}
[4,1,2,6,5,8,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[5,1,6,2,4,8,7,3]=>{{1,2,4,5},{3,6,8},{7}}
[6,1,5,4,2,8,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[7,1,5,4,8,2,6,3]=>{{1,2,6,7},{3,5,8},{4}}
[8,1,5,4,7,6,2,3]=>{{1,2,3,5,7,8},{4},{6}}
[1,8,6,7,4,5,3,2]=>{{1},{2,8},{3,4,5,6,7}}
[8,1,6,7,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,8,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[6,1,7,8,2,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[5,1,7,2,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,7,8,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,2,1,7,8,5,6,4]=>{{1,3},{2},{4,5,6,7,8}}
[3,2,8,7,1,5,4,6]=>{{1,3,5,6,8},{2},{4,7}}
[4,8,2,7,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,2,1,4,3,6]=>{{1,5},{2,4,6,8},{3,7}}
[6,8,7,1,2,4,3,5]=>{{1,4,6},{2,5,8},{3,7}}
[7,8,6,1,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,1,4,3,2,5]=>{{1,4,5,8},{2,7},{3,6}}
[1,7,6,8,4,3,5,2]=>{{1},{2,4,5,7,8},{3,6}}
[1,6,7,8,3,4,5,2]=>{{1},{2,4,6,8},{3,5,7}}
[8,6,7,1,3,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,1,3,2,4,5]=>{{1,4,7},{2,6},{3,5,8}}
[5,7,8,2,1,3,4,6]=>{{1,5},{2,4,7},{3,6,8}}
[4,7,2,8,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,2,6,8,4,1,5,7]=>{{1,3,6},{2},{4,5,7,8}}
[4,6,2,8,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,8,2,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,3,2,1,4,7]=>{{1,6},{2,5},{3,4,7,8}}
[7,5,8,3,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,3,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[1,5,7,3,8,4,6,2]=>{{1},{2,5,8},{3,4,6,7}}
[1,4,3,7,8,5,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[8,4,3,7,1,5,2,6]=>{{1,5,6,8},{2,4,7},{3}}
[6,4,3,8,2,1,5,7]=>{{1,6},{2,4,5,7,8},{3}}
[4,5,2,3,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,2,5,4,8,1,6,7]=>{{1,3,5,6,7,8},{2},{4}}
[4,5,2,3,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[6,4,3,1,2,8,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[7,4,3,1,8,2,6,5]=>{{1,2,4,6,7},{3},{5,8}}
[8,4,3,1,7,6,2,5]=>{{1,2,4,5,7,8},{3},{6}}
[1,5,8,3,7,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[8,5,1,3,7,6,2,4]=>{{1,3,4,8},{2,5,7},{6}}
[7,5,1,3,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,1,3,2,8,7,4]=>{{1,3,4,6,8},{2,5},{7}}
[5,6,1,2,3,8,7,4]=>{{1,3,5},{2,4,6,8},{7}}
[4,6,2,1,3,8,7,5]=>{{1,4},{2,3,5,6,8},{7}}
[3,2,6,1,4,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[3,2,7,1,8,4,6,5]=>{{1,3,4,6,7},{2},{5,8}}
[4,7,2,1,8,3,6,5]=>{{1,4},{2,3,6,7},{5,8}}
[5,7,1,2,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,8,2,3,5,4]=>{{1,3,6},{2,5,7},{4,8}}
[7,6,1,8,3,2,5,4]=>{{1,3,5,7},{2,6},{4,8}}
[8,6,1,7,3,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[1,6,8,7,3,5,4,2]=>{{1},{2,3,5,6,8},{4,7}}
[1,7,8,6,5,3,4,2]=>{{1},{2,3,4,6,7,8},{5}}
[8,7,1,6,5,3,2,4]=>{{1,3,4,6,8},{2,7},{5}}
[7,8,1,6,5,2,3,4]=>{{1,3,7},{2,4,6,8},{5}}
[6,8,1,7,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,2,7,6,3,4]=>{{1,3,5,7},{2,4,8},{6}}
[4,8,2,1,7,6,3,5]=>{{1,4},{2,3,5,7,8},{6}}
[3,2,8,1,7,6,4,5]=>{{1,3,4,5,7,8},{2},{6}}
[4,1,2,8,7,6,5,3]=>{{1,2,3,4,8},{5,7},{6}}
[5,1,8,2,7,6,4,3]=>{{1,2,4,5,7},{3,8},{6}}
[6,1,8,7,2,5,4,3]=>{{1,2,5,6},{3,8},{4,7}}
[7,1,8,6,5,2,4,3]=>{{1,2,4,6,7},{3,8},{5}}
[8,1,7,6,5,4,2,3]=>{{1,2,3,7,8},{4,6},{5}}
[3,1,2,6,5,8,7,4]=>{{1,2,3},{4,6,8},{5},{7}}
[3,1,6,2,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,1,5,2,4,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[4,5,1,2,3,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[4,6,1,2,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[1,6,5,3,4,8,7,2]=>{{1},{2,6,8},{3,4,5},{7}}
[6,1,5,2,4,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,5,1,2,3,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[6,4,1,2,3,8,7,5]=>{{1,3,5,6,8},{2,4},{7}}
[5,4,1,2,3,8,7,6]=>{{1,3,5},{2,4},{6,8},{7}}
[5,4,1,2,7,3,6,8]=>{{1,3,5,6,7},{2,4},{8}}
[6,4,1,7,2,3,5,8]=>{{1,3,6},{2,4,5,7},{8}}
[6,4,1,8,2,3,5,7]=>{{1,3,6},{2,4,5,7,8}}
[7,4,1,2,8,3,6,5]=>{{1,3,6,7},{2,4},{5,8}}
[7,5,1,2,8,3,6,4]=>{{1,3,6,7},{2,4,5,8}}
[7,1,5,2,8,4,6,3]=>{{1,2,4,6,7},{3,5,8}}
[1,7,5,3,8,4,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,3,7,4,6,2]=>{{1},{2,8},{3,4,5,6,7}}
[8,1,5,2,7,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,1,2,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,2,7,3,6,5]=>{{1,3,5,6,7,8},{2,4}}
[8,4,1,7,2,3,5,6]=>{{1,3,6,8},{2,4,5,7}}
[7,4,1,6,2,3,5,8]=>{{1,2,3,4,5,6,7},{8}}
[8,6,1,7,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,7,2,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,8,6,7,3,4,5,2]=>{{1},{2,8},{3,4,5,6,7}}
[1,7,6,8,3,4,5,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,6,8,2,4,5,3]=>{{1,2,5,7},{3,4,6,8}}
[7,6,1,8,2,3,5,4]=>{{1,2,3,5,6,7},{4,8}}
[4,7,1,2,8,3,6,5]=>{{1,2,3,4,6,7},{5,8}}
[3,1,7,2,8,4,6,5]=>{{1,2,3,4,6,7},{5,8}}
[3,1,2,7,8,5,6,4]=>{{1,2,3},{4,5,6,7,8}}
[1,4,3,8,7,5,6,2]=>{{1},{2,4,8},{3},{5,6,7}}
[4,1,2,8,7,5,6,3]=>{{1,2,3,4,8},{5,6,7}}
[3,1,2,8,7,5,6,4]=>{{1,2,3},{4,8},{5,6,7}}
[3,1,8,2,7,4,6,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,7,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,6,2,4,5,8]=>{{1,2,3,5,7},{4,6},{8}}
[4,7,1,6,2,3,5,8]=>{{1,3,4,6},{2,5,7},{8}}
[4,8,1,6,2,3,5,7]=>{{1,3,4,6},{2,5,7,8}}
[4,8,1,7,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,2,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,2,7,3,6,4]=>{{1,3,5,6,7},{2,4,8}}
[5,1,8,2,7,4,6,3]=>{{1,2,4,5,6,7},{3,8}}
[1,5,8,3,7,4,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,8,7,3,4,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,8,7,2,4,5,3]=>{{1,2,4,5,6,7},{3,8}}
[6,8,1,7,2,3,5,4]=>{{1,3,6},{2,4,5,7,8}}
[6,8,7,1,2,3,4,5]=>{{1,3,4,6,7},{2,5,8}}
[5,8,7,1,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,1,2,3,4,7]=>{{1,2,4,5,7,8},{3,6}}
[5,7,6,1,2,3,4,8]=>{{1,2,4,5,7},{3,6},{8}}
[7,8,1,6,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,6,2,4,5,3]=>{{1,2,5,7},{3,8},{4,6}}
[1,7,8,6,3,4,5,2]=>{{1},{2,3,5,7,8},{4,6}}
[1,8,7,6,3,4,5,2]=>{{1},{2,8},{3,5,7},{4,6}}
[8,1,7,6,2,4,5,3]=>{{1,2,3,5,7,8},{4,6}}
[8,7,1,6,2,3,5,4]=>{{1,3,4,6,8},{2,5,7}}
[3,2,5,1,6,4,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[3,2,5,4,7,1,8,6]=>{{1,3,5,6,7,8},{2},{4}}
[4,2,5,3,7,6,8,1]=>{{1,3,4,5,7,8},{2},{6}}
[4,2,5,3,7,1,8,6]=>{{1,3,4,5,6,7,8},{2}}
[4,2,5,3,6,1,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[4,2,5,1,6,3,8,7]=>{{1,4},{2},{3,5,6},{7,8}}
[3,1,5,4,6,2,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[4,1,5,3,6,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,3,5,1,6,2,8,7]=>{{1,4},{2,3,5,6},{7,8}}
[4,3,5,2,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,6,2,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,6,2,7,1,8,5]=>{{1,2,3,4,6},{5,7,8}}
[4,3,6,1,7,2,8,5]=>{{1,4},{2,3,6},{5,7,8}}
[4,3,5,1,7,2,8,6]=>{{1,4},{2,3,5,6,7,8}}
[3,1,5,4,7,2,8,6]=>{{1,2,3,5,6,7,8},{4}}
[2,1,5,4,7,3,8,6]=>{{1,2},{3,5,6,7,8},{4}}
[3,1,5,4,7,6,8,2]=>{{1,2,3,5,7,8},{4},{6}}
[4,1,5,3,7,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[4,3,5,1,7,6,8,2]=>{{1,4},{2,3,5,7,8},{6}}
[4,3,6,1,7,5,8,2]=>{{1,4},{2,3,5,6,7,8}}
[4,3,6,5,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,4,7,2,8,1]=>{{1,5,7,8},{2,3,6},{4}}
[5,3,6,4,7,1,8,2]=>{{1,2,3,5,6,7,8},{4}}
[5,3,6,1,7,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,3,7,4,8,2]=>{{1,2,5,7,8},{3,4,6}}
[4,1,6,3,7,5,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,1,6,4,7,5,8,2]=>{{1,2,3,5,6,7,8},{4}}
[2,1,6,4,7,5,8,3]=>{{1,2},{3,5,6,7,8},{4}}
[2,1,6,4,7,3,8,5]=>{{1,2},{3,6},{4},{5,7,8}}
[3,1,6,4,7,2,8,5]=>{{1,2,3,6},{4},{5,7,8}}
[4,1,6,3,7,2,8,5]=>{{1,2,3,4,6},{5,7,8}}
[5,1,6,3,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,1,7,2,8,4]=>{{1,4,5,7,8},{2,3,6}}
[5,3,6,2,7,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,2,7,4,8,1]=>{{1,5,7,8},{2,3,4,6}}
[5,2,6,3,7,4,8,1]=>{{1,5,7,8},{2},{3,4,6}}
[5,2,6,3,7,1,8,4]=>{{1,3,4,5,6,7,8},{2}}
[5,2,6,1,7,3,8,4]=>{{1,4,5,7,8},{2},{3,6}}
[4,2,5,1,7,3,8,6]=>{{1,4},{2},{3,5,6,7,8}}
[4,2,6,1,7,3,8,5]=>{{1,4},{2},{3,6},{5,7,8}}
[4,2,6,3,7,1,8,5]=>{{1,3,4,6},{2},{5,7,8}}
[4,2,6,3,7,5,8,1]=>{{1,3,4,5,6,7,8},{2}}
[3,2,6,4,7,5,8,1]=>{{1,3,5,6,7,8},{2},{4}}
[3,2,6,4,7,1,8,5]=>{{1,3,6},{2},{4},{5,7,8}}
[3,2,6,1,7,4,8,5]=>{{1,3,4,6},{2},{5,7,8}}
[3,2,5,1,7,4,8,6]=>{{1,3,4,5,6,7,8},{2}}
[3,2,4,1,7,5,8,6]=>{{1,3,4},{2},{5,6,7,8}}
[3,1,4,2,7,6,8,5]=>{{1,2,3,4},{5,7,8},{6}}
[3,2,5,1,7,6,8,4]=>{{1,3,4,5,7,8},{2},{6}}
[3,2,6,1,7,5,8,4]=>{{1,3,4,5,6,7,8},{2}}
[3,2,6,5,7,1,8,4]=>{{1,3,6},{2},{4,5,7,8}}
[4,2,6,5,7,3,8,1]=>{{1,4,5,7,8},{2},{3,6}}
[4,2,6,5,7,1,8,3]=>{{1,3,4,5,6,7,8},{2}}
[4,2,6,1,7,5,8,3]=>{{1,4},{2},{3,5,6,7,8}}
[4,2,5,1,7,6,8,3]=>{{1,4},{2},{3,5,7,8},{6}}
[4,1,5,2,7,6,8,3]=>{{1,2,4},{3,5,7,8},{6}}
[3,1,5,2,7,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[2,1,5,3,7,6,8,4]=>{{1,2},{3,4,5,7,8},{6}}
[2,1,6,3,7,5,8,4]=>{{1,2},{3,4,5,6,7,8}}
[3,1,6,2,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[4,1,6,2,7,5,8,3]=>{{1,2,4},{3,5,6,7,8}}
[5,1,6,2,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[5,2,6,1,7,4,8,3]=>{{1,3,4,5,6,7,8},{2}}
[5,2,6,4,7,1,8,3]=>{{1,3,5,6,7,8},{2},{4}}
[5,2,6,4,7,3,8,1]=>{{1,5,7,8},{2},{3,6},{4}}
[5,4,6,2,7,3,8,1]=>{{1,5,7,8},{2,4},{3,6}}
[5,4,6,2,7,1,8,3]=>{{1,3,5,6,7,8},{2,4}}
[5,4,6,1,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,4,7,2,8,3]=>{{1,2,3,5,6,7,8},{4}}
[4,1,6,5,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,1,6,5,7,2,8,4]=>{{1,2,3,6},{4,5,7,8}}
[2,1,6,5,7,3,8,4]=>{{1,2},{3,6},{4,5,7,8}}
[3,1,6,5,7,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[4,1,6,5,7,3,8,2]=>{{1,2,4,5,7,8},{3,6}}
[5,1,6,4,7,3,8,2]=>{{1,2,5,7,8},{3,6},{4}}
[5,4,6,1,7,3,8,2]=>{{1,2,4,5,7,8},{3,6}}
[5,4,6,3,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[8,3,5,2,1,6,4,7]=>{{1,2,3,4,5,7,8},{6}}
[8,6,3,5,2,4,1,7]=>{{1,7,8},{2,4,5,6},{3}}
[3,7,5,2,4,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,5,2,4,6,1]=>{{1,8},{2,3,4,5,6,7}}
[8,2,4,5,7,3,6,1]=>{{1,8},{2},{3,4,5,6,7}}
[2,4,5,7,3,1,8,6]=>{{1,2,4,6,7,8},{3,5}}
[8,2,4,6,5,3,1,7]=>{{1,7,8},{2},{3,4,6},{5}}
[8,2,5,4,6,1,3,7]=>{{1,3,5,6,7,8},{2},{4}}
[8,6,3,5,1,4,2,7]=>{{1,2,4,5,6,7,8},{3}}
[8,6,1,4,5,3,2,7]=>{{1,2,3,6,7,8},{4},{5}}
[8,1,5,6,4,3,2,7]=>{{1,2,7,8},{3,4,5,6}}
[5,7,4,3,2,1,8,6]=>{{1,2,5,6,7,8},{3,4}}
[8,5,7,4,3,2,6,1]=>{{1,8},{2,3,5,6,7},{4}}
[4,6,8,3,2,7,5,1]=>{{1,3,4,8},{2,5,6,7}}
[4,7,6,3,2,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[1,4,6,7,3,2,8,5]=>{{1},{2,3,4,5,6,7,8}}
[5,4,7,3,1,8,2,6]=>{{1,5},{2,3,4,7},{6,8}}
[1,7,4,5,3,2,8,6]=>{{1},{2,6,7,8},{3,4,5}}
[3,7,5,1,4,2,8,6]=>{{1,3,4,5},{2,6,7,8}}
[5,7,4,2,1,3,8,6]=>{{1,5},{2,3,4,6,7,8}}
[8,5,7,4,2,1,6,3]=>{{1,3,6,7,8},{2,5},{4}}
[8,3,7,5,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,7,5,3,6,2]=>{{1,2,3,4,6,7,8},{5}}
[4,6,3,8,7,1,5,2]=>{{1,2,4,6,8},{3},{5,7}}
[1,7,4,8,6,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,7,6,3,5,2,1]=>{{1,8},{2,3,4,5,6,7}}
[3,6,5,8,7,4,1,2]=>{{1,3,5,7},{2,4,6,8}}
[3,1,5,8,6,7,4,2]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,6,7,3,5,2]=>{{1,3,4,6},{2,8},{5,7}}
[3,6,4,1,8,7,5,2]=>{{1,3,4},{2,5,6,7,8}}
[8,2,6,1,4,7,5,3]=>{{1,3,4,5,6,7,8},{2}}
[2,7,6,8,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[3,7,1,6,4,8,2,5]=>{{1,3},{2,7},{4,5,6,8}}
[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[1,3,6,7,5,8,2,4]=>{{1},{2,3,4,6,7,8},{5}}
[3,7,6,5,8,2,1,4]=>{{1,2,3,6,7},{4,5,8}}
[3,6,8,5,7,2,4,1]=>{{1,3,8},{2,6},{4,5,7}}
[2,3,5,7,6,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[2,1,6,5,7,8,3,4]=>{{1,2},{3,4,5,6,7,8}}
[4,2,7,6,8,3,1,5]=>{{1,3,4,6,7},{2},{5,8}}
[4,2,6,8,7,3,5,1]=>{{1,4,8},{2},{3,6},{5,7}}
[3,8,2,4,6,7,5,1]=>{{1,2,3,8},{4},{5,6,7}}
[3,7,2,6,4,8,1,5]=>{{1,2,3,7},{4,5,6,8}}
[3,2,6,1,4,7,8,5]=>{{1,3,4,5,6,7,8},{2}}
[5,3,7,2,1,8,4,6]=>{{1,5},{2,3,4,7},{6,8}}
[4,7,3,2,1,5,8,6]=>{{1,2,4,5,6,7,8},{3}}
[8,7,6,1,3,4,2,5]=>{{1,3,4,5,6,8},{2,7}}
[8,5,7,3,2,1,6,4]=>{{1,3,4,6,7,8},{2,5}}
[8,3,6,7,2,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,6,2,1,5,4]=>{{1,3,4,6,8},{2,5,7}}
[8,7,6,3,5,2,4,1]=>{{1,8},{2,3,4,6,7},{5}}
[2,7,4,8,1,6,5,3]=>{{1,2,5,7},{3,4,8},{6}}
[4,6,8,2,1,7,5,3]=>{{1,2,4,5,6,7},{3,8}}
[8,4,1,5,7,2,6,3]=>{{1,3,8},{2,4,5,6,7}}
[8,5,3,7,1,6,2,4]=>{{1,2,4,5,7,8},{3},{6}}
[8,5,7,2,1,3,6,4]=>{{1,2,4,5,8},{3,6,7}}
[8,2,6,7,1,3,5,4]=>{{1,4,5,7,8},{2},{3,6}}
[8,3,6,1,7,5,2,4]=>{{1,4,8},{2,3,5,6,7}}
[4,6,1,8,7,2,5,3]=>{{1,3,4,8},{2,6},{5,7}}
[8,1,2,5,6,7,4,3]=>{{1,2,3,8},{4,5,6,7}}
[8,2,6,5,7,4,1,3]=>{{1,3,4,5,6,7,8},{2}}
[2,1,7,8,5,6,4,3]=>{{1,2},{3,4,7,8},{5},{6}}
[8,2,5,7,6,4,3,1]=>{{1,8},{2},{3,4,5,6,7}}
[2,7,6,8,5,4,1,3]=>{{1,2,7},{3,4,6,8},{5}}
[1,7,2,5,8,6,4,3]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,4,8,2,6,5,3]=>{{1},{2,5,7},{3,4,8},{6}}
[3,7,8,1,6,5,2,4]=>{{1,3,4,8},{2,7},{5,6}}
[2,7,8,6,1,3,5,4]=>{{1,2,5,7},{3,4,6,8}}
[8,7,6,3,5,1,4,2]=>{{1,2,3,4,6,7,8},{5}}
[8,4,7,6,5,1,3,2]=>{{1,2,4,6,8},{3,7},{5}}
[8,7,1,5,6,4,3,2]=>{{1,2,3,7,8},{4,5,6}}
[8,1,6,7,5,4,3,2]=>{{1,2,8},{3,4,6,7},{5}}
[6,5,3,1,2,4,8,7]=>{{1,4,6},{2,5},{3},{7,8}}
[4,6,3,5,1,2,8,7]=>{{1,4,5},{2,6},{3},{7,8}}
[8,5,3,7,2,1,4,6]=>{{1,6,8},{2,5},{3},{4,7}}
[6,8,1,4,5,7,3,2]=>{{1,3,6,7},{2,8},{4},{5}}
[8,7,2,4,5,1,3,6]=>{{1,6,8},{2,3,7},{4},{5}}
[3,6,2,4,5,1,8,7]=>{{1,2,3,6},{4},{5},{7,8}}
[2,6,1,4,5,3,8,7]=>{{1,2,3,6},{4},{5},{7,8}}
[6,1,2,4,5,3,8,7]=>{{1,2,3,6},{4},{5},{7,8}}
[5,6,3,2,1,4,8,7]=>{{1,5},{2,4,6},{3},{7,8}}
[5,4,3,6,1,2,8,7]=>{{1,5},{2,4,6},{3},{7,8}}
[6,3,1,4,5,2,8,7]=>{{1,2,3,6},{4},{5},{7,8}}
[3,1,6,4,5,2,8,7]=>{{1,2,3,6},{4},{5},{7,8}}
[8,3,7,4,5,1,2,6]=>{{1,6,8},{2,3,7},{4},{5}}
[5,8,7,4,2,6,3,1]=>{{1,2,5,8},{3,7},{4},{6}}
[2,8,7,4,1,6,3,5]=>{{1,2,5,8},{3,7},{4},{6}}
[8,1,7,4,2,6,3,5]=>{{1,2,5,8},{3,7},{4},{6}}
[3,7,8,4,5,1,2,6]=>{{1,3,6,8},{2,7},{4},{5}}
[2,1,8,7,5,3,4,6]=>{{1,2},{3,6,8},{4,7},{5}}
[2,1,6,8,5,7,3,4]=>{{1,2},{3,6,7},{4,8},{5}}
[5,6,3,8,1,7,2,4]=>{{1,5},{2,6,7},{3},{4,8}}
[7,6,1,4,5,8,3,2]=>{{1,3,7},{2,6,8},{4},{5}}
[3,7,6,4,5,8,2,1]=>{{1,3,6,8},{2,7},{4},{5}}
[8,5,7,4,1,6,3,2]=>{{1,2,5,8},{3,7},{4},{6}}
[5,1,8,4,7,6,2,3]=>{{1,2,5,7},{3,8},{4},{6}}
[2,5,8,4,7,6,1,3]=>{{1,2,5,7},{3,8},{4},{6}}
[2,4,8,3,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[4,1,8,3,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}
[3,8,4,2,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[8,4,1,3,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}
[7,5,8,4,3,6,1,2]=>{{1,7},{2,3,5,8},{4},{6}}
[6,5,3,8,4,1,7,2]=>{{1,6},{2,4,5,8},{3},{7}}
[2,1,5,8,4,6,7,3]=>{{1,2},{3,4,5,8},{6},{7}}
[2,1,4,8,3,6,7,5]=>{{1,2},{3,4,5,8},{6},{7}}
[6,4,3,8,2,1,7,5]=>{{1,6},{2,4,5,8},{3},{7}}
[7,3,8,4,2,6,1,5]=>{{1,7},{2,3,5,8},{4},{6}}
[8,3,1,2,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}
[3,1,8,2,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}
[2,3,8,1,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}
[4,3,8,2,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[4,8,2,3,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[3,8,2,1,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}
[2,8,1,3,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}
[8,1,2,3,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}
[7,8,2,4,3,6,1,5]=>{{1,7},{2,3,5,8},{4},{6}}
[6,8,3,2,4,1,7,5]=>{{1,6},{2,4,5,8},{3},{7}}
[2,1,8,3,4,6,7,5]=>{{1,2},{3,4,5,8},{6},{7}}
[2,1,7,8,5,4,3,6]=>{{1,2},{3,7},{4,6,8},{5}}
[5,7,3,8,1,4,2,6]=>{{1,5},{2,7},{3},{4,6,8}}
[7,1,8,4,5,3,2,6]=>{{1,2,7},{3,6,8},{4},{5}}
[2,7,8,4,5,3,1,6]=>{{1,2,7},{3,6,8},{4},{5}}
[8,7,1,4,3,6,2,5]=>{{1,3,5,8},{2,7},{4},{6}}
[3,8,7,4,2,6,1,5]=>{{1,3,7},{2,5,8},{4},{6}}
[5,7,8,4,3,6,2,1]=>{{1,3,5,8},{2,7},{4},{6}}
[5,6,3,8,4,2,7,1]=>{{1,4,5,8},{2,6},{3},{7}}
[4,8,3,6,2,1,7,5]=>{{1,4,6},{2,5,8},{3},{7}}
[8,6,3,1,4,2,7,5]=>{{1,4,5,8},{2,6},{3},{7}}
[7,5,3,8,2,4,1,6]=>{{1,7},{2,5},{3},{4,6,8}}
[2,4,3,1,8,5,7,6]=>{{1,2,4},{3},{5,6,8},{7}}
[4,1,3,2,6,8,7,5]=>{{1,2,4},{3},{5,6,8},{7}}
[7,5,3,6,2,8,1,4]=>{{1,7},{2,5},{3},{4,6,8}}
[8,6,3,5,1,2,7,4]=>{{1,4,5,8},{2,6},{3},{7}}
[5,8,3,2,6,1,7,4]=>{{1,5,6},{2,4,8},{3},{7}}
[4,5,3,8,6,2,7,1]=>{{1,4,8},{2,5,6},{3},{7}}
[3,5,8,4,7,6,2,1]=>{{1,3,8},{2,5,7},{4},{6}}
[5,8,2,4,7,6,1,3]=>{{1,5,7},{2,3,8},{4},{6}}
[8,7,5,4,1,6,2,3]=>{{1,3,5,8},{2,7},{4},{6}}
[2,7,6,4,5,8,1,3]=>{{1,2,7},{3,6,8},{4},{5}}
[7,1,6,4,5,8,2,3]=>{{1,2,7},{3,6,8},{4},{5}}
[5,7,3,6,1,8,2,4]=>{{1,5},{2,7},{3},{4,6,8}}
[2,1,7,6,5,8,3,4]=>{{1,2},{3,7},{4,6,8},{5}}
[2,1,8,5,3,6,7,4]=>{{1,2},{3,4,5,8},{6},{7}}
[6,8,3,5,2,1,7,4]=>{{1,6},{2,4,5,8},{3},{7}}
[7,8,5,4,2,6,1,3]=>{{1,7},{2,3,5,8},{4},{6}}
[8,1,4,2,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}
[2,8,4,1,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}
[4,8,1,2,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}
[3,4,8,1,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}
[3,4,2,8,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[2,4,1,8,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}
[4,1,2,8,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}
[8,4,2,1,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}
[7,5,2,4,8,6,1,3]=>{{1,7},{2,3,5,8},{4},{6}}
[6,5,3,2,8,1,7,4]=>{{1,6},{2,4,5,8},{3},{7}}
[2,1,5,3,8,6,7,4]=>{{1,2},{3,4,5,8},{6},{7}}
[6,4,3,5,8,1,7,2]=>{{1,6},{2,4,5,8},{3},{7}}
[7,3,5,4,8,6,1,2]=>{{1,7},{2,3,5,8},{4},{6}}
[8,3,4,1,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}
[4,3,1,8,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}
[3,1,4,8,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}
[6,5,3,7,2,8,4,1]=>{{1,6,8},{2,5},{3},{4,7}}
[6,3,7,4,5,8,2,1]=>{{1,6,8},{2,3,7},{4},{5}}
[6,7,2,4,5,8,3,1]=>{{1,6,8},{2,3,7},{4},{5}}
[5,1,7,4,8,6,3,2]=>{{1,2,5,8},{3,7},{4},{6}}
[2,5,7,4,8,6,3,1]=>{{1,2,5,8},{3,7},{4},{6}}
[5,6,3,7,1,8,4,2]=>{{1,5},{2,6,8},{3},{4,7}}
[3,8,7,4,5,2,1,6]=>{{1,3,7},{2,6,8},{4},{5}}
[3,7,5,4,8,6,2,1]=>{{1,3,5,8},{2,7},{4},{6}}
[5,7,1,4,8,6,2,3]=>{{1,3,5,8},{2,7},{4},{6}}
[5,6,3,1,8,2,7,4]=>{{1,4,5,8},{2,6},{3},{7}}
[4,6,3,5,8,2,7,1]=>{{1,4,5,8},{2,6},{3},{7}}
[4,6,3,8,1,2,7,5]=>{{1,4,5,8},{2,6},{3},{7}}
[3,7,8,4,1,6,2,5]=>{{1,3,5,8},{2,7},{4},{6}}
[3,2,5,1,6,8,4,7]=>{{1,3,4,5,6,7,8},{2}}
[3,6,2,5,4,8,1,7]=>{{1,2,3,6,7,8},{4,5}}
[3,5,2,4,7,1,8,6]=>{{1,2,3,5,6,7,8},{4}}
[3,5,8,2,4,7,6,1]=>{{1,3,8},{2,4,5},{6,7}}
[4,2,5,8,3,7,6,1]=>{{1,4,8},{2},{3,5},{6,7}}
[4,2,6,5,3,8,1,7]=>{{1,3,4,5,6,7,8},{2}}
[5,4,2,1,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,1,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[4,6,1,5,3,8,2,7]=>{{1,3,4,5},{2,6,7,8}}
[5,1,6,4,3,8,2,7]=>{{1,2,3,5,6,7,8},{4}}
[5,4,3,2,7,1,8,6]=>{{1,5,6,7,8},{2,4},{3}}
[5,4,3,8,2,7,6,1]=>{{1,2,4,5,8},{3},{6,7}}
[4,3,6,2,8,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,6,2,1,8,5]=>{{1,4,6},{2,3,5,7,8}}
[6,4,3,1,7,2,8,5]=>{{1,2,4,6},{3},{5,7,8}}
[7,5,4,3,1,8,2,6]=>{{1,2,5,7},{3,4},{6,8}}
[1,4,7,5,8,3,2,6]=>{{1},{2,3,4,5,6,7,8}}
[7,1,3,5,8,4,2,6]=>{{1,2,7},{3},{4,5,6,8}}
[7,2,5,8,4,1,3,6]=>{{1,3,4,5,6,7,8},{2}}
[2,8,5,7,4,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[3,5,8,7,1,4,6,2]=>{{1,2,3,5,8},{4,6,7}}
[1,4,5,8,7,3,6,2]=>{{1},{2,4,8},{3,5,6,7}}
[1,5,4,8,7,3,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,3,8,1,7,5,2]=>{{1,5,6,7},{2,4,8},{3}}
[4,3,7,1,8,6,5,2]=>{{1,4},{2,3,5,7,8},{6}}
[4,8,3,7,6,5,2,1]=>{{1,2,4,7,8},{3},{5,6}}
[5,3,8,7,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,5,3,1,8,6,4,2]=>{{1,4,7},{2,5,8},{3},{6}}
[1,8,6,5,3,7,4,2]=>{{1},{2,8},{3,4,5,6,7}}
[1,5,8,6,3,7,4,2]=>{{1},{2,3,5,8},{4,6,7}}
[4,6,1,8,7,3,5,2]=>{{1,2,3,4,6,8},{5,7}}
[6,8,7,3,1,4,5,2]=>{{1,3,4,5,6,7},{2,8}}
[6,2,8,7,4,5,1,3]=>{{1,4,5,6,7},{2},{3,8}}
[7,6,2,8,4,1,3,5]=>{{1,2,3,6,7},{4,5,8}}
[7,3,1,6,8,4,2,5]=>{{1,2,3,7},{4,6},{5,8}}
[1,7,6,4,8,3,2,5]=>{{1},{2,7},{3,6},{4},{5,8}}
[5,7,1,6,3,2,8,4]=>{{1,3,5},{2,4,6,7,8}}
[6,1,7,5,3,2,8,4]=>{{1,2,6},{3,4,5,7,8}}
[7,6,5,3,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,3,2,8,7,4,1]=>{{1,2,4,5,6,7,8},{3}}
[5,2,6,3,8,7,4,1]=>{{1,5,8},{2},{3,4,6,7}}
[5,2,7,6,3,1,8,4]=>{{1,3,4,5,6,7,8},{2}}
[6,5,2,1,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,2,7,4,1,8,3,6]=>{{1,5},{2},{3,7},{4},{6,8}}
[4,7,2,6,3,1,8,5]=>{{1,4,6},{2,3,5,7,8}}
[2,4,8,6,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,2,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[7,3,6,2,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,2,1,4,8,5]=>{{1,3,5,7,8},{2,4,6}}
[4,3,7,8,2,1,5,6]=>{{1,4,6,8},{2,3,5,7}}
[8,3,7,1,4,6,2,5]=>{{1,4,5,8},{2,3,7},{6}}
[3,8,2,5,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,3,6,2,7,1,5,4]=>{{1,2,3,4,6,8},{5,7}}
[7,8,3,6,2,1,5,4]=>{{1,2,4,5,6,7,8},{3}}
[8,7,3,6,2,5,4,1]=>{{1,8},{2,4,5,6,7},{3}}
[4,7,8,2,1,6,5,3]=>{{1,2,4,5,7},{3,8},{6}}
[4,2,6,8,1,7,5,3]=>{{1,3,4,5,6,7,8},{2}}
[5,4,8,2,7,1,6,3]=>{{1,5,6,7},{2,4},{3,8}}
[4,8,1,5,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,3,7,1,6,2,4]=>{{1,5},{2,4,7,8},{3},{6}}
[5,8,7,2,6,1,3,4]=>{{1,5,6},{2,4,8},{3,7}}
[8,6,2,7,5,1,3,4]=>{{1,2,3,4,6,7,8},{5}}
[3,6,8,1,7,5,2,4]=>{{1,3,4,8},{2,5,6,7}}
[5,1,6,8,2,7,4,3]=>{{1,2,5},{3,4,6,7,8}}
[6,5,2,8,1,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,2,7,1,8,6,4,3]=>{{1,3,4,5,7,8},{2},{6}}
[5,8,2,7,6,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,2,8,7,5,4,3,1]=>{{1,3,4,6,7,8},{2},{5}}
[7,6,2,1,8,5,4,3]=>{{1,4,7},{2,3,5,6,8}}
[6,1,7,2,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,8,2,6,4,3]=>{{1,3,4,7,8},{2,5},{6}}
[4,7,1,8,6,2,5,3]=>{{1,3,4,8},{2,5,6,7}}
[7,8,3,1,6,5,2,4]=>{{1,2,4,7,8},{3},{5,6}}
[8,7,4,6,1,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,1,6,4,3,2]=>{{1,2,4,5,6,8},{3,7}}
[6,8,1,7,5,4,3,2]=>{{1,3,4,6,7},{2,8},{5}}
[7,1,8,6,5,4,3,2]=>{{1,2,3,7,8},{4,6},{5}}
[5,4,2,3,7,6,1,8]=>{{1,5,7},{2,3,4},{6},{8}}
[6,4,2,7,3,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[7,4,2,6,3,5,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[8,4,2,6,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,2,7,6,4,5,1,8]=>{{1,3,7},{2},{4,5,6},{8}}
[4,7,2,6,3,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,7,6,2,3,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[1,6,5,2,3,8,4,7]=>{{1},{2,4,6,7,8},{3,5}}
[1,7,5,2,8,3,4,6]=>{{1},{2,4,7},{3,5,6,8}}
[6,8,5,2,3,1,4,7]=>{{1,6},{2,4,7,8},{3,5}}
[5,8,6,2,3,1,4,7]=>{{1,3,5,6},{2,4,7,8}}
[4,8,2,6,3,1,5,7]=>{{1,4,6},{2,3,5,7,8}}
[3,2,8,6,4,1,5,7]=>{{1,3,4,5,6,7,8},{2}}
[3,2,1,6,4,8,5,7]=>{{1,3},{2},{4,5,6,7,8}}
[7,1,5,2,8,3,4,6]=>{{1,2,4,7},{3,5,6,8}}
[1,8,5,2,7,3,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,7,2,3,4,5]=>{{1},{2,5,8},{3,6},{4,7}}
[8,1,6,7,2,3,4,5]=>{{1,2,5,8},{3,6},{4,7}}
[7,1,6,8,2,3,4,5]=>{{1,2,4,5,7,8},{3,6}}
[3,2,1,7,8,4,5,6]=>{{1,3},{2},{4,5,6,7,8}}
[3,2,8,7,1,4,5,6]=>{{1,3,4,5,6,7,8},{2}}
[5,8,7,2,1,3,4,6]=>{{1,5},{2,3,4,6,7,8}}
[1,7,6,8,2,3,4,5]=>{{1},{2,4,5,7,8},{3,6}}
[6,5,8,2,3,1,4,7]=>{{1,6},{2,3,4,5,7,8}}
[8,5,7,2,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[6,4,2,8,3,1,5,7]=>{{1,6},{2,3,4,5,7,8}}
[5,4,2,3,8,1,6,7]=>{{1,5,6,7,8},{2,3,4}}
[3,2,5,4,1,8,6,7]=>{{1,3,5},{2},{4},{6,7,8}}
[4,5,2,3,1,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[5,4,2,3,1,8,6,7]=>{{1,5},{2,3,4},{6,7,8}}
[6,4,2,1,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,1,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,1,7,3,5,6]=>{{1,2,3,4,6,8},{5,7}}
[1,4,2,8,7,3,5,6]=>{{1},{2,3,4,6,8},{5,7}}
[1,5,8,2,7,3,4,6]=>{{1},{2,4,5,7},{3,6,8}}
[8,5,1,2,7,3,4,6]=>{{1,3,6,8},{2,4,5,7}}
[7,5,1,2,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[6,5,1,2,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[4,6,2,1,3,8,5,7]=>{{1,4},{2,3,5,6,7,8}}
[3,2,6,1,4,8,5,7]=>{{1,3,4,5,6,7,8},{2}}
[3,2,7,1,8,4,5,6]=>{{1,3,4,5,6,7,8},{2}}
[4,7,2,1,8,3,5,6]=>{{1,4},{2,3,5,6,7,8}}
[7,6,1,8,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,6,1,7,2,3,4,5]=>{{1,2,3,5,6,8},{4,7}}
[1,6,8,7,2,3,4,5]=>{{1},{2,3,5,6,8},{4,7}}
[1,7,8,6,2,3,4,5]=>{{1},{2,3,4,5,6,7,8}}
[7,8,1,6,2,3,4,5]=>{{1,3,4,6,7},{2,5,8}}
[6,8,1,7,2,3,4,5]=>{{1,3,6},{2,5,8},{4,7}}
[4,8,2,1,7,3,5,6]=>{{1,4},{2,3,6,8},{5,7}}
[3,2,8,1,7,4,5,6]=>{{1,3,4,6,8},{2},{5,7}}
[3,2,1,8,7,4,5,6]=>{{1,3},{2},{4,6,8},{5,7}}
[5,1,8,2,7,3,4,6]=>{{1,2,4,5,7},{3,6,8}}
[6,1,8,7,2,3,4,5]=>{{1,2,3,5,6,8},{4,7}}
[8,1,7,6,2,3,4,5]=>{{1,2,5,8},{3,4,6,7}}
[1,8,7,6,2,3,4,5]=>{{1},{2,5,8},{3,4,6,7}}
[6,3,5,1,2,4,8,7]=>{{1,4,6},{2,3,5},{7,8}}
[4,3,5,6,1,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[8,3,7,5,2,1,4,6]=>{{1,6,8},{2,3,4,5,7}}
[6,3,7,5,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,7,1,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,7,4,1,3,6]=>{{1,6,8},{2,3,4,5,7}}
[2,6,1,5,4,3,8,7]=>{{1,2,3,6},{4,5},{7,8}}
[6,4,3,5,1,2,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[5,3,1,4,6,2,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[3,1,4,6,5,2,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[5,7,4,6,2,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,7,2,6,3,5]=>{{1,2,5,8},{3,4,7},{6}}
[3,4,7,8,5,2,1,6]=>{{1,3,7},{2,4,6,8},{5}}
[2,1,8,5,7,3,4,6]=>{{1,2},{3,6,8},{4,5,7}}
[8,6,3,5,1,7,4,2]=>{{1,2,4,5,6,7,8},{3}}
[5,8,2,4,6,7,3,1]=>{{1,2,3,5,6,7,8},{4}}
[3,4,8,6,5,7,1,2]=>{{1,2,3,4,6,7,8},{5}}
[7,5,4,8,1,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[5,1,4,6,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,5,4,6,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,3,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,1,6,3,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[3,7,4,2,8,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[7,4,1,3,5,8,6,2]=>{{1,2,3,4,6,7,8},{5}}
[6,5,8,4,1,7,3,2]=>{{1,2,3,5,6,7,8},{4}}
[8,5,3,7,4,1,6,2]=>{{1,2,4,5,6,7,8},{3}}
[2,1,4,8,3,7,6,5]=>{{1,2},{3,4,5,8},{6,7}}
[7,4,3,8,2,1,6,5]=>{{1,6,7},{2,4,5,8},{3}}
[6,3,7,4,1,8,2,5]=>{{1,5,6,8},{2,3,7},{4}}
[8,3,1,2,5,7,6,4]=>{{1,2,3,4,8},{5},{6,7}}
[3,1,8,2,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}
[2,3,8,1,6,7,5,4]=>{{1,2,3,4,8},{5,6,7}}
[4,3,7,2,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,7,2,3,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,2,1,7,5,6,4]=>{{1,2,3,4,8},{5,6,7}}
[2,8,1,3,6,5,7,4]=>{{1,2,3,4,8},{5,6},{7}}
[2,7,8,5,4,3,1,6]=>{{1,2,7},{3,6,8},{4,5}}
[8,7,1,6,3,4,2,5]=>{{1,3,5,8},{2,7},{4,6}}
[3,8,6,7,2,4,1,5]=>{{1,3,4,6,7},{2,5,8}}
[5,3,8,7,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,7,2,1,6,5]=>{{1,4,6,7},{2,3,5,8}}
[8,3,6,1,4,2,7,5]=>{{1,4,5,8},{2,3,6},{7}}
[7,3,5,8,2,4,1,6]=>{{1,7},{2,3,5},{4,6,8}}
[2,3,4,1,8,5,7,6]=>{{1,2,3,4},{5,6,8},{7}}
[4,1,3,2,6,7,8,5]=>{{1,2,4},{3},{5,6,7,8}}
[8,3,5,6,2,7,1,4]=>{{1,4,6,7,8},{2,3,5}}
[5,3,6,1,8,7,2,4]=>{{1,4,5,8},{2,3,6,7}}
[5,6,2,8,7,4,1,3]=>{{1,5,7},{2,3,4,6,8}}
[7,8,5,6,1,4,2,3]=>{{1,2,3,5,7,8},{4,6}}
[2,8,6,5,4,7,1,3]=>{{1,2,3,6,7,8},{4,5}}
[8,1,6,4,5,7,2,3]=>{{1,2,3,6,7,8},{4},{5}}
[5,8,3,6,1,7,2,4]=>{{1,5},{2,4,6,7,8},{3}}
[2,1,8,6,5,7,3,4]=>{{1,2},{3,4,6,7,8},{5}}
[2,1,7,5,3,6,8,4]=>{{1,2},{3,4,5,7,8},{6}}
[6,7,3,5,2,1,8,4]=>{{1,6},{2,4,5,7,8},{3}}
[7,1,4,2,5,6,8,3]=>{{1,2,3,4,7,8},{5},{6}}
[2,7,4,1,6,5,8,3]=>{{1,2,3,4,7,8},{5,6}}
[4,6,1,2,8,7,3,5]=>{{1,2,3,4,6,7},{5,8}}
[2,4,1,5,8,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[4,1,2,5,8,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[6,4,2,1,5,8,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[8,5,2,4,6,1,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[7,5,3,2,6,8,1,4]=>{{1,7},{2,4,5,6,8},{3}}
[2,1,5,3,6,8,7,4]=>{{1,2},{3,4,5,6,8},{7}}
[7,3,5,4,6,1,8,2]=>{{1,2,3,5,6,7,8},{4}}
[6,3,4,1,5,7,8,2]=>{{1,2,3,4,6,7,8},{5}}
[4,3,1,5,7,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[3,1,4,5,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,5,2,6,3,1,8,7]=>{{1,4,6},{2,3,5},{7,8}}
[6,5,2,1,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[6,5,2,7,4,8,3,1]=>{{1,6,8},{2,3,4,5,7}}
[8,5,2,7,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,5,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,5,2,8,4,1]=>{{1,6,8},{2,3,4,5,7}}
[3,1,6,5,4,2,8,7]=>{{1,2,3,6},{4,5},{7,8}}
[5,6,3,2,4,1,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[3,6,2,4,1,5,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[2,6,1,3,5,4,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[6,7,2,3,4,8,5,1]=>{{1,6,8},{2,3,4,5,7}}
[8,7,2,3,4,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[5,1,7,3,8,4,6,2]=>{{1,2,5,8},{3,4,6,7}}
[2,5,7,3,8,6,4,1]=>{{1,2,5,8},{3,4,7},{6}}
[7,6,1,3,5,8,4,2]=>{{1,3,4,7},{2,6,8},{5}}
[3,6,7,4,1,8,5,2]=>{{1,3,5,7},{2,6,8},{4}}
[5,6,3,7,4,8,1,2]=>{{1,4,5,7},{2,6,8},{3}}
[2,1,6,7,4,8,5,3]=>{{1,2},{3,6,8},{4,5,7}}
[2,1,8,7,4,3,6,5]=>{{1,2},{3,4,5,6,7,8}}
[5,8,3,7,4,2,6,1]=>{{1,2,4,5,6,7,8},{3}}
[3,8,7,4,1,2,6,5]=>{{1,2,3,5,6,7,8},{4}}
[7,8,1,3,5,2,6,4]=>{{1,2,3,4,6,7,8},{5}}
[5,8,7,3,2,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[2,8,6,3,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[8,1,6,3,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,1,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,8,1,2,7,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[3,8,4,2,5,7,1,6]=>{{1,2,3,4,6,7,8},{5}}
[6,8,3,5,2,7,4,1]=>{{1,2,4,5,6,7,8},{3}}
[2,1,5,3,8,7,6,4]=>{{1,2},{3,4,5,8},{6,7}}
[6,5,3,2,8,7,1,4]=>{{1,6,7},{2,4,5,8},{3}}
[7,5,2,4,8,1,6,3]=>{{1,6,7},{2,3,5,8},{4}}
[3,4,2,8,5,7,6,1]=>{{1,2,3,4,8},{5},{6,7}}
[2,4,1,8,7,6,5,3]=>{{1,2,3,4,8},{5,7},{6}}
[8,4,2,1,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,8,6,7,5,2]=>{{1,2,3,4,8},{5,6,7}}
[3,1,4,8,6,5,7,2]=>{{1,2,3,4,8},{5,6},{7}}
[7,1,6,5,4,8,2,3]=>{{1,2,7},{3,6,8},{4,5}}
[3,7,5,6,8,4,2,1]=>{{1,3,5,8},{2,7},{4,6}}
[5,7,1,6,8,2,4,3]=>{{1,3,5,8},{2,4,6,7}}
[8,6,2,5,1,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,6,2,1,8,7,3,4]=>{{1,4,5,8},{2,3,6,7}}
[4,6,2,5,8,3,7,1]=>{{1,4,5,8},{2,3,6},{7}}
[7,5,2,6,3,8,1,4]=>{{1,7},{2,3,5},{4,6,8}}
[4,1,2,3,6,8,7,5]=>{{1,2,3,4},{5,6,8},{7}}
[2,4,3,1,8,5,6,7]=>{{1,2,4},{3},{5,6,7,8}}
[7,5,2,8,3,4,6,1]=>{{1,4,6,7,8},{2,3,5}}
[5,6,2,8,4,3,1,7]=>{{1,4,5,7,8},{2,3,6}}
[4,7,2,8,1,5,3,6]=>{{1,4,5,6,8},{2,3,7}}
[8,7,2,1,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,6,8,7,1,5,4,2]=>{{1,2,3,5,6,8},{4,7}}
[5,7,8,6,3,4,1,2]=>{{1,2,3,5,7,8},{4,6}}
[7,1,8,5,4,3,6,2]=>{{1,2,3,6,7,8},{4,5}}
[2,7,8,4,5,3,6,1]=>{{1,2,3,6,7,8},{4},{5}}
[5,7,3,8,1,4,6,2]=>{{1,5},{2,4,6,7,8},{3}}
[2,1,7,8,5,4,6,3]=>{{1,2},{3,4,6,7,8},{5}}
[2,1,5,8,4,6,3,7]=>{{1,2},{3,4,5,7,8},{6}}
[6,5,3,8,4,1,2,7]=>{{1,6},{2,4,5,7,8},{3}}
[7,5,8,4,3,6,2,1]=>{{1,2,3,5,7,8},{4},{6}}
[2,4,8,3,5,6,1,7]=>{{1,2,3,4,7,8},{5},{6}}
[4,1,8,3,6,5,2,7]=>{{1,2,3,4,7,8},{5,6}}
[3,4,8,1,7,2,5,6]=>{{1,2,3,4,6,8},{5,7}}
[8,4,1,3,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,2,4,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[2,3,8,1,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[4,3,8,2,5,1,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[6,3,8,4,2,5,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[7,4,3,8,2,5,1,6]=>{{1,7},{2,4,5,6,8},{3}}
[2,1,4,8,3,5,7,6]=>{{1,2},{3,4,5,6,8},{7}}
[6,8,2,4,3,5,1,7]=>{{1,2,3,5,6,7,8},{4}}
[4,8,2,3,5,1,6,7]=>{{1,2,3,4,6,7,8},{5}}
[3,8,2,1,4,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[2,8,1,3,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,8,4,1,6,5,3,7]=>{{1,2,3,4,7,8},{5,6}}
[2,8,4,1,6,5,7,3]=>{{1,2,3,4,8},{5,6},{7}}
[2,8,7,6,1,4,3,5]=>{{1,2,5,8},{3,7},{4,6}}
[2,8,5,6,7,4,3,1]=>{{1,2,8},{3,5,7},{4,6}}
[7,5,8,6,1,4,2,3]=>{{1,2,5,7},{3,8},{4,6}}
[3,5,7,6,1,4,2,8]=>{{1,2,3,5,7},{4,6},{8}}
[3,5,7,2,4,1,6,8]=>{{1,3,6,7},{2,4,5},{8}}
[7,5,8,2,4,1,6,3]=>{{1,6,7},{2,4,5},{3,8}}
[2,8,5,3,4,7,6,1]=>{{1,2,8},{3,4,5},{6,7}}
[2,8,5,3,4,1,7,6]=>{{1,2,6,8},{3,4,5},{7}}
[2,8,5,3,4,1,6,7]=>{{1,2,6,7,8},{3,4,5}}
[2,8,7,6,1,4,5,3]=>{{1,2,3,5,7,8},{4,6}}
[2,8,5,3,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,8,5,6,7,4,1,3]=>{{1,2,3,5,7,8},{4,6}}
[2,8,5,3,4,7,1,6]=>{{1,2,6,7,8},{3,4,5}}
[2,8,5,3,4,6,1,7]=>{{1,2,7,8},{3,4,5},{6}}
[2,8,5,3,4,6,7,1]=>{{1,2,8},{3,4,5},{6},{7}}
[3,5,7,2,4,6,1,8]=>{{1,3,7},{2,4,5},{6},{8}}
[6,5,2,7,3,1,4,8]=>{{1,6},{2,3,5},{4,7},{8}}
[6,5,2,8,3,1,7,4]=>{{1,6},{2,3,5},{4,8},{7}}
[6,5,2,8,3,1,4,7]=>{{1,6},{2,3,5},{4,7,8}}
[7,5,8,2,4,6,3,1]=>{{1,3,7,8},{2,4,5},{6}}
[7,5,8,6,1,4,3,2]=>{{1,2,3,5,7,8},{4,6}}
[6,5,8,2,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[3,5,6,2,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[3,5,7,6,1,4,8,2]=>{{1,2,3,5,7,8},{4,6}}
[3,5,7,2,4,1,8,6]=>{{1,3,6,7,8},{2,4,5}}
[3,5,7,2,4,6,8,1]=>{{1,3,7,8},{2,4,5},{6}}
[6,5,2,7,3,1,8,4]=>{{1,6},{2,3,5},{4,7,8}}
[4,5,2,6,3,1,7,8]=>{{1,4,6},{2,3,5},{7},{8}}
[4,1,2,3,7,6,8,5]=>{{1,2,3,4},{5,7,8},{6}}
[6,5,2,7,3,4,8,1]=>{{1,4,6,7,8},{2,3,5}}
[5,1,6,7,4,3,8,2]=>{{1,2,4,5,7,8},{3,6}}
[5,1,2,6,4,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[5,1,2,8,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[5,1,6,8,7,3,4,2]=>{{1,2,4,5,7,8},{3,6}}
[6,5,2,8,3,7,4,1]=>{{1,4,6,7,8},{2,3,5}}
[4,1,2,3,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}
[4,1,2,3,8,6,5,7]=>{{1,2,3,4},{5,7,8},{6}}
[4,1,2,3,8,6,7,5]=>{{1,2,3,4},{5,8},{6},{7}}
[4,1,2,3,7,6,5,8]=>{{1,2,3,4},{5,7},{6},{8}}
[4,1,2,3,8,5,7,6]=>{{1,2,3,4},{5,6,8},{7}}
[7,1,6,8,4,3,5,2]=>{{1,2,4,5,7,8},{3,6}}
[6,1,2,8,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[5,6,8,2,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[6,5,8,2,4,3,1,7]=>{{1,3,6,7,8},{2,4,5}}
[6,5,8,2,4,3,7,1]=>{{1,3,6,8},{2,4,5},{7}}
[7,5,2,8,3,4,1,6]=>{{1,7},{2,3,5},{4,6,8}}
[6,5,2,8,3,7,1,4]=>{{1,6,7},{2,3,5},{4,8}}
[6,5,2,7,3,4,1,8]=>{{1,4,6,7},{2,3,5},{8}}
[5,1,6,7,4,3,2,8]=>{{1,2,4,5,7},{3,6},{8}}
[5,1,6,8,7,3,2,4]=>{{1,2,5,7},{3,6},{4,8}}
[7,1,6,8,4,3,2,5]=>{{1,2,7},{3,6},{4,5,8}}
[5,7,8,6,3,4,2,1]=>{{1,3,5,8},{2,7},{4,6}}
[4,1,8,3,6,5,7,2]=>{{1,2,3,4,8},{5,6},{7}}
[4,1,8,3,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,1,4,8,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,1,4,8,6,5,2,7]=>{{1,2,3,4,7,8},{5,6}}
[7,1,6,5,8,3,2,4]=>{{1,2,7},{3,6},{4,5,8}}
[4,1,6,7,8,3,2,5]=>{{1,2,4,7},{3,6},{5,8}}
[4,1,6,5,7,3,2,8]=>{{1,2,4,5,7},{3,6},{8}}
[4,5,2,6,3,7,1,8]=>{{1,4,6,7},{2,3,5},{8}}
[4,5,2,7,3,8,1,6]=>{{1,4,7},{2,3,5},{6,8}}
[3,5,6,2,4,8,7,1]=>{{1,3,6,8},{2,4,5},{7}}
[3,5,6,2,4,8,1,7]=>{{1,3,6,7,8},{2,4,5}}
[3,7,5,6,8,4,1,2]=>{{1,2,3,5,7,8},{4,6}}
[3,6,5,2,8,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[6,1,2,5,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[7,1,6,5,8,3,4,2]=>{{1,2,4,5,7,8},{3,6}}
[7,5,2,6,3,8,4,1]=>{{1,4,6,7,8},{2,3,5}}
[4,1,2,3,5,8,7,6]=>{{1,2,3,4},{5},{6,8},{7}}
[4,1,2,3,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}
[4,5,2,7,3,8,6,1]=>{{1,4,6,7,8},{2,3,5}}
[4,1,6,7,8,3,5,2]=>{{1,2,4,5,7,8},{3,6}}
[4,1,2,6,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[4,1,2,5,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[4,5,2,6,3,7,8,1]=>{{1,4,6,7,8},{2,3,5}}
[7,8,5,6,1,4,3,2]=>{{1,3,5,7},{2,8},{4,6}}
[7,8,4,2,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,2,1,6,5,3,4]=>{{1,2,3,4,7,8},{5,6}}
[6,4,1,2,5,7,3,8]=>{{1,3,6,7},{2,4},{5},{8}}
[2,4,8,1,5,7,3,6]=>{{1,2,4},{3,6,7,8},{5}}
[4,3,8,1,7,2,5,6]=>{{1,4},{2,3,6,8},{5,7}}
[6,3,1,4,7,2,5,8]=>{{1,2,3,6},{4},{5,7},{8}}
[7,8,3,4,5,1,6,2]=>{{1,6,7},{2,8},{3},{4},{5}}
[7,8,3,5,4,2,1,6]=>{{1,7},{2,6,8},{3},{4,5}}
[7,8,4,1,2,3,6,5]=>{{1,3,4,6,7},{2,5,8}}
[7,8,3,6,5,4,1,2]=>{{1,7},{2,8},{3},{4,6},{5}}
[7,8,2,1,5,3,4,6]=>{{1,4,7},{2,3,6,8},{5}}
[7,8,2,6,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,2,5,6,4,1,3]=>{{1,7},{2,3,8},{4,5,6}}
[7,8,1,6,5,4,3,2]=>{{1,3,7},{2,8},{4,6},{5}}
[6,2,1,7,5,4,3,8]=>{{1,3,4,6,7},{2},{5},{8}}
[2,1,8,7,5,4,3,6]=>{{1,2},{3,4,6,7,8},{5}}
[1,3,8,2,6,4,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[5,3,7,1,6,4,8,2]=>{{1,4,5,6},{2,3,7,8}}
[5,3,6,2,7,4,1,8]=>{{1,5,7},{2,3,4,6},{8}}
[6,1,2,5,8,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,8,4,2,7,5]=>{{1,2,3,6},{4,5,8},{7}}
[6,4,2,1,5,3,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[6,4,3,7,5,8,1,2]=>{{1,2,4,6,7,8},{3},{5}}
[4,3,8,7,5,6,1,2]=>{{1,4,7},{2,3,8},{5},{6}}
[2,4,7,1,5,3,6,8]=>{{1,2,4},{3,6,7},{5},{8}}
[1,3,7,6,4,2,8,5]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,5,6,8,4,3]=>{{1,2},{3,4,5,6,7,8}}
[3,7,2,8,6,4,1,5]=>{{1,2,3,7},{4,5,6,8}}
[3,8,1,7,6,4,5,2]=>{{1,3},{2,8},{4,5,6,7}}
[1,8,5,7,3,6,4,2]=>{{1},{2,8},{3,5},{4,7},{6}}
[2,7,5,8,3,6,1,4]=>{{1,2,7},{3,5},{4,8},{6}}
[1,5,6,8,2,4,7,3]=>{{1},{2,5},{3,4,6,8},{7}}
[2,6,8,5,3,1,4,7]=>{{1,2,6},{3,4,5,7,8}}
[2,6,1,4,7,3,5,8]=>{{1,2,3,6},{4},{5,7},{8}}
[5,6,7,3,8,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,2,8,1,4,7,3,6]=>{{1,4,5},{2},{3,6,7,8}}
[4,6,7,5,2,1,3,8]=>{{1,2,4,5,6},{3,7},{8}}
[4,5,6,7,2,8,1,3]=>{{1,4,7},{2,5},{3,6,8}}
[4,5,7,6,1,8,3,2]=>{{1,2,4,5,6,8},{3,7}}
[1,5,8,6,2,7,3,4]=>{{1},{2,5},{3,4,6,7,8}}
[1,6,5,8,3,2,7,4]=>{{1},{2,6},{3,5},{4,8},{7}}
[4,6,5,7,1,2,8,3]=>{{1,3,4,5,7,8},{2,6}}
[4,7,5,6,3,1,8,2]=>{{1,4,6},{2,7,8},{3,5}}
[5,1,6,3,4,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[5,7,1,4,2,3,8,6]=>{{1,2,3,5,6,7,8},{4}}
[5,7,6,4,3,8,1,2]=>{{1,2,3,5,6,7,8},{4}}
[6,3,4,5,8,7,1,2]=>{{1,6,7},{2,3,4,5,8}}
[6,2,4,1,8,3,7,5]=>{{1,3,4,6},{2},{5,8},{7}}
[6,2,3,5,4,8,1,7]=>{{1,6,7,8},{2},{3},{4,5}}
[6,1,3,4,5,8,7,2]=>{{1,2,6,8},{3},{4},{5},{7}}
[5,1,4,2,7,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[1,6,2,4,7,8,3,5]=>{{1},{2,3,5,6,7,8},{4}}
[5,7,2,4,1,6,3,8]=>{{1,5},{2,3,7},{4},{6},{8}}
[6,1,4,2,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[6,7,5,8,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,6,3,4,1,2]=>{{1,3,5,7},{2,8},{4,6}}
[5,8,7,6,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[4,1,7,2,6,5,3,8]=>{{1,2,4},{3,7},{5,6},{8}}
[4,8,2,1,5,6,3,7]=>{{1,4},{2,3,7,8},{5},{6}}
[4,2,7,8,1,6,3,5]=>{{1,4,5,8},{2},{3,7},{6}}
[2,1,8,7,6,5,3,4]=>{{1,2},{3,4,7,8},{5,6}}
[3,1,4,7,8,2,6,5]=>{{1,2,3,4,6,7},{5,8}}
[3,1,7,4,5,6,8,2]=>{{1,2,3,7,8},{4},{5},{6}}
[4,2,7,1,6,3,8,5]=>{{1,4},{2},{3,5,6,7,8}}
[4,3,7,5,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[4,8,6,3,5,7,1,2]=>{{1,3,4,6,7},{2,8},{5}}
[4,8,1,2,5,3,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[3,8,6,5,2,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[3,8,5,6,1,4,7,2]=>{{1,3,5},{2,8},{4,6},{7}}
[5,3,7,8,2,1,6,4]=>{{1,2,3,5,6,7},{4,8}}
[5,2,8,7,1,6,4,3]=>{{1,5},{2},{3,8},{4,7},{6}}
[1,6,8,7,5,2,4,3]=>{{1},{2,6},{3,8},{4,7},{5}}
[3,6,7,8,5,1,4,2]=>{{1,2,3,4,6,7,8},{5}}
[3,7,6,8,5,2,1,4]=>{{1,2,3,6,7},{4,8},{5}}
[3,7,8,5,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,1,6,4,2,5,8]=>{{1,3},{2,4,5,6,7},{8}}
[4,1,8,6,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,6,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,6,5,4,1,2]=>{{1,3,7},{2,8},{4,6},{5}}
[2,1,7,6,5,3,4,8]=>{{1,2},{3,4,6,7},{5},{8}}
[2,8,1,6,4,5,3,7]=>{{1,2,3,7,8},{4,5,6}}
[2,8,7,5,1,4,3,6]=>{{1,2,4,5,6,8},{3,7}}
[2,8,6,7,5,1,3,4]=>{{1,2,3,4,6,7,8},{5}}
[2,7,8,6,5,4,1,3]=>{{1,2,7},{3,8},{4,6},{5}}
[6,4,2,7,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,5,1,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,6,1,7,2,4]=>{{1,2,4,5,6,7,8},{3}}
[7,3,6,2,4,8,1,5]=>{{1,7},{2,3,4,5,6,8}}
[4,3,7,1,2,5,8,6]=>{{1,4},{2,3,5,6,7,8}}
[3,6,2,7,1,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,7,1,2,8,4]=>{{1,5},{2,3,6},{4,7,8}}
[6,3,7,4,1,2,8,5]=>{{1,2,3,5,6,7,8},{4}}
[4,7,1,5,2,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,5,1,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[7,6,4,2,3,8,1,5]=>{{1,7},{2,3,4,5,6,8}}
[8,6,4,2,3,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,7,6,3,8,1,2,5]=>{{1,3,4,6},{2,7},{5,8}}
[5,7,4,2,3,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[3,7,6,1,4,8,2,5]=>{{1,3,4,5,6,8},{2,7}}
[6,4,7,5,2,8,1,3]=>{{1,3,6,7,8},{2,4,5}}
[7,4,8,5,2,6,1,3]=>{{1,7},{2,4,5},{3,8},{6}}
[5,8,2,6,3,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,2,4,7,1,5]=>{{1,3,6,7},{2,4,5,8}}
[4,8,6,2,7,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[2,6,5,8,1,3,4,7]=>{{1,2,3,5,6},{4,7,8}}
[2,5,7,4,8,1,3,6]=>{{1,2,5,6,8},{3,7},{4}}
[5,4,6,7,2,8,1,3]=>{{1,2,4,5,7},{3,6,8}}
[3,5,7,1,4,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[5,3,7,2,4,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[5,4,7,3,8,1,2,6]=>{{1,5,6,8},{2,3,4,7}}
[7,4,6,3,8,1,2,5]=>{{1,2,3,4,6,7},{5,8}}
[8,4,6,3,7,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,6,7,2,3,5]=>{{1,3,5,7,8},{2,4,6}}
[7,4,1,6,8,2,3,5]=>{{1,3,7},{2,4,6},{5,8}}
[6,5,3,7,1,8,2,4]=>{{1,2,4,5,6,7,8},{3}}
[6,5,1,2,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,4,7,8,1,2]=>{{1,5,7},{2,3,6,8},{4}}
[6,3,7,4,8,5,1,2]=>{{1,2,3,5,6,7,8},{4}}
[4,7,1,5,8,6,2,3]=>{{1,3,4,5,8},{2,7},{6}}
[7,5,1,2,8,6,3,4]=>{{1,3,7},{2,4,5,8},{6}}
[7,6,1,8,5,2,3,4]=>{{1,3,7},{2,6},{4,8},{5}}
[8,6,1,7,5,2,3,4]=>{{1,3,4,7,8},{2,6},{5}}
[5,7,2,8,1,6,3,4]=>{{1,5},{2,3,7},{4,8},{6}}
[6,3,7,8,5,1,2,4]=>{{1,6},{2,3,7},{4,8},{5}}
[3,6,8,2,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,7,1,3,5,6]=>{{1,2,4,5,7},{3,6,8}}
[4,3,8,7,1,2,5,6]=>{{1,4,5,7},{2,3,6,8}}
[5,3,8,7,1,2,4,6]=>{{1,5},{2,3,6,8},{4,7}}
[8,3,7,6,1,2,4,5]=>{{1,5,8},{2,3,4,6,7}}
[8,4,7,6,1,2,3,5]=>{{1,5,8},{2,4,6},{3,7}}
[3,5,8,7,1,2,4,6]=>{{1,2,3,5,6,8},{4,7}}
[2,5,8,7,1,3,4,6]=>{{1,2,5},{3,6,8},{4,7}}
[6,8,4,7,5,1,2,3]=>{{1,6},{2,3,4,7,8},{5}}
[5,8,7,1,6,2,3,4]=>{{1,2,4,5,6,8},{3,7}}
[2,8,7,6,1,3,4,5]=>{{1,2,5,8},{3,4,6,7}}
[3,8,7,6,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,6,1,2,3,5]=>{{1,2,4,5,6,8},{3,7}}
[5,6,3,1,4,2,8,7]=>{{1,4,5},{2,6},{3},{7,8}}
[7,5,3,8,2,1,6,4]=>{{1,6,7},{2,5},{3},{4,8}}
[3,8,7,4,5,1,6,2]=>{{1,3,6,7},{2,8},{4},{5}}
[2,1,7,8,5,3,6,4]=>{{1,2},{3,6,7},{4,8},{5}}
[5,7,3,8,1,2,6,4]=>{{1,5},{2,6,7},{3},{4,8}}
[8,7,1,4,5,3,2,6]=>{{1,3,6,8},{2,7},{4},{5}}
[2,7,8,4,1,6,5,3]=>{{1,2,5,7},{3,8},{4},{6}}
[7,1,8,4,2,6,5,3]=>{{1,2,5,7},{3,8},{4},{6}}
[7,5,1,4,8,6,3,2]=>{{1,3,7},{2,5,8},{4},{6}}
[6,5,3,1,8,4,7,2]=>{{1,4,6},{2,5,8},{3},{7}}
[8,6,3,1,2,5,7,4]=>{{1,4,8},{2,5,6},{3},{7}}
[8,7,1,4,2,6,5,3]=>{{1,3,8},{2,5,7},{4},{6}}
[3,6,4,5,7,2,8,1]=>{{1,3,4,5,7,8},{2,6}}
[5,3,2,7,4,6,8,1]=>{{1,4,5,7,8},{2,3},{6}}
[7,5,3,6,2,4,8,1]=>{{1,7,8},{2,5},{3},{4,6}}
[6,3,2,5,1,8,4,7]=>{{1,4,5,6,7,8},{2,3}}
[8,5,3,6,2,7,1,4]=>{{1,4,6,7,8},{2,5},{3}}
[8,2,6,3,4,7,1,5]=>{{1,3,4,5,6,7,8},{2}}
[7,2,6,3,4,5,8,1]=>{{1,7,8},{2},{3,4,5,6}}
[6,2,7,3,4,5,8,1]=>{{1,3,4,5,6,7,8},{2}}
[4,2,5,7,3,6,8,1]=>{{1,4,7,8},{2},{3,5},{6}}
[5,4,7,6,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,3,5,2,4,8,1]=>{{1,2,4,5,6,7,8},{3}}
[3,7,6,2,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,3,4,5,8,1]=>{{1,2,7,8},{3,4,5,6}}
[6,5,3,1,2,8,4,7]=>{{1,4,6,7,8},{2,5},{3}}
[8,6,5,2,3,7,1,4]=>{{1,2,4,6,7,8},{3,5}}
[8,5,2,1,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,5,2,1,8,3,4,6]=>{{1,4,7},{2,3,5,6,8}}
[1,6,3,2,8,4,5,7]=>{{1},{2,4,6},{3},{5,7,8}}
[5,6,2,3,1,8,4,7]=>{{1,5},{2,3,4,6,7,8}}
[5,4,8,6,2,7,1,3]=>{{1,2,4,5,6,7},{3,8}}
[6,8,3,5,2,7,1,4]=>{{1,6,7},{2,4,5,8},{3}}
[7,8,5,2,3,6,1,4]=>{{1,7},{2,4,8},{3,5},{6}}
[6,8,2,1,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[1,8,6,3,7,2,4,5]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,7,3,4,5,6]=>{{1},{2,3,4,5,6,7,8}}
[2,8,1,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,1,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,5,7,2,3,6]=>{{1,3,4,5,7},{2,6,8}}
[4,2,8,3,7,1,5,6]=>{{1,3,4,6,8},{2},{5,7}}
[8,1,2,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,6,2,7,1,8,4,5]=>{{1,2,3,5,6,8},{4,7}}
[6,3,7,1,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,2,6,1,8,3,4,5]=>{{1,4,7},{2},{3,6},{5,8}}
[7,3,1,5,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,2,1,5,8,4,6,7]=>{{1,3},{2},{4,5,6,7,8}}
[5,4,1,3,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,5,3,4,6,8,2,7]=>{{1},{2,5,6,7,8},{3},{4}}
[4,3,5,1,6,8,2,7]=>{{1,4},{2,3,5,6,7,8}}
[5,4,6,3,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,5,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,3,4,8,7,1,2]=>{{1,6,7},{2,5,8},{3},{4}}
[5,3,2,8,7,1,4,6]=>{{1,4,5,6,7,8},{2,3}}
[5,3,1,8,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,7,6,1,2,4]=>{{1,2,4,5,6,7,8},{3}}
[6,1,8,3,7,2,4,5]=>{{1,2,6},{3,4,5,7,8}}
[6,3,8,1,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,2,3,5,1,4]=>{{1,7},{2,3,4,5,6,8}}
[3,7,8,2,4,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[6,7,3,8,2,5,1,4]=>{{1,2,5,6,7},{3},{4,8}}
[5,4,7,8,2,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[4,2,5,8,7,1,3,6]=>{{1,4,6,8},{2},{3,5,7}}
[2,3,8,7,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,2,8,6,1,3,4,5]=>{{1,3,4,5,6,7,8},{2}}
[2,1,8,7,3,4,5,6]=>{{1,2},{3,4,5,6,7,8}}
[8,2,7,6,1,3,4,5]=>{{1,5,8},{2},{3,4,6,7}}
[1,2,8,7,3,4,5,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,3,8,7,2,4,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,7,8,3,6,2,4,5]=>{{1},{2,3,4,5,6,7,8}}
[4,1,5,8,7,2,3,6]=>{{1,2,4,6,8},{3,5,7}}
[5,4,8,7,6,1,2,3]=>{{1,5,6},{2,4,7},{3,8}}
[6,8,3,7,5,1,2,4]=>{{1,6},{2,4,7,8},{3},{5}}
[7,8,6,2,5,1,3,4]=>{{1,3,6,7},{2,4,8},{5}}
[8,1,6,7,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,7,3,2,4,5]=>{{1,2,3,5,6,8},{4,7}}
[8,1,5,3,7,2,4,6]=>{{1,2,6,8},{3,4,5,7}}
[8,1,5,3,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,3,6,2,4,8]=>{{1,3,4,7},{2,5,6},{8}}
[7,5,8,3,6,2,4,1]=>{{1,3,4,7,8},{2,5,6}}
[7,4,8,3,2,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[7,4,1,3,2,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[8,1,4,3,2,6,5,7]=>{{1,2,5,7,8},{3,4},{6}}
[8,1,4,3,2,7,5,6]=>{{1,2,5,6,7,8},{3,4}}
[8,1,4,3,2,7,6,5]=>{{1,2,5,8},{3,4},{6,7}}
[8,1,5,4,6,7,2,3]=>{{1,2,3,5,6,7,8},{4}}
[8,1,5,3,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[8,1,4,3,2,6,7,5]=>{{1,2,5,8},{3,4},{6},{7}}
[8,1,4,3,2,5,7,6]=>{{1,2,5,6,8},{3,4},{7}}
[8,1,4,3,2,5,6,7]=>{{1,2,5,6,7,8},{3,4}}
[7,4,1,3,2,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[7,4,8,3,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,3,8,2,5,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[6,4,3,1,2,5,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[7,4,1,3,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,3,2,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[7,5,1,3,6,2,8,4]=>{{1,3,4,7,8},{2,5,6}}
[7,5,1,4,6,8,2,3]=>{{1,2,3,5,6,7,8},{4}}
[7,5,8,3,6,2,1,4]=>{{1,7},{2,5,6},{3,4,8}}
[7,4,8,3,2,6,1,5]=>{{1,7},{2,3,4,5,8},{6}}
[7,4,8,3,2,5,1,6]=>{{1,7},{2,3,4,5,6,8}}
[6,4,3,8,2,5,1,7]=>{{1,2,4,5,6,7,8},{3}}
[6,4,3,7,2,5,8,1]=>{{1,2,4,5,6,7,8},{3}}
[5,4,3,2,8,6,1,7]=>{{1,5,7,8},{2,4},{3},{6}}
[5,4,3,2,8,7,1,6]=>{{1,5,6,7,8},{2,4},{3}}
[6,5,3,8,7,2,1,4]=>{{1,2,5,6,7},{3},{4,8}}
[6,5,4,8,7,1,2,3]=>{{1,6},{2,5,7},{3,4,8}}
[6,5,4,1,7,8,2,3]=>{{1,3,4,6,8},{2,5,7}}
[6,5,3,1,7,2,8,4]=>{{1,2,4,5,6,7,8},{3}}
[6,4,3,1,2,7,8,5]=>{{1,2,4,5,6,7,8},{3}}
[5,4,3,2,1,8,6,7]=>{{1,5},{2,4},{3},{6,7,8}}
[6,5,3,1,8,2,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[6,5,4,1,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,4,8,6,2,3]=>{{1,2,3,5,7,8},{4},{6}}
[7,4,1,3,2,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,3,2,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[6,4,3,1,2,8,5,7]=>{{1,2,4,5,6,7,8},{3}}
[6,4,3,1,2,7,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[6,4,3,8,2,7,5,1]=>{{1,2,4,5,6,7,8},{3}}
[6,5,3,8,7,2,4,1]=>{{1,2,4,5,6,7,8},{3}}
[6,5,3,1,7,2,4,8]=>{{1,2,4,5,6,7},{3},{8}}
[6,5,3,1,8,2,4,7]=>{{1,2,4,5,6,7,8},{3}}
[7,5,1,3,8,2,4,6]=>{{1,3,4,7},{2,5,6,8}}
[7,6,1,8,3,2,4,5]=>{{1,3,4,5,7,8},{2,6}}
[7,6,1,8,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,1,4,5,2,3]=>{{1,2,4,5,6,7},{3,8}}
[7,6,8,1,3,2,5,4]=>{{1,3,4,5,7,8},{2,6}}
[6,5,3,7,8,2,4,1]=>{{1,2,5,6,8},{3},{4,7}}
[6,4,3,7,2,8,5,1]=>{{1,6,8},{2,4,5,7},{3}}
[6,4,3,7,2,1,5,8]=>{{1,6},{2,4,5,7},{3},{8}}
[7,4,8,3,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,8,3,2,1,6,5]=>{{1,6,7},{2,3,4,5,8}}
[7,5,8,3,1,2,6,4]=>{{1,2,5,6,7},{3,4,8}}
[7,5,8,4,1,6,2,3]=>{{1,2,5,7},{3,8},{4},{6}}
[6,5,4,8,1,7,2,3]=>{{1,2,5,6,7},{3,4,8}}
[6,5,3,8,1,2,7,4]=>{{1,2,5,6},{3},{4,8},{7}}
[5,4,3,2,8,1,7,6]=>{{1,5,6,8},{2,4},{3},{7}}
[6,4,3,7,2,1,8,5]=>{{1,6},{2,4,5,7,8},{3}}
[6,5,3,7,1,2,8,4]=>{{1,2,5,6},{3},{4,7,8}}
[6,5,4,7,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,3,7,8,2,1,4]=>{{1,2,4,5,6,7,8},{3}}
[6,4,3,7,2,8,1,5]=>{{1,2,4,5,6,7,8},{3}}
[5,4,3,2,7,8,1,6]=>{{1,5,7},{2,4},{3},{6,8}}
[5,4,3,2,6,8,1,7]=>{{1,5,6,7,8},{2,4},{3}}
[5,6,2,1,3,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[5,3,7,8,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,6,1,2,5,8,3,4]=>{{1,3,7},{2,4,6,8},{5}}
[2,1,7,8,4,3,5,6]=>{{1,2},{3,4,5,6,7,8}}
[7,8,1,2,5,4,6,3]=>{{1,2,3,4,6,7,8},{5}}
[8,4,1,3,7,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[6,5,2,1,8,7,4,3]=>{{1,4,6,7},{2,3,5,8}}
[4,7,2,8,1,3,6,5]=>{{1,4,5,8},{2,3,6,7}}
[7,3,8,6,1,2,5,4]=>{{1,5,7},{2,3,4,6,8}}
[3,4,7,1,8,2,6,5]=>{{1,2,3,4,6,7},{5,8}}
[1,8,2,4,3,5,6,7]=>{{1},{2,3,5,6,7,8},{4}}
[1,7,2,4,3,5,6,8]=>{{1},{2,3,5,6,7},{4},{8}}
[1,6,2,4,3,5,7,8]=>{{1},{2,3,5,6},{4},{7},{8}}
[1,5,2,4,3,6,7,8]=>{{1},{2,3,5},{4},{6},{7},{8}}
[1,6,2,5,3,4,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,7,2,5,3,4,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,2,5,3,4,6,7]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,6,3,4,5,7]=>{{1},{2,3,5,7,8},{4,6}}
[1,7,2,6,3,4,5,8]=>{{1},{2,3,5,7},{4,6},{8}}
[1,8,2,7,3,5,4,6]=>{{1},{2,3,5,6,8},{4,7}}
[1,7,2,8,3,5,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,6,2,8,3,5,4,7]=>{{1},{2,3,5,6},{4,7,8}}
[1,5,2,8,3,6,4,7]=>{{1},{2,3,5},{4,7,8},{6}}
[1,4,2,8,3,6,5,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,3,2,8,4,6,5,7]=>{{1},{2,3},{4,5,7,8},{6}}
[1,2,3,8,4,6,5,7]=>{{1},{2},{3},{4,5,7,8},{6}}
[1,2,3,7,4,6,5,8]=>{{1},{2},{3},{4,5,7},{6},{8}}
[1,3,2,7,4,6,5,8]=>{{1},{2,3},{4,5,7},{6},{8}}
[1,4,2,7,3,6,5,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,5,2,7,3,6,4,8]=>{{1},{2,3,5},{4,7},{6},{8}}
[1,6,2,7,3,5,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[1,7,2,6,3,5,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,2,6,3,5,4,7]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,5,3,6,4,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,2,5,3,6,4,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,6,2,5,3,7,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,5,2,4,3,7,6,8]=>{{1},{2,3,5},{4},{6,7},{8}}
[1,6,2,4,3,7,5,8]=>{{1},{2,3,5,6,7},{4},{8}}
[1,7,2,4,3,6,5,8]=>{{1},{2,3,5,7},{4},{6},{8}}
[1,8,2,4,3,6,5,7]=>{{1},{2,3,5,7,8},{4},{6}}
[1,8,2,3,4,6,5,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,2,3,4,6,5,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,8,2,3,4,7,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,4,3,7,5,6]=>{{1},{2,3,5,6,7,8},{4}}
[1,7,2,4,3,8,5,6]=>{{1},{2,3,5,7},{4},{6,8}}
[1,6,2,4,3,8,5,7]=>{{1},{2,3,5,6,7,8},{4}}
[1,5,2,4,3,8,6,7]=>{{1},{2,3,5},{4},{6,7,8}}
[1,6,2,5,3,8,4,7]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,5,3,8,4,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,8,2,5,3,7,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,6,3,7,4,5]=>{{1},{2,3,5,8},{4,6,7}}
[1,7,2,6,3,8,4,5]=>{{1},{2,3,4,5,6,7,8}}
[1,2,3,8,4,7,5,6]=>{{1},{2},{3},{4,5,6,7,8}}
[1,3,2,8,4,7,5,6]=>{{1},{2,3},{4,5,6,7,8}}
[1,4,2,8,3,7,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,5,2,8,3,7,4,6]=>{{1},{2,3,5},{4,6,7,8}}
[1,6,2,8,3,7,4,5]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,8,3,6,4,5]=>{{1},{2,3,4,5,7,8},{6}}
[1,8,2,7,3,6,4,5]=>{{1},{2,3,5,8},{4,7},{6}}
[4,6,3,7,2,5,1,8]=>{{1,4,7},{2,5,6},{3},{8}}
[4,6,3,7,5,2,1,8]=>{{1,4,7},{2,6},{3},{5},{8}}
[4,6,3,8,5,1,7,2]=>{{1,2,4,6,8},{3},{5},{7}}
[4,6,3,8,5,1,2,7]=>{{1,2,4,6,7,8},{3},{5}}
[5,6,8,3,4,1,2,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,8,3,4,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,6,2,7,5,3,1,8]=>{{1,4,7},{2,3,6},{5},{8}}
[5,6,7,2,4,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,8,4,3,1,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[5,6,8,4,3,1,2,7]=>{{1,2,3,5,6,7,8},{4}}
[5,7,8,4,1,6,2,3]=>{{1,5},{2,7},{3,8},{4},{6}}
[5,7,8,4,1,6,3,2]=>{{1,5},{2,3,7,8},{4},{6}}
[5,7,8,4,1,3,6,2]=>{{1,5},{2,3,6,7,8},{4}}
[5,6,8,4,2,1,7,3]=>{{1,2,5,6},{3,8},{4},{7}}
[5,6,8,2,4,1,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[4,6,2,8,5,1,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[3,2,6,8,5,1,7,4]=>{{1,3,6},{2},{4,8},{5},{7}}
[3,2,6,8,5,1,4,7]=>{{1,3,6},{2},{4,7,8},{5}}
[4,6,2,8,5,1,3,7]=>{{1,2,3,4,6,7,8},{5}}
[5,6,8,2,4,1,3,7]=>{{1,2,4,5,6},{3,7,8}}
[5,6,8,4,2,1,3,7]=>{{1,2,5,6},{3,7,8},{4}}
[5,7,8,4,1,3,2,6]=>{{1,5},{2,7},{3,6,8},{4}}
[5,7,8,4,1,2,6,3]=>{{1,5},{2,6,7},{3,8},{4}}
[5,7,8,4,1,2,3,6]=>{{1,5},{2,3,6,7,8},{4}}
[6,7,8,1,5,2,3,4]=>{{1,2,3,4,6,7,8},{5}}
[6,7,8,1,5,2,4,3]=>{{1,2,4,6,7},{3,8},{5}}
[6,7,8,1,5,3,2,4]=>{{1,3,4,6,8},{2,7},{5}}
[6,7,8,1,3,5,2,4]=>{{1,3,4,5,6,8},{2,7}}
[5,7,8,2,1,6,3,4]=>{{1,5},{2,3,4,7,8},{6}}
[4,7,2,8,1,6,3,5]=>{{1,4,5,8},{2,3,7},{6}}
[3,2,7,8,1,6,4,5]=>{{1,3,4,5,7,8},{2},{6}}
[3,2,7,8,1,6,5,4]=>{{1,3,5,7},{2},{4,8},{6}}
[4,7,2,8,1,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[5,7,8,2,1,6,4,3]=>{{1,5},{2,4,7},{3,8},{6}}
[6,7,8,1,3,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,1,5,3,4,2]=>{{1,2,3,4,6,7,8},{5}}
[6,7,8,1,5,4,3,2]=>{{1,4,6},{2,3,7,8},{5}}
[6,7,8,1,5,4,2,3]=>{{1,4,6},{2,7},{3,8},{5}}
[6,7,8,1,4,5,2,3]=>{{1,4,5,6},{2,7},{3,8}}
[6,7,8,1,4,5,3,2]=>{{1,4,5,6},{2,3,7,8}}
[6,7,8,1,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,1,3,4,5,2]=>{{1,4,6},{2,3,5,7,8}}
[5,7,8,2,1,4,6,3]=>{{1,5},{2,4,6,7},{3,8}}
[4,7,2,8,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,2,7,8,1,5,6,4]=>{{1,3,5,6,7},{2},{4,8}}
[3,2,6,8,4,1,7,5]=>{{1,3,6},{2},{4,5,8},{7}}
[4,6,2,8,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[5,6,8,3,2,1,7,4]=>{{1,2,5,6},{3,4,8},{7}}
[5,7,8,3,1,4,6,2]=>{{1,5},{2,3,4,6,7,8}}
[5,7,8,3,1,6,4,2]=>{{1,5},{2,3,4,7,8},{6}}
[5,7,8,3,1,6,2,4]=>{{1,5},{2,7},{3,4,8},{6}}
[4,7,3,8,1,6,2,5]=>{{1,4,5,8},{2,7},{3},{6}}
[4,7,3,8,1,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}
[4,7,3,8,1,5,6,2]=>{{1,2,4,5,6,7,8},{3}}
[4,6,3,8,2,1,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[4,5,3,2,8,1,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[4,5,2,3,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[3,2,5,4,8,1,7,6]=>{{1,3,5,6,8},{2},{4},{7}}
[4,5,3,2,8,1,6,7]=>{{1,2,4,5,6,7,8},{3}}
[4,6,3,8,2,1,5,7]=>{{1,2,4,5,6,7,8},{3}}
[4,7,3,8,1,5,2,6]=>{{1,4,5,6,8},{2,7},{3}}
[4,7,3,8,1,2,6,5]=>{{1,4,5,8},{2,6,7},{3}}
[4,7,3,8,1,2,5,6]=>{{1,2,4,5,6,7,8},{3}}
[5,7,8,3,1,2,4,6]=>{{1,5},{2,3,4,6,7,8}}
[5,7,8,3,1,2,6,4]=>{{1,5},{2,6,7},{3,4,8}}
[5,7,8,3,1,4,2,6]=>{{1,5},{2,7},{3,4,6,8}}
[5,6,8,3,2,1,4,7]=>{{1,2,5,6},{3,4,7,8}}
[3,2,7,8,1,5,4,6]=>{{1,3,4,5,6,7,8},{2}}
[5,7,8,2,1,4,3,6]=>{{1,5},{2,3,4,6,7,8}}
[6,7,8,1,3,4,2,5]=>{{1,4,6},{2,7},{3,5,8}}
[6,7,8,1,4,3,2,5]=>{{1,3,4,5,6,8},{2,7}}
[6,7,8,1,4,2,5,3]=>{{1,2,4,5,6,7},{3,8}}
[6,7,8,1,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,1,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,1,2,5,4,3]=>{{1,2,4,5,6,7},{3,8}}
[6,7,8,1,2,4,5,3]=>{{1,4,6},{2,5,7},{3,8}}
[6,7,8,1,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,2,1,3,6,4]=>{{1,5},{2,3,4,6,7,8}}
[3,2,7,8,1,4,6,5]=>{{1,3,4,5,6,7,8},{2}}
[6,7,8,1,3,2,4,5]=>{{1,2,4,6,7},{3,5,8}}
[6,7,8,1,2,4,3,5]=>{{1,4,6},{2,3,5,7,8}}
[6,7,8,1,2,3,5,4]=>{{1,3,4,6,8},{2,5,7}}
[7,2,8,5,1,6,4,3]=>{{1,4,5,7},{2},{3,8},{6}}
[1,3,7,5,2,6,4,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,3,7,5,4,2,6,8]=>{{1},{2,3,6,7},{4,5},{8}}
[7,2,8,5,4,1,6,3]=>{{1,6,7},{2},{3,8},{4,5}}
[2,8,5,4,3,1,7,6]=>{{1,2,6,8},{3,5},{4},{7}}
[2,8,4,5,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,8,6,5,7,3,1,4]=>{{1,2,4,5,7,8},{3,6}}
[2,8,4,5,3,7,1,6]=>{{1,2,6,7,8},{3,4,5}}
[2,8,4,3,5,6,1,7]=>{{1,2,7,8},{3,4},{5},{6}}
[7,2,8,4,5,6,1,3]=>{{1,7},{2},{3,8},{4},{5},{6}}
[1,6,3,7,5,2,4,8]=>{{1},{2,6},{3},{4,7},{5},{8}}
[6,2,3,8,5,1,7,4]=>{{1,6},{2},{3},{4,8},{5},{7}}
[6,3,2,8,5,1,4,7]=>{{1,6},{2,3},{4,7,8},{5}}
[7,4,8,2,5,6,3,1]=>{{1,3,7,8},{2,4},{5},{6}}
[7,4,8,5,2,1,3,6]=>{{1,3,6,7,8},{2,4,5}}
[6,4,8,5,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[6,3,7,5,2,1,8,4]=>{{1,6},{2,3,4,5,7,8}}
[4,3,7,5,1,2,8,6]=>{{1,4,5},{2,3,6,7,8}}
[4,3,7,1,5,6,8,2]=>{{1,4},{2,3,7,8},{5},{6}}
[3,6,1,7,5,2,8,4]=>{{1,3},{2,6},{4,7,8},{5}}
[3,4,1,2,7,6,8,5]=>{{1,3},{2,4},{5,7,8},{6}}
[3,4,2,1,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}
[3,6,5,7,1,4,8,2]=>{{1,3,5},{2,4,6,7,8}}
[6,5,2,7,4,1,8,3]=>{{1,6},{2,3,4,5,7,8}}
[3,5,2,6,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,3,1,8,6,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[5,6,1,8,7,2,4,3]=>{{1,3,4,5,7,8},{2,6}}
[6,3,5,8,2,7,4,1]=>{{1,4,6,7,8},{2,3,5}}
[6,5,8,4,2,3,7,1]=>{{1,3,6,8},{2,5},{4},{7}}
[6,2,5,8,3,7,1,4]=>{{1,6,7},{2},{3,5},{4,8}}
[1,6,5,7,3,4,2,8]=>{{1},{2,4,6,7},{3,5},{8}}
[1,5,2,7,4,6,3,8]=>{{1},{2,3,4,5,7},{6},{8}}
[5,2,1,8,7,6,3,4]=>{{1,3,5,7},{2},{4,8},{6}}
[7,1,3,8,4,6,2,5]=>{{1,2,7},{3},{4,5,8},{6}}
[2,3,4,8,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,3,4,8,6,5,1,7]=>{{1,2,3,4,7,8},{5,6}}
[2,7,3,5,8,6,1,4]=>{{1,2,7},{3},{4,5,8},{6}}
[3,2,4,7,8,6,1,5]=>{{1,3,4,7},{2},{5,8},{6}}
[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[5,2,4,7,1,8,3,6]=>{{1,5},{2},{3,4,7},{6,8}}
[5,3,6,4,1,8,7,2]=>{{1,5},{2,3,6,8},{4},{7}}
[5,3,6,1,4,8,2,7]=>{{1,4,5},{2,3,6,7,8}}
[7,3,5,6,8,4,2,1]=>{{1,2,3,5,7,8},{4,6}}
[6,3,5,1,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,6,1,5,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,7,6,5,8,3,4,1]=>{{1,2,4,5,7,8},{3,6}}
[5,7,1,6,3,8,4,2]=>{{1,3,5},{2,4,6,7,8}}
[3,2,4,1,7,8,5,6]=>{{1,3,4},{2},{5,7},{6,8}}
[3,1,4,2,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}
[5,1,4,7,2,8,6,3]=>{{1,2,5},{3,4,6,7,8}}
[3,6,4,7,8,2,5,1]=>{{1,3,4,5,7,8},{2,6}}
[3,1,4,6,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[6,3,4,5,7,1,8,2]=>{{1,6},{2,3,4,5,7,8}}
[2,5,4,6,1,7,8,3]=>{{1,2,5},{3,4,6,7,8}}
[7,2,1,4,3,6,5,8]=>{{1,3,5,7},{2},{4},{6},{8}}
[7,3,4,1,2,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[7,4,3,2,1,6,5,8]=>{{1,5,7},{2,4},{3},{6},{8}}
[7,6,3,2,5,4,1,8]=>{{1,7},{2,4,6},{3},{5},{8}}
[6,7,3,2,5,4,8,1]=>{{1,2,4,6,7,8},{3},{5}}
[1,8,3,2,5,4,7,6]=>{{1},{2,4,6,8},{3},{5},{7}}
[1,8,4,5,2,3,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[7,3,5,1,6,2,4,8]=>{{1,4,7},{2,3,5,6},{8}}
[7,2,1,5,6,3,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[7,2,1,6,5,4,3,8]=>{{1,3,7},{2},{4,6},{5},{8}}
[7,3,6,1,5,4,2,8]=>{{1,2,3,4,6,7},{5},{8}}
[7,4,6,5,1,3,2,8]=>{{1,2,4,5,7},{3,6},{8}}
[1,8,5,4,3,2,7,6]=>{{1},{2,6,8},{3,5},{4},{7}}
[1,8,6,4,3,7,2,5]=>{{1},{2,3,5,6,7,8},{4}}
[6,5,7,4,3,1,8,2]=>{{1,6},{2,3,5,7,8},{4}}
[6,4,7,5,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,1,5,4,8,2]=>{{1,4,6},{2,3,7,8},{5}}
[6,2,1,7,5,4,8,3]=>{{1,3,4,6,7,8},{2},{5}}
[3,2,1,8,5,4,7,6]=>{{1,3},{2},{4,6,8},{5},{7}}
[2,3,8,1,5,4,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[2,5,8,4,3,1,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[2,6,8,4,3,7,1,5]=>{{1,2,6,7},{3,5,8},{4}}
[2,7,8,4,3,6,5,1]=>{{1,2,3,5,7,8},{4},{6}}
[1,8,7,4,3,6,5,2]=>{{1},{2,8},{3,5,7},{4},{6}}
[1,8,7,5,6,3,4,2]=>{{1},{2,8},{3,4,5,6,7}}
[2,7,8,5,6,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,6,8,5,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,8,6,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,6,1,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[3,2,1,8,6,7,4,5]=>{{1,3},{2},{4,5,6,7,8}}
[5,3,7,1,6,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,7,6,1,8,3,2]=>{{1,5},{2,4,6,8},{3,7}}
[4,5,7,6,8,1,3,2]=>{{1,4,6},{2,5,8},{3,7}}
[4,6,7,5,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,8,6,5,7,3,2,4]=>{{1},{2,4,5,7,8},{3,6}}
[1,8,5,6,7,2,3,4]=>{{1},{2,4,6,8},{3,5,7}}
[4,6,5,7,8,2,1,3]=>{{1,4,7},{2,6},{3,5,8}}
[5,4,6,7,1,8,2,3]=>{{1,5},{2,4,7},{3,6,8}}
[5,3,6,1,7,8,2,4]=>{{1,2,3,4,5,6,7,8}}
[5,2,1,6,7,8,3,4]=>{{1,3,5,7},{2},{4,6,8}}
[6,2,1,5,7,3,8,4]=>{{1,3,6},{2},{4,5,7,8}}
[6,3,5,1,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[6,4,5,7,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,7,2,1,8,3]=>{{1,6},{2,5},{3,4,7,8}}
[5,6,4,7,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[1,8,4,6,2,7,3,5]=>{{1},{2,5,8},{3,4,6,7}}
[1,8,3,2,6,7,4,5]=>{{1},{2,4,5,6,7,8},{3}}
[5,7,3,2,6,8,4,1]=>{{1,5,6,8},{2,4,7},{3}}
[5,6,3,2,7,8,1,4]=>{{1,5,7},{2,4,6,8},{3}}
[6,5,3,2,7,1,8,4]=>{{1,6},{2,4,5,7,8},{3}}
[6,4,3,2,1,7,8,5]=>{{1,5,6,7,8},{2,4},{3}}
[6,2,1,4,3,7,8,5]=>{{1,3,5,6,7,8},{2},{4}}
[4,6,3,2,8,7,1,5]=>{{1,2,4,6,7},{3},{5,8}}
[4,7,3,2,8,6,5,1]=>{{1,2,4,5,7,8},{3},{6}}
[1,8,3,2,7,6,5,4]=>{{1},{2,4,8},{3},{5,7},{6}}
[1,8,4,7,2,6,5,3]=>{{1},{2,3,4,5,7,8},{6}}
[3,6,4,8,2,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,4,5,8,1,2,7,6]=>{{1,3,5},{2,4,6,8},{7}}
[4,3,5,1,8,2,7,6]=>{{1,4},{2,3,5,6,8},{7}}
[4,2,1,5,8,3,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[4,2,1,6,8,7,3,5]=>{{1,3,4,6,7},{2},{5,8}}
[3,4,6,8,1,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,8,7,1,2,4]=>{{1,3,6},{2,5,7},{4,8}}
[3,6,5,8,7,2,1,4]=>{{1,3,5,7},{2,6},{4,8}}
[1,8,5,7,6,2,4,3]=>{{1},{2,3,5,6,8},{4,7}}
[1,8,6,7,5,4,2,3]=>{{1},{2,3,4,6,7,8},{5}}
[3,6,7,8,5,4,1,2]=>{{1,3,7},{2,4,6,8},{5}}
[3,5,7,8,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,8,1,6,5,2]=>{{1,3,5,7},{2,4,8},{6}}
[4,2,1,7,8,6,5,3]=>{{1,3,4,5,7,8},{2},{6}}
[2,3,8,1,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}
[2,4,8,7,1,6,5,3]=>{{1,2,4,5,7},{3,8},{6}}
[7,4,6,1,8,3,5,2]=>{{1,2,4,5,7,8},{3,6}}
[8,3,5,1,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,1,7,5,6,2]=>{{1,2,3,4,8},{5,6,7}}
[4,8,3,1,7,5,6,2]=>{{1,4},{2,8},{3},{5,6,7}}
[4,6,2,1,7,5,8,3]=>{{1,4},{2,3,5,6,7,8}}
[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,7,5,2,6,8,4,3]=>{{1},{2,4,7},{3,5,6,8}}
[7,5,2,1,6,8,4,3]=>{{1,4,7},{2,3,5,6,8}}
[6,8,4,3,1,7,5,2]=>{{1,5,6,7},{2,8},{3,4}}
[3,6,8,4,1,7,5,2]=>{{1,2,3,5,6,7,8},{4}}
[3,6,7,5,1,8,4,2]=>{{1,3,4,5,7},{2,6,8}}
[7,5,6,1,8,3,4,2]=>{{1,4,7},{2,5,8},{3,6}}
[3,4,6,5,7,1,8,2]=>{{1,3,6},{2,4,5,7,8}}
[4,7,5,6,1,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,5,1,8,4,3,2]=>{{1,4,6},{2,3,5,7,8}}
[6,8,4,1,7,5,3,2]=>{{1,3,4,5,6,7},{2,8}}
[6,7,5,3,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,1,6,7,5,3]=>{{1,2,3,4,8},{5,6,7}}
[1,8,4,2,6,7,5,3]=>{{1},{2,3,4,8},{5,6,7}}
[1,5,3,2,7,6,8,4]=>{{1},{2,4,5,7,8},{3},{6}}
[5,3,2,1,7,6,8,4]=>{{1,4,5,7,8},{2,3},{6}}
[2,5,3,1,7,6,8,4]=>{{1,2,4,5,7,8},{3},{6}}
[2,8,4,1,6,7,5,3]=>{{1,2,3,4,8},{5,6,7}}
[2,7,5,1,6,8,4,3]=>{{1,2,4,7},{3,5,6,8}}
[2,4,6,1,7,5,8,3]=>{{1,2,4},{3,5,6,7,8}}
[4,7,1,6,5,8,2,3]=>{{1,3,4,6,8},{2,7},{5}}
[4,8,2,6,5,7,1,3]=>{{1,4,6,7},{2,3,8},{5}}
[4,6,1,2,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,2,6,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,2,6,7,5,3]=>{{1,3,8},{2,4},{5,6,7}}
[5,3,1,2,7,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[1,2,5,3,7,6,8,4]=>{{1},{2},{3,4,5,7,8},{6}}
[4,3,1,2,7,6,8,5]=>{{1,2,3,4},{5,7,8},{6}}
[3,5,1,2,7,6,8,4]=>{{1,3},{2,4,5,7,8},{6}}
[6,7,1,5,8,2,3,4]=>{{1,2,3,6,7},{4,5,8}}
[2,7,6,1,5,8,3,4]=>{{1,2,3,4,6,7,8},{5}}
[2,3,5,1,7,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[7,6,1,5,8,3,2,4]=>{{1,2,3,6,7},{4,5,8}}
[3,6,7,1,5,8,2,4]=>{{1,2,3,4,6,7,8},{5}}
[7,1,6,5,8,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,6,8,4,2,3]=>{{1,2,3,5,7,8},{4,6}}
[8,4,1,6,7,5,2,3]=>{{1,3,8},{2,4,5,6,7}}
[5,2,3,1,7,6,8,4]=>{{1,4,5,7,8},{2},{3},{6}}
[3,5,2,1,7,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[1,3,5,2,7,6,8,4]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,6,2,5,8,3,4]=>{{1},{2,3,4,6,7,8},{5}}
[7,6,2,1,5,8,3,4]=>{{1,2,3,4,6,7,8},{5}}
[8,3,1,5,7,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[6,2,4,1,7,5,8,3]=>{{1,3,4,5,6,7,8},{2}}
[6,2,5,1,7,4,8,3]=>{{1,4,6},{2},{3,5,7,8}}
[7,1,6,4,8,2,5,3]=>{{1,2,3,5,6,7,8},{4}}
[8,2,6,4,7,1,5,3]=>{{1,3,6,8},{2},{4},{5,7}}
[6,1,5,2,7,4,8,3]=>{{1,2,4,6},{3,5,7,8}}
[7,6,2,5,8,3,1,4]=>{{1,7},{2,3,6},{4,5,8}}
[8,3,5,7,6,2,1,4]=>{{1,4,7,8},{2,3,5,6}}
[1,8,3,5,7,6,2,4]=>{{1},{2,4,5,7,8},{3},{6}}
[1,5,2,3,7,6,8,4]=>{{1},{2,3,4,5,7,8},{6}}
[5,2,1,3,7,6,8,4]=>{{1,3,4,5,7,8},{2},{6}}
[7,5,2,6,8,4,1,3]=>{{1,7},{2,3,5,8},{4,6}}
[8,4,2,6,7,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,1,4,2,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[8,2,6,5,7,1,4,3]=>{{1,3,6,8},{2},{4,5,7}}
[3,6,8,2,5,7,1,4]=>{{1,2,3,4,6,7,8},{5}}
[8,3,2,5,7,6,1,4]=>{{1,4,5,7,8},{2,3},{6}}
[5,1,3,2,7,6,8,4]=>{{1,2,4,5,7,8},{3},{6}}
[4,1,3,2,7,6,8,5]=>{{1,2,4},{3},{5,7,8},{6}}
[4,2,1,3,7,6,8,5]=>{{1,3,4},{2},{5,7,8},{6}}
[1,4,2,3,7,6,8,5]=>{{1},{2,3,4},{5,7,8},{6}}
[2,4,1,3,7,6,8,5]=>{{1,2,3,4},{5,7,8},{6}}
[2,5,1,3,7,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[2,8,3,5,7,6,1,4]=>{{1,2,4,5,7,8},{3},{6}}
[6,8,2,3,5,7,1,4]=>{{1,6,7},{2,3,4,8},{5}}
[6,7,1,3,5,8,2,4]=>{{1,3,4,6,8},{2,7},{5}}
[8,3,5,7,6,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,2,3,7,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[3,1,2,4,7,6,8,5]=>{{1,2,3},{4},{5,7,8},{6}}
[8,1,2,4,3,6,5,7]=>{{1,2,3,5,7,8},{4},{6}}
[8,1,3,5,6,2,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[8,1,3,4,2,6,7,5]=>{{1,2,5,8},{3},{4},{6},{7}}
[8,1,3,2,4,5,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[2,7,8,3,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[2,6,3,8,4,5,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[6,3,2,1,4,5,8,7]=>{{1,4,5,6},{2,3},{7,8}}
[7,3,1,4,2,6,8,5]=>{{1,2,3,5,7,8},{4},{6}}
[7,4,1,5,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,5,6,1,2,3]=>{{1,4,5,6},{2,7},{3,8}}
[3,7,8,5,6,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,4,2,6,1,5]=>{{1,2,3,5,7,8},{4},{6}}
[3,7,8,2,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[3,6,2,8,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,6,7,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,4,8,6,1,7]=>{{1,2,3,5,7,8},{4},{6}}
[3,5,4,2,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,8,7,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,4,5,1,7,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,2,3,8,5,6]=>{{1,3,5,7},{2,4},{6,8}}
[6,2,4,1,3,7,5,8]=>{{1,3,4,5,6,7},{2},{8}}
[2,6,4,8,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[2,6,5,8,7,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,2,5,1,7,3,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[6,5,2,1,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,7,8,3,4,1]=>{{1,2,5,8},{3,6},{4,7}}
[2,4,6,7,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,2,6,7,3,1,5,8]=>{{1,3,4,5,6,7},{2},{8}}
[4,7,8,2,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,3,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[5,6,4,8,1,7,2,3]=>{{1,5},{2,6,7},{3,4,8}}
[5,6,3,8,1,2,7,4]=>{{1,5},{2,6},{3},{4,8},{7}}
[4,2,5,3,7,1,6,8]=>{{1,3,4,5,6,7},{2},{8}}
[4,3,6,7,2,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,4,6,7,2,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,4,5,2,7,8,1,6]=>{{1,3,5,7},{2,4},{6,8}}
[3,4,2,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,2,7,8,6,4,1,3]=>{{1,3,4,5,6,7,8},{2}}
[5,1,2,7,8,6,4,3]=>{{1,2,3,5,8},{4,7},{6}}
[4,7,1,8,6,5,2,3]=>{{1,3,4,8},{2,7},{5,6}}
[4,7,1,2,8,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[4,6,8,1,2,7,5,3]=>{{1,4},{2,5,6,7},{3,8}}
[6,8,7,1,5,3,2,4]=>{{1,2,3,4,6,7,8},{5}}
[6,8,7,3,5,1,2,4]=>{{1,6},{2,3,4,7,8},{5}}
[7,8,1,6,3,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,3,6,5,2,4]=>{{1,2,3,4,7,8},{5,6}}
[7,8,3,6,5,2,1,4]=>{{1,7},{2,4,6,8},{3},{5}}
[4,7,2,8,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,7,3,4,8,6,5,2]=>{{1},{2,5,7,8},{3},{4},{6}}
[4,2,7,1,8,6,5,3]=>{{1,4},{2},{3,5,7,8},{6}}
[7,8,2,3,6,5,1,4]=>{{1,7},{2,3,4,8},{5,6}}
[8,5,7,1,6,2,3,4]=>{{1,4,8},{2,5,6},{3,7}}
[8,5,7,1,2,6,3,4]=>{{1,4,8},{2,5},{3,7},{6}}
[6,8,2,7,1,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,2,5,3,1,4]=>{{1,3,6,7},{2,4,8},{5}}
[6,2,4,8,7,1,5,3]=>{{1,6},{2},{3,4,8},{5,7}}
[1,6,8,3,7,4,5,2]=>{{1},{2,3,4,6,8},{5,7}}
[1,6,8,3,4,7,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,4,8,1,7,5,3]=>{{1,5,6,7},{2},{3,4,8}}
[6,8,7,2,3,5,1,4]=>{{1,3,5,6,7},{2,4,8}}
[6,8,2,1,7,3,5,4]=>{{1,2,3,4,6,8},{5,7}}
[8,5,7,2,1,6,3,4]=>{{1,2,4,5,8},{3,7},{6}}
[8,5,7,1,2,3,6,4]=>{{1,4,8},{2,5},{3,6,7}}
[8,7,6,2,1,4,3,5]=>{{1,5,8},{2,3,4,6,7}}
[8,5,7,2,3,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,2,7,1,6,3]=>{{1,5,6,7},{2,3,4,8}}
[1,8,7,5,3,4,6,2]=>{{1},{2,8},{3,4,5,6,7}}
[1,8,7,3,5,4,6,2]=>{{1},{2,8},{3,4,6,7},{5}}
[8,2,5,4,7,1,6,3]=>{{1,3,5,6,7,8},{2},{4}}
[8,5,2,7,3,1,6,4]=>{{1,4,6,7,8},{2,3,5}}
[8,7,6,2,4,3,1,5]=>{{1,2,4,5,7,8},{3,6}}
[8,7,6,1,2,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,1,4,2,3,5]=>{{1,4,5,8},{2,3,6,7}}
[8,7,6,4,1,3,2,5]=>{{1,5,8},{2,7},{3,6},{4}}
[5,8,4,7,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,5,4,3,6,2]=>{{1},{2,8},{3,6,7},{4,5}}
[1,6,8,4,3,7,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[6,8,7,3,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[6,8,1,7,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,3,1,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[8,5,7,1,3,2,6,4]=>{{1,4,8},{2,3,5,6,7}}
[8,5,7,3,1,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,7,1,2,6,3]=>{{1,5},{2,3,4,6,7,8}}
[5,8,4,1,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,7,1,6,2,3]=>{{1,5},{2,3,4,7,8},{6}}
[8,1,2,6,5,7,4,3]=>{{1,2,3,8},{4,6,7},{5}}
[8,2,5,6,7,4,1,3]=>{{1,3,5,7,8},{2},{4,6}}
[4,8,5,7,1,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[4,8,5,7,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,1,7,2,6,3]=>{{1,4},{2,3,5,6,7,8}}
[8,5,3,1,7,2,6,4]=>{{1,4,8},{2,5,6,7},{3}}
[8,5,3,7,1,2,6,4]=>{{1,2,4,5,6,7,8},{3}}
[6,8,1,3,7,2,5,4]=>{{1,2,3,4,6,8},{5,7}}
[4,6,2,8,1,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,8,3,7,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,4,5,3,6,2]=>{{1},{2,8},{3,6,7},{4},{5}}
[4,8,5,7,2,1,6,3]=>{{1,4,6,7},{2,3,5,8}}
[8,5,3,7,2,1,6,4]=>{{1,4,6,7,8},{2,5},{3}}
[8,7,6,3,1,4,2,5]=>{{1,5,8},{2,7},{3,4,6}}
[8,7,6,1,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,2,7,1,6,4]=>{{1,2,4,5,6,7,8},{3}}
[4,8,5,2,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,4,3,5,6,2]=>{{1},{2,8},{3,5,6,7},{4}}
[1,8,7,3,4,5,6,2]=>{{1},{2,8},{3,4,5,6,7}}
[8,2,4,5,7,1,6,3]=>{{1,3,4,5,6,7,8},{2}}
[8,5,2,3,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,5,4,2,8,7]=>{{1,2,3,6},{4,5},{7,8}}
[8,3,1,5,2,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[8,5,4,2,1,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,2,1,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[6,5,4,2,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[6,5,4,2,3,1,8,7]=>{{1,6},{2,3,4,5},{7,8}}
[6,3,2,5,1,4,8,7]=>{{1,4,5,6},{2,3},{7,8}}
[6,5,4,3,1,2,8,7]=>{{1,2,5,6},{3,4},{7,8}}
[6,5,4,1,3,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[8,5,4,1,2,7,6,3]=>{{1,3,4,8},{2,5},{6,7}}
[8,7,4,1,6,3,2,5]=>{{1,3,4,5,6,8},{2,7}}
[8,7,4,1,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,1,6,5,3,2]=>{{1,2,3,4,7,8},{5,6}}
[8,5,4,1,3,7,6,2]=>{{1,2,3,4,5,8},{6,7}}
[8,5,4,3,1,7,6,2]=>{{1,2,5,8},{3,4},{6,7}}
[8,3,2,5,1,7,6,4]=>{{1,4,5,8},{2,3},{6,7}}
[2,1,8,5,3,7,6,4]=>{{1,2},{3,4,5,8},{6,7}}
[8,3,2,5,1,7,4,6]=>{{1,4,5,6,7,8},{2,3}}
[8,5,4,3,1,7,2,6]=>{{1,2,5,6,7,8},{3,4}}
[8,5,4,1,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,1,6,5,2,3]=>{{1,3,4,8},{2,7},{5,6}}
[8,7,4,1,6,2,5,3]=>{{1,3,4,8},{2,5,6,7}}
[8,7,6,5,2,1,4,3]=>{{1,3,6,8},{2,4,5,7}}
[8,7,4,3,6,2,1,5]=>{{1,2,5,6,7,8},{3,4}}
[8,3,2,7,6,4,1,5]=>{{1,4,5,6,7,8},{2,3}}
[2,1,8,7,6,4,3,5]=>{{1,2},{3,4,5,6,7,8}}
[2,1,8,7,6,4,5,3]=>{{1,2},{3,8},{4,5,6,7}}
[8,3,2,7,6,4,5,1]=>{{1,8},{2,3},{4,5,6,7}}
[8,7,4,3,6,2,5,1]=>{{1,8},{2,5,6,7},{3,4}}
[8,7,6,5,2,4,3,1]=>{{1,8},{2,3,4,5,6,7}}
[8,5,4,2,3,7,6,1]=>{{1,8},{2,3,4,5},{6,7}}
[8,7,4,2,6,5,3,1]=>{{1,8},{2,3,4,7},{5,6}}
[8,7,4,2,6,3,5,1]=>{{1,8},{2,3,4,5,6,7}}
[8,7,4,2,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,7,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,7,6,4,5,2]=>{{1,2,3,8},{4,5,6,7}}
[8,3,1,7,6,5,4,2]=>{{1,2,3,8},{4,7},{5,6}}
[8,3,1,5,4,7,6,2]=>{{1,2,3,8},{4,5},{6,7}}
[8,3,1,5,4,7,2,6]=>{{1,2,3,6,7,8},{4,5}}
[8,3,1,7,6,5,2,4]=>{{1,2,3,4,7,8},{5,6}}
[8,3,1,7,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,2,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,2,6,5,1,3]=>{{1,2,3,4,7,8},{5,6}}
[8,5,4,2,3,7,1,6]=>{{1,6,7,8},{2,3,4,5}}
[8,3,2,5,4,7,1,6]=>{{1,6,7,8},{2,3},{4,5}}
[2,1,8,5,4,7,3,6]=>{{1,2},{3,6,7,8},{4,5}}
[8,3,2,7,6,5,1,4]=>{{1,4,7,8},{2,3},{5,6}}
[8,7,4,3,6,5,1,2]=>{{1,2,7,8},{3,4},{5,6}}
[8,7,6,5,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,5,1,3,2,4]=>{{1,4,5,8},{2,7},{3,6}}
[8,7,6,5,1,3,4,2]=>{{1,2,4,5,7,8},{3,6}}
[8,7,6,5,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,5,4,1,3,2]=>{{1,2,3,6,7,8},{4,5}}
[8,7,4,3,6,1,5,2]=>{{1,2,5,6,7,8},{3,4}}
[8,3,2,7,6,1,5,4]=>{{1,4,5,6,7,8},{2,3}}
[2,1,8,7,6,3,5,4]=>{{1,2},{3,4,5,6,7,8}}
[8,3,2,7,6,1,4,5]=>{{1,5,6,8},{2,3},{4,7}}
[8,7,6,5,1,4,2,3]=>{{1,3,4,5,6,8},{2,7}}
[8,7,6,5,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[7,3,5,1,8,4,6,2]=>{{1,4,6,7},{2,3,5,8}}
[7,3,4,1,8,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,2,1,8,7,3]=>{{1,2,4,5},{3,6,8},{7}}
[1,6,5,2,7,4,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[7,4,3,1,8,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}
[7,6,5,1,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,4,1,8,5,3,2]=>{{1,3,4,7},{2,5,6,8}}
[6,4,2,1,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,2,7,5,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,5,3,2,7,6,4,8]=>{{1},{2,4,5,7},{3},{6},{8}}
[5,3,2,1,8,7,6,4]=>{{1,4,5,8},{2,3},{6,7}}
[2,5,3,1,7,8,6,4]=>{{1,2,4,5,6,7,8},{3}}
[2,6,4,1,7,8,5,3]=>{{1,2,3,4,6,8},{5,7}}
[2,6,5,1,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[4,5,7,1,6,8,2,3]=>{{1,4},{2,3,5,6,7,8}}
[6,5,1,2,8,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,2,8,5,3,7]=>{{1,3,5,6,7,8},{2,4}}
[5,3,1,2,8,6,4,7]=>{{1,2,3,4,5,7,8},{6}}
[4,3,1,2,8,6,5,7]=>{{1,2,3,4},{5,7,8},{6}}
[6,1,2,5,8,3,4,7]=>{{1,2,3,6},{4,5,7,8}}
[7,1,3,4,8,2,5,6]=>{{1,2,5,6,7,8},{3},{4}}
[7,1,5,6,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[2,6,1,5,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,6,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,2,3,1,8,6,7,4]=>{{1,4,5,8},{2},{3},{6},{7}}
[3,5,2,1,6,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[1,6,2,5,7,3,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[6,2,1,5,8,7,3,4]=>{{1,3,6,7},{2},{4,5,8}}
[7,3,1,5,8,6,2,4]=>{{1,2,3,7},{4,5,8},{6}}
[6,2,4,1,8,5,7,3]=>{{1,3,4,5,6,8},{2},{7}}
[6,2,5,1,8,4,7,3]=>{{1,4,6},{2},{3,5,8},{7}}
[7,3,1,4,8,6,2,5]=>{{1,2,3,7},{4},{5,8},{6}}
[6,2,1,4,8,7,3,5]=>{{1,3,6,7},{2},{4},{5,8}}
[1,6,2,4,7,3,5,8]=>{{1},{2,3,6},{4},{5,7},{8}}
[5,2,1,3,8,7,4,6]=>{{1,3,4,5,6,7,8},{2}}
[7,4,1,3,8,5,2,6]=>{{1,2,3,4,7},{5,6,8}}
[7,5,1,3,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,1,4,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[7,6,1,4,8,3,2,5]=>{{1,2,3,6,7},{4},{5,8}}
[4,2,1,3,8,7,5,6]=>{{1,3,4},{2},{5,6,7,8}}
[2,6,1,4,7,8,3,5]=>{{1,2,3,5,6,7,8},{4}}
[7,1,4,6,8,2,3,5]=>{{1,2,3,4,6,7},{5,8}}
[7,1,3,5,8,2,4,6]=>{{1,2,4,5,6,7,8},{3}}
[6,1,2,4,8,3,5,7]=>{{1,2,3,6},{4},{5,7,8}}
[5,2,3,1,6,4,8,7]=>{{1,4,5,6},{2},{3},{7,8}}
[7,4,5,2,3,1,8,6]=>{{1,6,7,8},{2,4},{3,5}}
[8,6,7,3,5,2,4,1]=>{{1,8},{2,6},{3,4,7},{5}}
[7,3,5,2,4,1,8,6]=>{{1,6,7,8},{2,3,4,5}}
[6,3,5,2,4,1,8,7]=>{{1,6},{2,3,4,5},{7,8}}
[5,2,4,1,6,3,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[4,1,6,3,5,2,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[6,3,4,1,5,2,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[5,2,6,3,4,1,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[5,2,7,3,4,1,8,6]=>{{1,3,4,5,6,7,8},{2}}
[5,2,8,6,7,3,4,1]=>{{1,3,4,5,6,7,8},{2}}
[6,2,8,5,7,3,4,1]=>{{1,3,6,8},{2},{4,5,7}}
[6,2,7,3,4,1,8,5]=>{{1,6},{2},{3,4,5,7,8}}
[7,3,4,1,5,2,8,6]=>{{1,2,3,4,6,7,8},{5}}
[4,1,7,3,5,2,8,6]=>{{1,2,3,4,6,7,8},{5}}
[3,1,7,4,5,2,8,6]=>{{1,2,3,6,7,8},{4},{5}}
[2,1,7,4,5,3,8,6]=>{{1,2},{3,6,7,8},{4},{5}}
[3,1,8,6,7,4,5,2]=>{{1,2,3,8},{4,6},{5,7}}
[4,1,8,6,7,3,5,2]=>{{1,2,3,4,6,8},{5,7}}
[8,6,7,3,4,1,5,2]=>{{1,2,6,8},{3,4,5,7}}
[8,5,7,3,4,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,2,7,3,4,1]=>{{1,8},{2,4,5,7},{3,6}}
[8,4,7,3,5,1,6,2]=>{{1,2,3,4,6,7,8},{5}}
[5,1,8,4,7,3,6,2]=>{{1,2,3,5,6,7,8},{4}}
[4,1,8,5,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,5,7,4,6,2]=>{{1,2,3,8},{4,5,6,7}}
[2,1,8,5,7,4,6,3]=>{{1,2},{3,8},{4,5,6,7}}
[2,1,7,4,6,3,8,5]=>{{1,2},{3,5,6,7,8},{4}}
[3,1,7,4,6,2,8,5]=>{{1,2,3,5,6,7,8},{4}}
[4,1,7,3,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,1,7,3,6,2,8,4]=>{{1,2,5,6},{3,4,7,8}}
[6,2,7,3,5,1,8,4]=>{{1,6},{2},{3,4,7,8},{5}}
[6,2,8,4,7,3,5,1]=>{{1,3,6,8},{2},{4},{5,7}}
[8,4,7,3,6,2,5,1]=>{{1,8},{2,3,4,5,6,7}}
[7,3,6,2,5,1,8,4]=>{{1,2,3,4,6,7,8},{5}}
[6,2,5,1,7,3,8,4]=>{{1,3,4,5,6,7,8},{2}}
[5,2,4,1,7,3,8,6]=>{{1,3,4,5,6,7,8},{2}}
[6,2,4,1,7,3,8,5]=>{{1,3,4,6},{2},{5,7,8}}
[8,5,7,3,6,2,4,1]=>{{1,8},{2,5,6},{3,4,7}}
[8,5,7,4,6,2,3,1]=>{{1,8},{2,5,6},{3,7},{4}}
[7,4,6,2,3,1,8,5]=>{{1,3,5,6,7,8},{2,4}}
[6,2,3,1,7,4,8,5]=>{{1,4,6},{2},{3},{5,7,8}}
[5,2,3,1,7,4,8,6]=>{{1,4,5,6,7,8},{2},{3}}
[4,2,3,1,7,5,8,6]=>{{1,4},{2},{3},{5,6,7,8}}
[3,1,4,2,8,6,7,5]=>{{1,2,3,4},{5,8},{6},{7}}
[6,2,3,1,8,5,7,4]=>{{1,4,5,6,8},{2},{3},{7}}
[8,5,6,2,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[7,4,8,5,6,2,3,1]=>{{1,3,7,8},{2,4,5,6}}
[7,3,8,5,6,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,2,4,1,7,3]=>{{1,3,6,8},{2,4,5},{7}}
[5,2,4,1,8,6,7,3]=>{{1,3,4,5,8},{2},{6},{7}}
[4,1,5,2,8,6,7,3]=>{{1,2,4},{3,5,8},{6},{7}}
[3,1,5,2,8,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[2,1,6,3,8,5,7,4]=>{{1,2},{3,4,5,6,8},{7}}
[3,1,6,2,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[4,1,6,2,8,5,7,3]=>{{1,2,4},{3,5,6,8},{7}}
[5,1,6,2,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[8,4,6,2,5,1,7,3]=>{{1,3,6,8},{2,4},{5},{7}}
[7,3,8,4,6,2,5,1]=>{{1,2,3,5,6,7,8},{4}}
[6,2,7,3,8,4,5,1]=>{{1,3,4,5,6,7,8},{2}}
[8,4,5,1,6,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[5,1,8,4,6,2,7,3]=>{{1,2,5,6},{3,8},{4},{7}}
[4,1,8,5,6,2,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[3,1,8,5,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,1,8,5,6,3,7,4]=>{{1,2},{3,4,5,6,8},{7}}
[2,1,7,4,8,5,6,3]=>{{1,2},{3,5,6,7,8},{4}}
[3,1,7,4,8,5,6,2]=>{{1,2,3,5,6,7,8},{4}}
[4,1,7,3,8,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,4,5,1,6,2]=>{{1,6,7},{2,3,8},{4},{5}}
[8,4,5,1,7,3,6,2]=>{{1,2,4,8},{3,5,6,7}}
[7,3,6,2,8,4,5,1]=>{{1,5,7,8},{2,3,4,6}}
[7,8,5,6,1,3,4,2]=>{{1,3,4,5,6,7},{2,8}}
[7,8,1,3,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[1,3,8,4,7,2,5,6]=>{{1},{2,3,6,8},{4},{5,7}}
[3,6,1,4,7,2,5,8]=>{{1,3},{2,6},{4},{5,7},{8}}
[4,6,1,2,5,7,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[1,4,8,2,5,7,3,6]=>{{1},{2,4},{3,6,7,8},{5}}
[7,8,2,4,5,6,1,3]=>{{1,7},{2,3,8},{4},{5},{6}}
[7,8,1,5,4,6,3,2]=>{{1,3,7},{2,8},{4,5},{6}}
[7,8,2,1,6,3,4,5]=>{{1,4,7},{2,3,5,6,8}}
[7,8,3,5,6,4,1,2]=>{{1,7},{2,8},{3},{4,5,6}}
[7,8,1,4,2,3,6,5]=>{{1,3,6,7},{2,5,8},{4}}
[7,8,5,1,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,5,3,1,6,2]=>{{1,6,7},{2,8},{3,4,5}}
[1,5,8,4,3,2,7,6]=>{{1},{2,3,5,6,8},{4},{7}}
[5,6,1,4,3,2,7,8]=>{{1,3,5},{2,6},{4},{7},{8}}
[2,6,4,8,3,7,1,5]=>{{1,2,6,7},{3,4,5,8}}
[1,4,6,8,3,7,5,2]=>{{1},{2,4,8},{3,5,6,7}}
[2,4,8,5,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,5,8,1,4,7,6,3]=>{{1,2,4,5},{3,8},{6,7}}
[3,5,8,4,7,6,1,2]=>{{1,2,3,5,7,8},{4},{6}}
[1,6,2,4,7,3,8,5]=>{{1},{2,3,6},{4},{5,7,8}}
[5,6,2,1,4,7,8,3]=>{{1,4,5},{2,3,6,7,8}}
[4,6,2,5,3,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,7,5,1,3,6,8,2]=>{{1,4},{2,7,8},{3,5},{6}}
[7,5,3,6,2,4,1,8]=>{{1,7},{2,5},{3},{4,6},{8}}
[5,7,3,6,1,4,8,2]=>{{1,5},{2,7,8},{3},{4,6}}
[5,3,6,7,2,1,8,4]=>{{1,2,3,5,6},{4,7,8}}
[6,1,7,5,2,4,8,3]=>{{1,2,4,5,6},{3,7,8}}
[6,3,1,2,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[1,4,7,2,5,3,8,6]=>{{1},{2,4},{3,6,7,8},{5}}
[4,6,7,8,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,8,4,2,5,7]=>{{1,3},{2,6},{4,5,7,8}}
[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,5,6,7,8,1,4,2]=>{{1,3,6},{2,5,8},{4,7}}
[3,6,5,7,8,2,1,4]=>{{1,3,4,5,7,8},{2,6}}
[5,2,7,6,1,4,3,8]=>{{1,5},{2},{3,7},{4,6},{8}}
[2,5,7,6,8,1,3,4]=>{{1,2,4,5,6,8},{3,7}}
[2,7,5,6,8,4,1,3]=>{{1,2,7},{3,5,8},{4,6}}
[2,1,6,8,4,5,3,7]=>{{1,2},{3,4,5,6,7,8}}
[2,7,1,8,5,3,4,6]=>{{1,2,3,4,6,7,8},{5}}
[3,7,6,8,5,4,1,2]=>{{1,2,3,4,6,7,8},{5}}
[4,3,8,5,6,7,1,2]=>{{1,4,5,6,7},{2,3,8}}
[4,2,8,1,6,3,7,5]=>{{1,4},{2},{3,5,6,8},{7}}
[3,1,8,5,4,6,7,2]=>{{1,2,3,8},{4,5},{6},{7}}
[3,2,8,4,5,6,1,7]=>{{1,3,7,8},{2},{4},{5},{6}}
[3,4,2,8,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,4,7,1,5,2,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[4,3,7,8,1,2,6,5]=>{{1,4,5,8},{2,3,6,7}}
[1,7,3,8,5,2,6,4]=>{{1},{2,6,7},{3},{4,8},{5}}
[4,1,8,3,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,6,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,6,1,3,4,2]=>{{1,5},{2,3,4,6,7,8}}
[7,6,5,8,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,3,8,2,5,7]=>{{1},{2,6},{3,4},{5,7,8}}
[7,1,3,4,8,2,6,5]=>{{1,2,6,7},{3},{4},{5,8}}
[3,6,5,4,1,2,7,8]=>{{1,3,5},{2,6},{4},{7},{8}}
[2,4,5,1,7,8,6,3]=>{{1,2,4},{3,5,6,7,8}}
[2,6,3,4,5,8,1,7]=>{{1,2,6,7,8},{3},{4},{5}}
[2,6,4,1,8,3,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[7,3,6,4,8,5,1,2]=>{{1,7},{2,3,5,6,8},{4}}
[7,2,1,4,8,3,5,6]=>{{1,3,5,6,7,8},{2},{4}}
[7,1,6,5,3,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,2,5,6,3,8,1,4]=>{{1,7},{2},{3,5},{4,6,8}}
[6,5,2,7,1,8,4,3]=>{{1,2,3,5,6,8},{4,7}}
[5,6,2,7,3,1,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[5,6,7,4,2,8,1,3]=>{{1,2,3,5,6,7,8},{4}}
[5,7,6,4,1,8,3,2]=>{{1,5},{2,3,6,7,8},{4}}
[6,7,1,5,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,7,5,2,4,8,3,6]=>{{1},{2,3,4,5,7},{6,8}}
[6,1,5,2,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[6,7,5,3,8,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,6,5,4,2,3,8,7]=>{{1},{2,3,5,6},{4},{7,8}}
[7,1,5,3,4,2,8,6]=>{{1,2,6,7,8},{3,4,5}}
[7,6,1,5,3,2,8,4]=>{{1,3,4,5,7,8},{2,6}}
[7,5,6,4,1,2,8,3]=>{{1,2,3,5,6,7,8},{4}}
[6,7,5,4,3,1,8,2]=>{{1,6},{2,7,8},{3,5},{4}}
[7,5,2,4,3,1,6,8]=>{{1,6,7},{2,3,5},{4},{8}}
[7,4,6,1,2,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[7,1,4,2,5,3,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[6,8,1,4,2,5,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[1,6,4,2,5,7,3,8]=>{{1},{2,3,4,6,7},{5},{8}}
[1,6,3,7,5,4,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[6,8,1,3,7,5,4,2]=>{{1,3,4,5,6,7},{2,8}}
[7,1,3,5,6,4,2,8]=>{{1,2,7},{3},{4,5,6},{8}}
[7,3,1,6,4,5,2,8]=>{{1,2,3,7},{4,5,6},{8}}
[7,4,2,6,5,1,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[7,4,6,3,1,5,2,8]=>{{1,2,3,4,5,6,7},{8}}
[7,2,4,1,5,3,6,8]=>{{1,3,4,6,7},{2},{5},{8}}
[7,2,3,5,4,1,6,8]=>{{1,6,7},{2},{3},{4,5},{8}}
[6,8,1,2,3,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[1,5,7,2,3,8,6,4]=>{{1},{2,3,4,5,6,7,8}}
[5,1,8,2,3,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[5,8,2,3,7,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[6,2,8,1,3,7,4,5]=>{{1,4,6,7},{2},{3,5,8}}
[6,8,2,3,5,4,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[6,8,2,4,1,5,7,3]=>{{1,5,6},{2,3,8},{4},{7}}
[6,8,3,1,2,4,7,5]=>{{1,4,6},{2,5,8},{3},{7}}
[2,6,4,1,5,7,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,6,3,5,7,1,4,8]=>{{1,2,6},{3},{4,5,7},{8}}
[2,5,1,7,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,3,6,8,4,7,1]=>{{1,2,5,8},{3},{4,6},{7}}
[2,1,4,7,8,5,6,3]=>{{1,2},{3,4,5,6,7,8}}
[2,4,7,6,8,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,3,7,6,1,8,4]=>{{1,2,5,6},{3},{4,7,8}}
[2,5,7,8,1,4,6,3]=>{{1,2,5},{3,4,6,7,8}}
[3,5,7,4,1,6,2,8]=>{{1,2,3,5,7},{4},{6},{8}}
[5,3,4,1,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[5,2,8,4,6,1,7,3]=>{{1,5,6},{2},{3,8},{4},{7}}
[5,2,1,8,6,3,7,4]=>{{1,3,5,6},{2},{4,8},{7}}
[4,2,8,6,5,3,7,1]=>{{1,3,4,6,8},{2},{5},{7}}
[4,2,8,5,7,6,3,1]=>{{1,3,4,5,7,8},{2},{6}}
[1,4,2,7,5,8,6,3]=>{{1},{2,3,4,6,7,8},{5}}
[4,1,8,6,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,7,6,2,4,1]=>{{1,2,3,5,6,8},{4,7}}
[5,8,4,7,6,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,4,3,6,1,2]=>{{1,3,5,7},{2,8},{4},{6}}
[6,4,8,3,1,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[6,4,2,8,7,1,3,5]=>{{1,6},{2,3,4,5,7,8}}
[6,3,8,7,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,3,7,1,6,4,2]=>{{1,5},{2,8},{3},{4,7},{6}}
[5,1,3,8,6,7,2,4]=>{{1,2,5,6,7},{3},{4,8}}
[1,5,3,7,8,6,2,4]=>{{1},{2,4,5,7,8},{3},{6}}
[1,5,7,6,4,2,8,3]=>{{1},{2,4,5,6},{3,7,8}}
[5,8,7,4,1,6,2,3]=>{{1,5},{2,3,7,8},{4},{6}}
[6,4,8,1,2,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,1,2,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[6,8,5,2,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[6,8,5,3,1,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[4,5,1,2,7,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,5,1,2,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[3,5,6,1,8,4,7,2]=>{{1,3,4,6},{2,5,8},{7}}
[3,5,7,1,2,8,6,4]=>{{1,3,4,6,7,8},{2,5}}
[3,6,2,7,5,1,4,8]=>{{1,2,3,6},{4,7},{5},{8}}
[4,2,6,1,7,3,5,8]=>{{1,4},{2},{3,6},{5,7},{8}}
[4,6,3,1,2,7,5,8]=>{{1,4},{2,5,6,7},{3},{8}}
[4,5,3,1,7,6,2,8]=>{{1,4},{2,5,7},{3},{6},{8}}
[4,2,5,7,1,6,3,8]=>{{1,3,4,5,7},{2},{6},{8}}
[3,5,2,7,8,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,7,5,6,2,8]=>{{1,2,3,4,7},{5},{6},{8}}
[3,4,6,5,8,7,1,2]=>{{1,3,6,7},{2,4,5,8}}
[3,1,4,5,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[3,4,6,8,5,2,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[3,5,6,2,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,2,5,6,1,8,7,3]=>{{1,3,4,5,6,8},{2},{7}}
[4,5,3,1,6,8,7,2]=>{{1,4},{2,5,6,8},{3},{7}}
[2,1,7,5,8,6,4,3]=>{{1,2},{3,4,5,7,8},{6}}
[1,2,7,5,3,8,6,4]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,2,7,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,7,5,2,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[6,1,3,7,5,2,4,8]=>{{1,2,6},{3},{4,7},{5},{8}}
[3,1,2,6,8,5,4,7]=>{{1,2,3},{4,5,6,7,8}}
[3,7,1,2,5,4,8,6]=>{{1,3},{2,4,6,7,8},{5}}
[1,3,7,2,4,8,6,5]=>{{1},{2,3,4,5,6,7,8}}
[2,4,1,7,8,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[3,4,7,5,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[2,7,4,1,5,8,6,3]=>{{1,2,3,4,6,7,8},{5}}
[2,3,7,1,5,8,6,4]=>{{1,2,3,4,6,7,8},{5}}
[5,2,8,1,3,7,4,6]=>{{1,3,4,5,6,7,8},{2}}
[2,1,6,8,3,4,7,5]=>{{1,2},{3,4,5,6,8},{7}}
[2,6,8,3,1,5,7,4]=>{{1,2,5,6},{3,4,8},{7}}
[2,8,6,4,1,5,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[3,6,4,8,5,1,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[6,3,7,4,5,1,8,2]=>{{1,6},{2,3,7,8},{4},{5}}
[2,6,3,7,5,8,1,4]=>{{1,2,4,6,7,8},{3},{5}}
[5,2,1,7,8,3,4,6]=>{{1,3,5,6,8},{2},{4,7}}
[4,7,2,3,6,8,1,5]=>{{1,2,3,4,7},{5,6,8}}
[5,2,7,3,6,8,1,4]=>{{1,3,4,5,6,7,8},{2}}
[5,7,4,6,2,8,1,3]=>{{1,2,5,7},{3,4,6,8}}
[5,7,3,4,6,1,8,2]=>{{1,5,6},{2,7,8},{3},{4}}
[5,3,8,4,6,1,7,2]=>{{1,5,6},{2,3,8},{4},{7}}
[8,5,2,4,1,6,7,3]=>{{1,2,3,5,8},{4},{6},{7}}
[8,2,3,5,1,6,7,4]=>{{1,4,5,8},{2},{3},{6},{7}}
[4,2,8,3,6,7,1,5]=>{{1,3,4,5,6,7,8},{2}}
[2,4,8,1,7,3,5,6]=>{{1,2,4},{3,6,8},{5,7}}
[8,4,1,3,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,8,3,1,7,2,5,6]=>{{1,4},{2,6,8},{3},{5,7}}
[5,2,8,4,7,1,6,3]=>{{1,5,6,7},{2},{3,8},{4}}
[5,8,4,7,3,1,6,2]=>{{1,3,4,5,6,7},{2,8}}
[4,6,8,3,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,3,8,2,7,1,5,4]=>{{1,6},{2,3,4,8},{5,7}}
[6,3,1,8,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[5,3,8,1,2,6,4,7]=>{{1,2,3,4,5,7,8},{6}}
[5,7,4,1,6,2,3,8]=>{{1,2,3,4,5,6,7},{8}}
[8,5,4,1,2,6,3,7]=>{{1,3,4,7,8},{2,5},{6}}
[5,1,8,4,2,7,3,6]=>{{1,2,5},{3,6,7,8},{4}}
[1,6,2,8,5,3,7,4]=>{{1},{2,3,6},{4,8},{5},{7}}
[6,8,5,3,1,7,4,2]=>{{1,3,4,5,6,7},{2,8}}
[8,4,5,1,2,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[5,6,3,7,1,2,4,8]=>{{1,5},{2,6},{3},{4,7},{8}}
[1,6,3,7,2,8,4,5]=>{{1},{2,5,6,8},{3},{4,7}}
[6,3,2,7,8,5,1,4]=>{{1,4,5,6,7,8},{2,3}}
[4,5,7,8,3,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,7,2,5,8,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,1,3,4,6,2,5,7]=>{{1,2,5,6,7,8},{3},{4}}
[3,8,2,4,6,7,1,5]=>{{1,2,3,5,6,7,8},{4}}
[3,5,6,8,2,7,1,4]=>{{1,3,6,7},{2,5},{4,8}}
[2,4,5,6,8,1,7,3]=>{{1,2,4,6},{3,5,8},{7}}
[4,8,3,5,6,1,7,2]=>{{1,4,5,6},{2,8},{3},{7}}
[5,6,2,3,7,8,1,4]=>{{1,5,7},{2,3,4,6,8}}
[5,8,7,3,4,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,3,4,1,2,5]=>{{1,6},{2,3,4,5,7,8}}
[6,8,4,7,1,5,3,2]=>{{1,5,6},{2,8},{3,4,7}}
[6,8,4,7,2,5,3,1]=>{{1,2,5,6,8},{3,4,7}}
[5,4,8,7,2,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[5,4,8,7,1,6,3,2]=>{{1,5},{2,3,4,7,8},{6}}
[5,3,8,7,6,1,2,4]=>{{1,5,6},{2,3,4,7,8}}
[4,3,8,7,6,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,3,7,5,1,2,6]=>{{1,2,4,6,7,8},{3},{5}}
[8,3,4,6,5,1,2,7]=>{{1,2,3,4,6,7,8},{5}}
[3,8,4,7,5,1,2,6]=>{{1,2,3,4,6,7,8},{5}}
[3,4,8,7,6,1,2,5]=>{{1,3,5,6,8},{2,4,7}}
[3,5,8,7,6,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[4,5,8,7,6,1,2,3]=>{{1,2,4,5,6,7},{3,8}}
[4,5,8,7,1,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[4,5,8,7,2,6,3,1]=>{{1,3,4,7,8},{2,5},{6}}
[3,5,8,2,7,6,4,1]=>{{1,3,8},{2,4,5,7},{6}}
[3,5,8,1,7,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[2,5,8,1,7,6,4,3]=>{{1,2,4,5,7},{3,8},{6}}
[2,5,8,7,1,6,3,4]=>{{1,2,5},{3,4,7,8},{6}}
[2,4,8,7,1,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[2,8,4,7,1,5,3,6]=>{{1,2,5,6,8},{3,4,7}}
[8,2,4,6,1,5,3,7]=>{{1,3,4,5,6,7,8},{2}}
[8,1,4,6,2,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,8,4,7,2,5,3,6]=>{{1},{2,5,6,8},{3,4,7}}
[1,4,8,7,2,6,3,5]=>{{1},{2,3,4,5,7,8},{6}}
[1,5,8,7,2,6,3,4]=>{{1},{2,5},{3,4,7,8},{6}}
[1,5,8,2,7,6,4,3]=>{{1},{2,4,5,7},{3,8},{6}}
[2,5,8,3,7,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[1,4,2,8,7,6,5,3]=>{{1},{2,3,4,8},{5,7},{6}}
[1,3,8,2,7,6,4,5]=>{{1},{2,3,4,5,7,8},{6}}
[1,8,3,2,7,5,4,6]=>{{1},{2,4,5,6,7,8},{3}}
[8,1,3,2,6,5,4,7]=>{{1,2,4,7,8},{3},{5,6}}
[8,2,3,1,6,5,4,7]=>{{1,4,7,8},{2},{3},{5,6}}
[2,8,3,1,7,5,4,6]=>{{1,2,4,5,6,7,8},{3}}
[2,3,8,1,7,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[3,4,1,8,7,6,5,2]=>{{1,3},{2,4,8},{5,7},{6}}
[4,3,1,8,7,6,5,2]=>{{1,2,3,4,8},{5,7},{6}}
[4,2,1,8,7,6,5,3]=>{{1,3,4,8},{2},{5,7},{6}}
[3,8,2,1,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,2,1,6,5,4,7]=>{{1,4,7,8},{2,3},{5,6}}
[8,4,2,6,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[4,2,8,7,1,6,3,5]=>{{1,3,4,5,7,8},{2},{6}}
[5,2,8,7,1,6,3,4]=>{{1,5},{2},{3,4,7,8},{6}}
[5,2,8,1,7,6,4,3]=>{{1,4,5,7},{2},{3,8},{6}}
[5,3,8,1,7,6,4,2]=>{{1,4,5,7},{2,3,8},{6}}
[5,3,8,2,7,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[6,8,3,2,7,5,4,1]=>{{1,2,4,5,6,7,8},{3}}
[6,8,3,1,7,5,4,2]=>{{1,4,5,6,7},{2,8},{3}}
[6,8,2,1,7,5,4,3]=>{{1,4,5,6,7},{2,3,8}}
[6,8,2,7,1,5,3,4]=>{{1,5,6},{2,3,4,7,8}}
[6,8,7,2,1,4,3,5]=>{{1,2,4,5,6,8},{3,7}}
[8,5,6,1,2,4,3,7]=>{{1,3,4,6,7,8},{2,5}}
[5,8,7,1,2,4,3,6]=>{{1,2,4,5,6,8},{3,7}}
[6,8,1,2,7,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,2,3,7,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[5,2,8,3,7,6,4,1]=>{{1,3,4,5,7,8},{2},{6}}
[5,1,8,3,7,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[5,1,8,7,2,6,3,4]=>{{1,2,5},{3,4,7,8},{6}}
[4,1,8,7,2,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[4,8,1,7,2,5,3,6]=>{{1,3,4,7},{2,5,6,8}}
[8,4,1,6,2,5,3,7]=>{{1,3,7,8},{2,4,5,6}}
[8,3,1,2,6,5,4,7]=>{{1,2,3,4,7,8},{5,6}}
[3,8,1,2,7,5,4,6]=>{{1,3},{2,4,5,6,7,8}}
[3,1,8,2,7,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[3,1,2,8,7,6,5,4]=>{{1,2,3},{4,8},{5,7},{6}}
[4,1,3,8,7,6,5,2]=>{{1,2,4,8},{3},{5,7},{6}}
[3,1,4,8,7,6,5,2]=>{{1,2,3,4,8},{5,7},{6}}
[2,1,8,3,7,6,4,5]=>{{1,2},{3,4,5,7,8},{6}}
[2,8,1,3,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,3,6,5,4,7]=>{{1,3,4,7,8},{2},{5,6}}
[8,1,2,3,6,5,4,7]=>{{1,2,3,4,7,8},{5,6}}
[1,8,2,3,7,5,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,3,7,6,4,5]=>{{1},{2},{3,4,5,7,8},{6}}
[1,4,3,6,8,2,5,7]=>{{1},{2,4,6},{3},{5,7,8}}
[3,1,6,2,5,8,4,7]=>{{1,2,3,4,6,7,8},{5}}
[3,5,1,8,2,4,7,6]=>{{1,3},{2,5},{4,6,8},{7}}
[1,4,5,2,8,3,7,6]=>{{1},{2,4},{3,5,6,8},{7}}
[1,4,2,6,5,8,3,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,5,4,2,6,8,3,7]=>{{1},{2,3,4,5,6,7,8}}
[3,1,6,5,8,2,4,7]=>{{1,2,3,6},{4,5,7,8}}
[1,6,4,2,5,8,3,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,5,2,6,4,8,3,7]=>{{1},{2,3,4,5,6,7,8}}
[1,2,6,5,4,8,3,7]=>{{1},{2},{3,6,7,8},{4,5}}
[1,2,5,4,7,3,8,6]=>{{1},{2},{3,5,6,7,8},{4}}
[4,1,2,6,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[7,1,5,4,2,8,3,6]=>{{1,2,3,5,7},{4},{6,8}}
[1,4,7,5,2,8,3,6]=>{{1},{2,4,5},{3,7},{6,8}}
[7,1,3,5,2,8,4,6]=>{{1,2,4,5,7},{3},{6,8}}
[7,2,5,1,8,3,4,6]=>{{1,4,7},{2},{3,5,6,8}}
[1,4,5,2,8,7,3,6]=>{{1},{2,4},{3,5,6,7,8}}
[1,6,4,2,8,3,7,5]=>{{1},{2,3,4,6},{5,8},{7}}
[1,4,2,8,3,7,6,5]=>{{1},{2,3,4,5,8},{6,7}}
[1,2,5,3,8,7,6,4]=>{{1},{2},{3,4,5,8},{6,7}}
[1,2,8,6,5,3,7,4]=>{{1},{2},{3,4,6,8},{5},{7}}
[1,5,2,8,6,3,7,4]=>{{1},{2,3,5,6},{4,8},{7}}
[1,6,4,2,8,7,3,5]=>{{1},{2,3,4,6,7},{5,8}}
[6,2,1,8,7,3,4,5]=>{{1,3,6},{2},{4,5,7,8}}
[7,6,2,1,8,3,4,5]=>{{1,4,7},{2,3,6},{5,8}}
[7,3,1,6,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[1,7,6,4,2,8,3,5]=>{{1},{2,3,5,6,7,8},{4}}
[1,7,5,2,6,3,8,4]=>{{1},{2,4,7,8},{3,5,6}}
[1,6,2,7,5,3,8,4]=>{{1},{2,3,6},{4,7,8},{5}}
[1,2,7,6,5,3,8,4]=>{{1},{2},{3,4,6,7,8},{5}}
[1,2,6,5,3,8,7,4]=>{{1},{2},{3,4,5,6,8},{7}}
[1,5,2,6,3,8,7,4]=>{{1},{2,3,5},{4,6,8},{7}}
[1,5,2,7,6,3,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[1,6,5,2,7,3,8,4]=>{{1},{2,3,4,5,6,7,8}}
[1,5,7,4,2,8,3,6]=>{{1},{2,5},{3,7},{4},{6,8}}
[4,1,2,8,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,1,8,6,2,4,7,5]=>{{1,2,3,5,8},{4,6},{7}}
[4,3,7,1,8,2,5,6]=>{{1,4},{2,3,5,6,7,8}}
[8,3,1,6,2,4,7,5]=>{{1,2,3,5,8},{4,6},{7}}
[7,1,8,3,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,3,2,4,6,5]=>{{1},{2,5,8},{3,4,6,7}}
[1,4,2,8,7,3,6,5]=>{{1},{2,3,4,5,6,7,8}}
[1,7,4,2,8,3,6,5]=>{{1},{2,3,4,6,7},{5,8}}
[8,1,5,4,2,7,3,6]=>{{1,2,3,5,6,7,8},{4}}
[1,4,8,5,2,7,3,6]=>{{1},{2,4,5},{3,6,7,8}}
[8,5,3,1,7,2,4,6]=>{{1,2,4,5,6,7,8},{3}}
[8,6,2,1,7,3,4,5]=>{{1,4,5,7,8},{2,3,6}}
[1,8,6,4,2,7,3,5]=>{{1},{2,5,8},{3,6,7},{4}}
[1,8,5,2,6,3,7,4]=>{{1},{2,4,8},{3,5,6},{7}}
[1,5,2,7,3,8,6,4]=>{{1},{2,3,5},{4,6,7,8}}
[1,2,8,5,3,7,6,4]=>{{1},{2},{3,4,5,8},{6,7}}
[1,2,6,3,8,7,5,4]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,7,6,3,8,5,4]=>{{1},{2},{3,5,7},{4,6,8}}
[1,6,2,7,3,8,5,4]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,8,5,3,6,4]=>{{1},{2,3,6,7},{4,8},{5}}
[1,7,4,2,8,6,3,5]=>{{1},{2,3,4,7},{5,8},{6}}
[7,1,8,3,2,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[7,2,1,8,6,3,4,5]=>{{1,3,4,5,6,7,8},{2}}
[1,8,7,3,2,6,4,5]=>{{1},{2,5,8},{3,4,7},{6}}
[1,4,2,8,7,6,3,5]=>{{1},{2,3,4,5,7,8},{6}}
[1,2,8,7,5,3,6,4]=>{{1},{2},{3,4,6,7,8},{5}}
[1,2,8,6,3,7,5,4]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,7,3,8,6,5,4]=>{{1},{2},{3,4,5,7,8},{6}}
[4,1,7,3,6,5,8,2]=>{{1,2,3,4,7,8},{5,6}}
[5,1,8,7,6,2,4,3]=>{{1,2,5,6},{3,8},{4,7}}
[8,1,7,6,3,4,5,2]=>{{1,2,8},{3,5,7},{4,6}}
[5,7,8,6,2,4,1,3]=>{{1,2,5,7},{3,8},{4,6}}
[5,7,1,6,2,4,3,8]=>{{1,2,3,5,7},{4,6},{8}}
[6,4,1,5,2,7,3,8]=>{{1,3,6,7},{2,4,5},{8}}
[8,1,4,5,3,7,6,2]=>{{1,2,8},{3,4,5},{6,7}}
[6,1,4,5,3,8,7,2]=>{{1,2,6,8},{3,4,5},{7}}
[6,1,4,5,3,7,8,2]=>{{1,2,6,7,8},{3,4,5}}
[5,1,7,8,6,2,4,3]=>{{1,2,5,6},{3,4,7,8}}
[6,1,4,8,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[7,1,8,6,3,4,5,2]=>{{1,2,3,5,7,8},{4,6}}
[7,1,4,5,3,8,6,2]=>{{1,2,6,7,8},{3,4,5}}
[7,1,4,5,3,6,8,2]=>{{1,2,7,8},{3,4,5},{6}}
[8,1,4,5,3,6,7,2]=>{{1,2,8},{3,4,5},{6},{7}}
[7,4,1,5,2,6,3,8]=>{{1,3,7},{2,4,5},{6},{8}}
[6,3,5,7,2,1,4,8]=>{{1,6},{2,3,5},{4,7},{8}}
[6,3,5,8,2,1,7,4]=>{{1,6},{2,3,5},{4,8},{7}}
[6,3,5,7,2,1,8,4]=>{{1,6},{2,3,5},{4,7,8}}
[8,4,5,7,3,6,1,2]=>{{1,2,4,7,8},{3,5},{6}}
[6,4,5,8,3,7,2,1]=>{{1,2,4,6,7,8},{3,5}}
[5,8,7,6,2,4,1,3]=>{{1,2,3,5,7,8},{4,6}}
[5,4,8,6,3,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[5,4,1,8,2,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,8,1,6,2,4,3,7]=>{{1,2,3,5,7,8},{4,6}}
[8,4,1,5,2,6,3,7]=>{{1,3,7,8},{2,4,5},{6}}
[6,3,5,8,2,1,4,7]=>{{1,6},{2,3,5},{4,7,8}}
[2,3,4,1,8,6,5,7]=>{{1,2,3,4},{5,7,8},{6}}
[8,3,5,6,2,1,4,7]=>{{1,4,6,7,8},{2,3,5}}
[2,3,8,5,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,3,8,6,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,8,6,7,1,3,5,4]=>{{1,2,4,5,7,8},{3,6}}
[8,3,5,7,2,1,6,4]=>{{1,4,6,7,8},{2,3,5}}
[2,3,8,5,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[7,4,5,6,3,1,8,2]=>{{1,2,4,6,7,8},{3,5}}
[8,4,5,6,3,1,7,2]=>{{1,2,4,6,8},{3,5},{7}}
[7,3,5,6,2,8,1,4]=>{{1,7},{2,3,5},{4,6,8}}
[7,3,5,8,2,1,6,4]=>{{1,6,7},{2,3,5},{4,8}}
[7,3,5,6,2,1,4,8]=>{{1,4,6,7},{2,3,5},{8}}
[2,7,6,5,1,3,4,8]=>{{1,2,4,5,7},{3,6},{8}}
[2,7,6,8,1,3,5,4]=>{{1,2,5,7},{3,6},{4,8}}
[2,7,6,5,8,3,1,4]=>{{1,2,7},{3,6},{4,5,8}}
[8,7,5,6,1,4,2,3]=>{{1,3,5,8},{2,7},{4,6}}
[2,6,4,1,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,6,1,3,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,7,1,3,6,5,8,4]=>{{1,2,3,4,7,8},{5,6}}
[2,7,6,8,4,3,1,5]=>{{1,2,7},{3,6},{4,5,8}}
[2,7,6,1,8,3,4,5]=>{{1,2,4,7},{3,6},{5,8}}
[2,7,6,1,4,3,5,8]=>{{1,2,4,5,7},{3,6},{8}}
[7,3,5,1,2,8,4,6]=>{{1,4,7},{2,3,5},{6,8}}
[8,4,1,5,2,3,7,6]=>{{1,3,6,8},{2,4,5},{7}}
[7,8,1,6,3,4,2,5]=>{{1,2,3,5,7,8},{4,6}}
[6,4,1,8,3,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,3,8,6,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,8,6,7,4,3,1,5]=>{{1,2,4,5,7,8},{3,6}}
[8,3,5,7,2,4,1,6]=>{{1,4,6,7,8},{2,3,5}}
[2,3,4,1,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}
[2,8,6,1,7,3,4,5]=>{{1,2,4,5,7,8},{3,6}}
[2,3,8,1,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,3,8,1,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,8,6,1,4,3,5,7]=>{{1,2,4,5,7,8},{3,6}}
[8,4,3,6,5,1,7,2]=>{{1,2,4,6,8},{3},{5},{7}}
[8,5,6,3,4,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[8,6,5,4,3,1,7,2]=>{{1,2,6,8},{3,5},{4},{7}}
[1,7,6,5,4,2,3,8]=>{{1},{2,3,6,7},{4,5},{8}}
[1,8,6,5,2,7,3,4]=>{{1},{2,4,5,8},{3,6,7}}
[8,7,5,4,1,6,3,2]=>{{1,2,3,5,7,8},{4},{6}}
[7,8,5,4,1,3,6,2]=>{{1,3,5,6,7},{2,8},{4}}
[6,8,5,4,2,1,7,3]=>{{1,6},{2,3,5,8},{4},{7}}
[5,8,6,2,4,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[4,8,2,6,5,1,7,3]=>{{1,4,6},{2,3,8},{5},{7}}
[3,2,8,6,5,1,7,4]=>{{1,3,4,6,8},{2},{5},{7}}
[3,2,1,7,6,4,5,8]=>{{1,3},{2},{4,5,6,7},{8}}
[4,1,3,7,6,2,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,1,7,3,6,2,4,8]=>{{1,2,5,6},{3,4,7},{8}}
[6,1,7,5,3,2,4,8]=>{{1,2,6},{3,4,5,7},{8}}
[7,1,6,5,2,4,3,8]=>{{1,2,3,4,5,6,7},{8}}
[8,1,6,5,2,3,7,4]=>{{1,2,4,5,8},{3,6},{7}}
[1,2,7,6,3,4,5,8]=>{{1},{2},{3,5,7},{4,6},{8}}
[1,2,8,3,7,4,5,6]=>{{1},{2},{3,4,6,8},{5,7}}
[8,1,7,2,6,3,5,4]=>{{1,2,4,8},{3,5,6,7}}
[7,1,8,2,6,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,1,8,2,4,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,3,2,7,4,6]=>{{1,2,5},{3,4,6,7,8}}
[4,1,3,8,2,7,5,6]=>{{1,2,4,5,6,7,8},{3}}
[3,2,1,8,4,7,5,6]=>{{1,3},{2},{4,5,6,7,8}}
[3,2,8,7,1,6,5,4]=>{{1,3,4,5,7,8},{2},{6}}
[4,8,2,7,1,6,5,3]=>{{1,4,5,7},{2,3,8},{6}}
[5,8,7,2,1,6,4,3]=>{{1,5},{2,3,4,7,8},{6}}
[6,8,7,1,3,5,4,2]=>{{1,3,4,5,6,7},{2,8}}
[7,8,6,1,5,3,4,2]=>{{1,4,7},{2,8},{3,6},{5}}
[8,7,6,1,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}
[1,8,7,2,6,5,3,4]=>{{1},{2,4,8},{3,7},{5,6}}
[1,7,8,2,5,6,3,4]=>{{1},{2,3,4,7,8},{5},{6}}
[8,6,7,1,4,5,3,2]=>{{1,2,4,5,6,8},{3,7}}
[7,6,8,1,4,3,5,2]=>{{1,4,5,7},{2,3,6,8}}
[6,5,8,3,2,1,7,4]=>{{1,6},{2,5},{3,4,8},{7}}
[7,5,8,3,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,3,1,6,4,2]=>{{1,2,5,8},{3,4,7},{6}}
[1,6,8,4,2,7,3,5]=>{{1},{2,3,5,6,7,8},{4}}
[1,5,4,8,2,7,3,6]=>{{1},{2,5},{3,4,6,7,8}}
[8,4,3,7,1,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}
[7,4,3,8,1,5,6,2]=>{{1,5,6,7},{2,4,8},{3}}
[6,4,3,1,5,2,7,8]=>{{1,2,4,6},{3},{5},{7},{8}}
[7,4,3,1,2,6,5,8]=>{{1,2,4,5,7},{3},{6},{8}}
[8,4,3,1,2,5,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[1,5,4,2,3,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,5,1,4,2,3,7,6]=>{{1,3,6,8},{2,5},{4},{7}}
[7,5,1,4,2,6,3,8]=>{{1,3,7},{2,5},{4},{6},{8}}
[6,5,1,4,3,2,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[5,6,1,3,4,2,7,8]=>{{1,3,4,5},{2,6},{7},{8}}
[4,6,2,1,5,3,7,8]=>{{1,4},{2,3,6},{5},{7},{8}}
[3,2,6,1,5,4,7,8]=>{{1,3,4,6},{2},{5},{7},{8}}
[3,2,7,1,4,6,5,8]=>{{1,3,4,5,7},{2},{6},{8}}
[4,7,2,1,3,6,5,8]=>{{1,4},{2,3,5,7},{6},{8}}
[5,7,1,3,2,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}
[6,7,1,2,4,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,1,2,5,4,3,8]=>{{1,3,7},{2,4,6},{5},{8}}
[8,6,1,2,5,3,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[1,7,2,3,6,4,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,7,1,2,3,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[7,8,1,2,3,5,6,4]=>{{1,3,5,6,7},{2,4,8}}
[6,8,1,2,4,3,7,5]=>{{1,3,6},{2,4,5,8},{7}}
[5,8,1,3,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,8,2,1,3,5,7,6]=>{{1,4},{2,3,5,6,8},{7}}
[3,2,8,1,4,5,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[4,1,3,2,5,6,7,8]=>{{1,2,4},{3},{5},{6},{7},{8}}
[5,1,2,4,3,6,7,8]=>{{1,2,3,5},{4},{6},{7},{8}}
[6,1,2,3,5,4,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[7,1,2,3,4,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[8,1,2,3,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[6,7,3,8,5,1,2,4]=>{{1,6},{2,7},{3},{4,8},{5}}
[6,7,4,5,1,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,7,6,8,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,8,6,1,2,4]=>{{1,5,6},{2,3,7},{4,8}}
[3,8,4,5,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,8,6,7,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,7,1,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,2,7,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,1,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,1,8,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,8,1,7,3,4]=>{{1,2,5},{3,6,7},{4,8}}
[8,2,4,5,1,6,3,7]=>{{1,3,4,5,7,8},{2},{6}}
[1,4,8,6,2,3,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[1,5,6,8,2,3,7,4]=>{{1},{2,5},{3,6},{4,8},{7}}
[1,5,6,2,8,4,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[2,5,6,3,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[1,4,2,6,8,5,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[8,1,3,2,5,4,6,7]=>{{1,2,4,6,7,8},{3},{5}}
[8,2,3,1,5,6,4,7]=>{{1,4,7,8},{2},{3},{5},{6}}
[2,8,3,1,5,7,4,6]=>{{1,2,4,6,7,8},{3},{5}}
[2,4,1,6,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,6,7,8,5,2]=>{{1,3},{2,4,6,8},{5,7}}
[4,3,1,7,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[5,2,7,8,1,6,3,4]=>{{1,5},{2},{3,7},{4,8},{6}}
[5,3,7,2,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,3,1,5,8,4,2]=>{{1,2,4,6,7,8},{3},{5}}
[6,7,2,1,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,8,1,5,3,4]=>{{1,5,6},{2,3,7},{4,8}}
[6,7,8,2,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,2,8,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,3,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[5,2,7,3,4,6,8,1]=>{{1,3,4,5,7,8},{2},{6}}
[5,1,7,3,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,1,7,8,2,3,6,4]=>{{1,2,5},{3,6,7},{4,8}}
[4,1,8,7,2,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,1,2,7,4,5,6]=>{{1,3},{2,4,6,8},{5,7}}
[4,1,3,7,5,8,6,2]=>{{1,2,4,6,7,8},{3},{5}}
[3,1,4,5,7,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[2,1,8,3,4,7,6,5]=>{{1,2},{3,4,5,8},{6,7}}
[8,2,1,3,4,6,5,7]=>{{1,3,4,5,7,8},{2},{6}}
[1,8,2,3,4,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,2,8,3,4,6,7,5]=>{{1},{2},{3,4,5,8},{6},{7}}
[4,2,1,6,5,8,7,3]=>{{1,3,4,6,8},{2},{5},{7}}
[5,2,6,1,4,8,7,3]=>{{1,4,5},{2},{3,6,8},{7}}
[5,2,6,4,1,8,7,3]=>{{1,5},{2},{3,6,8},{4},{7}}
[5,2,7,4,8,1,6,3]=>{{1,3,5,6,7,8},{2},{4}}
[5,2,7,4,8,6,1,3]=>{{1,3,5,7,8},{2},{4},{6}}
[5,7,2,3,8,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[5,7,2,3,8,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,6,2,3,1,8,7,4]=>{{1,5},{2,3,4,6,8},{7}}
[5,6,2,1,3,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[5,1,6,4,2,8,7,3]=>{{1,2,5},{3,6,8},{4},{7}}
[5,6,1,3,2,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[5,6,3,1,2,8,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[5,6,3,2,1,8,7,4]=>{{1,5},{2,4,6,8},{3},{7}}
[5,7,3,2,8,1,6,4]=>{{1,2,4,5,6,7,8},{3}}
[5,7,3,2,8,6,1,4]=>{{1,2,4,5,7,8},{3},{6}}
[6,7,3,8,2,1,5,4]=>{{1,6},{2,5,7},{3},{4,8}}
[6,7,3,8,1,2,5,4]=>{{1,2,5,6,7},{3},{4,8}}
[5,7,3,1,8,2,6,4]=>{{1,4,5,8},{2,6,7},{3}}
[5,7,1,3,8,2,6,4]=>{{1,3,4,5,8},{2,6,7}}
[5,1,7,4,8,2,6,3]=>{{1,2,3,5,6,7,8},{4}}
[1,5,7,4,8,3,6,2]=>{{1},{2,5,8},{3,6,7},{4}}
[1,5,7,4,8,6,3,2]=>{{1},{2,5,8},{3,7},{4},{6}}
[5,1,7,4,8,6,2,3]=>{{1,2,3,5,7,8},{4},{6}}
[5,7,1,3,8,6,2,4]=>{{1,3,4,5,8},{2,7},{6}}
[5,7,3,1,8,6,2,4]=>{{1,4,5,8},{2,7},{3},{6}}
[6,7,3,8,1,5,2,4]=>{{1,5,6},{2,7},{3},{4,8}}
[6,7,3,8,5,2,1,4]=>{{1,2,6,7},{3},{4,8},{5}}
[6,7,8,3,1,4,2,5]=>{{1,3,4,5,6,8},{2,7}}
[6,7,1,8,3,5,2,4]=>{{1,3,5,6},{2,7},{4,8}}
[6,1,7,8,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[1,6,7,8,4,5,3,2]=>{{1},{2,4,5,6,8},{3,7}}
[1,6,7,8,4,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,7,8,4,2,5,3]=>{{1,2,6},{3,4,5,7,8}}
[6,7,1,8,3,2,5,4]=>{{1,2,3,5,6,7},{4,8}}
[5,7,2,1,8,3,6,4]=>{{1,4,5,8},{2,3,6,7}}
[6,7,2,8,1,3,5,4]=>{{1,2,3,5,6,7},{4,8}}
[6,7,2,8,3,1,5,4]=>{{1,6},{2,3,5,7},{4,8}}
[6,7,2,8,3,5,1,4]=>{{1,2,3,5,6,7},{4,8}}
[6,2,7,8,4,5,1,3]=>{{1,3,4,5,6,7,8},{2}}
[6,2,7,8,4,1,5,3]=>{{1,6},{2},{3,4,5,7,8}}
[6,2,7,8,1,4,5,3]=>{{1,3,4,5,6,7,8},{2}}
[5,2,7,1,8,4,6,3]=>{{1,3,4,5,6,7,8},{2}}
[4,2,1,7,8,5,6,3]=>{{1,3,4,5,6,7,8},{2}}
[4,1,2,7,8,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[6,2,7,8,1,5,4,3]=>{{1,5,6},{2},{3,4,7,8}}
[6,2,7,8,5,1,4,3]=>{{1,6},{2},{3,4,7,8},{5}}
[6,2,7,8,5,4,1,3]=>{{1,3,4,6,7,8},{2},{5}}
[6,7,2,8,5,3,1,4]=>{{1,2,3,6,7},{4,8},{5}}
[5,7,2,1,8,6,3,4]=>{{1,4,5,8},{2,3,7},{6}}
[5,7,1,2,8,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[5,1,7,2,8,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[1,5,7,3,8,6,4,2]=>{{1},{2,5,8},{3,4,7},{6}}
[1,6,7,8,3,5,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,7,8,2,5,4,3]=>{{1,2,5,6},{3,4,7,8}}
[6,7,1,8,2,5,3,4]=>{{1,2,3,5,6,7},{4,8}}
[6,7,8,2,4,1,3,5]=>{{1,6},{2,3,4,5,7,8}}
[6,7,8,2,4,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,8,5,2,3,4]=>{{1,2,3,6,7},{4,8},{5}}
[6,1,7,8,5,2,4,3]=>{{1,2,6},{3,4,7,8},{5}}
[1,6,7,8,5,3,4,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,1,7,8,5,4,2,3]=>{{1,2,3,4,6,7,8},{5}}
[6,7,1,8,5,3,2,4]=>{{1,3,6},{2,7},{4,8},{5}}
[6,7,8,4,1,3,2,5]=>{{1,3,5,6,8},{2,7},{4}}
[6,3,8,5,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,8,4,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,4,5,8,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,6,1,4,8,7,3,2]=>{{1,2,3,5,6,7,8},{4}}
[3,6,4,8,5,7,1,2]=>{{1,2,3,4,6,7,8},{5}}
[5,1,4,8,6,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[3,4,7,1,8,6,5,2]=>{{1,2,3,4,5,7,8},{6}}
[6,3,8,4,2,7,1,5]=>{{1,6,7},{2,3,5,8},{4}}
[3,6,8,7,1,4,2,5]=>{{1,3,5,8},{2,4,6,7}}
[5,3,7,1,6,8,2,4]=>{{1,4,5,6,8},{2,3,7}}
[4,3,8,5,6,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,6,1,2,7,8,5,3]=>{{1,2,3,4,6,8},{5,7}}
[3,6,4,2,8,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,5,2,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,7,4,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,1,4,8,3,2,6]=>{{1,3,5,6,8},{2,7},{4}}
[7,8,3,5,1,4,6,2]=>{{1,4,5,6,7},{2,8},{3}}
[5,8,1,4,6,7,2,3]=>{{1,2,3,5,6,7,8},{4}}
[6,5,8,4,3,7,2,1]=>{{1,2,3,5,6,7,8},{4}}
[6,3,7,4,2,8,5,1]=>{{1,6,8},{2,3,5,7},{4}}
[8,7,1,6,2,4,5,3]=>{{1,3,8},{2,5,7},{4,6}}
[3,8,6,7,1,4,5,2]=>{{1,3,4,5,6,7},{2,8}}
[5,3,8,7,4,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,7,1,5,6,2]=>{{1,4,5,6,7},{2,3,8}}
[8,3,6,1,2,5,7,4]=>{{1,4,8},{2,3,5,6},{7}}
[5,6,1,8,7,3,2,4]=>{{1,2,3,5,6,7},{4,8}}
[5,4,2,7,3,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[7,5,3,6,4,2,8,1]=>{{1,7,8},{2,4,5,6},{3}}
[6,4,1,5,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[8,2,6,3,4,7,5,1]=>{{1,8},{2},{3,4,5,6,7}}
[7,2,6,3,5,4,8,1]=>{{1,7,8},{2},{3,4,6},{5}}
[6,2,7,4,3,5,8,1]=>{{1,3,5,6,7,8},{2},{4}}
[3,7,6,4,5,2,8,1]=>{{1,2,3,6,7,8},{4},{5}}
[2,7,6,5,3,4,8,1]=>{{1,2,7,8},{3,4,5,6}}
[6,5,4,3,1,8,2,7]=>{{1,2,5,6,7,8},{3,4}}
[8,6,5,4,2,7,3,1]=>{{1,8},{2,3,5,6,7},{4}}
[8,5,4,1,7,2,6,3]=>{{1,3,4,8},{2,5,6,7}}
[7,5,4,1,8,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[1,6,5,2,8,3,4,7]=>{{1},{2,3,4,5,6,7,8}}
[1,6,5,3,4,8,2,7]=>{{1},{2,6,7,8},{3,4,5}}
[5,4,6,3,1,8,2,7]=>{{1,5},{2,3,4,6,7,8}}
[6,5,8,4,2,7,3,1]=>{{1,3,6,7,8},{2,5},{4}}
[5,8,2,6,4,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,3,2,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[6,8,3,1,7,2,5,4]=>{{1,2,4,6,8},{3},{5,7}}
[1,8,6,3,7,5,2,4]=>{{1},{2,3,4,5,6,7,8}}
[8,7,5,2,6,4,3,1]=>{{1,8},{2,3,4,5,6,7}}
[8,7,1,6,2,5,4,3]=>{{1,3,8},{2,4,5,6,7}}
[7,8,1,6,3,2,5,4]=>{{1,3,5,7},{2,4,6,8}}
[2,8,1,7,3,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,3,7,2,6,5]=>{{1,3,4},{2,5,6,7,8}}
[4,2,8,5,7,3,6,1]=>{{1,3,4,5,6,7,8},{2}}
[5,1,7,6,8,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,3,1,8,4,2,5]=>{{1,4,6},{2,7},{3},{5,8}}
[1,7,3,8,4,5,2,6]=>{{1},{2,7},{3},{4,5,6,8}}
[1,7,2,8,5,3,4,6]=>{{1},{2,3,4,6,7,8},{5}}
[7,6,1,8,4,3,2,5]=>{{1,2,3,6,7},{4,5,8}}
[8,6,1,7,4,2,5,3]=>{{1,3,8},{2,6},{4,5,7}}
[8,1,2,7,3,4,6,5]=>{{1,2,3,5,8},{4,6,7}}
[7,1,2,8,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,2,6,1,7,3,5,4]=>{{1,4,8},{2},{3,6},{5,7}}
[4,2,1,5,8,3,6,7]=>{{1,3,4,5,6,7,8},{2}}
[5,4,3,1,6,8,2,7]=>{{1,2,4,5,6,7,8},{3}}
[4,7,5,6,8,3,2,1]=>{{1,3,4,5,6,8},{2,7}}
[6,5,4,8,2,7,3,1]=>{{1,3,4,6,7,8},{2,5}}
[6,5,1,8,7,4,2,3]=>{{1,3,4,6,8},{2,5,7}}
[8,6,4,7,5,3,2,1]=>{{1,8},{2,3,4,6,7},{5}}
[5,1,8,3,7,6,2,4]=>{{1,2,5,7},{3,4,8},{6}}
[5,4,8,1,7,2,6,3]=>{{1,2,4,5,6,7},{3,8}}
[3,6,8,2,4,7,5,1]=>{{1,3,8},{2,4,5,6,7}}
[5,7,3,8,2,6,4,1]=>{{1,2,4,5,7,8},{3},{6}}
[4,7,2,8,6,3,5,1]=>{{1,4,8},{2,3,5,6,7}}
[2,3,8,7,4,5,6,1]=>{{1,2,3,8},{4,5,6,7}}
[7,2,8,6,4,3,5,1]=>{{1,3,4,5,6,7,8},{2}}
[2,1,8,7,5,6,3,4]=>{{1,2},{3,4,7,8},{5},{6}}
[8,2,7,6,3,5,4,1]=>{{1,8},{2},{3,4,5,6,7}}
[8,1,7,6,5,2,4,3]=>{{1,2,3,4,6,7,8},{5}}
[7,1,8,6,5,3,2,4]=>{{1,2,7},{3,4,6,8},{5}}
[1,2,8,7,6,3,4,5]=>{{1},{2},{3,5,6,8},{4,7}}
[1,3,8,7,4,6,2,5]=>{{1},{2,3,4,5,7,8},{6}}
[5,1,6,8,7,4,2,3]=>{{1,2,5,7},{3,4,6,8}}
[6,8,7,2,5,4,3,1]=>{{1,2,4,6,8},{3,7},{5}}
[3,8,7,6,4,5,2,1]=>{{1,2,3,7,8},{4,5,6}}
[2,8,7,6,5,3,4,1]=>{{1,2,8},{3,4,6,7},{5}}
[1,8,7,6,5,4,2,3]=>{{1},{2,3,7,8},{4,6},{5}}
[5,8,6,7,3,4,1,2]=>{{1,3,4,5,6,7},{2,8}}
[4,8,6,7,3,5,1,2]=>{{1,4,7},{2,8},{3,5,6}}
[3,8,6,7,4,5,1,2]=>{{1,3,4,5,6,7},{2,8}}
[2,8,6,7,4,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[1,8,6,7,4,5,2,3]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,7,4,6,2,3]=>{{1},{2,3,4,5,7,8},{6}}
[3,8,5,7,4,6,1,2]=>{{1,3,4,5,7},{2,8},{6}}
[4,8,5,7,3,6,1,2]=>{{1,4,7},{2,8},{3,5},{6}}
[7,8,3,6,4,5,1,2]=>{{1,7},{2,8},{3},{4,5,6}}
[6,8,3,7,4,5,1,2]=>{{1,4,5,6,7},{2,8},{3}}
[5,8,3,7,4,6,1,2]=>{{1,4,5,7},{2,8},{3},{6}}
[3,7,4,8,5,6,1,2]=>{{1,2,3,4,7,8},{5},{6}}
[4,7,3,8,5,6,1,2]=>{{1,2,4,7,8},{3},{5},{6}}
[4,7,2,8,5,6,1,3]=>{{1,2,3,4,7,8},{5},{6}}
[4,7,1,8,5,6,2,3]=>{{1,3,4,8},{2,7},{5},{6}}
[3,7,1,8,5,6,2,4]=>{{1,3},{2,7},{4,8},{5},{6}}
[3,7,2,8,5,6,1,4]=>{{1,2,3,7},{4,8},{5},{6}}
[2,7,3,8,5,6,1,4]=>{{1,2,7},{3},{4,8},{5},{6}}
[2,7,4,8,5,6,1,3]=>{{1,2,7},{3,4,8},{5},{6}}
[5,8,2,7,4,6,1,3]=>{{1,4,5,7},{2,3,8},{6}}
[6,8,2,7,4,5,1,3]=>{{1,4,5,6,7},{2,3,8}}
[7,8,2,6,4,5,1,3]=>{{1,7},{2,3,8},{4,5,6}}
[7,8,1,6,4,5,2,3]=>{{1,2,3,7,8},{4,5,6}}
[6,8,1,7,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,7,4,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[1,7,4,8,5,6,2,3]=>{{1},{2,7},{3,4,8},{5},{6}}
[1,7,3,8,5,6,2,4]=>{{1},{2,7},{3},{4,8},{5},{6}}
[2,8,5,6,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,8,5,6,2,7,3,4]=>{{1},{2,3,4,5,6,7,8}}
[1,7,3,8,4,6,2,5]=>{{1},{2,7},{3},{4,5,8},{6}}
[4,8,1,7,3,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[5,8,1,7,3,6,2,4]=>{{1,3,5},{2,4,7,8},{6}}
[6,8,1,7,3,5,2,4]=>{{1,3,5,6},{2,4,7,8}}
[7,8,2,6,3,5,1,4]=>{{1,7},{2,3,4,5,6,8}}
[6,8,2,7,3,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,2,7,3,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[4,8,2,7,3,6,1,5]=>{{1,4,7},{2,3,5,8},{6}}
[2,7,3,8,4,6,1,5]=>{{1,2,7},{3},{4,5,8},{6}}
[3,7,2,8,4,6,1,5]=>{{1,2,3,7},{4,5,8},{6}}
[3,7,1,8,4,6,2,5]=>{{1,3},{2,7},{4,5,8},{6}}
[1,8,4,7,3,6,2,5]=>{{1},{2,3,4,5,7,8},{6}}
[2,8,4,7,3,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[3,8,4,7,2,6,1,5]=>{{1,3,4,7},{2,5,8},{6}}
[4,8,5,7,2,6,1,3]=>{{1,4,7},{2,3,5,8},{6}}
[3,8,5,7,2,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[2,8,5,7,3,6,1,4]=>{{1,2,4,7,8},{3,5},{6}}
[1,8,5,7,3,6,2,4]=>{{1},{2,4,7,8},{3,5},{6}}
[1,8,6,7,3,5,2,4]=>{{1},{2,4,7,8},{3,5,6}}
[2,8,6,7,3,5,1,4]=>{{1,2,4,7,8},{3,5,6}}
[3,8,6,7,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[4,8,6,7,2,5,1,3]=>{{1,4,7},{2,3,5,6,8}}
[5,8,6,7,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,7,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,7,1,4,2,3]=>{{1,5},{2,3,4,6,7,8}}
[4,8,6,7,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,7,1,5,2,4]=>{{1,3,5,6},{2,4,7,8}}
[1,5,2,8,6,7,3,4]=>{{1},{2,3,5,6,7},{4,8}}
[2,5,1,8,6,7,3,4]=>{{1,2,3,5,6,7},{4,8}}
[2,6,1,8,5,7,3,4]=>{{1,2,3,6,7},{4,8},{5}}
[1,6,2,8,5,7,3,4]=>{{1},{2,3,6,7},{4,8},{5}}
[3,8,5,7,1,6,2,4]=>{{1,3,5},{2,4,7,8},{6}}
[6,8,4,7,1,5,2,3]=>{{1,5,6},{2,3,4,7,8}}
[7,8,4,6,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[7,8,3,6,1,5,2,4]=>{{1,2,4,5,6,7,8},{3}}
[6,8,3,7,1,5,2,4]=>{{1,5,6},{2,4,7,8},{3}}
[4,8,3,7,1,6,2,5]=>{{1,2,4,5,7,8},{3},{6}}
[3,8,4,7,1,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[1,6,2,8,4,7,3,5]=>{{1},{2,3,6,7},{4,5,8}}
[2,6,1,8,4,7,3,5]=>{{1,2,3,6,7},{4,5,8}}
[3,7,2,6,1,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[3,7,1,6,2,8,4,5]=>{{1,3},{2,4,5,6,7,8}}
[4,8,1,6,2,7,3,5]=>{{1,3,4,6,7},{2,5,8}}
[5,8,1,6,2,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,5,2,6,3,4]=>{{1,3,7},{2,4,5,8},{6}}
[7,8,2,5,1,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[6,8,2,5,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,2,6,1,7,3,4]=>{{1,5},{2,3,4,6,7,8}}
[4,8,2,6,1,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[1,7,3,6,2,8,4,5]=>{{1},{2,4,5,6,7,8},{3}}
[2,7,3,6,1,8,4,5]=>{{1,2,4,5,6,7,8},{3}}
[6,7,4,8,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,5,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,6,2,3,1,8]=>{{1,2,5,7},{3,4,6},{8}}
[5,7,4,6,3,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,8,3,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[6,8,4,5,3,7,1,2]=>{{1,6,7},{2,8},{3,4,5}}
[5,8,4,6,3,7,1,2]=>{{1,3,4,5,6,7},{2,8}}
[5,6,4,8,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,3,7,2,4,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,6,3,7,2,8,1,4]=>{{1,2,4,5,6,7,8},{3}}
[5,6,3,8,2,7,1,4]=>{{1,2,5,6,7},{3},{4,8}}
[5,6,4,8,2,7,1,3]=>{{1,2,5,6,7},{3,4,8}}
[5,8,4,6,2,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,5,2,7,1,3]=>{{1,6,7},{2,3,4,5,8}}
[7,8,4,5,2,6,1,3]=>{{1,7},{2,3,4,5,8},{6}}
[6,8,4,5,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,6,2,3,1,7]=>{{1,2,5,7,8},{3,4,6}}
[5,6,4,8,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,3,8,2,4,1,7]=>{{1,2,4,5,6,7,8},{3}}
[5,6,3,4,2,8,1,7]=>{{1,2,5,6,7,8},{3},{4}}
[4,6,3,5,2,7,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[4,6,3,5,2,8,1,7]=>{{1,2,4,5,6,7,8},{3}}
[4,6,3,8,2,5,1,7]=>{{1,4,7,8},{2,5,6},{3}}
[4,8,3,6,2,5,1,7]=>{{1,2,4,5,6,7,8},{3}}
[5,8,3,6,2,4,1,7]=>{{1,2,5,7,8},{3},{4,6}}
[6,8,3,5,2,4,1,7]=>{{1,2,4,5,6,7,8},{3}}
[7,8,3,5,2,4,1,6]=>{{1,7},{2,4,5,6,8},{3}}
[7,8,3,5,2,6,1,4]=>{{1,7},{2,4,5,8},{3},{6}}
[5,8,3,6,2,7,1,4]=>{{1,2,4,5,6,7,8},{3}}
[4,8,3,6,2,7,1,5]=>{{1,4,6,7},{2,5,8},{3}}
[4,6,3,8,2,7,1,5]=>{{1,2,4,5,6,7,8},{3}}
[4,6,3,7,2,8,1,5]=>{{1,4,7},{2,5,6,8},{3}}
[4,7,3,6,2,5,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[4,7,3,6,2,8,1,5]=>{{1,2,4,5,6,7,8},{3}}
[4,7,3,8,2,6,1,5]=>{{1,2,4,5,7,8},{3},{6}}
[5,7,4,8,2,6,1,3]=>{{1,2,5,7},{3,4,8},{6}}
[5,7,3,6,2,8,1,4]=>{{1,2,5,7},{3},{4,6,8}}
[5,7,3,6,2,4,1,8]=>{{1,2,5,7},{3},{4,6},{8}}
[6,7,3,5,2,4,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[6,7,3,5,2,8,1,4]=>{{1,2,4,5,6,7,8},{3}}
[6,7,4,8,2,5,1,3]=>{{1,2,5,6,7},{3,4,8}}
[6,7,5,8,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,7,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,8,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,3,8,2,4,1,5]=>{{1,2,4,5,6,7,8},{3}}
[6,7,3,4,2,8,1,5]=>{{1,2,5,6,7,8},{3},{4}}
[5,7,3,4,2,6,1,8]=>{{1,2,5,7},{3},{4},{6},{8}}
[5,7,3,4,2,8,1,6]=>{{1,2,5,7},{3},{4},{6,8}}
[5,7,4,8,2,3,1,6]=>{{1,2,5,7},{3,4,6,8}}
[5,8,4,7,2,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,7,2,3,1,5]=>{{1,3,4,6,7},{2,5,8}}
[7,8,4,6,2,3,1,5]=>{{1,7},{2,5,8},{3,4,6}}
[7,8,3,6,2,4,1,5]=>{{1,7},{2,5,8},{3},{4,6}}
[6,8,3,7,2,4,1,5]=>{{1,4,6,7},{2,5,8},{3}}
[5,8,3,7,2,4,1,6]=>{{1,2,4,5,6,7,8},{3}}
[4,8,3,7,2,5,1,6]=>{{1,4,7},{2,5,6,8},{3}}
[4,7,3,8,2,5,1,6]=>{{1,2,4,5,6,7,8},{3}}
[4,7,3,5,2,8,1,6]=>{{1,2,4,5,7},{3},{6,8}}
[4,7,3,5,2,6,1,8]=>{{1,2,4,5,7},{3},{6},{8}}
[4,5,3,7,2,6,1,8]=>{{1,4,7},{2,5},{3},{6},{8}}
[4,5,3,7,2,8,1,6]=>{{1,4,7},{2,5},{3},{6,8}}
[4,5,3,8,2,7,1,6]=>{{1,4,6,7,8},{2,5},{3}}
[4,8,3,5,2,7,1,6]=>{{1,2,4,5,6,7,8},{3}}
[5,8,3,4,2,7,1,6]=>{{1,2,5,6,7,8},{3},{4}}
[6,8,3,4,2,7,1,5]=>{{1,6,7},{2,5,8},{3},{4}}
[7,8,3,4,2,6,1,5]=>{{1,7},{2,5,8},{3},{4},{6}}
[6,8,3,4,2,5,1,7]=>{{1,2,5,6,7,8},{3},{4}}
[5,8,3,4,2,6,1,7]=>{{1,2,5,7,8},{3},{4},{6}}
[4,8,3,5,2,6,1,7]=>{{1,2,4,5,7,8},{3},{6}}
[4,5,3,8,2,6,1,7]=>{{1,4,7,8},{2,5},{3},{6}}
[4,5,3,6,2,8,1,7]=>{{1,4,6,7,8},{2,5},{3}}
[4,7,5,2,1,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[4,8,5,2,1,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[4,6,5,2,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[5,6,4,2,3,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[6,4,5,3,1,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[5,4,6,1,3,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,6,8,1,7,3,2,5]=>{{1,4},{2,3,5,6,7,8}}
[4,7,8,1,6,3,5,2]=>{{1,4},{2,3,5,6,7,8}}
[7,4,8,1,6,5,3,2]=>{{1,2,3,4,7,8},{5,6}}
[5,4,8,1,3,7,6,2]=>{{1,2,3,4,5,8},{6,7}}
[8,4,5,3,1,7,6,2]=>{{1,2,3,4,5,8},{6,7}}
[5,4,7,1,3,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[6,4,8,1,7,5,2,3]=>{{1,2,4,5,6,7},{3,8}}
[5,6,8,7,2,1,3,4]=>{{1,2,5,6},{3,4,7,8}}
[8,5,7,6,4,2,1,3]=>{{1,3,7,8},{2,4,5,6}}
[8,4,6,3,7,2,1,5]=>{{1,5,7,8},{2,3,4,6}}
[6,3,2,8,7,4,1,5]=>{{1,4,5,6,7,8},{2,3}}
[2,1,6,8,7,4,3,5]=>{{1,2},{3,4,5,6,7,8}}
[2,1,7,8,6,4,5,3]=>{{1,2},{3,4,5,6,7,8}}
[7,3,2,8,6,4,5,1]=>{{1,4,5,6,7,8},{2,3}}
[7,6,8,5,2,4,3,1]=>{{1,3,7,8},{2,4,5,6}}
[5,7,8,6,2,3,1,4]=>{{1,2,5,7},{3,4,6,8}}
[5,8,7,6,3,2,1,4]=>{{1,3,5,7},{2,4,6,8}}
[6,8,7,5,3,2,4,1]=>{{1,2,6,8},{3,4,5,7}}
[5,8,4,2,3,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[7,8,4,2,6,5,3,1]=>{{1,2,3,4,7,8},{5,6}}
[4,8,7,2,6,3,5,1]=>{{1,2,4,8},{3,5,6,7}}
[4,8,6,2,7,3,1,5]=>{{1,2,4,5,7,8},{3,6}}
[3,6,1,8,7,4,2,5]=>{{1,3},{2,4,5,6,7,8}}
[3,7,1,8,6,4,5,2]=>{{1,3},{2,4,5,6,7,8}}
[3,8,1,6,7,5,2,4]=>{{1,3},{2,4,5,6,7,8}}
[3,7,1,6,8,2,5,4]=>{{1,3},{2,4,5,6,7,8}}
[4,7,6,2,8,1,3,5]=>{{1,2,3,4,6,7},{5,8}}
[6,7,4,2,8,1,5,3]=>{{1,6},{2,3,4,5,7,8}}
[6,8,4,2,7,5,1,3]=>{{1,5,6,7},{2,3,4,8}}
[2,1,8,6,7,5,3,4]=>{{1,2},{3,4,5,6,7,8}}
[8,3,2,6,7,5,1,4]=>{{1,4,5,6,7,8},{2,3}}
[8,6,4,3,7,5,1,2]=>{{1,2,5,6,7,8},{3,4}}
[5,8,6,7,3,1,2,4]=>{{1,3,5,6},{2,4,7,8}}
[6,7,5,8,1,3,4,2]=>{{1,3,5,6},{2,4,7,8}}
[7,6,5,8,1,4,3,2]=>{{1,3,5,7},{2,4,6,8}}
[8,6,5,7,4,1,3,2]=>{{1,2,6,8},{3,4,5,7}}
[7,6,4,3,8,1,5,2]=>{{1,2,5,6,7,8},{3,4}}
[7,3,2,6,8,1,5,4]=>{{1,4,5,6,7,8},{2,3}}
[2,1,7,6,8,3,5,4]=>{{1,2},{3,4,5,6,7,8}}
[7,5,6,8,1,4,2,3]=>{{1,2,5,7},{3,4,6,8}}
[6,5,7,8,1,2,4,3]=>{{1,2,5,6},{3,4,7,8}}
[8,1,3,7,4,6,5,2]=>{{1,2,8},{3},{4,5,7},{6}}
[5,2,8,7,4,6,1,3]=>{{1,4,5,7},{2},{3,8},{6}}
[1,6,2,5,4,7,3,8]=>{{1},{2,3,6,7},{4,5},{8}}
[6,2,7,5,4,8,3,1]=>{{1,6,8},{2},{3,7},{4,5}}
[8,1,3,5,4,7,6,2]=>{{1,2,8},{3},{4,5},{6,7}}
[6,1,5,4,3,8,7,2]=>{{1,2,6,8},{3,5},{4},{7}}
[6,1,8,3,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[7,1,5,3,4,8,6,2]=>{{1,2,6,7,8},{3,4,5}}
[7,1,4,3,5,6,8,2]=>{{1,2,7,8},{3,4},{5},{6}}
[8,1,3,4,5,6,7,2]=>{{1,2,8},{3},{4},{5},{6},{7}}
[1,7,2,4,5,6,3,8]=>{{1},{2,3,7},{4},{5},{6},{8}}
[6,3,2,7,5,1,8,4]=>{{1,6},{2,3},{4,7,8},{5}}
[8,4,7,2,5,6,1,3]=>{{1,3,7,8},{2,4},{5},{6}}
[6,5,8,2,4,7,3,1]=>{{1,3,6,7,8},{2,4,5}}
[8,5,2,1,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[6,5,2,8,4,1,3,7]=>{{1,6},{2,3,4,5,7,8}}
[5,6,2,1,4,8,3,7]=>{{1,4,5},{2,3,6,7,8}}
[3,6,1,8,5,2,4,7]=>{{1,3},{2,6},{4,7,8},{5}}
[1,2,6,3,5,4,7,8]=>{{1},{2},{3,4,6},{5},{7},{8}}
[3,4,1,2,8,6,5,7]=>{{1,3},{2,4},{5,7,8},{6}}
[4,3,1,2,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}
[5,8,1,6,3,2,4,7]=>{{1,3,5},{2,4,6,7,8}}
[6,3,8,5,2,1,4,7]=>{{1,6},{2,3,4,5,7,8}}
[8,3,1,5,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[3,8,2,6,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[3,8,6,7,2,1,5,4]=>{{1,3,6},{2,4,5,7,8}}
[8,5,6,4,2,1,7,3]=>{{1,3,6,8},{2,5},{4},{7}}
[7,2,5,8,3,1,6,4]=>{{1,6,7},{2},{3,5},{4,8}}
[1,7,5,6,3,2,4,8]=>{{1},{2,4,6,7},{3,5},{8}}
[6,1,2,3,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[7,1,2,3,6,5,8,4]=>{{1,2,3,4,7,8},{5,6}}
[7,2,1,3,8,6,4,5]=>{{1,3,4,7},{2},{5,8},{6}}
[1,5,7,3,2,4,6,8]=>{{1},{2,5},{3,4,6,7},{8}}
[5,2,7,3,1,8,4,6]=>{{1,5},{2},{3,4,7},{6,8}}
[5,8,2,4,1,3,7,6]=>{{1,5},{2,3,6,8},{4},{7}}
[8,7,2,6,3,4,1,5]=>{{1,2,3,5,7,8},{4,6}}
[4,8,1,6,3,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,1,8,6,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[8,1,6,7,4,3,2,5]=>{{1,2,4,5,7,8},{3,6}}
[3,5,8,7,2,4,1,6]=>{{1,3,4,6,7,8},{2,5}}
[4,2,1,3,7,8,5,6]=>{{1,3,4},{2},{5,7},{6,8}}
[2,4,1,3,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}
[2,5,8,3,1,7,4,6]=>{{1,2,5},{3,4,6,7,8}}
[8,6,1,3,7,2,4,5]=>{{1,3,4,5,7,8},{2,6}}
[2,8,1,3,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[6,8,2,3,4,1,5,7]=>{{1,6},{2,3,4,5,7,8}}
[5,1,8,3,2,4,6,7]=>{{1,2,5},{3,4,6,7,8}}
[1,4,2,7,8,6,3,5]=>{{1},{2,3,4,7},{5,8},{6}}
[1,6,2,4,8,5,3,7]=>{{1},{2,3,5,6,7,8},{4}}
[1,6,2,4,7,5,3,8]=>{{1},{2,3,5,6,7},{4},{8}}
[1,7,3,8,5,2,4,6]=>{{1},{2,4,6,7,8},{3},{5}}
[1,7,3,2,8,6,4,5]=>{{1},{2,4,7},{3},{5,8},{6}}
[4,2,5,7,8,6,1,3]=>{{1,4,7},{2},{3,5,8},{6}}
[7,2,3,1,8,5,6,4]=>{{1,4,5,6,7,8},{2},{3}}
[8,2,5,1,7,3,4,6]=>{{1,3,4,5,6,7,8},{2}}
[6,2,1,8,3,4,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[6,2,8,3,5,1,7,4]=>{{1,6},{2},{3,4,8},{5},{7}}
[6,2,4,8,5,7,1,3]=>{{1,6,7},{2},{3,4,8},{5}}
[1,3,6,4,8,5,7,2]=>{{1},{2,3,5,6,8},{4},{7}}
[1,3,6,4,7,5,8,2]=>{{1},{2,3,5,6,7,8},{4}}
[6,2,4,7,5,8,1,3]=>{{1,3,4,6,7,8},{2},{5}}
[6,2,1,3,7,8,4,5]=>{{1,3,4,5,6,7,8},{2}}
[7,8,2,1,4,3,5,6]=>{{1,4,5,7},{2,3,6,8}}
[7,6,4,2,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,7,2,3,1,6,8,4]=>{{1,5},{2,3,4,7,8},{6}}
[7,5,4,2,6,8,1,3]=>{{1,7},{2,3,4,5,6,8}}
[1,7,5,3,4,6,8,2]=>{{1},{2,7,8},{3,4,5},{6}}
[8,2,5,4,6,7,1,3]=>{{1,3,5,6,7,8},{2},{4}}
[5,2,6,3,1,8,7,4]=>{{1,5},{2},{3,4,6,8},{7}}
[8,2,6,4,3,1,7,5]=>{{1,3,5,6,8},{2},{4},{7}}
[8,2,7,4,1,3,5,6]=>{{1,3,5,6,7,8},{2},{4}}
[1,2,8,4,3,5,6,7]=>{{1},{2},{3,5,6,7,8},{4}}
[1,7,4,2,3,5,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,8,4,1,3,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,4,3,2,5,6]=>{{1},{2,6,8},{3,5,7},{4}}
[1,6,3,8,2,4,7,5]=>{{1},{2,4,5,6,8},{3},{7}}
[5,3,8,1,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,3,2,6,4,7]=>{{1,2,5},{3,4,7,8},{6}}
[5,7,3,1,2,6,4,8]=>{{1,2,4,5,7},{3},{6},{8}}
[1,7,5,4,2,6,3,8]=>{{1},{2,3,5,7},{4},{6},{8}}
[1,5,8,2,4,6,3,7]=>{{1},{2,4,5},{3,7,8},{6}}
[1,5,8,4,2,7,3,6]=>{{1},{2,5},{3,6,7,8},{4}}
[1,4,6,2,8,3,7,5]=>{{1},{2,4},{3,6},{5,8},{7}}
[5,3,1,6,7,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[5,3,6,1,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,3,2,7,8,4,5]=>{{1},{2,4,5,6,7,8},{3}}
[1,7,4,5,3,8,6,2]=>{{1},{2,6,7,8},{3,4,5}}
[6,3,4,1,2,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[6,3,1,4,2,7,5,8]=>{{1,2,3,5,6,7},{4},{8}}
[1,8,3,2,4,5,6,7]=>{{1},{2,4,5,6,7,8},{3}}
[8,6,3,2,4,1,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[8,5,3,2,6,7,1,4]=>{{1,2,4,5,6,7,8},{3}}
[4,5,2,6,8,1,7,3]=>{{1,4,6},{2,3,5,8},{7}}
[4,2,5,6,7,8,1,3]=>{{1,3,4,5,6,7,8},{2}}
[5,2,3,6,7,1,8,4]=>{{1,4,5,6,7,8},{2},{3}}
[6,2,3,4,1,7,8,5]=>{{1,5,6,7,8},{2},{3},{4}}
[7,2,3,1,4,5,8,6]=>{{1,4,5,6,7,8},{2},{3}}
[8,6,1,4,3,2,5,7]=>{{1,3,5,7,8},{2,6},{4}}
[8,3,1,6,5,2,4,7]=>{{1,2,3,4,6,7,8},{5}}
[3,7,5,1,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[4,1,5,2,8,7,3,6]=>{{1,2,4},{3,5,6,7,8}}
[8,1,2,4,6,5,3,7]=>{{1,2,3,7,8},{4},{5,6}}
[8,1,2,5,4,6,3,7]=>{{1,2,3,7,8},{4,5},{6}}
[8,2,6,5,1,3,4,7]=>{{1,4,5,7,8},{2},{3,6}}
[8,3,1,6,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,6,4,5,3,7]=>{{1,2,3,7,8},{4,5,6}}
[8,1,2,5,6,4,3,7]=>{{1,2,3,7,8},{4,5,6}}
[8,1,2,6,5,4,3,7]=>{{1,2,3,7,8},{4,6},{5}}
[1,7,5,4,2,8,3,6]=>{{1},{2,3,5,7},{4},{6,8}}
[5,1,4,8,2,7,3,6]=>{{1,2,5},{3,4,6,7,8}}
[1,4,6,8,2,7,3,5]=>{{1},{2,4,5,8},{3,6,7}}
[1,4,7,6,2,8,3,5]=>{{1},{2,4,5,6,8},{3,7}}
[5,1,4,7,2,8,3,6]=>{{1,2,5},{3,4,7},{6,8}}
[1,7,4,5,2,8,3,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,7,5,1,2,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[5,7,2,8,1,3,4,6]=>{{1,5},{2,3,4,6,7,8}}
[5,2,8,7,1,3,4,6]=>{{1,5},{2},{3,6,8},{4,7}}
[4,1,5,8,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[1,4,6,2,8,7,3,5]=>{{1},{2,4},{3,6,7},{5,8}}
[1,4,2,8,6,7,3,5]=>{{1},{2,3,4,5,6,7,8}}
[3,1,2,6,4,8,7,5]=>{{1,2,3},{4,5,6,8},{7}}
[2,1,7,6,3,4,8,5]=>{{1,2},{3,5,7,8},{4,6}}
[3,1,2,7,4,6,8,5]=>{{1,2,3},{4,5,7,8},{6}}
[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[1,2,3,6,8,5,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[5,1,4,2,7,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[1,4,2,7,6,8,3,5]=>{{1},{2,3,4,7},{5,6,8}}
[1,4,2,6,8,7,3,5]=>{{1},{2,3,4,6,7},{5,8}}
[3,1,2,8,4,6,7,5]=>{{1,2,3},{4,5,8},{6},{7}}
[3,1,2,7,6,4,8,5]=>{{1,2,3},{4,5,6,7,8}}
[5,3,7,1,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[1,7,4,3,2,5,8,6]=>{{1},{2,5,6,7,8},{3,4}}
[4,8,7,2,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,3,4,2,5,6]=>{{1},{2,6,8},{3,4,5,7}}
[3,1,7,8,2,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[1,4,2,7,8,3,6,5]=>{{1},{2,3,4,6,7},{5,8}}
[5,2,8,1,3,4,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[2,1,8,6,3,4,7,5]=>{{1,2},{3,5,8},{4,6},{7}}
[1,4,2,6,8,3,7,5]=>{{1},{2,3,4,6},{5,8},{7}}
[1,2,3,7,8,5,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,7,5,8,6,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[1,4,2,7,3,8,6,5]=>{{1},{2,3,4,5,6,7,8}}
[3,1,7,2,8,6,4,5]=>{{1,2,3,4,7},{5,8},{6}}
[2,1,7,8,3,4,6,5]=>{{1,2},{3,4,5,6,7,8}}
[1,2,3,8,7,5,6,4]=>{{1},{2},{3},{4,8},{5,6,7}}
[4,7,8,5,6,2,1,3]=>{{1,2,4,5,6,7},{3,8}}
[5,7,8,4,2,6,1,3]=>{{1,2,5,7},{3,8},{4},{6}}
[6,7,8,4,2,5,1,3]=>{{1,2,5,6,7},{3,8},{4}}
[8,6,3,7,2,1,5,4]=>{{1,2,4,5,6,7,8},{3}}
[7,6,3,8,2,1,5,4]=>{{1,2,5,6,7},{3},{4,8}}
[6,7,8,3,2,1,5,4]=>{{1,6},{2,5,7},{3,4,8}}
[5,7,8,3,2,1,6,4]=>{{1,2,5,6,7},{3,4,8}}
[2,7,8,4,3,5,6,1]=>{{1,2,3,5,6,7,8},{4}}
[3,7,8,4,2,5,1,6]=>{{1,2,3,5,6,7,8},{4}}
[4,7,8,3,2,1,5,6]=>{{1,3,4,6,8},{2,5,7}}
[5,7,8,3,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,6,3,8,2,1,4,5]=>{{1,2,4,5,6,7,8},{3}}
[8,6,3,7,2,1,4,5]=>{{1,2,5,6,8},{3},{4,7}}
[5,6,3,8,2,1,4,7]=>{{1,2,5,6},{3},{4,7,8}}
[3,6,4,8,2,5,1,7]=>{{1,3,4,7,8},{2,5,6}}
[2,6,4,8,3,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,6,4,7,3,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,7,2,5,1,8]=>{{1,3,4,7},{2,5,6},{8}}
[4,6,3,7,2,1,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,6,3,7,2,1,4,8]=>{{1,2,5,6},{3},{4,7},{8}}
[8,4,3,2,1,6,5,7]=>{{1,5,7,8},{2,4},{3},{6}}
[6,4,3,2,1,7,5,8]=>{{1,5,6,7},{2,4},{3},{8}}
[4,5,3,2,7,1,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[3,5,4,2,8,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[6,4,3,2,1,8,5,7]=>{{1,5,6,7,8},{2,4},{3}}
[7,4,3,2,1,8,5,6]=>{{1,5,7},{2,4},{3},{6,8}}
[8,4,3,2,1,7,5,6]=>{{1,5,6,7,8},{2,4},{3}}
[8,4,3,2,1,7,6,5]=>{{1,5,8},{2,4},{3},{6,7}}
[7,4,3,2,1,8,6,5]=>{{1,5,6,7,8},{2,4},{3}}
[6,4,3,2,1,8,7,5]=>{{1,5,6,8},{2,4},{3},{7}}
[5,6,3,8,2,1,7,4]=>{{1,2,5,6},{3},{4,8},{7}}
[7,5,3,2,8,1,6,4]=>{{1,6,7},{2,4,5,8},{3}}
[8,5,4,2,7,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[7,5,4,2,8,6,1,3]=>{{1,7},{2,3,4,5,8},{6}}
[6,5,4,2,8,7,1,3]=>{{1,6,7},{2,3,4,5,8}}
[4,6,5,8,7,2,1,3]=>{{1,3,4,5,7,8},{2,6}}
[2,6,5,7,8,3,4,1]=>{{1,2,3,5,6,8},{4,7}}
[6,5,4,2,7,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,2,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,2,6,1,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[7,5,3,2,6,1,8,4]=>{{1,2,4,5,6,7,8},{3}}
[5,6,3,7,2,1,8,4]=>{{1,2,5,6},{3},{4,7,8}}
[4,6,3,7,2,1,8,5]=>{{1,2,4,5,6,7,8},{3}}
[3,6,4,7,2,8,1,5]=>{{1,3,4,7},{2,5,6,8}}
[2,6,4,7,3,8,5,1]=>{{1,2,6,8},{3,4,5,7}}
[3,5,4,2,7,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[4,5,3,2,7,1,8,6]=>{{1,2,4,5,6,7,8},{3}}
[7,4,3,2,1,6,8,5]=>{{1,5,7,8},{2,4},{3},{6}}
[8,4,3,2,1,6,7,5]=>{{1,5,8},{2,4},{3},{6},{7}}
[8,4,3,2,1,5,7,6]=>{{1,5,6,8},{2,4},{3},{7}}
[7,4,3,2,1,5,8,6]=>{{1,5,6,7,8},{2,4},{3}}
[6,4,3,2,1,5,8,7]=>{{1,5,6},{2,4},{3},{7,8}}
[3,5,4,2,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,3,4,1,2,8,7]=>{{1,5},{2,6},{3},{4},{7,8}}
[8,5,3,7,2,6,4,1]=>{{1,8},{2,5},{3},{4,7},{6}}
[8,5,7,4,2,6,3,1]=>{{1,8},{2,5},{3,7},{4},{6}}
[7,5,8,4,2,6,1,3]=>{{1,7},{2,5},{3,8},{4},{6}}
[2,1,7,8,5,6,3,4]=>{{1,2},{3,7},{4,8},{5},{6}}
[6,8,3,7,5,1,4,2]=>{{1,6},{2,8},{3},{4,7},{5}}
[5,7,3,8,1,6,2,4]=>{{1,5},{2,7},{3},{4,8},{6}}
[3,2,6,4,8,5,1,7]=>{{1,3,5,6,7,8},{2},{4}}
[3,2,5,8,4,6,1,7]=>{{1,3,4,5,7,8},{2},{6}}
[3,5,2,4,1,7,6,8]=>{{1,2,3,5},{4},{6,7},{8}}
[4,2,1,5,7,3,6,8]=>{{1,3,4,5,6,7},{2},{8}}
[4,5,2,3,7,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[4,2,5,3,8,1,6,7]=>{{1,3,4,5,6,7,8},{2}}
[4,2,5,8,3,1,6,7]=>{{1,4,6,7,8},{2},{3,5}}
[3,1,5,4,2,8,6,7]=>{{1,2,3,5},{4},{6,7,8}}
[4,1,5,3,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,5,8,3,2,6,7]=>{{1,2,4,6,7,8},{3,5}}
[4,3,8,5,2,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,7,3,5,2,1,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[4,3,2,7,5,1,6,8]=>{{1,4,6,7},{2,3},{5},{8}}
[4,3,6,2,5,1,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[4,6,3,2,5,1,7,8]=>{{1,2,4,6},{3},{5},{7},{8}}
[4,6,7,1,3,2,5,8]=>{{1,4},{2,6},{3,5,7},{8}}
[4,5,1,7,3,2,6,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,1,3,7,2,6,8]=>{{1,3,4},{2,5,6,7},{8}}
[3,5,1,4,2,7,6,8]=>{{1,3},{2,5},{4},{6,7},{8}}
[2,5,1,4,3,7,8,6]=>{{1,2,3,5},{4},{6,7,8}}
[5,2,1,4,3,7,8,6]=>{{1,3,5},{2},{4},{6,7,8}}
[5,3,1,4,2,7,6,8]=>{{1,2,3,5},{4},{6,7},{8}}
[4,3,1,5,7,2,6,8]=>{{1,2,3,4,5,6,7},{8}}
[4,3,1,7,5,2,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[4,3,6,1,5,2,7,8]=>{{1,4},{2,3,6},{5},{7},{8}}
[4,6,3,1,5,2,7,8]=>{{1,4},{2,6},{3},{5},{7},{8}}
[5,3,6,4,1,2,7,8]=>{{1,5},{2,3,6},{4},{7},{8}}
[4,3,6,1,7,2,5,8]=>{{1,4},{2,3,6},{5,7},{8}}
[6,3,4,1,2,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[6,2,4,1,3,7,8,5]=>{{1,3,4,5,6,7,8},{2}}
[3,6,4,1,2,7,5,8]=>{{1,3,4},{2,5,6,7},{8}}
[4,6,3,1,7,2,5,8]=>{{1,4},{2,6},{3},{5,7},{8}}
[5,3,6,2,1,4,7,8]=>{{1,5},{2,3,4,6},{7},{8}}
[5,6,2,7,1,3,4,8]=>{{1,5},{2,3,6},{4,7},{8}}
[4,5,2,7,3,1,6,8]=>{{1,4,6,7},{2,3,5},{8}}
[4,6,7,2,3,1,5,8]=>{{1,2,4,6},{3,5,7},{8}}
[4,6,2,1,7,3,5,8]=>{{1,4},{2,3,6},{5,7},{8}}
[3,2,6,1,4,7,5,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,6,2,1,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,6,7,2,4,5,1,8]=>{{1,3,7},{2,4,5,6},{8}}
[3,5,2,7,4,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[3,7,2,4,8,5,1,6]=>{{1,2,3,7},{4},{5,6,8}}
[7,2,1,4,6,3,8,5]=>{{1,3,5,6,7,8},{2},{4}}
[7,3,1,4,6,8,2,5]=>{{1,2,3,7},{4},{5,6,8}}
[3,2,6,1,5,7,4,8]=>{{1,3,4,6,7},{2},{5},{8}}
[3,6,2,1,5,7,4,8]=>{{1,2,3,4,6,7},{5},{8}}
[6,3,2,1,5,7,4,8]=>{{1,4,6,7},{2,3},{5},{8}}
[6,4,2,1,5,3,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[4,2,6,1,5,3,7,8]=>{{1,4},{2},{3,6},{5},{7},{8}}
[4,2,1,7,5,3,6,8]=>{{1,3,4,6,7},{2},{5},{8}}
[7,4,1,5,6,2,3,8]=>{{1,3,7},{2,4,5,6},{8}}
[7,3,1,5,2,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}
[7,2,1,5,3,6,8,4]=>{{1,3,4,5,7,8},{2},{6}}
[6,2,5,1,3,7,8,4]=>{{1,4,6,7,8},{2},{3,5}}
[6,3,5,1,2,7,4,8]=>{{1,4,6,7},{2,3,5},{8}}
[6,4,5,1,7,2,3,8]=>{{1,2,4,6},{3,5,7},{8}}
[5,2,6,4,1,3,7,8]=>{{1,5},{2},{3,6},{4},{7},{8}}
[4,6,5,1,7,2,3,8]=>{{1,4},{2,6},{3,5,7},{8}}
[3,6,5,1,2,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,5,2,1,4,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,3,1,4,7,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[2,3,1,8,5,4,7,6]=>{{1,2,3},{4,6,8},{5},{7}}
[2,4,1,5,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,4,1,5,3,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[3,4,5,1,2,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[3,4,5,1,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[3,4,5,8,2,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[3,4,5,2,8,1,7,6]=>{{1,3,5,6,8},{2,4},{7}}
[3,4,6,2,1,7,8,5]=>{{1,3,5,6,7,8},{2,4}}
[3,4,6,2,1,7,5,8]=>{{1,3,5,6,7},{2,4},{8}}
[3,5,6,2,7,1,4,8]=>{{1,3,6},{2,4,5,7},{8}}
[3,5,6,2,7,1,8,4]=>{{1,3,6},{2,4,5,7,8}}
[3,5,6,2,7,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,6,3,7,1,5]=>{{1,2,4,6,7},{3,5,8}}
[1,8,4,6,3,7,2,5]=>{{1},{2,3,4,5,6,7,8}}
[3,4,6,8,2,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,4,6,2,8,7,5,1]=>{{1,3,5,6,7,8},{2,4}}
[3,5,6,2,7,8,4,1]=>{{1,3,6,8},{2,4,5,7}}
[3,5,6,2,7,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,6,7,2,8,3,1]=>{{1,3,4,6,7,8},{2,5}}
[3,5,6,8,7,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,5,8,6,7,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,5,8,6,7,3,1,4]=>{{1,2,5,7},{3,4,6,8}}
[3,5,6,8,7,2,1,4]=>{{1,2,3,5,6,7},{4,8}}
[4,5,6,7,2,1,8,3]=>{{1,3,4,6,7,8},{2,5}}
[2,3,1,8,6,7,4,5]=>{{1,2,3},{4,5,6,7,8}}
[1,8,3,2,6,7,5,4]=>{{1},{2,4,8},{3},{5,6,7}}
[2,5,1,6,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,1,6,7,4,8,3]=>{{1,2,3,5,7,8},{4,6}}
[2,5,1,6,7,4,3,8]=>{{1,2,3,5,7},{4,6},{8}}
[3,5,6,1,7,4,2,8]=>{{1,3,4,6},{2,5,7},{8}}
[3,5,6,1,7,4,8,2]=>{{1,3,4,6},{2,5,7,8}}
[3,4,6,8,1,7,5,2]=>{{1,3,5,6,7},{2,4,8}}
[2,4,8,6,1,7,5,3]=>{{1,2,4,5,6,7},{3,8}}
[3,5,6,8,7,1,4,2]=>{{1,3,6},{2,4,5,7,8}}
[4,5,6,7,8,1,3,2]=>{{1,3,4,6,7},{2,5,8}}
[4,5,6,7,1,3,8,2]=>{{1,2,4,5,7,8},{3,6}}
[4,5,6,7,1,3,2,8]=>{{1,2,4,5,7},{3,6},{8}}
[4,5,6,7,3,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,8,7,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[2,5,8,6,7,4,1,3]=>{{1,2,5,7},{3,8},{4,6}}
[2,5,8,6,7,4,3,1]=>{{1,2,3,5,7,8},{4,6}}
[8,2,5,3,7,1,6,4]=>{{1,3,4,5,6,7,8},{2}}
[8,2,4,3,7,1,6,5]=>{{1,5,6,7,8},{2},{3,4}}
[5,8,2,4,3,7,1,6]=>{{1,2,3,5,6,7,8},{4}}
[4,2,5,6,1,8,3,7]=>{{1,3,4,5,6,7,8},{2}}
[4,2,5,6,1,7,3,8]=>{{1,3,4,5,6,7},{2},{8}}
[6,1,5,7,3,2,4,8]=>{{1,2,6},{3,5},{4,7},{8}}
[6,1,5,8,3,2,4,7]=>{{1,2,6},{3,5},{4,7,8}}
[3,8,2,4,7,1,5,6]=>{{1,2,3,6,8},{4},{5,7}}
[3,6,8,2,4,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,3,5,6,7,1,8,2]=>{{1,4,6},{2,3,5,7,8}}
[3,7,1,5,6,8,2,4]=>{{1,3},{2,7},{4,5,6,8}}
[3,7,1,5,8,2,4,6]=>{{1,3},{2,4,5,6,7,8}}
[8,3,2,4,6,1,5,7]=>{{1,5,6,7,8},{2,3},{4}}
[7,3,2,4,6,1,5,8]=>{{1,5,6,7},{2,3},{4},{8}}
[3,2,5,1,7,4,6,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,2,5,1,8,4,6,7]=>{{1,3,4,5,6,7,8},{2}}
[3,2,5,1,7,8,4,6]=>{{1,3,4,5,7},{2},{6,8}}
[7,8,3,2,4,6,1,5]=>{{1,7},{2,4,5,8},{3},{6}}
[6,1,5,7,8,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[4,2,5,6,1,7,8,3]=>{{1,3,4,5,6,7,8},{2}}
[5,7,6,1,8,3,4,2]=>{{1,2,4,5,7,8},{3,6}}
[5,8,6,1,7,3,4,2]=>{{1,4,5,7},{2,8},{3,6}}
[6,1,5,8,7,3,2,4]=>{{1,2,3,5,6,7},{4,8}}
[8,7,3,2,4,6,1,5]=>{{1,2,4,5,7,8},{3},{6}}
[3,2,5,1,8,7,4,6]=>{{1,3,4,5,6,7,8},{2}}
[3,2,5,1,6,4,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[3,2,4,1,8,7,5,6]=>{{1,3,4},{2},{5,6,7,8}}
[3,2,5,1,6,8,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[3,8,6,5,1,7,4,2]=>{{1,3,4,5,6,7},{2,8}}
[3,7,6,5,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,1,7,8,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,2,5,1,6,7,8,4]=>{{1,3,4,5,6,7,8},{2}}
[3,2,4,1,8,5,6,7]=>{{1,3,4},{2},{5,6,7,8}}
[3,2,4,1,7,5,6,8]=>{{1,3,4},{2},{5,6,7},{8}}
[3,2,4,1,6,8,5,7]=>{{1,3,4},{2},{5,6,7,8}}
[3,2,4,1,8,5,7,6]=>{{1,3,4},{2},{5,6,8},{7}}
[8,3,2,4,7,6,1,5]=>{{1,5,7,8},{2,3},{4},{6}}
[3,2,5,1,8,4,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[3,2,5,1,6,7,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[6,5,1,7,4,2,3,8]=>{{1,2,3,4,5,6,7},{8}}
[6,5,1,8,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,3,7,5,1,6]=>{{1,5,6,7,8},{2,3,4}}
[4,2,6,1,8,3,7,5]=>{{1,4},{2},{3,6},{5,8},{7}}
[5,2,6,1,8,3,7,4]=>{{1,4,5,8},{2},{3,6},{7}}
[8,4,6,1,7,3,5,2]=>{{1,2,4,8},{3,6},{5,7}}
[5,2,6,1,8,4,7,3]=>{{1,3,4,5,6,8},{2},{7}}
[7,4,2,3,8,5,1,6]=>{{1,7},{2,3,4},{5,6,8}}
[8,5,1,6,4,2,3,7]=>{{1,3,7,8},{2,4,5,6}}
[7,5,1,6,4,2,3,8]=>{{1,3,7},{2,4,5,6},{8}}
[3,2,5,1,7,6,4,8]=>{{1,3,4,5,7},{2},{6},{8}}
[3,2,5,1,8,6,4,7]=>{{1,3,4,5,7,8},{2},{6}}
[7,3,2,4,8,6,1,5]=>{{1,7},{2,3},{4},{5,8},{6}}
[8,6,1,5,7,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[4,2,6,1,8,5,7,3]=>{{1,4},{2},{3,5,6,8},{7}}
[8,5,6,1,7,3,4,2]=>{{1,2,4,5,7,8},{3,6}}
[3,6,8,5,1,7,4,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,1,6,7,4,2,3]=>{{1,3,8},{2,5,7},{4,6}}
[3,2,5,1,8,6,7,4]=>{{1,3,4,5,8},{2},{6},{7}}
[3,2,4,1,8,6,5,7]=>{{1,3,4},{2},{5,7,8},{6}}
[3,2,4,1,5,8,6,7]=>{{1,3,4},{2},{5},{6,7,8}}
[3,2,5,1,7,8,6,4]=>{{1,3,4,5,6,7,8},{2}}
[7,8,5,1,6,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,8,5,1,7,6,4,2]=>{{1,3,4,5,7},{2,8},{6}}
[3,7,5,1,8,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[8,7,5,1,6,4,2,3]=>{{1,3,4,5,6,8},{2,7}}
[3,2,5,1,8,7,6,4]=>{{1,3,4,5,8},{2},{6,7}}
[6,5,7,3,1,8,4,2]=>{{1,2,5,6,8},{3,4,7}}
[4,6,3,7,1,8,5,2]=>{{1,4,5,7},{2,6,8},{3}}
[4,6,3,7,5,1,8,2]=>{{1,2,4,6,7,8},{3},{5}}
[4,2,6,1,7,5,3,8]=>{{1,4},{2},{3,5,6,7},{8}}
[2,5,7,4,1,6,3,8]=>{{1,2,5},{3,7},{4},{6},{8}}
[2,5,7,4,1,6,8,3]=>{{1,2,5},{3,7,8},{4},{6}}
[5,4,7,3,6,1,8,2]=>{{1,5,6},{2,3,4,7,8}}
[5,4,7,8,3,1,6,2]=>{{1,3,5,6,7},{2,4,8}}
[4,3,7,5,1,8,6,2]=>{{1,4,5},{2,3,6,7,8}}
[6,4,3,8,5,1,7,2]=>{{1,6},{2,4,8},{3},{5},{7}}
[5,8,4,3,6,1,7,2]=>{{1,5,6},{2,8},{3,4},{7}}
[5,4,8,3,6,1,7,2]=>{{1,5,6},{2,3,4,8},{7}}
[5,4,3,6,7,1,8,2]=>{{1,2,4,5,6,7,8},{3}}
[2,5,4,6,1,7,3,8]=>{{1,2,5},{3,4,6,7},{8}}
[3,2,5,8,1,6,7,4]=>{{1,3,5},{2},{4,8},{6},{7}}
[2,5,4,6,8,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[5,2,8,4,1,6,7,3]=>{{1,5},{2},{3,8},{4},{6},{7}}
[4,6,2,1,8,5,7,3]=>{{1,4},{2,3,5,6,8},{7}}
[2,4,1,7,5,8,6,3]=>{{1,2,3,4,6,7,8},{5}}
[2,4,1,7,5,3,8,6]=>{{1,2,3,4,6,7,8},{5}}
[2,6,4,1,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,2,1,6,3,7]=>{{1,5},{2,4},{3,7,8},{6}}
[2,5,8,4,1,6,3,7]=>{{1,2,5},{3,7,8},{4},{6}}
[3,2,5,6,1,8,4,7]=>{{1,3,5},{2},{4,6,7,8}}
[4,8,3,2,6,1,5,7]=>{{1,2,4,5,6,7,8},{3}}
[3,5,2,8,1,6,4,7]=>{{1,2,3,5},{4,7,8},{6}}
[3,2,1,6,8,5,4,7]=>{{1,3},{2},{4,5,6,7,8}}
[3,2,7,1,5,4,8,6]=>{{1,3,4,6,7,8},{2},{5}}
[3,2,7,1,5,8,6,4]=>{{1,3,4,6,7,8},{2},{5}}
[3,8,2,5,1,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[4,8,3,2,6,7,1,5]=>{{1,2,4,5,6,7,8},{3}}
[4,3,8,2,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,3,2,6,7,8,1,5]=>{{1,4,5,6,7,8},{2,3}}
[4,3,2,6,7,1,5,8]=>{{1,4,6},{2,3},{5,7},{8}}
[4,3,7,2,6,8,1,5]=>{{1,2,3,4,7},{5,6,8}}
[4,3,7,8,2,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[2,5,7,4,8,1,6,3]=>{{1,2,3,5,6,7,8},{4}}
[3,2,5,7,8,1,6,4]=>{{1,3,4,5,6,7,8},{2}}
[3,2,5,7,1,6,8,4]=>{{1,3,5},{2},{4,7,8},{6}}
[3,2,5,7,1,6,4,8]=>{{1,3,5},{2},{4,7},{6},{8}}
[6,3,2,7,1,5,4,8]=>{{1,5,6},{2,3},{4,7},{8}}
[6,3,2,7,1,5,8,4]=>{{1,5,6},{2,3},{4,7,8}}
[6,3,2,7,8,1,5,4]=>{{1,6},{2,3},{4,5,7,8}}
[4,2,6,1,7,8,5,3]=>{{1,4},{2},{3,6,8},{5,7}}
[6,5,2,1,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,5,3,8,6,4]=>{{1,2},{3,4,5,6,7,8}}
[6,2,1,8,5,3,7,4]=>{{1,3,6},{2},{4,8},{5},{7}}
[6,3,2,7,1,4,8,5]=>{{1,4,5,6,7,8},{2,3}}
[6,3,2,1,4,7,8,5]=>{{1,4,5,6,7,8},{2,3}}
[6,3,2,1,4,7,5,8]=>{{1,4,5,6,7},{2,3},{8}}
[3,5,2,1,7,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,2,1,7,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[5,8,4,2,1,7,3,6]=>{{1,5},{2,3,4,6,7,8}}
[4,6,2,1,8,3,7,5]=>{{1,4},{2,3,6},{5,8},{7}}
[2,4,1,7,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[3,2,7,1,4,8,6,5]=>{{1,3,4,5,6,7,8},{2}}
[3,5,8,2,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,3,7,2,1,5,6]=>{{1,2,4,5,6,7,8},{3}}
[4,3,7,2,8,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,2,1,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[4,8,3,2,7,1,5,6]=>{{1,2,4,6,8},{3},{5,7}}
[3,5,2,8,1,7,4,6]=>{{1,2,3,5},{4,6,7,8}}
[6,3,2,8,1,4,7,5]=>{{1,4,5,6,8},{2,3},{7}}
[3,2,1,4,7,5,8,6]=>{{1,3},{2},{4},{5,6,7,8}}
[5,3,2,1,8,4,6,7]=>{{1,4,5,6,7,8},{2,3}}
[4,8,3,2,1,5,6,7]=>{{1,2,4,5,6,7,8},{3}}
[4,3,8,2,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[6,2,3,1,5,4,8,7]=>{{1,4,6},{2},{3},{5},{7,8}}
[8,4,5,2,3,1,7,6]=>{{1,6,8},{2,4},{3,5},{7}}
[8,6,7,2,5,3,4,1]=>{{1,8},{2,3,4,6,7},{5}}
[8,2,5,3,4,1,7,6]=>{{1,6,8},{2},{3,4,5},{7}}
[6,2,5,3,4,1,8,7]=>{{1,6},{2},{3,4,5},{7,8}}
[6,1,5,2,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[6,4,5,1,3,2,8,7]=>{{1,2,4,6},{3,5},{7,8}}
[6,1,5,3,4,2,8,7]=>{{1,2,6},{3,4,5},{7,8}}
[6,3,5,1,4,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[8,3,5,2,4,1,7,6]=>{{1,6,8},{2,3,4,5},{7}}
[8,3,7,5,6,2,4,1]=>{{1,8},{2,3,4,5,6,7}}
[8,3,7,2,4,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,5,1,4,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[8,1,5,3,4,2,7,6]=>{{1,2,6,8},{3,4,5},{7}}
[8,4,5,1,3,2,7,6]=>{{1,2,4,6,8},{3,5},{7}}
[2,1,8,4,5,3,7,6]=>{{1,2},{3,6,8},{4},{5},{7}}
[8,6,7,4,5,1,3,2]=>{{1,2,6,8},{3,7},{4},{5}}
[8,6,7,1,5,3,4,2]=>{{1,2,3,4,6,7,8},{5}}
[8,6,7,3,5,1,4,2]=>{{1,2,6,8},{3,4,7},{5}}
[8,3,7,5,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,3,6,1,4,2]=>{{1,2,5,6,8},{3,4,7}}
[8,3,7,4,6,2,5,1]=>{{1,8},{2,3,5,6,7},{4}}
[8,3,7,4,6,1,5,2]=>{{1,2,3,5,6,7,8},{4}}
[8,3,7,1,6,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,3,6,4,5,2]=>{{1,2,8},{3,4,5,6,7}}
[8,1,7,5,6,3,4,2]=>{{1,2,8},{3,4,5,6,7}}
[8,4,7,5,6,1,3,2]=>{{1,2,4,5,6,8},{3,7}}
[2,1,8,4,7,5,6,3]=>{{1,2},{3,8},{4},{5,6,7}}
[8,1,7,3,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,3,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,1,6,2,5,4]=>{{1,4,8},{2,3,5,6,7}}
[8,3,7,2,6,4,5,1]=>{{1,8},{2,3,4,5,6,7}}
[8,2,7,3,6,4,5,1]=>{{1,8},{2},{3,4,5,6,7}}
[8,2,7,3,6,1,5,4]=>{{1,3,4,5,6,7,8},{2}}
[8,2,7,1,6,3,5,4]=>{{1,4,8},{2},{3,5,6,7}}
[8,1,7,2,4,3,6,5]=>{{1,2,4,5,8},{3,6,7}}
[8,1,3,2,7,4,6,5]=>{{1,2,4,5,6,7,8},{3}}
[2,1,8,3,7,4,6,5]=>{{1,2},{3,4,5,6,7,8}}
[8,1,5,2,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[8,2,7,1,4,3,6,5]=>{{1,4,5,8},{2},{3,6,7}}
[8,2,7,3,4,1,6,5]=>{{1,3,4,5,6,7,8},{2}}
[8,2,7,5,6,3,4,1]=>{{1,8},{2},{3,4,5,6,7}}
[8,4,7,5,6,2,3,1]=>{{1,8},{2,4,5,6},{3,7}}
[8,4,7,2,3,1,6,5]=>{{1,3,5,6,7,8},{2,4}}
[8,2,3,1,7,4,6,5]=>{{1,4,5,6,7,8},{2},{3}}
[8,2,3,1,5,4,7,6]=>{{1,4,6,8},{2},{3},{5},{7}}
[4,2,3,1,8,5,7,6]=>{{1,4},{2},{3},{5,6,8},{7}}
[4,1,3,2,8,6,7,5]=>{{1,2,4},{3},{5,8},{6},{7}}
[8,6,7,2,3,1,5,4]=>{{1,2,4,6,8},{3,5,7}}
[8,2,3,1,7,5,6,4]=>{{1,4,8},{2},{3},{5,6,7}}
[8,5,7,2,6,3,4,1]=>{{1,8},{2,3,4,5,6,7}}
[8,5,7,2,6,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[8,2,7,5,6,1,4,3]=>{{1,3,4,5,6,7,8},{2}}
[8,6,7,2,5,1,4,3]=>{{1,2,3,4,6,7,8},{5}}
[8,6,7,1,5,2,4,3]=>{{1,3,4,7,8},{2,6},{5}}
[8,6,7,1,3,2,5,4]=>{{1,4,8},{2,6},{3,5,7}}
[2,1,8,6,7,3,5,4]=>{{1,2},{3,4,6,8},{5,7}}
[2,1,8,3,7,5,6,4]=>{{1,2},{3,4,8},{5,6,7}}
[8,1,3,2,7,5,6,4]=>{{1,2,4,8},{3},{5,6,7}}
[8,1,7,5,6,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,2,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[8,2,7,1,6,4,5,3]=>{{1,3,4,5,6,7,8},{2}}
[8,2,7,4,6,1,5,3]=>{{1,3,5,6,7,8},{2},{4}}
[8,2,7,4,6,3,5,1]=>{{1,8},{2},{3,5,6,7},{4}}
[8,4,7,2,6,3,5,1]=>{{1,8},{2,4},{3,5,6,7}}
[8,4,7,2,6,1,5,3]=>{{1,3,5,6,7,8},{2,4}}
[8,4,7,1,6,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,4,6,2,5,3]=>{{1,2,3,5,6,7,8},{4}}
[8,5,7,1,6,2,4,3]=>{{1,3,4,7,8},{2,5,6}}
[2,1,8,5,7,3,6,4]=>{{1,2},{3,4,5,6,7,8}}
[8,5,7,4,6,1,3,2]=>{{1,2,5,6,8},{3,7},{4}}
[8,5,7,1,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,4,6,3,5,2]=>{{1,2,8},{3,5,6,7},{4}}
[8,4,7,1,6,3,5,2]=>{{1,2,4,8},{3,5,6,7}}
[8,4,7,3,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,3,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[6,5,8,1,3,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[4,5,8,6,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[6,5,8,7,3,1,2,4]=>{{1,6},{2,3,4,5,7,8}}
[1,5,8,7,3,6,2,4]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,2,8,4,6,5,3]=>{{1},{2,3,4,5,7,8},{6}}
[6,7,2,8,4,1,5,3]=>{{1,6},{2,3,4,5,7,8}}
[3,6,2,8,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,6,1,8,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,8,4,6,1,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,3,1,8,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[3,1,6,8,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[2,3,6,8,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[6,3,7,8,4,1,5,2]=>{{1,6},{2,3,4,5,7,8}}
[1,3,7,8,4,6,5,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,5,7,8,2,4,6,3]=>{{1},{2,5},{3,4,6,7,8}}
[5,1,7,8,2,4,6,3]=>{{1,2,5},{3,4,6,7,8}}
[3,6,7,8,4,2,5,1]=>{{1,3,4,5,7,8},{2,6}}
[7,6,1,8,4,2,5,3]=>{{1,3,4,5,7,8},{2,6}}
[5,6,8,7,3,2,1,4]=>{{1,3,4,5,7,8},{2,6}}
[2,8,3,7,1,6,5,4]=>{{1,2,4,5,7,8},{3},{6}}
[5,2,8,7,3,6,1,4]=>{{1,3,4,5,7,8},{2},{6}}
[7,2,1,8,4,6,5,3]=>{{1,3,4,5,7,8},{2},{6}}
[3,2,7,8,4,6,5,1]=>{{1,3,4,5,7,8},{2},{6}}
[5,2,7,8,1,4,6,3]=>{{1,5},{2},{3,4,6,7,8}}
[1,2,7,8,5,4,6,3]=>{{1},{2},{3,4,6,7,8},{5}}
[4,2,1,3,8,5,6,7]=>{{1,3,4},{2},{5,6,7,8}}
[7,2,5,8,3,4,6,1]=>{{1,4,6,7,8},{2},{3,5}}
[6,2,8,5,4,3,1,7]=>{{1,3,6,7,8},{2},{4,5}}
[2,8,3,5,4,1,6,7]=>{{1,2,6,7,8},{3},{4,5}}
[2,8,4,5,3,1,6,7]=>{{1,2,6,7,8},{3,4,5}}
[6,4,8,5,2,3,1,7]=>{{1,3,6,7,8},{2,4,5}}
[7,3,5,8,2,4,6,1]=>{{1,4,6,7,8},{2,3,5}}
[4,3,1,2,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}
[3,4,2,1,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}
[2,7,6,8,4,3,5,1]=>{{1,2,4,5,7,8},{3,6}}
[5,7,1,8,3,4,6,2]=>{{1,3,5},{2,4,6,7,8}}
[3,7,5,8,1,4,6,2]=>{{1,3,5},{2,4,6,7,8}}
[1,7,5,8,3,4,6,2]=>{{1},{2,4,6,7,8},{3,5}}
[1,6,8,5,4,3,2,7]=>{{1},{2,3,6,7,8},{4,5}}
[4,6,8,5,1,3,2,7]=>{{1,4,5},{2,3,6,7,8}}
[5,6,8,1,4,3,2,7]=>{{1,4,5},{2,3,6,7,8}}
[7,5,8,6,3,4,2,1]=>{{1,2,3,5,7,8},{4,6}}
[2,4,8,3,6,5,1,7]=>{{1,2,3,4,7,8},{5,6}}
[2,8,4,1,5,6,3,7]=>{{1,2,3,4,7,8},{5},{6}}
[4,1,8,3,5,6,2,7]=>{{1,2,3,4,7,8},{5},{6}}
[5,6,8,4,1,3,2,7]=>{{1,5},{2,3,6,7,8},{4}}
[4,6,8,1,5,3,2,7]=>{{1,4},{2,3,6,7,8},{5}}
[1,6,8,4,5,3,2,7]=>{{1},{2,3,6,7,8},{4},{5}}
[1,7,3,8,5,4,6,2]=>{{1},{2,4,6,7,8},{3},{5}}
[3,7,1,8,5,4,6,2]=>{{1,3},{2,4,6,7,8},{5}}
[2,7,3,8,4,6,5,1]=>{{1,2,4,5,7,8},{3},{6}}
[7,1,3,8,4,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}
[5,7,8,4,3,6,1,2]=>{{1,2,3,5,7,8},{4},{6}}
[2,8,7,4,1,6,5,3]=>{{1,2,3,5,7,8},{4},{6}}
[2,8,5,4,3,1,6,7]=>{{1,2,6,7,8},{3,5},{4}}
[6,5,8,4,2,3,1,7]=>{{1,3,6,7,8},{2,5},{4}}
[4,1,3,2,8,5,6,7]=>{{1,2,4},{3},{5,6,7,8}}
[1,4,3,2,8,5,6,7]=>{{1},{2,4},{3},{5,6,7,8}}
[7,3,2,8,5,4,6,1]=>{{1,4,6,7,8},{2,3},{5}}
[6,4,8,2,5,3,1,7]=>{{1,3,6,7,8},{2,4},{5}}
[2,8,4,3,5,1,6,7]=>{{1,2,6,7,8},{3,4},{5}}
[2,8,3,4,5,1,6,7]=>{{1,2,6,7,8},{3},{4},{5}}
[6,2,8,4,5,3,1,7]=>{{1,3,6,7,8},{2},{4},{5}}
[7,2,3,8,5,4,6,1]=>{{1,4,6,7,8},{2},{3},{5}}
[4,2,3,1,8,5,6,7]=>{{1,4},{2},{3},{5,6,7,8}}
[3,2,1,4,8,5,6,7]=>{{1,3},{2},{4},{5,6,7,8}}
[5,1,3,2,4,8,6,7]=>{{1,2,4,5},{3},{6,7,8}}
[2,8,1,5,3,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[1,2,8,4,5,3,7,6]=>{{1},{2},{3,6,8},{4},{5},{7}}
[1,4,2,8,5,3,6,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,8,4,2,5,3,6,7]=>{{1},{2,3,4,6,7,8},{5}}
[8,1,5,3,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,8,1,5,2,4,6,7]=>{{1,3},{2,4,5,6,7,8}}
[3,5,1,4,8,2,6,7]=>{{1,3},{2,5,6,7,8},{4}}
[1,5,2,8,4,3,6,7]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,5,4,3,6,7]=>{{1},{2},{3,6,7,8},{4,5}}
[1,2,5,4,3,8,6,7]=>{{1},{2},{3,5},{4},{6,7,8}}
[1,2,4,8,5,3,7,6]=>{{1},{2},{3,4,6,8},{5},{7}}
[1,2,7,4,8,5,3,6]=>{{1},{2},{3,7},{4},{5,6,8}}
[1,5,2,7,8,4,3,6]=>{{1},{2,3,4,5,6,7,8}}
[5,1,2,7,4,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[8,3,5,1,4,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,5,4,7,3,6]=>{{1,2,3,6,7,8},{4,5}}
[1,2,8,5,7,4,3,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,4,8,7,5,3,6]=>{{1},{2},{3,4,5,6,7,8}}
[2,8,1,4,3,7,6,5]=>{{1,2,3,5,8},{4},{6,7}}
[6,1,2,8,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,2,8,7,3,5]=>{{1,3,6,7},{2,4},{5,8}}
[3,6,4,8,1,7,2,5]=>{{1,3,4,5,8},{2,6,7}}
[7,6,1,4,2,8,3,5]=>{{1,3,7},{2,5,6,8},{4}}
[7,1,6,2,8,4,3,5]=>{{1,2,3,4,6,7},{5,8}}
[1,6,7,2,8,4,3,5]=>{{1},{2,4,6},{3,7},{5,8}}
[6,7,1,4,2,8,3,5]=>{{1,2,3,5,6,7,8},{4}}
[6,3,7,1,4,8,2,5]=>{{1,4,5,6,8},{2,3,7}}
[3,7,8,1,5,2,4,6]=>{{1,2,3,4,6,7,8},{5}}
[7,1,2,8,5,3,4,6]=>{{1,2,3,4,6,7,8},{5}}
[1,7,2,8,4,5,3,6]=>{{1},{2,3,7},{4,5,6,8}}
[1,4,2,7,8,5,3,6]=>{{1},{2,3,4,7},{5,6,8}}
[6,1,2,8,4,3,7,5]=>{{1,2,3,6},{4,5,8},{7}}
[6,4,1,2,8,3,7,5]=>{{1,3,6},{2,4},{5,8},{7}}
[7,6,1,3,2,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,3,2,4,8,5]=>{{1,3,4,6},{2,5,7,8}}
[1,2,7,3,5,8,4,6]=>{{1},{2},{3,4,7},{5},{6,8}}
[1,2,7,5,8,3,4,6]=>{{1},{2},{3,4,5,6,7,8}}
[5,8,1,3,7,2,4,6]=>{{1,3,4,5,7},{2,6,8}}
[1,2,5,8,7,3,4,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,5,8,3,7,4,6]=>{{1},{2},{3,5},{4,6,7,8}}
[2,8,1,7,3,5,4,6]=>{{1,2,3,5,6,8},{4,7}}
[8,6,1,3,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,2,8,1,7,3,6,5]=>{{1,4},{2},{3,5,6,7,8}}
[2,8,1,7,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[7,1,2,8,4,3,6,5]=>{{1,2,3,6,7},{4,5,8}}
[1,2,8,4,7,5,3,6]=>{{1},{2},{3,5,6,7,8},{4}}
[1,2,8,7,4,5,3,6]=>{{1},{2},{3,4,5,6,7,8}}
[2,8,1,7,5,3,4,6]=>{{1,2,3,6,8},{4,7},{5}}
[8,3,7,1,5,2,4,6]=>{{1,2,3,4,6,7,8},{5}}
[3,8,6,1,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,6,1,4,2,7,3,5]=>{{1,2,3,5,6,7,8},{4}}
[8,1,6,2,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,1,2,8,6,4,3,5]=>{{1,2,3,7},{4,5,6,8}}
[7,4,1,2,8,6,3,5]=>{{1,3,7},{2,4},{5,8},{6}}
[3,7,4,8,1,6,2,5]=>{{1,3,4,5,8},{2,7},{6}}
[3,4,8,7,1,6,2,5]=>{{1,3,5,8},{2,4,7},{6}}
[4,2,8,1,7,6,3,5]=>{{1,4},{2},{3,5,7,8},{6}}
[2,8,1,7,6,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,3,4,1,5,2,6]=>{{1,2,5,6,7,8},{3},{4}}
[7,8,3,4,1,6,2,5]=>{{1,2,5,7,8},{3},{4},{6}}
[6,8,3,4,1,7,2,5]=>{{1,2,5,6,7,8},{3},{4}}
[6,7,3,4,1,8,2,5]=>{{1,5,6,8},{2,7},{3},{4}}
[5,7,3,4,1,8,2,6]=>{{1,5},{2,7},{3},{4},{6,8}}
[5,8,3,4,1,7,2,6]=>{{1,5},{2,6,7,8},{3},{4}}
[5,8,3,4,1,6,2,7]=>{{1,5},{2,7,8},{3},{4},{6}}
[6,8,3,4,1,5,2,7]=>{{1,5,6},{2,7,8},{3},{4}}
[6,7,3,4,1,5,2,8]=>{{1,5,6},{2,7},{3},{4},{8}}
[5,7,3,4,1,6,2,8]=>{{1,5},{2,7},{3},{4},{6},{8}}
[5,6,2,8,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,2,7,3,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,2,8,3,5,1,7]=>{{1,4,7,8},{2,3,5,6}}
[4,7,3,5,1,6,2,8]=>{{1,4,5},{2,7},{3},{6},{8}}
[4,8,3,5,1,6,2,7]=>{{1,4,5},{2,7,8},{3},{6}}
[4,8,3,5,1,7,2,6]=>{{1,4,5},{2,6,7,8},{3}}
[4,7,3,5,1,8,2,6]=>{{1,4,5},{2,7},{3},{6,8}}
[5,6,2,3,1,7,4,8]=>{{1,5},{2,3,4,6,7},{8}}
[5,6,2,4,1,8,3,7]=>{{1,5},{2,3,6,7,8},{4}}
[5,6,2,4,1,7,3,8]=>{{1,5},{2,3,6,7},{4},{8}}
[4,6,2,5,1,7,3,8]=>{{1,4,5},{2,3,6,7},{8}}
[4,6,2,5,1,8,3,7]=>{{1,4,5},{2,3,6,7,8}}
[4,5,1,8,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,7,3,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[4,6,2,7,3,8,1,5]=>{{1,4,7},{2,3,5,6,8}}
[5,6,2,7,3,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,6,2,7,4,8,1,3]=>{{1,4,5,7},{2,3,6,8}}
[5,6,3,8,4,7,1,2]=>{{1,2,4,5,6,7,8},{3}}
[5,6,2,8,4,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,6,2,8,3,7,1,4]=>{{1,2,3,5,6,7},{4,8}}
[4,6,2,8,3,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,7,3,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,5,1,8,3,6,2,7]=>{{1,2,3,4,5,7,8},{6}}
[6,5,3,2,1,4,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[4,6,3,5,2,1,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[8,7,3,5,2,4,1,6]=>{{1,2,4,5,6,7,8},{3}}
[6,8,2,4,5,7,3,1]=>{{1,2,3,6,7,8},{4},{5}}
[8,7,2,4,5,3,1,6]=>{{1,2,3,6,7,8},{4},{5}}
[3,6,1,4,5,2,8,7]=>{{1,3},{2,6},{4},{5},{7,8}}
[8,3,7,4,5,2,1,6]=>{{1,2,3,6,7,8},{4},{5}}
[6,3,8,4,5,7,2,1]=>{{1,2,3,6,7,8},{4},{5}}
[5,8,7,4,3,6,2,1]=>{{1,2,3,5,7,8},{4},{6}}
[2,8,7,4,3,6,1,5]=>{{1,2,3,5,7,8},{4},{6}}
[8,1,7,4,3,6,2,5]=>{{1,2,3,5,7,8},{4},{6}}
[8,7,3,5,1,4,2,6]=>{{1,4,5,6,8},{2,7},{3}}
[2,1,6,8,5,7,4,3]=>{{1,2},{3,4,6,7,8},{5}}
[6,8,3,5,1,7,4,2]=>{{1,4,5,6,7},{2,8},{3}}
[5,1,8,4,7,6,3,2]=>{{1,2,3,5,7,8},{4},{6}}
[2,5,8,4,7,6,3,1]=>{{1,2,3,5,7,8},{4},{6}}
[4,3,8,1,5,6,7,2]=>{{1,4},{2,3,8},{5},{6},{7}}
[4,8,1,3,5,6,7,2]=>{{1,3,4},{2,8},{5},{6},{7}}
[5,8,7,4,1,6,3,2]=>{{1,5},{2,8},{3,7},{4},{6}}
[5,8,3,6,1,4,7,2]=>{{1,5},{2,8},{3},{4,6},{7}}
[4,8,3,6,1,2,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[3,8,7,4,1,6,2,5]=>{{1,2,3,5,7,8},{4},{6}}
[3,8,1,2,5,6,7,4]=>{{1,3},{2,4,8},{5},{6},{7}}
[8,7,1,4,2,6,3,5]=>{{1,2,3,5,7,8},{4},{6}}
[8,6,3,1,2,4,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[8,1,7,4,5,2,3,6]=>{{1,2,6,8},{3,7},{4},{5}}
[2,8,7,4,5,1,3,6]=>{{1,2,6,8},{3,7},{4},{5}}
[8,7,2,4,1,6,3,5]=>{{1,5,8},{2,3,7},{4},{6}}
[5,8,3,6,2,4,7,1]=>{{1,2,5,8},{3},{4,6},{7}}
[8,6,3,2,1,4,7,5]=>{{1,5,8},{2,4,6},{3},{7}}
[8,7,3,5,2,1,4,6]=>{{1,6,8},{2,4,5,7},{3}}
[5,8,3,6,2,1,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[5,8,7,4,2,6,1,3]=>{{1,2,3,5,7,8},{4},{6}}
[2,6,8,4,5,7,1,3]=>{{1,2,6,7},{3,8},{4},{5}}
[6,1,8,4,5,7,2,3]=>{{1,2,6,7},{3,8},{4},{5}}
[6,8,3,5,1,7,2,4]=>{{1,2,4,5,6,7,8},{3}}
[2,1,5,8,3,6,7,4]=>{{1,2},{3,5},{4,8},{6},{7}}
[5,8,3,6,1,2,7,4]=>{{1,5},{2,4,6,8},{3},{7}}
[4,1,8,2,5,6,7,3]=>{{1,2,4},{3,8},{5},{6},{7}}
[2,4,8,1,5,6,7,3]=>{{1,2,4},{3,8},{5},{6},{7}}
[4,8,2,1,5,6,7,3]=>{{1,4},{2,3,8},{5},{6},{7}}
[3,4,8,2,5,6,7,1]=>{{1,3,8},{2,4},{5},{6},{7}}
[5,8,1,4,7,6,2,3]=>{{1,2,3,5,7,8},{4},{6}}
[5,8,3,1,6,2,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[4,5,3,8,6,1,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[3,4,1,8,5,6,7,2]=>{{1,3},{2,4,8},{5},{6},{7}}
[4,5,7,6,2,3,8,1]=>{{1,3,4,6,7,8},{2,5}}
[3,5,7,2,6,4,8,1]=>{{1,3,7,8},{2,4,5,6}}
[2,5,7,3,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[1,5,7,3,6,8,4,2]=>{{1},{2,5,6,8},{3,4,7}}
[8,4,3,7,6,1,5,2]=>{{1,2,4,5,6,7,8},{3}}
[6,7,2,3,5,4,8,1]=>{{1,2,3,4,6,7,8},{5}}
[5,2,7,3,6,4,8,1]=>{{1,3,4,5,6,7,8},{2}}
[8,3,4,7,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,2,4,7,1,6,5,3]=>{{1,3,4,5,7,8},{2},{6}}
[3,1,4,7,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,1,3,7,6,8,5,2]=>{{1,2,4,5,6,7,8},{3}}
[5,1,7,3,6,8,4,2]=>{{1,2,5,6,8},{3,4,7}}
[6,7,1,3,5,8,4,2]=>{{1,2,3,4,6,7,8},{5}}
[5,8,7,3,6,1,4,2]=>{{1,5,6},{2,8},{3,4,7}}
[4,8,3,7,6,1,5,2]=>{{1,4,5,6,7},{2,8},{3}}
[3,8,4,7,6,1,5,2]=>{{1,3,4,5,6,7},{2,8}}
[2,8,4,7,1,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[8,1,4,7,2,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[8,1,3,2,7,6,5,4]=>{{1,2,4,8},{3},{5,7},{6}}
[2,8,3,1,7,6,5,4]=>{{1,2,4,8},{3},{5,7},{6}}
[3,8,2,1,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}
[6,7,1,2,8,5,4,3]=>{{1,3,5,6,8},{2,4,7}}
[8,2,3,1,7,6,5,4]=>{{1,4,8},{2},{3},{5,7},{6}}
[8,3,2,1,7,6,5,4]=>{{1,4,8},{2,3},{5,7},{6}}
[3,4,1,7,6,8,5,2]=>{{1,3},{2,4,5,6,7,8}}
[1,4,2,7,8,6,5,3]=>{{1},{2,3,4,5,7,8},{6}}
[8,4,2,7,1,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[8,5,7,2,1,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[1,5,7,2,8,6,4,3]=>{{1},{2,3,4,5,7,8},{6}}
[2,5,7,1,8,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[3,5,7,1,6,8,4,2]=>{{1,3,4,7},{2,5,6,8}}
[6,7,4,5,8,1,3,2]=>{{1,6},{2,3,4,5,7,8}}
[5,4,7,6,8,1,3,2]=>{{1,2,4,5,6,8},{3,7}}
[2,5,7,8,1,6,4,3]=>{{1,2,5},{3,4,7,8},{6}}
[1,5,7,8,2,6,4,3]=>{{1},{2,5},{3,4,7,8},{6}}
[8,5,7,1,2,6,4,3]=>{{1,3,4,7,8},{2,5},{6}}
[8,4,1,7,2,6,5,3]=>{{1,3,8},{2,4,5,7},{6}}
[1,4,8,7,2,6,5,3]=>{{1},{2,4,5,7},{3,8},{6}}
[3,4,8,7,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,7,6,1,5,2]=>{{1,4,5,6,7},{2,3,8}}
[5,3,7,8,6,1,4,2]=>{{1,5,6},{2,3,4,7,8}}
[6,7,2,8,1,5,4,3]=>{{1,5,6},{2,3,4,7,8}}
[5,2,7,8,1,6,4,3]=>{{1,5},{2},{3,4,7,8},{6}}
[4,2,8,7,1,6,5,3]=>{{1,4,5,7},{2},{3,8},{6}}
[3,2,8,1,7,6,5,4]=>{{1,3,4,8},{2},{5,7},{6}}
[1,3,8,2,7,6,5,4]=>{{1},{2,3,4,8},{5,7},{6}}
[8,3,1,2,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}
[8,2,1,3,7,6,5,4]=>{{1,3,4,8},{2},{5,7},{6}}
[1,2,8,3,7,6,5,4]=>{{1},{2},{3,4,8},{5,7},{6}}
[2,1,8,3,7,6,5,4]=>{{1,2},{3,4,8},{5,7},{6}}
[4,1,8,7,2,6,5,3]=>{{1,2,4,5,7},{3,8},{6}}
[5,1,7,8,2,6,4,3]=>{{1,2,5},{3,4,7,8},{6}}
[6,7,1,8,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,1,2,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[4,8,1,7,2,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[3,8,1,2,7,6,5,4]=>{{1,3},{2,4,8},{5,7},{6}}
[2,8,1,3,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}
[1,8,2,3,7,6,5,4]=>{{1},{2,3,4,8},{5,7},{6}}
[8,1,2,3,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}
[6,7,1,8,4,5,2,3]=>{{1,3,4,5,6,8},{2,7}}
[3,7,1,5,8,2,6,4]=>{{1,3},{2,6,7},{4,5,8}}
[2,7,1,5,8,3,6,4]=>{{1,2,3,6,7},{4,5,8}}
[2,6,5,1,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[3,6,5,1,8,2,7,4]=>{{1,3,4,5,8},{2,6},{7}}
[4,6,5,1,8,7,2,3]=>{{1,4},{2,6,7},{3,5,8}}
[5,6,4,1,8,7,2,3]=>{{1,3,4,5,8},{2,6,7}}
[8,1,4,5,7,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[6,4,5,1,8,7,2,3]=>{{1,2,4,6,7},{3,5,8}}
[5,4,6,1,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,1,8,7,2,3]=>{{1,4},{2,3,5,6,7,8}}
[3,5,6,1,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,5,6,1,8,3,7,4]=>{{1,2,4,5,8},{3,6},{7}}
[2,4,6,1,3,8,7,5]=>{{1,2,4},{3,5,6,8},{7}}
[3,4,6,1,2,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,3,6,1,2,8,7,5]=>{{1,4},{2,3,5,6,8},{7}}
[5,3,6,1,8,2,7,4]=>{{1,4,5,8},{2,3,6},{7}}
[7,3,1,5,8,2,6,4]=>{{1,2,3,6,7},{4,5,8}}
[8,1,3,5,7,2,6,4]=>{{1,2,4,5,6,7,8},{3}}
[8,1,2,5,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,2,1,5,8,3,6,4]=>{{1,3,6,7},{2},{4,5,8}}
[6,2,5,1,8,3,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[4,2,6,1,3,8,7,5]=>{{1,4},{2},{3,5,6,8},{7}}
[2,3,6,1,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,2,5,3,1,8,7,6]=>{{1,3,4,5},{2},{6,8},{7}}
[6,2,4,1,3,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[7,2,1,4,3,8,6,5]=>{{1,3,5,6,7,8},{2},{4}}
[8,1,2,4,3,7,6,5]=>{{1,2,3,5,8},{4},{6,7}}
[8,1,3,4,2,7,6,5]=>{{1,2,5,8},{3},{4},{6,7}}
[7,3,1,4,2,8,6,5]=>{{1,2,3,5,6,7,8},{4}}
[6,3,4,1,2,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,6,3,1,2,8,7,5]=>{{1,4},{2,5,6,8},{3},{7}}
[3,6,4,1,2,8,7,5]=>{{1,3,4},{2,5,6,8},{7}}
[2,6,4,1,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,7,1,4,3,8,6,5]=>{{1,2,3,5,6,7,8},{4}}
[3,7,1,4,2,8,6,5]=>{{1,3},{2,5,6,7,8},{4}}
[4,7,1,3,2,8,6,5]=>{{1,3,4},{2,5,6,7,8}}
[8,1,6,7,2,3,5,4]=>{{1,2,4,5,7,8},{3,6}}
[4,7,1,2,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[3,7,1,2,4,8,6,5]=>{{1,3},{2,4,5,6,7,8}}
[2,7,1,3,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[2,6,3,1,4,8,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[3,6,2,1,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[5,6,2,1,8,3,7,4]=>{{1,4,5,8},{2,3,6},{7}}
[6,5,2,1,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[8,1,5,2,7,3,6,4]=>{{1,2,4,8},{3,5,6,7}}
[8,1,4,2,3,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[7,4,1,2,3,8,6,5]=>{{1,3,5,6,7,8},{2,4}}
[6,4,2,1,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[5,4,2,3,1,8,7,6]=>{{1,5},{2,3,4},{6,8},{7}}
[3,5,2,4,1,8,7,6]=>{{1,2,3,5},{4},{6,8},{7}}
[6,3,2,1,4,8,7,5]=>{{1,4,5,6,8},{2,3},{7}}
[7,3,1,2,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,3,2,4,7,6,5]=>{{1,2,4,5,8},{3},{6,7}}
[8,1,2,3,4,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[7,2,1,3,4,8,6,5]=>{{1,3,4,5,6,7,8},{2}}
[6,2,3,1,4,8,7,5]=>{{1,4,5,6,8},{2},{3},{7}}
[2,4,3,6,1,5,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[2,4,3,6,5,8,1,7]=>{{1,2,4,6,7,8},{3},{5}}
[2,4,6,3,5,8,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[2,4,6,3,5,8,1,7]=>{{1,2,3,4,6,7,8},{5}}
[4,2,6,5,3,1,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[4,2,6,5,1,8,7,3]=>{{1,4,5},{2},{3,6,8},{7}}
[4,2,6,5,8,1,7,3]=>{{1,3,4,5,6,8},{2},{7}}
[4,2,6,5,8,1,3,7]=>{{1,3,4,5,6,7,8},{2}}
[4,2,6,5,8,3,1,7]=>{{1,4,5,7,8},{2},{3,6}}
[2,4,6,1,5,8,3,7]=>{{1,2,4},{3,6,7,8},{5}}
[2,4,1,6,5,8,3,7]=>{{1,2,3,4,6,7,8},{5}}
[2,1,4,6,5,8,3,7]=>{{1,2},{3,4,6,7,8},{5}}
[2,4,1,6,5,8,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[4,2,6,5,8,3,7,1]=>{{1,4,5,8},{2},{3,6},{7}}
[2,6,4,3,8,7,5,1]=>{{1,2,5,6,7,8},{3,4}}
[4,2,6,8,5,3,7,1]=>{{1,4,8},{2},{3,6},{5},{7}}
[2,4,6,8,1,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,4,6,1,8,5,7,3]=>{{1,2,4},{3,5,6,8},{7}}
[2,4,1,6,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,1,4,6,8,5,7,3]=>{{1,2},{3,4,5,6,8},{7}}
[2,1,4,6,8,5,3,7]=>{{1,2},{3,4,5,6,7,8}}
[2,4,1,6,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,1,8,5,3,7]=>{{1,2,4},{3,5,6,7,8}}
[2,4,6,8,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[4,2,6,8,5,1,3,7]=>{{1,3,4,6,7,8},{2},{5}}
[2,4,6,8,3,5,7,1]=>{{1,2,4,8},{3,5,6},{7}}
[2,4,6,8,3,5,1,7]=>{{1,2,4,7,8},{3,5,6}}
[2,4,6,8,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,3,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,3,8,1,5,7]=>{{1,2,3,4,6},{5,7,8}}
[2,4,6,3,8,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,3,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,4,3,6,8,5,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[2,4,3,6,8,5,1,7]=>{{1,2,4,5,6,7,8},{3}}
[2,4,3,6,8,1,5,7]=>{{1,2,4,6},{3},{5,7,8}}
[2,4,3,1,6,8,5,7]=>{{1,2,4},{3},{5,6,7,8}}
[2,4,1,3,6,8,7,5]=>{{1,2,3,4},{5,6,8},{7}}
[2,4,3,6,1,8,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[2,4,3,6,8,1,7,5]=>{{1,2,4,6},{3},{5,8},{7}}
[4,6,5,2,8,7,1,3]=>{{1,2,4,6,7},{3,5,8}}
[2,4,6,3,8,1,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[2,1,4,6,8,3,7,5]=>{{1,2},{3,4,6},{5,8},{7}}
[2,4,1,6,8,3,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[2,4,6,8,1,3,7,5]=>{{1,2,4,5,8},{3,6},{7}}
[2,4,6,8,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,6,2,8,5,7,1,3]=>{{1,2,3,4,6,7,8},{5}}
[6,2,4,8,7,1,3,5]=>{{1,6},{2},{3,4,5,7,8}}
[6,4,2,8,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,6,4,8,1,7,5,3]=>{{1,2,5,6,7},{3,4,8}}
[2,6,4,1,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[2,6,1,4,8,7,5,3]=>{{1,2,3,5,6,7,8},{4}}
[2,1,6,4,8,7,5,3]=>{{1,2},{3,5,6,7,8},{4}}
[2,6,1,4,8,7,3,5]=>{{1,2,3,6,7},{4},{5,8}}
[6,4,2,8,7,5,1,3]=>{{1,5,6,7},{2,3,4,8}}
[1,6,4,7,3,8,2,5]=>{{1},{2,3,4,5,6,7,8}}
[1,3,7,4,5,8,2,6]=>{{1},{2,3,7},{4},{5},{6,8}}
[5,2,4,7,3,6,8,1]=>{{1,3,4,5,7,8},{2},{6}}
[1,7,6,3,4,8,2,5]=>{{1},{2,7},{3,4,5,6,8}}
[8,1,6,3,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,3,8,2,4,5]=>{{1,2,3,4,6,7},{5,8}}
[1,2,7,4,8,3,5,6]=>{{1},{2},{3,5,6,7,8},{4}}
[6,1,7,3,4,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,4,5,8,3,6]=>{{1,2},{3,7},{4},{5},{6,8}}
[5,1,4,7,3,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[4,3,1,7,5,8,2,6]=>{{1,2,3,4,7},{5},{6,8}}
[2,8,6,3,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[6,8,1,3,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[5,8,2,1,7,3,4,6]=>{{1,4,5,7},{2,3,6,8}}
[5,7,2,1,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,3,8,2,4,5]=>{{1,2,3,4,6,7},{5,8}}
[5,1,2,4,8,3,6,7]=>{{1,2,3,5,6,7,8},{4}}
[4,3,6,1,5,8,2,7]=>{{1,4},{2,3,6,7,8},{5}}
[2,6,1,4,5,8,3,7]=>{{1,2,3,6,7,8},{4},{5}}
[6,5,1,3,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,2,4,8,3,5,7]=>{{1},{2,3,6},{4},{5,7,8}}
[8,5,1,3,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[1,5,3,2,8,4,6,7]=>{{1},{2,4,5,6,7,8},{3}}
[6,4,2,1,5,8,3,7]=>{{1,2,3,4,6,7,8},{5}}
[2,5,3,4,1,8,6,7]=>{{1,2,5},{3},{4},{6,7,8}}
[4,3,5,2,1,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[2,6,4,8,7,1,3,5]=>{{1,2,6},{3,4,5,7,8}}
[1,6,4,8,7,2,3,5]=>{{1},{2,6},{3,4,5,7,8}}
[2,7,8,3,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[4,3,2,8,7,1,5,6]=>{{1,4,6,8},{2,3},{5,7}}
[5,2,4,8,7,1,3,6]=>{{1,3,4,5,6,7,8},{2}}
[6,2,8,3,7,1,4,5]=>{{1,6},{2},{3,4,5,7,8}}
[5,1,4,8,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,2,5,1,3,7,6]=>{{1,4,5},{2,3,6,8},{7}}
[4,7,2,5,1,3,8,6]=>{{1,4,5},{2,3,6,7,8}}
[3,7,2,1,5,4,8,6]=>{{1,2,3,4,6,7,8},{5}}
[3,8,2,1,5,4,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[8,3,2,1,5,4,6,7]=>{{1,4,6,7,8},{2,3},{5}}
[8,3,2,1,6,4,5,7]=>{{1,4,5,6,7,8},{2,3}}
[8,4,2,5,1,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[8,3,2,1,5,6,4,7]=>{{1,4,7,8},{2,3},{5},{6}}
[8,3,2,1,4,6,5,7]=>{{1,4,5,7,8},{2,3},{6}}
[3,8,2,1,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[3,7,2,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,2,7,1,4,6,8,5]=>{{1,3,4,5,7,8},{2},{6}}
[3,2,8,1,4,6,7,5]=>{{1,3,4,5,8},{2},{6},{7}}
[3,2,8,1,4,7,6,5]=>{{1,3,4,5,8},{2},{6,7}}
[3,8,2,1,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,8,2,1,5,7,4,6]=>{{1,2,3,4,6,7,8},{5}}
[4,8,2,5,1,7,3,6]=>{{1,4,5},{2,3,6,7,8}}
[4,7,2,5,1,8,3,6]=>{{1,4,5},{2,3,7},{6,8}}
[3,7,2,1,5,8,4,6]=>{{1,2,3,4,7},{5},{6,8}}
[3,7,2,1,4,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[3,2,1,7,5,8,6,4]=>{{1,3},{2},{4,6,7,8},{5}}
[3,2,7,1,6,8,4,5]=>{{1,3,4,7},{2},{5,6,8}}
[4,2,7,6,1,8,3,5]=>{{1,4,5,6,8},{2},{3,7}}
[4,3,7,6,8,1,2,5]=>{{1,4,6},{2,3,7},{5,8}}
[4,3,8,6,7,1,2,5]=>{{1,4,6},{2,3,5,7,8}}
[4,2,8,6,1,7,3,5]=>{{1,3,4,5,6,7,8},{2}}
[3,2,8,1,6,7,4,5]=>{{1,3,4,5,6,7,8},{2}}
[3,2,1,8,7,5,6,4]=>{{1,3},{2},{4,8},{5,6,7}}
[3,8,2,1,7,4,5,6]=>{{1,2,3,4,6,8},{5,7}}
[3,2,8,1,7,4,6,5]=>{{1,3,4,5,6,7,8},{2}}
[3,2,8,1,6,4,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[3,2,7,1,6,4,8,5]=>{{1,3,4,5,6,7,8},{2}}
[4,2,7,6,1,3,8,5]=>{{1,3,4,5,6,7,8},{2}}
[4,2,8,6,1,3,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[4,2,8,7,1,3,6,5]=>{{1,3,4,5,6,7,8},{2}}
[5,7,8,3,4,1,2,6]=>{{1,3,4,5,6,8},{2,7}}
[4,2,7,8,1,3,6,5]=>{{1,4,5,8},{2},{3,6,7}}
[4,2,6,8,1,3,7,5]=>{{1,4,5,8},{2},{3,6},{7}}
[4,2,6,7,1,3,8,5]=>{{1,4,5,7,8},{2},{3,6}}
[3,2,6,1,8,4,7,5]=>{{1,3,4,6},{2},{5,8},{7}}
[3,7,2,1,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,2,1,8,5,4,6]=>{{1,2,3,4,7},{5,6,8}}
[4,7,3,8,5,1,2,6]=>{{1,4,6,8},{2,7},{3},{5}}
[4,3,7,8,6,1,2,5]=>{{1,4,5,6,8},{2,3,7}}
[3,2,7,1,8,6,4,5]=>{{1,3,4,7},{2},{5,8},{6}}
[3,2,1,6,8,5,7,4]=>{{1,3},{2},{4,5,6,8},{7}}
[3,2,6,1,8,7,4,5]=>{{1,3,4,6,7},{2},{5,8}}
[4,2,6,8,1,7,3,5]=>{{1,4,5,8},{2},{3,6,7}}
[4,3,6,8,7,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,2,6,7,1,8,3,5]=>{{1,3,4,5,6,7,8},{2}}
[3,2,6,1,7,8,4,5]=>{{1,3,4,5,6,7,8},{2}}
[3,4,6,8,7,5,1,2]=>{{1,3,5,6,7},{2,4,8}}
[5,3,6,4,8,7,1,2]=>{{1,2,3,5,6,7,8},{4}}
[1,4,6,2,7,8,5,3]=>{{1},{2,4},{3,6,8},{5,7}}
[3,1,8,5,4,2,6,7]=>{{1,2,3,6,7,8},{4,5}}
[1,2,7,5,4,8,6,3]=>{{1},{2},{3,6,7,8},{4,5}}
[6,3,7,5,4,8,1,2]=>{{1,2,3,6,7,8},{4,5}}
[7,3,8,5,4,6,1,2]=>{{1,7},{2,3,8},{4,5},{6}}
[3,8,7,5,4,6,1,2]=>{{1,3,7},{2,8},{4,5},{6}}
[4,3,6,7,8,5,1,2]=>{{1,4,7},{2,3,5,6,8}}
[4,5,6,3,8,7,1,2]=>{{1,3,4,6,7},{2,5,8}}
[3,6,8,5,4,7,1,2]=>{{1,2,3,6,7,8},{4,5}}
[6,8,3,5,4,7,1,2]=>{{1,6,7},{2,8},{3},{4,5}}
[7,6,3,5,4,8,1,2]=>{{1,7},{2,6,8},{3},{4,5}}
[1,6,2,5,4,8,7,3]=>{{1},{2,3,6,8},{4,5},{7}}
[7,1,2,5,8,3,6,4]=>{{1,2,3,6,7},{4,5,8}}
[1,8,2,5,7,3,6,4]=>{{1},{2,3,4,5,6,7,8}}
[6,2,1,5,4,8,7,3]=>{{1,3,6,8},{2},{4,5},{7}}
[4,1,6,2,8,7,5,3]=>{{1,2,4},{3,5,6,7,8}}
[7,8,1,2,4,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[7,8,3,1,4,2,6,5]=>{{1,2,4,5,6,7,8},{3}}
[4,3,6,1,8,2,7,5]=>{{1,4},{2,3,6},{5,8},{7}}
[2,3,8,5,4,1,6,7]=>{{1,2,3,6,7,8},{4,5}}
[4,8,1,5,2,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[7,5,1,6,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[5,8,1,6,4,3,2,7]=>{{1,3,4,5,6},{2,7,8}}
[6,1,5,7,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[1,5,8,6,4,3,2,7]=>{{1},{2,3,4,5,6,7,8}}
[3,4,6,1,5,8,2,7]=>{{1,2,3,4,6,7,8},{5}}
[7,8,4,1,5,3,2,6]=>{{1,2,3,4,6,7,8},{5}}
[7,8,5,1,6,3,2,4]=>{{1,2,4,7,8},{3,5,6}}
[2,6,1,5,7,3,8,4]=>{{1,2,3,6},{4,5,7,8}}
[1,6,8,7,4,3,2,5]=>{{1},{2,3,4,5,6,7,8}}
[6,8,1,7,4,3,2,5]=>{{1,3,6},{2,4,5,7,8}}
[5,6,1,7,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[5,1,7,6,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[6,1,7,8,4,3,2,5]=>{{1,2,3,6,7},{4,5,8}}
[7,1,8,6,4,3,2,5]=>{{1,2,7},{3,4,5,6,8}}
[1,8,7,6,4,3,2,5]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,5,6,3,8,4]=>{{1,2},{3,4,5,6,7,8}}
[3,1,6,7,5,8,2,4]=>{{1,2,3,4,6,7,8},{5}}
[7,8,1,6,5,3,2,4]=>{{1,2,3,4,6,7,8},{5}}
[7,8,2,1,4,5,6,3]=>{{1,4,5,6,7},{2,3,8}}
[2,8,1,5,4,6,7,3]=>{{1,2,3,8},{4,5},{6},{7}}
[7,2,1,5,4,6,8,3]=>{{1,3,7,8},{2},{4,5},{6}}
[1,2,8,5,6,3,7,4]=>{{1},{2},{3,4,5,6,8},{7}}
[6,1,2,5,7,3,8,4]=>{{1,2,3,6},{4,5,7,8}}
[4,2,1,5,6,3,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[4,3,6,1,5,7,2,8]=>{{1,4},{2,3,6,7},{5},{8}}
[5,1,6,3,7,8,2,4]=>{{1,2,5,7},{3,4,6,8}}
[1,3,6,8,5,7,2,4]=>{{1},{2,3,6,7},{4,8},{5}}
[2,4,6,3,7,1,8,5]=>{{1,2,3,4,6},{5,7,8}}
[1,3,6,4,8,7,2,5]=>{{1},{2,3,6,7},{4},{5,8}}
[4,1,6,7,3,8,2,5]=>{{1,2,4,7},{3,5,6,8}}
[5,4,6,1,3,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[6,4,1,5,2,3,7,8]=>{{1,3,6},{2,4,5},{7},{8}}
[4,1,7,5,2,3,8,6]=>{{1,2,4,5},{3,6,7,8}}
[1,2,4,5,8,3,7,6]=>{{1},{2},{3,4,5,6,8},{7}}
[7,2,3,5,4,1,8,6]=>{{1,6,7,8},{2},{3},{4,5}}
[2,8,3,5,4,1,7,6]=>{{1,2,6,8},{3},{4,5},{7}}
[4,2,6,3,8,1,7,5]=>{{1,3,4,6},{2},{5,8},{7}}
[7,8,2,3,4,1,6,5]=>{{1,6,7},{2,3,4,5,8}}
[7,8,1,4,6,3,2,5]=>{{1,2,3,5,6,7,8},{4}}
[3,1,6,4,7,8,2,5]=>{{1,2,3,5,6,7,8},{4}}
[1,8,5,7,4,3,2,6]=>{{1},{2,3,4,5,6,7,8}}
[7,1,5,8,4,3,2,6]=>{{1,2,7},{3,4,5,6,8}}
[5,1,8,7,4,3,2,6]=>{{1,2,4,5,7},{3,6,8}}
[6,5,1,8,4,3,2,7]=>{{1,3,6},{2,4,5,7,8}}
[6,5,7,1,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,8,1,4,3,2,6]=>{{1,2,4,5,7},{3,6,8}}
[5,8,7,1,4,3,2,6]=>{{1,4,5},{2,3,6,7,8}}
[1,5,7,8,4,3,2,6]=>{{1},{2,3,4,5,6,7,8}}
[2,4,7,5,1,3,8,6]=>{{1,2,4,5},{3,6,7,8}}
[7,8,4,6,1,3,2,5]=>{{1,2,5,7,8},{3,4,6}}
[7,8,5,4,1,3,2,6]=>{{1,2,3,5,6,7,8},{4}}
[3,5,6,4,1,8,2,7]=>{{1,2,3,5,6,7,8},{4}}
[2,6,4,5,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[1,6,5,8,4,3,2,7]=>{{1},{2,3,4,5,6,7,8}}
[6,8,5,1,4,3,2,7]=>{{1,3,4,5,6},{2,7,8}}
[7,6,5,1,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[3,4,6,2,7,1,5,8]=>{{1,3,6},{2,4},{5,7},{8}}
[3,6,2,5,4,1,7,8]=>{{1,2,3,6},{4,5},{7},{8}}
[3,2,7,5,4,1,6,8]=>{{1,3,6,7},{2},{4,5},{8}}
[4,3,6,2,8,1,5,7]=>{{1,2,3,4,6},{5,7,8}}
[6,1,2,5,4,7,8,3]=>{{1,2,3,6,7,8},{4,5}}
[6,2,4,5,1,3,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[4,2,8,5,1,3,7,6]=>{{1,4,5},{2},{3,6,8},{7}}
[4,3,6,8,1,7,2,5]=>{{1,4,5,8},{2,3,6,7}}
[5,3,6,4,1,7,2,8]=>{{1,5},{2,3,6,7},{4},{8}}
[6,2,1,5,8,3,7,4]=>{{1,3,6},{2},{4,5,8},{7}}
[1,6,7,4,8,3,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,7,2,5,8,1,3]=>{{1,2,3,4,6,7,8},{5}}
[2,4,6,1,7,5,3,8]=>{{1,2,4},{3,5,6,7},{8}}
[2,7,5,4,1,6,3,8]=>{{1,2,3,5,7},{4},{6},{8}}
[7,5,4,6,2,8,1,3]=>{{1,7},{2,5},{3,4,6,8}}
[1,7,5,4,3,8,6,2]=>{{1},{2,6,7,8},{3,5},{4}}
[1,4,6,3,5,8,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[1,5,8,4,3,6,7,2]=>{{1},{2,3,5,8},{4},{6},{7}}
[5,4,6,2,7,8,1,3]=>{{1,5,7},{2,4},{3,6,8}}
[2,5,4,1,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,3,2,7,1,4,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,6,3,2,7,1,8,4]=>{{1,2,4,5,6,7,8},{3}}
[8,5,6,3,2,7,1,4]=>{{1,3,4,6,7,8},{2,5}}
[5,4,6,2,8,1,7,3]=>{{1,3,5,6,8},{2,4},{7}}
[2,4,1,7,8,5,3,6]=>{{1,2,3,4,7},{5,6,8}}
[2,5,4,1,6,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[5,6,3,2,1,8,4,7]=>{{1,5},{2,4,6,7,8},{3}}
[3,5,2,1,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[6,8,4,3,2,1,5,7]=>{{1,6},{2,5,7,8},{3,4}}
[5,3,8,2,1,6,4,7]=>{{1,5},{2,3,4,7,8},{6}}
[3,7,5,8,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,3,2,8,5,1,6,4]=>{{1,6,7},{2,3},{4,8},{5}}
[8,4,6,3,2,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[8,6,4,3,2,1,7,5]=>{{1,2,5,6,8},{3,4},{7}}
[7,6,4,3,2,1,8,5]=>{{1,2,5,6,7,8},{3,4}}
[7,8,4,3,2,1,6,5]=>{{1,6,7},{2,5,8},{3,4}}
[5,4,7,2,1,8,6,3]=>{{1,5},{2,4},{3,6,7,8}}
[7,5,8,3,2,6,1,4]=>{{1,7},{2,5},{3,4,8},{6}}
[5,7,3,2,1,6,8,4]=>{{1,5},{2,4,7,8},{3},{6}}
[5,7,3,2,1,6,4,8]=>{{1,5},{2,4,7},{3},{6},{8}}
[6,3,7,2,5,1,8,4]=>{{1,6},{2,3,4,7,8},{5}}
[6,7,8,3,5,2,1,4]=>{{1,2,6,7},{3,4,8},{5}}
[6,2,5,7,8,4,1,3]=>{{1,4,6,7},{2},{3,5,8}}
[2,1,5,7,8,6,3,4]=>{{1,2},{3,4,5,7,8},{6}}
[3,6,7,2,8,1,4,5]=>{{1,2,3,4,6,7},{5,8}}
[6,3,7,2,8,1,4,5]=>{{1,6},{2,3,4,7},{5,8}}
[3,2,6,1,7,4,5,8]=>{{1,3,4,6},{2},{5,7},{8}}
[3,5,2,1,4,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[7,3,5,2,1,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[2,5,4,1,3,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[2,5,8,4,1,3,7,6]=>{{1,2,5},{3,6,8},{4},{7}}
[2,4,1,7,8,3,6,5]=>{{1,2,3,4,6,7},{5,8}}
[3,7,2,8,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,8,2,1,7,4,5]=>{{1,3,5,8},{2,4,6,7}}
[5,3,8,2,1,4,7,6]=>{{1,5},{2,3,4,6,8},{7}}
[4,8,7,3,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,7,3,2,1,5,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[8,4,7,3,2,1,5,6]=>{{1,6,8},{2,3,4,5,7}}
[8,3,5,2,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[7,3,2,8,6,1,4,5]=>{{1,4,5,6,7,8},{2,3}}
[3,5,2,1,4,6,8,7]=>{{1,2,3,4,5},{6},{7,8}}
[7,8,3,5,4,6,1,2]=>{{1,7},{2,8},{3},{4,5},{6}}
[8,6,3,7,5,2,4,1]=>{{1,8},{2,6},{3},{4,7},{5}}
[5,4,1,6,3,2,8,7]=>{{1,3,5},{2,4,6},{7,8}}
[5,4,1,6,2,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[5,7,1,6,2,8,3,4]=>{{1,2,3,5,7},{4,6,8}}
[5,7,1,6,2,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,5,1,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,5,1,8,4,3]=>{{1,2,4,5,7},{3,6,8}}
[2,3,6,5,1,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,3,6,4,1,5,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[2,3,6,1,5,4,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[2,7,6,1,4,8,5,3]=>{{1,2,4,5,7},{3,6,8}}
[2,7,6,1,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,3,5,1,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[7,3,5,1,8,6,4,2]=>{{1,4,7},{2,3,5,8},{6}}
[2,7,6,1,5,8,4,3]=>{{1,2,4,7},{3,6,8},{5}}
[2,7,6,4,1,8,5,3]=>{{1,2,5,7},{3,6,8},{4}}
[2,1,7,6,3,8,5,4]=>{{1,2},{3,5,7},{4,6,8}}
[2,1,7,6,3,8,4,5]=>{{1,2},{3,4,5,6,7,8}}
[5,7,3,6,2,8,4,1]=>{{1,2,4,5,6,7,8},{3}}
[2,7,6,4,1,8,3,5]=>{{1,2,3,5,6,7,8},{4}}
[7,3,5,1,8,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[6,3,5,1,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,8,7,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[2,3,4,8,5,7,1,6]=>{{1,2,3,4,6,7,8},{5}}
[7,3,5,4,8,1,2,6]=>{{1,2,3,5,6,7,8},{4}}
[6,4,3,5,8,7,2,1]=>{{1,2,4,5,6,7,8},{3}}
[2,1,4,5,8,7,3,6]=>{{1,2},{3,4,5,6,7,8}}
[6,4,3,5,8,7,1,2]=>{{1,6,7},{2,4,5,8},{3}}
[7,3,5,4,8,1,6,2]=>{{1,6,7},{2,3,5,8},{4}}
[2,3,4,8,7,5,6,1]=>{{1,2,3,4,8},{5,6,7}}
[2,3,4,8,7,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,5,4,8,1,3]=>{{1,2,7},{3,6,8},{4,5}}
[7,3,5,6,8,4,1,2]=>{{1,7},{2,3,5,8},{4,6}}
[7,3,5,6,8,1,4,2]=>{{1,4,6,7},{2,3,5,8}}
[7,3,5,6,8,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,5,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,5,8,7,3,2]=>{{1,3,6,7},{2,4,5,8}}
[6,4,1,5,8,3,7,2]=>{{1,3,6},{2,4,5,8},{7}}
[5,7,1,6,3,8,2,4]=>{{1,3,5},{2,7},{4,6,8}}
[6,4,1,5,8,3,2,7]=>{{1,3,6},{2,4,5,7,8}}
[7,4,1,5,8,2,3,6]=>{{1,3,7},{2,4,5,6,8}}
[7,4,1,5,8,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,7,8,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,7,8,2,4,1]=>{{1,2,3,5,6,8},{4,7}}
[2,7,6,4,5,8,3,1]=>{{1,2,3,6,7,8},{4},{5}}
[5,7,3,6,1,8,4,2]=>{{1,5},{2,4,6,7,8},{3}}
[2,1,4,5,8,6,3,7]=>{{1,2},{3,4,5,7,8},{6}}
[7,3,5,4,8,6,2,1]=>{{1,2,3,5,7,8},{4},{6}}
[2,3,4,8,5,6,1,7]=>{{1,2,3,4,7,8},{5},{6}}
[2,3,4,8,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,8,1,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[2,3,4,8,1,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[2,3,4,8,5,1,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[6,3,5,4,8,2,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[7,4,3,5,8,2,1,6]=>{{1,7},{2,4,5,6,8},{3}}
[2,1,4,5,8,3,7,6]=>{{1,2},{3,4,5,6,8},{7}}
[7,4,3,5,8,2,6,1]=>{{1,2,4,5,6,7,8},{3}}
[6,3,5,4,8,2,1,7]=>{{1,2,3,5,6,7,8},{4}}
[2,3,4,8,5,1,6,7]=>{{1,2,3,4,6,7,8},{5}}
[2,3,4,8,1,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[2,3,4,8,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[7,8,2,6,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,6,2,5,3,4]=>{{1,3,7},{2,4,5,6,8}}
[1,8,6,7,2,5,3,4]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,7,2,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}
[5,8,1,7,2,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[5,8,2,7,1,6,3,4]=>{{1,5},{2,3,4,7,8},{6}}
[2,8,6,7,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,5,7,1,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[2,8,1,7,5,6,3,4]=>{{1,2,3,4,7,8},{5},{6}}
[1,8,2,7,5,6,3,4]=>{{1},{2,3,4,7,8},{5},{6}}
[1,8,2,7,4,6,3,5]=>{{1},{2,3,4,5,7,8},{6}}
[2,8,1,7,4,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[2,8,4,7,1,6,3,5]=>{{1,2,5,8},{3,4,7},{6}}
[4,8,2,7,1,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[4,8,1,7,2,6,3,5]=>{{1,3,4,7},{2,5,8},{6}}
[1,8,4,7,2,6,3,5]=>{{1},{2,5,8},{3,4,7},{6}}
[4,8,1,7,5,6,2,3]=>{{1,2,3,4,7,8},{5},{6}}
[1,8,4,7,5,6,2,3]=>{{1},{2,3,4,7,8},{5},{6}}
[1,8,3,7,5,6,2,4]=>{{1},{2,4,7,8},{3},{5},{6}}
[3,8,1,7,5,6,2,4]=>{{1,3},{2,4,7,8},{5},{6}}
[3,8,1,7,4,6,2,5]=>{{1,3},{2,4,5,7,8},{6}}
[1,8,3,7,4,6,2,5]=>{{1},{2,4,5,7,8},{3},{6}}
[1,8,3,7,2,6,4,5]=>{{1},{2,5,8},{3},{4,7},{6}}
[3,8,1,7,2,6,4,5]=>{{1,3},{2,5,8},{4,7},{6}}
[3,8,2,7,1,6,4,5]=>{{1,2,3,5,8},{4,7},{6}}
[3,8,2,7,4,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[3,8,2,7,5,6,1,4]=>{{1,2,3,4,7,8},{5},{6}}
[4,8,2,7,5,6,1,3]=>{{1,4,7},{2,3,8},{5},{6}}
[4,8,3,7,5,6,1,2]=>{{1,4,7},{2,8},{3},{5},{6}}
[3,8,4,7,5,6,1,2]=>{{1,3,4,7},{2,8},{5},{6}}
[2,8,4,7,5,6,1,3]=>{{1,2,3,4,7,8},{5},{6}}
[2,8,3,7,5,6,1,4]=>{{1,2,4,7,8},{3},{5},{6}}
[2,8,3,7,4,6,1,5]=>{{1,2,4,5,7,8},{3},{6}}
[2,8,3,7,1,6,4,5]=>{{1,2,5,8},{3},{4,7},{6}}
[2,8,1,7,3,6,4,5]=>{{1,2,3,5,8},{4,7},{6}}
[7,5,2,8,6,4,1,3]=>{{1,7},{2,3,4,5,6,8}}
[7,5,1,8,6,2,3,4]=>{{1,3,7},{2,5,6},{4,8}}
[7,4,8,6,1,5,2,3]=>{{1,2,4,5,6,7},{3,8}}
[7,1,8,4,5,2,6,3]=>{{1,2,6,7},{3,8},{4},{5}}
[6,8,1,7,4,2,5,3]=>{{1,2,3,6,8},{4,5,7}}
[1,6,7,4,2,8,5,3]=>{{1},{2,3,5,6,7,8},{4}}
[1,6,7,3,8,5,2,4]=>{{1},{2,3,4,5,6,7,8}}
[7,1,8,3,5,6,2,4]=>{{1,2,7},{3,4,8},{5},{6}}
[7,3,8,6,2,5,1,4]=>{{1,7},{2,3,4,5,6,8}}
[7,4,2,8,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,3,1,8,4,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,2,8,4,1,5,3,6]=>{{1,3,5,6,7,8},{2},{4}}
[7,2,8,3,5,1,6,4]=>{{1,6,7},{2},{3,4,8},{5}}
[7,2,8,3,4,6,1,5]=>{{1,7},{2},{3,4,5,8},{6}}
[1,5,7,8,2,6,3,4]=>{{1},{2,5},{3,7},{4,8},{6}}
[6,2,3,8,5,7,4,1]=>{{1,4,6,7,8},{2},{3},{5}}
[6,2,4,8,5,3,1,7]=>{{1,3,4,6,7,8},{2},{5}}
[6,3,1,4,8,5,2,7]=>{{1,2,3,5,6,7,8},{4}}
[2,6,3,7,8,5,4,1]=>{{1,2,5,6,8},{3},{4,7}}
[2,6,3,7,8,4,5,1]=>{{1,2,4,5,6,7,8},{3}}
[2,4,7,3,5,6,8,1]=>{{1,2,3,4,7,8},{5},{6}}
[2,4,7,3,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[2,5,3,7,8,1,6,4]=>{{1,2,4,5,6,7,8},{3}}
[3,1,5,4,7,8,2,6]=>{{1,2,3,5,7},{4},{6,8}}
[5,3,1,4,8,2,6,7]=>{{1,2,3,5,6,7,8},{4}}
[5,2,4,8,6,1,3,7]=>{{1,5,6},{2},{3,4,7,8}}
[5,2,3,8,4,6,7,1]=>{{1,4,5,8},{2},{3},{6},{7}}
[4,8,2,3,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,8,2,3,5,7,1,6]=>{{1,2,3,4,6,7,8},{5}}
[1,4,7,8,3,6,2,5]=>{{1},{2,3,4,5,7,8},{6}}
[4,8,1,3,6,7,2,5]=>{{1,3,4},{2,5,6,7,8}}
[5,3,8,2,4,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,8,1,2,7,6]=>{{1,5},{2,4,6,8},{3},{7}}
[6,4,2,8,1,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[6,3,8,2,5,1,7,4]=>{{1,6},{2,3,4,8},{5},{7}}
[6,3,8,1,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,3,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[1,5,7,4,2,6,8,3]=>{{1},{2,5},{3,7,8},{4},{6}}
[5,8,1,4,2,6,3,7]=>{{1,2,3,5,7,8},{4},{6}}
[5,8,4,1,2,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[6,5,1,2,8,7,3,4]=>{{1,3,6,7},{2,4,5,8}}
[6,5,3,1,4,2,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[5,3,1,6,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,2,6,4,1,7,3,8]=>{{1,5},{2},{3,6,7},{4},{8}}
[4,6,1,7,5,2,8,3]=>{{1,3,4,7,8},{2,6},{5}}
[4,5,1,7,2,6,3,8]=>{{1,3,4,7},{2,5},{6},{8}}
[3,5,6,1,2,8,7,4]=>{{1,3,4,6,8},{2,5},{7}}
[3,5,7,1,8,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[3,6,2,7,5,1,8,4]=>{{1,2,3,6},{4,7,8},{5}}
[4,2,5,7,1,8,6,3]=>{{1,3,4,5,6,7,8},{2}}
[3,4,7,2,8,6,1,5]=>{{1,3,7},{2,4},{5,8},{6}}
[3,4,5,8,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,6,2,8,1,5,7]=>{{1,3,6},{2,4},{5,7,8}}
[3,5,2,6,8,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[4,2,5,6,1,3,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[4,3,1,2,5,6,8,7]=>{{1,2,3,4},{5},{6},{7,8}}
[5,3,6,8,4,7,2,1]=>{{1,4,5,8},{2,3,6,7}}
[3,7,2,5,4,8,6,1]=>{{1,2,3,6,7,8},{4,5}}
[8,4,2,5,7,3,6,1]=>{{1,8},{2,3,4,5,6,7}}
[4,7,2,5,8,3,6,1]=>{{1,4,5,8},{2,3,6,7}}
[5,2,6,8,4,3,7,1]=>{{1,4,5,8},{2},{3,6},{7}}
[3,1,6,5,4,8,2,7]=>{{1,2,3,6,7,8},{4,5}}
[4,1,6,5,8,3,2,7]=>{{1,2,4,5,7,8},{3,6}}
[5,1,6,8,4,3,2,7]=>{{1,2,4,5,7,8},{3,6}}
[8,5,4,7,6,3,2,1]=>{{1,8},{2,3,4,5,6,7}}
[5,7,1,8,4,3,2,6]=>{{1,3,4,5,6,8},{2,7}}
[2,7,1,5,4,3,8,6]=>{{1,2,3,6,7,8},{4,5}}
[8,2,1,5,4,3,7,6]=>{{1,3,6,8},{2},{4,5},{7}}
[8,4,1,5,7,3,2,6]=>{{1,3,6,8},{2,4,5,7}}
[8,5,6,7,1,3,2,4]=>{{1,2,4,5,7,8},{3,6}}
[8,4,6,1,7,3,2,5]=>{{1,2,4,5,7,8},{3,6}}
[8,3,6,1,4,7,2,5]=>{{1,4,5,8},{2,3,6,7}}
[2,7,6,1,4,3,8,5]=>{{1,2,4,5,7,8},{3,6}}
[6,7,8,5,1,3,2,4]=>{{1,3,4,5,6,8},{2,7}}
[5,7,6,8,2,3,4,1]=>{{1,2,4,5,7,8},{3,6}}
[5,7,2,8,4,3,6,1]=>{{1,4,5,8},{2,3,6,7}}
[6,7,8,2,4,3,5,1]=>{{1,3,6,8},{2,4,5,7}}
[4,7,6,2,8,3,5,1]=>{{1,2,4,5,7,8},{3,6}}
[8,3,6,2,4,7,5,1]=>{{1,8},{2,3,4,5,6,7}}
[3,7,6,2,4,8,5,1]=>{{1,3,6,8},{2,4,5,7}}
[5,7,3,8,4,6,2,1]=>{{1,4,5,8},{2,7},{3},{6}}
[4,7,3,5,8,6,2,1]=>{{1,4,5,8},{2,7},{3},{6}}
[8,7,2,1,4,3,6,5]=>{{1,4,5,8},{2,3,6,7}}
[8,7,3,1,4,6,2,5]=>{{1,4,5,8},{2,7},{3},{6}}
[8,7,6,3,2,5,4,1]=>{{1,8},{2,3,4,5,6,7}}
[8,7,3,5,1,6,2,4]=>{{1,4,5,8},{2,7},{3},{6}}
[8,7,2,5,1,3,6,4]=>{{1,4,5,8},{2,3,6,7}}
[8,2,6,5,1,3,7,4]=>{{1,4,5,8},{2},{3,6},{7}}
[8,4,6,5,7,1,2,3]=>{{1,3,6,8},{2,4,5,7}}
[5,7,6,8,4,1,2,3]=>{{1,3,4,5,6,8},{2,7}}
[4,7,6,5,8,1,2,3]=>{{1,3,4,5,6,8},{2,7}}
[3,7,6,5,1,8,2,4]=>{{1,3,4,5,6,8},{2,7}}
[3,6,4,8,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,4,3,8,7,1,2]=>{{1,2,5,6,7,8},{3,4}}
[1,6,2,4,7,8,5,3]=>{{1},{2,3,6,8},{4},{5,7}}
[3,6,2,4,8,1,5,7]=>{{1,2,3,6},{4},{5,7,8}}
[3,4,7,2,8,1,6,5]=>{{1,3,6,7},{2,4},{5,8}}
[1,4,7,2,5,8,6,3]=>{{1},{2,4},{3,6,7,8},{5}}
[7,3,8,4,5,6,1,2]=>{{1,7},{2,3,8},{4},{5},{6}}
[3,5,6,4,8,7,1,2]=>{{1,3,6,7},{2,5,8},{4}}
[4,6,8,5,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,3,4,7,1,2]=>{{1,6,7},{2,8},{3,4,5}}
[1,6,5,4,2,8,7,3]=>{{1},{2,3,5,6,8},{4},{7}}
[1,8,5,2,7,3,6,4]=>{{1},{2,4,8},{3,5,6,7}}
[4,2,7,5,1,8,6,3]=>{{1,4,5},{2},{3,6,7,8}}
[7,8,1,4,2,6,5,3]=>{{1,2,3,5,7,8},{4},{6}}
[1,3,6,4,8,2,5,7]=>{{1},{2,3,6},{4},{5,7,8}}
[4,1,7,5,3,2,6,8]=>{{1,2,3,4,5,6,7},{8}}
[6,5,1,3,4,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,8,5,3,1,7,2,6]=>{{1,3,4,5},{2,6,7,8}}
[7,4,5,3,2,8,1,6]=>{{1,7},{2,3,4,5},{6,8}}
[5,8,3,6,1,4,2,7]=>{{1,5},{2,7,8},{3},{4,6}}
[2,5,8,6,4,1,3,7]=>{{1,2,4,5,6},{3,7,8}}
[1,4,6,2,5,8,3,7]=>{{1},{2,4},{3,6,7,8},{5}}
[3,6,2,5,8,1,7,4]=>{{1,2,3,6},{4,5,8},{7}}
[1,6,8,7,4,2,3,5]=>{{1},{2,6},{3,4,5,7,8}}
[6,1,7,8,2,4,3,5]=>{{1,2,4,5,6,8},{3,7}}
[7,1,8,6,3,4,2,5]=>{{1,2,7},{3,5,8},{4,6}}
[7,2,1,4,5,6,8,3]=>{{1,3,7,8},{2},{4},{5},{6}}
[1,2,8,3,6,5,7,4]=>{{1},{2},{3,4,8},{5,6},{7}}
[6,1,3,2,7,5,8,4]=>{{1,2,4,5,6,7,8},{3}}
[1,6,3,8,5,7,2,4]=>{{1},{2,6,7},{3},{4,8},{5}}
[2,6,4,1,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,8,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,7,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,3,7,2,8,5]=>{{1},{2,6},{3,4},{5,7,8}}
[2,6,3,4,8,7,1,5]=>{{1,2,6,7},{3},{4},{5,8}}
[7,1,3,4,5,2,8,6]=>{{1,2,6,7,8},{3},{4},{5}}
[1,8,3,5,4,2,7,6]=>{{1},{2,6,8},{3},{4,5},{7}}
[4,1,6,3,8,2,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[7,8,2,4,6,3,1,5]=>{{1,7},{2,3,5,6,8},{4}}
[3,2,6,4,7,8,1,5]=>{{1,3,5,6,7,8},{2},{4}}
[2,8,5,7,4,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[7,2,5,8,3,4,1,6]=>{{1,7},{2},{3,5},{4,6,8}}
[5,3,8,7,1,2,6,4]=>{{1,5},{2,3,4,6,7,8}}
[6,5,3,8,2,1,7,4]=>{{1,6},{2,5},{3},{4,8},{7}}
[7,5,8,4,1,2,3,6]=>{{1,2,3,5,6,7,8},{4}}
[5,8,7,4,1,3,2,6]=>{{1,5},{2,3,6,7,8},{4}}
[3,5,7,8,4,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[1,4,7,5,3,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,4,6,7,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,6,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[2,6,4,5,3,8,1,7]=>{{1,2,6,7,8},{3,4,5}}
[3,6,5,8,4,2,1,7]=>{{1,3,4,5,7,8},{2,6}}
[5,6,8,4,2,3,1,7]=>{{1,2,3,5,6,7,8},{4}}
[6,8,5,4,3,1,2,7]=>{{1,6},{2,7,8},{3,5},{4}}
[6,1,4,2,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[4,8,6,5,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[8,6,5,1,2,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,7,5,8,2,1,4,3]=>{{1,6},{2,3,4,5,7,8}}
[1,7,5,8,2,6,4,3]=>{{1},{2,3,4,5,7,8},{6}}
[1,3,8,5,7,6,2,4]=>{{1},{2,3,4,5,7,8},{6}}
[6,3,8,5,7,1,2,4]=>{{1,6},{2,3,4,5,7,8}}
[8,3,1,5,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[6,8,5,2,1,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[3,8,2,5,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,8,1,5,6,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[8,1,2,5,6,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[1,8,2,5,7,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}
[5,1,8,6,2,7,3,4]=>{{1,2,5},{3,4,6,7,8}}
[2,5,8,6,1,7,3,4]=>{{1,2,5},{3,4,6,7,8}}
[8,6,1,5,7,2,3,4]=>{{1,3,4,5,7,8},{2,6}}
[3,8,6,5,7,1,2,4]=>{{1,3,6},{2,4,5,7,8}}
[7,6,5,8,1,2,4,3]=>{{1,3,4,5,7,8},{2,6}}
[5,1,7,6,8,4,2,3]=>{{1,2,3,5,7,8},{4,6}}
[5,1,3,7,8,6,2,4]=>{{1,2,4,5,7,8},{3},{6}}
[7,2,5,8,1,6,4,3]=>{{1,3,4,5,7,8},{2},{6}}
[3,2,8,5,7,6,1,4]=>{{1,3,4,5,7,8},{2},{6}}
[8,2,1,5,7,6,3,4]=>{{1,3,4,5,7,8},{2},{6}}
[5,2,8,6,1,7,3,4]=>{{1,5},{2},{3,4,6,7,8}}
[1,2,8,6,5,7,3,4]=>{{1},{2},{3,4,6,7,8},{5}}
[4,2,1,3,6,7,8,5]=>{{1,3,4},{2},{5,6,7,8}}
[8,2,5,6,3,7,1,4]=>{{1,4,6,7,8},{2},{3,5}}
[7,2,6,5,4,1,8,3]=>{{1,3,6,7,8},{2},{4,5}}
[6,1,3,5,4,7,8,2]=>{{1,2,6,7,8},{3},{4,5}}
[6,1,5,3,4,7,8,2]=>{{1,2,6,7,8},{3,4,5}}
[7,5,6,2,4,1,8,3]=>{{1,3,6,7,8},{2,4,5}}
[8,5,2,6,3,7,1,4]=>{{1,4,6,7,8},{2,3,5}}
[4,3,1,2,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}
[8,1,6,5,7,3,2,4]=>{{1,2,4,5,7,8},{3,6}}
[3,5,8,6,2,7,1,4]=>{{1,3,4,6,7,8},{2,5}}
[5,8,1,6,3,7,2,4]=>{{1,3,5},{2,4,6,7,8}}
[1,8,5,6,3,7,2,4]=>{{1},{2,4,6,7,8},{3,5}}
[1,7,6,5,4,2,8,3]=>{{1},{2,3,6,7,8},{4,5}}
[5,7,6,1,4,2,8,3]=>{{1,4,5},{2,3,6,7,8}}
[7,1,4,2,6,5,8,3]=>{{1,2,3,4,7,8},{5,6}}
[4,1,7,3,5,6,8,2]=>{{1,2,3,4,7,8},{5},{6}}
[2,7,4,1,5,6,8,3]=>{{1,2,3,4,7,8},{5},{6}}
[5,7,6,4,1,2,8,3]=>{{1,5},{2,3,6,7,8},{4}}
[4,7,6,1,5,2,8,3]=>{{1,4},{2,3,6,7,8},{5}}
[1,7,6,4,5,2,8,3]=>{{1},{2,3,6,7,8},{4},{5}}
[1,8,3,6,5,7,2,4]=>{{1},{2,4,6,7,8},{3},{5}}
[3,8,1,6,5,7,2,4]=>{{1,3},{2,4,6,7,8},{5}}
[8,1,3,5,7,6,2,4]=>{{1,2,4,5,7,8},{3},{6}}
[7,8,5,4,1,6,2,3]=>{{1,2,3,5,7,8},{4},{6}}
[6,1,5,4,3,7,8,2]=>{{1,2,6,7,8},{3,5},{4}}
[7,5,6,4,2,1,8,3]=>{{1,3,6,7,8},{2,5},{4}}
[8,3,2,6,5,7,1,4]=>{{1,4,6,7,8},{2,3},{5}}
[7,4,6,2,5,1,8,3]=>{{1,3,6,7,8},{2,4},{5}}
[6,1,4,3,5,7,8,2]=>{{1,2,6,7,8},{3,4},{5}}
[6,1,3,4,5,7,8,2]=>{{1,2,6,7,8},{3},{4},{5}}
[7,2,6,4,5,1,8,3]=>{{1,3,6,7,8},{2},{4},{5}}
[8,2,3,6,5,7,1,4]=>{{1,4,6,7,8},{2},{3},{5}}
[5,4,7,3,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,8,5,6,1,2]=>{{1,3,7},{2,4,8},{5},{6}}
[3,4,7,2,5,1,6,8]=>{{1,3,6,7},{2,4},{5},{8}}
[1,4,7,2,5,8,3,6]=>{{1},{2,4},{3,7},{5},{6,8}}
[3,6,2,4,7,1,5,8]=>{{1,2,3,6},{4},{5,7},{8}}
[6,8,3,4,5,7,1,2]=>{{1,6,7},{2,8},{3},{4},{5}}
[4,3,6,7,5,8,1,2]=>{{1,4,7},{2,3,6,8},{5}}
[6,3,7,5,8,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,6,4,5,1,2]=>{{1,7},{2,3,8},{4,5,6}}
[3,2,7,6,5,1,4,8]=>{{1,3,4,6,7},{2},{5},{8}}
[1,2,7,6,5,8,3,4]=>{{1},{2},{3,7},{4,6,8},{5}}
[4,8,2,6,1,5,3,7]=>{{1,4,5,6},{2,3,7,8}}
[2,3,8,6,4,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,6,2,5,1,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[7,8,3,2,5,1,4,6]=>{{1,2,4,6,7,8},{3},{5}}
[7,8,1,2,5,6,3,4]=>{{1,3,7},{2,4,8},{5},{6}}
[4,1,6,2,5,7,3,8]=>{{1,2,4},{3,6,7},{5},{8}}
[6,1,2,5,8,7,3,4]=>{{1,2,3,6,7},{4,5,8}}
[2,1,8,6,4,7,3,5]=>{{1,2},{3,4,5,6,7,8}}
[7,1,3,6,8,4,2,5]=>{{1,2,7},{3},{4,6},{5,8}}
[1,8,3,6,7,4,5,2]=>{{1},{2,8},{3},{4,6},{5,7}}
[7,1,5,8,3,6,2,4]=>{{1,2,7},{3,5},{4,8},{6}}
[5,1,8,7,2,3,6,4]=>{{1,2,5},{3,4,6,7,8}}
[6,1,5,7,4,2,8,3]=>{{1,2,6},{3,4,5,7,8}}
[3,1,6,4,7,2,5,8]=>{{1,2,3,6},{4},{5,7},{8}}
[2,4,7,5,1,8,3,6]=>{{1,2,4,5},{3,7},{6,8}}
[6,5,7,1,4,2,3,8]=>{{1,2,4,5,6},{3,7},{8}}
[5,6,8,1,3,2,4,7]=>{{1,3,4,5,7,8},{2,6}}
[6,8,5,1,3,4,2,7]=>{{1,4,6},{2,7,8},{3,5}}
[2,8,3,4,5,1,7,6]=>{{1,2,6,8},{3},{4},{5},{7}}
[6,2,4,3,1,5,7,8]=>{{1,5,6},{2},{3,4},{7},{8}}
[4,2,8,3,1,7,5,6]=>{{1,3,4,5,6,7,8},{2}}
[1,3,7,4,8,2,5,6]=>{{1},{2,3,5,6,7,8},{4}}
[5,3,7,4,1,6,2,8]=>{{1,5},{2,3,7},{4},{6},{8}}
[2,4,7,3,6,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,6,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,6,8,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[2,4,7,1,6,5,3,8]=>{{1,2,4},{3,7},{5,6},{8}}
[1,2,7,8,5,4,3,6]=>{{1},{2},{3,7},{4,6,8},{5}}
[6,3,1,2,8,4,5,7]=>{{1,2,3,4,6},{5,7,8}}
[4,2,1,3,6,5,8,7]=>{{1,3,4},{2},{5,6},{7,8}}
[2,8,1,4,5,6,3,7]=>{{1,2,3,7,8},{4},{5},{6}}
[7,2,1,5,4,6,3,8]=>{{1,3,7},{2},{4,5},{6},{8}}
[4,2,6,1,8,5,3,7]=>{{1,4},{2},{3,5,6,7,8}}
[7,8,2,1,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,1,5,3,6,2]=>{{1,3,4,6,7},{2,8},{5}}
[3,4,6,1,5,8,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[7,5,1,6,4,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,6,3,4,7,2]=>{{1,3,5},{2,8},{4,6},{7}}
[6,5,1,8,2,7,4,3]=>{{1,3,4,6,7,8},{2,5}}
[6,8,1,7,5,2,3,4]=>{{1,2,3,4,6,7,8},{5}}
[7,6,1,8,5,3,2,4]=>{{1,2,3,6,7},{4,8},{5}}
[5,6,1,7,4,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,5,7,4,2,8]=>{{1,3},{2,4,5,6,7},{8}}
[2,5,6,1,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,5,6,4,8,2]=>{{1,2,3,7,8},{4,5,6}}
[5,1,7,6,4,8,3,2]=>{{1,2,4,5,6,8},{3,7}}
[6,1,7,8,5,3,4,2]=>{{1,2,3,4,6,7,8},{5}}
[7,1,8,6,5,4,2,3]=>{{1,2,7},{3,8},{4,6},{5}}
[2,6,5,7,3,4,8,1]=>{{1,2,4,6,7,8},{3,5}}
[1,6,4,7,5,8,2,3]=>{{1},{2,3,4,6,7,8},{5}}
[8,5,3,6,2,7,4,1]=>{{1,8},{2,5},{3},{4,6,7}}
[1,3,7,4,6,8,2,5]=>{{1},{2,3,7},{4},{5,6,8}}
[4,7,5,6,3,2,8,1]=>{{1,2,4,6,7,8},{3,5}}
[1,7,6,5,4,8,2,3]=>{{1},{2,7},{3,6,8},{4,5}}
[8,1,6,5,7,2,4,3]=>{{1,2,3,6,8},{4,5,7}}
[1,2,7,6,8,3,4,5]=>{{1},{2},{3,4,6,7},{5,8}}
[6,1,7,5,3,8,2,4]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,5,6,8,3,4]=>{{1,2},{3,7},{4,5,6,8}}
[5,4,1,7,6,8,2,3]=>{{1,3,5,6,8},{2,4,7}}
[4,8,5,6,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,4,2,7,5,1]=>{{1,2,3,5,6,7,8},{4}}
[7,8,5,2,4,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[2,8,6,3,7,4,5,1]=>{{1,2,8},{3,4,6},{5,7}}
[7,8,1,6,2,4,5,3]=>{{1,2,3,5,7,8},{4,6}}
[6,8,1,4,7,2,5,3]=>{{1,2,3,6,8},{4},{5,7}}
[3,8,4,1,7,2,6,5]=>{{1,3,4},{2,5,6,7,8}}
[5,4,7,1,8,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,4,1,8,5,2,6]=>{{1,3,4},{2,7},{5,6,8}}
[6,7,1,4,8,3,2,5]=>{{1,3,6},{2,7},{4},{5,8}}
[2,7,1,8,4,5,3,6]=>{{1,2,3,7},{4,5,6,8}}
[6,1,2,8,4,3,5,7]=>{{1,2,3,6},{4,5,7,8}}
[6,5,1,4,3,8,2,7]=>{{1,2,3,5,6,7,8},{4}}
[1,6,2,5,8,3,4,7]=>{{1},{2,3,6},{4,5,7,8}}
[8,5,1,3,7,2,6,4]=>{{1,3,4,8},{2,5,6,7}}
[8,4,2,1,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,1,8,5,3,6]=>{{1,2,3,4,7},{5,6,8}}
[1,5,4,2,8,3,6,7]=>{{1},{2,3,4,5,6,7,8}}
[6,4,3,1,5,8,2,7]=>{{1,2,4,6,7,8},{3},{5}}
[3,7,6,8,4,5,2,1]=>{{1,3,4,5,6,8},{2,7}}
[2,7,6,8,5,3,4,1]=>{{1,2,4,7,8},{3,6},{5}}
[1,7,6,8,5,4,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[1,4,8,6,7,5,2,3]=>{{1},{2,4,5,6,7},{3,8}}
[2,4,8,6,7,3,5,1]=>{{1,2,3,4,6,8},{5,7}}
[7,3,8,5,4,6,2,1]=>{{1,2,3,7,8},{4,5},{6}}
[3,4,8,5,6,7,2,1]=>{{1,3,8},{2,4,5,6,7}}
[6,3,5,8,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,8,6,7,2,1]=>{{1,2,4,5,6,7,8},{3}}
[5,4,2,8,7,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[6,2,5,8,7,3,4,1]=>{{1,3,4,5,6,7,8},{2}}
[3,2,8,5,7,4,6,1]=>{{1,3,8},{2},{4,5,6,7}}
[1,3,8,7,5,6,2,4]=>{{1},{2,3,4,7,8},{5},{6}}
[2,1,8,7,4,6,3,5]=>{{1,2},{3,4,5,7,8},{6}}
[3,1,8,5,7,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[6,1,5,8,7,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,4,1,8,7,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[5,8,6,7,4,3,2,1]=>{{1,2,4,5,7,8},{3,6}}
[4,8,7,5,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,2,1,6,3,5,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[6,2,1,4,3,5,8,7]=>{{1,3,5,6},{2},{4},{7,8}}
[6,2,1,4,3,8,5,7]=>{{1,3,5,6,7,8},{2},{4}}
[8,2,1,4,3,6,5,7]=>{{1,3,5,7,8},{2},{4},{6}}
[6,2,4,1,3,8,5,7]=>{{1,3,4,5,6,7,8},{2}}
[6,2,4,1,3,5,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[2,1,6,4,3,5,8,7]=>{{1,2},{3,5,6},{4},{7,8}}
[2,6,1,4,3,5,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[2,6,4,1,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,6,2,1,3,5,8,7]=>{{1,4},{2,3,5,6},{7,8}}
[6,4,2,1,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[8,4,2,1,3,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[8,4,2,1,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[6,4,2,1,8,3,5,7]=>{{1,2,3,4,6},{5,7,8}}
[2,6,1,4,3,8,5,7]=>{{1,2,3,5,6,7,8},{4}}
[2,1,6,4,3,8,5,7]=>{{1,2},{3,5,6,7,8},{4}}
[2,1,8,4,3,6,5,7]=>{{1,2},{3,5,7,8},{4},{6}}
[2,8,1,4,3,6,5,7]=>{{1,2,3,5,7,8},{4},{6}}
[2,8,4,1,3,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[4,8,2,1,3,6,5,7]=>{{1,4},{2,3,5,7,8},{6}}
[6,8,2,1,4,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,1,4,3,5,7]=>{{1,4,5,7,8},{2,3,6}}
[2,8,1,4,6,3,5,7]=>{{1,2,3,5,6,7,8},{4}}
[2,6,1,4,8,3,5,7]=>{{1,2,3,6},{4},{5,7,8}}
[2,6,4,1,8,3,5,7]=>{{1,2,3,4,6},{5,7,8}}
[2,6,4,8,1,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,6,2,8,1,3,5,7]=>{{1,4,5,7,8},{2,3,6}}
[4,2,6,1,8,3,5,7]=>{{1,4},{2},{3,6},{5,7,8}}
[6,2,4,1,8,3,5,7]=>{{1,3,4,6},{2},{5,7,8}}
[4,2,1,6,8,3,5,7]=>{{1,3,4,6},{2},{5,7,8}}
[4,2,1,6,3,8,5,7]=>{{1,3,4,5,6,7,8},{2}}
[4,2,1,3,6,8,5,7]=>{{1,3,4},{2},{5,6,7,8}}
[2,1,4,3,8,6,5,7]=>{{1,2},{3,4},{5,7,8},{6}}
[2,4,1,3,8,6,5,7]=>{{1,2,3,4},{5,7,8},{6}}
[4,2,1,3,8,6,5,7]=>{{1,3,4},{2},{5,7,8},{6}}
[4,2,1,8,3,6,5,7]=>{{1,3,4,5,7,8},{2},{6}}
[4,2,1,8,6,3,5,7]=>{{1,3,4,5,6,7,8},{2}}
[8,2,1,6,4,3,5,7]=>{{1,3,4,5,6,7,8},{2}}
[8,2,6,1,4,3,5,7]=>{{1,4,5,7,8},{2},{3,6}}
[4,2,8,1,3,6,5,7]=>{{1,4},{2},{3,5,7,8},{6}}
[2,4,8,1,3,6,5,7]=>{{1,2,4},{3,5,7,8},{6}}
[2,4,1,8,3,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[2,1,4,8,3,6,5,7]=>{{1,2},{3,4,5,7,8},{6}}
[2,1,4,8,6,3,5,7]=>{{1,2},{3,4,5,6,7,8}}
[2,4,8,1,6,3,5,7]=>{{1,2,4},{3,5,6,7,8}}
[2,4,8,6,1,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,2,8,6,1,3,5,7]=>{{1,3,4,5,6,7,8},{2}}
[8,4,6,2,1,3,5,7]=>{{1,5,7,8},{2,4},{3,6}}
[4,6,8,2,1,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,6,8,4,1,3,5,7]=>{{1,2,3,5,6,7,8},{4}}
[2,6,8,1,4,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,6,1,8,4,3,5,7]=>{{1,2,3,6},{4,5,7,8}}
[2,1,6,8,4,3,5,7]=>{{1,2},{3,6},{4,5,7,8}}
[2,1,8,6,4,3,5,7]=>{{1,2},{3,4,5,6,7,8}}
[2,8,6,4,1,3,5,7]=>{{1,2,5,7,8},{3,6},{4}}
[4,8,6,2,1,3,5,7]=>{{1,2,4,5,7,8},{3,6}}
[6,8,4,2,1,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,2,6,1,5,4,8,7]=>{{1,3,4,6},{2},{5},{7,8}}
[5,2,4,3,8,1,7,6]=>{{1,5,6,8},{2},{3,4},{7}}
[6,2,4,1,5,3,8,7]=>{{1,3,4,6},{2},{5},{7,8}}
[4,3,6,1,5,2,8,7]=>{{1,4},{2,3,6},{5},{7,8}}
[4,3,5,2,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,3,7,2,6,5,8,1]=>{{1,2,3,4,7,8},{5,6}}
[4,3,8,2,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,3,8,1,7,2,6,5]=>{{1,4},{2,3,5,6,7,8}}
[4,3,8,1,5,2,7,6]=>{{1,4},{2,3,6,8},{5},{7}}
[5,1,8,3,4,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,4,8,1,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,1,5,4,8,3,7,6]=>{{1,2},{3,5,6,8},{4},{7}}
[5,1,7,6,8,3,4,2]=>{{1,2,5,8},{3,4,6,7}}
[4,3,7,6,8,1,5,2]=>{{1,4,6},{2,3,5,7,8}}
[4,3,7,1,8,5,6,2]=>{{1,4},{2,3,5,6,7,8}}
[4,3,6,5,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[6,3,5,4,7,2,8,1]=>{{1,2,3,5,6,7,8},{4}}
[6,3,5,4,8,1,7,2]=>{{1,6},{2,3,5,8},{4},{7}}
[7,1,6,3,8,4,5,2]=>{{1,2,5,7,8},{3,4,6}}
[7,4,6,5,8,1,3,2]=>{{1,3,6,7},{2,4,5,8}}
[2,1,8,4,6,3,7,5]=>{{1,2},{3,5,6,8},{4},{7}}
[8,4,6,1,3,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[8,1,6,3,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[8,1,6,3,7,2,5,4]=>{{1,2,3,4,6,8},{5,7}}
[8,3,5,1,7,2,6,4]=>{{1,4,8},{2,3,5,6,7}}
[8,3,5,2,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[7,3,5,2,6,4,8,1]=>{{1,7,8},{2,3,4,5,6}}
[8,2,6,3,5,1,7,4]=>{{1,3,4,6,8},{2},{5},{7}}
[8,2,7,1,5,3,6,4]=>{{1,4,8},{2},{3,6,7},{5}}
[8,2,4,1,5,3,7,6]=>{{1,3,4,6,8},{2},{5},{7}}
[8,2,4,1,7,3,6,5]=>{{1,3,4,5,6,7,8},{2}}
[8,2,4,3,6,1,7,5]=>{{1,5,6,8},{2},{3,4},{7}}
[3,2,8,4,6,1,7,5]=>{{1,3,5,6,8},{2},{4},{7}}
[3,2,8,1,5,4,7,6]=>{{1,3,4,6,8},{2},{5},{7}}
[3,2,7,6,8,1,5,4]=>{{1,3,4,5,6,7,8},{2}}
[3,2,7,1,8,5,6,4]=>{{1,3,4,5,6,7,8},{2}}
[3,2,6,5,8,1,7,4]=>{{1,3,6},{2},{4,5,8},{7}}
[6,5,7,2,4,3,8,1]=>{{1,3,6,7,8},{2,4,5}}
[6,5,8,2,4,1,7,3]=>{{1,6},{2,4,5},{3,8},{7}}
[7,2,4,1,8,5,6,3]=>{{1,3,4,5,6,7,8},{2}}
[7,6,8,2,4,1,5,3]=>{{1,2,4,5,6,7},{3,8}}
[7,6,8,1,5,2,4,3]=>{{1,4,7},{2,6},{3,8},{5}}
[2,1,7,3,8,5,6,4]=>{{1,2},{3,4,5,6,7,8}}
[7,1,3,2,8,5,6,4]=>{{1,2,4,5,6,7,8},{3}}
[7,1,8,5,6,2,4,3]=>{{1,2,4,5,6,7},{3,8}}
[7,1,8,2,6,4,5,3]=>{{1,2,4,5,6,7},{3,8}}
[7,2,8,1,5,4,6,3]=>{{1,4,6,7},{2},{3,8},{5}}
[6,2,7,4,5,3,8,1]=>{{1,3,6,7,8},{2},{4},{5}}
[5,4,7,2,6,3,8,1]=>{{1,3,5,6,7,8},{2,4}}
[5,4,8,2,6,1,7,3]=>{{1,5,6},{2,4},{3,8},{7}}
[6,5,8,1,7,2,4,3]=>{{1,2,4,5,6,7},{3,8}}
[2,1,6,5,8,3,7,4]=>{{1,2},{3,6},{4,5,8},{7}}
[6,5,7,4,8,1,3,2]=>{{1,6},{2,5,8},{3,7},{4}}
[6,5,7,1,8,3,4,2]=>{{1,3,4,6,7},{2,5,8}}
[6,1,7,4,8,3,5,2]=>{{1,2,3,5,6,7,8},{4}}
[5,4,7,1,8,3,6,2]=>{{1,2,4,5,8},{3,6,7}}
[5,4,6,3,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[2,8,3,1,5,4,6,7]=>{{1,2,4,6,7,8},{3},{5}}
[2,5,3,4,7,1,8,6]=>{{1,2,5,6,7,8},{3},{4}}
[2,4,8,3,5,7,6,1]=>{{1,2,3,4,8},{5},{6,7}}
[4,2,5,3,1,8,6,7]=>{{1,3,4,5},{2},{6,7,8}}
[4,2,1,8,5,3,6,7]=>{{1,3,4,6,7,8},{2},{5}}
[5,4,1,3,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,1,4,8,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,5,8,4,3,2,6,7]=>{{1},{2,3,5,6,7,8},{4}}
[1,8,5,4,3,2,6,7]=>{{1},{2,6,7,8},{3,5},{4}}
[1,7,4,3,8,5,2,6]=>{{1},{2,7},{3,4},{5,6,8}}
[1,5,7,3,8,4,2,6]=>{{1},{2,3,4,5,6,7,8}}
[5,1,4,7,8,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,5,7,3,6,2]=>{{1,3,4,5,6,7},{2,8}}
[8,1,5,3,7,4,6,2]=>{{1,2,8},{3,4,5,6,7}}
[3,8,4,7,6,5,2,1]=>{{1,2,3,4,7,8},{5,6}}
[1,6,8,5,3,7,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,8,1,7,4,3,5,2]=>{{1,3,6},{2,8},{4,5,7}}
[6,4,8,1,7,3,5,2]=>{{1,2,3,4,6,8},{5,7}}
[6,4,8,7,1,5,2,3]=>{{1,5,6},{2,4,7},{3,8}}
[7,6,4,1,3,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[1,7,5,6,3,2,8,4]=>{{1},{2,4,6,7,8},{3,5}}
[4,2,1,7,8,5,3,6]=>{{1,3,4,7},{2},{5,6,8}}
[2,7,4,6,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,6,8,4,3,7,5,1]=>{{1,2,3,5,6,7,8},{4}}
[6,2,4,8,3,7,5,1]=>{{1,3,4,5,6,7,8},{2}}
[7,2,6,3,4,1,8,5]=>{{1,3,4,5,6,7,8},{2}}
[2,6,7,3,1,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,7,1,8,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,3,5,8,4,6]=>{{1,2},{3,4,7},{5},{6,8}}
[8,7,1,3,6,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,7,3,5,6,4]=>{{1,3,4,5,6,7,8},{2}}
[7,8,2,6,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,2,6,3,5,4,1]=>{{1,8},{2,3,4,5,6,7}}
[1,2,8,7,4,5,6,3]=>{{1},{2},{3,8},{4,5,6,7}}
[8,3,7,1,5,6,2,4]=>{{1,4,8},{2,3,7},{5},{6}}
[8,6,1,2,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,2,7,4,5,3]=>{{1,2,3,4,6,8},{5,7}}
[1,8,5,2,6,7,4,3]=>{{1},{2,3,4,5,6,7,8}}
[5,2,1,8,6,7,4,3]=>{{1,3,4,5,6,7,8},{2}}
[2,8,5,7,6,4,3,1]=>{{1,2,8},{3,4,5,6,7}}
[1,7,8,5,2,6,4,3]=>{{1},{2,4,5,7},{3,8},{6}}
[7,8,1,6,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,8,6,1,5,3,2,4]=>{{1,2,4,7,8},{3,6},{5}}
[7,3,8,6,1,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,1,5,3,4,2]=>{{1,2,4,7,8},{3,6},{5}}
[8,7,1,6,4,5,3,2]=>{{1,2,3,7,8},{4,5,6}}
[8,1,7,5,6,4,3,2]=>{{1,2,8},{3,7},{4,5,6}}
[1,8,6,7,5,4,3,2]=>{{1},{2,8},{3,4,6,7},{5}}
[6,3,5,2,1,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[6,3,5,7,2,8,4,1]=>{{1,6,8},{2,3,5},{4,7}}
[8,5,2,7,4,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[4,5,3,6,1,2,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[3,5,1,4,6,2,8,7]=>{{1,3},{2,5,6},{4},{7,8}}
[8,3,4,5,7,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,6,3,8,2,1]=>{{1,3,4,5,6,8},{2,7}}
[2,8,4,6,3,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,7,3,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[8,3,4,7,5,1,2,6]=>{{1,6,8},{2,3,4,7},{5}}
[8,5,1,4,7,3,2,6]=>{{1,3,6,8},{2,5,7},{4}}
[8,5,3,7,1,4,2,6]=>{{1,2,4,5,6,7,8},{3}}
[2,1,8,5,7,4,3,6]=>{{1,2},{3,4,5,6,7,8}}
[6,5,3,7,1,8,4,2]=>{{1,2,5,6,8},{3},{4,7}}
[6,5,1,4,7,8,3,2]=>{{1,2,3,5,6,7,8},{4}}
[6,3,4,7,5,8,1,2]=>{{1,2,3,4,6,7,8},{5}}
[5,1,4,6,8,3,7,2]=>{{1,2,5,8},{3,4,6},{7}}
[4,7,1,3,5,8,6,2]=>{{1,3,4},{2,6,7,8},{5}}
[4,8,3,7,1,2,6,5]=>{{1,2,4,5,6,7,8},{3}}
[3,8,6,4,1,7,2,5]=>{{1,2,3,5,6,7,8},{4}}
[3,8,1,2,5,7,6,4]=>{{1,3},{2,4,8},{5},{6,7}}
[2,8,7,5,4,1,3,6]=>{{1,2,6,8},{3,7},{4,5}}
[8,7,2,6,4,1,3,5]=>{{1,4,5,6,8},{2,3,7}}
[3,8,6,7,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,8,4,2,3,1]=>{{1,4,5,8},{2,3,6,7}}
[5,3,7,8,2,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[8,3,6,2,1,4,7,5]=>{{1,5,8},{2,3,4,6},{7}}
[5,3,7,6,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,2,8,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,6,4,2,1,3]=>{{1,2,4,5,6,7},{3,8}}
[2,6,7,5,4,8,1,3]=>{{1,2,3,6,7,8},{4,5}}
[6,1,7,4,5,8,2,3]=>{{1,2,3,6,7,8},{4},{5}}
[6,7,3,5,1,8,2,4]=>{{1,4,5,6,8},{2,7},{3}}
[2,1,6,7,5,8,3,4]=>{{1,2},{3,4,6,7,8},{5}}
[2,1,5,7,3,6,8,4]=>{{1,2},{3,5},{4,7,8},{6}}
[5,7,3,6,1,2,8,4]=>{{1,5},{2,4,6,7,8},{3}}
[4,1,7,2,5,6,8,3]=>{{1,2,4},{3,7,8},{5},{6}}
[2,4,7,1,6,5,8,3]=>{{1,2,4},{3,7,8},{5,6}}
[4,6,2,1,8,7,5,3]=>{{1,4},{2,3,5,6,7,8}}
[3,4,6,2,7,8,5,1]=>{{1,3,6,8},{2,4},{5,7}}
[4,6,1,2,5,8,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[5,6,1,4,8,2,7,3]=>{{1,3,5,8},{2,6},{4},{7}}
[5,6,3,1,8,7,2,4]=>{{1,4,5,8},{2,6,7},{3}}
[3,5,6,4,7,1,8,2]=>{{1,3,6},{2,5,7,8},{4}}
[3,4,6,1,5,7,8,2]=>{{1,2,3,4,6,7,8},{5}}
[3,4,1,5,7,6,8,2]=>{{1,3},{2,4,5,7,8},{6}}
[3,8,2,7,1,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[3,8,2,7,6,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[3,8,2,7,6,5,1,4]=>{{1,2,3,4,7,8},{5,6}}
[3,8,2,7,6,5,4,1]=>{{1,2,3,8},{4,7},{5,6}}
[4,8,7,2,6,5,3,1]=>{{1,2,4,8},{3,7},{5,6}}
[4,8,7,2,6,5,1,3]=>{{1,2,3,4,7,8},{5,6}}
[4,8,7,2,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,2,1,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[4,8,7,3,1,6,5,2]=>{{1,3,4,5,7},{2,8},{6}}
[4,8,7,3,2,1,6,5]=>{{1,3,4,6,7},{2,5,8}}
[4,8,7,3,2,6,1,5]=>{{1,3,4,7},{2,5,8},{6}}
[4,8,7,3,2,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[4,8,7,3,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,3,6,2,1,5]=>{{1,3,4,7},{2,5,6,8}}
[4,8,7,3,6,1,5,2]=>{{1,3,4,5,6,7},{2,8}}
[4,8,7,3,6,5,1,2]=>{{1,3,4,7},{2,8},{5,6}}
[4,8,7,3,6,5,2,1]=>{{1,2,3,4,7,8},{5,6}}
[5,8,7,6,3,4,2,1]=>{{1,2,3,5,7,8},{4,6}}
[5,8,7,6,3,1,4,2]=>{{1,3,4,5,6,7},{2,8}}
[5,8,7,6,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,6,2,4,3,1]=>{{1,2,5,8},{3,7},{4,6}}
[5,8,7,6,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,6,4,2,3,1]=>{{1,2,4,5,6,8},{3,7}}
[5,8,7,6,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,6,4,1,3,2]=>{{1,4,5,6},{2,8},{3,7}}
[5,8,7,6,4,3,1,2]=>{{1,3,4,5,6,7},{2,8}}
[7,3,5,2,6,4,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[7,2,1,5,6,4,3,8]=>{{1,3,7},{2},{4,5,6},{8}}
[1,4,6,7,3,8,2,5]=>{{1},{2,4,7},{3,5,6,8}}
[6,4,5,7,1,3,8,2]=>{{1,3,5,6},{2,4,7,8}}
[6,3,5,1,7,4,8,2]=>{{1,4,6},{2,3,5,7,8}}
[6,2,1,5,7,4,8,3]=>{{1,3,4,5,6,7,8},{2}}
[3,2,1,5,7,4,8,6]=>{{1,3},{2},{4,5,6,7,8}}
[2,4,6,7,3,8,1,5]=>{{1,2,4,7},{3,5,6,8}}
[1,4,6,7,3,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,6,7,8,3,4,2]=>{{1},{2,5,8},{3,6},{4,7}}
[2,5,6,7,8,3,1,4]=>{{1,2,4,5,7,8},{3,6}}
[3,2,1,6,7,8,4,5]=>{{1,3},{2},{4,5,6,7,8}}
[5,2,1,6,7,8,4,3]=>{{1,3,4,5,6,7,8},{2}}
[5,3,6,1,7,8,4,2]=>{{1,4,5,7},{2,3,6,8}}
[5,4,6,7,1,8,3,2]=>{{1,5},{2,3,4,6,7,8}}
[1,5,6,7,8,3,2,4]=>{{1},{2,4,5,7,8},{3,6}}
[6,4,5,7,2,1,8,3]=>{{1,6},{2,3,4,5,7,8}}
[5,4,6,7,2,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,2,7,1,8,4]=>{{1,6},{2,3,4,5,7,8}}
[6,3,4,2,1,7,8,5]=>{{1,5,6,7,8},{2,3,4}}
[4,3,6,2,7,8,5,1]=>{{1,2,3,4,6,8},{5,7}}
[3,4,6,7,2,8,5,1]=>{{1,3,6,8},{2,4,5,7}}
[4,2,1,5,7,3,8,6]=>{{1,3,4,5,6,7,8},{2}}
[1,5,6,7,8,2,4,3]=>{{1},{2,3,5,6,8},{4,7}}
[1,5,6,7,8,4,2,3]=>{{1},{2,3,4,5,6,7,8}}
[3,4,6,7,1,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,3,6,1,7,8,5,2]=>{{1,4},{2,3,6,8},{5,7}}
[1,4,3,6,2,5,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[1,4,3,7,2,5,6,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,4,3,7,6,8,2,5]=>{{1},{2,4,7},{3},{5,6,8}}
[1,4,3,7,5,8,2,6]=>{{1},{2,4,7},{3},{5},{6,8}}
[1,4,3,7,2,6,5,8]=>{{1},{2,4,5,7},{3},{6},{8}}
[1,5,3,7,4,8,2,6]=>{{1},{2,4,5,7},{3},{6,8}}
[1,3,2,6,5,8,4,7]=>{{1},{2,3},{4,6,7,8},{5}}
[1,5,4,8,2,6,3,7]=>{{1},{2,5},{3,4,7,8},{6}}
[1,5,4,8,3,7,2,6]=>{{1},{2,3,4,5,6,7,8}}
[1,2,3,6,5,8,4,7]=>{{1},{2},{3},{4,6,7,8},{5}}
[6,8,2,4,5,7,1,3]=>{{1,6,7},{2,3,8},{4},{5}}
[3,7,8,4,5,2,6,1]=>{{1,3,8},{2,6,7},{4},{5}}
[7,8,1,4,5,3,6,2]=>{{1,3,6,7},{2,8},{4},{5}}
[3,8,7,4,1,6,5,2]=>{{1,3,5,7},{2,8},{4},{6}}
[4,8,3,6,1,5,7,2]=>{{1,4,5,6},{2,8},{3},{7}}
[5,8,3,1,6,4,7,2]=>{{1,4,5,6},{2,8},{3},{7}}
[5,8,1,4,7,6,3,2]=>{{1,3,5,7},{2,8},{4},{6}}
[7,5,1,8,6,2,4,3]=>{{1,3,4,7,8},{2,5,6}}
[7,4,1,8,2,6,3,5]=>{{1,3,7},{2,4,5,8},{6}}
[7,1,8,4,2,6,3,5]=>{{1,2,3,5,7,8},{4},{6}}
[1,6,3,8,5,2,4,7]=>{{1},{2,6},{3},{4,7,8},{5}}
[6,1,3,8,5,2,4,7]=>{{1,2,6},{3},{4,7,8},{5}}
[7,1,8,3,6,2,5,4]=>{{1,2,5,6,7},{3,4,8}}
[7,3,1,8,4,2,6,5]=>{{1,2,3,6,7},{4,5,8}}
[7,2,8,4,1,6,5,3]=>{{1,5,7},{2},{3,8},{4},{6}}
[7,2,8,3,6,5,1,4]=>{{1,7},{2},{3,4,8},{5,6}}
[7,2,8,3,6,1,5,4]=>{{1,5,6,7},{2},{3,4,8}}
[7,1,8,2,3,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[6,1,2,8,3,5,4,7]=>{{1,2,3,5,6},{4,7,8}}
[1,5,2,3,8,4,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[5,1,2,3,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,2,3,8,1,4,7,6]=>{{1,5},{2},{3},{4,6,8},{7}}
[6,2,8,1,3,5,4,7]=>{{1,3,4,5,6,7,8},{2}}
[6,2,4,1,8,7,3,5]=>{{1,3,4,6,7},{2},{5,8}}
[6,3,1,4,2,8,5,7]=>{{1,2,3,5,6,7,8},{4}}
[3,1,6,4,2,8,5,7]=>{{1,2,3,5,6,7,8},{4}}
[2,6,3,8,7,1,5,4]=>{{1,2,6},{3},{4,8},{5,7}}
[2,6,3,8,5,1,4,7]=>{{1,2,6},{3},{4,7,8},{5}}
[2,5,1,8,3,4,7,6]=>{{1,2,3,5},{4,6,8},{7}}
[2,5,1,3,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[1,2,5,3,8,4,7,6]=>{{1},{2},{3,4,5,6,8},{7}}
[1,2,4,8,3,7,6,5]=>{{1},{2},{3,4,5,8},{6,7}}
[2,4,8,1,3,7,6,5]=>{{1,2,4},{3,5,8},{6,7}}
[2,4,8,3,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,3,7,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[2,5,3,8,1,7,4,6]=>{{1,2,5},{3},{4,6,7,8}}
[2,5,4,1,3,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[3,1,5,4,8,2,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[5,3,1,4,8,2,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[5,2,3,8,4,7,1,6]=>{{1,4,5,6,7,8},{2},{3}}
[4,8,2,3,7,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[4,8,2,3,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,2,3,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[1,4,8,2,3,7,6,5]=>{{1},{2,4},{3,5,8},{6,7}}
[1,4,8,3,7,2,6,5]=>{{1},{2,3,4,5,6,7,8}}
[6,3,8,1,5,2,4,7]=>{{1,2,3,4,6,7,8},{5}}
[5,3,8,1,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,1,3,8,2,4,7,6]=>{{1,2,5},{3},{4,6,8},{7}}
[1,5,3,8,2,4,7,6]=>{{1},{2,5},{3},{4,6,8},{7}}
[1,5,4,8,2,7,6,3]=>{{1},{2,5},{3,4,8},{6,7}}
[5,1,4,8,2,7,6,3]=>{{1,2,5},{3,4,8},{6,7}}
[5,4,8,1,2,7,6,3]=>{{1,2,4,5},{3,8},{6,7}}
[6,5,1,2,8,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,6,4,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[5,1,6,2,8,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[4,1,5,8,2,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[4,1,2,5,8,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[1,4,2,5,8,7,6,3]=>{{1},{2,3,4,5,8},{6,7}}
[1,3,5,2,8,7,4,6]=>{{1},{2,3,4,5,6,7,8}}
[3,5,1,2,8,7,4,6]=>{{1,3},{2,4,5,6,7,8}}
[3,6,2,8,7,5,1,4]=>{{1,2,3,5,6,7},{4,8}}
[4,2,6,1,8,7,3,5]=>{{1,4},{2},{3,6,7},{5,8}}
[4,3,1,5,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[3,5,2,8,7,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,8,7,2,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[3,4,8,7,1,2,6,5]=>{{1,3,5,8},{2,4,6,7}}
[3,4,8,1,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[1,3,4,8,7,2,6,5]=>{{1},{2,3,4,5,6,7,8}}
[1,3,4,8,2,7,6,5]=>{{1},{2,3,4,5,8},{6,7}}
[3,4,8,1,2,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[3,4,8,2,7,1,6,5]=>{{1,3,5,6,7,8},{2,4}}
[3,4,8,2,7,6,1,5]=>{{1,3,5,7,8},{2,4},{6}}
[4,2,5,8,1,7,6,3]=>{{1,3,4,5,8},{2},{6,7}}
[4,3,1,2,5,8,7,6]=>{{1,2,3,4},{5},{6,8},{7}}
[3,1,4,2,5,8,7,6]=>{{1,2,3,4},{5},{6,8},{7}}
[2,3,5,1,8,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[7,8,2,1,5,3,6,4]=>{{1,2,3,4,6,7,8},{5}}
[6,4,1,2,7,3,5,8]=>{{1,3,6},{2,4},{5,7},{8}}
[2,3,7,5,4,1,8,6]=>{{1,2,3,6,7,8},{4,5}}
[6,3,1,5,4,2,7,8]=>{{1,2,3,6},{4,5},{7},{8}}
[7,8,1,5,4,2,6,3]=>{{1,2,3,6,7,8},{4,5}}
[7,8,3,5,4,1,6,2]=>{{1,6,7},{2,8},{3},{4,5}}
[7,8,2,5,4,1,3,6]=>{{1,2,3,6,7,8},{4,5}}
[7,8,2,5,4,6,1,3]=>{{1,7},{2,3,8},{4,5},{6}}
[6,2,1,5,4,7,3,8]=>{{1,3,6,7},{2},{4,5},{8}}
[5,3,6,1,4,7,8,2]=>{{1,4,5},{2,3,6,7,8}}
[5,3,6,2,4,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[6,4,2,1,7,3,8,5]=>{{1,2,3,4,6},{5,7,8}}
[4,3,7,5,8,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[4,2,7,1,8,3,6,5]=>{{1,4},{2},{3,6,7},{5,8}}
[3,2,6,7,4,8,1,5]=>{{1,3,4,5,6,7,8},{2}}
[3,1,6,7,4,8,5,2]=>{{1,2,3,6,8},{4,5,7}}
[1,7,6,5,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,6,5,3,8,1,4]=>{{1,2,7},{3,4,5,6,8}}
[1,7,6,5,2,4,8,3]=>{{1},{2,3,4,5,6,7,8}}
[2,7,6,5,3,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,7,1,4,8,3,5,6]=>{{1,2,3,5,6,7,8},{4}}
[3,7,6,4,8,5,1,2]=>{{1,2,3,5,6,7,8},{4}}
[5,7,6,3,8,4,1,2]=>{{1,2,5,7,8},{3,4,6}}
[5,1,6,2,4,8,3,7]=>{{1,2,4,5},{3,6,7,8}}
[4,7,6,5,2,1,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,7,6,5,2,8,1,3]=>{{1,2,4,5,7},{3,6,8}}
[4,7,6,5,1,8,3,2]=>{{1,4,5},{2,3,6,7,8}}
[1,7,6,5,2,8,3,4]=>{{1},{2,3,4,5,6,7,8}}
[1,7,6,5,3,2,8,4]=>{{1},{2,3,4,5,6,7,8}}
[4,7,6,5,1,2,8,3]=>{{1,4,5},{2,3,6,7,8}}
[4,7,6,5,3,1,8,2]=>{{1,3,4,5,6},{2,7,8}}
[6,1,3,5,4,8,7,2]=>{{1,2,6,8},{3},{4,5},{7}}
[5,2,6,3,4,1,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[5,1,6,2,4,7,8,3]=>{{1,2,4,5},{3,6,7,8}}
[1,2,6,3,4,8,7,5]=>{{1},{2},{3,4,5,6,8},{7}}
[1,7,2,4,8,3,6,5]=>{{1},{2,3,6,7},{4},{5,8}}
[6,1,4,2,8,3,5,7]=>{{1,2,3,4,6},{5,7,8}}
[4,1,8,2,6,3,5,7]=>{{1,2,4},{3,5,6,7,8}}
[4,7,2,1,5,3,6,8]=>{{1,4},{2,3,6,7},{5},{8}}
[4,7,1,6,2,3,8,5]=>{{1,3,4,6},{2,5,7,8}}
[1,7,2,6,8,3,5,4]=>{{1},{2,3,4,5,6,7,8}}
[1,2,6,7,4,8,5,3]=>{{1},{2},{3,6,8},{4,5,7}}
[3,1,6,7,4,2,8,5]=>{{1,2,3,6},{4,5,7,8}}
[3,2,8,5,4,6,1,7]=>{{1,3,7,8},{2},{4,5},{6}}
[4,7,6,3,5,8,1,2]=>{{1,2,3,4,6,7,8},{5}}
[4,7,1,2,5,3,8,6]=>{{1,2,3,4,6,7,8},{5}}
[3,7,6,5,2,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[3,7,6,5,1,4,8,2]=>{{1,3,4,5,6},{2,7,8}}
[3,7,6,5,2,1,8,4]=>{{1,3,6},{2,4,5,7,8}}
[1,7,6,5,8,2,4,3]=>{{1},{2,3,4,5,6,7,8}}
[3,7,6,5,8,1,4,2]=>{{1,3,6},{2,4,5,7,8}}
[3,7,6,5,1,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[3,1,6,8,4,2,5,7]=>{{1,2,3,6},{4,5,7,8}}
[4,7,6,8,3,5,1,2]=>{{1,2,4,7,8},{3,5,6}}
[2,7,6,5,1,4,3,8]=>{{1,2,3,4,5,6,7},{8}}
[2,7,6,5,8,1,3,4]=>{{1,2,3,6,7},{4,5,8}}
[2,7,6,5,8,4,1,3]=>{{1,2,7},{3,4,5,6,8}}
[6,3,2,1,7,4,8,5]=>{{1,4,6},{2,3},{5,7,8}}
[4,2,1,7,3,5,8,6]=>{{1,3,4,5,6,7,8},{2}}
[7,3,1,5,4,2,8,6]=>{{1,2,3,6,7,8},{4,5}}
[8,4,1,5,2,7,6,3]=>{{1,3,8},{2,4,5},{6,7}}
[8,2,5,1,3,7,6,4]=>{{1,4,8},{2},{3,5},{6,7}}
[4,3,7,2,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,7,2,5,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,4,1,3,8,6]=>{{1,2,3,5,6,7,8},{4}}
[7,5,4,3,2,1,8,6]=>{{1,6,7,8},{2,5},{3,4}}
[6,5,2,1,8,4,3,7]=>{{1,4,6},{2,3,5,7,8}}
[5,7,4,3,2,8,1,6]=>{{1,2,5,7},{3,4},{6,8}}
[1,7,6,2,4,8,3,5]=>{{1},{2,3,4,5,6,7,8}}
[2,7,3,6,4,8,1,5]=>{{1,2,7},{3},{4,5,6,8}}
[6,2,7,5,3,8,1,4]=>{{1,3,4,5,6,7,8},{2}}
[7,1,8,5,3,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[5,8,3,2,7,1,6,4]=>{{1,5,6,7},{2,4,8},{3}}
[8,7,3,1,6,5,4,2]=>{{1,2,4,7,8},{3},{5,6}}
[8,7,2,6,1,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[1,8,5,7,4,3,6,2]=>{{1},{2,8},{3,4,5,6,7}}
[1,8,5,7,2,4,6,3]=>{{1},{2,3,5,8},{4,6,7}}
[3,8,6,1,7,2,5,4]=>{{1,2,3,4,6,8},{5,7}}
[7,2,8,5,6,1,4,3]=>{{1,4,5,6,7},{2},{3,8}}
[6,3,7,5,8,2,1,4]=>{{1,2,3,6,7},{4,5,8}}
[3,7,2,6,8,4,1,5]=>{{1,2,3,7},{4,6},{5,8}}
[3,6,5,8,1,4,2,7]=>{{1,3,5},{2,4,6,7,8}}
[2,6,5,8,4,1,3,7]=>{{1,2,6},{3,4,5,7,8}}
[6,5,4,8,3,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,1,8,4,2,7]=>{{1,4,6},{2,3,5,7,8}}
[8,4,1,5,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,1,6,8,2,3,7]=>{{1,3,5,7,8},{2,4,6}}
[6,3,7,4,8,5,2,1]=>{{1,5,6,8},{2,3,7},{4}}
[4,7,2,5,8,6,3,1]=>{{1,4,5,8},{2,3,7},{6}}
[6,3,1,8,4,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,3,8,7,4,1,2]=>{{1,2,4,5,6,7,8},{3}}
[5,4,8,1,7,6,2,3]=>{{1,2,4,5,7},{3,8},{6}}
[5,2,8,1,7,3,6,4]=>{{1,3,4,5,6,7,8},{2}}
[6,4,7,8,1,5,3,2]=>{{1,5,6},{2,4,8},{3,7}}
[6,3,7,8,5,2,4,1]=>{{1,2,3,4,6,7,8},{5}}
[2,5,8,7,1,3,6,4]=>{{1,2,5},{3,4,6,7,8}}
[5,3,8,7,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,6,1,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[8,2,7,6,5,1,4,3]=>{{1,3,4,6,7,8},{2},{5}}
[4,3,8,7,6,2,1,5]=>{{1,4,7},{2,3,5,6,8}}
[2,4,8,7,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[3,5,8,7,2,6,1,4]=>{{1,3,4,7,8},{2,5},{6}}
[4,7,3,8,6,5,1,2]=>{{1,2,4,7,8},{3},{5,6}}
[7,5,8,6,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,3,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,6,2,5,3,1]=>{{1,2,4,5,6,8},{3,7}}
[3,8,7,6,5,1,4,2]=>{{1,3,4,6,7},{2,8},{5}}
[2,8,7,6,5,4,1,3]=>{{1,2,3,7,8},{4,6},{5}}
[3,6,5,1,2,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,7,5,8,2,4,1,6]=>{{1,2,3,5,7},{4,6,8}}
[3,8,5,7,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,1,7,8,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[5,1,2,6,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[6,1,2,5,4,3,8,7]=>{{1,2,3,6},{4,5},{7,8}}
[5,1,2,4,6,3,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[4,1,2,6,5,3,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[4,1,5,7,8,3,2,6]=>{{1,2,4,7},{3,5,6,8}}
[4,1,5,8,7,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,7,1,8,3,6,2,5]=>{{1,3,4,5,8},{2,7},{6}}
[4,1,7,8,5,2,3,6]=>{{1,2,4,6,8},{3,7},{5}}
[5,1,7,4,8,2,3,6]=>{{1,2,5,6,8},{3,7},{4}}
[7,5,3,8,1,4,2,6]=>{{1,2,5,7},{3},{4,6,8}}
[2,1,5,8,7,3,4,6]=>{{1,2},{3,4,5,6,7,8}}
[5,1,8,4,7,2,3,6]=>{{1,2,3,5,6,7,8},{4}}
[4,1,8,7,5,2,3,6]=>{{1,2,3,4,6,7,8},{5}}
[4,7,1,6,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,1,2,3,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,2,3,8,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[7,1,2,3,5,8,6,4]=>{{1,2,3,4,6,7,8},{5}}
[6,8,1,4,3,7,2,5]=>{{1,2,3,5,6,7,8},{4}}
[8,7,3,2,4,1,6,5]=>{{1,2,4,5,6,7,8},{3}}
[2,1,7,3,4,8,6,5]=>{{1,2},{3,4,5,6,7,8}}
[7,8,3,2,4,1,6,5]=>{{1,6,7},{2,4,5,8},{3}}
[6,7,1,4,3,8,2,5]=>{{1,3,5,6,8},{2,7},{4}}
[8,1,2,3,5,7,6,4]=>{{1,2,3,4,8},{5},{6,7}}
[8,1,2,3,6,7,5,4]=>{{1,2,3,4,8},{5,6,7}}
[7,1,2,3,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,2,3,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,3,7,5,6,4]=>{{1,2,3,4,8},{5,6,7}}
[8,1,2,3,6,5,7,4]=>{{1,2,3,4,8},{5,6},{7}}
[7,1,8,5,4,3,2,6]=>{{1,2,7},{3,6,8},{4,5}}
[7,8,2,6,3,4,1,5]=>{{1,7},{2,3,5,8},{4,6}}
[6,8,2,7,3,4,1,5]=>{{1,4,6,7},{2,3,5,8}}
[6,7,2,8,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,1,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,1,4,2,6,5]=>{{1,3,4,5,8},{2,6,7}}
[3,6,8,1,4,2,7,5]=>{{1,3,4,5,8},{2,6},{7}}
[3,5,7,8,2,4,1,6]=>{{1,3,7},{2,5},{4,6,8}}
[3,6,7,1,4,2,8,5]=>{{1,3,4,5,7,8},{2,6}}
[7,6,2,8,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,7,3,1,4,5]=>{{1,2,3,5,6,8},{4,7}}
[8,1,7,5,4,3,2,6]=>{{1,2,3,6,7,8},{4,5}}
[8,1,7,4,5,3,2,6]=>{{1,2,3,6,7,8},{4},{5}}
[5,8,3,7,1,4,2,6]=>{{1,5},{2,4,6,7,8},{3}}
[2,1,7,3,4,6,8,5]=>{{1,2},{3,4,5,7,8},{6}}
[6,7,3,2,4,1,8,5]=>{{1,6},{2,4,5,7,8},{3}}
[8,7,2,4,3,6,1,5]=>{{1,2,3,5,7,8},{4},{6}}
[7,1,2,3,5,6,8,4]=>{{1,2,3,4,7,8},{5},{6}}
[6,1,2,3,8,7,4,5]=>{{1,2,3,4,6,7},{5,8}}
[5,1,2,3,7,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,2,3,8,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[5,1,2,3,8,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[6,1,2,3,5,8,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[8,6,2,4,3,1,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[7,6,3,2,4,8,1,5]=>{{1,7},{2,4,5,6,8},{3}}
[2,1,6,3,4,8,7,5]=>{{1,2},{3,4,5,6,8},{7}}
[8,6,3,2,4,7,1,5]=>{{1,2,4,5,6,7,8},{3}}
[7,6,2,4,3,1,8,5]=>{{1,2,3,5,6,7,8},{4}}
[6,1,2,3,5,7,8,4]=>{{1,2,3,4,6,7,8},{5}}
[5,1,2,3,6,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[7,8,1,2,6,3,5,4]=>{{1,3,5,6,7},{2,4,8}}
[1,4,8,2,7,3,5,6]=>{{1},{2,4},{3,6,8},{5,7}}
[1,2,8,5,4,7,3,6]=>{{1},{2},{3,6,7,8},{4,5}}
[1,3,8,5,4,2,7,6]=>{{1},{2,3,6,8},{4,5},{7}}
[2,3,6,8,4,7,1,5]=>{{1,2,3,6,7},{4,5,8}}
[1,3,6,8,4,7,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,8,1,7,3,6,5]=>{{1,2,4},{3,5,6,7,8}}
[3,4,8,5,7,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[1,2,6,8,4,5,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[7,5,1,2,4,3,6,8]=>{{1,3,6,7},{2,4,5},{8}}
[7,4,6,1,5,2,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[7,1,4,2,6,3,5,8]=>{{1,2,3,4,5,6,7},{8}}
[6,8,1,4,7,2,3,5]=>{{1,2,3,5,6,7,8},{4}}
[1,6,4,2,8,3,5,7]=>{{1},{2,3,4,6},{5,7,8}}
[1,6,3,8,5,4,2,7]=>{{1},{2,4,6,7,8},{3},{5}}
[6,8,1,7,3,5,4,2]=>{{1,3,5,6},{2,8},{4,7}}
[7,1,3,6,5,4,2,8]=>{{1,2,7},{3},{4,6},{5},{8}}
[7,3,1,6,5,4,2,8]=>{{1,2,3,7},{4,6},{5},{8}}
[7,2,1,4,6,3,5,8]=>{{1,3,5,6,7},{2},{4},{8}}
[7,2,3,6,5,1,4,8]=>{{1,4,6,7},{2},{3},{5},{8}}
[7,1,2,3,6,5,4,8]=>{{1,2,3,4,7},{5,6},{8}}
[6,8,1,2,7,3,5,4]=>{{1,3,6},{2,4,8},{5,7}}
[1,6,2,3,8,5,4,7]=>{{1},{2,3,4,5,6,7,8}}
[1,5,8,2,7,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}
[5,1,8,2,7,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[5,8,2,7,6,3,4,1]=>{{1,2,3,5,6,8},{4,7}}
[6,2,8,1,7,3,5,4]=>{{1,3,4,6,8},{2},{5,7}}
[6,8,2,1,7,4,3,5]=>{{1,4,6},{2,3,5,7,8}}
[3,6,4,1,2,8,5,7]=>{{1,3,4},{2,5,6,7,8}}
[2,1,6,3,8,5,4,7]=>{{1,2},{3,4,5,6,7,8}}
[2,5,1,8,7,6,3,4]=>{{1,2,3,5,7},{4,8},{6}}
[2,5,3,8,7,4,6,1]=>{{1,2,4,5,6,7,8},{3}}
[1,2,5,3,8,7,4,6]=>{{1},{2},{3,4,5,6,7,8}}
[2,4,8,7,6,5,1,3]=>{{1,2,4,7},{3,8},{5,6}}
[2,5,3,8,7,1,6,4]=>{{1,2,5,6,7},{3},{4,8}}
[2,5,8,4,1,7,6,3]=>{{1,2,5},{3,8},{4},{6,7}}
[3,5,8,7,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,4,1,7,6,2]=>{{1,5},{2,3,8},{4},{6,7}}
[4,2,8,7,6,3,5,1]=>{{1,3,4,5,6,7,8},{2}}
[4,2,8,7,6,5,3,1]=>{{1,3,4,7,8},{2},{5,6}}
[4,1,8,7,6,5,3,2]=>{{1,2,3,4,7,8},{5,6}}
[4,3,8,7,6,5,1,2]=>{{1,4,7},{2,3,8},{5,6}}
[6,3,1,8,7,2,5,4]=>{{1,2,3,6},{4,8},{5,7}}
[5,8,3,7,6,1,4,2]=>{{1,5,6},{2,8},{3},{4,7}}
[5,1,3,8,7,6,2,4]=>{{1,2,5,7},{3},{4,8},{6}}
[1,5,3,8,7,6,2,4]=>{{1},{2,5,7},{3},{4,8},{6}}
[1,5,8,4,7,2,6,3]=>{{1},{2,5,6,7},{3,8},{4}}
[5,1,8,4,7,2,6,3]=>{{1,2,5,6,7},{3,8},{4}}
[5,8,7,4,6,1,2,3]=>{{1,5,6},{2,3,7,8},{4}}
[6,8,5,1,2,4,7,3]=>{{1,4,6},{2,3,5,8},{7}}
[5,6,3,1,2,4,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[5,6,2,4,3,1,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[5,6,1,2,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,5,8,1,7,2,3,6]=>{{1,4},{2,3,5,6,7,8}}
[4,5,8,1,7,2,6,3]=>{{1,4},{2,5,6,7},{3,8}}
[1,3,2,5,8,7,4,6]=>{{1},{2,3},{4,5,6,7,8}}
[3,5,1,8,7,4,6,2]=>{{1,3},{2,4,5,6,7,8}}
[3,5,1,8,7,2,6,4]=>{{1,3},{2,5,6,7},{4,8}}
[4,3,6,1,2,8,5,7]=>{{1,4},{2,3,5,6,7,8}}
[4,5,8,3,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,5,2,8,7,1,3,6]=>{{1,4,6,8},{2,3,5,7}}
[3,2,5,8,7,1,6,4]=>{{1,3,5,6,7},{2},{4,8}}
[3,4,8,7,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,8,7,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[3,4,8,7,6,5,1,2]=>{{1,2,3,4,7,8},{5,6}}
[1,3,4,8,7,6,2,5]=>{{1},{2,3,4,5,7,8},{6}}
[3,4,8,7,6,2,5,1]=>{{1,3,8},{2,4,5,6,7}}
[3,2,5,8,7,4,6,1]=>{{1,3,4,5,6,7,8},{2}}
[4,5,8,3,1,7,6,2]=>{{1,2,3,4,5,8},{6,7}}
[2,1,3,5,8,7,4,6]=>{{1,2},{3},{4,5,6,7,8}}
[1,2,7,5,8,6,4,3]=>{{1},{2},{3,4,5,7,8},{6}}
[7,1,4,8,2,6,5,3]=>{{1,2,5,7},{3,4,8},{6}}
[6,8,1,3,7,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,1,2,6,5,4]=>{{1,3,4,8},{2,5,7},{6}}
[1,3,7,8,2,6,5,4]=>{{1},{2,3,5,7},{4,8},{6}}
[2,3,7,8,1,6,5,4]=>{{1,2,3,5,7},{4,8},{6}}
[2,7,8,1,3,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[8,1,2,6,7,3,5,4]=>{{1,2,3,4,6,8},{5,7}}
[8,1,2,6,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,2,5,7,1,3,6,4]=>{{1,3,4,5,6,7,8},{2}}
[2,8,1,6,7,3,5,4]=>{{1,2,3,4,6,8},{5,7}}
[2,6,8,3,7,1,5,4]=>{{1,2,6},{3,4,8},{5,7}}
[2,8,6,4,7,1,5,3]=>{{1,2,3,6,8},{4},{5,7}}
[6,8,3,4,1,7,5,2]=>{{1,5,6,7},{2,8},{3},{4}}
[6,8,3,7,4,1,5,2]=>{{1,6},{2,8},{3},{4,5,7}}
[2,6,8,3,7,5,1,4]=>{{1,2,5,6,7},{3,4,8}}
[2,8,1,6,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,2,5,7,1,6,3,4]=>{{1,3,4,5,7,8},{2},{6}}
[8,4,7,2,3,6,1,5]=>{{1,3,5,7,8},{2,4},{6}}
[8,5,7,4,2,6,1,3]=>{{1,3,7,8},{2,5},{4},{6}}
[8,3,5,7,4,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,4,7,1,6,3]=>{{1,2,3,5,6,7,8},{4}}
[8,2,3,5,7,1,6,4]=>{{1,4,5,6,7,8},{2},{3}}
[8,2,4,7,3,6,1,5]=>{{1,3,4,5,7,8},{2},{6}}
[8,2,7,1,4,6,3,5]=>{{1,4,5,8},{2},{3,7},{6}}
[8,7,1,2,4,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[8,7,1,4,6,2,3,5]=>{{1,2,3,5,6,7,8},{4}}
[8,4,7,1,3,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[1,6,8,3,7,2,5,4]=>{{1},{2,6},{3,4,8},{5,7}}
[8,3,5,7,1,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,1,3,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[8,5,4,7,1,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[8,5,4,7,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,1,4,7,2,6,3]=>{{1,3,8},{2,5,6,7},{4}}
[1,4,6,8,2,7,5,3]=>{{1},{2,3,4,5,6,7,8}}
[1,6,5,8,2,7,4,3]=>{{1},{2,3,4,5,6,7,8}}
[8,5,6,3,1,7,4,2]=>{{1,2,5,8},{3,4,6,7}}
[5,6,2,8,1,7,4,3]=>{{1,5},{2,3,4,6,7,8}}
[1,8,4,5,7,2,6,3]=>{{1},{2,3,4,5,6,7,8}}
[5,8,7,3,6,1,2,4]=>{{1,5,6},{2,3,4,7,8}}
[8,3,5,7,1,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[1,6,8,3,7,5,2,4]=>{{1},{2,5,6,7},{3,4,8}}
[6,3,8,2,7,5,1,4]=>{{1,5,6,7},{2,3,4,8}}
[6,8,4,2,7,1,5,3]=>{{1,6},{2,3,4,8},{5,7}}
[8,6,4,7,3,1,5,2]=>{{1,2,6,8},{3,4,5,7}}
[8,4,5,7,3,1,6,2]=>{{1,2,4,6,7,8},{3,5}}
[8,4,2,5,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,7,2,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[8,7,1,3,4,6,2,5]=>{{1,3,4,5,8},{2,7},{6}}
[8,3,7,2,4,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[2,8,4,5,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,4,5,1,6,2]=>{{1,2,6,7,8},{3},{4},{5}}
[8,7,4,5,2,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[5,8,7,2,3,6,1,4]=>{{1,3,5,7},{2,4,8},{6}}
[8,7,2,3,4,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[8,7,2,3,6,1,4,5]=>{{1,5,6,8},{2,3,4,7}}
[1,3,2,8,5,4,7,6]=>{{1},{2,3},{4,6,8},{5},{7}}
[4,2,8,5,3,7,1,6]=>{{1,3,4,5,6,7,8},{2}}
[5,2,1,8,4,3,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[6,2,8,4,3,7,5,1]=>{{1,3,5,6,7,8},{2},{4}}
[7,2,8,4,3,1,6,5]=>{{1,6,7},{2},{3,5,8},{4}}
[7,3,4,8,2,1,6,5]=>{{1,6,7},{2,3,4,5,8}}
[6,3,4,8,2,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[5,3,4,1,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[8,1,4,5,2,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[8,1,5,4,3,2,7,6]=>{{1,2,6,8},{3,5},{4},{7}}
[3,5,4,2,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,5,3,2,8,7,1,6]=>{{1,2,4,5,6,7,8},{3}}
[6,4,3,2,8,7,5,1]=>{{1,5,6,7,8},{2,4},{3}}
[6,5,3,2,1,7,8,4]=>{{1,2,4,5,6,7,8},{3}}
[5,6,3,2,7,8,4,1]=>{{1,2,4,5,6,7,8},{3}}
[4,1,6,3,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,2,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,4,3,7,2,5]=>{{1,2,3,5,6,7,8},{4}}
[8,1,7,4,3,6,5,2]=>{{1,2,8},{3,5,7},{4},{6}}
[2,7,4,1,3,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[3,7,4,2,6,1,5,8]=>{{1,2,3,4,5,6,7},{8}}
[4,1,7,3,2,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[5,7,3,2,6,4,8,1]=>{{1,2,4,5,6,7,8},{3}}
[6,7,3,2,5,4,1,8]=>{{1,2,4,6,7},{3},{5},{8}}
[7,6,3,2,1,5,4,8]=>{{1,2,4,5,6,7},{3},{8}}
[4,7,5,6,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,5,6,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,7,5,6,1,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,6,5,7,1,3,8,4]=>{{1,2,3,5,6},{4,7,8}}
[4,6,5,7,2,8,1,3]=>{{1,4,7},{2,3,5,6,8}}
[5,6,4,7,2,8,3,1]=>{{1,2,5,6,8},{3,4,7}}
[6,5,4,1,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,4,6,2,1,8,3]=>{{1,3,4,6,7,8},{2,5}}
[6,4,5,7,1,8,2,3]=>{{1,3,5,6,8},{2,4,7}}
[5,4,6,1,7,8,2,3]=>{{1,2,4,5,7},{3,6,8}}
[8,1,5,6,7,2,3,4]=>{{1,2,4,6,8},{3,5,7}}
[2,1,4,6,8,7,3,5]=>{{1,2},{3,4,6,7},{5,8}}
[3,4,6,8,7,1,2,5]=>{{1,3,6},{2,4,5,7,8}}
[4,3,1,6,8,7,2,5]=>{{1,2,3,4,6,7},{5,8}}
[5,3,6,8,7,2,4,1]=>{{1,4,5,7,8},{2,3,6}}
[6,3,5,1,8,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,3,5,8,6,2,1,4]=>{{1,7},{2,3,5,6},{4,8}}
[7,2,8,5,6,3,1,4]=>{{1,7},{2},{3,4,5,6,8}}
[6,2,8,5,1,7,3,4]=>{{1,3,4,5,6,7,8},{2}}
[4,2,1,8,6,7,3,5]=>{{1,3,4,5,6,7,8},{2}}
[1,3,2,8,6,7,4,5]=>{{1},{2,3},{4,5,6,7,8}}
[2,3,8,6,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,3,2,6,7,4,5]=>{{1,2,4,5,6,7,8},{3}}
[2,3,8,7,1,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[4,2,8,7,6,1,5,3]=>{{1,4,5,6,7},{2},{3,8}}
[5,2,8,7,6,4,1,3]=>{{1,4,5,6,7},{2},{3,8}}
[7,2,1,8,6,5,4,3]=>{{1,3,4,7,8},{2},{5,6}}
[7,3,6,1,8,5,4,2]=>{{1,4,7},{2,3,5,6,8}}
[6,3,7,8,5,4,2,1]=>{{1,4,6,8},{2,3,7},{5}}
[5,3,7,8,6,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,7,8,6,5,2]=>{{1,2,3,4,5,7,8},{6}}
[3,4,7,8,6,1,5,2]=>{{1,3,5,6,7},{2,4,8}}
[8,1,5,7,6,2,4,3]=>{{1,2,3,5,6,8},{4,7}}
[3,5,7,6,8,1,4,2]=>{{1,3,4,6,7},{2,5,8}}
[4,5,7,6,8,3,1,2]=>{{1,3,4,6,7},{2,5,8}}
[5,4,1,7,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,5,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,5,1,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,6,4,3,1,8,2]=>{{1,2,3,5,6,7,8},{4}}
[6,5,1,7,4,3,8,2]=>{{1,3,6},{2,4,5,7,8}}
[4,6,7,5,3,8,1,2]=>{{1,3,4,5,7},{2,6,8}}
[3,6,7,5,1,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,7,5,4,2,3]=>{{1,2,3,4,6,7,8},{5}}
[8,1,7,6,5,4,3,2]=>{{1,2,8},{3,7},{4,6},{5}}
[2,7,6,1,5,4,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[3,7,6,5,1,4,2,8]=>{{1,3,4,5,6},{2,7},{8}}
[4,7,6,5,3,1,2,8]=>{{1,3,4,5,6},{2,7},{8}}
[8,6,4,3,1,5,7,2]=>{{1,2,5,6,8},{3,4},{7}}
[8,6,4,1,5,2,7,3]=>{{1,3,4,8},{2,6},{5},{7}}
[8,6,5,1,3,2,7,4]=>{{1,4,8},{2,6},{3,5},{7}}
[8,6,3,1,7,2,4,5]=>{{1,4,5,7,8},{2,6},{3}}
[8,7,3,1,5,2,4,6]=>{{1,2,4,6,7,8},{3},{5}}
[5,3,1,7,2,4,6,8]=>{{1,2,3,5},{4,6,7},{8}}
[8,7,1,2,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[8,6,1,2,4,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[8,5,1,2,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,1,6,4,2,7,3]=>{{1,3,8},{2,4,5,6},{7}}
[8,5,1,3,6,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[8,6,1,5,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[8,6,1,5,2,4,7,3]=>{{1,3,8},{2,4,5,6},{7}}
[8,6,1,2,5,7,3,4]=>{{1,2,3,4,6,7,8},{5}}
[8,6,1,2,7,4,3,5]=>{{1,3,5,7,8},{2,4,6}}
[8,7,1,2,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}
[5,1,4,2,3,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[5,1,4,2,7,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[7,1,5,8,2,6,3,4]=>{{1,2,3,5,7},{4,8},{6}}
[5,7,8,1,2,4,6,3]=>{{1,2,4,5,6,7},{3,8}}
[5,7,8,1,3,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,7,3,4,6,2]=>{{1,3,5},{2,8},{4,6,7}}
[8,1,5,7,2,4,6,3]=>{{1,2,3,5,8},{4,6,7}}
[8,4,1,2,7,6,3,5]=>{{1,3,5,7,8},{2,4},{6}}
[1,4,2,3,8,7,5,6]=>{{1},{2,3,4},{5,6,7,8}}
[1,4,2,7,6,3,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,1,2,8,7,5,3,4]=>{{1,2,3,5,6,7},{4,8}}
[6,1,2,4,8,7,5,3]=>{{1,2,3,5,6,7,8},{4}}
[3,1,8,4,6,7,5,2]=>{{1,2,3,8},{4},{5,6,7}}
[3,1,7,6,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[7,1,2,4,6,8,5,3]=>{{1,2,3,5,6,7,8},{4}}
[7,1,2,6,8,5,3,4]=>{{1,2,3,7},{4,5,6,8}}
[6,1,2,7,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,1,2,7,4,8,5,3]=>{{1,2,3,6,8},{4,5,7}}
[3,1,6,4,7,8,5,2]=>{{1,2,3,6,8},{4},{5,7}}
[5,7,1,3,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,7,1,8,4,2,6,3]=>{{1,3,4,5,8},{2,6,7}}
[7,1,5,3,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,4,5,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,3,1,5,8,6,2]=>{{1,4},{2,6,7,8},{3},{5}}
[4,8,7,3,1,5,6,2]=>{{1,3,4,5,6,7},{2,8}}
[8,1,7,4,5,2,6,3]=>{{1,2,3,6,7,8},{4},{5}}
[8,1,7,5,3,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,1,2,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[3,1,2,8,4,7,5,6]=>{{1,2,3},{4,5,6,7,8}}
[3,1,2,8,6,4,5,7]=>{{1,2,3},{4,5,6,7,8}}
[3,1,7,2,6,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[1,4,2,3,8,6,5,7]=>{{1},{2,3,4},{5,7,8},{6}}
[1,4,2,3,8,5,7,6]=>{{1},{2,3,4},{5,6,8},{7}}
[5,8,1,7,2,4,6,3]=>{{1,2,3,5,8},{4,6,7}}
[5,8,1,3,4,7,6,2]=>{{1,3,4,5},{2,8},{6,7}}
[3,1,8,6,4,7,5,2]=>{{1,2,3,8},{4,5,6,7}}
[8,1,2,6,7,4,5,3]=>{{1,2,3,8},{4,6},{5,7}}
[6,1,2,8,7,3,5,4]=>{{1,2,3,6},{4,8},{5,7}}
[1,2,3,5,8,4,7,6]=>{{1},{2},{3},{4,5,6,8},{7}}
[1,2,3,5,8,6,4,7]=>{{1},{2},{3},{4,5,7,8},{6}}
[7,1,2,8,3,6,5,4]=>{{1,2,3,5,7},{4,8},{6}}
[7,1,2,8,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,8,4,6,5,2]=>{{1,2,3,4,5,7,8},{6}}
[3,1,8,7,6,4,5,2]=>{{1,2,3,8},{4,5,6,7}}
[8,1,2,7,4,6,5,3]=>{{1,2,3,8},{4,5,7},{6}}
[8,1,2,7,3,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[1,2,3,5,8,7,4,6]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,6,8,5,4,7]=>{{1},{2},{3},{4,5,6,7,8}}
[7,8,5,6,3,1,4,2]=>{{1,4,6,7},{2,8},{3,5}}
[7,5,6,3,1,4,2,8]=>{{1,2,5,7},{3,4,6},{8}}
[7,5,8,3,1,4,2,6]=>{{1,2,5,7},{3,4,6,8}}
[7,8,5,3,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,3,1,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[7,8,5,3,1,6,4,2]=>{{1,3,4,5,7},{2,8},{6}}
[7,8,5,3,6,1,4,2]=>{{1,3,4,5,6,7},{2,8}}
[7,8,5,3,6,4,1,2]=>{{1,7},{2,8},{3,4,5,6}}
[7,5,8,3,4,1,6,2]=>{{1,6,7},{2,3,4,5,8}}
[7,5,6,3,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,6,3,1,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,3,6,1,2,8,4]=>{{1,2,4,5,6,7,8},{3}}
[7,5,3,1,4,2,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,5,3,1,6,4,8,2]=>{{1,2,4,5,6,7,8},{3}}
[7,5,3,6,4,1,8,2]=>{{1,2,4,5,6,7,8},{3}}
[7,5,3,6,4,8,1,2]=>{{1,7},{2,4,5,6,8},{3}}
[7,5,3,8,4,6,1,2]=>{{1,7},{2,4,5,8},{3},{6}}
[7,5,3,8,1,4,6,2]=>{{1,2,4,5,6,7,8},{3}}
[7,5,3,1,8,4,6,2]=>{{1,4,6,7},{2,5,8},{3}}
[7,5,3,1,8,2,6,4]=>{{1,2,4,5,6,7,8},{3}}
[7,5,3,1,6,4,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,5,3,1,8,4,2,6]=>{{1,2,4,5,6,7,8},{3}}
[7,5,3,1,8,6,2,4]=>{{1,2,4,5,7,8},{3},{6}}
[7,5,3,8,1,6,4,2]=>{{1,2,4,5,7,8},{3},{6}}
[7,5,3,8,6,1,4,2]=>{{1,2,4,5,6,7,8},{3}}
[7,5,3,8,6,4,1,2]=>{{1,7},{2,4,5,6,8},{3}}
[7,5,8,3,6,4,1,2]=>{{1,7},{2,3,4,5,6,8}}
[7,5,8,3,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,3,1,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[7,5,3,6,1,4,2,8]=>{{1,2,5,7},{3},{4,6},{8}}
[7,5,3,8,4,1,2,6]=>{{1,2,4,5,6,7,8},{3}}
[7,5,8,6,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,6,3,1,4,2]=>{{1,4,6,7},{2,3,5,8}}
[7,5,8,6,3,4,1,2]=>{{1,7},{2,3,5,8},{4,6}}
[7,5,6,8,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,6,3,8,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,3,4,1,8,2,6]=>{{1,2,5,7},{3},{4},{6,8}}
[7,5,6,3,1,8,2,4]=>{{1,2,5,7},{3,4,6,8}}
[7,5,6,3,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,6,3,8,1,4,2]=>{{1,3,4,6,7},{2,5,8}}
[7,5,6,3,8,4,1,2]=>{{1,7},{2,5,8},{3,4,6}}
[7,5,3,6,1,8,4,2]=>{{1,2,4,5,6,7,8},{3}}
[7,5,3,1,6,8,2,4]=>{{1,2,4,5,6,7,8},{3}}
[7,5,3,1,2,8,4,6]=>{{1,4,7},{2,5},{3},{6,8}}
[7,5,3,1,2,8,6,4]=>{{1,4,6,7,8},{2,5},{3}}
[7,5,3,1,4,8,6,2]=>{{1,2,4,5,6,7,8},{3}}
[7,5,3,4,8,1,6,2]=>{{1,6,7},{2,5,8},{3},{4}}
[7,5,3,4,1,6,8,2]=>{{1,2,5,7,8},{3},{4},{6}}
[7,5,3,1,4,6,8,2]=>{{1,2,4,5,7,8},{3},{6}}
[3,6,2,5,4,1,8,7]=>{{1,2,3,6},{4,5},{7,8}}
[3,5,2,8,4,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[5,4,7,3,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,3,2,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[6,4,5,3,2,1,8,7]=>{{1,6},{2,3,4,5},{7,8}}
[5,3,2,6,4,1,8,7]=>{{1,4,5,6},{2,3},{7,8}}
[4,5,8,3,2,7,6,1]=>{{1,3,4,8},{2,5},{6,7}}
[4,7,6,3,8,5,2,1]=>{{1,3,4,5,6,8},{2,7}}
[4,8,6,3,7,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,3,2,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[5,8,4,3,2,7,6,1]=>{{1,2,5,8},{3,4},{6,7}}
[5,3,2,8,4,7,6,1]=>{{1,4,5,8},{2,3},{6,7}}
[2,1,5,8,4,7,6,3]=>{{1,2},{3,4,5,8},{6,7}}
[5,3,2,7,4,8,6,1]=>{{1,4,5,6,7,8},{2,3}}
[5,7,4,3,2,8,6,1]=>{{1,2,5,6,7,8},{3,4}}
[4,7,5,3,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,3,6,5,2,1]=>{{1,3,4,8},{2,7},{5,6}}
[4,6,8,3,7,5,2,1]=>{{1,3,4,8},{2,5,6,7}}
[7,6,4,3,8,5,2,1]=>{{1,2,5,6,7,8},{3,4}}
[7,3,2,6,8,5,4,1]=>{{1,4,5,6,7,8},{2,3}}
[2,1,8,6,7,5,4,3]=>{{1,2},{3,8},{4,5,6,7}}
[8,3,2,6,7,5,4,1]=>{{1,8},{2,3},{4,5,6,7}}
[8,6,4,3,7,5,2,1]=>{{1,8},{2,5,6,7},{3,4}}
[8,5,7,6,4,3,2,1]=>{{1,8},{2,3,4,5,6,7}}
[8,4,5,3,2,7,6,1]=>{{1,8},{2,3,4,5},{6,7}}
[8,4,7,3,6,5,2,1]=>{{1,8},{2,3,4,7},{5,6}}
[8,4,6,3,7,5,2,1]=>{{1,8},{2,3,4,5,6,7}}
[7,4,6,3,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,7,2,6,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,2,6,7,5,4,1]=>{{1,2,3,8},{4,5,6,7}}
[3,8,2,5,4,7,6,1]=>{{1,2,3,8},{4,5},{6,7}}
[3,7,2,8,6,5,4,1]=>{{1,2,3,4,7,8},{5,6}}
[3,6,2,8,7,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,3,8,5,2,1]=>{{1,5,6,8},{2,3,4,7}}
[6,4,8,3,7,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,8,3,6,5,2,1]=>{{1,2,3,4,7,8},{5,6}}
[7,4,5,3,2,8,6,1]=>{{1,6,7,8},{2,3,4,5}}
[7,5,4,3,2,8,6,1]=>{{1,6,7,8},{2,5},{3,4}}
[7,3,2,5,4,8,6,1]=>{{1,6,7,8},{2,3},{4,5}}
[2,1,7,5,4,8,6,3]=>{{1,2},{3,6,7,8},{4,5}}
[7,3,2,8,6,5,4,1]=>{{1,4,7,8},{2,3},{5,6}}
[7,8,4,3,6,5,2,1]=>{{1,2,7,8},{3,4},{5,6}}
[6,8,5,7,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,3,7,5,2,1]=>{{1,2,5,6,7,8},{3,4}}
[6,3,2,8,7,5,4,1]=>{{1,4,5,6,7,8},{2,3}}
[6,3,2,7,8,5,4,1]=>{{1,5,6,8},{2,3},{4,7}}
[6,7,4,3,8,5,2,1]=>{{1,5,6,8},{2,7},{3,4}}
[4,6,8,3,5,7,1,2]=>{{1,2,3,4,6,7,8},{5}}
[6,8,1,2,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[3,5,8,2,4,7,1,6]=>{{1,3,6,7,8},{2,4,5}}
[8,3,5,2,4,1,6,7]=>{{1,6,7,8},{2,3,4,5}}
[4,2,5,7,3,6,1,8]=>{{1,4,7},{2},{3,5},{6},{8}}
[4,5,2,8,3,1,6,7]=>{{1,4,6,7,8},{2,3,5}}
[4,2,5,8,3,7,1,6]=>{{1,4,6,7,8},{2},{3,5}}
[2,1,6,8,4,7,3,5]=>{{1,2},{3,6,7},{4,5,8}}
[1,2,5,8,3,6,7,4]=>{{1},{2},{3,5},{4,8},{6},{7}}
[5,3,6,8,4,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,6,5,8,2,4,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[3,1,2,6,8,5,7,4]=>{{1,2,3},{4,5,6,8},{7}}
[1,4,3,8,2,6,7,5]=>{{1},{2,4,5,8},{3},{6},{7}}
[5,4,8,3,2,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,7,2,6,1,8]=>{{1,2,4,5,7},{3},{6},{8}}
[4,3,6,2,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,3,2,1,8,5,7]=>{{1,2,4,5,6,7,8},{3}}
[4,1,7,3,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,7,8,2,6,5]=>{{1,2,3,4,6,7},{5,8}}
[3,5,1,2,7,8,6,4]=>{{1,3},{2,4,5,6,7,8}}
[7,5,1,4,8,2,6,3]=>{{1,2,3,5,6,7,8},{4}}
[5,4,7,3,8,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[5,8,4,7,6,3,1,2]=>{{1,3,4,5,6,7},{2,8}}
[5,8,7,1,4,2,6,3]=>{{1,4,5},{2,3,6,7,8}}
[8,3,5,1,2,7,6,4]=>{{1,4,8},{2,3,5},{6,7}}
[4,8,3,1,7,2,6,5]=>{{1,4},{2,5,6,7,8},{3}}
[1,8,4,3,5,2,7,6]=>{{1},{2,6,8},{3,4},{5},{7}}
[4,6,3,1,5,2,8,7]=>{{1,4},{2,6},{3},{5},{7,8}}
[4,7,3,6,5,2,1,8]=>{{1,2,4,6,7},{3},{5},{8}}
[5,3,7,6,4,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[1,6,3,4,2,8,7,5]=>{{1},{2,5,6,8},{3},{4},{7}}
[1,8,3,6,2,7,5,4]=>{{1},{2,4,5,6,7,8},{3}}
[1,6,8,7,4,2,5,3]=>{{1},{2,6},{3,8},{4,5,7}}
[6,4,8,7,5,3,1,2]=>{{1,2,3,4,6,7,8},{5}}
[7,6,4,3,8,5,1,2]=>{{1,7},{2,5,6,8},{3,4}}
[1,7,6,2,8,4,5,3]=>{{1},{2,3,4,5,6,7,8}}
[7,1,3,2,6,8,5,4]=>{{1,2,4,5,6,7,8},{3}}
[1,5,3,2,7,4,8,6]=>{{1},{2,4,5,6,7,8},{3}}
[6,3,2,1,8,5,4,7]=>{{1,4,5,6,7,8},{2,3}}
[6,5,3,2,7,4,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,2,6,3,7,4,1,8]=>{{1,5,7},{2},{3,4,6},{8}}
[2,8,5,3,1,6,4,7]=>{{1,2,3,4,5,7,8},{6}}
[2,1,7,3,8,5,4,6]=>{{1,2},{3,4,7},{5,6,8}}
[1,6,2,3,7,8,5,4]=>{{1},{2,3,4,6,8},{5,7}}
[1,6,7,2,8,4,5,3]=>{{1},{2,4,6},{3,5,7,8}}
[5,7,1,8,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[5,1,2,7,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[2,4,1,7,8,6,3,5]=>{{1,2,3,4,7},{5,8},{6}}
[4,2,1,7,3,8,5,6]=>{{1,3,4,5,7},{2},{6,8}}
[6,2,8,4,3,1,5,7]=>{{1,6},{2},{3,5,7,8},{4}}
[7,3,2,1,8,4,5,6]=>{{1,4,5,6,7,8},{2,3}}
[7,8,3,2,5,6,1,4]=>{{1,7},{2,4,8},{3},{5},{6}}
[7,1,8,2,4,5,6,3]=>{{1,2,4,5,6,7},{3,8}}
[8,7,6,1,2,4,5,3]=>{{1,3,4,6,8},{2,5,7}}
[8,3,7,6,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[3,2,8,7,5,1,4,6]=>{{1,3,6,8},{2},{4,7},{5}}
[8,3,6,5,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[7,6,3,5,2,4,1,8]=>{{1,7},{2,4,5,6},{3},{8}}
[7,4,6,2,5,3,1,8]=>{{1,7},{2,4},{3,6},{5},{8}}
[8,2,4,1,6,5,3,7]=>{{1,3,4,7,8},{2},{5,6}}
[4,2,8,1,7,5,3,6]=>{{1,4},{2},{3,5,6,7,8}}
[8,2,4,1,7,6,3,5]=>{{1,3,4,5,7,8},{2},{6}}
[8,7,1,5,6,2,4,3]=>{{1,3,8},{2,4,5,6,7}}
[8,5,7,3,6,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,8,3,7,5,4,1,2]=>{{1,4,6,7},{2,8},{3},{5}}
[8,1,6,7,5,2,4,3]=>{{1,2,3,6,8},{4,7},{5}}
[8,1,2,6,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,8,1,7,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}
[2,5,1,8,6,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[5,7,2,6,4,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[6,2,7,5,4,3,1,8]=>{{1,3,6,7},{2},{4,5},{8}}
[2,1,8,6,5,4,3,7]=>{{1,2},{3,7,8},{4,6},{5}}
[1,2,7,5,4,3,8,6]=>{{1},{2},{3,6,7,8},{4,5}}
[1,7,2,4,3,8,6,5]=>{{1},{2,3,5,6,7,8},{4}}
[1,7,2,8,3,6,5,4]=>{{1},{2,3,5,7},{4,8},{6}}
[1,7,8,6,5,2,4,3]=>{{1},{2,4,6,7},{3,8},{5}}
[7,3,8,6,5,4,1,2]=>{{1,7},{2,3,8},{4,6},{5}}
[1,8,7,6,5,2,4,3]=>{{1},{2,3,4,6,7,8},{5}}
[8,1,7,3,2,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[5,1,4,3,2,8,7,6]=>{{1,2,5},{3,4},{6,8},{7}}
[8,6,5,3,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[8,6,3,2,1,7,4,5]=>{{1,5,8},{2,4,6,7},{3}}
[8,6,5,4,1,7,2,3]=>{{1,3,5,8},{2,6,7},{4}}
[8,6,5,1,7,3,2,4]=>{{1,4,8},{2,3,5,6,7}}
[8,6,1,7,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,3,2,7,5,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[1,4,3,7,2,5,8,6]=>{{1},{2,4,5,6,7,8},{3}}
[7,4,8,3,1,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[7,1,5,8,3,2,6,4]=>{{1,2,6,7},{3,5},{4,8}}
[5,7,4,1,8,2,6,3]=>{{1,3,4,5,8},{2,6,7}}
[5,7,4,3,1,8,6,2]=>{{1,5},{2,6,7,8},{3,4}}
[1,8,7,2,5,4,6,3]=>{{1},{2,3,4,6,7,8},{5}}
[1,8,5,3,7,2,6,4]=>{{1},{2,3,4,5,6,7,8}}
[4,3,1,8,7,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[1,4,8,6,3,5,2,7]=>{{1},{2,3,4,5,6,7,8}}
[7,4,6,3,5,2,1,8]=>{{1,7},{2,3,4,6},{5},{8}}
[1,3,5,6,8,4,2,7]=>{{1},{2,3,5,7,8},{4,6}}
[3,5,4,8,7,1,2,6]=>{{1,3,4,6,8},{2,5,7}}
[3,1,4,6,8,7,2,5]=>{{1,2,3,4,6,7},{5,8}}
[1,6,3,8,7,2,5,4]=>{{1},{2,6},{3},{4,8},{5,7}}
[1,6,2,4,8,7,5,3]=>{{1},{2,3,5,6,7,8},{4}}
[8,4,1,6,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,4,8,5,2,3]=>{{1,2,7},{3,5,6,8},{4}}
[7,3,6,8,5,1,2,4]=>{{1,2,3,6,7},{4,8},{5}}
[1,3,7,2,6,8,4,5]=>{{1},{2,3,4,7},{5,6,8}}
[3,6,5,2,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,6,5,7,2,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,2,6,3,8,1,5,7]=>{{1,3,4,6},{2},{5,7,8}}
[4,2,6,7,3,5,1,8]=>{{1,4,7},{2},{3,5,6},{8}}
[3,6,2,4,7,5,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[3,6,2,4,1,8,5,7]=>{{1,2,3,5,6,7,8},{4}}
[7,3,8,2,1,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[7,3,5,2,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,4,3,1,5,2]=>{{1,2,3,5,6,7,8},{4}}
[8,7,6,4,1,5,2,3]=>{{1,3,5,6,8},{2,7},{4}}
[3,8,7,2,1,4,6,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,2,7,1,5,4,6]=>{{1,2,3,5,6,8},{4,7}}
[3,6,8,2,1,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,1,6,5,3,7]=>{{1,2,4},{3,7,8},{5,6}}
[4,2,8,1,5,7,3,6]=>{{1,4},{2},{3,6,7,8},{5}}
[8,5,7,6,1,4,2,3]=>{{1,2,3,5,7,8},{4,6}}
[8,6,1,7,3,5,4,2]=>{{1,2,3,5,6,8},{4,7}}
[8,6,1,7,5,4,2,3]=>{{1,3,8},{2,4,6,7},{5}}
[1,6,2,8,7,3,5,4]=>{{1},{2,3,6},{4,8},{5,7}}
[1,8,2,4,6,7,3,5]=>{{1},{2,3,5,6,7,8},{4}}
[2,8,5,4,7,1,3,6]=>{{1,2,6,8},{3,5,7},{4}}
[2,1,5,8,6,4,3,7]=>{{1,2},{3,4,5,6,7,8}}
[7,2,5,6,4,3,1,8]=>{{1,7},{2},{3,4,5,6},{8}}
[1,2,5,7,8,4,3,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,7,4,8,6,3,5]=>{{1},{2},{3,7},{4},{5,8},{6}}
[1,2,7,8,3,6,5,4]=>{{1},{2},{3,5,7},{4,8},{6}}
[7,1,8,6,3,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,6,3,5,2,4]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,4,6,3,2,5]=>{{1},{2,3,5,6,7,8},{4}}
[7,1,5,8,3,4,6,2]=>{{1,2,4,6,7,8},{3,5}}
[7,1,6,4,2,3,5,8]=>{{1,2,5,7},{3,6},{4},{8}}
[8,6,2,4,7,3,5,1]=>{{1,8},{2,3,6},{4},{5,7}}
[8,6,2,4,5,7,3,1]=>{{1,8},{2,3,6,7},{4},{5}}
[2,7,1,4,5,8,3,6]=>{{1,2,3,7},{4},{5},{6,8}}
[7,1,6,4,5,2,3,8]=>{{1,2,3,6,7},{4},{5},{8}}
[7,1,4,5,6,8,2,3]=>{{1,2,7},{3,4,5,6,8}}
[7,1,4,6,5,8,3,2]=>{{1,2,3,4,6,7,8},{5}}
[7,1,2,3,8,5,4,6]=>{{1,2,3,4,7},{5,6,8}}
[7,1,5,4,3,8,2,6]=>{{1,2,7},{3,5},{4},{6,8}}
[7,1,3,4,2,6,8,5]=>{{1,2,5,7,8},{3},{4},{6}}
[7,1,5,4,6,2,8,3]=>{{1,2,3,5,6,7,8},{4}}
[7,1,5,6,4,3,8,2]=>{{1,2,7,8},{3,4,5,6}}
[7,1,6,5,4,3,2,8]=>{{1,2,7},{3,6},{4,5},{8}}
[8,6,2,5,4,3,7,1]=>{{1,8},{2,3,6},{4,5},{7}}
[2,5,1,7,4,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[2,5,1,4,7,8,6,3]=>{{1,2,3,5,6,7,8},{4}}
[3,5,1,4,8,6,2,7]=>{{1,3},{2,5,7,8},{4},{6}}
[3,6,2,4,7,8,1,5]=>{{1,2,3,5,6,7,8},{4}}
[5,6,2,4,8,7,1,3]=>{{1,2,3,5,6,7,8},{4}}
[6,3,8,2,4,7,1,5]=>{{1,6,7},{2,3,4,5,8}}
[6,5,8,7,2,3,1,4]=>{{1,3,4,6,7,8},{2,5}}
[6,5,7,8,2,4,1,3]=>{{1,3,4,6,7,8},{2,5}}
[6,3,4,2,8,5,1,7]=>{{1,5,6,7,8},{2,3,4}}
[3,4,7,2,5,8,1,6]=>{{1,3,7},{2,4},{5},{6,8}}
[4,6,8,1,3,5,2,7]=>{{1,4},{2,3,5,6,7,8}}
[4,3,8,1,2,7,5,6]=>{{1,4},{2,3,5,6,7,8}}
[3,6,4,1,7,2,5,8]=>{{1,3,4},{2,6},{5,7},{8}}
[2,8,3,1,5,6,4,7]=>{{1,2,4,7,8},{3},{5},{6}}
[3,8,7,1,5,4,2,6]=>{{1,2,3,4,6,7,8},{5}}
[4,3,1,7,6,8,2,5]=>{{1,2,3,4,7},{5,6,8}}
[3,4,1,7,5,6,8,2]=>{{1,3},{2,4,7,8},{5},{6}}
[3,4,1,5,7,6,2,8]=>{{1,3},{2,4,5,7},{6},{8}}
[3,7,4,1,6,2,8,5]=>{{1,3,4},{2,5,6,7,8}}
[8,4,7,2,5,3,6,1]=>{{1,8},{2,4},{3,6,7},{5}}
[4,7,8,1,2,3,6,5]=>{{1,4},{2,3,5,6,7,8}}
[2,8,6,1,5,3,7,4]=>{{1,2,4,8},{3,6},{5},{7}}
[7,6,5,1,3,8,2,4]=>{{1,2,4,6,7,8},{3,5}}
[7,6,5,1,3,4,8,2]=>{{1,2,4,6,7,8},{3,5}}
[7,2,6,4,1,3,8,5]=>{{1,5,7,8},{2},{3,6},{4}}
[6,7,5,2,1,3,8,4]=>{{1,3,5,6},{2,4,7,8}}
[8,4,5,3,7,2,6,1]=>{{1,8},{2,3,4,5,6,7}}
[4,7,5,2,8,1,6,3]=>{{1,2,4,6,7},{3,5,8}}
[2,6,4,3,1,5,7,8]=>{{1,2,5,6},{3,4},{7},{8}}
[7,3,8,4,1,5,2,6]=>{{1,2,3,5,6,7,8},{4}}
[7,2,3,4,1,6,5,8]=>{{1,5,7},{2},{3},{4},{6},{8}}
[4,2,8,3,6,1,5,7]=>{{1,3,4,5,6,7,8},{2}}
[6,8,5,7,2,1,3,4]=>{{1,6},{2,3,4,5,7,8}}
[4,8,5,2,7,1,3,6]=>{{1,2,4,6,8},{3,5,7}}
[6,3,5,2,1,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,8,5,3,1,4,2,7]=>{{1,3,4,5,6},{2,7,8}}
[3,6,5,4,2,8,1,7]=>{{1,2,3,5,6,7,8},{4}}
[1,6,4,7,2,5,3,8]=>{{1},{2,5,6},{3,4,7},{8}}
[1,6,4,8,2,5,3,7]=>{{1},{2,5,6},{3,4,7,8}}
[1,6,5,8,2,4,3,7]=>{{1},{2,3,4,5,6,7,8}}
[1,6,8,2,4,3,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,2,4,3,7,8,5]=>{{1},{2,3,5,6,7,8},{4}}
[1,5,6,2,4,7,3,8]=>{{1},{2,4,5},{3,6,7},{8}}
[1,5,6,2,4,7,8,3]=>{{1},{2,4,5},{3,6,7,8}}
[1,5,8,2,4,7,3,6]=>{{1},{2,4,5},{3,6,7,8}}
[1,5,7,2,4,8,3,6]=>{{1},{2,4,5},{3,7},{6,8}}
[1,6,5,7,2,4,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,7,2,4,3,8,5]=>{{1},{2,3,4,5,6,7,8}}
[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,5,8,2,4,6,7,3]=>{{1},{2,4,5},{3,8},{6},{7}}
[1,5,7,2,4,6,8,3]=>{{1},{2,4,5},{3,7,8},{6}}
[1,5,7,8,3,2,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,5,8,3,2,4,6,7]=>{{1},{2,5},{3,4,6,7,8}}
[1,5,6,2,4,8,3,7]=>{{1},{2,4,5},{3,6,7,8}}
[1,7,6,2,8,3,4,5]=>{{1},{2,4,7},{3,6},{5,8}}
[1,7,3,4,2,8,6,5]=>{{1},{2,5,6,7,8},{3},{4}}
[1,6,2,4,3,8,7,5]=>{{1},{2,3,5,6,8},{4},{7}}
[1,5,6,2,4,8,7,3]=>{{1},{2,4,5},{3,6,8},{7}}
[1,5,8,7,3,2,4,6]=>{{1},{2,3,5,6,8},{4,7}}
[1,4,2,3,5,8,7,6]=>{{1},{2,3,4},{5},{6,8},{7}}
[1,5,2,3,4,8,7,6]=>{{1},{2,3,4,5},{6,8},{7}}
[1,6,5,2,3,8,7,4]=>{{1},{2,4,6,8},{3,5},{7}}
[1,7,4,2,8,6,5,3]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,6,5,2,8,4,3]=>{{1},{2,4,5,7},{3,6,8}}
[1,6,7,5,2,3,8,4]=>{{1},{2,3,4,5,6,7,8}}
[1,7,5,2,8,4,3,6]=>{{1},{2,3,4,5,6,7,8}}
[1,7,5,6,2,8,3,4]=>{{1},{2,3,5,7},{4,6,8}}
[1,5,7,6,2,4,8,3]=>{{1},{2,5},{3,7,8},{4,6}}
[1,5,8,3,2,4,7,6]=>{{1},{2,5},{3,4,6,8},{7}}
[1,6,5,2,3,7,4,8]=>{{1},{2,4,6,7},{3,5},{8}}
[1,6,5,2,3,7,8,4]=>{{1},{2,4,6,7,8},{3,5}}
[1,6,8,4,2,3,7,5]=>{{1},{2,3,5,6,8},{4},{7}}
[1,7,4,6,2,8,3,5]=>{{1},{2,3,4,5,6,7,8}}
[1,7,3,5,2,8,4,6]=>{{1},{2,4,5,7},{3},{6,8}}
[1,6,8,5,2,3,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,4,2,3,7,8,5]=>{{1},{2,3,4,5,6,7,8}}
[1,6,4,2,3,7,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,5,8,6,2,4,7,3]=>{{1},{2,5},{3,8},{4,6},{7}}
[1,5,7,3,2,4,8,6]=>{{1},{2,5},{3,4,6,7,8}}
[1,7,3,4,2,8,5,6]=>{{1},{2,5,7},{3},{4},{6,8}}
[1,7,4,2,8,5,3,6]=>{{1},{2,3,4,7},{5,6,8}}
[1,6,7,4,2,3,8,5]=>{{1},{2,3,5,6,7,8},{4}}
[1,6,4,2,3,8,5,7]=>{{1},{2,3,4,5,6,7,8}}
[1,7,6,4,2,8,5,3]=>{{1},{2,5,7},{3,6,8},{4}}
[1,7,5,2,8,6,4,3]=>{{1},{2,4,7},{3,5,8},{6}}
[1,6,4,2,3,8,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[7,3,5,6,1,4,8,2]=>{{1,2,3,5,7,8},{4,6}}
[3,7,5,6,1,4,8,2]=>{{1,3,5},{2,7,8},{4,6}}
[8,2,4,1,6,7,5,3]=>{{1,3,4,8},{2},{5,6,7}}
[8,6,1,4,2,7,5,3]=>{{1,3,8},{2,5,6,7},{4}}
[3,6,1,4,2,8,5,7]=>{{1,3},{2,5,6,7,8},{4}}
[1,6,7,4,3,5,8,2]=>{{1},{2,3,5,6,7,8},{4}}
[6,7,1,4,3,5,8,2]=>{{1,3,5,6},{2,7,8},{4}}
[7,6,1,4,3,5,8,2]=>{{1,2,3,5,6,7,8},{4}}
[3,5,4,1,6,7,8,2]=>{{1,3,4},{2,5,6,7,8}}
[4,7,1,6,3,5,8,2]=>{{1,3,4,5,6},{2,7,8}}
[3,1,4,7,6,5,8,2]=>{{1,2,3,4,7,8},{5,6}}
[6,1,7,4,3,5,8,2]=>{{1,2,3,5,6,7,8},{4}}
[7,1,6,4,3,5,8,2]=>{{1,2,7,8},{3,5,6},{4}}
[1,7,6,4,3,5,8,2]=>{{1},{2,7,8},{3,5,6},{4}}
[8,1,6,4,2,7,5,3]=>{{1,2,3,5,6,7,8},{4}}
[8,4,1,3,7,2,5,6]=>{{1,2,3,4,6,8},{5,7}}
[4,7,1,3,8,2,5,6]=>{{1,3,4},{2,5,6,7,8}}
[7,4,1,3,8,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[1,3,6,4,2,8,5,7]=>{{1},{2,3,5,6,7,8},{4}}
[4,7,3,1,2,8,5,6]=>{{1,4},{2,5,7},{3},{6,8}}
[4,7,8,1,2,6,5,3]=>{{1,4},{2,5,7},{3,8},{6}}
[6,8,1,4,2,7,5,3]=>{{1,2,3,5,6,7,8},{4}}
[1,8,6,4,2,7,5,3]=>{{1},{2,3,5,6,7,8},{4}}
[4,8,1,3,7,2,5,6]=>{{1,3,4},{2,6,8},{5,7}}
[8,7,1,3,6,2,5,4]=>{{1,3,4,8},{2,5,6,7}}
[6,8,5,7,3,2,1,4]=>{{1,2,4,6,7,8},{3,5}}
[1,8,4,3,7,2,5,6]=>{{1},{2,6,8},{3,4},{5,7}}
[2,8,3,4,7,6,1,5]=>{{1,2,5,7,8},{3},{4},{6}}
[3,7,8,4,6,2,1,5]=>{{1,2,3,5,6,7,8},{4}}
[3,7,4,6,8,2,1,5]=>{{1,2,3,4,6,7},{5,8}}
[2,4,3,7,8,6,1,5]=>{{1,2,4,7},{3},{5,8},{6}}
[1,4,7,3,8,2,5,6]=>{{1},{2,3,4,5,6,7,8}}
[5,7,6,8,3,2,1,4]=>{{1,2,3,5,6,7},{4,8}}
[2,5,3,4,8,6,1,7]=>{{1,2,5,7,8},{3},{4},{6}}
[3,7,5,4,8,2,1,6]=>{{1,2,3,5,6,7,8},{4}}
[7,1,3,4,2,8,5,6]=>{{1,2,5,7},{3},{4},{6,8}}
[6,1,4,3,8,2,5,7]=>{{1,2,6},{3,4},{5,7,8}}
[4,1,7,3,8,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,3,7,2,5,6]=>{{1,2,6,8},{3,4},{5,7}}
[8,2,3,4,7,6,1,5]=>{{1,5,7,8},{2},{3},{4},{6}}
[4,2,3,7,8,6,1,5]=>{{1,4,7},{2},{3},{5,8},{6}}
[5,2,3,4,8,6,1,7]=>{{1,5,7,8},{2},{3},{4},{6}}
[2,7,5,6,3,8,1,4]=>{{1,2,7},{3,5},{4,6,8}}
[5,7,2,6,3,8,1,4]=>{{1,2,3,5,7},{4,6,8}}
[5,7,2,6,8,4,1,3]=>{{1,2,3,5,7,8},{4,6}}
[7,2,5,6,8,4,1,3]=>{{1,7},{2},{3,5,8},{4,6}}
[4,2,3,8,5,6,1,7]=>{{1,4,7,8},{2},{3},{5},{6}}
[5,2,3,8,7,6,1,4]=>{{1,5,7},{2},{3},{4,8},{6}}
[8,2,3,7,5,6,1,4]=>{{1,4,7,8},{2},{3},{5},{6}}
[6,1,8,3,7,2,5,4]=>{{1,2,6},{3,4,8},{5,7}}
[1,7,8,4,2,6,5,3]=>{{1},{2,5,7},{3,8},{4},{6}}
[4,7,1,8,2,5,6,3]=>{{1,3,4,8},{2,5,6,7}}
[3,7,4,8,5,2,1,6]=>{{1,2,3,4,6,7,8},{5}}
[2,4,3,8,5,6,1,7]=>{{1,2,4,7,8},{3},{5},{6}}
[1,4,8,3,6,2,5,7]=>{{1},{2,3,4,5,6,7,8}}
[7,5,8,6,3,2,1,4]=>{{1,7},{2,3,4,5,6,8}}
[6,5,8,7,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,6,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,3,8,7,6,1,4]=>{{1,2,5,7},{3},{4,8},{6}}
[3,7,5,8,6,2,1,4]=>{{1,2,3,5,6,7},{4,8}}
[3,7,8,6,5,2,1,4]=>{{1,2,3,4,6,7,8},{5}}
[1,8,7,3,6,2,5,4]=>{{1},{2,3,4,5,6,7,8}}
[6,8,7,5,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,8,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,8,4,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,5,4,7,6,8,2,3]=>{{1},{2,3,4,5,6,7,8}}
[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[3,7,4,6,5,8,1,2]=>{{1,2,3,4,6,7,8},{5}}
[3,5,4,8,6,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[3,8,4,6,5,7,1,2]=>{{1,3,4,6,7},{2,8},{5}}
[3,6,4,7,5,8,1,2]=>{{1,3,4,7},{2,6,8},{5}}
[1,6,2,7,5,8,3,4]=>{{1},{2,3,4,6,7,8},{5}}
[1,6,4,8,5,7,2,3]=>{{1},{2,6,7},{3,4,8},{5}}
[1,8,4,6,5,7,2,3]=>{{1},{2,3,4,6,7,8},{5}}
[1,5,4,8,6,7,2,3]=>{{1},{2,5,6,7},{3,4,8}}
[7,8,1,5,4,6,2,3]=>{{1,2,3,7,8},{4,5},{6}}
[7,8,1,5,2,4,3,6]=>{{1,3,7},{2,4,5,6,8}}
[1,8,2,6,5,7,3,4]=>{{1},{2,3,4,6,7,8},{5}}
[1,7,2,8,5,6,3,4]=>{{1},{2,3,7},{4,8},{5},{6}}
[1,7,2,6,5,8,3,4]=>{{1},{2,3,7},{4,6,8},{5}}
[1,5,2,7,6,8,3,4]=>{{1},{2,3,4,5,6,7,8}}
[1,7,6,8,2,5,3,4]=>{{1},{2,3,5,6,7},{4,8}}
[1,7,6,8,4,5,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[5,7,6,8,1,4,2,3]=>{{1,5},{2,7},{3,4,6,8}}
[7,8,5,6,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,7,1,3,2,4]=>{{1,5},{2,4,7,8},{3,6}}
[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[1,7,6,8,2,4,3,5]=>{{1},{2,3,4,5,6,7,8}}
[7,8,1,3,2,6,4,5]=>{{1,3,4,7},{2,5,8},{6}}
[7,8,1,6,2,4,3,5]=>{{1,3,7},{2,5,8},{4,6}}
[1,8,6,7,2,4,3,5]=>{{1},{2,5,8},{3,4,6,7}}
[7,8,1,4,2,6,3,5]=>{{1,3,7},{2,5,8},{4},{6}}
[7,8,1,4,2,5,3,6]=>{{1,3,7},{2,5,6,8},{4}}
[7,8,2,1,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,2,4,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,6,5,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[3,4,6,5,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,6,2,3,8,7,4,5]=>{{1},{2,3,4,6,7},{5,8}}
[1,7,4,3,2,8,6,5]=>{{1},{2,5,6,7,8},{3,4}}
[1,4,7,6,2,5,8,3]=>{{1},{2,4,5,6},{3,7,8}}
[1,2,6,5,3,7,4,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,6,5,3,7,8,4]=>{{1},{2},{3,4,5,6,7,8}}
[1,3,7,5,2,6,8,4]=>{{1},{2,3,4,5,7,8},{6}}
[1,3,7,4,2,6,8,5]=>{{1},{2,3,5,7,8},{4},{6}}
[1,2,6,4,3,7,8,5]=>{{1},{2},{3,5,6,7,8},{4}}
[1,2,6,4,3,7,5,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[1,4,7,3,2,5,8,6]=>{{1},{2,3,4,5,6,7,8}}
[1,4,3,2,5,8,6,7]=>{{1},{2,4},{3},{5},{6,7,8}}
[1,5,3,2,4,8,6,7]=>{{1},{2,4,5},{3},{6,7,8}}
[1,7,5,3,2,8,6,4]=>{{1},{2,3,4,5,6,7,8}}
[1,5,3,2,4,8,7,6]=>{{1},{2,4,5},{3},{6,8},{7}}
[7,6,5,4,3,1,8,2]=>{{1,2,6,7,8},{3,5},{4}}
[6,8,5,4,3,2,1,7]=>{{1,2,6,7,8},{3,5},{4}}
[7,1,5,4,3,8,6,2]=>{{1,2,6,7,8},{3,5},{4}}
[3,6,5,4,8,1,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[6,8,1,4,3,2,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[2,8,5,4,3,7,1,6]=>{{1,2,6,7,8},{3,5},{4}}
[7,6,1,4,3,8,5,2]=>{{1,3,5,7},{2,6,8},{4}}
[4,6,5,8,3,1,7,2]=>{{1,2,4,6,8},{3,5},{7}}
[6,8,5,1,3,2,7,4]=>{{1,2,4,6,8},{3,5},{7}}
[1,8,2,4,3,7,6,5]=>{{1},{2,3,5,8},{4},{6,7}}
[3,8,5,4,7,2,1,6]=>{{1,3,5,7},{2,6,8},{4}}
[7,6,5,1,3,8,4,2]=>{{1,4,7},{2,6,8},{3,5}}
[1,6,3,4,8,7,5,2]=>{{1},{2,5,6,7,8},{3},{4}}
[1,4,5,8,3,7,6,2]=>{{1},{2,4,8},{3,5},{6,7}}
[6,8,5,4,1,2,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[1,8,5,2,3,7,6,4]=>{{1},{2,4,8},{3,5},{6,7}}
[6,8,2,4,3,7,1,5]=>{{1,6,7},{2,3,5,8},{4}}
[1,8,3,4,7,2,6,5]=>{{1},{2,5,6,7,8},{3},{4}}
[7,5,8,4,3,2,1,6]=>{{1,7},{2,3,5,6,8},{4}}
[4,8,5,7,3,2,1,6]=>{{1,4,7},{2,6,8},{3,5}}
[5,1,7,6,8,4,3,2]=>{{1,2,5,8},{3,7},{4,6}}
[8,4,7,5,2,6,1,3]=>{{1,3,7,8},{2,4,5},{6}}
[5,4,6,8,2,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[8,4,6,5,2,1,7,3]=>{{1,3,6,8},{2,4,5},{7}}
[4,8,7,5,6,1,3,2]=>{{1,4,5,6},{2,8},{3,7}}
[2,7,5,1,8,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,7,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,6,7,4,3,5,1]=>{{1,2,8},{3,6},{4,5,7}}
[3,6,5,2,4,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[5,2,3,6,4,1,8,7]=>{{1,4,5,6},{2},{3},{7,8}}
[6,1,4,5,3,2,8,7]=>{{1,2,6},{3,4,5},{7,8}}
[3,8,7,1,4,6,5,2]=>{{1,3,4,5,7},{2,8},{6}}
[5,7,1,2,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,6,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,8,1,7,2,4]=>{{1,5},{2,3,6,7},{4,8}}
[3,2,6,8,5,7,1,4]=>{{1,3,6,7},{2},{4,8},{5}}
[6,3,7,2,4,8,5,1]=>{{1,6,8},{2,3,4,5,7}}
[7,4,8,6,5,2,1,3]=>{{1,7},{2,4,6},{3,8},{5}}
[7,1,8,2,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}
[2,5,3,7,4,1,8,6]=>{{1,2,4,5,6,7,8},{3}}
[3,6,4,7,5,1,8,2]=>{{1,2,3,4,6,7,8},{5}}
[8,4,7,6,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,1,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[4,2,8,7,3,5,6,1]=>{{1,3,4,5,6,7,8},{2}}
[8,1,7,4,2,5,6,3]=>{{1,2,3,5,6,7,8},{4}}
[7,4,3,8,2,5,6,1]=>{{1,2,4,5,6,7,8},{3}}
[6,4,1,5,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,5,8,7,3,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[2,1,5,8,7,4,6,3]=>{{1,2},{3,4,5,6,7,8}}
[8,3,5,6,7,4,1,2]=>{{1,2,3,5,7,8},{4,6}}
[7,4,3,2,8,5,6,1]=>{{1,5,6,7,8},{2,4},{3}}
[4,2,7,1,8,5,6,3]=>{{1,4},{2},{3,5,6,7,8}}
[4,1,7,2,8,5,6,3]=>{{1,2,4},{3,5,6,7,8}}
[2,4,8,7,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,3,1,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,2,8,5,6,1]=>{{1,3,5,6,7,8},{2,4}}
[3,7,1,4,8,5,6,2]=>{{1,3},{2,5,6,7,8},{4}}
[7,2,3,4,8,5,6,1]=>{{1,5,6,7,8},{2},{3},{4}}
[6,1,8,5,2,7,4,3]=>{{1,2,4,5,6,7},{3,8}}
[2,1,7,4,5,8,6,3]=>{{1,2},{3,6,7,8},{4},{5}}
[2,1,8,3,6,7,5,4]=>{{1,2},{3,4,8},{5,6,7}}
[8,2,1,6,4,7,5,3]=>{{1,3,8},{2},{4,5,6,7}}
[7,8,2,6,4,1,5,3]=>{{1,4,5,6,7},{2,3,8}}
[2,6,3,5,8,7,1,4]=>{{1,2,6,7},{3},{4,5,8}}
[7,6,2,1,5,8,4,3]=>{{1,4,7},{2,3,6,8},{5}}
[4,5,2,7,6,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,8,4,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,6,8,7,5,2,1,4]=>{{1,3,4,7,8},{2,6},{5}}
[7,4,8,6,5,2,3,1]=>{{1,3,7,8},{2,4,6},{5}}
[8,1,6,4,7,3,2,5]=>{{1,2,5,7,8},{3,6},{4}}
[7,6,4,1,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,6,4,8,5,3,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[7,3,5,8,4,2,1,6]=>{{1,7},{2,3,4,5,6,8}}
[3,2,5,8,4,1,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[8,4,7,1,5,2,3,6]=>{{1,2,4,6,8},{3,7},{5}}
[4,8,7,5,6,1,2,3]=>{{1,4,5,6},{2,3,7,8}}
[6,1,4,8,7,3,5,2]=>{{1,2,3,4,6,8},{5,7}}
[7,2,8,4,3,5,6,1]=>{{1,3,5,6,7,8},{2},{4}}
[4,7,8,1,3,5,6,2]=>{{1,4},{2,3,5,6,7,8}}
[8,7,3,4,1,5,6,2]=>{{1,2,5,6,7,8},{3},{4}}
[4,8,2,7,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,7,2,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[3,8,1,7,2,5,6,4]=>{{1,3},{2,4,5,6,7,8}}
[8,2,3,7,1,5,6,4]=>{{1,4,5,6,7,8},{2},{3}}
[6,4,8,7,1,3,2,5]=>{{1,3,5,6,8},{2,4,7}}
[2,8,4,6,7,3,1,5]=>{{1,2,5,7,8},{3,4,6}}
[4,3,8,2,7,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[6,8,4,2,1,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[7,8,2,4,3,5,6,1]=>{{1,2,3,5,6,7,8},{4}}
[2,8,3,7,1,5,6,4]=>{{1,2,4,5,6,7,8},{3}}
[8,1,2,7,3,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,3,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,6,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,2,8,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,5,1,8,2,6]=>{{1,4,5},{2,3,7},{6,8}}
[6,8,5,2,7,4,3,1]=>{{1,2,4,6,8},{3,5,7}}
[7,2,5,4,3,8,1,6]=>{{1,7},{2},{3,5},{4},{6,8}}
[3,6,8,1,4,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[6,8,1,2,4,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,2,4,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,1,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,6,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,6,5,8,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,6,2,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,6,1,4,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,6,8,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,4,3,8,1,6]=>{{1,2,7},{3,5},{4},{6,8}}
[6,3,8,7,4,2,5,1]=>{{1,2,3,6,8},{4,5,7}}
[5,8,4,3,7,6,1,2]=>{{1,5,7},{2,8},{3,4},{6}}
[8,7,4,3,1,6,2,5]=>{{1,5,8},{2,7},{3,4},{6}}
[1,7,4,3,8,6,2,5]=>{{1},{2,7},{3,4},{5,8},{6}}
[7,1,5,3,4,8,2,6]=>{{1,2,7},{3,4,5},{6,8}}
[2,8,6,1,7,4,5,3]=>{{1,2,3,4,6,8},{5,7}}
[4,8,6,5,7,2,1,3]=>{{1,4,5,7},{2,3,6,8}}
[4,7,6,8,2,1,5,3]=>{{1,3,4,6,8},{2,5,7}}
[6,1,8,7,4,3,5,2]=>{{1,2,3,6,8},{4,5,7}}
[8,5,4,3,1,6,7,2]=>{{1,2,5,8},{3,4},{6},{7}}
[1,5,8,6,3,4,7,2]=>{{1},{2,3,5,8},{4,6},{7}}
[2,5,8,6,3,4,7,1]=>{{1,2,3,5,8},{4,6},{7}}
[4,1,3,8,5,6,7,2]=>{{1,2,4,8},{3},{5},{6},{7}}
[6,5,8,4,3,1,7,2]=>{{1,6},{2,3,5,8},{4},{7}}
[4,6,5,2,8,1,7,3]=>{{1,2,4,6},{3,5,8},{7}}
[7,2,8,1,3,6,4,5]=>{{1,4,7},{2},{3,5,8},{6}}
[1,8,5,2,3,6,7,4]=>{{1},{2,4,8},{3,5},{6},{7}}
[1,8,3,2,5,6,7,4]=>{{1},{2,4,8},{3},{5},{6},{7}}
[2,8,3,1,5,6,7,4]=>{{1,2,4,8},{3},{5},{6},{7}}
[4,8,3,2,5,6,7,1]=>{{1,2,4,8},{3},{5},{6},{7}}
[8,2,3,1,5,6,7,4]=>{{1,4,8},{2},{3},{5},{6},{7}}
[2,1,8,3,5,6,7,4]=>{{1,2},{3,4,8},{5},{6},{7}}
[1,4,8,2,3,6,7,5]=>{{1},{2,4},{3,5,8},{6},{7}}
[3,1,2,7,8,6,4,5]=>{{1,2,3},{4,7},{5,8},{6}}
[7,5,1,8,2,4,3,6]=>{{1,3,7},{2,5},{4,6,8}}
[3,5,8,1,2,4,7,6]=>{{1,3,4,6,8},{2,5},{7}}
[4,5,8,1,2,3,7,6]=>{{1,4},{2,5},{3,6,8},{7}}
[4,2,7,1,8,6,3,5]=>{{1,4},{2},{3,7},{5,8},{6}}
[3,8,4,1,2,6,7,5]=>{{1,3,4},{2,5,8},{6},{7}}
[5,4,8,2,3,6,7,1]=>{{1,3,5,8},{2,4},{6},{7}}
[5,8,3,6,7,4,1,2]=>{{1,5,7},{2,8},{3},{4,6}}
[2,3,1,6,8,4,7,5]=>{{1,2,3},{4,6},{5,8},{7}}
[2,4,3,7,1,8,5,6]=>{{1,2,4,5,7},{3},{6,8}}
[1,4,7,3,2,8,5,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,7,1,4,3,8,5,6]=>{{1,2,3,5,7},{4},{6,8}}
[2,4,1,8,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[8,4,1,3,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[6,8,5,1,7,2,3,4]=>{{1,2,4,6,8},{3,5,7}}
[7,3,6,5,8,2,1,4]=>{{1,7},{2,3,6},{4,5,8}}
[7,6,3,5,8,2,1,4]=>{{1,7},{2,6},{3},{4,5,8}}
[4,5,8,7,3,6,1,2]=>{{1,4,7},{2,3,5,8},{6}}
[3,5,2,8,6,1,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[8,2,5,6,1,4,7,3]=>{{1,3,5,8},{2},{4,6},{7}}
[8,6,5,4,1,2,7,3]=>{{1,3,5,8},{2,6},{4},{7}}
[2,6,1,8,3,7,5,4]=>{{1,2,3,5,6,7},{4,8}}
[4,7,1,6,2,8,5,3]=>{{1,3,4,6,8},{2,5,7}}
[6,1,5,3,8,7,2,4]=>{{1,2,6,7},{3,4,5,8}}
[2,8,6,3,7,1,5,4]=>{{1,2,3,4,6,8},{5,7}}
[7,6,1,5,8,2,3,4]=>{{1,3,7},{2,6},{4,5,8}}
[3,6,8,5,1,2,7,4]=>{{1,3,4,5,8},{2,6},{7}}
[6,5,2,4,8,1,7,3]=>{{1,6},{2,3,5,8},{4},{7}}
[5,1,4,8,2,6,7,3]=>{{1,2,5},{3,4,8},{6},{7}}
[4,8,2,5,1,6,7,3]=>{{1,4,5},{2,3,8},{6},{7}}
[3,4,8,5,2,6,7,1]=>{{1,3,8},{2,4,5},{6},{7}}
[4,2,1,8,5,6,7,3]=>{{1,3,4,8},{2},{5},{6},{7}}
[1,5,4,8,2,6,7,3]=>{{1},{2,5},{3,4,8},{6},{7}}
[7,2,1,5,8,6,3,4]=>{{1,3,7},{2},{4,5,8},{6}}
[2,8,4,5,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[5,4,8,3,7,6,1,2]=>{{1,5,7},{2,3,4,8},{6}}
[3,1,5,8,6,2,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[6,3,4,8,5,1,7,2]=>{{1,6},{2,3,4,8},{5},{7}}
[5,3,4,8,1,6,7,2]=>{{1,5},{2,3,4,8},{6},{7}}
[7,6,1,2,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,4,1,2,6,3]=>{{1,2,5,6,7},{3,8},{4}}
[7,5,8,4,6,1,3,2]=>{{1,2,3,5,6,7,8},{4}}
[6,5,4,8,7,1,3,2]=>{{1,6},{2,3,4,5,7,8}}
[6,5,4,8,1,2,7,3]=>{{1,2,5,6},{3,4,8},{7}}
[7,5,1,6,2,3,8,4]=>{{1,3,4,6,7,8},{2,5}}
[7,5,1,6,8,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,1,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,5,4,7,1,2,8,3]=>{{1,2,5,6},{3,4,7,8}}
[6,5,4,7,8,1,3,2]=>{{1,6},{2,5,8},{3,4,7}}
[6,5,3,7,1,4,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[6,5,3,1,8,4,2,7]=>{{1,4,6},{2,5,7,8},{3}}
[7,5,1,4,8,3,2,6]=>{{1,2,3,5,6,7,8},{4}}
[8,1,6,4,7,3,5,2]=>{{1,2,8},{3,6},{4},{5,7}}
[7,5,1,4,8,3,6,2]=>{{1,3,6,7},{2,5,8},{4}}
[6,5,3,7,1,4,8,2]=>{{1,2,4,5,6,7,8},{3}}
[6,4,3,1,5,8,7,2]=>{{1,2,4,6,8},{3},{5},{7}}
[7,4,1,5,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,1,5,4,3,7,6,2]=>{{1,2,8},{3,5},{4},{6,7}}
[8,1,5,4,3,7,2,6]=>{{1,2,6,7,8},{3,5},{4}}
[7,4,1,5,3,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[7,4,1,5,3,2,6,8]=>{{1,2,3,4,5,6,7},{8}}
[8,1,5,4,3,2,6,7]=>{{1,2,6,7,8},{3,5},{4}}
[8,1,6,4,2,5,3,7]=>{{1,2,3,5,6,7,8},{4}}
[6,5,3,1,2,7,4,8]=>{{1,4,6,7},{2,5},{3},{8}}
[6,5,3,8,1,4,2,7]=>{{1,2,4,5,6,7,8},{3}}
[7,6,8,1,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,2,5,4,3,6]=>{{1,2,4,6,8},{3,7},{5}}
[8,1,7,2,5,4,6,3]=>{{1,2,3,4,6,7,8},{5}}
[7,6,1,2,5,4,8,3]=>{{1,3,7,8},{2,4,6},{5}}
[6,5,3,8,1,4,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[6,5,3,1,2,7,8,4]=>{{1,4,6,7,8},{2,5},{3}}
[7,5,1,4,2,6,8,3]=>{{1,3,7,8},{2,5},{4},{6}}
[8,1,6,4,2,5,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[7,4,1,5,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[6,4,3,1,5,2,8,7]=>{{1,2,4,6},{3},{5},{7,8}}
[6,4,3,1,5,7,2,8]=>{{1,2,4,6,7},{3},{5},{8}}
[7,4,1,5,3,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}
[8,1,5,4,3,6,2,7]=>{{1,2,7,8},{3,5},{4},{6}}
[8,1,5,4,3,6,7,2]=>{{1,2,8},{3,5},{4},{6},{7}}
[7,4,1,5,3,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[6,4,3,1,5,7,8,2]=>{{1,2,4,6,7,8},{3},{5}}
[6,7,3,8,4,5,1,2]=>{{1,2,4,5,6,7,8},{3}}
[6,7,4,5,1,8,2,3]=>{{1,3,4,5,6,8},{2,7}}
[4,7,5,6,2,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,7,5,6,1,8,2,3]=>{{1,3,4,5,6,8},{2,7}}
[4,7,5,6,3,8,1,2]=>{{1,2,4,6,7,8},{3,5}}
[3,7,5,8,4,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[4,5,3,8,6,7,1,2]=>{{1,2,4,5,6,7,8},{3}}
[4,8,3,6,5,7,1,2]=>{{1,4,6,7},{2,8},{3},{5}}
[5,6,4,7,1,8,2,3]=>{{1,5},{2,3,4,6,7,8}}
[5,6,1,7,3,8,2,4]=>{{1,3,5},{2,4,6,7,8}}
[5,6,1,8,2,7,3,4]=>{{1,2,3,5,6,7},{4,8}}
[5,6,1,8,4,7,2,3]=>{{1,3,4,5,8},{2,6,7}}
[4,8,1,6,5,7,2,3]=>{{1,2,3,4,6,7,8},{5}}
[4,5,1,8,6,7,2,3]=>{{1,3,4,8},{2,5,6,7}}
[7,8,4,5,1,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[4,8,2,3,1,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[5,6,2,8,1,4,3,7]=>{{1,5},{2,3,4,6,7,8}}
[5,6,3,4,1,8,2,7]=>{{1,5},{2,6,7,8},{3},{4}}
[3,6,4,5,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[3,6,4,5,1,8,2,7]=>{{1,3,4,5},{2,6,7,8}}
[2,6,4,8,1,5,3,7]=>{{1,2,5,6},{3,4,7,8}}
[2,8,3,6,1,5,4,7]=>{{1,2,4,5,6,7,8},{3}}
[2,8,3,4,1,6,5,7]=>{{1,2,5,7,8},{3},{4},{6}}
[7,8,2,5,3,4,1,6]=>{{1,7},{2,3,4,5,6,8}}
[7,8,1,5,3,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[1,5,3,8,6,7,2,4]=>{{1},{2,5,6,7},{3},{4,8}}
[1,8,3,6,2,7,4,5]=>{{1},{2,5,8},{3},{4,6,7}}
[1,6,4,8,2,7,3,5]=>{{1},{2,3,4,5,6,7,8}}
[2,6,4,7,3,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[2,7,3,6,4,5,1,8]=>{{1,2,7},{3},{4,5,6},{8}}
[1,7,3,6,4,8,2,5]=>{{1},{2,7},{3},{4,5,6,8}}
[1,7,2,8,4,6,3,5]=>{{1},{2,3,7},{4,5,8},{6}}
[1,7,5,8,4,6,2,3]=>{{1},{2,7},{3,4,5,8},{6}}
[1,7,5,8,2,6,3,4]=>{{1},{2,3,5,7},{4,8},{6}}
[1,7,5,6,3,8,2,4]=>{{1},{2,7},{3,5},{4,6,8}}
[2,7,5,6,3,4,1,8]=>{{1,2,7},{3,5},{4,6},{8}}
[6,7,2,5,3,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[6,7,1,5,3,8,2,4]=>{{1,3,4,5,6,8},{2,7}}
[6,7,5,8,1,4,2,3]=>{{1,3,4,5,6,8},{2,7}}
[5,8,6,7,2,3,1,4]=>{{1,2,4,5,7,8},{3,6}}
[6,7,2,3,1,8,4,5]=>{{1,5,6,8},{2,3,4,7}}
[6,7,2,8,1,4,3,5]=>{{1,4,5,6,8},{2,3,7}}
[3,4,2,7,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}
[3,4,1,7,5,8,2,6]=>{{1,3},{2,4,7},{5},{6,8}}
[2,7,5,8,1,4,3,6]=>{{1,2,3,5,7},{4,6,8}}
[2,3,1,7,5,8,4,6]=>{{1,2,3},{4,7},{5},{6,8}}
[2,3,1,8,4,7,5,6]=>{{1,2,3},{4,5,6,7,8}}
[7,8,2,3,1,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[7,8,2,6,1,4,3,5]=>{{1,2,3,5,7,8},{4,6}}
[2,8,6,7,1,4,3,5]=>{{1,2,5,8},{3,4,6,7}}
[2,8,1,4,3,7,5,6]=>{{1,2,3,5,6,7,8},{4}}
[3,7,2,5,4,6,1,8]=>{{1,2,3,7},{4,5},{6},{8}}
[4,5,2,7,3,6,1,8]=>{{1,4,7},{2,3,5},{6},{8}}
[4,5,1,8,2,7,3,6]=>{{1,3,4,6,7,8},{2,5}}
[3,4,1,8,2,7,5,6]=>{{1,3},{2,4,5,6,7,8}}
[3,4,1,8,6,7,2,5]=>{{1,3},{2,4,5,6,7,8}}
[3,4,2,5,1,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[3,4,2,8,1,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[3,8,2,5,1,6,4,7]=>{{1,2,3,4,5,7,8},{6}}
[4,5,2,8,1,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[4,5,3,6,1,8,2,7]=>{{1,2,4,5,6,7,8},{3}}
[7,1,5,8,4,6,2,3]=>{{1,2,7},{3,4,5,8},{6}}
[8,6,7,1,4,2,5,3]=>{{1,3,4,5,7,8},{2,6}}
[8,6,3,7,5,1,2,4]=>{{1,2,4,6,7,8},{3},{5}}
[8,6,1,7,3,2,5,4]=>{{1,3,4,5,7,8},{2,6}}
[7,6,1,8,3,5,2,4]=>{{1,2,3,5,6,7},{4,8}}
[7,6,1,3,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,2,4,5,1,3]=>{{1,7},{2,4,5,6},{3,8}}
[7,6,2,8,3,5,1,4]=>{{1,7},{2,3,5,6},{4,8}}
[7,6,2,3,8,5,1,4]=>{{1,7},{2,3,4,5,6,8}}
[8,7,1,5,2,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[8,7,1,5,2,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,3,1,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[8,6,2,3,7,1,5,4]=>{{1,2,3,4,6,8},{5,7}}
[8,6,2,7,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,2,4,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,3,4,1,5,2]=>{{1,6},{2,8},{3,4,5,7}}
[8,7,2,5,1,6,3,4]=>{{1,4,5,8},{2,3,7},{6}}
[8,7,2,1,4,6,3,5]=>{{1,4,5,8},{2,3,7},{6}}
[8,4,2,1,7,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[8,5,2,7,1,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[8,5,7,2,1,4,3,6]=>{{1,2,4,5,6,8},{3,7}}
[5,8,7,3,1,4,2,6]=>{{1,5},{2,3,4,6,7,8}}
[5,8,7,3,1,4,6,2]=>{{1,5},{2,8},{3,4,6,7}}
[8,5,7,2,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,7,1,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,1,3,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[8,7,4,1,2,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,1,2,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[8,4,3,1,7,2,6,5]=>{{1,2,4,5,6,7,8},{3}}
[8,4,3,1,2,7,6,5]=>{{1,2,4,5,8},{3},{6,7}}
[8,6,1,3,7,2,5,4]=>{{1,3,4,8},{2,6},{5,7}}
[8,5,1,3,2,7,6,4]=>{{1,3,4,8},{2,5},{6,7}}
[8,5,7,4,1,6,2,3]=>{{1,2,3,5,7,8},{4},{6}}
[8,5,7,4,1,2,6,3]=>{{1,2,3,5,6,7,8},{4}}
[8,1,5,4,2,7,6,3]=>{{1,2,3,5,8},{4},{6,7}}
[8,1,6,4,7,2,5,3]=>{{1,2,3,6,8},{4},{5,7}}
[6,1,5,8,4,2,7,3]=>{{1,2,6},{3,4,5,8},{7}}
[5,8,3,6,4,1,2,7]=>{{1,4,5,6},{2,7,8},{3}}
[5,2,8,6,4,1,3,7]=>{{1,4,5,6},{2},{3,7,8}}
[8,4,7,5,1,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[8,4,7,5,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,5,1,2,3,6]=>{{1,2,4,5,6,8},{3,7}}
[8,7,3,5,1,2,6,4]=>{{1,4,5,8},{2,6,7},{3}}
[8,3,2,6,5,1,4,7]=>{{1,4,6,7,8},{2,3},{5}}
[4,8,6,3,5,1,2,7]=>{{1,3,4,6},{2,7,8},{5}}
[4,8,7,3,1,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,2,1,5,3,6]=>{{1,5,6,8},{2,4},{3,7}}
[8,3,2,7,1,5,4,6]=>{{1,5,6,8},{2,3},{4,7}}
[8,3,2,1,7,6,4,5]=>{{1,4,5,7,8},{2,3},{6}}
[8,7,3,1,4,2,6,5]=>{{1,4,5,8},{2,6,7},{3}}
[8,7,3,1,6,2,4,5]=>{{1,2,4,5,6,7,8},{3}}
[8,7,3,1,2,6,4,5]=>{{1,2,4,5,7,8},{3},{6}}
[8,7,3,1,2,4,6,5]=>{{1,2,4,5,6,7,8},{3}}
[8,3,2,1,4,7,6,5]=>{{1,4,5,8},{2,3},{6,7}}
[8,3,2,1,7,4,6,5]=>{{1,4,5,6,7,8},{2,3}}
[8,3,2,7,1,5,6,4]=>{{1,4,5,6,7,8},{2,3}}
[8,4,7,2,1,5,6,3]=>{{1,3,5,6,7,8},{2,4}}
[3,8,7,4,1,2,5,6]=>{{1,3,5,7},{2,6,8},{4}}
[8,7,2,1,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,2,1,3,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[8,7,2,1,3,4,6,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,5,4,1,2,8,7]=>{{1,3,5},{2,6},{4},{7,8}}
[3,8,5,6,7,4,1,2]=>{{1,3,5,7},{2,8},{4,6}}
[4,7,5,8,6,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,8,6,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,7,6,3,1,2]=>{{1,4,7},{2,8},{3,5,6}}
[4,6,3,2,1,5,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[6,2,1,5,3,4,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[5,8,1,3,7,6,4,2]=>{{1,3,4,5,7},{2,8},{6}}
[4,7,2,3,6,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,7,4,2,8,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,2,6,8,5,7,3,1]=>{{1,4,8},{2},{3,6,7},{5}}
[6,4,2,7,3,8,5,1]=>{{1,6,8},{2,3,4,5,7}}
[8,1,6,7,5,3,4,2]=>{{1,2,8},{3,6},{4,7},{5}}
[2,1,5,8,7,6,3,4]=>{{1,2},{3,5,7},{4,8},{6}}
[2,1,4,7,6,3,8,5]=>{{1,2},{3,4,5,6,7,8}}
[6,4,7,8,5,3,2,1]=>{{1,2,3,4,6,7,8},{5}}
[4,1,3,7,6,2,8,5]=>{{1,2,4,5,6,7,8},{3}}
[8,5,1,6,3,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[6,3,7,1,5,2,8,4]=>{{1,2,3,4,6,7,8},{5}}
[3,2,6,8,4,7,5,1]=>{{1,3,4,5,6,7,8},{2}}
[8,4,6,1,3,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,2,8,6,7,3,1,5]=>{{1,3,4,5,6,7,8},{2}}
[7,4,3,8,2,1,5,6]=>{{1,2,4,5,6,7,8},{3}}
[4,7,5,8,1,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[6,4,3,2,7,8,1,5]=>{{1,5,6,7,8},{2,4},{3}}
[4,2,5,1,6,7,8,3]=>{{1,4},{2},{3,5,6,7,8}}
[2,4,8,5,7,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,1,4,6,8,5,2]=>{{1,3},{2,5,6,7,8},{4}}
[7,8,2,5,6,1,4,3]=>{{1,4,5,6,7},{2,3,8}}
[2,4,3,8,7,5,6,1]=>{{1,2,4,8},{3},{5,6,7}}
[2,6,7,3,5,1,8,4]=>{{1,2,6},{3,4,7,8},{5}}
[7,6,8,4,2,5,3,1]=>{{1,3,7,8},{2,5,6},{4}}
[8,5,7,1,6,3,2,4]=>{{1,4,8},{2,3,5,6,7}}
[6,5,7,2,8,4,3,1]=>{{1,2,4,5,6,8},{3,7}}
[3,4,8,6,5,2,1,7]=>{{1,3,7,8},{2,4,6},{5}}
[2,7,6,1,4,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,2,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,4,3,5,1,6,8,2]=>{{1,2,4,5,7,8},{3},{6}}
[4,1,6,3,5,8,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[6,2,5,8,4,3,7,1]=>{{1,3,4,5,6,8},{2},{7}}
[8,6,7,1,5,4,3,2]=>{{1,2,4,6,8},{3,7},{5}}
[2,1,6,5,8,4,7,3]=>{{1,2},{3,4,5,6,8},{7}}
[2,1,6,8,5,4,3,7]=>{{1,2},{3,4,6,7,8},{5}}
[4,1,8,5,6,2,3,7]=>{{1,2,4,5,6},{3,7,8}}
[2,6,4,8,7,3,5,1]=>{{1,2,3,4,6,8},{5,7}}
[6,2,8,4,3,5,1,7]=>{{1,3,5,6,7,8},{2},{4}}
[4,8,2,7,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,2,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,8,1,2,6,7,4,5]=>{{1,3},{2,4,5,6,7,8}}
[5,8,4,3,2,7,1,6]=>{{1,2,5,6,7,8},{3,4}}
[7,4,8,6,3,2,5,1]=>{{1,3,5,7,8},{2,4,6}}
[5,8,4,7,2,1,3,6]=>{{1,2,5,6,8},{3,4,7}}
[2,1,8,4,3,7,5,6]=>{{1,2},{3,5,6,7,8},{4}}
[6,3,8,2,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,8,4,2,3,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[5,8,2,4,3,1,6,7]=>{{1,2,3,5,6,7,8},{4}}
[2,8,3,1,6,4,5,7]=>{{1,2,4,5,6,7,8},{3}}
[8,2,1,3,4,7,5,6]=>{{1,3,4,5,6,7,8},{2}}
[1,4,8,2,6,3,5,7]=>{{1},{2,4},{3,5,6,7,8}}
[1,2,7,3,5,4,8,6]=>{{1},{2},{3,4,6,7,8},{5}}
[1,2,3,8,4,5,7,6]=>{{1},{2},{3},{4,5,6,8},{7}}
[1,2,8,3,4,5,7,6]=>{{1},{2},{3,4,5,6,8},{7}}
[1,3,8,2,6,4,5,7]=>{{1},{2,3,4,5,6,7,8}}
[1,5,7,2,3,6,4,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,7,2,3,5,4,8,6]=>{{1},{2,3,4,6,7,8},{5}}
[1,3,8,2,4,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,2,3,8,4,6,7,5]=>{{1},{2},{3},{4,5,8},{6},{7}}
[1,8,2,3,5,4,6,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,7,8,2,3,6,4,5]=>{{1},{2,4,7},{3,5,8},{6}}
[1,6,7,8,2,3,5,4]=>{{1},{2,3,5,6,7},{4,8}}
[1,7,8,2,5,3,6,4]=>{{1},{2,3,4,6,7,8},{5}}
[1,7,8,2,4,5,3,6]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,3,6,4,5,7]=>{{1},{2},{3,4,5,6,7,8}}
[1,8,2,3,6,4,5,7]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,3,5,4,6,7]=>{{1},{2},{3,4,6,7,8},{5}}
[1,2,7,8,3,6,4,5]=>{{1},{2},{3,4,5,7,8},{6}}
[1,5,2,7,8,3,6,4]=>{{1},{2,3,4,5,6,7,8}}
[1,3,2,8,4,6,7,5]=>{{1},{2,3},{4,5,8},{6},{7}}
[1,8,2,3,4,6,7,5]=>{{1},{2,3,4,5,8},{6},{7}}
[1,7,8,2,4,3,6,5]=>{{1},{2,3,4,5,6,7,8}}
[6,7,3,1,5,2,8,4]=>{{1,2,4,6,7,8},{3},{5}}
[6,8,3,1,5,2,7,4]=>{{1,2,4,6,8},{3},{5},{7}}
[6,7,4,5,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,3,6,1,5,2,4,8]=>{{1,4,7},{2,3,6},{5},{8}}
[6,7,5,4,1,2,8,3]=>{{1,2,3,5,6,7,8},{4}}
[5,8,6,4,1,7,2,3]=>{{1,5},{2,3,6,7,8},{4}}
[5,7,6,4,1,8,2,3]=>{{1,5},{2,7},{3,6,8},{4}}
[6,4,7,5,1,2,8,3]=>{{1,2,4,5,6},{3,7,8}}
[6,2,1,7,5,3,8,4]=>{{1,3,6},{2},{4,7,8},{5}}
[6,3,8,1,5,2,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[5,6,8,4,1,7,2,3]=>{{1,5},{2,6,7},{3,8},{4}}
[4,6,8,5,7,1,2,3]=>{{1,2,4,5,6,7},{3,8}}
[4,5,8,6,7,1,2,3]=>{{1,4,6},{2,5,7},{3,8}}
[5,4,8,6,1,7,2,3]=>{{1,5},{2,4,6,7},{3,8}}
[5,3,8,1,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[5,2,1,7,6,8,3,4]=>{{1,3,4,5,6,7,8},{2}}
[5,4,7,6,1,8,2,3]=>{{1,5},{2,3,4,6,7,8}}
[4,8,6,5,7,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,6,8,1,2,3]=>{{1,4,6},{2,7},{3,5,8}}
[4,6,5,7,8,1,2,3]=>{{1,2,4,6,7},{3,5,8}}
[5,7,4,6,1,8,2,3]=>{{1,5},{2,7},{3,4,6,8}}
[5,8,4,6,1,7,2,3]=>{{1,5},{2,3,4,6,7,8}}
[5,8,3,1,6,7,2,4]=>{{1,2,4,5,6,7,8},{3}}
[5,7,3,1,6,8,2,4]=>{{1,4,5,6,8},{2,7},{3}}
[5,6,3,1,7,8,2,4]=>{{1,2,4,5,6,7,8},{3}}
[5,8,3,1,7,6,2,4]=>{{1,2,4,5,7,8},{3},{6}}
[5,7,4,8,1,6,2,3]=>{{1,5},{2,7},{3,4,8},{6}}
[5,4,6,8,1,7,2,3]=>{{1,5},{2,3,4,6,7,8}}
[4,8,6,7,5,1,2,3]=>{{1,2,3,4,6,7,8},{5}}
[5,2,1,7,8,6,3,4]=>{{1,3,4,5,7,8},{2},{6}}
[5,3,8,1,7,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[5,4,8,7,1,6,2,3]=>{{1,5},{2,4,7},{3,8},{6}}
[4,6,8,7,5,1,2,3]=>{{1,2,4,6,7},{3,8},{5}}
[4,8,7,6,5,1,2,3]=>{{1,4,6},{2,3,7,8},{5}}
[2,5,4,7,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[2,4,6,3,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,2,7,3,6,5,1,8]=>{{1,3,4,7},{2},{5,6},{8}}
[4,2,6,3,1,5,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[2,5,3,1,6,4,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[2,5,3,7,6,4,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[2,6,5,3,7,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,2,7,6,3,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[2,7,5,3,6,4,1,8]=>{{1,2,7},{3,4,5,6},{8}}
[2,6,3,7,5,4,1,8]=>{{1,2,4,6,7},{3},{5},{8}}
[1,7,5,2,3,8,4,6]=>{{1},{2,4,7},{3,5},{6,8}}
[2,1,3,7,5,4,8,6]=>{{1,2},{3},{4,6,7,8},{5}}
[2,3,1,8,6,5,4,7]=>{{1,2,3},{4,7,8},{5,6}}
[2,5,3,1,8,6,4,7]=>{{1,2,4,5,7,8},{3},{6}}
[4,2,8,3,1,6,5,7]=>{{1,3,4,5,7,8},{2},{6}}
[8,3,2,6,4,1,5,7]=>{{1,4,5,6,7,8},{2,3}}
[3,6,8,2,1,4,5,7]=>{{1,3,5,7,8},{2,4,6}}
[1,5,2,8,3,4,7,6]=>{{1},{2,3,5},{4,6,8},{7}}
[1,2,6,3,8,7,4,5]=>{{1},{2},{3,4,6,7},{5,8}}
[1,2,8,3,6,4,7,5]=>{{1},{2},{3,4,5,6,8},{7}}
[1,2,7,6,3,4,8,5]=>{{1},{2},{3,5,7,8},{4,6}}
[2,1,3,8,7,5,4,6]=>{{1,2},{3},{4,5,6,7,8}}
[1,2,3,8,6,4,7,5]=>{{1},{2},{3},{4,5,6,8},{7}}
[1,2,3,7,4,8,6,5]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,7,6,3,8,4,5]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,3,6,4,8,7,5]=>{{1},{2},{3},{4,5,6,8},{7}}
[1,2,3,7,6,4,8,5]=>{{1},{2},{3},{4,5,6,7,8}}
[2,6,3,1,8,5,4,7]=>{{1,2,4,5,6,7,8},{3}}
[2,1,3,8,5,4,7,6]=>{{1,2},{3},{4,6,8},{5},{7}}
[7,1,8,4,2,3,5,6]=>{{1,2,5,7},{3,6,8},{4}}
[2,1,8,4,3,5,7,6]=>{{1,2},{3,5,6,8},{4},{7}}
[4,2,6,3,1,8,5,7]=>{{1,3,4,5,6,7,8},{2}}
[5,4,2,8,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,8,2,4,1,6,7]=>{{1,3,6,7,8},{2,4,5}}
[2,5,4,8,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,2,1,8,3,5,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[1,8,7,4,2,3,5,6]=>{{1},{2,3,5,6,7,8},{4}}
[1,5,2,8,7,3,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,2,7,3,6,4,8,5]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,8,6,3,7,4,5]=>{{1},{2},{3,5,8},{4,6,7}}
[1,2,7,3,8,6,4,5]=>{{1},{2},{3,4,7},{5,8},{6}}
[1,2,3,8,4,7,6,5]=>{{1},{2},{3},{4,5,8},{6,7}}
[1,2,7,3,4,8,6,5]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,6,3,8,4,7,5]=>{{1},{2},{3,4,6},{5,8},{7}}
[1,5,2,3,8,7,4,6]=>{{1},{2,3,4,5,6,7,8}}
[4,2,1,8,3,7,5,6]=>{{1,3,4,5,6,7,8},{2}}
[8,3,2,1,7,4,5,6]=>{{1,4,6,8},{2,3},{5,7}}
[1,8,4,2,7,3,5,6]=>{{1},{2,3,4,6,8},{5,7}}
[1,2,8,6,3,4,7,5]=>{{1},{2},{3,5,8},{4,6},{7}}
[1,2,7,3,8,4,6,5]=>{{1},{2},{3,4,6,7},{5,8}}
[1,2,3,8,7,4,6,5]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,8,7,6,4,5]=>{{1},{2},{3},{4,5,7,8},{6}}
[2,5,3,8,1,6,4,7]=>{{1,2,5},{3},{4,7,8},{6}}
[2,6,4,7,1,5,3,8]=>{{1,2,5,6},{3,4,7},{8}}
[2,6,5,7,1,4,3,8]=>{{1,2,3,4,5,6,7},{8}}
[3,8,5,7,1,2,6,4]=>{{1,3,5},{2,4,6,7,8}}
[3,8,5,7,2,6,4,1]=>{{1,2,3,5,8},{4,7},{6}}
[3,4,8,6,2,5,7,1]=>{{1,3,8},{2,4,5,6},{7}}
[3,4,8,6,1,2,5,7]=>{{1,3,5,7,8},{2,4,6}}
[2,5,7,1,4,8,6,3]=>{{1,2,4,5},{3,6,7,8}}
[2,4,8,1,5,7,6,3]=>{{1,2,4},{3,8},{5},{6,7}}
[2,4,3,8,1,6,5,7]=>{{1,2,4,5,7,8},{3},{6}}
[2,8,1,7,5,6,4,3]=>{{1,2,3,8},{4,7},{5},{6}}
[2,3,8,1,6,5,7,4]=>{{1,2,3,4,8},{5,6},{7}}
[2,4,8,1,3,5,7,6]=>{{1,2,4},{3,5,6,8},{7}}
[3,5,7,6,1,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,7,6,2,4,8,1]=>{{1,3,7,8},{2,5},{4,6}}
[4,8,6,7,2,3,5,1]=>{{1,2,4,5,7,8},{3,6}}
[4,8,6,7,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,6,7,1,3,5,2]=>{{1,4,5,7},{2,8},{3,6}}
[3,4,8,6,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[3,8,5,7,1,6,4,2]=>{{1,3,5},{2,8},{4,7},{6}}
[3,2,8,5,6,1,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[3,8,5,7,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[3,4,8,6,2,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,6,2,1,4,8]=>{{1,3,4,6,7},{2,5},{8}}
[4,8,6,7,2,1,3,5]=>{{1,3,4,6,7},{2,5,8}}
[4,8,6,7,3,5,2,1]=>{{1,2,4,7,8},{3,5,6}}
[5,8,6,7,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,7,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,7,2,1,4,3]=>{{1,2,3,5,6,8},{4,7}}
[4,8,6,7,2,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,7,5,2,8,6]=>{{1,2,3,4,6,7,8},{5}}
[4,3,2,8,5,1,7,6]=>{{1,4,6,8},{2,3},{5},{7}}
[4,3,8,5,1,6,7,2]=>{{1,4,5},{2,3,8},{6},{7}}
[4,8,6,7,1,5,3,2]=>{{1,3,4,5,6,7},{2,8}}
[5,8,6,7,1,4,3,2]=>{{1,5},{2,8},{3,4,6,7}}
[5,8,6,7,2,3,4,1]=>{{1,2,5,8},{3,6},{4,7}}
[5,8,6,7,2,4,3,1]=>{{1,2,5,8},{3,4,6,7}}
[5,8,6,7,1,2,4,3]=>{{1,5},{2,3,6,8},{4,7}}
[4,2,3,8,5,1,6,7]=>{{1,4,6,7,8},{2},{3},{5}}
[4,2,8,5,1,7,6,3]=>{{1,4,5},{2},{3,8},{6,7}}
[3,4,2,8,5,6,1,7]=>{{1,2,3,4,7,8},{5},{6}}
[3,2,4,8,6,1,5,7]=>{{1,3,4,5,6,7,8},{2}}
[3,2,5,7,6,1,4,8]=>{{1,3,5,6},{2},{4,7},{8}}
[4,8,6,7,1,3,2,5]=>{{1,2,4,5,7,8},{3,6}}
[4,8,6,7,1,2,5,3]=>{{1,4,5,7},{2,3,6,8}}
[4,8,6,7,2,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,5,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[4,3,8,5,1,2,6,7]=>{{1,4,5},{2,3,6,7,8}}
[4,2,6,7,5,1,3,8]=>{{1,3,4,6,7},{2},{5},{8}}
[3,8,5,7,1,4,2,6]=>{{1,3,5},{2,4,6,7,8}}
[3,8,4,7,1,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,8,4,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[3,5,1,7,4,6,2,8]=>{{1,3},{2,4,5,7},{6},{8}}
[3,8,4,7,2,5,1,6]=>{{1,3,4,7},{2,5,6,8}}
[4,1,3,8,5,2,6,7]=>{{1,2,4,6,7,8},{3},{5}}
[4,1,2,6,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,2,6,7,5,3,8,1]=>{{1,4,7,8},{2},{3,6},{5}}
[4,8,6,7,3,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,8,6,7,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,5,7,6,2,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[3,4,1,7,5,6,2,8]=>{{1,3},{2,4,7},{5},{6},{8}}
[4,1,7,5,2,8,6,3]=>{{1,2,4,5},{3,6,7,8}}
[4,1,6,7,5,2,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[4,8,6,7,2,3,1,5]=>{{1,4,7},{2,5,8},{3,6}}
[5,8,6,7,3,2,4,1]=>{{1,2,3,5,6,8},{4,7}}
[5,8,6,7,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,7,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,7,4,1,3,2]=>{{1,3,4,5,6,7},{2,8}}
[5,8,6,7,3,1,4,2]=>{{1,3,5,6},{2,8},{4,7}}
[4,8,6,7,3,1,5,2]=>{{1,3,4,5,6,7},{2,8}}
[4,1,6,7,5,3,8,2]=>{{1,2,4,7,8},{3,6},{5}}
[4,1,7,5,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,2,8,5,3,1,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[4,2,1,6,7,5,3,8]=>{{1,3,4,5,6,7},{2},{8}}
[4,8,6,7,3,2,1,5]=>{{1,4,7},{2,3,5,6,8}}
[5,8,6,7,4,2,1,3]=>{{1,4,5,7},{2,3,6,8}}
[5,8,6,7,4,3,1,2]=>{{1,4,5,7},{2,8},{3,6}}
[7,3,5,8,1,4,2,6]=>{{1,2,3,5,7},{4,6,8}}
[3,8,7,6,1,4,2,5]=>{{1,2,3,5,7,8},{4,6}}
[5,1,8,3,6,7,2,4]=>{{1,2,5,6,7},{3,4,8}}
[1,4,7,8,5,6,2,3]=>{{1},{2,3,4,7,8},{5},{6}}
[3,4,7,1,5,8,6,2]=>{{1,2,3,4,6,7,8},{5}}
[3,6,1,4,7,8,5,2]=>{{1,3},{2,6,8},{4},{5,7}}
[1,6,8,4,7,5,2,3]=>{{1},{2,5,6,7},{3,8},{4}}
[6,8,1,3,5,7,2,4]=>{{1,2,3,4,6,7,8},{5}}
[7,6,1,4,3,8,2,5]=>{{1,2,3,5,6,7,8},{4}}
[3,8,1,6,5,4,2,7]=>{{1,3},{2,7,8},{4,6},{5}}
[4,1,3,7,5,8,2,6]=>{{1,2,4,7},{3},{5},{6,8}}
[6,1,7,3,8,4,2,5]=>{{1,2,3,4,6,7},{5,8}}
[7,1,8,6,3,5,2,4]=>{{1,2,7},{3,4,5,6,8}}
[3,1,7,6,5,8,4,2]=>{{1,2,3,4,6,7,8},{5}}
[8,2,7,6,5,3,4,1]=>{{1,8},{2},{3,4,6,7},{5}}
[8,4,2,6,7,5,3,1]=>{{1,8},{2,3,4,5,6,7}}
[4,8,1,6,7,5,3,2]=>{{1,3,4,5,6,7},{2,8}}
[7,4,1,6,8,2,5,3]=>{{1,3,5,7,8},{2,4,6}}
[1,3,8,6,2,7,5,4]=>{{1},{2,3,4,5,6,7,8}}
[6,1,3,2,7,8,4,5]=>{{1,2,4,5,6,7,8},{3}}
[1,8,6,2,5,3,4,7]=>{{1},{2,4,7,8},{3,6},{5}}
[4,7,2,6,8,1,5,3]=>{{1,4,6},{2,3,5,7,8}}
[8,7,3,6,4,5,2,1]=>{{1,8},{2,7},{3},{4,5,6}}
[5,7,8,6,2,1,4,3]=>{{1,2,4,5,6,7},{3,8}}
[2,7,4,1,6,8,3,5]=>{{1,2,3,4,7},{5,6,8}}
[3,7,2,4,5,1,6,8]=>{{1,2,3,6,7},{4},{5},{8}}
[1,8,6,4,5,2,3,7]=>{{1},{2,3,6,7,8},{4},{5}}
[2,8,4,6,5,1,3,7]=>{{1,2,3,4,6,7,8},{5}}
[3,4,1,7,5,2,6,8]=>{{1,3},{2,4,6,7},{5},{8}}
[7,5,8,6,1,2,4,3]=>{{1,2,4,5,6,7},{3,8}}
[5,6,8,7,3,1,4,2]=>{{1,2,3,5,6,8},{4,7}}
[2,5,4,3,6,8,1,7]=>{{1,2,5,6,7,8},{3,4}}
[3,8,5,4,6,2,1,7]=>{{1,2,3,5,6,7,8},{4}}
[4,8,2,1,3,7,5,6]=>{{1,4},{2,3,5,6,7,8}}
[6,4,1,2,7,5,8,3]=>{{1,3,5,6,7,8},{2,4}}
[4,1,8,3,6,7,5,2]=>{{1,2,3,4,8},{5,6,7}}
[8,3,7,4,5,2,6,1]=>{{1,8},{2,3,6,7},{4},{5}}
[4,3,7,8,5,1,6,2]=>{{1,2,3,4,6,7,8},{5}}
[5,4,8,2,7,6,1,3]=>{{1,5,7},{2,4},{3,8},{6}}
[1,2,7,3,6,5,8,4]=>{{1},{2},{3,4,7,8},{5,6}}
[2,8,7,6,3,4,1,5]=>{{1,2,3,5,7,8},{4,6}}
[5,8,2,6,3,4,1,7]=>{{1,2,3,5,7,8},{4,6}}
[4,1,7,5,8,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[5,1,7,8,4,3,6,2]=>{{1,2,4,5,8},{3,6,7}}
[8,2,7,5,4,3,6,1]=>{{1,8},{2},{3,6,7},{4,5}}
[6,3,8,1,4,7,5,2]=>{{1,4,5,6,7},{2,3,8}}
[3,8,4,5,6,1,2,7]=>{{1,3,4,5,6},{2,7,8}}
[1,4,3,5,7,8,2,6]=>{{1},{2,4,5,7},{3},{6,8}}
[6,5,8,7,1,3,4,2]=>{{1,2,3,5,6,8},{4,7}}
[3,6,7,2,4,8,1,5]=>{{1,3,7},{2,4,5,6,8}}
[1,5,2,7,4,3,8,6]=>{{1},{2,3,4,5,6,7,8}}
[2,8,5,6,4,3,1,7]=>{{1,2,7,8},{3,4,5,6}}
[1,8,6,5,4,3,2,7]=>{{1},{2,7,8},{3,6},{4,5}}
[6,1,5,2,8,4,7,3]=>{{1,2,4,6},{3,5,8},{7}}
[4,6,1,8,5,7,2,3]=>{{1,3,4,8},{2,6,7},{5}}
[4,7,1,2,8,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[1,4,7,2,8,5,6,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,7,3,5,8,6,2,4]=>{{1},{2,7},{3},{4,5,8},{6}}
[7,3,5,8,6,1,2,4]=>{{1,2,3,5,6,7},{4,8}}
[3,6,8,1,5,7,2,4]=>{{1,3,4,8},{2,6,7},{5}}
[3,4,6,5,8,1,7,2]=>{{1,3,6},{2,4,5,8},{7}}
[6,8,1,5,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,2,5,8,6,3,4]=>{{1,2,3,7},{4,5,8},{6}}
[1,7,2,5,8,6,3,4]=>{{1},{2,3,7},{4,5,8},{6}}
[1,7,6,8,2,3,5,4]=>{{1},{2,5,7},{3,6},{4,8}}
[7,6,8,1,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[2,7,1,5,8,6,3,4]=>{{1,2,3,7},{4,5,8},{6}}
[2,4,7,1,8,5,6,3]=>{{1,2,4},{3,5,6,7,8}}
[4,7,5,8,3,1,6,2]=>{{1,2,4,6,7,8},{3,5}}
[4,7,2,1,8,5,6,3]=>{{1,4},{2,3,5,6,7,8}}
[7,6,8,2,1,3,5,4]=>{{1,5,7},{2,3,4,6,8}}
[1,2,7,6,8,3,5,4]=>{{1},{2},{3,4,5,6,7,8}}
[3,7,6,8,2,1,5,4]=>{{1,3,6},{2,5,7},{4,8}}
[7,4,2,1,6,8,5,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,1,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,3,1,8,5,2]=>{{1,2,5,6,7,8},{3,4}}
[2,7,4,1,6,8,5,3]=>{{1,2,3,4,5,6,7,8}}
[2,3,7,6,8,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,6,8,5,1,3]=>{{1,7},{2,3,4,5,6,8}}
[7,3,2,5,8,6,1,4]=>{{1,7},{2,3},{4,5,8},{6}}
[3,1,7,6,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,8,1,2,5,4]=>{{1,2,3,5,6,7},{4,8}}
[1,3,7,6,8,2,5,4]=>{{1},{2,3,4,5,6,7,8}}
[1,7,4,2,6,8,5,3]=>{{1},{2,3,4,5,6,7,8}}
[7,4,1,2,6,8,5,3]=>{{1,3,5,6,7,8},{2,4}}
[7,1,4,2,8,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,2,5,4,6,3]=>{{1,2,4,6,7},{3,8},{5}}
[7,3,8,4,6,1,5,2]=>{{1,5,6,7},{2,3,8},{4}}
[7,2,8,1,6,4,5,3]=>{{1,4,5,6,7},{2},{3,8}}
[7,1,6,8,5,4,2,3]=>{{1,2,7},{3,4,6,8},{5}}
[7,1,2,6,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[1,7,2,6,8,5,4,3]=>{{1},{2,3,4,5,6,7,8}}
[1,7,6,8,3,2,5,4]=>{{1},{2,3,5,6,7},{4,8}}
[7,6,8,3,1,2,5,4]=>{{1,5,7},{2,6},{3,4,8}}
[7,1,5,8,6,3,2,4]=>{{1,2,7},{3,5,6},{4,8}}
[7,2,5,8,6,3,1,4]=>{{1,7},{2},{3,5,6},{4,8}}
[3,6,7,1,8,5,4,2]=>{{1,3,4,7},{2,5,6,8}}
[7,2,6,8,5,4,1,3]=>{{1,7},{2},{3,4,6,8},{5}}
[7,6,8,2,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,8,3,1,5,4]=>{{1,2,3,5,6,7},{4,8}}
[2,7,1,6,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,3,1,8,5,4,2]=>{{1,2,4,5,6,7,8},{3}}
[6,7,1,8,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}
[7,2,1,6,8,5,4,3]=>{{1,3,4,5,6,7,8},{2}}
[7,6,8,3,2,1,5,4]=>{{1,2,5,6,7},{3,4,8}}
[4,7,8,5,6,1,3,2]=>{{1,4,5,6},{2,3,7,8}}
[4,6,5,8,7,1,3,2]=>{{1,2,4,6,8},{3,5,7}}
[5,6,4,8,1,2,7,3]=>{{1,5},{2,6},{3,4,8},{7}}
[8,1,5,6,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,4,5,1,8,2,7,3]=>{{1,2,4,6},{3,5,8},{7}}
[5,4,6,7,1,2,8,3]=>{{1,5},{2,3,4,6,7,8}}
[4,3,6,7,2,1,5,8]=>{{1,2,3,4,5,6,7},{8}}
[5,3,6,7,1,4,2,8]=>{{1,5},{2,3,4,6,7},{8}}
[8,1,4,6,7,3,2,5]=>{{1,2,5,7,8},{3,4,6}}
[8,1,3,6,7,4,5,2]=>{{1,2,8},{3},{4,6},{5,7}}
[7,2,1,6,8,4,5,3]=>{{1,3,5,7,8},{2},{4,6}}
[5,2,6,7,1,4,8,3]=>{{1,5},{2},{3,4,6,7,8}}
[4,2,6,7,3,1,8,5]=>{{1,3,4,5,6,7,8},{2}}
[6,2,4,1,5,8,7,3]=>{{1,3,4,6,8},{2},{5},{7}}
[7,2,1,5,4,8,6,3]=>{{1,3,6,7,8},{2},{4,5}}
[8,1,4,5,3,7,2,6]=>{{1,2,6,7,8},{3,4,5}}
[7,3,1,5,4,8,2,6]=>{{1,2,3,7},{4,5},{6,8}}
[6,3,4,1,5,8,2,7]=>{{1,2,3,4,6,7,8},{5}}
[5,3,4,2,1,8,6,7]=>{{1,5},{2,3,4},{6,7,8}}
[4,3,5,2,7,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,3,8,1,4,2,7]=>{{1,5},{2,4,6,7,8},{3}}
[8,1,7,2,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[7,6,1,2,4,5,8,3]=>{{1,3,7,8},{2,4,5,6}}
[4,7,8,2,3,1,6,5]=>{{1,2,4,6,7},{3,5,8}}
[5,6,2,8,1,4,7,3]=>{{1,5},{2,3,4,6,8},{7}}
[6,5,2,1,3,7,8,4]=>{{1,4,6,7,8},{2,3,5}}
[7,5,1,3,2,6,8,4]=>{{1,3,4,7,8},{2,5},{6}}
[8,1,6,3,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[7,4,1,3,5,2,8,6]=>{{1,2,3,4,6,7,8},{5}}
[5,4,2,3,1,6,8,7]=>{{1,5},{2,3,4},{6},{7,8}}
[7,3,1,4,5,6,2,8]=>{{1,2,3,7},{4},{5},{6},{8}}
[8,1,4,3,5,6,2,7]=>{{1,2,7,8},{3,4},{5},{6}}
[6,2,3,1,5,7,8,4]=>{{1,4,6,7,8},{2},{3},{5}}
[7,8,4,2,1,6,5,3]=>{{1,5,7},{2,3,4,8},{6}}
[7,8,4,2,1,5,6,3]=>{{1,5,6,7},{2,3,4,8}}
[6,2,3,4,8,7,1,5]=>{{1,6,7},{2},{3},{4},{5,8}}
[6,2,3,4,7,8,1,5]=>{{1,5,6,7,8},{2},{3},{4}}
[7,8,3,4,6,2,1,5]=>{{1,7},{2,5,6,8},{3},{4}}
[7,8,3,6,4,2,1,5]=>{{1,7},{2,4,5,6,8},{3}}
[7,8,3,5,6,2,1,4]=>{{1,7},{2,4,5,6,8},{3}}
[6,2,3,8,7,5,1,4]=>{{1,5,6,7},{2},{3},{4,8}}
[6,2,3,7,8,5,1,4]=>{{1,4,5,6,7,8},{2},{3}}
[5,2,6,3,8,1,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[6,3,2,5,8,7,1,4]=>{{1,6,7},{2,3},{4,5,8}}
[6,3,2,8,4,7,1,5]=>{{1,6,7},{2,3},{4,5,8}}
[6,4,3,8,7,5,1,2]=>{{1,5,6,7},{2,4,8},{3}}
[6,4,3,7,8,5,1,2]=>{{1,2,4,5,6,7,8},{3}}
[6,2,4,1,7,3,5,8]=>{{1,3,4,6},{2},{5,7},{8}}
[6,3,2,7,4,8,1,5]=>{{1,4,5,6,7,8},{2,3}}
[6,3,2,5,7,8,1,4]=>{{1,4,5,6,7,8},{2,3}}
[5,7,2,3,6,1,8,4]=>{{1,5,6},{2,3,4,7,8}}
[5,8,2,3,6,1,7,4]=>{{1,5,6},{2,3,4,8},{7}}
[4,7,5,8,3,2,1,6]=>{{1,2,4,6,7,8},{3,5}}
[4,5,6,8,3,2,1,7]=>{{1,4,7,8},{2,3,5,6}}
[4,6,8,5,3,2,1,7]=>{{1,3,4,5,7,8},{2,6}}
[5,6,1,4,2,3,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[5,6,8,4,3,7,1,2]=>{{1,2,3,5,6,7,8},{4}}
[5,6,1,4,2,3,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[5,2,8,3,4,1,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[4,5,8,6,3,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,8,3,2,1,7]=>{{1,4,7,8},{2,6},{3,5}}
[4,7,5,6,3,2,1,8]=>{{1,2,4,6,7},{3,5},{8}}
[6,2,3,4,5,8,1,7]=>{{1,6,7,8},{2},{3},{4},{5}}
[5,1,4,3,6,2,8,7]=>{{1,2,5,6},{3,4},{7,8}}
[5,1,4,3,7,2,8,6]=>{{1,2,5,6,7,8},{3,4}}
[5,1,4,3,8,2,7,6]=>{{1,2,5,6,8},{3,4},{7}}
[5,6,2,4,1,7,8,3]=>{{1,5},{2,3,6,7,8},{4}}
[5,6,2,4,1,8,7,3]=>{{1,5},{2,3,6,8},{4},{7}}
[5,7,2,4,1,8,6,3]=>{{1,5},{2,3,6,7,8},{4}}
[6,1,4,2,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[6,1,4,2,7,8,5,3]=>{{1,2,3,4,6,8},{5,7}}
[5,8,2,4,1,7,6,3]=>{{1,5},{2,3,8},{4},{6,7}}
[5,2,7,4,1,6,8,3]=>{{1,5},{2},{3,7,8},{4},{6}}
[5,4,1,3,7,2,6,8]=>{{1,2,3,4,5,6,7},{8}}
[5,1,4,3,6,2,7,8]=>{{1,2,5,6},{3,4},{7},{8}}
[5,8,6,4,3,7,1,2]=>{{1,3,5,6,7},{2,8},{4}}
[5,8,1,4,2,3,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[5,1,6,3,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[4,8,6,5,3,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,6,3,2,1,7]=>{{1,2,4,6,7,8},{3,5}}
[5,4,7,8,3,2,1,6]=>{{1,3,5,7},{2,4,6,8}}
[5,4,8,7,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[4,6,8,7,3,2,1,5]=>{{1,4,7},{2,6},{3,5,8}}
[4,6,7,8,3,2,1,5]=>{{1,3,4,5,7,8},{2,6}}
[4,7,6,8,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,5,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,7,1,3,4,2,6,8]=>{{1,3,4,5},{2,6,7},{8}}
[5,1,8,4,2,3,6,7]=>{{1,2,5},{3,6,7,8},{4}}
[5,1,7,4,2,3,6,8]=>{{1,2,5},{3,6,7},{4},{8}}
[5,8,1,3,4,2,6,7]=>{{1,3,4,5},{2,6,7,8}}
[4,8,7,5,3,2,1,6]=>{{1,3,4,5,7},{2,6,8}}
[4,7,8,6,3,2,1,5]=>{{1,2,4,6,7},{3,5,8}}
[4,8,7,6,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,2,6,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,1,6,2,5,7]=>{{1,4},{2,3,5,6,7,8}}
[4,3,8,7,2,5,1,6]=>{{1,4,7},{2,3,5,6,8}}
[5,8,4,3,7,1,6,2]=>{{1,5,6,7},{2,8},{3,4}}
[6,8,1,2,4,3,5,7]=>{{1,3,6},{2,4,5,7,8}}
[5,8,7,1,3,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,6,3,1,2,5]=>{{1,4,6},{2,3,5,7,8}}
[4,3,8,2,7,5,6,1]=>{{1,2,3,4,8},{5,6,7}}
[1,4,3,8,2,6,5,7]=>{{1},{2,4,5,7,8},{3},{6}}
[4,3,2,8,1,6,5,7]=>{{1,4,5,7,8},{2,3},{6}}
[4,1,3,8,2,6,5,7]=>{{1,2,4,5,7,8},{3},{6}}
[4,1,8,3,7,5,6,2]=>{{1,2,3,4,8},{5,6,7}}
[3,7,8,1,5,4,2,6]=>{{1,3,4,6,8},{2,7},{5}}
[7,3,8,1,5,4,6,2]=>{{1,4,6,7},{2,3,8},{5}}
[3,4,8,1,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,4,2,1,8,6,5,7]=>{{1,2,3,4},{5,7,8},{6}}
[3,6,7,8,4,1,2,5]=>{{1,2,3,6,7},{4,5,8}}
[4,1,7,8,5,3,2,6]=>{{1,2,3,4,6,7,8},{5}}
[3,7,6,8,4,2,1,5]=>{{1,2,3,6,7},{4,5,8}}
[3,7,8,2,6,4,5,1]=>{{1,3,8},{2,4,5,6,7}}
[4,2,3,8,1,6,5,7]=>{{1,4,5,7,8},{2},{3},{6}}
[4,3,1,8,2,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[4,3,7,8,5,2,1,6]=>{{1,2,3,4,6,7,8},{5}}
[2,6,8,4,7,3,1,5]=>{{1,2,3,5,6,7,8},{4}}
[7,3,6,8,4,2,1,5]=>{{1,7},{2,3,6},{4,5,8}}
[7,6,2,8,3,5,4,1]=>{{1,4,7,8},{2,3,5,6}}
[3,2,4,8,1,6,5,7]=>{{1,3,4,5,7,8},{2},{6}}
[2,4,8,3,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,8,5,2,6,3]=>{{1,2,3,4,6,7,8},{5}}
[1,3,2,4,8,6,5,7]=>{{1},{2,3},{4},{5,7,8},{6}}
[3,1,2,4,8,6,5,7]=>{{1,2,3},{4},{5,7,8},{6}}
[3,1,4,8,2,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[3,7,4,8,5,1,2,6]=>{{1,3,4,6,8},{2,7},{5}}
[6,7,2,8,3,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,1,3,4,8,6,5,7]=>{{1,2},{3},{4},{5,7,8},{6}}
[1,2,3,4,8,6,5,7]=>{{1},{2},{3},{4},{5,7,8},{6}}
[4,8,3,6,2,1,5,7]=>{{1,4,6},{2,5,7,8},{3}}
[3,5,8,2,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,6,5,8,2,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,7,2,4,6,1]=>{{1,2,3,5,8},{4,6,7}}
[2,8,4,5,7,3,6,1]=>{{1,2,8},{3,4,5,6,7}}
[2,4,5,7,3,8,1,6]=>{{1,2,4,7},{3,5},{6,8}}
[6,2,4,5,8,3,1,7]=>{{1,3,4,5,6,7,8},{2}}
[4,8,1,2,5,6,3,7]=>{{1,2,3,4,7,8},{5},{6}}
[8,1,3,5,2,6,4,7]=>{{1,2,4,5,7,8},{3},{6}}
[5,2,1,6,3,8,4,7]=>{{1,3,5},{2},{4,6,7,8}}
[6,2,5,1,8,4,3,7]=>{{1,4,6},{2},{3,5,7,8}}
[3,6,1,5,8,4,2,7]=>{{1,3},{2,4,5,6,7,8}}
[6,1,4,5,8,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,4,8,1,3,2,7]=>{{1,5},{2,3,4,6,7,8}}
[6,5,4,3,8,2,1,7]=>{{1,2,5,6,7,8},{3,4}}
[5,4,3,7,2,8,1,6]=>{{1,2,4,5,7},{3},{6,8}}
[5,8,4,3,7,2,6,1]=>{{1,2,5,6,7,8},{3,4}}
[4,6,8,3,7,2,5,1]=>{{1,3,4,8},{2,6},{5,7}}
[7,4,6,3,2,8,1,5]=>{{1,7},{2,3,4,5,6,8}}
[1,4,3,6,2,7,8,5]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,4,3,7,2,8,6]=>{{1},{2,5,6,7,8},{3,4}}
[4,7,8,5,3,1,2,6]=>{{1,3,4,5,6,8},{2,7}}
[5,7,3,4,1,2,8,6]=>{{1,5},{2,6,7,8},{3},{4}}
[8,5,4,7,6,2,1,3]=>{{1,3,4,7,8},{2,5,6}}
[8,5,7,4,3,6,1,2]=>{{1,2,3,5,7,8},{4},{6}}
[4,3,8,1,6,7,5,2]=>{{1,4},{2,3,8},{5,6,7}}
[4,7,8,3,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,6,7,4,1,2]=>{{1,5,7},{2,3,8},{4,6}}
[1,3,8,6,4,7,5,2]=>{{1},{2,3,8},{4,5,6,7}}
[8,6,2,7,4,1,5,3]=>{{1,2,3,6,8},{4,5,7}}
[7,6,2,1,4,3,8,5]=>{{1,4,5,7,8},{2,3,6}}
[7,6,1,3,4,2,8,5]=>{{1,3,4,5,7,8},{2,6}}
[1,5,7,3,2,6,8,4]=>{{1},{2,5},{3,4,7,8},{6}}
[1,6,7,3,2,5,8,4]=>{{1},{2,5,6},{3,4,7,8}}
[3,2,6,8,5,7,4,1]=>{{1,3,4,6,7,8},{2},{5}}
[5,8,2,3,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[7,5,2,3,1,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[1,6,4,7,2,3,8,5]=>{{1},{2,3,4,5,6,7,8}}
[3,1,7,5,2,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[2,5,7,4,1,8,3,6]=>{{1,2,5},{3,7},{4},{6,8}}
[4,2,6,1,7,8,3,5]=>{{1,4},{2},{3,5,6,7,8}}
[4,2,7,6,3,8,1,5]=>{{1,3,4,5,6,7,8},{2}}
[6,4,8,7,2,3,5,1]=>{{1,3,6,8},{2,4,5,7}}
[3,2,6,8,7,4,5,1]=>{{1,3,4,6,8},{2},{5,7}}
[3,2,7,4,1,6,8,5]=>{{1,3,5,7,8},{2},{4},{6}}
[6,3,2,1,7,8,4,5]=>{{1,4,5,6,7,8},{2,3}}
[3,7,1,8,4,2,5,6]=>{{1,3},{2,4,5,6,7,8}}
[4,2,1,3,7,5,8,6]=>{{1,3,4},{2},{5,6,7,8}}
[8,1,3,7,4,2,6,5]=>{{1,2,4,5,6,7,8},{3}}
[8,4,3,7,6,2,1,5]=>{{1,2,4,5,6,7,8},{3}}
[8,3,5,2,7,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[3,6,2,8,7,1,5,4]=>{{1,2,3,6},{4,8},{5,7}}
[7,3,2,8,1,6,5,4]=>{{1,5,7},{2,3},{4,8},{6}}
[3,8,7,2,6,5,4,1]=>{{1,2,3,4,7,8},{5,6}}
[4,2,7,8,6,1,5,3]=>{{1,3,4,5,6,7,8},{2}}
[6,8,2,4,7,1,5,3]=>{{1,6},{2,3,8},{4},{5,7}}
[5,2,1,8,7,3,6,4]=>{{1,3,5,6,7},{2},{4,8}}
[8,2,1,6,3,7,5,4]=>{{1,3,4,5,6,7,8},{2}}
[6,8,3,1,7,5,2,4]=>{{1,2,4,5,6,7,8},{3}}
[5,8,1,6,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,2,8,1,5,7,4,3]=>{{1,4,6,7},{2},{3,8},{5}}
[5,7,8,2,6,1,4,3]=>{{1,5,6},{2,4,7},{3,8}}
[8,7,2,5,6,4,3,1]=>{{1,8},{2,3,7},{4,5,6}}
[8,6,7,5,2,4,3,1]=>{{1,8},{2,4,5,6},{3,7}}
[7,2,6,8,1,5,4,3]=>{{1,3,4,5,6,7,8},{2}}
[1,2,7,8,5,6,4,3]=>{{1},{2},{3,4,7,8},{5},{6}}
[7,4,8,1,6,2,5,3]=>{{1,2,4,5,6,7},{3,8}}
[3,7,1,8,2,6,5,4]=>{{1,3},{2,5,7},{4,8},{6}}
[2,1,7,3,8,6,5,4]=>{{1,2},{3,4,5,7,8},{6}}
[8,2,1,7,6,5,4,3]=>{{1,3,8},{2},{4,7},{5,6}}
[8,1,4,7,6,5,3,2]=>{{1,2,8},{3,4,7},{5,6}}
[8,6,7,5,1,4,3,2]=>{{1,2,4,5,6,8},{3,7}}
[7,8,6,5,4,1,3,2]=>{{1,3,6,7},{2,8},{4,5}}
[5,8,4,3,2,1,6,7]=>{{1,2,5,6,7,8},{3,4}}
[6,4,7,3,2,1,8,5]=>{{1,6},{2,3,4,5,7,8}}
[5,4,7,3,2,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[6,5,3,7,2,1,4,8]=>{{1,6},{2,5},{3},{4,7},{8}}
[5,8,3,6,2,1,4,7]=>{{1,2,4,5,6,7,8},{3}}
[6,3,7,8,2,1,4,5]=>{{1,6},{2,3,4,5,7,8}}
[5,3,7,6,2,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[3,8,7,6,2,1,4,5]=>{{1,3,4,6,7},{2,5,8}}
[5,8,4,2,6,1,3,7]=>{{1,5,6},{2,3,4,7,8}}
[4,8,7,2,5,1,3,6]=>{{1,2,4,6,8},{3,7},{5}}
[5,8,3,2,6,1,4,7]=>{{1,5,6},{2,4,7,8},{3}}
[4,8,3,2,5,1,7,6]=>{{1,2,4,6,8},{3},{5},{7}}
[4,3,7,2,5,1,8,6]=>{{1,2,3,4,6,7,8},{5}}
[3,8,7,2,5,1,4,6]=>{{1,2,3,4,6,7,8},{5}}
[6,4,2,7,5,1,3,8]=>{{1,6},{2,3,4,7},{5},{8}}
[6,3,2,7,5,1,4,8]=>{{1,6},{2,3},{4,7},{5},{8}}
[5,3,2,6,7,1,4,8]=>{{1,4,5,6,7},{2,3},{8}}
[3,8,2,6,5,1,4,7]=>{{1,2,3,4,6,7,8},{5}}
[6,2,7,8,5,1,3,4]=>{{1,6},{2},{3,7},{4,8},{5}}
[5,2,7,6,8,1,3,4]=>{{1,4,5,6,8},{2},{3,7}}
[4,2,7,6,5,1,3,8]=>{{1,4,6},{2},{3,7},{5},{8}}
[2,8,7,6,5,1,3,4]=>{{1,2,4,6,8},{3,7},{5}}
[6,5,4,3,1,7,8,2]=>{{1,2,5,6,7,8},{3,4}}
[6,4,7,3,1,5,8,2]=>{{1,5,6},{2,3,4,7,8}}
[5,4,7,3,1,8,6,2]=>{{1,5},{2,3,4,6,7,8}}
[6,4,3,7,1,5,8,2]=>{{1,5,6},{2,4,7,8},{3}}
[5,4,3,6,1,8,7,2]=>{{1,5},{2,4,6,8},{3},{7}}
[6,3,7,8,1,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,6,1,4,8,2]=>{{1,5},{2,3,7,8},{4,6}}
[4,3,7,6,1,5,8,2]=>{{1,4,5,6},{2,3,7,8}}
[3,8,7,6,1,4,5,2]=>{{1,3,5,7},{2,8},{4,6}}
[6,5,4,2,1,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[6,4,7,2,1,5,3,8]=>{{1,5,6},{2,4},{3,7},{8}}
[4,8,7,2,1,5,3,6]=>{{1,2,4,5,6,8},{3,7}}
[5,8,3,2,1,4,7,6]=>{{1,5},{2,4,6,8},{3},{7}}
[4,8,3,2,1,5,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[5,3,7,2,1,4,8,6]=>{{1,5},{2,3,4,6,7,8}}
[3,8,7,2,1,4,5,6]=>{{1,3,5,7},{2,4,6,8}}
[6,5,2,7,1,4,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,8,2,6,1,4,3,7]=>{{1,5},{2,3,7,8},{4,6}}
[6,4,2,7,1,5,3,8]=>{{1,5,6},{2,3,4,7},{8}}
[5,4,2,6,1,8,3,7]=>{{1,5},{2,3,4,6,7,8}}
[4,3,2,6,1,5,8,7]=>{{1,4,5,6},{2,3},{7,8}}
[6,2,7,8,1,4,3,5]=>{{1,4,5,6,8},{2},{3,7}}
[4,2,7,6,1,5,3,8]=>{{1,4,5,6},{2},{3,7},{8}}
[3,2,7,6,1,4,5,8]=>{{1,3,5,7},{2},{4,6},{8}}
[6,5,4,1,8,7,3,2]=>{{1,3,4,6,7},{2,5,8}}
[5,8,4,1,6,7,3,2]=>{{1,3,4,5,6,7},{2,8}}
[6,4,7,1,5,8,3,2]=>{{1,2,4,6,8},{3,7},{5}}
[5,4,7,1,6,8,3,2]=>{{1,2,4,5,6,8},{3,7}}
[4,8,7,1,5,6,3,2]=>{{1,4},{2,8},{3,7},{5},{6}}
[5,4,3,1,6,8,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[4,8,3,1,5,6,7,2]=>{{1,4},{2,8},{3},{5},{6},{7}}
[3,8,7,1,5,4,6,2]=>{{1,3,4,6,7},{2,8},{5}}
[5,8,2,1,6,4,3,7]=>{{1,4,5,6},{2,3,7,8}}
[6,3,2,1,5,4,8,7]=>{{1,4,6},{2,3},{5},{7,8}}
[5,3,2,1,6,4,8,7]=>{{1,4,5,6},{2,3},{7,8}}
[3,8,2,1,5,4,6,7]=>{{1,2,3,4,6,7,8},{5}}
[6,2,7,1,5,4,3,8]=>{{1,4,6},{2},{3,7},{5},{8}}
[5,2,7,1,6,4,3,8]=>{{1,4,5,6},{2},{3,7},{8}}
[4,2,7,1,5,6,3,8]=>{{1,4},{2},{3,7},{5},{6},{8}}
[3,2,7,1,5,4,6,8]=>{{1,3,4,6,7},{2},{5},{8}}
[2,8,7,1,5,4,3,6]=>{{1,2,4,6,8},{3,7},{5}}
[6,5,1,7,8,4,3,2]=>{{1,3,4,6,7},{2,5,8}}
[5,8,1,6,7,4,3,2]=>{{1,3,5,7},{2,8},{4,6}}
[6,4,1,7,5,8,3,2]=>{{1,2,3,4,6,7,8},{5}}
[5,4,1,6,7,8,3,2]=>{{1,3,5,7},{2,4,6,8}}
[4,8,1,6,5,7,3,2]=>{{1,3,4,6,7},{2,8},{5}}
[6,3,1,7,5,4,8,2]=>{{1,2,3,4,6,7,8},{5}}
[5,3,1,6,7,4,8,2]=>{{1,2,3,5,7,8},{4,6}}
[4,3,1,6,5,7,8,2]=>{{1,2,3,4,6,7,8},{5}}
[3,8,1,6,5,4,7,2]=>{{1,3},{2,8},{4,6},{5},{7}}
[5,2,1,6,7,4,3,8]=>{{1,3,5,7},{2},{4,6},{8}}
[4,2,1,6,5,7,3,8]=>{{1,3,4,6,7},{2},{5},{8}}
[2,8,1,6,5,4,3,7]=>{{1,2,3,7,8},{4,6},{5}}
[6,1,7,8,5,4,3,2]=>{{1,2,4,6,8},{3,7},{5}}
[4,1,7,6,5,8,3,2]=>{{1,2,4,6,8},{3,7},{5}}
[3,1,7,6,5,4,8,2]=>{{1,2,3,7,8},{4,6},{5}}
[4,5,8,1,2,6,3,7]=>{{1,4},{2,5},{3,7,8},{6}}
[1,4,5,7,2,6,3,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,7,3,5,6,2,4,8]=>{{1},{2,4,5,6,7},{3},{8}}
[8,1,3,5,7,2,4,6]=>{{1,2,6,8},{3},{4,5,7}}
[3,6,8,1,7,2,4,5]=>{{1,3,4,5,7,8},{2,6}}
[3,4,5,6,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,5,8,2,6,7,1,3]=>{{1,2,4,5,6,7},{3,8}}
[8,2,3,5,6,7,1,4]=>{{1,4,5,6,7,8},{2},{3}}
[1,7,2,3,5,4,6,8]=>{{1},{2,3,4,6,7},{5},{8}}
[8,1,2,3,5,4,6,7]=>{{1,2,3,4,6,7,8},{5}}
[2,7,8,1,3,5,4,6]=>{{1,2,4,7},{3,5,6,8}}
[2,7,8,3,5,6,1,4]=>{{1,2,7},{3,4,8},{5},{6}}
[2,4,5,7,8,1,6,3]=>{{1,2,4,6,7},{3,5,8}}
[4,5,8,1,7,6,3,2]=>{{1,4},{2,3,5,7,8},{6}}
[4,5,8,7,2,1,6,3]=>{{1,4,6,7},{2,5},{3,8}}
[8,7,3,5,6,2,1,4]=>{{1,2,4,5,6,7,8},{3}}
[8,7,2,1,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,6,8,7,2,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,6,4,1,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,4,3,1,8,5,2]=>{{1,5,7},{2,6,8},{3,4}}
[2,3,6,7,8,1,5,4]=>{{1,2,3,6},{4,5,7,8}}
[3,6,8,1,2,5,4,7]=>{{1,3,4,7,8},{2,5,6}}
[1,3,6,7,2,5,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[7,4,1,8,5,2,3,6]=>{{1,3,7},{2,4,6,8},{5}}
[7,1,4,2,8,3,6,5]=>{{1,2,3,4,6,7},{5,8}}
[7,1,8,2,5,3,6,4]=>{{1,2,3,4,6,7,8},{5}}
[8,1,7,5,4,2,3,6]=>{{1,2,6,8},{3,7},{4,5}}
[1,7,2,6,5,4,3,8]=>{{1},{2,3,7},{4,6},{5},{8}}
[1,7,6,3,2,5,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,6,3,1,2,5,4,7]=>{{1,4,7,8},{2,5,6},{3}}
[8,1,7,6,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,2,5,7,6,3,1,4]=>{{1,4,7,8},{2},{3,5,6}}
[3,6,8,1,7,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[8,2,6,7,5,4,1,3]=>{{1,3,4,6,7,8},{2},{5}}
[2,7,8,6,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,1,6,5,4,3]=>{{1,2,4,7},{3,8},{5,6}}
[7,3,1,8,6,5,4,2]=>{{1,2,3,4,7,8},{5,6}}
[8,7,2,1,6,5,4,3]=>{{1,2,3,4,7,8},{5,6}}
[8,7,6,3,2,1,5,4]=>{{1,3,4,6,8},{2,5,7}}
[2,1,8,6,3,7,4,5]=>{{1,2},{3,5,8},{4,6,7}}
[8,6,1,5,2,7,4,3]=>{{1,3,8},{2,4,5,6,7}}
[8,5,1,7,4,2,6,3]=>{{1,3,8},{2,4,5,6,7}}
[2,1,7,5,4,3,8,6]=>{{1,2},{3,6,7,8},{4,5}}
[2,1,7,8,3,6,5,4]=>{{1,2},{3,5,7},{4,8},{6}}
[2,1,4,8,5,7,3,6]=>{{1,2},{3,4,6,7,8},{5}}
[8,5,3,1,6,2,4,7]=>{{1,4,7,8},{2,5,6},{3}}
[6,4,1,5,2,3,8,7]=>{{1,3,6},{2,4,5},{7,8}}
[8,3,7,5,2,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[5,3,7,4,6,8,1,2]=>{{1,2,3,5,6,7,8},{4}}
[5,8,3,7,6,2,1,4]=>{{1,2,4,5,6,7,8},{3}}
[4,2,6,3,8,5,1,7]=>{{1,3,4,5,6,7,8},{2}}
[3,8,2,4,7,5,1,6]=>{{1,2,3,5,6,7,8},{4}}
[5,8,2,1,7,6,4,3]=>{{1,4,5,7},{2,3,8},{6}}
[8,3,2,4,1,7,5,6]=>{{1,5,6,7,8},{2,3},{4}}
[7,8,3,1,5,4,6,2]=>{{1,4,6,7},{2,8},{3},{5}}
[7,2,8,1,4,6,5,3]=>{{1,4,5,7},{2},{3,8},{6}}
[5,6,1,4,3,2,8,7]=>{{1,3,5},{2,6},{4},{7,8}}
[5,7,1,8,3,6,2,4]=>{{1,3,5},{2,7},{4,8},{6}}
[6,8,1,4,5,3,2,7]=>{{1,3,6},{2,7,8},{4},{5}}
[8,2,6,1,4,7,3,5]=>{{1,4,5,8},{2},{3,6,7}}
[8,3,5,6,1,7,4,2]=>{{1,2,3,5,8},{4,6,7}}
[6,3,5,4,1,2,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[8,7,3,6,5,1,4,2]=>{{1,2,4,6,7,8},{3},{5}}
[2,7,4,3,6,1,8,5]=>{{1,2,5,6,7,8},{3,4}}
[4,2,3,5,8,1,6,7]=>{{1,4,5,6,7,8},{2},{3}}
[3,8,4,7,1,6,5,2]=>{{1,3,4,5,7},{2,8},{6}}
[3,2,4,6,1,5,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[8,3,4,5,7,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[3,2,4,5,6,8,1,7]=>{{1,3,4,5,6,7,8},{2}}
[5,6,8,1,4,2,7,3]=>{{1,4,5},{2,6},{3,8},{7}}
[1,5,7,8,4,6,2,3]=>{{1},{2,3,4,5,7,8},{6}}
[1,3,5,7,8,6,2,4]=>{{1},{2,3,4,5,7,8},{6}}
[3,5,7,8,6,1,2,4]=>{{1,2,3,5,6,7},{4,8}}
[3,5,1,6,8,2,7,4]=>{{1,3},{2,4,5,6,8},{7}}
[3,1,5,6,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,3,5,6,8,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[5,6,4,8,2,1,7,3]=>{{1,2,5,6},{3,4,8},{7}}
[5,1,6,3,8,4,7,2]=>{{1,2,5,8},{3,4,6},{7}}
[2,5,1,6,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[5,1,2,6,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[5,7,1,8,6,2,3,4]=>{{1,2,3,5,6,7},{4,8}}
[1,5,2,7,8,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}
[1,6,7,5,2,8,3,4]=>{{1},{2,4,5,6,8},{3,7}}
[6,1,7,5,2,8,3,4]=>{{1,2,4,5,6,8},{3,7}}
[2,6,7,5,1,8,3,4]=>{{1,2,4,5,6,8},{3,7}}
[5,7,2,8,6,1,3,4]=>{{1,5,6},{2,3,7},{4,8}}
[3,5,7,8,6,2,1,4]=>{{1,3,7},{2,5,6},{4,8}}
[5,1,7,8,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[5,1,3,7,8,6,4,2]=>{{1,2,5,8},{3},{4,7},{6}}
[5,2,7,8,4,6,1,3]=>{{1,3,4,5,7,8},{2},{6}}
[3,2,5,7,8,6,1,4]=>{{1,3,4,5,7,8},{2},{6}}
[6,2,7,5,1,8,3,4]=>{{1,4,5,6,8},{2},{3,7}}
[1,2,6,7,5,8,3,4]=>{{1},{2},{3,4,6,7,8},{5}}
[6,2,7,5,4,1,8,3]=>{{1,6},{2},{3,7,8},{4,5}}
[6,7,5,2,4,1,8,3]=>{{1,6},{2,3,4,5,7,8}}
[6,7,2,5,3,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,5,2,1,8,3]=>{{1,6},{2,3,4,5,7,8}}
[5,1,7,8,6,4,3,2]=>{{1,2,4,5,6,8},{3,7}}
[2,5,7,8,6,3,1,4]=>{{1,2,3,5,6,7},{4,8}}
[5,1,7,8,6,3,2,4]=>{{1,2,3,5,6,7},{4,8}}
[6,3,7,5,1,8,2,4]=>{{1,4,5,6,8},{2,3,7}}
[1,6,7,5,3,8,2,4]=>{{1},{2,3,4,5,6,7,8}}
[1,6,7,5,4,2,8,3]=>{{1},{2,6},{3,7,8},{4,5}}
[6,7,5,1,4,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,6,4,1,2,3]=>{{1,4,5,6},{2,7},{3,8}}
[4,1,7,2,6,5,8,3]=>{{1,2,4},{3,7,8},{5,6}}
[2,4,7,1,5,6,8,3]=>{{1,2,4},{3,7,8},{5},{6}}
[6,7,4,1,5,2,8,3]=>{{1,2,3,4,6,7,8},{5}}
[1,6,7,4,5,2,8,3]=>{{1},{2,6},{3,7,8},{4},{5}}
[1,6,3,7,5,8,2,4]=>{{1},{2,4,6,7,8},{3},{5}}
[6,3,1,7,5,8,2,4]=>{{1,2,3,4,6,7,8},{5}}
[2,5,3,7,8,6,1,4]=>{{1,2,4,5,7,8},{3},{6}}
[6,7,5,4,2,1,8,3]=>{{1,6},{2,3,5,7,8},{4}}
[6,3,2,7,5,8,1,4]=>{{1,4,6,7,8},{2,3},{5}}
[6,7,4,2,5,1,8,3]=>{{1,6},{2,3,4,7,8},{5}}
[6,2,7,4,5,1,8,3]=>{{1,6},{2},{3,7,8},{4},{5}}
[6,2,3,7,5,8,1,4]=>{{1,4,6,7,8},{2},{3},{5}}
[7,5,1,6,3,8,2,4]=>{{1,2,3,5,7},{4,6,8}}
[2,7,6,1,3,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[7,3,5,1,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,3,5,1,8,2,4,6]=>{{1,4,7},{2,3,5,6,8}}
[3,7,5,1,8,6,2,4]=>{{1,3,4,5,8},{2,7},{6}}
[2,6,7,4,1,8,3,5]=>{{1,2,5,6,8},{3,7},{4}}
[2,1,6,7,3,8,5,4]=>{{1,2},{3,4,5,6,7,8}}
[3,6,5,1,8,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[3,6,5,1,8,4,2,7]=>{{1,2,3,4,5,6,7,8}}
[3,7,5,4,8,1,6,2]=>{{1,2,3,5,6,7,8},{4}}
[4,6,1,5,8,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,6,2,8,4,3]=>{{1,3,4,6,7,8},{2,5}}
[2,3,4,7,8,1,6,5]=>{{1,2,3,4,6,7},{5,8}}
[6,8,5,4,3,2,7,1]=>{{1,2,6,8},{3,5},{4},{7}}
[6,8,5,4,3,7,2,1]=>{{1,2,6,7,8},{3,5},{4}}
[5,8,4,3,2,1,7,6]=>{{1,2,5,6,8},{3,4},{7}}
[6,5,4,3,1,8,7,2]=>{{1,2,5,6,8},{3,4},{7}}
[8,7,5,4,3,1,6,2]=>{{1,2,6,7,8},{3,5},{4}}
[8,3,4,6,2,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,2,1,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,6,8,4,1,7]=>{{1,2,3,5,7,8},{4,6}}
[7,5,3,2,8,4,1,6]=>{{1,7},{2,4,5,6,8},{3}}
[7,5,3,2,8,4,6,1]=>{{1,2,4,5,6,7,8},{3}}
[2,4,5,7,3,8,6,1]=>{{1,2,4,6,7,8},{3,5}}
[4,2,5,6,8,3,1,7]=>{{1,3,4,5,6,7,8},{2}}
[4,2,8,1,5,6,3,7]=>{{1,4},{2},{3,7,8},{5},{6}}
[2,5,6,1,8,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,8,1,4,2,7]=>{{1,5},{2,3,4,6,7,8}}
[4,5,6,8,1,3,2,7]=>{{1,2,4,5,7,8},{3,6}}
[1,4,5,6,8,3,2,7]=>{{1},{2,3,4,5,6,7,8}}
[4,5,6,3,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,3,7,2,8,6,1]=>{{1,4,6,7,8},{2,5},{3}}
[6,4,7,3,2,8,5,1]=>{{1,6,8},{2,3,4,5,7}}
[6,1,4,7,3,2,8,5]=>{{1,2,6},{3,4,5,7,8}}
[1,7,8,4,5,3,2,6]=>{{1},{2,7},{3,6,8},{4},{5}}
[5,1,7,3,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[2,5,1,7,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,4,1,8,6,3]=>{{1,2,5},{3,6,7,8},{4}}
[5,3,7,1,4,8,6,2]=>{{1,4,5},{2,3,6,7,8}}
[6,4,3,1,7,8,5,2]=>{{1,2,4,6,8},{3},{5,7}}
[6,4,1,7,3,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,3,7,8,4,2,1]=>{{1,5,8},{2,4,6,7},{3}}
[5,1,6,3,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,1,3,7,8,4,2]=>{{1,3,4,5,7},{2,6,8}}
[5,6,1,7,8,3,4,2]=>{{1,2,3,5,6,8},{4,7}}
[1,6,3,7,4,8,5,2]=>{{1},{2,6,8},{3},{4,5,7}}
[6,7,2,4,1,8,5,3]=>{{1,2,3,5,6,7,8},{4}}
[6,7,2,1,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,3,1,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,6,3,1,2,7,8,4]=>{{1,2,4,5,6,7,8},{3}}
[5,6,1,3,2,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,6,3,2,1,7,8,4]=>{{1,5},{2,4,6,7,8},{3}}
[2,5,6,3,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,3,1,7,8,4]=>{{1,2,5},{3,4,6,7,8}}
[2,6,4,7,3,1,8,5]=>{{1,2,6},{3,4,5,7,8}}
[6,3,7,2,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,2,8,4,1,5]=>{{1,2,3,4,6,7},{5,8}}
[6,3,2,7,1,8,4,5]=>{{1,5,6,8},{2,3},{4,7}}
[7,5,3,2,1,8,4,6]=>{{1,2,4,5,7},{3},{6,8}}
[7,3,8,4,2,1,5,6]=>{{1,2,3,5,6,7,8},{4}}
[4,7,2,1,3,8,6,5]=>{{1,4},{2,3,5,6,7,8}}
[1,3,7,8,6,4,2,5]=>{{1},{2,3,7},{4,5,6,8}}
[7,3,8,4,6,2,1,5]=>{{1,7},{2,3,5,6,8},{4}}
[5,7,3,8,2,1,6,4]=>{{1,2,5,6,7},{3},{4,8}}
[6,3,7,8,5,2,1,4]=>{{1,2,3,6,7},{4,8},{5}}
[4,6,2,7,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[4,6,2,1,7,8,5,3]=>{{1,4},{2,3,6,8},{5,7}}
[7,4,5,8,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,1,7,3,8,6,4]=>{{1,2,3,5},{4,6,7,8}}
[6,7,2,1,3,8,5,4]=>{{1,4,6,8},{2,3,5,7}}
[5,1,6,7,8,2,4,3]=>{{1,2,3,5,6,8},{4,7}}
[6,3,7,1,8,5,2,4]=>{{1,4,5,6,8},{2,3,7}}
[6,2,1,7,3,8,5,4]=>{{1,3,4,5,6,7,8},{2}}
[6,2,7,1,8,5,4,3]=>{{1,3,4,5,6,7,8},{2}}
[6,3,1,7,8,5,4,2]=>{{1,2,3,5,6,8},{4,7}}
[4,1,3,6,8,2,5,7]=>{{1,2,4,6},{3},{5,7,8}}
[4,2,3,6,8,1,5,7]=>{{1,4,6},{2},{3},{5,7,8}}
[5,3,2,1,8,4,7,6]=>{{1,4,5,6,8},{2,3},{7}}
[3,6,5,8,2,1,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[4,5,2,1,3,8,7,6]=>{{1,4},{2,3,5},{6,8},{7}}
[3,2,6,4,5,8,1,7]=>{{1,3,6,7,8},{2},{4},{5}}
[2,4,6,5,8,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,2,4,5,8,3,7]=>{{1},{2,3,6,7,8},{4},{5}}
[5,3,2,1,6,8,4,7]=>{{1,4,5,6,7,8},{2,3}}
[6,2,4,5,8,1,3,7]=>{{1,6},{2},{3,4,5,7,8}}
[1,3,4,6,5,8,2,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,6,3,4,5,8,2,7]=>{{1},{2,6,7,8},{3},{4},{5}}
[3,4,1,8,5,2,7,6]=>{{1,3},{2,4,6,8},{5},{7}}
[2,8,4,1,7,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[8,1,4,2,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[1,5,3,2,8,7,4,6]=>{{1},{2,4,5,6,7,8},{3}}
[8,2,1,7,5,3,4,6]=>{{1,3,6,8},{2},{4,7},{5}}
[1,7,6,4,5,8,3,2]=>{{1},{2,3,6,7,8},{4},{5}}
[5,8,7,4,1,2,6,3]=>{{1,5},{2,3,6,7,8},{4}}
[5,8,7,4,6,2,1,3]=>{{1,2,3,5,6,7,8},{4}}
[3,4,2,5,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[4,1,3,5,6,8,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[2,4,8,6,7,1,3,5]=>{{1,2,4,6},{3,5,7,8}}
[4,3,6,2,8,1,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[3,7,4,8,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,8,6,7,1,4]=>{{1,2,3,5,6,7},{4,8}}
[3,2,5,6,8,7,1,4]=>{{1,3,4,5,6,7,8},{2}}
[2,1,8,5,6,7,3,4]=>{{1,2},{3,4,5,6,7,8}}
[1,2,8,3,5,6,7,4]=>{{1},{2},{3,4,8},{5},{6},{7}}
[4,2,3,7,1,8,6,5]=>{{1,4,5,6,7,8},{2},{3}}
[3,2,6,4,8,1,7,5]=>{{1,3,6},{2},{4},{5,8},{7}}
[8,2,1,6,7,3,4,5]=>{{1,3,4,5,6,7,8},{2}}
[2,7,8,5,4,1,3,6]=>{{1,2,3,6,7,8},{4,5}}
[1,7,5,3,8,4,2,6]=>{{1},{2,7},{3,4,5,6,8}}
[4,7,5,3,1,2,8,6]=>{{1,3,4,5},{2,6,7,8}}
[7,2,4,8,5,3,1,6]=>{{1,7},{2},{3,4,6,8},{5}}
[4,8,3,1,2,7,6,5]=>{{1,4},{2,5,8},{3},{6,7}}
[3,5,2,7,4,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,3,7,1,5,6]=>{{1,6,8},{2,3,4},{5,7}}
[2,8,4,7,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,2,4,6,7,1,3,5]=>{{1,3,4,5,6,7,8},{2}}
[4,8,2,3,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,7,6,1,8,4]=>{{1,2,3,5,6},{4,7,8}}
[1,6,3,2,5,8,7,4]=>{{1},{2,4,6,8},{3},{5},{7}}
[5,8,3,2,1,6,7,4]=>{{1,5},{2,4,8},{3},{6},{7}}
[5,8,7,3,4,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[5,8,2,7,4,1,6,3]=>{{1,4,5,6,7},{2,3,8}}
[5,1,4,2,8,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[4,7,6,5,8,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,1,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,2,6,8,7,1,3,4]=>{{1,3,5,6,7},{2},{4,8}}
[6,3,2,1,8,5,7,4]=>{{1,4,5,6,8},{2,3},{7}}
[2,7,5,4,1,8,6,3]=>{{1,2,3,5,6,7,8},{4}}
[4,2,5,6,8,7,1,3]=>{{1,4,6,7},{2},{3,5,8}}
[1,8,4,2,5,6,7,3]=>{{1},{2,3,4,8},{5},{6},{7}}
[3,8,4,1,5,6,7,2]=>{{1,3,4},{2,8},{5},{6},{7}}
[4,2,8,5,6,7,1,3]=>{{1,4,5,6,7},{2},{3,8}}
[5,2,4,7,1,8,6,3]=>{{1,5},{2},{3,4,6,7,8}}
[5,3,4,7,1,8,6,2]=>{{1,5},{2,3,4,6,7,8}}
[8,6,4,1,3,2,5,7]=>{{1,3,4,5,7,8},{2,6}}
[8,1,3,6,5,2,4,7]=>{{1,2,4,6,7,8},{3},{5}}
[8,1,4,3,6,5,2,7]=>{{1,2,7,8},{3,4},{5,6}}
[3,6,5,2,1,8,7,4]=>{{1,3,5},{2,4,6,8},{7}}
[8,3,2,4,6,5,1,7]=>{{1,7,8},{2,3},{4},{5,6}}
[8,4,2,1,6,5,3,7]=>{{1,2,3,4,7,8},{5,6}}
[8,4,1,2,6,5,3,7]=>{{1,3,7,8},{2,4},{5,6}}
[8,6,4,2,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,6,4,1,5,2,7]=>{{1,2,3,5,6,7,8},{4}}
[8,2,6,3,4,5,1,7]=>{{1,7,8},{2},{3,4,5,6}}
[1,3,4,8,5,7,2,6]=>{{1},{2,3,4,6,7,8},{5}}
[5,8,4,7,6,2,3,1]=>{{1,2,5,6,8},{3,4,7}}
[1,3,4,7,5,8,2,6]=>{{1},{2,3,4,7},{5},{6,8}}
[1,3,5,2,4,8,7,6]=>{{1},{2,3,4,5},{6,8},{7}}
[2,6,5,1,3,8,7,4]=>{{1,2,4,6,8},{3,5},{7}}
[4,7,1,6,5,8,3,2]=>{{1,2,3,4,6,7,8},{5}}
[5,4,8,7,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[2,8,5,1,4,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[4,3,1,5,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[4,1,3,5,8,6,7,2]=>{{1,2,4,5,8},{3},{6},{7}}
[6,5,3,8,4,7,1,2]=>{{1,6,7},{2,4,5,8},{3}}
[5,4,2,1,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,8,4,3,2,7,1,5]=>{{1,6,7},{2,5,8},{3,4}}
[3,4,7,8,2,1,6,5]=>{{1,3,6,7},{2,4,5,8}}
[5,1,3,2,8,6,7,4]=>{{1,2,4,5,8},{3},{6},{7}}
[5,3,1,2,8,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[5,2,3,1,6,8,7,4]=>{{1,4,5,6,8},{2},{3},{7}}
[5,3,2,1,8,6,7,4]=>{{1,4,5,8},{2,3},{6},{7}}
[5,2,1,3,6,8,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[2,4,7,3,8,1,6,5]=>{{1,2,3,4,6,7},{5,8}}
[6,3,8,2,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,3,6,4,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[3,5,1,7,8,4,2,6]=>{{1,3},{2,4,5,6,7,8}}
[2,7,4,5,8,3,1,6]=>{{1,2,7},{3,4,5,6,8}}
[1,8,4,3,7,2,6,5]=>{{1},{2,5,6,7,8},{3,4}}
[3,4,8,7,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[5,4,7,8,3,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[6,4,3,8,7,2,1,5]=>{{1,2,4,5,6,7,8},{3}}
[6,3,8,7,4,1,2,5]=>{{1,6},{2,3,4,5,7,8}}
[3,5,7,2,4,8,1,6]=>{{1,3,7},{2,4,5},{6,8}}
[8,4,7,2,3,1,5,6]=>{{1,6,8},{2,4},{3,5,7}}
[8,4,7,1,3,2,5,6]=>{{1,2,4,6,8},{3,5,7}}
[8,4,7,2,1,3,5,6]=>{{1,3,5,6,7,8},{2,4}}
[8,6,4,2,1,3,7,5]=>{{1,5,8},{2,3,4,6},{7}}
[8,6,4,1,3,2,7,5]=>{{1,3,4,5,8},{2,6},{7}}
[8,6,4,2,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,5,7,2,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[6,1,3,8,5,7,2,4]=>{{1,2,6,7},{3},{4,8},{5}}
[5,8,3,2,6,7,1,4]=>{{1,5,6,7},{2,4,8},{3}}
[4,8,5,3,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,8,1,5,4,7,6,3]=>{{1,2,3,8},{4,5},{6,7}}
[1,5,8,7,4,6,2,3]=>{{1},{2,4,5,7},{3,8},{6}}
[2,1,7,6,4,5,8,3]=>{{1,2},{3,7,8},{4,5,6}}
[1,7,2,4,6,5,8,3]=>{{1},{2,3,7,8},{4},{5,6}}
[3,5,1,7,6,8,2,4]=>{{1,3},{2,4,5,6,7,8}}
[5,8,2,6,1,3,7,4]=>{{1,5},{2,3,4,6,8},{7}}
[6,3,5,8,7,2,1,4]=>{{1,2,3,5,6,7},{4,8}}
[2,5,7,8,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[4,2,8,1,5,6,7,3]=>{{1,4},{2},{3,8},{5},{6},{7}}
[4,1,5,2,6,8,7,3]=>{{1,2,4},{3,5,6,8},{7}}
[3,4,5,1,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,2,8,5,1,6,7,3]=>{{1,4,5},{2},{3,8},{6},{7}}
[4,1,8,5,2,6,7,3]=>{{1,2,4,5},{3,8},{6},{7}}
[2,7,1,8,5,4,6,3]=>{{1,2,3,4,6,7,8},{5}}
[5,8,6,2,1,3,7,4]=>{{1,5},{2,4,8},{3,6},{7}}
[8,2,4,1,5,6,7,3]=>{{1,3,4,8},{2},{5},{6},{7}}
[4,6,3,5,8,1,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[1,7,8,3,5,4,6,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,4,5,1,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[3,8,1,4,5,6,7,2]=>{{1,3},{2,8},{4},{5},{6},{7}}
[3,4,5,7,8,2,6,1]=>{{1,3,5,8},{2,4,6,7}}
[3,4,6,2,8,5,1,7]=>{{1,3,5,6,7,8},{2,4}}
[3,4,6,8,1,5,2,7]=>{{1,3,5,6},{2,4,7,8}}
[3,4,7,2,1,8,6,5]=>{{1,3,5,6,7,8},{2,4}}
[3,4,8,2,1,5,6,7]=>{{1,3,5,6,7,8},{2,4}}
[3,5,2,7,8,4,6,1]=>{{1,2,3,5,8},{4,6,7}}
[3,5,6,2,8,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,8,4,1,2,7]=>{{1,3,6},{2,4,5,7,8}}
[3,5,7,2,4,8,6,1]=>{{1,3,6,7,8},{2,4,5}}
[3,5,7,2,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,8,4,1,6,2]=>{{1,3,6,7},{2,4,5,8}}
[3,6,2,1,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,2,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[3,6,8,2,4,5,1,7]=>{{1,3,7,8},{2,4,5,6}}
[3,7,2,1,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[3,7,2,8,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,2,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,5,6,7,8,3,2]=>{{1,2,4,6,8},{3,5,7}}
[4,1,5,7,3,8,6,2]=>{{1,2,4,6,7,8},{3,5}}
[4,1,6,3,8,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,6,7,3,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,1,6,8,3,5,2,7]=>{{1,2,4,7,8},{3,5,6}}
[4,1,7,3,2,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[4,1,8,3,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,2,6,8,1,3,7]=>{{1,4,6},{2,3,5,7,8}}
[4,5,7,3,8,1,6,2]=>{{1,3,4,6,7},{2,5,8}}
[4,5,8,3,2,1,6,7]=>{{1,3,4,6,7,8},{2,5}}
[4,6,2,7,8,5,1,3]=>{{1,4,7},{2,3,5,6,8}}
[4,6,7,3,2,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,7,2,8,3,5,6,1]=>{{1,4,8},{2,3,5,6,7}}
[4,7,8,3,2,5,6,1]=>{{1,3,4,8},{2,5,6,7}}
[4,8,2,3,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,1,2,6,8,4,3,7]=>{{1,2,3,5,7,8},{4,6}}
[5,1,6,3,8,4,2,7]=>{{1,2,5,7,8},{3,4,6}}
[5,1,6,7,4,8,2,3]=>{{1,2,4,5,7},{3,6,8}}
[5,6,2,3,8,4,1,7]=>{{1,5,7,8},{2,3,4,6}}
[5,6,2,7,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,6,8,3,4,2,1,7]=>{{1,3,4,5,7,8},{2,6}}
[5,7,2,3,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,3,4,2,6,1]=>{{1,3,4,5,8},{2,6,7}}
[5,8,2,3,4,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[6,1,2,3,7,8,5,4]=>{{1,2,3,4,6,8},{5,7}}
[6,1,2,3,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[6,1,2,7,8,5,4,3]=>{{1,2,3,5,6,8},{4,7}}
[6,1,7,3,8,5,4,2]=>{{1,2,5,6,8},{3,4,7}}
[6,1,7,8,4,5,3,2]=>{{1,2,4,5,6,8},{3,7}}
[6,1,8,3,4,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,3,8,5,4,1]=>{{1,5,6,8},{2,3,4,7}}
[6,7,2,8,4,5,3,1]=>{{1,4,5,6,8},{2,3,7}}
[7,1,2,3,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[7,1,2,8,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,3,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,8,2,3,7,5]=>{{1,3,6},{2,4,5,8},{7}}
[5,8,1,2,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[1,3,5,7,2,6,4,8]=>{{1},{2,3,5},{4,7},{6},{8}}
[3,5,8,6,1,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,6,8,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,6,2,8,1,5,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[2,6,1,3,8,4,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[1,7,5,2,3,4,6,8]=>{{1},{2,4,6,7},{3,5},{8}}
[2,7,5,1,3,8,4,6]=>{{1,2,4,7},{3,5},{6,8}}
[8,2,5,7,4,6,1,3]=>{{1,3,4,5,7,8},{2},{6}}
[8,2,1,3,7,6,4,5]=>{{1,3,4,5,7,8},{2},{6}}
[8,2,5,1,3,7,4,6]=>{{1,4,6,7,8},{2},{3,5}}
[8,2,7,5,3,1,6,4]=>{{1,3,4,5,6,7,8},{2}}
[8,2,6,5,4,7,1,3]=>{{1,3,6,7,8},{2},{4,5}}
[7,6,5,2,4,8,1,3]=>{{1,7},{2,3,4,5,6,8}}
[7,8,2,5,3,1,6,4]=>{{1,6,7},{2,3,4,5,8}}
[7,1,8,6,3,2,4,5]=>{{1,2,4,6,7},{3,5,8}}
[6,8,1,5,3,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,7,5,3,2,4,8]=>{{1},{2,6},{3,4,5,7},{8}}
[6,5,1,2,4,8,3,7]=>{{1,3,6,7,8},{2,4,5}}
[7,8,1,6,4,2,3,5]=>{{1,3,7},{2,4,5,6,8}}
[8,4,1,2,5,6,3,7]=>{{1,3,7,8},{2,4},{5},{6}}
[1,7,3,6,5,2,4,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[8,1,3,7,2,6,4,5]=>{{1,2,5,8},{3},{4,7},{6}}
[7,3,2,6,5,1,8,4]=>{{1,4,6,7,8},{2,3},{5}}
[7,8,4,2,5,6,1,3]=>{{1,7},{2,3,4,8},{5},{6}}
[8,2,7,4,5,6,1,3]=>{{1,3,7,8},{2},{4},{5},{6}}
[8,2,3,6,5,1,7,4]=>{{1,4,6,8},{2},{3},{5},{7}}
[4,8,6,5,7,3,2,1]=>{{1,2,4,5,7,8},{3,6}}
[3,8,7,5,4,6,2,1]=>{{1,2,3,7,8},{4,5},{6}}
[4,8,5,6,7,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[2,8,7,6,4,3,5,1]=>{{1,2,8},{3,4,5,6,7}}
[3,8,7,4,5,6,2,1]=>{{1,2,3,7,8},{4},{5},{6}}
[1,8,7,6,5,3,2,4]=>{{1},{2,3,4,6,7,8},{5}}
[2,8,7,6,3,4,5,1]=>{{1,2,8},{3,5,7},{4,6}}
[1,8,7,6,5,2,3,4]=>{{1},{2,4,6,8},{3,7},{5}}
[7,2,8,6,5,4,1,3]=>{{1,7},{2},{3,8},{4,6},{5}}
[7,2,8,5,4,6,1,3]=>{{1,7},{2},{3,8},{4,5},{6}}
[6,3,2,8,5,1,7,4]=>{{1,6},{2,3},{4,8},{5},{7}}
[8,4,7,2,5,6,3,1]=>{{1,8},{2,4},{3,7},{5},{6}}
[6,8,5,4,3,1,7,2]=>{{1,6},{2,8},{3,5},{4},{7}}
[5,8,6,4,1,3,7,2]=>{{1,5},{2,8},{3,6},{4},{7}}
[4,8,6,1,5,3,7,2]=>{{1,4},{2,8},{3,6},{5},{7}}
[3,6,1,8,5,2,7,4]=>{{1,3},{2,6},{4,8},{5},{7}}
[3,4,1,2,8,6,7,5]=>{{1,3},{2,4},{5,8},{6},{7}}
[6,8,3,5,4,1,7,2]=>{{1,6},{2,8},{3},{4,5},{7}}
[7,2,5,8,3,6,1,4]=>{{1,7},{2},{3,5},{4,8},{6}}
[1,7,5,6,3,4,2,8]=>{{1},{2,7},{3,5},{4,6},{8}}
[7,2,6,8,5,3,1,4]=>{{1,7},{2},{3,6},{4,8},{5}}
[7,6,3,8,5,2,1,4]=>{{1,7},{2,6},{3},{4,8},{5}}
[7,2,6,4,8,3,1,5]=>{{1,7},{2},{3,6},{4},{5,8}}
[1,5,7,4,2,6,3,8]=>{{1},{2,5},{3,7},{4},{6},{8}}
[4,2,3,1,7,8,5,6]=>{{1,4},{2},{3},{5,7},{6,8}}
[5,2,8,4,1,7,6,3]=>{{1,5},{2},{3,8},{4},{6,7}}
[8,6,3,4,7,2,5,1]=>{{1,8},{2,6},{3},{4},{5,7}}
[6,8,3,4,5,1,7,2]=>{{1,6},{2,8},{3},{4},{5},{7}}
[1,6,3,2,5,8,4,7]=>{{1},{2,4,6,7,8},{3},{5}}
[8,3,2,1,5,4,7,6]=>{{1,4,6,8},{2,3},{5},{7}}
[6,3,7,1,5,8,4,2]=>{{1,2,3,4,6,7,8},{5}}
[2,5,1,8,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[6,2,5,4,8,1,3,7]=>{{1,6},{2},{3,5,7,8},{4}}
[4,3,1,6,5,8,2,7]=>{{1,2,3,4,6,7,8},{5}}
[1,3,5,4,6,8,2,7]=>{{1},{2,3,5,6,7,8},{4}}
[6,1,3,4,5,8,2,7]=>{{1,2,6,7,8},{3},{4},{5}}
[8,3,4,1,5,2,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[7,5,4,2,6,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[8,2,6,4,1,7,3,5]=>{{1,5,8},{2},{3,6,7},{4}}
[7,3,8,4,5,2,1,6]=>{{1,7},{2,3,6,8},{4},{5}}
[7,2,5,1,8,4,3,6]=>{{1,3,4,5,6,7,8},{2}}
[1,7,3,2,5,4,8,6]=>{{1},{2,4,6,7,8},{3},{5}}
[8,7,2,1,5,3,4,6]=>{{1,2,3,4,6,7,8},{5}}
[3,6,1,5,8,7,4,2]=>{{1,3},{2,4,5,6,7,8}}
[8,3,6,4,5,1,7,2]=>{{1,2,3,6,8},{4},{5},{7}}
[5,4,6,8,1,2,7,3]=>{{1,5},{2,3,4,6,8},{7}}
[6,4,7,2,3,5,8,1]=>{{1,3,5,6,7,8},{2,4}}
[6,8,4,1,3,5,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[3,4,7,8,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,1,3,5,7,8,6,2]=>{{1,2,4,5,6,7,8},{3}}
[6,5,1,8,4,7,3,2]=>{{1,3,6,7},{2,4,5,8}}
[5,3,1,8,4,7,6,2]=>{{1,2,3,4,5,8},{6,7}}
[8,2,7,4,6,1,3,5]=>{{1,5,6,8},{2},{3,7},{4}}
[4,7,3,2,8,1,6,5]=>{{1,2,4,6,7},{3},{5,8}}
[6,3,1,4,7,2,8,5]=>{{1,2,3,6},{4},{5,7,8}}
[8,7,3,6,1,5,2,4]=>{{1,4,5,6,8},{2,7},{3}}
[7,4,3,6,8,2,5,1]=>{{1,5,7,8},{2,4,6},{3}}
[2,4,7,3,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[2,8,6,1,5,7,3,4]=>{{1,2,4,8},{3,6,7},{5}}
[7,8,2,5,4,3,1,6]=>{{1,7},{2,3,6,8},{4,5}}
[1,8,3,4,2,7,6,5]=>{{1},{2,5,8},{3},{4},{6,7}}
[8,5,3,7,4,2,6,1]=>{{1,8},{2,4,5,6,7},{3}}
[5,7,3,2,4,1,8,6]=>{{1,2,4,5,6,7,8},{3}}
[2,8,3,4,7,1,5,6]=>{{1,2,6,8},{3},{4},{5,7}}
[4,1,3,6,7,8,2,5]=>{{1,2,4,5,6,7,8},{3}}
[1,7,6,3,2,5,8,4]=>{{1},{2,3,4,5,6,7,8}}
[3,8,1,5,6,2,7,4]=>{{1,3},{2,4,5,6,8},{7}}
[8,2,5,6,1,7,4,3]=>{{1,3,5,8},{2},{4,6,7}}
[7,1,5,2,8,6,4,3]=>{{1,2,4,7},{3,5,8},{6}}
[6,5,4,8,7,2,1,3]=>{{1,2,5,6,7},{3,4,8}}
[1,8,6,4,5,2,7,3]=>{{1},{2,3,6,8},{4},{5},{7}}
[1,8,5,3,6,2,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[3,6,2,1,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,1,8,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[4,7,2,6,5,8,1,3]=>{{1,2,3,4,6,7,8},{5}}
[6,8,1,4,2,7,3,5]=>{{1,3,6,7},{2,5,8},{4}}
[6,3,4,7,1,8,2,5]=>{{1,5,6,8},{2,3,4,7}}
[3,4,7,8,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[1,8,2,4,5,6,7,3]=>{{1},{2,3,8},{4},{5},{6},{7}}
[5,2,4,1,6,8,7,3]=>{{1,3,4,5,6,8},{2},{7}}
[3,2,5,7,6,1,8,4]=>{{1,3,5,6},{2},{4,7,8}}
[4,3,5,6,1,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[5,3,4,1,7,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[3,1,4,6,5,7,8,2]=>{{1,2,3,4,6,7,8},{5}}
[1,4,7,3,5,6,8,2]=>{{1},{2,3,4,7,8},{5},{6}}
[5,1,3,6,4,8,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[1,3,2,7,5,8,6,4]=>{{1},{2,3},{4,6,7,8},{5}}
[1,4,2,5,8,3,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,4,2,7,8,5,6,3]=>{{1},{2,3,4,5,6,7,8}}
[5,1,2,6,8,4,7,3]=>{{1,2,3,5,8},{4,6},{7}}
[3,1,2,6,5,8,4,7]=>{{1,2,3},{4,6,7,8},{5}}
[4,1,2,6,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,5,2,4,8,7,6,3]=>{{1},{2,3,5,8},{4},{6,7}}
[1,2,6,4,8,7,5,3]=>{{1},{2},{3,5,6,7,8},{4}}
[1,2,7,4,8,6,5,3]=>{{1},{2},{3,5,7,8},{4},{6}}
[1,3,2,7,5,8,4,6]=>{{1},{2,3},{4,7},{5},{6,8}}
[2,3,1,7,5,4,8,6]=>{{1,2,3},{4,6,7,8},{5}}
[1,3,2,8,5,7,4,6]=>{{1},{2,3},{4,6,7,8},{5}}
[1,4,2,5,8,7,3,6]=>{{1},{2,3,4,5,6,7,8}}
[1,5,2,4,8,7,3,6]=>{{1},{2,3,5,6,7,8},{4}}
[1,2,6,4,8,7,3,5]=>{{1},{2},{3,6,7},{4},{5,8}}
[1,2,7,8,5,6,3,4]=>{{1},{2},{3,7},{4,8},{5},{6}}
[1,2,6,8,5,7,3,4]=>{{1},{2},{3,6,7},{4,8},{5}}
[1,5,6,8,2,7,3,4]=>{{1},{2,5},{3,6,7},{4,8}}
[1,3,8,2,6,7,4,5]=>{{1},{2,3,4,5,6,7,8}}
[1,4,7,2,8,6,3,5]=>{{1},{2,4},{3,7},{5,8},{6}}
[1,6,7,8,2,5,3,4]=>{{1},{2,5,6},{3,7},{4,8}}
[1,2,6,8,3,7,5,4]=>{{1},{2},{3,5,6,7},{4,8}}
[1,5,7,8,2,3,6,4]=>{{1},{2,5},{3,6,7},{4,8}}
[1,5,2,7,8,4,6,3]=>{{1},{2,3,5,8},{4,6,7}}
[1,4,7,2,8,3,6,5]=>{{1},{2,4},{3,6,7},{5,8}}
[1,3,6,2,4,8,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,7,3,4,8,5,2]=>{{1},{2,6,8},{3,4,5,7}}
[1,5,3,7,4,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,8,4,1,5,3,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[3,8,4,1,5,7,2,6]=>{{1,3,4},{2,6,7,8},{5}}
[1,3,6,4,2,8,7,5]=>{{1},{2,3,5,6,8},{4},{7}}
[1,3,7,4,2,8,6,5]=>{{1},{2,3,5,6,7,8},{4}}
[1,3,8,4,2,7,6,5]=>{{1},{2,3,5,8},{4},{6,7}}
[1,2,8,4,7,3,6,5]=>{{1},{2},{3,5,6,7,8},{4}}
[1,2,7,4,8,3,6,5]=>{{1},{2},{3,6,7},{4},{5,8}}
[1,2,6,4,8,3,7,5]=>{{1},{2},{3,6},{4},{5,8},{7}}
[1,5,2,4,8,3,7,6]=>{{1},{2,3,5,6,8},{4},{7}}
[1,8,4,5,7,2,3,6]=>{{1},{2,6,8},{3,4,5,7}}
[1,8,3,5,2,7,4,6]=>{{1},{2,4,5,6,7,8},{3}}
[2,8,3,5,1,4,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[2,3,8,6,1,4,7,5]=>{{1,2,3,5,8},{4,6},{7}}
[1,3,8,6,2,7,4,5]=>{{1},{2,3,5,8},{4,6,7}}
[1,4,8,6,7,2,3,5]=>{{1},{2,4,6},{3,5,7,8}}
[1,5,6,8,7,2,3,4]=>{{1},{2,3,5,6,7},{4,8}}
[1,2,6,8,5,3,7,4]=>{{1},{2},{3,6},{4,8},{5},{7}}
[1,2,7,8,5,3,6,4]=>{{1},{2},{3,6,7},{4,8},{5}}
[1,2,5,8,7,3,6,4]=>{{1},{2},{3,5,6,7},{4,8}}
[1,2,6,8,7,3,5,4]=>{{1},{2},{3,6},{4,8},{5,7}}
[1,2,7,8,6,3,5,4]=>{{1},{2},{3,5,6,7},{4,8}}
[1,6,7,8,5,2,3,4]=>{{1},{2,6},{3,7},{4,8},{5}}
[1,5,7,8,6,2,3,4]=>{{1},{2,5,6},{3,7},{4,8}}
[1,4,7,6,8,2,3,5]=>{{1},{2,4,6},{3,7},{5,8}}
[1,3,7,6,2,8,4,5]=>{{1},{2,3,4,5,6,7,8}}
[2,3,8,7,4,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[1,2,8,4,7,6,3,5]=>{{1},{2},{3,5,7,8},{4},{6}}
[1,2,5,8,7,6,3,4]=>{{1},{2},{3,5,7},{4,8},{6}}
[1,2,6,8,7,5,3,4]=>{{1},{2},{3,5,6,7},{4,8}}
[1,2,7,8,6,5,3,4]=>{{1},{2},{3,7},{4,8},{5,6}}
[5,2,6,7,3,4,8,1]=>{{1,3,4,5,6,7,8},{2}}
[5,2,4,7,6,3,8,1]=>{{1,3,4,5,6,7,8},{2}}
[5,6,2,1,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,6,2,1,4,8,7,3]=>{{1,4,5},{2,3,6,8},{7}}
[2,6,1,4,5,8,7,3]=>{{1,2,3,6,8},{4},{5},{7}}
[5,4,2,7,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,3,7,6,4,5,8,1]=>{{1,2,3,7,8},{4,5,6}}
[2,6,1,7,5,8,3,4]=>{{1,2,3,4,6,7,8},{5}}
[2,6,1,7,4,8,5,3]=>{{1,2,3,6,8},{4,5,7}}
[5,1,2,7,8,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,6,1,7,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,1,7,8,2,5]=>{{1,3,4},{2,5,6,7,8}}
[5,4,6,1,3,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[3,6,4,1,5,8,7,2]=>{{1,3,4},{2,6,8},{5},{7}}
[2,6,1,5,4,8,7,3]=>{{1,2,3,6,8},{4,5},{7}}
[2,6,1,4,7,8,5,3]=>{{1,2,3,6,8},{4},{5,7}}
[5,1,2,4,8,6,7,3]=>{{1,2,3,5,8},{4},{6},{7}}
[5,1,2,4,8,7,3,6]=>{{1,2,3,5,6,7,8},{4}}
[5,1,2,4,8,7,6,3]=>{{1,2,3,5,8},{4},{6,7}}
[1,2,3,8,5,4,7,6]=>{{1},{2},{3},{4,6,8},{5},{7}}
[4,3,1,2,8,5,7,6]=>{{1,2,3,4},{5,6,8},{7}}
[2,1,5,3,8,6,4,7]=>{{1,2},{3,4,5,7,8},{6}}
[1,2,3,8,5,6,4,7]=>{{1},{2},{3},{4,7,8},{5},{6}}
[1,2,3,8,6,4,5,7]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,8,6,5,4,7]=>{{1},{2},{3},{4,7,8},{5,6}}
[1,2,3,8,5,4,6,7]=>{{1},{2},{3},{4,6,7,8},{5}}
[2,6,1,5,4,8,3,7]=>{{1,2,3,6,7,8},{4,5}}
[5,1,2,4,8,6,3,7]=>{{1,2,3,5,7,8},{4},{6}}
[5,1,2,4,8,3,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[5,6,3,1,4,8,2,7]=>{{1,4,5},{2,6,7,8},{3}}
[2,5,4,3,1,8,6,7]=>{{1,2,5},{3,4},{6,7,8}}
[5,4,6,3,1,8,7,2]=>{{1,5},{2,3,4,6,8},{7}}
[3,6,4,5,1,8,7,2]=>{{1,3,4,5},{2,6,8},{7}}
[3,6,5,4,1,8,7,2]=>{{1,3,5},{2,6,8},{4},{7}}
[5,2,6,1,7,8,4,3]=>{{1,4,5,7},{2},{3,6,8}}
[5,1,6,2,8,7,3,4]=>{{1,2,4,5,8},{3,6,7}}
[2,1,3,7,8,6,4,5]=>{{1,2},{3},{4,7},{5,8},{6}}
[2,1,3,7,8,5,6,4]=>{{1,2},{3},{4,5,6,7,8}}
[5,2,4,1,7,8,6,3]=>{{1,3,4,5,6,7,8},{2}}
[4,3,1,2,8,6,7,5]=>{{1,2,3,4},{5,8},{6},{7}}
[5,1,4,2,8,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[2,1,3,6,8,5,7,4]=>{{1,2},{3},{4,5,6,8},{7}}
[1,2,3,8,6,7,4,5]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,8,7,5,4,6]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,8,7,4,5,6]=>{{1},{2},{3},{4,6,8},{5,7}}
[1,2,3,8,5,7,4,6]=>{{1},{2},{3},{4,6,7,8},{5}}
[2,1,3,6,8,7,4,5]=>{{1,2},{3},{4,6,7},{5,8}}
[5,4,1,2,8,7,6,3]=>{{1,3,5,8},{2,4},{6,7}}
[3,1,6,2,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[1,8,3,4,2,5,6,7]=>{{1},{2,5,6,7,8},{3},{4}}
[1,8,4,3,2,5,6,7]=>{{1},{2,5,6,7,8},{3,4}}
[8,4,7,6,5,3,2,1]=>{{1,8},{2,3,4,6,7},{5}}
[8,4,7,5,6,3,2,1]=>{{1,8},{2,3,4,5,6,7}}
[8,5,7,4,6,3,2,1]=>{{1,8},{2,3,5,6,7},{4}}
[8,7,6,3,5,4,2,1]=>{{1,8},{2,7},{3,4,6},{5}}
[8,6,7,3,5,4,2,1]=>{{1,8},{2,3,4,6,7},{5}}
[8,5,7,3,6,4,2,1]=>{{1,8},{2,3,4,5,6,7}}
[8,1,7,4,6,5,3,2]=>{{1,2,8},{3,7},{4},{5,6}}
[8,1,7,3,6,5,4,2]=>{{1,2,8},{3,4,7},{5,6}}
[8,2,7,3,6,5,4,1]=>{{1,8},{2},{3,4,7},{5,6}}
[8,3,7,2,6,5,4,1]=>{{1,8},{2,3,4,7},{5,6}}
[8,5,7,2,6,4,3,1]=>{{1,8},{2,4,5,6},{3,7}}
[8,6,7,2,5,4,3,1]=>{{1,8},{2,4,6},{3,7},{5}}
[8,7,6,2,5,4,3,1]=>{{1,8},{2,3,4,6,7},{5}}
[8,4,7,1,6,5,3,2]=>{{1,2,4,8},{3,7},{5,6}}
[8,3,7,1,6,5,4,2]=>{{1,2,3,4,7,8},{5,6}}
[8,2,7,1,6,5,4,3]=>{{1,3,4,7,8},{2},{5,6}}
[8,1,7,2,6,5,4,3]=>{{1,2,3,4,7,8},{5,6}}
[8,7,6,2,5,3,4,1]=>{{1,8},{2,4,7},{3,6},{5}}
[8,1,7,6,5,3,4,2]=>{{1,2,8},{3,4,6,7},{5}}
[8,3,7,6,5,2,4,1]=>{{1,8},{2,3,4,6,7},{5}}
[8,4,7,6,5,2,3,1]=>{{1,8},{2,4,6},{3,7},{5}}
[8,5,7,6,4,2,3,1]=>{{1,8},{2,4,5,6},{3,7}}
[8,6,7,5,4,1,3,2]=>{{1,2,6,8},{3,7},{4,5}}
[8,5,7,6,4,1,3,2]=>{{1,2,4,5,6,8},{3,7}}
[8,3,7,6,5,1,4,2]=>{{1,2,3,4,6,7,8},{5}}
[8,7,6,4,5,1,3,2]=>{{1,2,3,6,7,8},{4},{5}}
[8,7,6,2,5,1,4,3]=>{{1,3,6,8},{2,4,7},{5}}
[8,7,6,1,5,2,4,3]=>{{1,2,3,4,6,7,8},{5}}
[6,8,1,3,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[6,8,1,4,2,5,3,7]=>{{1,2,3,5,6,7,8},{4}}
[7,8,3,6,1,4,2,5]=>{{1,2,5,7,8},{3},{4,6}}
[7,8,2,5,3,6,1,4]=>{{1,7},{2,3,4,5,8},{6}}
[7,8,2,5,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,4,3,6,2,5]=>{{1,2,3,5,7,8},{4},{6}}
[5,8,1,4,3,7,2,6]=>{{1,3,5},{2,6,7,8},{4}}
[6,8,2,5,1,4,3,7]=>{{1,4,5,6},{2,3,7,8}}
[6,8,2,5,3,7,1,4]=>{{1,6,7},{2,3,4,5,8}}
[6,8,2,5,4,7,1,3]=>{{1,6,7},{2,3,8},{4,5}}
[2,5,4,7,6,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,3,7,6,8,1,4]=>{{1,2,4,5,6,7,8},{3}}
[2,5,1,4,3,7,6,8]=>{{1,2,3,5},{4},{6,7},{8}}
[2,6,1,4,3,7,5,8]=>{{1,2,3,5,6,7},{4},{8}}
[2,6,5,8,1,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[2,6,1,5,3,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,6,3,7,4,8,1,5]=>{{1,2,4,5,6,7,8},{3}}
[2,6,4,7,5,8,1,3]=>{{1,2,3,4,6,7,8},{5}}
[5,8,3,6,4,7,1,2]=>{{1,4,5,6,7},{2,8},{3}}
[5,8,2,6,4,7,1,3]=>{{1,4,5,6,7},{2,3,8}}
[4,8,2,6,3,7,1,5]=>{{1,4,6,7},{2,3,5,8}}
[4,8,1,5,3,7,2,6]=>{{1,3,4,5},{2,6,7,8}}
[4,8,1,5,2,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[4,8,3,7,1,5,2,6]=>{{1,2,4,5,6,7,8},{3}}
[6,8,3,7,1,4,2,5]=>{{1,2,4,5,6,7,8},{3}}
[5,8,1,3,2,6,4,7]=>{{1,2,3,4,5,7,8},{6}}
[5,8,4,7,1,3,2,6]=>{{1,5},{2,3,4,6,7,8}}
[6,8,4,7,1,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,7,1,3,2,4]=>{{1,3,5,6},{2,4,7,8}}
[5,7,6,8,2,4,1,3]=>{{1,2,5,7},{3,4,6,8}}
[4,7,6,8,1,3,2,5]=>{{1,4,5,8},{2,7},{3,6}}
[4,7,5,8,1,3,2,6]=>{{1,3,4,5,6,8},{2,7}}
[4,7,1,3,2,6,5,8]=>{{1,3,4},{2,5,7},{6},{8}}
[3,7,1,4,2,6,5,8]=>{{1,3},{2,5,7},{4},{6},{8}}
[3,7,5,8,1,4,2,6]=>{{1,3,5},{2,7},{4,6,8}}
[3,7,6,8,1,4,2,5]=>{{1,3,4,5,6,8},{2,7}}
[3,7,6,8,2,5,1,4]=>{{1,2,3,5,6,7},{4,8}}
[4,7,6,8,2,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,8,3,6,1,2]=>{{1,2,4,7,8},{3,5},{6}}
[4,7,5,8,2,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[3,7,5,8,2,6,1,4]=>{{1,2,3,5,7},{4,8},{6}}
[3,7,4,8,2,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[3,7,4,8,1,5,2,6]=>{{1,3,4,5,6,8},{2,7}}
[3,7,1,5,2,6,4,8]=>{{1,3},{2,4,5,7},{6},{8}}
[3,7,2,6,1,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[3,7,2,6,5,8,1,4]=>{{1,2,3,7},{4,6,8},{5}}
[4,7,3,6,5,8,1,2]=>{{1,2,4,6,7,8},{3},{5}}
[3,6,5,8,4,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[2,6,5,8,4,7,1,3]=>{{1,2,6,7},{3,4,5,8}}
[2,6,5,8,3,7,1,4]=>{{1,2,6,7},{3,5},{4,8}}
[2,6,3,7,1,5,4,8]=>{{1,2,5,6},{3},{4,7},{8}}
[7,6,4,2,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,4,3,8,2,5,1]=>{{1,5,7,8},{2,6},{3,4}}
[7,6,4,8,5,2,3,1]=>{{1,3,4,7,8},{2,6},{5}}
[6,8,4,3,7,2,1,5]=>{{1,2,5,6,7,8},{3,4}}
[6,7,4,3,5,1,8,2]=>{{1,6},{2,7,8},{3,4},{5}}
[6,7,3,5,4,8,2,1]=>{{1,6,8},{2,7},{3},{4,5}}
[6,8,3,7,5,2,4,1]=>{{1,2,6,8},{3},{4,7},{5}}
[7,6,8,3,5,2,4,1]=>{{1,3,4,7,8},{2,6},{5}}
[7,6,3,5,8,2,4,1]=>{{1,4,5,7,8},{2,6},{3}}
[7,6,3,5,2,4,8,1]=>{{1,7,8},{2,4,5,6},{3}}
[7,6,4,2,5,1,8,3]=>{{1,2,3,4,6,7,8},{5}}
[7,6,2,8,4,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,6,3,8,2,4,1,5]=>{{1,7},{2,4,5,6,8},{3}}
[7,6,3,4,8,2,5,1]=>{{1,5,7,8},{2,6},{3},{4}}
[6,8,3,7,4,5,2,1]=>{{1,2,4,5,6,7,8},{3}}
[6,7,3,5,8,4,2,1]=>{{1,4,5,6,8},{2,7},{3}}
[5,7,8,3,6,2,1,4]=>{{1,2,5,6,7},{3,4,8}}
[5,8,3,6,7,2,1,4]=>{{1,5,7},{2,4,6,8},{3}}
[6,3,4,8,7,2,5,1]=>{{1,2,3,4,6,8},{5,7}}
[6,3,8,4,7,2,1,5]=>{{1,2,3,5,6,7,8},{4}}
[6,2,8,4,1,7,5,3]=>{{1,5,6,7},{2},{3,8},{4}}
[6,2,7,4,1,5,3,8]=>{{1,5,6},{2},{3,7},{4},{8}}
[6,3,4,7,5,8,2,1]=>{{1,6,8},{2,3,4,7},{5}}
[6,3,5,7,8,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,3,6,8,2,1,4]=>{{1,2,4,5,6,7,8},{3}}
[5,6,8,3,7,2,1,4]=>{{1,5,7},{2,6},{3,4,8}}
[5,6,7,3,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,8,3,5,2,1]=>{{1,4,8},{2,3,5,6,7}}
[4,6,8,3,5,7,2,1]=>{{1,3,4,8},{2,6,7},{5}}
[4,7,3,5,6,8,2,1]=>{{1,4,5,6,8},{2,7},{3}}
[4,7,3,5,8,2,6,1]=>{{1,4,5,8},{2,6,7},{3}}
[5,3,4,7,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,2,4,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,4,8,2,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[4,8,3,6,2,5,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[4,8,3,5,7,2,6,1]=>{{1,2,4,5,6,7,8},{3}}
[4,8,3,5,6,7,2,1]=>{{1,2,4,5,6,7,8},{3}}
[4,7,8,3,5,6,2,1]=>{{1,3,4,8},{2,7},{5},{6}}
[4,7,8,3,6,2,5,1]=>{{1,3,4,8},{2,5,6,7}}
[4,8,3,6,7,2,5,1]=>{{1,2,4,6,8},{3},{5,7}}
[4,8,3,7,2,5,6,1]=>{{1,2,4,5,6,7,8},{3}}
[5,3,4,8,2,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[5,3,8,2,4,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,2,8,4,1,7,3,6]=>{{1,5},{2},{3,6,7,8},{4}}
[6,4,2,5,1,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,4,3,5,8,2,1,7]=>{{1,2,4,5,6,7,8},{3}}
[6,3,5,8,7,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[5,8,3,7,2,6,4,1]=>{{1,2,5,8},{3},{4,7},{6}}
[5,7,3,4,8,2,1,6]=>{{1,2,5,6,7,8},{3},{4}}
[5,8,4,2,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,2,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[6,4,5,3,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,5,3,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,3,8,5,7,2,1]=>{{1,2,4,6,7,8},{3},{5}}
[6,4,2,8,5,3,1,7]=>{{1,2,3,4,6,7,8},{5}}
[6,4,2,7,3,1,8,5]=>{{1,6},{2,3,4,5,7,8}}
[6,4,3,7,8,5,2,1]=>{{1,5,6,8},{2,4,7},{3}}
[6,4,5,3,7,1,8,2]=>{{1,6},{2,3,4,5,7,8}}
[5,7,4,2,3,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,3,7,1,8,2,4]=>{{1,5},{2,4,6,7,8},{3}}
[5,6,3,4,7,1,8,2]=>{{1,2,5,6,7,8},{3},{4}}
[5,6,3,4,8,2,1,7]=>{{1,5,7,8},{2,6},{3},{4}}
[6,3,5,7,4,8,2,1]=>{{1,6,8},{2,3,4,5,7}}
[6,3,5,4,7,8,2,1]=>{{1,6,8},{2,3,5,7},{4}}
[6,4,3,5,7,1,8,2]=>{{1,6},{2,4,5,7,8},{3}}
[6,4,2,5,1,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,3,7,2,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[5,3,4,7,2,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,7,3,6,2,5,8,1]=>{{1,2,4,5,6,7,8},{3}}
[4,7,3,6,8,2,5,1]=>{{1,2,4,5,6,7,8},{3}}
[4,6,7,3,5,8,2,1]=>{{1,2,3,4,6,7,8},{5}}
[4,5,7,8,3,6,2,1]=>{{1,4,8},{2,3,5,7},{6}}
[4,5,8,3,6,7,2,1]=>{{1,3,4,8},{2,5,6,7}}
[4,5,8,3,7,2,6,1]=>{{1,3,4,8},{2,5,6,7}}
[5,3,4,6,8,2,1,7]=>{{1,5,7,8},{2,3,4,6}}
[5,3,6,8,2,1,4,7]=>{{1,2,3,5,6},{4,7,8}}
[5,3,6,7,1,8,2,4]=>{{1,5},{2,3,4,6,7,8}}
[5,3,4,6,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[4,6,3,5,7,8,2,1]=>{{1,2,4,5,6,7,8},{3}}
[4,5,7,3,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,8,3,7,2,1]=>{{1,4,8},{2,3,5,6,7}}
[5,7,4,8,6,3,2,1]=>{{1,3,4,5,6,8},{2,7}}
[3,2,6,5,1,8,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[3,5,6,7,2,8,4,1]=>{{1,3,6,8},{2,5},{4,7}}
[1,6,2,5,3,4,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[1,3,8,2,4,6,5,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,2,3,6,4,8,5]=>{{1},{2,3,4,5,6,7,8}}
[1,6,8,2,5,3,7,4]=>{{1},{2,3,4,6,8},{5},{7}}
[1,8,2,5,3,4,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,8,2,3,6,4,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[1,3,5,2,8,4,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,2,7,3,5,4,6,8]=>{{1},{2},{3,4,6,7},{5},{8}}
[1,8,2,7,3,4,6,5]=>{{1},{2,3,5,8},{4,6,7}}
[1,5,8,2,3,7,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,6,8,2,3,5,4,7]=>{{1},{2,3,4,5,6,7,8}}
[5,3,6,1,2,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[7,1,5,8,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,5,7,4,2,3,6]=>{{1,2,6,8},{3,4,5,7}}
[7,1,4,5,8,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,6,2,8,3,5]=>{{1,3,7},{2,4,5,6,8}}
[8,4,1,7,2,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[8,1,4,7,5,2,3,6]=>{{1,2,6,8},{3,4,7},{5}}
[8,1,5,4,7,2,3,6]=>{{1,2,6,8},{3,5,7},{4}}
[2,1,7,5,8,3,4,6]=>{{1,2},{3,4,5,6,7,8}}
[7,1,5,4,8,2,3,6]=>{{1,2,3,5,6,7,8},{4}}
[7,1,4,8,5,2,3,6]=>{{1,2,3,4,6,7,8},{5}}
[6,4,1,7,2,3,8,5]=>{{1,3,6},{2,4,5,7,8}}
[7,8,3,1,2,4,6,5]=>{{1,4,6,7},{2,5,8},{3}}
[8,7,1,6,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[8,6,1,7,4,2,3,5]=>{{1,3,4,5,7,8},{2,6}}
[7,6,1,8,4,2,3,5]=>{{1,3,7},{2,6},{4,5,8}}
[7,3,8,1,2,4,6,5]=>{{1,4,6,7},{2,3,5,8}}
[8,3,7,1,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,6,1,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[8,3,7,5,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,3,6,1,2,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,8,4,2,3,5]=>{{1,2,3,6,7},{4,5,8}}
[6,8,1,7,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,5,4,2,3,6]=>{{1,2,3,6,7,8},{4,5}}
[7,1,8,4,5,2,3,6]=>{{1,2,3,6,7,8},{4},{5}}
[2,1,7,8,5,3,4,6]=>{{1,2},{3,4,6,7,8},{5}}
[7,6,3,1,2,4,8,5]=>{{1,2,4,5,6,7,8},{3}}
[6,1,2,3,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[6,8,1,4,2,3,7,5]=>{{1,3,6},{2,5,8},{4},{7}}
[6,8,3,1,2,7,4,5]=>{{1,4,6,7},{2,5,8},{3}}
[6,7,3,1,2,8,4,5]=>{{1,2,4,5,6,7,8},{3}}
[6,7,1,4,2,3,8,5]=>{{1,3,6},{2,5,7,8},{4}}
[4,3,6,8,5,7,1,2]=>{{1,2,3,4,6,7,8},{5}}
[6,1,2,5,4,8,3,7]=>{{1,2,3,6,7,8},{4,5}}
[7,2,1,5,8,3,4,6]=>{{1,3,4,5,6,7,8},{2}}
[1,3,6,8,7,4,2,5]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,5,7,3,4,6]=>{{1},{2},{3,6,8},{4,5,7}}
[2,6,1,5,8,3,4,7]=>{{1,2,3,6},{4,5,7,8}}
[5,7,1,6,8,4,3,2]=>{{1,2,3,5,7,8},{4,6}}
[4,8,1,2,5,7,3,6]=>{{1,2,3,4,6,7,8},{5}}
[8,4,6,2,5,7,3,1]=>{{1,8},{2,4},{3,6,7},{5}}
[8,3,6,4,7,2,5,1]=>{{1,8},{2,3,6},{4},{5,7}}
[3,8,1,4,7,2,5,6]=>{{1,3},{2,6,8},{4},{5,7}}
[1,7,8,4,6,2,5,3]=>{{1},{2,5,6,7},{3,8},{4}}
[3,7,4,8,5,1,6,2]=>{{1,2,3,4,6,7,8},{5}}
[3,7,1,6,5,4,8,2]=>{{1,3},{2,7,8},{4,6},{5}}
[2,7,3,1,5,8,4,6]=>{{1,2,4,7},{3},{5},{6,8}}
[2,7,4,6,8,1,3,5]=>{{1,2,3,4,6,7},{5,8}}
[2,7,5,8,6,4,1,3]=>{{1,2,7},{3,4,5,6,8}}
[8,2,6,7,5,4,3,1]=>{{1,8},{2},{3,4,6,7},{5}}
[3,8,7,1,6,4,5,2]=>{{1,3,4,5,6,7},{2,8}}
[3,6,8,2,7,4,1,5]=>{{1,3,5,7,8},{2,4,6}}
[1,5,2,8,7,4,6,3]=>{{1},{2,3,4,5,6,7,8}}
[3,4,2,7,8,1,6,5]=>{{1,2,3,4,6,7},{5,8}}
[4,1,3,7,5,6,8,2]=>{{1,2,4,7,8},{3},{5},{6}}
[6,3,8,1,7,4,2,5]=>{{1,4,6},{2,3,5,7,8}}
[6,5,8,7,1,4,2,3]=>{{1,2,4,5,6,7},{3,8}}
[4,1,7,3,8,5,2,6]=>{{1,2,3,4,7},{5,6,8}}
[3,6,1,4,5,8,2,7]=>{{1,3},{2,6,7,8},{4},{5}}
[1,6,7,4,5,3,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[6,1,7,3,5,4,8,2]=>{{1,2,3,4,6,7,8},{5}}
[6,3,1,2,5,8,4,7]=>{{1,2,3,4,6,7,8},{5}}
[1,4,7,2,8,5,3,6]=>{{1},{2,4},{3,7},{5,6,8}}
[5,6,8,7,2,4,1,3]=>{{1,2,4,5,6,7},{3,8}}
[6,8,5,7,1,2,4,3]=>{{1,2,3,5,6,8},{4,7}}
[2,8,4,1,7,5,6,3]=>{{1,2,3,4,8},{5,6,7}}
[8,2,4,3,7,5,6,1]=>{{1,8},{2},{3,4},{5,6,7}}
[6,8,2,1,5,7,3,4]=>{{1,2,3,4,6,7,8},{5}}
[7,2,8,4,1,6,3,5]=>{{1,3,5,7,8},{2},{4},{6}}
[1,2,4,8,6,5,3,7]=>{{1},{2},{3,4,7,8},{5,6}}
[7,1,5,6,8,4,3,2]=>{{1,2,3,5,7,8},{4,6}}
[2,7,8,1,4,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[4,8,2,5,7,1,6,3]=>{{1,4,5,6,7},{2,3,8}}
[4,1,6,8,5,3,7,2]=>{{1,2,4,8},{3,6},{5},{7}}
[5,2,6,4,8,3,1,7]=>{{1,5,7,8},{2},{3,6},{4}}
[6,7,1,3,4,5,8,2]=>{{1,3,4,5,6},{2,7,8}}
[1,7,3,2,4,8,5,6]=>{{1},{2,4,5,7},{3},{6,8}}
[1,3,6,5,2,8,4,7]=>{{1},{2,3,4,5,6,7,8}}
[7,1,6,5,3,4,8,2]=>{{1,2,7,8},{3,4,5,6}}
[6,3,4,2,8,7,5,1]=>{{1,5,6,7,8},{2,3,4}}
[4,3,8,7,5,2,6,1]=>{{1,2,3,4,6,7,8},{5}}
[6,8,7,4,2,3,5,1]=>{{1,2,3,5,6,7,8},{4}}
[3,6,4,5,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[8,6,1,3,5,4,2,7]=>{{1,2,3,4,6,7,8},{5}}
[5,3,8,6,1,2,4,7]=>{{1,5},{2,3,4,6,7,8}}
[2,5,6,3,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,5,3,6,8,7,4,1]=>{{1,2,5,8},{3},{4,6,7}}
[4,8,7,3,5,2,6,1]=>{{1,2,3,4,6,7,8},{5}}
[3,8,7,2,6,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,4,8,7,2,1]=>{{1,2,3,5,6,7,8},{4}}
[4,3,8,6,1,5,2,7]=>{{1,4,5,6},{2,3,7,8}}
[4,7,6,2,5,3,8,1]=>{{1,2,4,7,8},{3,6},{5}}
[7,5,2,6,8,1,4,3]=>{{1,4,6,7},{2,3,5,8}}
[8,5,2,7,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[1,8,5,3,6,2,4,7]=>{{1},{2,3,4,5,6,7,8}}
[5,1,7,2,4,3,8,6]=>{{1,2,4,5},{3,6,7,8}}
[1,5,3,4,8,6,2,7]=>{{1},{2,5,7,8},{3},{4},{6}}
[5,4,1,3,8,6,2,7]=>{{1,2,3,4,5,7,8},{6}}
[5,1,8,6,3,4,2,7]=>{{1,2,3,5,7,8},{4,6}}
[4,5,2,8,3,7,6,1]=>{{1,4,8},{2,3,5},{6,7}}
[8,2,3,7,6,4,5,1]=>{{1,8},{2},{3},{4,5,6,7}}
[5,8,2,4,7,6,3,1]=>{{1,2,3,5,7,8},{4},{6}}
[6,8,2,5,3,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,2,5,6,4,8,1,3]=>{{1,7},{2},{3,4,5,6,8}}
[1,6,7,4,8,2,3,5]=>{{1},{2,6},{3,7},{4},{5,8}}
[7,1,3,5,8,2,6,4]=>{{1,2,6,7},{3},{4,5,8}}
[8,2,1,3,5,6,7,4]=>{{1,3,4,8},{2},{5},{6},{7}}
[6,3,1,4,7,5,8,2]=>{{1,2,3,5,6,7,8},{4}}
[4,1,3,8,2,6,7,5]=>{{1,2,4,5,8},{3},{6},{7}}
[2,8,3,6,7,5,4,1]=>{{1,2,8},{3},{4,5,6,7}}
[3,1,7,2,8,5,4,6]=>{{1,2,3,4,7},{5,6,8}}
[3,6,1,4,7,2,8,5]=>{{1,3},{2,6},{4},{5,7,8}}
[1,5,8,4,7,2,3,6]=>{{1},{2,3,5,6,7,8},{4}}
[7,1,3,6,2,8,4,5]=>{{1,2,4,5,6,7,8},{3}}
[6,2,7,4,5,8,1,3]=>{{1,3,6,7,8},{2},{4},{5}}
[2,1,8,4,5,7,3,6]=>{{1,2},{3,6,7,8},{4},{5}}
[1,8,5,7,3,2,4,6]=>{{1},{2,6,8},{3,5},{4,7}}
[2,1,8,5,4,3,6,7]=>{{1,2},{3,6,7,8},{4,5}}
[2,7,4,1,5,3,8,6]=>{{1,2,3,4,6,7,8},{5}}
[7,4,8,6,2,3,1,5]=>{{1,7},{2,3,4,5,6,8}}
[2,7,1,4,6,3,8,5]=>{{1,2,3,5,6,7,8},{4}}
[4,7,5,6,8,1,3,2]=>{{1,4,6},{2,3,5,7,8}}
[7,1,3,2,8,5,4,6]=>{{1,2,4,7},{3},{5,6,8}}
[2,8,5,4,1,3,6,7]=>{{1,2,3,5,6,7,8},{4}}
[5,1,7,4,2,3,8,6]=>{{1,2,5},{3,6,7,8},{4}}
[3,8,6,5,1,4,2,7]=>{{1,3,4,5,6},{2,7,8}}
[1,3,4,8,6,5,2,7]=>{{1},{2,3,4,7,8},{5,6}}
[4,1,8,6,5,3,2,7]=>{{1,2,3,4,6,7,8},{5}}
[4,8,5,2,7,3,6,1]=>{{1,2,4,8},{3,5,6,7}}
[7,2,8,5,3,6,4,1]=>{{1,3,4,5,7,8},{2},{6}}
[5,2,8,4,3,7,6,1]=>{{1,3,5,8},{2},{4},{6,7}}
[8,4,7,5,2,3,6,1]=>{{1,8},{2,4,5},{3,6,7}}
[7,5,2,8,4,6,1,3]=>{{1,7},{2,3,4,5,8},{6}}
[5,7,4,3,6,2,8,1]=>{{1,2,5,6,7,8},{3,4}}
[6,7,5,1,2,8,3,4]=>{{1,4,6,8},{2,3,5,7}}
[5,2,6,8,3,4,7,1]=>{{1,3,4,5,6,8},{2},{7}}
[7,6,2,4,5,8,3,1]=>{{1,2,3,6,7,8},{4},{5}}
[3,6,8,4,7,2,5,1]=>{{1,3,8},{2,6},{4},{5,7}}
[7,6,3,8,4,2,5,1]=>{{1,4,5,7,8},{2,6},{3}}
[2,6,3,8,4,7,5,1]=>{{1,2,4,5,6,7,8},{3}}
[7,2,3,6,5,8,4,1]=>{{1,4,6,7,8},{2},{3},{5}}
[6,2,7,5,8,3,1,4]=>{{1,3,6,7},{2},{4,5,8}}
[2,8,3,6,4,5,7,1]=>{{1,2,8},{3},{4,5,6},{7}}
[2,1,5,6,8,3,7,4]=>{{1,2},{3,4,5,6,8},{7}}
[5,8,1,2,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[1,6,8,3,2,7,4,5]=>{{1},{2,3,4,5,6,7,8}}
[6,5,7,2,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,2,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,3,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,8,2,7,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,5,8,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,3,6,4,8,2,1]=>{{1,4,5,6,8},{2,7},{3}}
[1,5,6,4,8,2,7,3]=>{{1},{2,3,5,6,8},{4},{7}}
[3,1,5,6,4,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[3,5,1,6,4,7,8,2]=>{{1,3},{2,4,5,6,7,8}}
[3,6,1,4,2,7,8,5]=>{{1,3},{2,5,6,7,8},{4}}
[1,2,6,4,3,8,5,7]=>{{1},{2},{3,5,6,7,8},{4}}
[1,2,6,3,5,8,7,4]=>{{1},{2},{3,4,6,8},{5},{7}}
[2,3,5,1,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,3,6,1,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,5,4,8,6,2]=>{{1,2,3,6,7,8},{4,5}}
[1,2,7,6,4,8,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,7,3,6,8,5,4]=>{{1},{2},{3,4,5,6,7,8}}
[2,3,6,1,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[1,2,5,8,4,7,3,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,3,6,8,5,2,7,4]=>{{1},{2,3,6},{4,8},{5},{7}}
[1,2,6,8,5,4,3,7]=>{{1},{2},{3,4,6,7,8},{5}}
[1,3,5,8,2,4,7,6]=>{{1},{2,3,5},{4,6,8},{7}}
[1,4,6,8,3,2,5,7]=>{{1},{2,3,4,5,6,7,8}}
[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[1,2,6,7,3,8,5,4]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,5,7,3,8,6,4]=>{{1},{2},{3,5},{4,6,7,8}}
[3,1,5,7,6,8,4,2]=>{{1,2,3,5,6,8},{4,7}}
[3,5,4,6,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,3,6,5,8,7,1,4]=>{{1,2,3,6,7},{4,5,8}}
[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,1,6,7,5,8,4,2]=>{{1,2,3,6,8},{4,7},{5}}
[4,6,2,7,5,8,3,1]=>{{1,2,3,4,6,7,8},{5}}
[3,5,7,4,8,2,6,1]=>{{1,2,3,5,6,7,8},{4}}
[2,4,7,6,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[1,4,6,8,3,5,7,2]=>{{1},{2,4,8},{3,5,6},{7}}
[1,3,5,8,2,7,4,6]=>{{1},{2,3,5},{4,6,7,8}}
[1,2,5,8,4,7,6,3]=>{{1},{2},{3,4,5,8},{6,7}}
[1,2,5,8,7,4,3,6]=>{{1},{2},{3,5,7},{4,6,8}}
[1,3,5,8,7,2,4,6]=>{{1},{2,3,4,5,6,7,8}}
[5,7,1,2,8,6,4,3]=>{{1,3,5,8},{2,4,7},{6}}
[6,4,5,7,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,3,4,7,2,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[3,2,7,4,6,8,1,5]=>{{1,3,7},{2},{4},{5,6,8}}
[5,3,6,2,7,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,6,3,4,7,1,5,8]=>{{1,2,6},{3},{4},{5,7},{8}}
[2,7,3,4,5,8,1,6]=>{{1,2,7},{3},{4},{5},{6,8}}
[3,7,4,5,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,3,6,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[4,7,6,2,3,8,1,5]=>{{1,2,4,7},{3,5,6,8}}
[7,3,5,2,4,8,1,6]=>{{1,7},{2,3,4,5},{6,8}}
[7,6,2,4,5,8,1,3]=>{{1,7},{2,3,6,8},{4},{5}}
[6,5,2,3,4,8,1,7]=>{{1,6,7,8},{2,3,4,5}}
[5,3,1,2,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[6,5,2,3,7,1,4,8]=>{{1,6},{2,3,4,5,7},{8}}
[5,2,1,7,3,4,6,8]=>{{1,3,5},{2},{4,6,7},{8}}
[5,2,1,8,3,4,6,7]=>{{1,3,5},{2},{4,6,7,8}}
[6,3,2,8,4,5,7,1]=>{{1,4,5,6,8},{2,3},{7}}
[7,3,1,2,8,4,6,5]=>{{1,2,3,4,6,7},{5,8}}
[6,4,1,3,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[6,2,3,1,8,4,7,5]=>{{1,4,6},{2},{3},{5,8},{7}}
[8,3,5,2,7,1,4,6]=>{{1,6,8},{2,3,4,5,7}}
[8,6,2,4,7,1,5,3]=>{{1,2,3,6,8},{4},{5,7}}
[8,5,2,3,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,7,3,4,5,6]=>{{1,3,4,5,6,7,8},{2}}
[8,6,3,7,2,4,5,1]=>{{1,8},{2,4,5,6,7},{3}}
[7,1,6,2,3,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[8,2,7,3,4,5,6,1]=>{{1,8},{2},{3,4,5,6,7}}
[8,1,6,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,3,4,5,6,2]=>{{1,2,8},{3,4,5,6,7}}
[8,6,1,7,2,4,5,3]=>{{1,3,8},{2,4,5,6,7}}
[8,1,5,7,2,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[1,7,5,8,2,3,6,4]=>{{1},{2,3,5,6,7},{4,8}}
[7,2,1,8,3,4,5,6]=>{{1,3,5,7},{2},{4,6,8}}
[7,3,8,2,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,2,8,3,4,5,6,1]=>{{1,3,4,5,6,7,8},{2}}
[1,7,8,3,4,5,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,4,5,8,3,6,7,2]=>{{1},{2,4,8},{3,5},{6},{7}}
[2,5,7,1,8,3,6,4]=>{{1,2,4,5,8},{3,6,7}}
[6,2,7,1,8,4,5,3]=>{{1,4,6},{2},{3,5,7,8}}
[4,7,1,3,8,5,6,2]=>{{1,3,4},{2,5,6,7,8}}
[1,6,2,8,4,5,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[4,1,3,6,8,2,7,5]=>{{1,2,4,6},{3},{5,8},{7}}
[5,3,4,6,8,2,7,1]=>{{1,5,8},{2,3,4,6},{7}}
[4,6,3,8,7,1,2,5]=>{{1,2,4,5,6,7,8},{3}}
[6,4,5,8,7,1,2,3]=>{{1,6},{2,3,4,5,7,8}}
[5,3,4,8,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[3,2,8,7,1,4,6,5]=>{{1,3,5,8},{2},{4,6,7}}
[3,1,8,7,2,4,6,5]=>{{1,2,3,5,8},{4,6,7}}
[5,3,7,6,1,2,4,8]=>{{1,5},{2,3,4,6,7},{8}}
[1,8,3,7,2,4,5,6]=>{{1},{2,4,5,6,7,8},{3}}
[3,8,1,7,2,4,5,6]=>{{1,3},{2,4,5,6,7,8}}
[6,8,2,3,5,1,4,7]=>{{1,6},{2,3,4,7,8},{5}}
[4,7,8,2,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,2,8,7,1,4,5,3]=>{{1,4,5,6,7},{2},{3,8}}
[3,8,7,1,4,5,6,2]=>{{1,3,4,5,6,7},{2,8}}
[2,8,6,1,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,1,3,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[1,7,6,2,3,4,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,6,2,3,4,5,7]=>{{1},{2,3,4,5,6,7,8}}
[2,8,7,3,4,5,6,1]=>{{1,2,8},{3,4,5,6,7}}
[3,8,7,2,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,8,3,6,2,4,5,1]=>{{1,2,5,7,8},{3},{4,6}}
[1,5,8,7,2,3,6,4]=>{{1},{2,5},{3,4,6,7,8}}
[8,7,6,1,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[3,6,2,4,7,1,8,5]=>{{1,2,3,6},{4},{5,7,8}}
[3,4,7,2,5,1,8,6]=>{{1,3,6,7,8},{2,4},{5}}
[2,1,6,4,8,5,3,7]=>{{1,2},{3,5,6,7,8},{4}}
[4,1,8,5,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[3,6,2,5,7,1,4,8]=>{{1,2,3,6},{4,5,7},{8}}
[1,2,8,3,7,5,4,6]=>{{1},{2},{3,4,5,6,7,8}}
[6,1,3,2,8,5,4,7]=>{{1,2,4,5,6,7,8},{3}}
[5,6,1,2,8,4,3,7]=>{{1,3,5,7,8},{2,4,6}}
[1,6,3,8,7,4,2,5]=>{{1},{2,4,5,6,7,8},{3}}
[4,3,8,1,2,6,7,5]=>{{1,4},{2,3,5,8},{6},{7}}
[3,6,8,7,1,2,5,4]=>{{1,3,4,5,7,8},{2,6}}
[6,5,7,2,4,8,1,3]=>{{1,3,6,7,8},{2,4,5}}
[3,4,1,6,5,8,7,2]=>{{1,3},{2,4,6,8},{5},{7}}
[3,5,1,2,4,8,7,6]=>{{1,3},{2,4,5},{6,8},{7}}
[3,7,5,2,1,4,6,8]=>{{1,3,5},{2,4,6,7},{8}}
[3,8,5,2,7,4,1,6]=>{{1,3,5,7},{2,4,6,8}}
[5,2,8,4,7,3,1,6]=>{{1,5,7},{2},{3,6,8},{4}}
[5,2,7,4,1,3,6,8]=>{{1,5},{2},{3,6,7},{4},{8}}
[4,3,5,1,2,8,7,6]=>{{1,4},{2,3,5},{6,8},{7}}
[3,1,4,6,2,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[1,4,6,5,2,8,7,3]=>{{1},{2,4,5},{3,6,8},{7}}
[3,4,5,6,1,8,7,2]=>{{1,3,5},{2,4,6,8},{7}}
[3,4,5,8,7,2,1,6]=>{{1,3,5,7},{2,4,6,8}}
[1,4,7,2,6,3,5,8]=>{{1},{2,4},{3,5,6,7},{8}}
[8,4,7,5,2,1,6,3]=>{{1,3,6,7,8},{2,4,5}}
[8,1,4,7,2,3,6,5]=>{{1,2,5,8},{3,4,6,7}}
[1,8,5,7,3,4,6,2]=>{{1},{2,8},{3,5},{4,6,7}}
[6,3,5,1,7,4,2,8]=>{{1,4,6},{2,3,5,7},{8}}
[6,1,4,8,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,5,7,1,2,3]=>{{1,6},{2,4,5,7},{3,8}}
[5,4,8,1,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,4,8,6,3,7,2,5]=>{{1},{2,4,6,7},{3,5,8}}
[5,4,7,6,3,8,1,2]=>{{1,3,5,7},{2,4,6,8}}
[4,6,3,7,5,8,1,2]=>{{1,4,7},{2,6,8},{3},{5}}
[4,1,3,5,8,6,2,7]=>{{1,2,4,5,7,8},{3},{6}}
[5,7,4,3,8,1,2,6]=>{{1,5,6,8},{2,7},{3,4}}
[1,4,8,3,7,6,5,2]=>{{1},{2,3,4,8},{5,7},{6}}
[4,3,8,2,1,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[3,8,4,2,7,1,5,6]=>{{1,2,3,4,6,8},{5,7}}
[3,1,2,5,7,6,4,8]=>{{1,2,3},{4,5,7},{6},{8}}
[1,8,2,7,6,5,4,3]=>{{1},{2,3,8},{4,7},{5,6}}
[3,8,1,6,7,5,4,2]=>{{1,3},{2,8},{4,5,6,7}}
[3,7,2,6,8,5,1,4]=>{{1,2,3,7},{4,5,6,8}}
[7,2,3,8,5,6,1,4]=>{{1,7},{2},{3},{4,8},{5},{6}}
[8,2,1,7,5,6,4,3]=>{{1,3,8},{2},{4,7},{5},{6}}
[8,1,3,6,5,7,4,2]=>{{1,2,8},{3},{4,6,7},{5}}
[8,2,4,3,6,1,5,7]=>{{1,5,6,7,8},{2},{3,4}}
[1,7,8,5,4,3,6,2]=>{{1},{2,3,6,7,8},{4,5}}
[1,8,4,5,3,2,6,7]=>{{1},{2,6,7,8},{3,4,5}}
[7,8,5,4,3,1,6,2]=>{{1,6,7},{2,8},{3,5},{4}}
[7,1,6,3,4,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[6,8,7,1,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,4,2,7,5,8]=>{{1,3},{2,5,6,7},{4},{8}}
[3,4,1,8,5,7,6,2]=>{{1,3},{2,4,8},{5},{6,7}}
[3,6,5,1,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,8,5,6,7,2,1,4]=>{{1,3,5,7},{2,4,6,8}}
[8,1,7,6,2,4,3,5]=>{{1,2,5,8},{3,7},{4,6}}
[8,5,6,1,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,4,7,1,3,2]=>{{1,2,6,8},{3,5,7},{4}}
[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,3,6,1,7,2,4,5]=>{{1,4,5,7,8},{2,3,6}}
[1,8,6,5,7,3,4,2]=>{{1},{2,8},{3,6},{4,5,7}}
[1,7,5,3,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,1,6,5,8,3,2]=>{{1,3,7},{2,4,6,8},{5}}
[4,1,5,8,7,6,3,2]=>{{1,2,4,8},{3,5,7},{6}}
[1,2,5,8,6,7,3,4]=>{{1},{2},{3,5,6,7},{4,8}}
[4,2,1,5,8,7,3,6]=>{{1,3,4,5,6,7,8},{2}}
[5,2,4,6,1,7,3,8]=>{{1,5},{2},{3,4,6,7},{8}}
[1,5,3,6,8,7,4,2]=>{{1},{2,5,8},{3},{4,6,7}}
[3,5,4,6,1,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,5,7,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}
[1,4,5,6,8,7,2,3]=>{{1},{2,4,6,7},{3,5,8}}
[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[1,7,3,6,5,2,8,4]=>{{1},{2,4,6,7,8},{3},{5}}
[8,6,2,5,4,1,7,3]=>{{1,2,3,6,8},{4,5},{7}}
[3,7,2,6,5,4,1,8]=>{{1,2,3,7},{4,6},{5},{8}}
[7,6,2,5,4,3,1,8]=>{{1,7},{2,3,6},{4,5},{8}}
[4,7,5,2,6,3,1,8]=>{{1,2,4,7},{3,5,6},{8}}
[3,2,6,4,7,5,1,8]=>{{1,3,5,6,7},{2},{4},{8}}
[6,2,3,7,5,4,1,8]=>{{1,4,6,7},{2},{3},{5},{8}}
[1,3,4,7,6,2,8,5]=>{{1},{2,3,4,5,6,7,8}}
[2,8,3,6,1,7,5,4]=>{{1,2,4,5,6,7,8},{3}}
[8,7,2,5,1,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[3,8,2,6,5,1,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[7,8,2,5,4,1,6,3]=>{{1,6,7},{2,3,8},{4,5}}
[4,8,5,2,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[4,5,1,3,7,2,8,6]=>{{1,3,4},{2,5,6,7,8}}
[6,1,3,7,5,2,8,4]=>{{1,2,6},{3},{4,7,8},{5}}
[7,1,3,6,2,8,5,4]=>{{1,2,5,7},{3},{4,6,8}}
[8,1,3,6,2,7,5,4]=>{{1,2,4,5,6,7,8},{3}}
[1,2,4,7,3,8,6,5]=>{{1},{2},{3,4,5,6,7,8}}
[7,1,8,2,6,5,4,3]=>{{1,2,4,7},{3,8},{5,6}}
[3,1,8,6,2,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[4,1,7,8,2,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[5,6,1,8,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[4,2,7,8,1,6,5,3]=>{{1,3,4,5,7,8},{2},{6}}
[3,2,8,6,1,7,5,4]=>{{1,3,4,5,6,7,8},{2}}
[7,2,8,1,6,5,4,3]=>{{1,4,7},{2},{3,8},{5,6}}
[1,8,7,2,6,5,4,3]=>{{1},{2,3,4,7,8},{5,6}}
[2,8,7,1,6,5,4,3]=>{{1,2,3,4,7,8},{5,6}}
[3,8,7,1,6,5,4,2]=>{{1,3,4,7},{2,8},{5,6}}
[4,8,7,5,1,6,3,2]=>{{1,4,5},{2,8},{3,7},{6}}
[6,7,8,5,1,4,3,2]=>{{1,4,5,6},{2,3,7,8}}
[5,6,3,8,4,1,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[7,3,8,5,4,1,6,2]=>{{1,6,7},{2,3,8},{4,5}}
[3,4,8,6,5,1,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[8,3,7,5,1,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[1,4,8,6,2,7,5,3]=>{{1},{2,4,5,6,7},{3,8}}
[8,4,6,7,1,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,4,7,8,1,3,2]=>{{1,2,5,6,8},{3,4,7}}
[3,4,6,5,1,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[7,3,5,1,2,8,6,4]=>{{1,4,6,7,8},{2,3,5}}
[1,4,6,2,3,8,7,5]=>{{1},{2,4},{3,5,6,8},{7}}
[1,3,2,7,4,8,6,5]=>{{1},{2,3},{4,5,6,7,8}}
[7,2,1,6,3,8,5,4]=>{{1,3,5,7},{2},{4,6,8}}
[2,3,1,7,6,4,8,5]=>{{1,2,3},{4,5,6,7,8}}
[4,5,2,1,7,3,8,6]=>{{1,4},{2,3,5,6,7,8}}
[5,6,7,1,2,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,1,2,8,6,3]=>{{1,4},{2,3,5,6,7,8}}
[3,7,1,6,2,8,5,4]=>{{1,3},{2,5,7},{4,6,8}}
[7,6,1,2,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[2,7,1,3,8,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[8,6,1,2,7,5,4,3]=>{{1,3,8},{2,4,5,6,7}}
[1,7,2,3,8,6,5,4]=>{{1},{2,3,4,5,7,8},{6}}
[8,7,1,2,6,5,4,3]=>{{1,3,8},{2,4,7},{5,6}}
[7,8,1,2,6,5,4,3]=>{{1,2,3,4,7,8},{5,6}}
[3,8,1,6,2,7,5,4]=>{{1,3},{2,4,5,6,7,8}}
[4,8,5,1,2,7,6,3]=>{{1,4},{2,3,5,8},{6,7}}
[5,6,8,1,2,7,4,3]=>{{1,2,4,5,6,7},{3,8}}
[2,1,3,7,4,8,6,5]=>{{1,2},{3},{4,5,6,7,8}}
[4,2,7,3,6,8,1,5]=>{{1,3,4,7},{2},{5,6,8}}
[5,3,6,4,2,8,1,7]=>{{1,2,3,5,6,7,8},{4}}
[4,1,5,3,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,2,6,4,7,3,1,8]=>{{1,5,7},{2},{3,6},{4},{8}}
[2,6,3,4,7,5,1,8]=>{{1,2,5,6,7},{3},{4},{8}}
[2,6,3,5,4,8,1,7]=>{{1,2,6,7,8},{3},{4,5}}
[2,7,4,3,5,8,1,6]=>{{1,2,7},{3,4},{5},{6,8}}
[7,3,6,4,2,8,1,5]=>{{1,7},{2,3,5,6,8},{4}}
[7,6,4,5,2,8,1,3]=>{{1,7},{2,3,4,5,6,8}}
[5,4,3,1,8,2,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[6,5,4,2,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,1,7,2,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[5,4,1,8,3,2,6,7]=>{{1,3,5},{2,4,6,7,8}}
[6,5,2,8,3,4,7,1]=>{{1,4,6,8},{2,3,5},{7}}
[7,4,2,1,8,3,6,5]=>{{1,2,3,4,6,7},{5,8}}
[6,5,3,4,8,2,7,1]=>{{1,2,5,6,8},{3},{4},{7}}
[6,1,5,3,8,2,7,4]=>{{1,2,6},{3,4,5,8},{7}}
[4,6,3,1,8,2,7,5]=>{{1,4},{2,6},{3},{5,8},{7}}
[5,8,4,2,7,3,1,6]=>{{1,5,7},{2,3,4,6,8}}
[8,2,6,4,7,3,1,5]=>{{1,5,7,8},{2},{3,6},{4}}
[8,6,2,5,7,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,2,6,4,1,7]=>{{1,7,8},{2,4,5,6},{3}}
[8,3,1,7,2,5,4,6]=>{{1,2,3,5,6,8},{4,7}}
[7,5,2,6,4,3,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[7,1,6,2,5,4,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[8,1,7,3,5,6,4,2]=>{{1,2,8},{3,4,7},{5},{6}}
[8,6,1,7,4,5,2,3]=>{{1,3,8},{2,4,5,6,7}}
[8,1,3,7,2,6,5,4]=>{{1,2,4,5,7,8},{3},{6}}
[1,7,6,8,3,2,4,5]=>{{1},{2,3,4,5,6,7,8}}
[7,1,5,8,4,2,6,3]=>{{1,2,6,7},{3,4,5,8}}
[7,3,8,4,5,2,6,1]=>{{1,2,3,6,7,8},{4},{5}}
[7,2,8,5,3,4,6,1]=>{{1,3,4,5,6,7,8},{2}}
[6,1,8,4,3,2,5,7]=>{{1,2,6},{3,5,7,8},{4}}
[6,1,7,4,2,5,3,8]=>{{1,2,5,6},{3,7},{4},{8}}
[1,2,7,3,4,6,5,8]=>{{1},{2},{3,4,5,7},{6},{8}}
[1,7,8,4,3,5,6,2]=>{{1},{2,3,5,6,7,8},{4}}
[1,6,2,8,3,5,7,4]=>{{1},{2,3,5,6},{4,8},{7}}
[2,6,1,7,3,5,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[3,1,5,8,4,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,6,8,2,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[5,7,4,8,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,2,7,3,1,6]=>{{1,5,7},{2,4},{3,6,8}}
[5,2,8,7,3,4,1,6]=>{{1,3,4,5,6,7,8},{2}}
[6,4,7,5,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[1,8,3,7,6,2,4,5]=>{{1},{2,5,6,8},{3},{4,7}}
[5,8,3,2,6,4,1,7]=>{{1,2,4,5,6,7,8},{3}}
[6,8,2,4,7,5,1,3]=>{{1,5,6,7},{2,3,8},{4}}
[7,3,8,2,6,4,1,5]=>{{1,7},{2,3,4,5,6,8}}
[4,6,8,2,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,6,8,7,3,4,1,5]=>{{1,2,4,6,7},{3,5,8}}
[7,2,8,6,3,5,1,4]=>{{1,7},{2},{3,4,5,6,8}}
[6,8,1,7,2,5,4,3]=>{{1,2,3,5,6,8},{4,7}}
[3,8,7,4,5,6,1,2]=>{{1,3,7},{2,8},{4},{5},{6}}
[2,8,6,4,3,5,1,7]=>{{1,2,7,8},{3,5,6},{4}}
[2,7,6,3,5,4,1,8]=>{{1,2,7},{3,4,6},{5},{8}}
[1,7,6,5,2,4,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,6,5,3,2,4,7]=>{{1},{2,3,4,5,6,7,8}}
[3,8,7,4,6,2,5,1]=>{{1,2,3,5,6,7,8},{4}}
[5,8,3,7,6,2,4,1]=>{{1,2,5,6,8},{3},{4,7}}
[7,1,8,6,5,2,3,4]=>{{1,2,3,4,6,7,8},{5}}
[8,4,7,5,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,2,5,4,3,1,6]=>{{1,2,3,6,7,8},{4,5}}
[6,8,3,2,5,4,7,1]=>{{1,2,4,6,8},{3},{5},{7}}
[1,5,7,8,4,3,6,2]=>{{1},{2,4,5,8},{3,6,7}}
[6,3,8,1,5,4,7,2]=>{{1,4,6},{2,3,8},{5},{7}}
[6,2,1,8,5,4,7,3]=>{{1,3,4,6,8},{2},{5},{7}}
[2,6,5,7,4,1,3,8]=>{{1,2,6},{3,4,5,7},{8}}
[2,5,6,8,4,3,7,1]=>{{1,2,4,5,8},{3,6},{7}}
[2,5,4,7,1,8,6,3]=>{{1,2,5},{3,4,6,7,8}}
[5,2,1,8,7,6,4,3]=>{{1,3,4,5,7,8},{2},{6}}
[4,8,6,7,5,3,1,2]=>{{1,4,7},{2,8},{3,6},{5}}
[6,5,4,8,2,1,7,3]=>{{1,6},{2,5},{3,4,8},{7}}
[5,8,4,7,2,6,3,1]=>{{1,2,5,8},{3,4,7},{6}}
[5,8,3,2,7,6,4,1]=>{{1,2,4,5,7,8},{3},{6}}
[5,2,1,4,3,6,7,8]=>{{1,3,5},{2},{4},{6},{7},{8}}
[3,5,7,4,2,6,1,8]=>{{1,3,7},{2,5},{4},{6},{8}}
[4,2,1,6,5,3,7,8]=>{{1,3,4,6},{2},{5},{7},{8}}
[4,2,1,5,7,6,3,8]=>{{1,3,4,5,7},{2},{6},{8}}
[3,5,4,7,1,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}
[3,4,5,8,6,7,1,2]=>{{1,3,5,6,7},{2,4,8}}
[4,3,5,1,6,8,7,2]=>{{1,4},{2,3,5,6,8},{7}}
[2,1,7,3,8,4,6,5]=>{{1,2},{3,4,6,7},{5,8}}
[4,1,8,2,7,3,6,5]=>{{1,2,4},{3,5,6,7,8}}
[4,1,7,2,8,3,6,5]=>{{1,2,4},{3,6,7},{5,8}}
[7,1,3,2,8,4,6,5]=>{{1,2,4,6,7},{3},{5,8}}
[7,1,8,2,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,2,5,3,6,4]=>{{1,2,4,8},{3,6,7},{5}}
[7,1,5,2,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,7,2,8,3,6,4]=>{{1,2,4,5,8},{3,6,7}}
[5,1,8,2,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,2,4,3,7,6]=>{{1,2,4,5},{3,6,8},{7}}
[8,1,6,2,4,3,7,5]=>{{1,2,4,5,8},{3,6},{7}}
[6,1,8,2,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[6,1,8,2,5,3,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[8,1,6,2,5,3,7,4]=>{{1,2,4,8},{3,6},{5},{7}}
[8,1,6,2,7,3,5,4]=>{{1,2,4,8},{3,6},{5,7}}
[6,1,8,2,7,3,5,4]=>{{1,2,3,4,6,8},{5,7}}
[6,1,7,2,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[6,1,7,2,5,3,8,4]=>{{1,2,3,4,6,7,8},{5}}
[6,1,7,2,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,2,4,3,8,7]=>{{1,2,4,5},{3,6},{7,8}}
[7,1,5,2,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,2,4,3,8,5]=>{{1,2,4,5,7,8},{3,6}}
[7,1,6,2,5,3,8,4]=>{{1,2,4,7,8},{3,6},{5}}
[7,1,6,2,8,3,5,4]=>{{1,2,4,5,7,8},{3,6}}
[7,1,8,2,6,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[1,8,2,7,5,4,6,3]=>{{1},{2,3,8},{4,6,7},{5}}
[1,8,2,7,4,3,5,6]=>{{1},{2,3,6,8},{4,5,7}}
[1,8,6,4,7,2,3,5]=>{{1},{2,3,5,6,7,8},{4}}
[1,8,4,2,6,3,5,7]=>{{1},{2,3,4,5,6,7,8}}
[7,4,8,1,5,2,3,6]=>{{1,2,3,4,6,7,8},{5}}
[4,1,7,2,6,3,5,8]=>{{1,2,4},{3,5,6,7},{8}}
[5,1,7,4,3,6,2,8]=>{{1,2,3,5,7},{4},{6},{8}}
[7,5,8,3,2,4,1,6]=>{{1,7},{2,5},{3,4,6,8}}
[1,8,5,4,3,6,2,7]=>{{1},{2,7,8},{3,5},{4},{6}}
[1,8,5,4,3,7,2,6]=>{{1},{2,6,7,8},{3,5},{4}}
[1,8,5,4,7,2,6,3]=>{{1},{2,3,5,6,7,8},{4}}
[1,8,4,2,5,3,7,6]=>{{1},{2,3,4,6,8},{5},{7}}
[1,8,5,4,2,6,7,3]=>{{1},{2,3,5,8},{4},{6},{7}}
[7,4,8,2,1,3,5,6]=>{{1,5,7},{2,4},{3,6,8}}
[4,1,7,3,2,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,4,8,2,3,6,1]=>{{1,3,4,6,7,8},{2,5}}
[3,1,7,2,6,8,4,5]=>{{1,2,3,4,7},{5,6,8}}
[5,1,7,4,2,6,8,3]=>{{1,2,5},{3,7,8},{4},{6}}
[4,1,6,3,2,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,3,1,6,2,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[6,5,4,3,7,1,8,2]=>{{1,6},{2,5,7,8},{3,4}}
[6,5,1,7,3,8,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,3,2,8,5,7,1,4]=>{{1,6,7},{2,3},{4,8},{5}}
[6,5,4,3,8,2,7,1]=>{{1,2,5,6,8},{3,4},{7}}
[6,5,4,3,8,7,1,2]=>{{1,6,7},{2,5,8},{3,4}}
[7,6,3,8,5,4,1,2]=>{{1,7},{2,4,6,8},{3},{5}}
[5,4,8,2,1,7,3,6]=>{{1,5},{2,4},{3,6,7,8}}
[6,4,2,8,5,1,3,7]=>{{1,6},{2,3,4,7,8},{5}}
[7,6,4,8,5,1,2,3]=>{{1,2,6,7},{3,4,8},{5}}
[7,2,8,6,3,1,4,5]=>{{1,4,6,7},{2},{3,5,8}}
[7,2,8,6,1,5,3,4]=>{{1,3,4,5,6,7,8},{2}}
[2,1,7,8,3,6,4,5]=>{{1,2},{3,4,5,7,8},{6}}
[6,4,1,7,8,2,3,5]=>{{1,2,3,4,6,7},{5,8}}
[4,2,1,6,7,3,5,8]=>{{1,3,4,6},{2},{5,7},{8}}
[4,3,1,5,2,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[5,4,2,7,3,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[4,1,5,3,2,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[3,1,6,2,8,7,4,5]=>{{1,2,3,4,6,7},{5,8}}
[6,3,1,7,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,1,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,1,6,7,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[6,5,4,2,7,8,3,1]=>{{1,6,8},{2,3,4,5,7}}
[5,4,2,6,3,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,3,1,5,2,6,8,7]=>{{1,2,3,4,5},{6},{7,8}}
[5,4,2,1,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,1,6,7,8,2]=>{{1,2,4,5,6,7,8},{3}}
[6,3,8,1,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[3,6,7,1,2,5,8,4]=>{{1,3,4,7,8},{2,5,6}}
[7,8,3,1,2,5,6,4]=>{{1,2,4,5,6,7,8},{3}}
[7,8,1,3,2,4,6,5]=>{{1,3,4,6,7},{2,5,8}}
[7,8,2,1,3,5,4,6]=>{{1,4,7},{2,3,5,6,8}}
[5,2,3,7,1,8,6,4]=>{{1,5},{2},{3},{4,6,7,8}}
[2,5,3,6,1,8,7,4]=>{{1,2,5},{3},{4,6,8},{7}}
[2,6,7,3,1,8,4,5]=>{{1,2,5,6,8},{3,4,7}}
[2,6,7,1,3,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,2,8,3,1,7,4,5]=>{{1,3,4,5,6,7,8},{2}}
[3,2,5,7,1,8,4,6]=>{{1,3,5},{2},{4,7},{6,8}}
[4,3,1,2,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}
[5,1,2,7,3,6,4,8]=>{{1,2,3,5},{4,7},{6},{8}}
[5,1,4,7,8,2,3,6]=>{{1,2,5,6,8},{3,4,7}}
[5,3,4,7,8,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[3,5,4,6,8,7,1,2]=>{{1,3,4,6,7},{2,5,8}}
[1,5,4,6,8,2,3,7]=>{{1},{2,3,4,5,6,7,8}}
[1,6,7,3,2,4,8,5]=>{{1},{2,3,4,5,6,7,8}}
[1,5,3,6,2,7,8,4]=>{{1},{2,5},{3},{4,6,7,8}}
[5,1,3,7,2,6,8,4]=>{{1,2,5},{3},{4,7,8},{6}}
[5,2,4,7,8,1,6,3]=>{{1,3,4,5,6,7,8},{2}}
[4,2,5,7,6,1,8,3]=>{{1,3,4,5,6,7,8},{2}}
[4,5,2,8,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[5,3,1,8,2,6,7,4]=>{{1,2,3,5},{4,8},{6},{7}}
[6,1,8,3,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,3,5,7,6,8,1,2]=>{{1,4,7},{2,3,5,6,8}}
[4,1,5,7,6,2,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,1,8,6,2,3,7]=>{{1,3,4,7,8},{2,5,6}}
[5,2,1,8,3,6,4,7]=>{{1,3,5},{2},{4,7,8},{6}}
[3,4,2,1,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}
[7,6,5,4,2,1,8,3]=>{{1,2,3,5,6,7,8},{4}}
[7,6,5,4,8,1,3,2]=>{{1,2,3,5,6,7,8},{4}}
[7,6,5,8,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,3,2,1,7,6]=>{{1,6,8},{2,5},{3,4},{7}}
[7,6,5,4,1,8,3,2]=>{{1,3,5,7},{2,6,8},{4}}
[7,6,5,2,8,1,4,3]=>{{1,2,4,6,7},{3,5,8}}
[7,6,5,8,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,5,2,1,4,3]=>{{1,2,4,5,6,7},{3,8}}
[7,8,6,3,2,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,3,2,1,6,5]=>{{1,2,5,6,7,8},{3,4}}
[7,8,2,4,5,1,3,6]=>{{1,2,3,6,7,8},{4},{5}}
[4,6,7,2,5,1,3,8]=>{{1,2,4,6},{3,7},{5},{8}}
[7,8,1,3,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,1,5,2,3,6]=>{{1,3,4,7},{2,6,8},{5}}
[3,6,7,2,1,4,5,8]=>{{1,3,5,7},{2,4,6},{8}}
[5,2,3,6,1,4,7,8]=>{{1,5},{2},{3},{4,6},{7},{8}}
[2,5,3,6,1,4,7,8]=>{{1,2,5},{3},{4,6},{7},{8}}
[2,6,7,3,1,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,7,1,5,2,3,8]=>{{1,4},{2,6},{3,7},{5},{8}}
[4,6,7,3,5,8,1,2]=>{{1,3,4,7},{2,6,8},{5}}
[6,4,7,1,5,2,3,8]=>{{1,2,4,6},{3,7},{5},{8}}
[6,2,7,3,1,4,5,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,2,5,6,1,4,7,8]=>{{1,3,5},{2},{4,6},{7},{8}}
[3,5,2,6,1,4,7,8]=>{{1,2,3,5},{4,6},{7},{8}}
[5,1,4,6,7,2,3,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,4,6,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,5,4,6,7,2,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,7,3,2,4,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,5,3,6,2,4,7,8]=>{{1},{2,5},{3},{4,6},{7},{8}}
[5,1,3,6,2,4,7,8]=>{{1,2,5},{3},{4,6},{7},{8}}
[5,2,4,6,7,1,3,8]=>{{1,3,4,5,6,7},{2},{8}}
[2,5,4,6,7,1,3,8]=>{{1,2,3,4,5,6,7},{8}}
[2,6,7,4,5,1,3,8]=>{{1,2,6},{3,7},{4},{5},{8}}
[6,2,7,4,5,1,3,8]=>{{1,6},{2},{3,7},{4},{5},{8}}
[4,2,5,6,7,1,3,8]=>{{1,4,6},{2},{3,5,7},{8}}
[4,5,2,6,7,1,3,8]=>{{1,4,6},{2,3,5,7},{8}}
[5,3,1,6,2,4,7,8]=>{{1,2,3,5},{4,6},{7},{8}}
[6,1,7,3,2,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[6,1,7,4,5,2,3,8]=>{{1,2,6},{3,7},{4},{5},{8}}
[6,3,7,4,5,8,1,2]=>{{1,2,3,6,7,8},{4},{5}}
[5,4,1,6,7,2,3,8]=>{{1,3,5,7},{2,4,6},{8}}
[5,2,1,6,3,4,7,8]=>{{1,3,5},{2},{4,6},{7},{8}}
[7,3,2,5,4,1,6,8]=>{{1,6,7},{2,3},{4,5},{8}}
[7,3,5,4,2,1,6,8]=>{{1,6,7},{2,3,5},{4},{8}}
[7,3,5,2,4,1,6,8]=>{{1,6,7},{2,3,4,5},{8}}
[7,6,5,2,1,4,3,8]=>{{1,3,5,7},{2,4,6},{8}}
[1,3,6,7,5,2,8,4]=>{{1},{2,3,6},{4,7,8},{5}}
[7,3,4,1,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[7,3,4,1,6,5,2,8]=>{{1,2,3,4,7},{5,6},{8}}
[7,3,4,1,5,6,2,8]=>{{1,2,3,4,7},{5},{6},{8}}
[7,3,2,5,1,6,4,8]=>{{1,4,5,7},{2,3},{6},{8}}
[7,6,5,4,1,3,2,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,3,4,1,5,2,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[1,3,6,7,2,5,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[1,7,4,6,2,8,5,3]=>{{1},{2,5,7},{3,4,6,8}}
[4,3,1,7,2,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[5,6,1,4,7,3,8,2]=>{{1,2,3,5,6,7,8},{4}}
[5,3,2,1,7,4,8,6]=>{{1,4,5,6,7,8},{2,3}}
[1,3,4,5,8,7,2,6]=>{{1},{2,3,4,5,6,7,8}}
[6,3,4,5,8,1,7,2]=>{{1,6},{2,3,4,5,8},{7}}
[2,4,5,1,6,8,7,3]=>{{1,2,4},{3,5,6,8},{7}}
[3,1,2,5,6,8,7,4]=>{{1,2,3},{4,5,6,8},{7}}
[4,3,2,5,6,8,1,7]=>{{1,4,5,6,7,8},{2,3}}
[3,7,5,4,6,8,1,2]=>{{1,2,3,5,6,7,8},{4}}
[3,1,4,6,5,8,2,7]=>{{1,2,3,4,6,7,8},{5}}
[2,3,4,5,8,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[2,3,4,5,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[3,1,4,6,5,8,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[3,7,5,4,6,8,2,1]=>{{1,3,5,6,8},{2,7},{4}}
[5,6,1,4,7,2,8,3]=>{{1,3,5,7,8},{2,6},{4}}
[4,3,1,7,5,6,8,2]=>{{1,2,3,4,7,8},{5},{6}}
[4,3,1,7,6,5,8,2]=>{{1,2,3,4,7,8},{5,6}}
[3,1,4,6,7,8,5,2]=>{{1,2,3,4,6,8},{5,7}}
[1,4,5,2,6,8,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[3,7,5,2,6,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[3,7,5,2,6,8,4,1]=>{{1,3,5,6,8},{2,4,7}}
[5,6,1,2,7,4,8,3]=>{{1,3,5,7,8},{2,4,6}}
[6,3,5,2,4,7,8,1]=>{{1,6,7,8},{2,3,4,5}}
[5,3,2,1,4,7,8,6]=>{{1,4,5},{2,3},{6,7,8}}
[5,3,1,4,2,7,8,6]=>{{1,2,3,5},{4},{6,7,8}}
[5,3,1,2,4,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[7,1,5,2,6,8,4,3]=>{{1,2,4,7},{3,5,6,8}}
[7,1,5,2,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,7,4,6,1,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[2,7,4,6,1,8,5,3]=>{{1,2,5,7},{3,4,6,8}}
[2,3,6,7,1,5,8,4]=>{{1,2,3,5,6},{4,7,8}}
[2,3,6,7,5,1,8,4]=>{{1,2,3,6},{4,7,8},{5}}
[4,3,2,6,7,1,8,5]=>{{1,4,6},{2,3},{5,7,8}}
[7,3,2,5,6,8,1,4]=>{{1,7},{2,3},{4,5,6,8}}
[7,1,5,4,6,8,2,3]=>{{1,2,7},{3,5,6,8},{4}}
[2,7,4,6,5,8,1,3]=>{{1,2,7},{3,4,6,8},{5}}
[7,3,4,5,8,6,1,2]=>{{1,7},{2,3,4,5,8},{6}}
[7,3,4,5,8,1,6,2]=>{{1,6,7},{2,3,4,5,8}}
[7,3,4,5,8,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[1,3,4,5,8,6,2,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,3,4,5,8,2,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[6,3,4,5,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[6,3,4,5,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,3,4,5,8,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[2,7,4,6,5,8,3,1]=>{{1,2,3,4,6,7,8},{5}}
[7,1,5,4,6,8,3,2]=>{{1,2,3,5,6,7,8},{4}}
[7,3,2,5,6,8,4,1]=>{{1,4,5,6,7,8},{2,3}}
[5,7,4,6,1,8,3,2]=>{{1,5},{2,3,4,6,7,8}}
[6,3,4,5,8,1,2,7]=>{{1,6},{2,3,4,5,7,8}}
[7,3,4,5,8,2,1,6]=>{{1,7},{2,3,4,5,6,8}}
[7,3,4,5,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[4,8,6,1,7,5,2,3]=>{{1,4},{2,3,5,6,7,8}}
[4,7,8,2,6,1,5,3]=>{{1,2,4,5,6,7},{3,8}}
[7,6,4,2,8,3,5,1]=>{{1,5,7,8},{2,3,4,6}}
[8,6,4,2,7,5,3,1]=>{{1,8},{2,3,4,5,6,7}}
[8,4,7,3,6,5,1,2]=>{{1,2,3,4,7,8},{5,6}}
[8,4,6,1,7,5,3,2]=>{{1,2,4,8},{3,5,6,7}}
[6,4,7,1,8,3,2,5]=>{{1,2,3,4,6,7},{5,8}}
[7,4,8,3,6,1,5,2]=>{{1,5,6,7},{2,3,4,8}}
[6,2,1,7,3,5,4,8]=>{{1,3,5,6},{2},{4,7},{8}}
[2,1,8,6,3,5,4,7]=>{{1,2},{3,4,5,6,7,8}}
[2,1,7,3,5,8,6,4]=>{{1,2},{3,4,6,7,8},{5}}
[2,7,3,1,5,4,6,8]=>{{1,2,4,6,7},{3},{5},{8}}
[2,6,3,1,4,8,5,7]=>{{1,2,4,5,6,7,8},{3}}
[4,2,1,8,3,6,7,5]=>{{1,3,4,5,8},{2},{6},{7}}
[2,1,8,6,3,5,7,4]=>{{1,2},{3,4,5,6,8},{7}}
[6,2,1,7,3,5,8,4]=>{{1,3,5,6},{2},{4,7,8}}
[2,7,3,1,4,8,5,6]=>{{1,2,4,5,7},{3},{6,8}}
[3,2,1,6,4,5,7,8]=>{{1,3},{2},{4,5,6},{7},{8}}
[3,2,1,5,7,8,4,6]=>{{1,3},{2},{4,5,7},{6,8}}
[2,1,7,3,6,8,4,5]=>{{1,2},{3,4,7},{5,6,8}}
[2,7,3,1,5,6,8,4]=>{{1,2,4,7,8},{3},{5},{6}}
[2,4,7,5,1,6,8,3]=>{{1,2,4,5},{3,7,8},{6}}
[4,3,7,5,6,1,8,2]=>{{1,4,5,6},{2,3,7,8}}
[4,3,6,8,5,1,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[2,6,1,8,3,5,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[2,1,6,8,3,7,4,5]=>{{1,2},{3,4,5,6,7,8}}
[2,1,8,3,5,7,4,6]=>{{1,2},{3,4,6,7,8},{5}}
[3,2,1,5,6,8,4,7]=>{{1,3},{2},{4,5,6,7,8}}
[3,2,1,5,7,4,6,8]=>{{1,3},{2},{4,5,6,7},{8}}
[2,1,7,3,6,4,5,8]=>{{1,2},{3,4,5,6,7},{8}}
[2,1,6,3,5,8,4,7]=>{{1,2},{3,4,6,7,8},{5}}
[8,2,4,1,7,5,6,3]=>{{1,3,4,8},{2},{5,6,7}}
[3,8,4,7,5,1,6,2]=>{{1,3,4,6,7},{2,8},{5}}
[8,4,3,6,1,7,5,2]=>{{1,2,4,5,6,7,8},{3}}
[8,2,1,7,3,5,4,6]=>{{1,3,5,6,8},{2},{4,7}}
[2,6,1,8,3,5,4,7]=>{{1,2,3,5,6},{4,7,8}}
[2,7,3,1,5,6,4,8]=>{{1,2,4,7},{3},{5},{6},{8}}
[2,4,7,5,1,6,3,8]=>{{1,2,4,5},{3,7},{6},{8}}
[8,2,4,1,7,5,3,6]=>{{1,3,4,5,6,7,8},{2}}
[5,8,6,3,1,7,4,2]=>{{1,5},{2,8},{3,4,6,7}}
[2,4,7,1,8,5,3,6]=>{{1,2,4},{3,7},{5,6,8}}
[2,4,8,5,1,6,3,7]=>{{1,2,4,5},{3,7,8},{6}}
[6,2,1,7,3,4,8,5]=>{{1,3,4,5,6,7,8},{2}}
[6,2,1,7,8,3,5,4]=>{{1,3,6},{2},{4,5,7,8}}
[2,7,1,8,3,5,6,4]=>{{1,2,3,5,6,7},{4,8}}
[2,1,8,3,6,4,5,7]=>{{1,2},{3,4,5,6,7,8}}
[3,2,1,6,7,4,5,8]=>{{1,3},{2},{4,6},{5,7},{8}}
[3,2,1,7,4,5,6,8]=>{{1,3},{2},{4,5,6,7},{8}}
[3,2,1,6,8,4,5,7]=>{{1,3},{2},{4,6},{5,7,8}}
[2,1,8,3,7,4,5,6]=>{{1,2},{3,4,6,8},{5,7}}
[2,1,8,3,6,7,4,5]=>{{1,2},{3,4,5,6,7,8}}
[2,4,8,5,1,6,7,3]=>{{1,2,4,5},{3,8},{6},{7}}
[4,3,8,5,6,1,7,2]=>{{1,4,5,6},{2,3,8},{7}}
[3,2,1,8,4,5,6,7]=>{{1,3},{2},{4,5,6,7,8}}
[1,6,8,3,7,2,4,5]=>{{1},{2,6},{3,4,5,7,8}}
[3,8,1,5,7,2,4,6]=>{{1,3},{2,6,8},{4,5,7}}
[1,2,6,8,4,7,3,5]=>{{1},{2},{3,6,7},{4,5,8}}
[6,1,5,8,2,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[1,2,4,8,3,6,7,5]=>{{1},{2},{3,4,5,8},{6},{7}}
[4,1,2,7,8,3,6,5]=>{{1,2,3,4,6,7},{5,8}}
[3,5,7,4,8,6,1,2]=>{{1,3,7},{2,5,8},{4},{6}}
[5,3,8,4,7,6,1,2]=>{{1,5,7},{2,3,8},{4},{6}}
[8,7,1,2,5,4,6,3]=>{{1,3,8},{2,4,6,7},{5}}
[5,8,1,2,3,7,6,4]=>{{1,3,5},{2,4,8},{6,7}}
[1,2,8,4,3,5,7,6]=>{{1},{2},{3,5,6,8},{4},{7}}
[1,2,5,3,7,6,4,8]=>{{1},{2},{3,4,5,7},{6},{8}}
[6,1,2,8,7,4,5,3]=>{{1,2,3,4,6,8},{5,7}}
[7,1,6,2,8,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,2,6,3,8,5,4,7]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,8,5,3,6,4,7]=>{{1},{2},{3,4,5,7,8},{6}}
[1,2,7,3,8,5,4,6]=>{{1},{2},{3,4,7},{5,6,8}}
[4,1,2,7,8,6,3,5]=>{{1,2,3,4,7},{5,8},{6}}
[1,6,2,8,4,3,5,7]=>{{1},{2,3,6},{4,5,7,8}}
[1,6,4,2,7,3,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[1,8,6,3,2,4,5,7]=>{{1},{2,5,7,8},{3,4,6}}
[1,7,3,2,8,4,5,6]=>{{1},{2,4,5,6,7,8},{3}}
[3,1,7,8,6,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,2,4,5,6,3]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,3,5,6,2,4]=>{{1},{2,3,4,7,8},{5},{6}}
[1,3,2,8,7,4,5,6]=>{{1},{2,3},{4,6,8},{5,7}}
[1,8,3,2,6,4,5,7]=>{{1},{2,4,5,6,7,8},{3}}
[1,7,6,3,2,4,5,8]=>{{1},{2,5,7},{3,4,6},{8}}
[1,2,8,4,3,7,5,6]=>{{1},{2},{3,5,6,7,8},{4}}
[8,5,1,7,2,4,6,3]=>{{1,3,8},{2,5},{4,6,7}}
[5,3,8,7,4,6,1,2]=>{{1,4,5,7},{2,3,8},{6}}
[3,8,6,4,7,5,1,2]=>{{1,3,5,6,7},{2,8},{4}}
[6,1,8,2,7,4,5,3]=>{{1,2,4,6},{3,8},{5,7}}
[1,2,5,3,8,6,4,7]=>{{1},{2},{3,4,5,7,8},{6}}
[1,2,7,5,3,6,4,8]=>{{1},{2},{3,4,5,7},{6},{8}}
[1,2,6,3,7,5,4,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,3,7,5,4,8,6]=>{{1},{2},{3},{4,6,7,8},{5}}
[3,7,4,8,6,5,1,2]=>{{1,2,3,4,7,8},{5,6}}
[1,8,2,7,6,4,5,3]=>{{1},{2,3,8},{4,5,6,7}}
[2,8,7,6,5,1,4,3]=>{{1,2,3,4,6,7,8},{5}}
[7,1,6,3,2,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,7,6,3,1,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,8,4,3,6,5,2,7]=>{{1},{2,7,8},{3,4},{5,6}}
[1,8,4,6,5,3,2,7]=>{{1},{2,7,8},{3,4,6},{5}}
[7,4,2,1,6,5,3,8]=>{{1,2,3,4,7},{5,6},{8}}
[7,6,1,4,3,5,2,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,4,1,3,5,2,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[7,3,1,2,4,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[1,8,6,3,4,5,2,7]=>{{1},{2,7,8},{3,4,5,6}}
[1,8,6,7,4,2,5,3]=>{{1},{2,3,6,8},{4,5,7}}
[3,6,2,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,2,4,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[3,4,7,1,5,2,8,6]=>{{1,2,3,4,6,7,8},{5}}
[3,6,7,4,1,5,8,2]=>{{1,2,3,5,6,7,8},{4}}
[4,3,2,7,1,5,8,6]=>{{1,4,5,6,7,8},{2,3}}
[3,1,2,8,6,5,4,7]=>{{1,2,3},{4,7,8},{5,6}}
[5,4,8,6,1,2,3,7]=>{{1,5},{2,4,6},{3,7,8}}
[5,6,8,7,4,3,1,2]=>{{1,4,5,7},{2,3,6,8}}
[1,8,2,7,4,3,6,5]=>{{1},{2,3,4,5,6,7,8}}
[6,5,8,2,3,7,1,4]=>{{1,6,7},{2,3,4,5,8}}
[6,4,8,5,3,1,7,2]=>{{1,6},{2,3,4,5,8},{7}}
[5,7,8,6,1,3,2,4]=>{{1,5},{2,7},{3,4,6,8}}
[2,4,8,1,6,3,7,5]=>{{1,2,4},{3,5,6,8},{7}}
[3,1,2,8,6,4,7,5]=>{{1,2,3},{4,5,6,8},{7}}
[5,3,2,6,4,8,1,7]=>{{1,4,5,6,7,8},{2,3}}
[4,1,6,3,5,8,2,7]=>{{1,2,3,4,6,7,8},{5}}
[2,4,5,3,8,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[1,8,5,3,2,7,6,4]=>{{1},{2,3,4,5,8},{6,7}}
[1,8,4,5,2,6,7,3]=>{{1},{2,3,4,5,8},{6},{7}}
[4,1,2,7,6,5,8,3]=>{{1,2,3,4,7,8},{5,6}}
[2,4,1,6,7,8,5,3]=>{{1,2,3,4,6,8},{5,7}}
[1,8,4,3,6,2,7,5]=>{{1},{2,5,6,8},{3,4},{7}}
[5,6,7,3,2,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,3,6,8,4,1]=>{{1,2,5,6,8},{3,4,7}}
[5,3,2,1,4,8,6,7]=>{{1,4,5},{2,3},{6,7,8}}
[5,3,1,4,2,8,6,7]=>{{1,2,3,5},{4},{6,7,8}}
[7,6,1,3,8,5,4,2]=>{{1,3,4,7},{2,5,6,8}}
[3,4,7,8,1,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,8,1,4,5,2]=>{{1,3,5,7},{2,4,6,8}}
[3,6,2,8,1,5,4,7]=>{{1,2,3,5,6},{4,7,8}}
[2,3,6,8,5,1,4,7]=>{{1,2,3,6},{4,7,8},{5}}
[3,1,6,4,8,2,5,7]=>{{1,2,3,6},{4},{5,7,8}}
[7,3,2,6,8,5,1,4]=>{{1,7},{2,3},{4,5,6,8}}
[7,3,5,8,4,6,1,2]=>{{1,7},{2,3,4,5,8},{6}}
[7,5,2,8,4,1,6,3]=>{{1,6,7},{2,3,4,5,8}}
[7,4,5,8,2,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[1,8,5,2,4,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,8,4,2,3,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[6,4,2,8,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[6,3,4,8,2,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,5,4,8,3,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[2,7,4,8,5,3,6,1]=>{{1,2,3,4,6,7,8},{5}}
[7,1,5,4,8,3,6,2]=>{{1,2,3,5,6,7,8},{4}}
[7,3,2,5,8,4,6,1]=>{{1,4,5,6,7,8},{2,3}}
[8,4,6,3,7,2,5,1]=>{{1,8},{2,3,4,6},{5,7}}
[7,4,6,3,8,5,1,2]=>{{1,7},{2,3,4,5,6,8}}
[2,5,6,8,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,6,2,7,5,3,1]=>{{1,8},{2,4},{3,5,6,7}}
[2,5,7,8,4,1,3,6]=>{{1,2,4,5,6,8},{3,7}}
[3,5,6,8,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,8,1,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[6,5,7,8,3,1,4,2]=>{{1,6},{2,3,4,5,7,8}}
[2,5,7,8,3,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,3,8,1,5,2]=>{{1,6},{2,3,4,5,7,8}}
[7,4,6,3,8,2,1,5]=>{{1,7},{2,3,4,6},{5,8}}
[6,3,2,5,4,8,1,7]=>{{1,6,7,8},{2,3},{4,5}}
[6,4,5,2,3,8,1,7]=>{{1,6,7,8},{2,4},{3,5}}
[6,4,5,3,2,8,1,7]=>{{1,6,7,8},{2,3,4,5}}
[5,4,6,3,8,2,1,7]=>{{1,5,7,8},{2,3,4,6}}
[5,4,7,3,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,8,3,1,6,4]=>{{1,2,3,5,6,7},{4,8}}
[4,5,6,8,2,3,1,7]=>{{1,4,7,8},{2,5},{3,6}}
[5,4,6,2,8,3,1,7]=>{{1,5,7,8},{2,4},{3,6}}
[4,6,7,8,1,3,2,5]=>{{1,4,5,8},{2,3,6,7}}
[4,6,7,8,1,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,8,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,8,1,2,5,3]=>{{1,3,4,5,7,8},{2,6}}
[4,5,7,8,2,1,6,3]=>{{1,3,4,6,7,8},{2,5}}
[5,4,7,2,8,1,6,3]=>{{1,3,5,6,7,8},{2,4}}
[4,3,2,7,8,1,6,5]=>{{1,4,6,7},{2,3},{5,8}}
[3,6,7,8,1,2,5,4]=>{{1,3,5,7},{2,6},{4,8}}
[3,6,7,8,1,5,2,4]=>{{1,2,3,5,6,7},{4,8}}
[3,6,7,8,1,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[2,6,7,8,1,5,4,3]=>{{1,2,5,6},{3,4,7,8}}
[4,2,7,1,5,3,8,6]=>{{1,4},{2},{3,6,7,8},{5}}
[4,2,8,6,1,5,3,7]=>{{1,4,5,6},{2},{3,7,8}}
[3,2,6,7,5,1,4,8]=>{{1,3,6},{2},{4,7},{5},{8}}
[2,7,1,3,5,4,8,6]=>{{1,2,3,4,6,7,8},{5}}
[4,7,2,1,5,8,6,3]=>{{1,4},{2,3,6,7,8},{5}}
[7,2,1,3,5,8,6,4]=>{{1,3,4,6,7,8},{2},{5}}
[2,3,6,4,7,1,5,8]=>{{1,2,3,6},{4},{5,7},{8}}
[1,3,4,8,2,7,5,6]=>{{1},{2,3,4,5,6,7,8}}
[3,1,4,8,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[8,3,1,6,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[4,8,6,2,1,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[4,8,3,6,5,1,7,2]=>{{1,4,6},{2,8},{3},{5},{7}}
[6,4,7,3,5,1,8,2]=>{{1,6},{2,3,4,7,8},{5}}
[6,4,7,5,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,7,5,8,2,4]=>{{1,3},{2,4,6,7,8},{5}}
[7,3,5,1,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}
[4,7,3,5,6,1,8,2]=>{{1,4,5,6},{2,7,8},{3}}
[3,4,6,8,5,1,7,2]=>{{1,3,6},{2,4,8},{5},{7}}
[4,6,8,2,1,5,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[6,8,2,1,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[1,8,2,3,5,7,4,6]=>{{1},{2,3,4,6,7,8},{5}}
[2,7,3,6,1,4,5,8]=>{{1,2,5,7},{3},{4,6},{8}}
[2,6,1,3,5,8,4,7]=>{{1,2,3,4,6,7,8},{5}}
[7,3,2,5,6,1,4,8]=>{{1,4,5,6,7},{2,3},{8}}
[4,7,5,2,6,1,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,2,8,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,2,7,5,3,6]=>{{1,3,5,6,7,8},{2,4}}
[4,5,6,2,7,1,3,8]=>{{1,2,3,4,5,6,7},{8}}
[8,5,1,2,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,2,7,4,8,3,5]=>{{1},{2,3,4,5,6,7,8}}
[6,2,1,7,8,5,3,4]=>{{1,3,4,5,6,7,8},{2}}
[6,7,3,8,4,1,5,2]=>{{1,6},{2,4,5,7,8},{3}}
[2,7,8,4,1,5,6,3]=>{{1,2,5,6,7},{3,8},{4}}
[2,7,1,8,5,6,3,4]=>{{1,2,3,7},{4,8},{5},{6}}
[8,2,5,1,6,7,3,4]=>{{1,4,8},{2},{3,5,6,7}}
[8,2,4,5,1,6,7,3]=>{{1,3,4,5,8},{2},{6},{7}}
[3,8,4,5,6,1,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[4,5,8,3,6,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[4,5,8,3,7,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[4,2,8,3,7,1,6,5]=>{{1,3,4,5,6,7,8},{2}}
[7,2,3,4,8,1,6,5]=>{{1,6,7},{2},{3},{4},{5,8}}
[7,2,3,4,8,1,5,6]=>{{1,5,6,7,8},{2},{3},{4}}
[7,6,3,4,8,5,1,2]=>{{1,7},{2,5,6,8},{3},{4}}
[7,6,3,5,8,4,1,2]=>{{1,7},{2,4,5,6,8},{3}}
[7,6,3,8,4,5,1,2]=>{{1,7},{2,4,5,6,8},{3}}
[7,2,3,8,5,1,4,6]=>{{1,4,6,7,8},{2},{3},{5}}
[7,2,3,8,5,1,6,4]=>{{1,6,7},{2},{3},{4,8},{5}}
[2,6,4,8,1,5,7,3]=>{{1,2,5,6},{3,4,8},{7}}
[7,2,3,8,4,1,5,6]=>{{1,4,5,6,7,8},{2},{3}}
[7,2,3,5,8,1,4,6]=>{{1,4,5,6,7,8},{2},{3}}
[7,8,2,3,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,2,3,6,1,5,4]=>{{1,5,6,7},{2,3,4,8}}
[4,2,6,3,7,1,5,8]=>{{1,3,4,6},{2},{5,7},{8}}
[7,2,3,5,8,1,6,4]=>{{1,6,7},{2},{3},{4,5,8}}
[7,2,3,8,4,1,6,5]=>{{1,6,7},{2},{3},{4,5,8}}
[2,6,4,8,1,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,6,4,8,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,1,2,3,8,4]=>{{1,4,7,8},{2,3,5,6}}
[7,6,5,1,4,2,8,3]=>{{1,3,4,5,7,8},{2,6}}
[2,6,4,5,1,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[3,5,6,4,1,2,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[7,8,5,4,1,2,6,3]=>{{1,2,3,5,6,7,8},{4}}
[3,5,6,4,1,2,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[7,6,5,1,4,2,3,8]=>{{1,3,4,5,7},{2,6},{8}}
[7,6,5,1,2,4,3,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,5,1,2,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,1,3,2,8,4]=>{{1,4,7,8},{2,6},{3,5}}
[7,6,5,1,3,2,4,8]=>{{1,4,7},{2,6},{3,5},{8}}
[7,6,5,1,3,4,2,8]=>{{1,2,4,6,7},{3,5},{8}}
[7,2,3,4,5,1,8,6]=>{{1,6,7,8},{2},{3},{4},{5}}
[2,6,4,3,1,5,8,7]=>{{1,2,5,6},{3,4},{7,8}}
[2,6,4,3,1,8,5,7]=>{{1,2,5,6,7,8},{3,4}}
[2,6,4,3,1,8,7,5]=>{{1,2,5,6,8},{3,4},{7}}
[3,5,8,4,1,2,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[3,5,8,4,1,2,6,7]=>{{1,2,3,5,6,7,8},{4}}
[3,5,8,4,1,6,2,7]=>{{1,2,3,5,7,8},{4},{6}}
[4,2,8,3,6,1,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[3,5,8,4,1,6,7,2]=>{{1,2,3,5,8},{4},{6},{7}}
[2,5,8,4,1,7,3,6]=>{{1,2,5},{3,6,7,8},{4}}
[3,6,4,2,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,2,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,6,4,1,8,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[2,6,4,5,1,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[7,6,5,1,4,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,1,2,8,4,3]=>{{1,4,7},{2,3,5,6,8}}
[7,6,5,1,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,1,8,2,4,3]=>{{1,4,7},{2,6},{3,5,8}}
[7,6,5,1,8,2,3,4]=>{{1,3,4,5,7,8},{2,6}}
[7,6,5,1,8,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,1,4,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,5,1,7,2,8]=>{{1,3,4,5},{2,6,7},{8}}
[2,5,6,4,1,7,8,3]=>{{1,2,5},{3,6,7,8},{4}}
[7,8,5,4,1,6,3,2]=>{{1,3,5,7},{2,8},{4},{6}}
[2,5,6,4,1,7,3,8]=>{{1,2,5},{3,6,7},{4},{8}}
[3,6,4,5,1,7,8,2]=>{{1,3,4,5},{2,6,7,8}}
[7,6,5,1,4,8,3,2]=>{{1,3,4,5,7},{2,6,8}}
[7,6,5,1,8,3,4,2]=>{{1,4,7},{2,3,5,6,8}}
[7,6,5,1,8,4,2,3]=>{{1,2,4,6,7},{3,5,8}}
[4,1,7,6,2,8,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,8,6,2,1,3,5,4]=>{{1,5,7},{2,4,8},{3,6}}
[3,7,6,1,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,6,5,3,1,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,6,1,5,3,2,8,7]=>{{1,3,4,5},{2,6},{7,8}}
[3,6,1,4,2,5,8,7]=>{{1,3},{2,5,6},{4},{7,8}}
[2,6,4,5,7,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,1,6,5,2,4,3]=>{{1,3,8},{2,4,6,7},{5}}
[7,2,5,6,8,1,3,4]=>{{1,3,4,5,6,7,8},{2}}
[6,1,3,4,2,8,7,5]=>{{1,2,5,6,8},{3},{4},{7}}
[2,4,5,6,1,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[8,4,1,6,5,7,3,2]=>{{1,2,3,4,6,7,8},{5}}
[2,8,3,4,7,5,1,6]=>{{1,2,5,6,7,8},{3},{4}}
[6,8,2,7,4,3,5,1]=>{{1,2,3,6,8},{4,5,7}}
[4,7,8,5,1,6,3,2]=>{{1,4,5},{2,3,7,8},{6}}
[8,2,6,4,7,3,5,1]=>{{1,8},{2},{3,6},{4},{5,7}}
[4,8,6,1,7,3,2,5]=>{{1,4},{2,5,7,8},{3,6}}
[8,7,3,2,1,5,4,6]=>{{1,5,6,8},{2,4,7},{3}}
[3,8,5,1,7,2,4,6]=>{{1,3,4,5,7},{2,6,8}}
[6,8,7,1,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,5,1,8,7,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,7,1,8,4,5,6,2]=>{{1,3},{2,4,5,6,7,8}}
[6,2,3,8,4,7,5,1]=>{{1,4,5,6,7,8},{2},{3}}
[8,6,4,3,1,7,2,5]=>{{1,5,8},{2,6,7},{3,4}}
[8,3,7,4,6,1,2,5]=>{{1,5,6,8},{2,3,7},{4}}
[7,1,3,8,6,4,5,2]=>{{1,2,4,5,6,7,8},{3}}
[2,3,5,8,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,1,8,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[4,6,7,2,5,8,3,1]=>{{1,2,4,6,8},{3,7},{5}}
[7,6,2,5,3,8,1,4]=>{{1,7},{2,3,4,5,6,8}}
[6,2,1,3,4,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[6,5,4,2,8,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,1,8,7,2,6]=>{{1,2,4,5,6,7,8},{3}}
[6,1,4,3,8,5,2,7]=>{{1,2,5,6,7,8},{3,4}}
[4,7,6,2,8,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[6,4,5,1,7,8,3,2]=>{{1,2,4,6,8},{3,5,7}}
[4,2,3,1,7,8,6,5]=>{{1,4},{2},{3},{5,6,7,8}}
[3,4,2,1,8,6,7,5]=>{{1,2,3,4},{5,8},{6},{7}}
[2,7,6,8,1,5,3,4]=>{{1,2,3,5,6,7},{4,8}}
[6,4,5,8,3,1,2,7]=>{{1,6},{2,4,7,8},{3,5}}
[8,1,3,2,5,6,7,4]=>{{1,2,4,8},{3},{5},{6},{7}}
[3,6,8,1,5,2,4,7]=>{{1,3,4,7,8},{2,6},{5}}
[3,2,8,7,4,5,1,6]=>{{1,3,4,5,6,7,8},{2}}
[6,3,8,5,7,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,8,5,1,2,3]=>{{1,2,3,4,6,7,8},{5}}
[2,1,4,8,7,5,3,6]=>{{1,2},{3,4,5,6,7,8}}
[2,1,6,8,3,7,5,4]=>{{1,2},{3,5,6,7},{4,8}}
[3,6,8,2,4,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[6,2,8,1,7,5,4,3]=>{{1,4,5,6,7},{2},{3,8}}
[2,6,5,4,8,1,3,7]=>{{1,2,6},{3,5,7,8},{4}}
[6,5,3,4,8,1,7,2]=>{{1,6},{2,5,8},{3},{4},{7}}
[8,4,3,2,5,1,7,6]=>{{1,6,8},{2,4},{3},{5},{7}}
[4,2,8,1,5,3,6,7]=>{{1,4},{2},{3,6,7,8},{5}}
[5,1,8,2,6,4,3,7]=>{{1,2,4,5,6},{3,7,8}}
[7,4,8,6,2,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,2,8,3,7,5,1]=>{{1,4,8},{2,3,5,6,7}}
[2,1,5,8,3,6,4,7]=>{{1,2},{3,5},{4,7,8},{6}}
[2,8,5,3,6,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,6,4,1,3,2]=>{{1,3,4,5,6,7},{2,8}}
[5,8,4,1,6,3,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[4,8,1,3,5,7,6,2]=>{{1,3,4},{2,8},{5},{6,7}}
[3,8,1,4,5,6,2,7]=>{{1,3},{2,7,8},{4},{5},{6}}
[7,6,8,3,5,1,4,2]=>{{1,2,3,4,6,7,8},{5}}
[7,8,6,3,5,1,4,2]=>{{1,3,4,6,7},{2,8},{5}}
[5,3,8,7,6,1,4,2]=>{{1,5,6},{2,3,8},{4,7}}
[6,5,8,4,7,1,3,2]=>{{1,6},{2,3,5,7,8},{4}}
[6,7,4,2,5,3,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[7,6,4,8,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[7,4,8,5,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,5,6,3,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[4,2,7,5,6,3,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,4,7,5,6,2,1,8]=>{{1,3,7},{2,4,5,6},{8}}
[4,7,3,5,6,2,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[3,7,2,5,6,4,1,8]=>{{1,2,3,7},{4,5,6},{8}}
[7,8,3,5,6,1,4,2]=>{{1,4,5,6,7},{2,8},{3}}
[1,6,8,5,2,7,4,3]=>{{1},{2,4,5,6,7},{3,8}}
[6,2,8,5,1,7,4,3]=>{{1,4,5,6,7},{2},{3,8}}
[6,7,4,8,2,1,5,3]=>{{1,6},{2,5,7},{3,4,8}}
[3,2,7,8,6,1,5,4]=>{{1,3,5,6,7},{2},{4,8}}
[6,8,4,1,2,3,7,5]=>{{1,3,4,6},{2,5,8},{7}}
[4,1,8,5,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,8,2,5,6,4,3,7]=>{{1},{2,3,7,8},{4,5,6}}
[6,1,8,5,3,7,4,2]=>{{1,2,3,4,5,6,7,8}}
[3,8,1,5,2,7,6,4]=>{{1,3},{2,4,5,8},{6,7}}
[8,2,1,5,3,7,6,4]=>{{1,3,4,5,8},{2},{6,7}}
[1,5,2,4,6,7,8,3]=>{{1},{2,3,5,6,7,8},{4}}
[4,1,5,3,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,5,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,4,6,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,2,6,4,1,7,8,5]=>{{1,3,5,6,7,8},{2},{4}}
[7,6,4,3,1,2,8,5]=>{{1,5,7,8},{2,6},{3,4}}
[8,6,3,5,1,7,2,4]=>{{1,4,5,8},{2,6,7},{3}}
[4,5,3,1,6,7,8,2]=>{{1,4},{2,5,6,7,8},{3}}
[3,5,2,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,2,3,1,6,7,8,4]=>{{1,4,5,6,7,8},{2},{3}}
[1,5,3,2,6,7,8,4]=>{{1},{2,4,5,6,7,8},{3}}
[8,4,6,5,1,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,4,6,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,2,5,6,1,7,8,4]=>{{1,3,5},{2},{4,6,7,8}}
[3,2,8,7,6,1,4,5]=>{{1,3,5,6,8},{2},{4,7}}
[6,8,4,7,2,1,3,5]=>{{1,6},{2,5,8},{3,4,7}}
[3,8,7,5,6,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[8,2,7,5,6,1,3,4]=>{{1,4,5,6,8},{2},{3,7}}
[4,8,6,5,1,7,3,2]=>{{1,4,5},{2,8},{3,6,7}}
[1,7,4,6,2,3,8,5]=>{{1},{2,5,7,8},{3,4,6}}
[7,6,4,2,1,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,6,1,3,8,2]=>{{1,5},{2,7,8},{3,4,6}}
[8,6,4,7,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[5,2,4,3,7,1,8,6]=>{{1,5,6,7,8},{2},{3,4}}
[3,5,4,2,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,6,4,1,3,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,1,5,3,8,2]=>{{1,3,4,6},{2,7,8},{5}}
[7,5,4,1,2,6,8,3]=>{{1,3,4,7,8},{2,5},{6}}
[1,7,4,2,3,6,8,5]=>{{1},{2,3,4,5,7,8},{6}}
[1,8,2,5,3,7,6,4]=>{{1},{2,3,4,5,8},{6,7}}
[6,8,1,5,4,7,3,2]=>{{1,3,6,7},{2,8},{4,5}}
[8,2,1,5,6,4,3,7]=>{{1,3,7,8},{2},{4,5,6}}
[3,8,1,5,6,4,2,7]=>{{1,3},{2,7,8},{4,5,6}}
[6,8,4,1,2,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[3,2,8,1,6,5,4,7]=>{{1,3,4,7,8},{2},{5,6}}
[3,2,6,1,5,7,8,4]=>{{1,3,4,6,7,8},{2},{5}}
[7,6,4,1,5,2,8,3]=>{{1,3,4,7,8},{2,6},{5}}
[8,6,1,5,4,7,2,3]=>{{1,3,8},{2,6,7},{4,5}}
[3,5,1,4,6,7,8,2]=>{{1,3},{2,5,6,7,8},{4}}
[5,2,1,4,6,7,8,3]=>{{1,3,5,6,7,8},{2},{4}}
[5,4,1,3,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,5,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[7,5,4,1,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,2,5,1,4,7,8,6]=>{{1,3,4,5},{2},{6,7,8}}
[7,1,4,3,5,2,8,6]=>{{1,2,6,7,8},{3,4},{5}}
[8,1,3,5,4,7,2,6]=>{{1,2,6,7,8},{3},{4,5}}
[5,1,3,4,6,7,8,2]=>{{1,2,5,6,7,8},{3},{4}}
[3,1,8,2,5,7,4,6]=>{{1,2,3,4,6,7,8},{5}}
[8,3,2,6,1,4,7,5]=>{{1,5,8},{2,3},{4,6},{7}}
[2,8,1,6,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,6,1,3,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,1,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[2,6,8,1,5,7,4,3]=>{{1,2,4,6,7},{3,8},{5}}
[2,7,1,5,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[2,7,1,6,4,8,3,5]=>{{1,2,3,7},{4,5,6,8}}
[2,7,1,6,5,3,8,4]=>{{1,2,3,4,6,7,8},{5}}
[2,8,1,7,6,5,4,3]=>{{1,2,3,8},{4,7},{5,6}}
[8,3,2,7,1,6,5,4]=>{{1,4,5,7,8},{2,3},{6}}
[4,1,8,7,3,2,6,5]=>{{1,2,4,6,7},{3,5,8}}
[4,1,7,2,8,6,5,3]=>{{1,2,4},{3,5,7,8},{6}}
[3,7,1,8,6,5,4,2]=>{{1,3},{2,4,7,8},{5,6}}
[3,7,6,1,4,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,7,5,1,4,6,8,2]=>{{1,3,4,5},{2,7,8},{6}}
[3,6,8,5,1,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[7,3,5,8,2,1,4,6]=>{{1,4,6,7,8},{2,3,5}}
[7,3,6,2,1,4,5,8]=>{{1,5,7},{2,3,4,6},{8}}
[7,3,6,2,1,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[7,4,2,8,1,6,5,3]=>{{1,5,7},{2,3,4,8},{6}}
[8,7,5,3,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,2,6,3,1,4,8]=>{{1,4,6,7},{2,3,5},{8}}
[7,4,6,2,1,8,3,5]=>{{1,3,5,6,7,8},{2,4}}
[6,8,4,5,2,1,7,3]=>{{1,6},{2,3,4,5,8},{7}}
[4,6,8,5,1,7,3,2]=>{{1,4,5},{2,3,6,7,8}}
[4,7,5,1,3,8,6,2]=>{{1,4},{2,6,7,8},{3,5}}
[4,7,6,1,5,3,2,8]=>{{1,4},{2,7},{3,6},{5},{8}}
[5,1,7,6,3,8,2,4]=>{{1,2,3,5,7},{4,6,8}}
[5,1,7,6,4,2,8,3]=>{{1,2,4,5,6},{3,7,8}}
[5,1,8,7,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,1,7,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[8,5,2,1,6,3,7,4]=>{{1,4,8},{2,3,5,6},{7}}
[5,1,8,6,3,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[3,6,1,7,4,8,2,5]=>{{1,3},{2,4,5,6,7,8}}
[4,1,8,6,3,7,2,5]=>{{1,2,4,6,7},{3,5,8}}
[8,4,2,5,7,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,6,8,5,7,1,2]=>{{1,3,6,7},{2,4,8},{5}}
[5,4,8,2,7,3,6,1]=>{{1,3,5,6,7,8},{2,4}}
[5,4,8,7,3,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[8,5,4,7,3,6,2,1]=>{{1,8},{2,3,4,5,7},{6}}
[6,4,3,8,7,1,2,5]=>{{1,6},{2,4,5,7,8},{3}}
[6,3,7,2,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[5,6,8,4,2,7,3,1]=>{{1,2,3,5,6,7,8},{4}}
[5,7,4,2,8,1,3,6]=>{{1,5,6,8},{2,3,4,7}}
[6,5,2,7,1,3,8,4]=>{{1,2,3,5,6},{4,7,8}}
[8,6,5,4,2,1,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[6,4,7,3,1,8,2,5]=>{{1,5,6,8},{2,3,4,7}}
[5,7,4,3,8,6,1,2]=>{{1,2,5,7,8},{3,4},{6}}
[7,5,8,4,6,3,2,1]=>{{1,2,3,5,6,7,8},{4}}
[7,6,4,8,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,3,8,2,4,1]=>{{1,3,4,5,7,8},{2,6}}
[5,6,3,7,4,2,1,8]=>{{1,4,5,7},{2,6},{3},{8}}
[7,6,3,8,5,1,4,2]=>{{1,2,4,6,7,8},{3},{5}}
[6,4,8,1,3,2,5,7]=>{{1,2,4,6},{3,5,7,8}}
[7,4,8,6,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,2,7,6,5,3,1,8]=>{{1,3,4,6,7},{2},{5},{8}}
[3,7,2,4,6,5,1,8]=>{{1,2,3,7},{4},{5,6},{8}}
[8,1,3,4,5,2,6,7]=>{{1,2,6,7,8},{3},{4},{5}}
[1,6,8,4,2,5,3,7]=>{{1},{2,5,6},{3,7,8},{4}}
[6,2,8,4,1,5,7,3]=>{{1,5,6},{2},{3,8},{4},{7}}
[6,7,4,8,5,1,2,3]=>{{1,6},{2,7},{3,4,8},{5}}
[3,2,7,8,5,1,6,4]=>{{1,3,6,7},{2},{4,8},{5}}
[3,2,8,1,5,4,6,7]=>{{1,3,4,6,7,8},{2},{5}}
[6,1,4,8,5,3,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[1,4,8,5,2,6,7,3]=>{{1},{2,4,5},{3,8},{6},{7}}
[6,1,8,4,3,7,2,5]=>{{1,2,6,7},{3,5,8},{4}}
[3,7,1,4,2,5,8,6]=>{{1,3},{2,5,6,7,8},{4}}
[7,2,1,4,3,5,6,8]=>{{1,3,5,6,7},{2},{4},{8}}
[4,1,5,3,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[6,1,8,5,3,2,7,4]=>{{1,2,6},{3,4,5,8},{7}}
[7,1,4,6,3,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[3,2,6,4,1,8,7,5]=>{{1,3,5,6,8},{2},{4},{7}}
[7,6,4,3,1,8,2,5]=>{{1,2,5,6,7,8},{3,4}}
[3,5,2,1,8,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[1,5,3,2,8,6,4,7]=>{{1},{2,4,5,7,8},{3},{6}}
[5,4,2,1,7,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,2,7,6,5,1,3,4]=>{{1,4,6,8},{2},{3,7},{5}}
[8,6,2,7,1,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,7,3,6,2,8,5,4]=>{{1},{2,5,7},{3},{4,6,8}}
[7,6,3,2,1,8,5,4]=>{{1,5,7},{2,4,6,8},{3}}
[8,6,3,7,4,1,2,5]=>{{1,2,4,5,6,7,8},{3}}
[5,2,3,4,7,1,8,6]=>{{1,5,6,7,8},{2},{3},{4}}
[8,6,3,1,4,5,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[6,7,3,1,5,4,2,8]=>{{1,4,6},{2,7},{3},{5},{8}}
[5,8,3,1,2,4,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[8,1,3,2,4,5,6,7]=>{{1,2,4,5,6,7,8},{3}}
[8,4,1,7,2,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,6,5,4,7,3]=>{{1,3,8},{2},{4,6},{5},{7}}
[3,8,1,5,6,4,7,2]=>{{1,3},{2,8},{4,5,6},{7}}
[6,8,4,1,2,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[3,2,8,1,6,5,7,4]=>{{1,3,4,8},{2},{5,6},{7}}
[7,6,4,1,5,2,3,8]=>{{1,3,4,7},{2,6},{5},{8}}
[8,6,1,5,4,7,3,2]=>{{1,2,3,6,7,8},{4,5}}
[3,5,1,4,6,7,2,8]=>{{1,3},{2,5,6,7},{4},{8}}
[5,2,1,4,7,6,3,8]=>{{1,3,5,7},{2},{4},{6},{8}}
[4,5,8,2,1,3,7,6]=>{{1,2,4,5},{3,6,8},{7}}
[5,8,2,3,1,4,6,7]=>{{1,5},{2,3,4,6,7,8}}
[4,2,1,3,5,8,7,6]=>{{1,3,4},{2},{5},{6,8},{7}}
[5,4,1,3,6,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[8,5,4,1,3,6,2,7]=>{{1,2,3,4,5,7,8},{6}}
[3,2,5,1,4,6,8,7]=>{{1,3,4,5},{2},{6},{7,8}}
[8,1,4,3,5,6,7,2]=>{{1,2,8},{3,4},{5},{6},{7}}
[7,1,3,5,4,6,2,8]=>{{1,2,7},{3},{4,5},{6},{8}}
[5,1,3,4,6,2,7,8]=>{{1,2,5,6},{3},{4},{7},{8}}
[4,1,3,2,5,7,6,8]=>{{1,2,4},{3},{5},{6,7},{8}}
[4,6,7,3,1,5,2,8]=>{{1,2,3,4,5,6,7},{8}}
[6,8,1,3,5,2,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[6,8,3,1,4,5,7,2]=>{{1,4,5,6},{2,8},{3},{7}}
[7,5,1,8,2,3,6,4]=>{{1,3,6,7},{2,5},{4,8}}
[5,3,8,4,2,6,7,1]=>{{1,2,3,5,8},{4},{6},{7}}
[4,1,8,3,5,7,2,6]=>{{1,2,3,4,6,7,8},{5}}
[4,5,7,2,3,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[2,6,3,4,7,5,8,1]=>{{1,2,5,6,7,8},{3},{4}}
[4,5,2,7,1,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[3,4,1,6,5,8,2,7]=>{{1,3},{2,4,6,7,8},{5}}
[7,3,1,4,8,5,6,2]=>{{1,2,3,5,6,7,8},{4}}
[6,4,2,8,7,1,5,3]=>{{1,6},{2,3,4,8},{5,7}}
[7,2,4,8,1,5,3,6]=>{{1,3,4,5,6,7,8},{2}}
[4,6,3,1,7,8,5,2]=>{{1,4},{2,6,8},{3},{5,7}}
[5,3,1,6,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[4,1,6,2,7,8,5,3]=>{{1,2,4},{3,6,8},{5,7}}
[2,1,3,4,8,7,5,6]=>{{1,2},{3},{4},{5,6,7,8}}
[4,8,3,7,6,5,1,2]=>{{1,4,7},{2,8},{3},{5,6}}
[6,3,8,7,5,4,1,2]=>{{1,4,6,7},{2,3,8},{5}}
[5,3,8,7,6,4,1,2]=>{{1,4,5,6,7},{2,3,8}}
[2,8,7,6,1,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,2,8,7,6,1,4,3]=>{{1,5,6},{2},{3,8},{4,7}}
[6,2,8,7,5,1,4,3]=>{{1,6},{2},{3,8},{4,7},{5}}
[7,8,2,6,5,1,4,3]=>{{1,4,6,7},{2,3,8},{5}}
[6,1,8,7,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}
[3,1,8,7,6,5,4,2]=>{{1,2,3,8},{4,7},{5,6}}
[7,8,2,6,1,5,4,3]=>{{1,4,5,6,7},{2,3,8}}
[6,2,8,7,1,5,4,3]=>{{1,5,6},{2},{3,8},{4,7}}
[4,2,8,1,7,6,5,3]=>{{1,4},{2},{3,8},{5,7},{6}}
[4,8,2,7,6,1,5,3]=>{{1,4,5,6,7},{2,3,8}}
[3,8,7,2,1,6,5,4]=>{{1,3,5,7},{2,4,8},{6}}
[6,5,8,7,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,7,6,5,3,2]=>{{1,3,4,7},{2,8},{5,6}}
[5,4,1,8,7,6,3,2]=>{{1,3,5,7},{2,4,8},{6}}
[6,4,8,1,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,1,6,5,3,2]=>{{1,3,4,7},{2,8},{5,6}}
[7,8,3,1,6,5,4,2]=>{{1,4,7},{2,8},{3},{5,6}}
[6,3,8,1,7,5,4,2]=>{{1,4,5,6,7},{2,3,8}}
[5,3,1,8,7,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[7,8,2,1,6,5,4,3]=>{{1,4,7},{2,3,8},{5,6}}
[6,5,3,1,8,7,4,2]=>{{1,4,6,7},{2,5,8},{3}}
[6,4,3,1,8,7,5,2]=>{{1,2,4,5,6,7,8},{3}}
[5,4,3,1,8,7,6,2]=>{{1,2,4,5,8},{3},{6,7}}
[7,5,2,1,8,6,4,3]=>{{1,4,7},{2,3,5,8},{6}}
[5,4,2,1,8,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[7,3,2,1,8,6,5,4]=>{{1,4,5,7,8},{2,3},{6}}
[6,3,2,1,8,7,5,4]=>{{1,4,5,6,7,8},{2,3}}
[6,1,4,2,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[8,6,1,4,2,3,5,7]=>{{1,2,3,5,6,7,8},{4}}
[6,8,1,4,2,3,5,7]=>{{1,3,6},{2,5,7,8},{4}}
[8,1,4,2,3,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[4,1,8,2,3,6,5,7]=>{{1,2,4},{3,5,7,8},{6}}
[8,2,3,6,1,4,5,7]=>{{1,5,7,8},{2},{3},{4,6}}
[6,2,3,8,1,4,5,7]=>{{1,4,5,6,7,8},{2},{3}}
[4,6,2,3,8,1,5,7]=>{{1,2,3,4,6},{5,7,8}}
[4,8,2,3,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,2,3,6,4,1,5,7]=>{{1,4,5,6,7,8},{2},{3}}
[8,4,3,6,2,1,5,7]=>{{1,2,4,5,6,7,8},{3}}
[6,2,3,8,4,1,5,7]=>{{1,6},{2},{3},{4,5,7,8}}
[8,4,2,3,6,1,5,7]=>{{1,5,6,7,8},{2,3,4}}
[6,4,2,3,8,1,5,7]=>{{1,6},{2,3,4},{5,7,8}}
[2,6,4,3,8,1,5,7]=>{{1,2,6},{3,4},{5,7,8}}
[2,8,4,3,6,1,5,7]=>{{1,2,5,6,7,8},{3,4}}
[2,6,3,8,4,1,5,7]=>{{1,2,6},{3},{4,5,7,8}}
[6,3,8,4,2,1,5,7]=>{{1,6},{2,3,5,7,8},{4}}
[2,6,3,8,1,4,5,7]=>{{1,2,4,5,6,7,8},{3}}
[2,8,3,6,1,4,5,7]=>{{1,2,5,7,8},{3},{4,6}}
[8,3,6,4,2,1,5,7]=>{{1,2,3,5,6,7,8},{4}}
[2,8,3,6,4,1,5,7]=>{{1,2,4,5,6,7,8},{3}}
[8,3,6,2,4,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,6,2,1,4,5,7]=>{{1,5,7,8},{2,3,4,6}}
[6,2,1,3,8,4,5,7]=>{{1,3,4,6},{2},{5,7,8}}
[8,2,1,3,6,4,5,7]=>{{1,3,4,5,6,7,8},{2}}
[6,3,8,2,4,1,5,7]=>{{1,6},{2,3,4,5,7,8}}
[6,2,4,3,8,1,5,7]=>{{1,6},{2},{3,4},{5,7,8}}
[3,6,4,7,8,5,1,2]=>{{1,3,4,7},{2,5,6,8}}
[1,6,4,2,7,5,8,3]=>{{1},{2,3,4,5,6,7,8}}
[3,6,4,2,7,1,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[1,4,7,2,5,6,8,3]=>{{1},{2,4},{3,7,8},{5},{6}}
[6,4,8,5,3,7,1,2]=>{{1,6,7},{2,3,4,5,8}}
[1,6,5,4,2,7,8,3]=>{{1},{2,3,5,6,7,8},{4}}
[4,2,5,3,6,1,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[7,1,5,3,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,6,5,2,4,8,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[1,4,6,2,8,5,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[7,8,1,4,2,5,6,3]=>{{1,2,3,5,6,7,8},{4}}
[3,4,8,5,2,1,6,7]=>{{1,3,6,7,8},{2,4,5}}
[4,8,5,3,1,6,2,7]=>{{1,3,4,5},{2,7,8},{6}}
[6,1,3,5,8,2,7,4]=>{{1,2,6},{3},{4,5,8},{7}}
[6,1,8,7,4,2,3,5]=>{{1,2,6},{3,4,5,7,8}}
[1,2,8,5,7,3,6,4]=>{{1},{2},{3,4,5,6,7,8}}
[1,3,6,8,7,5,2,4]=>{{1},{2,3,5,6,7},{4,8}}
[1,8,2,5,4,7,6,3]=>{{1},{2,3,8},{4,5},{6,7}}
[7,1,2,4,5,8,6,3]=>{{1,2,3,6,7,8},{4},{5}}
[1,2,7,3,5,8,6,4]=>{{1},{2},{3,4,6,7,8},{5}}
[6,1,3,2,5,7,8,4]=>{{1,2,4,6,7,8},{3},{5}}
[4,6,2,1,7,5,3,8]=>{{1,4},{2,3,5,6,7},{8}}
[1,6,3,7,8,5,2,4]=>{{1},{2,4,5,6,7,8},{3}}
[4,6,2,3,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,3,7,1,2,8,5]=>{{1,4,5,7,8},{2,6},{3}}
[4,2,1,3,5,7,8,6]=>{{1,3,4},{2},{5},{6,7,8}}
[7,3,2,4,5,1,8,6]=>{{1,6,7,8},{2,3},{4},{5}}
[3,8,2,5,4,1,7,6]=>{{1,2,3,6,8},{4,5},{7}}
[7,8,4,2,6,3,1,5]=>{{1,7},{2,3,4,5,6,8}}
[4,2,6,3,8,7,1,5]=>{{1,3,4,6,7},{2},{5,8}}
[5,8,2,7,4,3,1,6]=>{{1,4,5,7},{2,3,6,8}}
[4,3,8,5,1,7,2,6]=>{{1,4,5},{2,3,6,7,8}}
[4,3,6,8,1,2,7,5]=>{{1,4,5,8},{2,3,6},{7}}
[6,4,3,5,2,8,1,7]=>{{1,6,7,8},{2,4,5},{3}}
[6,5,3,8,4,2,1,7]=>{{1,2,4,5,6,7,8},{3}}
[3,8,1,7,5,6,4,2]=>{{1,3},{2,8},{4,7},{5},{6}}
[8,2,5,7,3,6,4,1]=>{{1,8},{2},{3,5},{4,7},{6}}
[1,8,6,7,5,3,4,2]=>{{1},{2,8},{3,6},{4,7},{5}}
[8,2,6,7,5,3,4,1]=>{{1,8},{2},{3,6},{4,7},{5}}
[1,5,8,7,2,6,4,3]=>{{1},{2,5},{3,8},{4,7},{6}}
[5,4,8,6,2,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,7,6,1,3,5,4,8]=>{{1,2,4,7},{3,5,6},{8}}
[6,4,1,8,2,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,8,6,1,3,5,4,7]=>{{1,2,4,7,8},{3,5,6}}
[4,1,3,6,5,8,7,2]=>{{1,2,4,6,8},{3},{5},{7}}
[2,1,6,3,5,8,7,4]=>{{1,2},{3,4,6,8},{5},{7}}
[2,4,1,3,8,5,7,6]=>{{1,2,3,4},{5,6,8},{7}}
[2,4,1,3,5,8,7,6]=>{{1,2,3,4},{5},{6,8},{7}}
[2,6,1,3,5,8,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[4,6,1,3,5,8,7,2]=>{{1,3,4},{2,6,8},{5},{7}}
[6,1,4,3,5,8,7,2]=>{{1,2,6,8},{3,4},{5},{7}}
[6,4,1,3,5,8,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[6,2,1,3,5,8,7,4]=>{{1,3,4,6,8},{2},{5},{7}}
[4,2,1,3,6,5,7,8]=>{{1,3,4},{2},{5,6},{7},{8}}
[4,2,1,6,3,5,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[6,2,1,8,3,5,7,4]=>{{1,3,5,6},{2},{4,8},{7}}
[6,2,1,3,8,5,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[6,1,4,3,8,5,7,2]=>{{1,2,5,6,8},{3,4},{7}}
[1,6,4,3,8,5,7,2]=>{{1},{2,5,6,8},{3,4},{7}}
[8,1,4,3,6,5,7,2]=>{{1,2,8},{3,4},{5,6},{7}}
[8,4,1,3,6,5,7,2]=>{{1,2,3,4,8},{5,6},{7}}
[8,2,1,3,6,5,7,4]=>{{1,3,4,8},{2},{5,6},{7}}
[8,2,1,6,3,5,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[8,2,1,4,3,5,7,6]=>{{1,3,5,6,8},{2},{4},{7}}
[6,2,1,4,3,5,7,8]=>{{1,3,5,6},{2},{4},{7},{8}}
[8,2,4,1,3,5,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[8,2,6,1,3,5,7,4]=>{{1,4,8},{2},{3,5,6},{7}}
[8,4,6,1,3,5,7,2]=>{{1,2,4,8},{3,5,6},{7}}
[8,4,1,6,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[8,1,4,6,3,5,7,2]=>{{1,2,8},{3,4,5,6},{7}}
[1,8,4,6,3,5,7,2]=>{{1},{2,8},{3,4,5,6},{7}}
[1,6,4,8,3,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[6,4,1,8,3,5,7,2]=>{{1,3,5,6},{2,4,8},{7}}
[6,4,8,1,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[6,2,8,1,3,5,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[4,2,8,1,3,5,7,6]=>{{1,4},{2},{3,5,6,8},{7}}
[2,6,8,1,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[4,6,8,1,3,5,7,2]=>{{1,4},{2,3,5,6,8},{7}}
[4,6,1,8,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,1,6,8,3,5,7,2]=>{{1,2,4,8},{3,5,6},{7}}
[1,4,6,3,8,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[4,6,1,3,8,5,7,2]=>{{1,3,4},{2,5,6,8},{7}}
[2,4,1,8,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,1,6,8,3,5,7,4]=>{{1,2},{3,5,6},{4,8},{7}}
[4,1,3,6,8,5,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[1,4,3,6,8,5,7,2]=>{{1},{2,4,5,6,8},{3},{7}}
[4,1,3,8,6,5,7,2]=>{{1,2,4,8},{3},{5,6},{7}}
[2,1,8,3,6,5,7,4]=>{{1,2},{3,4,8},{5,6},{7}}
[2,1,6,4,3,5,7,8]=>{{1,2},{3,5,6},{4},{7},{8}}
[2,6,1,4,3,5,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[2,8,1,4,3,5,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[2,8,1,6,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[4,8,1,3,6,5,7,2]=>{{1,3,4},{2,8},{5,6},{7}}
[1,4,8,3,6,5,7,2]=>{{1},{2,3,4,8},{5,6},{7}}
[1,4,8,6,3,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[4,1,8,6,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,8,1,6,3,5,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[4,8,6,1,3,5,7,2]=>{{1,4},{2,8},{3,5,6},{7}}
[2,8,6,1,3,5,7,4]=>{{1,2,4,8},{3,5,6},{7}}
[2,8,4,1,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,6,4,1,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[4,6,2,1,3,5,7,8]=>{{1,4},{2,3,5,6},{7},{8}}
[6,8,1,4,3,5,7,2]=>{{1,3,5,6},{2,8},{4},{7}}
[6,1,8,4,3,5,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[1,6,8,4,3,5,7,2]=>{{1},{2,3,5,6,8},{4},{7}}
[1,8,6,4,3,5,7,2]=>{{1},{2,8},{3,5,6},{4},{7}}
[8,1,6,4,3,5,7,2]=>{{1,2,8},{3,5,6},{4},{7}}
[8,6,1,4,3,5,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[8,6,4,1,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[8,6,2,1,3,5,7,4]=>{{1,4,8},{2,3,5,6},{7}}
[8,4,2,1,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[7,8,6,5,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,1,8,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[5,6,4,2,8,3,7,1]=>{{1,5,8},{2,3,4,6},{7}}
[5,6,4,2,7,3,1,8]=>{{1,5,7},{2,3,4,6},{8}}
[5,7,1,4,6,3,2,8]=>{{1,3,5,6},{2,7},{4},{8}}
[5,8,1,4,6,3,7,2]=>{{1,3,5,6},{2,8},{4},{7}}
[3,6,7,4,5,8,2,1]=>{{1,2,3,6,7,8},{4},{5}}
[3,5,7,4,6,8,2,1]=>{{1,2,3,5,6,7,8},{4}}
[6,8,4,1,7,2,5,3]=>{{1,2,3,4,6,8},{5,7}}
[5,4,6,1,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,4,1,8,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[3,5,8,4,6,7,2,1]=>{{1,3,8},{2,5,6,7},{4}}
[3,6,8,4,5,7,2,1]=>{{1,3,8},{2,6,7},{4},{5}}
[3,7,8,4,5,6,2,1]=>{{1,3,8},{2,7},{4},{5},{6}}
[6,8,1,4,5,3,7,2]=>{{1,3,6},{2,8},{4},{5},{7}}
[6,7,1,4,5,3,2,8]=>{{1,3,6},{2,7},{4},{5},{8}}
[3,7,1,5,4,6,2,8]=>{{1,3},{2,7},{4,5},{6},{8}}
[3,8,1,5,4,6,7,2]=>{{1,3},{2,8},{4,5},{6},{7}}
[3,7,1,5,4,6,8,2]=>{{1,3},{2,7,8},{4,5},{6}}
[6,7,1,4,5,3,8,2]=>{{1,3,6},{2,7,8},{4},{5}}
[5,7,1,4,6,3,8,2]=>{{1,3,5,6},{2,7,8},{4}}
[5,6,4,2,7,3,8,1]=>{{1,5,7,8},{2,3,4,6}}
[5,4,7,2,8,3,1,6]=>{{1,3,5,6,7,8},{2,4}}
[5,4,7,2,8,3,6,1]=>{{1,5,8},{2,4},{3,6,7}}
[5,6,4,2,8,3,1,7]=>{{1,5,7,8},{2,3,4,6}}
[5,8,1,4,6,3,2,7]=>{{1,3,5,6},{2,7,8},{4}}
[3,8,1,5,4,6,2,7]=>{{1,3},{2,7,8},{4,5},{6}}
[3,6,1,5,4,2,7,8]=>{{1,3},{2,6},{4,5},{7},{8}}
[3,6,1,5,4,8,2,7]=>{{1,3},{2,6,7,8},{4,5}}
[6,8,3,1,4,2,5,7]=>{{1,2,4,5,6,7,8},{3}}
[7,3,8,1,4,2,5,6]=>{{1,4,5,7},{2,3,6,8}}
[6,7,3,1,4,2,8,5]=>{{1,2,4,5,6,7,8},{3}}
[3,6,1,5,4,7,8,2]=>{{1,3},{2,6,7,8},{4,5}}
[3,4,1,2,7,6,5,8]=>{{1,3},{2,4},{5,7},{6},{8}}
[3,4,1,2,6,8,7,5]=>{{1,3},{2,4},{5,6,8},{7}}
[6,8,3,1,4,7,2,5]=>{{1,2,4,5,6,7,8},{3}}
[6,4,7,2,8,5,1,3]=>{{1,3,5,6,7,8},{2,4}}
[5,8,1,4,7,3,2,6]=>{{1,2,3,5,6,7,8},{4}}
[7,8,1,4,5,3,2,6]=>{{1,2,3,6,7,8},{4},{5}}
[3,8,1,5,4,7,2,6]=>{{1,3},{2,6,7,8},{4,5}}
[3,6,1,5,4,8,7,2]=>{{1,3},{2,6,8},{4,5},{7}}
[3,6,1,5,4,7,2,8]=>{{1,3},{2,6,7},{4,5},{8}}
[6,7,3,1,4,2,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[6,8,3,1,4,2,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[7,8,3,1,4,6,2,5]=>{{1,2,4,5,7,8},{3},{6}}
[7,8,4,2,6,5,1,3]=>{{1,7},{2,3,4,8},{5,6}}
[6,5,8,7,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,8,3,1,4,6,5,2]=>{{1,4,5,7},{2,8},{3},{6}}
[6,7,3,1,4,5,2,8]=>{{1,4,5,6},{2,7},{3},{8}}
[3,7,1,5,4,2,6,8]=>{{1,3},{2,6,7},{4,5},{8}}
[3,8,1,5,4,2,7,6]=>{{1,3},{2,6,8},{4,5},{7}}
[5,8,1,4,7,3,6,2]=>{{1,3,5,6,7},{2,8},{4}}
[6,8,4,2,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,2,8,5,3,1]=>{{1,5,6,8},{2,4},{3,7}}
[6,3,7,1,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,8,3,1,4,7,5,2]=>{{1,4,5,6,7},{2,8},{3}}
[3,7,1,5,4,8,6,2]=>{{1,3},{2,6,7,8},{4,5}}
[3,4,1,2,8,5,7,6]=>{{1,3},{2,4},{5,6,8},{7}}
[3,4,1,2,5,8,7,6]=>{{1,3},{2,4},{5},{6,8},{7}}
[3,7,1,5,4,2,8,6]=>{{1,3},{2,6,7,8},{4,5}}
[6,7,3,1,4,5,8,2]=>{{1,4,5,6},{2,7,8},{3}}
[7,3,8,1,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,1,4,5,6,2]=>{{1,4,5,6,7},{2,3,8}}
[6,8,3,1,4,5,2,7]=>{{1,4,5,6},{2,7,8},{3}}
[3,8,1,5,4,2,6,7]=>{{1,3},{2,6,7,8},{4,5}}
[8,7,6,3,5,2,1,4]=>{{1,2,3,4,6,7,8},{5}}
[8,7,4,6,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,4,3,2,1,6]=>{{1,2,3,5,6,7,8},{4}}
[8,7,6,2,5,4,1,3]=>{{1,2,3,4,6,7,8},{5}}
[8,5,4,7,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,6,5,2,1,4]=>{{1,2,4,6,7,8},{3},{5}}
[6,5,8,4,3,2,1,7]=>{{1,2,3,5,6,7,8},{4}}
[8,4,7,6,3,2,1,5]=>{{1,3,5,7,8},{2,4,6}}
[5,8,7,4,3,2,1,6]=>{{1,3,5,7},{2,6,8},{4}}
[5,8,6,2,3,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,5,2,7,3,1,8,6]=>{{1,4,6,7,8},{2,3,5}}
[4,8,2,6,3,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,1,7,2,5,8,6,3]=>{{1,2,4},{3,6,7,8},{5}}
[7,8,2,1,5,6,4,3]=>{{1,4,7},{2,3,8},{5},{6}}
[1,6,2,5,8,4,3,7]=>{{1},{2,3,4,5,6,7,8}}
[7,3,1,6,8,5,2,4]=>{{1,2,3,7},{4,5,6,8}}
[5,2,7,1,8,6,3,4]=>{{1,4,5,8},{2},{3,7},{6}}
[6,5,2,8,1,7,3,4]=>{{1,2,3,5,6,7},{4,8}}
[2,8,3,5,1,7,4,6]=>{{1,2,4,5,6,7,8},{3}}
[5,4,3,8,7,1,6,2]=>{{1,5,6,7},{2,4,8},{3}}
[8,5,4,3,7,2,6,1]=>{{1,8},{2,5,6,7},{3,4}}
[8,3,7,4,2,6,5,1]=>{{1,8},{2,3,5,7},{4},{6}}
[2,8,6,5,1,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,2,8,4,1,7,5]=>{{1,6},{2,3},{4,5,8},{7}}
[2,8,3,4,1,7,5,6]=>{{1,2,5,6,7,8},{3},{4}}
[5,4,2,8,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,8,4,3,1,7,6,5]=>{{1,2,5,8},{3,4},{6,7}}
[2,8,5,3,1,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[2,8,6,4,1,7,5,3]=>{{1,2,3,5,6,7,8},{4}}
[3,8,7,5,1,6,4,2]=>{{1,3,4,5,7},{2,8},{6}}
[8,3,7,5,2,6,4,1]=>{{1,8},{2,3,4,5,7},{6}}
[8,4,7,6,2,5,3,1]=>{{1,8},{2,4,5,6},{3,7}}
[4,8,7,6,1,5,3,2]=>{{1,4,5,6},{2,8},{3,7}}
[7,4,8,6,2,1,5,3]=>{{1,2,4,5,6,7},{3,8}}
[7,3,8,5,2,1,6,4]=>{{1,6,7},{2,3,4,5,8}}
[7,3,8,4,2,1,6,5]=>{{1,6,7},{2,3,5,8},{4}}
[7,5,4,3,8,2,1,6]=>{{1,7},{2,5,6,8},{3,4}}
[3,7,8,4,1,2,6,5]=>{{1,3,5,8},{2,6,7},{4}}
[3,7,8,5,1,2,6,4]=>{{1,3,4,5,8},{2,6,7}}
[4,7,8,6,1,2,5,3]=>{{1,2,4,5,6,7},{3,8}}
[8,7,4,6,3,5,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[5,7,8,6,1,2,4,3]=>{{1,5},{2,4,6,7},{3,8}}
[6,4,7,8,3,1,2,5]=>{{1,6},{2,3,4,5,7,8}}
[7,3,4,8,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,6,4,8,3,2,1,5]=>{{1,7},{2,6},{3,4,5,8}}
[7,5,8,6,2,1,4,3]=>{{1,4,6,7},{2,5},{3,8}}
[6,5,8,7,3,1,4,2]=>{{1,6},{2,3,5,8},{4,7}}
[2,4,8,3,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[6,3,2,4,8,1,5,7]=>{{1,6},{2,3},{4},{5,7,8}}
[2,3,8,4,1,6,7,5]=>{{1,2,3,5,8},{4},{6},{7}}
[2,3,8,5,1,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[6,4,8,7,3,1,5,2]=>{{1,6},{2,3,4,5,7,8}}
[8,6,4,7,3,2,5,1]=>{{1,8},{2,6},{3,4,5,7}}
[8,3,4,7,2,5,6,1]=>{{1,8},{2,3,4,5,6,7}}
[3,4,8,7,1,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,6,1,5,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[2,5,8,6,1,4,7,3]=>{{1,2,5},{3,8},{4,6},{7}}
[8,3,5,7,2,4,6,1]=>{{1,8},{2,3,5},{4,6,7}}
[8,4,6,7,2,3,5,1]=>{{1,8},{2,4,5,7},{3,6}}
[4,6,8,7,1,3,5,2]=>{{1,4,5,7},{2,3,6,8}}
[2,6,8,5,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,6,8,4,1,3,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[2,5,8,3,1,4,7,6]=>{{1,2,5},{3,4,6,8},{7}}
[5,6,8,7,1,3,4,2]=>{{1,5},{2,3,6,8},{4,7}}
[7,4,6,8,2,1,3,5]=>{{1,3,6,7},{2,4,5,8}}
[2,3,5,4,1,8,6,7]=>{{1,2,3,5},{4},{6,7,8}}
[2,3,6,4,8,1,5,7]=>{{1,2,3,6},{4},{5,7,8}}
[1,8,4,6,3,5,2,7]=>{{1},{2,7,8},{3,4,5,6}}
[5,4,8,6,2,1,3,7]=>{{1,2,4,5,6},{3,7,8}}
[2,3,6,8,1,5,4,7]=>{{1,2,3,5,6},{4,7,8}}
[2,5,6,1,4,7,8,3]=>{{1,2,4,5},{3,6,7,8}}
[2,5,6,1,4,7,3,8]=>{{1,2,4,5},{3,6,7},{8}}
[7,3,5,1,6,8,4,2]=>{{1,4,7},{2,3,5,6,8}}
[2,7,6,1,8,5,4,3]=>{{1,2,4,7},{3,5,6,8}}
[2,7,6,8,1,4,5,3]=>{{1,2,5,7},{3,4,6,8}}
[1,8,7,6,3,2,5,4]=>{{1},{2,4,6,8},{3,5,7}}
[1,8,7,6,3,2,4,5]=>{{1},{2,3,4,5,6,7,8}}
[5,7,8,6,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,1,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,1,7,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,3,4,7,6,1,5,8]=>{{1,2,3,4,5,6,7},{8}}
[7,3,5,8,4,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[1,8,4,5,2,7,3,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,4,5,2,7,6,3]=>{{1},{2,3,4,5,8},{6,7}}
[7,3,5,8,4,1,6,2]=>{{1,6,7},{2,3,4,5,8}}
[2,7,6,4,8,5,1,3]=>{{1,2,7},{3,5,6,8},{4}}
[7,3,5,4,6,8,1,2]=>{{1,7},{2,3,5,6,8},{4}}
[6,3,5,4,7,1,8,2]=>{{1,6},{2,3,5,7,8},{4}}
[6,3,5,4,7,1,2,8]=>{{1,6},{2,3,5,7},{4},{8}}
[3,4,1,5,6,8,7,2]=>{{1,3},{2,4,5,6,8},{7}}
[3,7,1,6,8,5,2,4]=>{{1,3},{2,7},{4,5,6,8}}
[2,3,1,8,6,4,7,5]=>{{1,2,3},{4,5,6,8},{7}}
[1,8,4,3,6,2,5,7]=>{{1},{2,5,6,7,8},{3,4}}
[2,3,1,8,6,4,5,7]=>{{1,2,3},{4,5,6,7,8}}
[3,7,1,6,8,5,4,2]=>{{1,3},{2,4,5,6,7,8}}
[6,3,5,4,7,2,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,3,5,4,6,8,2,1]=>{{1,2,3,5,6,7,8},{4}}
[2,7,6,4,8,5,3,1]=>{{1,2,3,5,6,7,8},{4}}
[1,8,4,5,2,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}
[6,4,8,5,3,1,2,7]=>{{1,6},{2,3,4,5,7,8}}
[7,3,5,8,4,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[2,3,4,6,5,8,1,7]=>{{1,2,3,4,6,7,8},{5}}
[2,3,4,7,5,1,8,6]=>{{1,2,3,4,6,7,8},{5}}
[2,3,4,7,5,1,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,3,4,7,1,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[2,3,4,7,1,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[2,3,4,6,1,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[6,3,5,8,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,4,8,5,3,2,1,6]=>{{1,7},{2,3,4,5,6,8}}
[1,8,4,5,2,3,6,7]=>{{1},{2,3,4,5,6,7,8}}
[7,4,8,5,3,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,8,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,2,4,6,8,3,7,1]=>{{1,5,8},{2},{3,4,6},{7}}
[1,5,7,4,6,3,2,8]=>{{1},{2,3,5,6,7},{4},{8}}
[5,2,8,4,6,3,7,1]=>{{1,3,5,6,8},{2},{4},{7}}
[3,8,5,4,6,7,2,1]=>{{1,2,3,5,6,7,8},{4}}
[6,8,3,4,5,7,2,1]=>{{1,2,6,7,8},{3},{4},{5}}
[2,5,7,4,6,3,8,1]=>{{1,2,3,5,6,7,8},{4}}
[5,4,1,7,8,3,2,6]=>{{1,3,5,6,8},{2,4,7}}
[5,4,2,7,8,3,6,1]=>{{1,5,8},{2,3,4,6,7}}
[5,1,4,6,8,3,2,7]=>{{1,2,5,7,8},{3,4,6}}
[5,1,8,4,6,3,2,7]=>{{1,2,3,5,6,7,8},{4}}
[8,1,6,4,5,3,2,7]=>{{1,2,7,8},{3,6},{4},{5}}
[8,1,3,5,4,6,2,7]=>{{1,2,7,8},{3},{4,5},{6}}
[8,1,6,2,4,3,5,7]=>{{1,2,4,5,7,8},{3,6}}
[8,7,1,2,4,3,5,6]=>{{1,3,6,8},{2,4,5,7}}
[1,7,6,2,4,3,5,8]=>{{1},{2,4,5,7},{3,6},{8}}
[8,7,3,2,4,6,5,1]=>{{1,8},{2,4,5,7},{3},{6}}
[8,2,6,3,4,5,7,1]=>{{1,8},{2},{3,4,5,6},{7}}
[1,7,6,3,4,5,2,8]=>{{1},{2,7},{3,4,5,6},{8}}
[1,7,2,5,4,3,6,8]=>{{1},{2,3,6,7},{4,5},{8}}
[8,7,2,4,5,3,6,1]=>{{1,8},{2,3,6,7},{4},{5}}
[5,8,2,4,7,3,6,1]=>{{1,2,3,5,6,7,8},{4}}
[6,8,3,2,4,7,5,1]=>{{1,2,4,5,6,7,8},{3}}
[8,7,1,3,4,5,2,6]=>{{1,3,4,5,6,8},{2,7}}
[8,1,6,3,4,5,2,7]=>{{1,2,7,8},{3,4,5,6}}
[8,1,2,5,4,3,6,7]=>{{1,2,3,6,7,8},{4,5}}
[3,4,8,7,5,2,6,1]=>{{1,3,8},{2,4,6,7},{5}}
[3,2,8,6,1,5,4,7]=>{{1,3,4,5,6,7,8},{2}}
[8,6,1,2,4,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,6,4,2,5,1]=>{{1,8},{2,4,5,6,7},{3}}
[3,8,7,2,5,4,6,1]=>{{1,2,3,4,6,7,8},{5}}
[8,7,2,4,5,6,3,1]=>{{1,8},{2,3,7},{4},{5},{6}}
[5,3,6,2,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[3,5,2,8,6,1,4,7]=>{{1,2,3,5,6},{4,7,8}}
[3,7,2,5,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,6,2,3,4,7]=>{{1,2,5},{3,4,6,7,8}}
[2,5,4,1,8,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[3,7,6,1,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[7,6,3,1,8,2,4,5]=>{{1,4,7},{2,6},{3},{5,8}}
[8,2,3,6,1,4,7,5]=>{{1,5,8},{2},{3},{4,6},{7}}
[1,8,2,6,3,4,7,5]=>{{1},{2,3,5,8},{4,6},{7}}
[8,1,3,6,4,7,2,5]=>{{1,2,4,5,6,7,8},{3}}
[7,1,3,6,4,8,2,5]=>{{1,2,7},{3},{4,5,6,8}}
[8,2,1,3,5,7,4,6]=>{{1,3,4,6,7,8},{2},{5}}
[8,2,6,3,1,4,7,5]=>{{1,5,8},{2},{3,4,6},{7}}
[7,5,4,1,3,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[2,7,5,8,3,4,1,6]=>{{1,2,7},{3,5},{4,6,8}}
[7,3,8,5,4,1,2,6]=>{{1,2,3,6,7,8},{4,5}}
[7,2,3,6,1,4,8,5]=>{{1,5,7,8},{2},{3},{4,6}}
[1,3,7,2,5,8,4,6]=>{{1},{2,3,4,7},{5},{6,8}}
[1,7,2,3,5,8,4,6]=>{{1},{2,3,4,7},{5},{6,8}}
[7,4,8,1,3,6,2,5]=>{{1,2,4,7},{3,5,8},{6}}
[8,1,2,3,5,7,4,6]=>{{1,2,3,4,6,7,8},{5}}
[7,1,2,3,5,8,4,6]=>{{1,2,3,4,7},{5},{6,8}}
[8,6,1,4,7,3,2,5]=>{{1,2,3,5,6,7,8},{4}}
[2,6,3,7,1,4,8,5]=>{{1,2,4,5,6,7,8},{3}}
[2,6,3,8,1,4,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[7,5,4,8,1,3,2,6]=>{{1,2,5,7},{3,4,6,8}}
[8,5,4,7,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,1,8,5,4,6,7]=>{{1,2,3},{4,6,7,8},{5}}
[8,6,5,1,3,4,2,7]=>{{1,2,4,6,7,8},{3,5}}
[8,5,1,7,6,3,4,2]=>{{1,2,3,5,6,8},{4,7}}
[3,4,7,6,1,8,5,2]=>{{1,3,5,7},{2,4,6,8}}
[3,5,2,6,7,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[3,2,8,4,7,5,1,6]=>{{1,3,5,6,7,8},{2},{4}}
[8,4,7,5,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[3,8,1,6,5,2,7,4]=>{{1,3},{2,4,6,8},{5},{7}}
[6,1,2,8,3,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[6,8,3,1,7,2,4,5]=>{{1,2,4,5,6,7,8},{3}}
[3,7,2,5,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,2,5,1,7,3]=>{{1,6},{2,3,4,8},{5},{7}}
[2,7,5,3,8,4,1,6]=>{{1,2,7},{3,4,5,6,8}}
[8,3,1,4,7,2,6,5]=>{{1,2,3,5,6,7,8},{4}}
[8,3,2,1,5,7,4,6]=>{{1,4,6,7,8},{2,3},{5}}
[2,8,3,6,4,7,1,5]=>{{1,2,4,5,6,7,8},{3}}
[7,3,6,4,8,1,2,5]=>{{1,2,3,6,7},{4},{5,8}}
[8,3,6,4,7,1,2,5]=>{{1,2,3,5,6,7,8},{4}}
[1,2,8,3,5,7,4,6]=>{{1},{2},{3,4,6,7,8},{5}}
[1,8,3,2,5,7,4,6]=>{{1},{2,4,6,7,8},{3},{5}}
[6,5,1,7,4,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,3,6,4,8,2,1,5]=>{{1,7},{2,3,6},{4},{5,8}}
[4,6,1,7,3,5,2,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,1,7,3,4,2,8]=>{{1,3,5},{2,4,6,7},{8}}
[6,1,7,3,4,2,8,5]=>{{1,2,6},{3,4,5,7,8}}
[7,3,8,1,6,5,2,4]=>{{1,2,3,4,7,8},{5,6}}
[8,3,7,1,6,5,2,4]=>{{1,4,8},{2,3,7},{5,6}}
[5,1,7,4,2,8,6,3]=>{{1,2,5},{3,6,7,8},{4}}
[2,8,1,7,6,5,3,4]=>{{1,2,3,4,7,8},{5,6}}
[4,2,8,6,5,1,7,3]=>{{1,4,6},{2},{3,8},{5},{7}}
[6,4,2,8,5,1,7,3]=>{{1,6},{2,3,4,8},{5},{7}}
[8,6,4,7,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[7,6,4,8,1,5,2,3]=>{{1,2,5,6,7},{3,4,8}}
[5,1,6,4,2,3,8,7]=>{{1,2,5},{3,6},{4},{7,8}}
[4,2,3,8,7,5,1,6]=>{{1,4,5,6,7,8},{2},{3}}
[3,8,7,1,6,5,2,4]=>{{1,2,3,4,7,8},{5,6}}
[2,4,3,8,1,6,7,5]=>{{1,2,4,5,8},{3},{6},{7}}
[2,4,3,7,1,6,8,5]=>{{1,2,4,5,7,8},{3},{6}}
[4,2,3,7,8,5,1,6]=>{{1,4,7},{2},{3},{5,6,8}}
[5,1,6,4,2,3,7,8]=>{{1,2,5},{3,6},{4},{7},{8}}
[6,4,7,8,1,5,2,3]=>{{1,5,6},{2,3,4,7,8}}
[8,7,4,6,1,5,2,3]=>{{1,3,4,5,6,8},{2,7}}
[6,5,7,8,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,6,1,5,2,3]=>{{1,4,5,6},{2,7},{3,8}}
[3,2,4,7,8,1,5,6]=>{{1,3,4,5,6,7,8},{2}}
[3,2,4,8,7,1,5,6]=>{{1,3,4,6,8},{2},{5,7}}
[4,8,7,6,1,5,2,3]=>{{1,4,5,6},{2,3,7,8}}
[5,8,7,6,1,4,2,3]=>{{1,5},{2,3,7,8},{4,6}}
[8,6,5,7,1,4,2,3]=>{{1,3,5,8},{2,4,6,7}}
[5,1,6,7,4,2,3,8]=>{{1,2,3,4,5,6,7},{8}}
[6,7,4,8,1,5,2,3]=>{{1,5,6},{2,7},{3,4,8}}
[8,4,7,6,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,3,2,4,7,1,5,6]=>{{1,6,8},{2,3},{4},{5,7}}
[7,3,2,4,8,1,5,6]=>{{1,5,6,7,8},{2,3},{4}}
[2,5,3,7,1,6,4,8]=>{{1,2,5},{3},{4,7},{6},{8}}
[8,4,6,7,1,5,2,3]=>{{1,3,5,6,8},{2,4,7}}
[7,4,6,8,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,8,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[4,2,3,7,5,1,6,8]=>{{1,4,6,7},{2},{3},{5},{8}}
[3,7,5,8,1,6,2,4]=>{{1,3,5},{2,7},{4,8},{6}}
[2,4,3,7,1,6,5,8]=>{{1,2,4,5,7},{3},{6},{8}}
[2,4,7,1,5,8,6,3]=>{{1,2,4},{3,6,7,8},{5}}
[3,2,4,7,6,1,5,8]=>{{1,3,4,5,6,7},{2},{8}}
[4,7,6,8,1,5,2,3]=>{{1,3,4,5,6,8},{2,7}}
[8,5,6,7,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,5,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,5,1,4,2,3]=>{{1,2,4,5,6,7},{3,8}}
[6,8,7,5,1,4,2,3]=>{{1,4,5,6},{2,3,7,8}}
[5,6,8,7,1,4,2,3]=>{{1,5},{2,4,6,7},{3,8}}
[4,6,8,7,1,5,2,3]=>{{1,2,4,5,6,7},{3,8}}
[2,4,6,7,1,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,2,4,6,1,5,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[6,7,8,5,1,4,2,3]=>{{1,4,5,6},{2,7},{3,8}}
[7,8,6,5,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,5,4,2,8,6]=>{{1,2,3,6,7,8},{4,5}}
[2,1,8,5,4,6,3,7]=>{{1,2},{3,7,8},{4,5},{6}}
[4,1,8,5,2,3,6,7]=>{{1,2,4,5},{3,6,7,8}}
[5,4,1,3,6,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[8,4,1,2,6,3,7,5]=>{{1,3,5,6,8},{2,4},{7}}
[8,2,7,1,5,3,4,6]=>{{1,3,4,6,7,8},{2},{5}}
[3,2,7,1,5,8,4,6]=>{{1,3,4,7},{2},{5},{6,8}}
[6,3,7,1,5,4,2,8]=>{{1,4,6},{2,3,7},{5},{8}}
[7,3,8,1,5,4,2,6]=>{{1,2,3,4,6,7,8},{5}}
[7,1,5,3,8,4,2,6]=>{{1,2,7},{3,4,5,6,8}}
[4,5,1,3,6,8,2,7]=>{{1,3,4},{2,5,6,7,8}}
[3,6,8,1,5,4,2,7]=>{{1,2,3,4,6,7,8},{5}}
[6,8,3,1,5,4,2,7]=>{{1,4,6},{2,7,8},{3},{5}}
[7,6,3,1,5,4,2,8]=>{{1,2,4,6,7},{3},{5},{8}}
[3,6,2,1,5,8,4,7]=>{{1,2,3,4,6,7,8},{5}}
[8,6,2,1,5,3,4,7]=>{{1,4,7,8},{2,3,6},{5}}
[4,8,2,1,7,5,3,6]=>{{1,4},{2,3,5,6,7,8}}
[2,3,8,1,5,7,4,6]=>{{1,2,3,4,6,7,8},{5}}
[7,1,3,2,8,6,4,5]=>{{1,2,4,7},{3},{5,8},{6}}
[7,1,6,2,8,3,4,5]=>{{1,2,4,7},{3,6},{5,8}}
[4,7,1,2,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,1,5,3,4,6]=>{{1,2,4,7},{3,6,8},{5}}
[6,7,2,1,5,3,4,8]=>{{1,2,3,4,6,7},{5},{8}}
[4,7,2,1,8,5,3,6]=>{{1,4},{2,3,7},{5,6,8}}
[8,7,2,1,4,5,3,6]=>{{1,4,5,6,8},{2,3,7}}
[8,7,5,6,1,4,3,2]=>{{1,2,3,5,7,8},{4,6}}
[5,7,8,6,1,4,3,2]=>{{1,5},{2,3,7,8},{4,6}}
[2,7,4,1,6,5,3,8]=>{{1,2,3,4,7},{5,6},{8}}
[3,7,1,4,5,6,8,2]=>{{1,3},{2,7,8},{4},{5},{6}}
[7,1,6,4,5,8,3,2]=>{{1,2,3,6,7,8},{4},{5}}
[3,5,1,4,7,6,8,2]=>{{1,3},{2,5,7,8},{4},{6}}
[2,6,4,1,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,8,7,1,4,3,2]=>{{1,5},{2,3,4,6,7,8}}
[6,8,5,7,1,4,3,2]=>{{1,3,4,5,6,7},{2,8}}
[8,6,5,7,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,6,1,4,3,2]=>{{1,2,5,8},{3,7},{4,6}}
[6,5,7,8,1,4,3,2]=>{{1,2,4,5,6,8},{3,7}}
[7,2,3,1,5,6,4,8]=>{{1,4,7},{2},{3},{5},{6},{8}}
[4,2,8,1,6,5,3,7]=>{{1,4},{2},{3,7,8},{5,6}}
[6,2,4,1,8,5,3,7]=>{{1,3,4,5,6,7,8},{2}}
[8,3,1,4,5,6,7,2]=>{{1,2,3,8},{4},{5},{6},{7}}
[5,3,1,4,8,6,7,2]=>{{1,2,3,5,8},{4},{6},{7}}
[7,5,1,6,3,4,8,2]=>{{1,2,3,5,7,8},{4,6}}
[7,1,5,8,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,6,4,3,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[5,3,1,8,4,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[8,3,1,5,4,6,7,2]=>{{1,2,3,8},{4,5},{6},{7}}
[8,2,6,1,4,5,3,7]=>{{1,3,4,5,6,7,8},{2}}
[6,2,8,1,4,5,3,7]=>{{1,4,5,6},{2},{3,7,8}}
[7,2,6,1,5,3,4,8]=>{{1,4,7},{2},{3,6},{5},{8}}
[2,8,6,1,5,3,4,7]=>{{1,2,4,7,8},{3,6},{5}}
[4,2,1,5,6,3,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[7,1,2,5,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,1,4,5,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,7,1,4,3,2]=>{{1,2,5,8},{3,4,6,7}}
[7,6,8,5,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,5,1,4,3,2]=>{{1,4,5,6},{2,8},{3,7}}
[2,6,7,1,4,5,3,8]=>{{1,2,4,5,6},{3,7},{8}}
[3,5,1,7,4,6,8,2]=>{{1,3},{2,4,5,7,8},{6}}
[7,1,5,6,4,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,5,4,8,3,2]=>{{1,2,3,6,7,8},{4,5}}
[2,7,6,1,4,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,7,6,8,1,4,3,2]=>{{1,5},{2,3,4,6,7,8}}
[7,8,6,5,1,4,3,2]=>{{1,3,4,5,6,7},{2,8}}
[4,3,1,6,5,8,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[5,3,1,2,4,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[5,3,6,2,1,8,7,4]=>{{1,5},{2,3,4,6,8},{7}}
[5,3,7,2,1,4,6,8]=>{{1,5},{2,3,4,6,7},{8}}
[5,3,7,2,8,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[7,2,4,5,8,3,1,6]=>{{1,7},{2},{3,4,5,6,8}}
[7,2,4,5,1,3,6,8]=>{{1,3,4,5,6,7},{2},{8}}
[6,2,4,5,1,8,7,3]=>{{1,3,4,5,6,8},{2},{7}}
[3,1,4,5,2,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[1,6,4,5,2,8,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[3,7,4,5,1,2,6,8]=>{{1,3,4,5},{2,6,7},{8}}
[3,7,4,5,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[1,7,4,2,6,3,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,7,4,5,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,1,8,4,2,5]=>{{1,4,6},{2,3,7},{5,8}}
[5,7,4,1,6,3,2,8]=>{{1,3,4,5,6},{2,7},{8}}
[1,7,4,8,6,3,2,5]=>{{1},{2,7},{3,4,5,6,8}}
[5,7,4,8,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[4,8,3,5,6,7,1,2]=>{{1,4,5,6,7},{2,8},{3}}
[1,8,3,5,6,7,2,4]=>{{1},{2,4,5,6,7,8},{3}}
[4,8,1,5,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[4,1,3,5,6,7,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,8,4,3,6,1,2,7]=>{{1,5,6},{2,7,8},{3,4}}
[5,3,8,4,1,7,2,6]=>{{1,5},{2,3,6,7,8},{4}}
[1,5,8,4,6,7,3,2]=>{{1},{2,3,5,6,7,8},{4}}
[1,4,8,3,6,7,5,2]=>{{1},{2,3,4,8},{5,6,7}}
[4,3,8,2,1,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,8,4,2,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,8,2,5,6,7,4,3]=>{{1},{2,3,8},{4,5,6,7}}
[3,8,1,5,6,7,4,2]=>{{1,3},{2,8},{4,5,6,7}}
[3,8,2,5,6,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,5,6,7,4,3]=>{{1,3,8},{2},{4,5,6,7}}
[8,1,3,5,6,7,4,2]=>{{1,2,8},{3},{4,5,6,7}}
[7,1,4,3,6,2,5,8]=>{{1,2,5,6,7},{3,4},{8}}
[7,8,4,3,6,2,1,5]=>{{1,7},{2,5,6,8},{3,4}}
[4,3,1,8,5,7,6,2]=>{{1,2,3,4,8},{5},{6,7}}
[4,3,1,6,8,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,8,2,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,8,2,7,1,4]=>{{1,6,7},{2,3,5},{4,8}}
[7,5,4,8,6,2,1,3]=>{{1,7},{2,5,6},{3,4,8}}
[7,1,4,8,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,5,4,1,6,2,3,8]=>{{1,3,4,7},{2,5,6},{8}}
[7,6,4,5,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,5,8,2,3,7]=>{{1},{2,6},{3,4,5,7,8}}
[7,3,6,1,8,2,4,5]=>{{1,4,7},{2,3,6},{5,8}}
[1,7,6,5,8,3,4,2]=>{{1},{2,4,5,7,8},{3,6}}
[1,8,5,3,6,7,4,2]=>{{1},{2,8},{3,4,5,6,7}}
[8,3,5,2,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,5,6,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,5,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[4,1,8,5,6,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[1,2,8,5,6,7,3,4]=>{{1},{2},{3,4,5,6,7,8}}
[4,2,1,5,6,7,3,8]=>{{1,3,4,5,6,7},{2},{8}}
[1,5,3,8,6,7,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,4,5,8,6,7,3,2]=>{{1},{2,4,8},{3,5,6,7}}
[4,3,5,8,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[3,5,4,8,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,4,8,5,6,7,2,3]=>{{1},{2,4,5,6,7},{3,8}}
[3,4,8,5,6,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[2,7,1,5,6,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,7,1,4,3,6,5,8]=>{{1,2,3,5,7},{4},{6},{8}}
[4,3,7,2,5,6,8,1]=>{{1,2,3,4,7,8},{5},{6}}
[2,6,3,1,4,5,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[3,7,1,4,2,6,8,5]=>{{1,3},{2,5,7,8},{4},{6}}
[3,7,1,5,6,2,8,4]=>{{1,3},{2,4,5,6,7,8}}
[4,7,1,5,6,8,2,3]=>{{1,3,4,5,6,8},{2,7}}
[8,5,2,6,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,6,3,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,3,5,7,1,6]=>{{1,6,7,8},{2,3,4},{5}}
[4,7,3,2,5,6,1,8]=>{{1,2,4,7},{3},{5},{6},{8}}
[5,3,4,6,2,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,4,2,8,1,6]=>{{1,2,3,5,7},{4},{6,8}}
[6,4,7,2,3,8,1,5]=>{{1,3,5,6,7,8},{2,4}}
[6,5,7,2,8,3,1,4]=>{{1,3,6,7},{2,4,5,8}}
[5,3,7,2,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[2,6,5,1,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,1,4,5,2,3]=>{{1,3,4,5,6,8},{2,7}}
[8,7,6,1,3,2,5,4]=>{{1,4,8},{2,3,5,6,7}}
[8,7,2,4,3,1,6,5]=>{{1,2,3,5,6,7,8},{4}}
[8,7,4,5,1,6,2,3]=>{{1,3,4,5,8},{2,7},{6}}
[8,5,6,4,1,7,2,3]=>{{1,2,3,5,6,7,8},{4}}
[8,5,6,3,1,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[8,4,6,2,3,1,7,5]=>{{1,3,5,6,8},{2,4},{7}}
[8,3,5,4,2,1,7,6]=>{{1,6,8},{2,3,5},{4},{7}}
[5,7,3,4,2,1,8,6]=>{{1,2,5,6,7,8},{3},{4}}
[6,7,4,2,3,1,8,5]=>{{1,6},{2,3,4,5,7,8}}
[6,7,5,3,1,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,5,4,1,8,2,3]=>{{1,3,5,6,8},{2,7},{4}}
[7,3,5,4,1,8,6,2]=>{{1,2,3,5,6,7,8},{4}}
[2,6,5,7,3,1,8,4]=>{{1,2,6},{3,5},{4,7,8}}
[6,3,2,4,7,5,1,8]=>{{1,5,6,7},{2,3},{4},{8}}
[4,2,1,6,3,7,5,8]=>{{1,3,4,5,6,7},{2},{8}}
[4,2,1,6,3,7,8,5]=>{{1,3,4,5,6,7,8},{2}}
[4,2,1,3,7,8,6,5]=>{{1,3,4},{2},{5,6,7,8}}
[5,8,1,7,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,2,1,8,3,5,6,7]=>{{1,3,4,5,6,7,8},{2}}
[4,2,1,6,3,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[7,3,4,2,6,8,1,5]=>{{1,7},{2,3,4},{5,6,8}}
[3,6,7,5,2,4,8,1]=>{{1,3,7,8},{2,4,5,6}}
[3,6,7,5,2,4,1,8]=>{{1,3,7},{2,4,5,6},{8}}
[4,2,1,7,3,6,5,8]=>{{1,3,4,5,7},{2},{6},{8}}
[3,7,6,8,4,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,7,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,6,2,4,5,1]=>{{1,3,8},{2,5,7},{4,6}}
[4,2,1,3,5,8,6,7]=>{{1,3,4},{2},{5},{6,7,8}}
[4,8,1,7,3,6,5,2]=>{{1,3,4,5,7},{2,8},{6}}
[4,2,1,8,3,7,6,5]=>{{1,3,4,5,8},{2},{6,7}}
[2,6,1,5,4,7,8,3]=>{{1,2,3,6,7,8},{4,5}}
[4,6,3,5,8,7,1,2]=>{{1,2,4,5,6,7,8},{3}}
[3,5,6,1,4,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[2,7,5,1,8,3,4,6]=>{{1,2,4,7},{3,5,6,8}}
[4,7,5,2,1,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,6,2,4,1,7,8]=>{{1,3,6},{2,4,5},{7},{8}}
[2,5,6,1,4,8,3,7]=>{{1,2,4,5},{3,6,7,8}}
[6,7,8,4,1,5,3,2]=>{{1,5,6},{2,3,7,8},{4}}
[7,1,6,8,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,5,2,8,1,3]=>{{1,7},{2,4,5},{3,6,8}}
[7,1,5,6,4,2,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,7,4,6,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,1,4,6,3,2]=>{{1,4,5},{2,3,7,8},{6}}
[8,1,5,7,4,6,3,2]=>{{1,2,8},{3,4,5,7},{6}}
[1,8,4,6,7,5,3,2]=>{{1},{2,8},{3,4,5,6,7}}
[6,1,8,4,7,5,3,2]=>{{1,2,3,5,6,7,8},{4}}
[4,5,8,6,1,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,1,6,7,3,2]=>{{1,4},{2,8},{3,5,6,7}}
[8,1,4,5,6,7,3,2]=>{{1,2,8},{3,4,5,6,7}}
[5,6,7,1,4,2,3,8]=>{{1,4,5},{2,6},{3,7},{8}}
[8,4,2,6,1,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[4,8,5,2,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[5,1,8,4,2,6,3,7]=>{{1,2,5},{3,7,8},{4},{6}}
[1,8,4,6,2,5,3,7]=>{{1},{2,3,4,5,6,7,8}}
[6,1,5,2,3,4,7,8]=>{{1,2,4,6},{3,5},{7},{8}}
[8,3,1,4,6,2,5,7]=>{{1,2,3,5,6,7,8},{4}}
[3,1,8,2,5,6,4,7]=>{{1,2,3,4,7,8},{5},{6}}
[3,5,1,8,2,6,4,7]=>{{1,3},{2,5},{4,7,8},{6}}
[3,5,1,2,8,4,7,6]=>{{1,3},{2,4,5,6,8},{7}}
[2,3,5,8,6,1,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[8,2,4,3,6,7,1,5]=>{{1,5,6,7,8},{2},{3,4}}
[3,2,8,5,7,1,6,4]=>{{1,3,4,5,6,7,8},{2}}
[3,6,2,8,5,1,7,4]=>{{1,2,3,6},{4,8},{5},{7}}
[6,2,1,8,4,7,5,3]=>{{1,3,4,5,6,7,8},{2}}
[2,8,7,1,4,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[8,2,7,1,5,4,6,3]=>{{1,3,4,6,7,8},{2},{5}}
[7,2,5,3,6,8,1,4]=>{{1,7},{2},{3,4,5,6,8}}
[7,3,1,5,6,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[3,7,5,1,6,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,7,3,6,5,8,1,4]=>{{1,2,7},{3},{4,6,8},{5}}
[8,7,2,4,1,6,5,3]=>{{1,2,3,5,7,8},{4},{6}}
[1,8,7,2,3,6,5,4]=>{{1},{2,4,8},{3,5,7},{6}}
[1,7,8,2,6,4,3,5]=>{{1},{2,3,4,5,6,7,8}}
[1,7,3,8,2,6,4,5]=>{{1},{2,4,5,7,8},{3},{6}}
[1,2,7,3,6,4,5,8]=>{{1},{2},{3,4,5,6,7},{8}}
[7,1,5,8,3,2,4,6]=>{{1,2,4,6,7,8},{3,5}}
[1,6,2,8,4,3,7,5]=>{{1},{2,3,6},{4,5,8},{7}}
[1,3,8,7,2,4,6,5]=>{{1},{2,3,5,8},{4,6,7}}
[1,8,3,7,2,5,4,6]=>{{1},{2,5,6,8},{3},{4,7}}
[8,1,4,7,3,2,5,6]=>{{1,2,6,8},{3,4,5,7}}
[4,7,8,1,3,2,5,6]=>{{1,4},{2,3,5,6,7,8}}
[7,1,4,2,3,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[8,2,1,4,7,3,5,6]=>{{1,3,6,8},{2},{4},{5,7}}
[2,1,3,8,4,6,7,5]=>{{1,2},{3},{4,5,8},{6},{7}}
[1,2,3,4,8,5,7,6]=>{{1},{2},{3},{4},{5,6,8},{7}}
[2,4,7,5,6,8,3,1]=>{{1,2,4,5,6,8},{3,7}}
[2,4,8,7,5,6,3,1]=>{{1,2,3,4,7,8},{5},{6}}
[2,5,3,8,4,7,6,1]=>{{1,2,4,5,8},{3},{6,7}}
[3,1,8,5,2,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[2,8,6,3,4,5,7,1]=>{{1,2,8},{3,4,5,6},{7}}
[2,5,7,3,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,6,1,4,5,2]=>{{1,2,3,5,7,8},{4,6}}
[3,1,7,8,2,5,6,4]=>{{1,2,3,5,6,7},{4,8}}
[7,3,8,5,1,6,4,2]=>{{1,4,5,7},{2,3,8},{6}}
[7,5,1,2,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,5,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,5,3,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[4,3,6,8,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,1,8,2,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[6,4,8,1,2,5,3,7]=>{{1,2,4,5,6},{3,7,8}}
[6,7,3,1,4,8,5,2]=>{{1,2,4,5,6,7,8},{3}}
[5,4,1,6,8,2,7,3]=>{{1,3,5,8},{2,4,6},{7}}
[5,4,7,1,2,8,6,3]=>{{1,2,4,5},{3,6,7,8}}
[6,7,4,1,2,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,5,1,2,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,1,2,3,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[6,7,4,1,2,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[2,4,6,3,5,7,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[8,6,2,5,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[8,2,3,4,5,1,7,6]=>{{1,6,8},{2},{3},{4},{5},{7}}
[1,8,3,4,2,7,5,6]=>{{1},{2,5,6,7,8},{3},{4}}
[2,8,3,4,1,6,7,5]=>{{1,2,5,8},{3},{4},{6},{7}}
[8,7,2,3,1,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[3,8,2,4,6,1,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[7,8,2,4,3,1,6,5]=>{{1,6,7},{2,3,5,8},{4}}
[4,5,8,2,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,1,4,3,7,2,6,8]=>{{1,2,5,6,7},{3,4},{8}}
[6,1,3,5,7,2,4,8]=>{{1,2,6},{3},{4,5,7},{8}}
[2,1,4,7,5,3,6,8]=>{{1,2},{3,4,6,7},{5},{8}}
[7,1,3,6,2,5,4,8]=>{{1,2,4,5,6,7},{3},{8}}
[8,1,3,6,2,4,7,5]=>{{1,2,5,8},{3},{4,6},{7}}
[2,1,8,3,7,5,4,6]=>{{1,2},{3,4,5,6,7,8}}
[7,1,8,2,5,6,3,4]=>{{1,2,3,4,7,8},{5},{6}}
[6,1,5,8,2,7,3,4]=>{{1,2,3,5,6,7},{4,8}}
[4,5,2,8,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[6,2,5,8,1,4,7,3]=>{{1,3,4,5,6,8},{2},{7}}
[3,2,8,5,1,6,7,4]=>{{1,3,4,5,8},{2},{6},{7}}
[8,2,7,1,4,6,5,3]=>{{1,3,4,5,7,8},{2},{6}}
[1,3,8,2,5,7,4,6]=>{{1},{2,3,4,6,7,8},{5}}
[2,8,7,1,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,1,5,6,4,2]=>{{1,3,4,7},{2,8},{5},{6}}
[3,4,8,5,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[8,3,7,4,1,6,5,2]=>{{1,2,3,5,7,8},{4},{6}}
[1,4,8,6,2,7,3,5]=>{{1},{2,3,4,5,6,7,8}}
[8,4,5,7,1,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[3,5,6,8,4,1,7,2]=>{{1,3,6},{2,4,5,8},{7}}
[6,2,3,1,5,4,7,8]=>{{1,4,6},{2},{3},{5},{7},{8}}
[7,2,3,1,4,6,5,8]=>{{1,4,5,7},{2},{3},{6},{8}}
[8,2,3,1,4,5,7,6]=>{{1,4,5,6,8},{2},{3},{7}}
[8,5,1,3,2,4,7,6]=>{{1,3,4,6,8},{2,5},{7}}
[7,5,1,3,2,6,4,8]=>{{1,3,4,7},{2,5},{6},{8}}
[2,6,1,4,5,3,7,8]=>{{1,2,3,6},{4},{5},{7},{8}}
[3,6,4,1,5,2,7,8]=>{{1,3,4},{2,6},{5},{7},{8}}
[4,5,6,1,3,2,7,8]=>{{1,4},{2,3,5,6},{7},{8}}
[4,5,7,1,2,6,3,8]=>{{1,4},{2,5},{3,7},{6},{8}}
[3,7,4,1,2,6,5,8]=>{{1,3,4},{2,5,7},{6},{8}}
[6,7,1,4,2,5,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[2,7,1,3,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}
[8,6,1,2,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,8,1,3,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[7,8,1,2,5,3,6,4]=>{{1,3,6,7},{2,4,8},{5}}
[3,8,4,1,2,5,7,6]=>{{1,3,4},{2,5,6,8},{7}}
[1,2,6,7,5,3,8,4]=>{{1},{2},{3,6},{4,7,8},{5}}
[1,7,5,3,2,8,4,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,6,7,5,3,8,4,2]=>{{1},{2,6,8},{3,4,5,7}}
[1,6,5,7,2,3,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[1,3,8,2,6,5,7,4]=>{{1},{2,3,4,8},{5,6},{7}}
[1,2,5,7,6,3,4,8]=>{{1},{2},{3,5,6},{4,7},{8}}
[1,3,4,8,2,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,5,7,6,2,3,4,8]=>{{1},{2,5},{3,4,6,7},{8}}
[1,5,3,8,2,6,4,7]=>{{1},{2,5},{3},{4,7,8},{6}}
[1,4,8,3,2,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,4,8,3,5,7,6,2]=>{{1},{2,3,4,8},{5},{6,7}}
[1,2,4,8,3,5,7,6]=>{{1},{2},{3,4,5,6,8},{7}}
[1,3,8,4,2,6,7,5]=>{{1},{2,3,5,8},{4},{6},{7}}
[1,4,8,2,3,5,7,6]=>{{1},{2,4},{3,5,6,8},{7}}
[6,5,7,3,8,2,4,1]=>{{1,2,5,6,8},{3,4,7}}
[4,2,6,7,5,8,3,1]=>{{1,3,4,6,7,8},{2},{5}}
[6,7,5,2,1,8,4,3]=>{{1,3,5,6,8},{2,4,7}}
[3,4,8,7,5,2,1,6]=>{{1,2,3,4,6,7,8},{5}}
[1,7,5,2,8,4,6,3]=>{{1},{2,4,6,7},{3,5,8}}
[5,6,8,3,1,7,2,4]=>{{1,5},{2,6,7},{3,4,8}}
[6,1,4,8,3,2,7,5]=>{{1,2,6},{3,4,5,8},{7}}
[3,4,7,1,8,6,2,5]=>{{1,2,3,4,7},{5,8},{6}}
[3,4,6,8,2,1,5,7]=>{{1,3,6},{2,4,5,7,8}}
[3,8,2,5,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,8,6,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,2,5,7,3,8,6,1]=>{{1,4,6,7,8},{2},{3,5}}
[7,4,2,5,3,8,1,6]=>{{1,7},{2,3,4,5},{6,8}}
[3,1,2,8,5,6,4,7]=>{{1,2,3},{4,7,8},{5},{6}}
[5,2,1,6,8,3,4,7]=>{{1,3,4,5,6,7,8},{2}}
[5,2,6,8,4,1,3,7]=>{{1,3,4,5,6,7,8},{2}}
[1,5,6,8,3,4,2,7]=>{{1},{2,3,4,5,6,7,8}}
[4,5,8,1,6,3,2,7]=>{{1,4},{2,3,5,6,7,8}}
[4,5,1,6,8,3,2,7]=>{{1,3,4,6},{2,5,7,8}}
[4,5,7,3,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,3,7,8,2,5,1]=>{{1,2,4,5,6,7,8},{3}}
[6,4,3,1,7,8,2,5]=>{{1,2,4,5,6,7,8},{3}}
[4,5,3,1,7,8,2,6]=>{{1,4},{2,5,7},{3},{6,8}}
[7,1,3,5,4,8,2,6]=>{{1,2,7},{3},{4,5},{6,8}}
[7,5,2,8,1,4,3,6]=>{{1,2,3,5,7},{4,6,8}}
[5,7,3,8,4,6,1,2]=>{{1,2,4,5,7,8},{3},{6}}
[1,4,5,7,3,8,6,2]=>{{1},{2,4,6,7,8},{3,5}}
[4,6,3,7,8,5,2,1]=>{{1,2,4,5,6,7,8},{3}}
[5,3,6,7,8,4,2,1]=>{{1,5,8},{2,3,4,6,7}}
[1,5,3,6,7,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,6,1,7,3,8,5,2]=>{{1,3,4,5,7},{2,6,8}}
[6,3,7,1,8,4,5,2]=>{{1,4,6},{2,3,5,7,8}}
[6,7,2,4,8,1,5,3]=>{{1,6},{2,3,5,7,8},{4}}
[2,6,1,4,7,3,8,5]=>{{1,2,3,6},{4},{5,7,8}}
[3,2,5,6,7,8,1,4]=>{{1,3,5,7},{2},{4,6,8}}
[5,2,3,6,7,8,4,1]=>{{1,4,5,6,7,8},{2},{3}}
[6,7,1,3,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[6,2,7,1,3,4,8,5]=>{{1,4,6},{2},{3,5,7,8}}
[5,2,1,7,3,8,4,6]=>{{1,3,5},{2},{4,7},{6,8}}
[6,4,2,7,1,8,3,5]=>{{1,5,6,8},{2,3,4,7}}
[4,2,6,3,7,8,1,5]=>{{1,3,4,5,6,7,8},{2}}
[4,2,6,3,7,8,5,1]=>{{1,3,4,6,8},{2},{5,7}}
[6,7,3,8,2,4,5,1]=>{{1,4,6,8},{2,5,7},{3}}
[3,6,2,7,4,1,8,5]=>{{1,2,3,6},{4,5,7,8}}
[6,7,3,2,1,4,8,5]=>{{1,2,4,5,6,7,8},{3}}
[7,1,8,3,4,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,2,4,1,8,3,5,6]=>{{1,3,4,5,6,7,8},{2}}
[7,2,4,8,6,1,3,5]=>{{1,3,4,5,6,7,8},{2}}
[7,3,4,8,6,2,1,5]=>{{1,7},{2,3,4,5,6,8}}
[3,5,7,2,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,3,2,5,1,4]=>{{1,2,5,6,7},{3,4,8}}
[6,3,7,8,2,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,6,7,4,8,5,3,1]=>{{1,2,5,6,8},{3,7},{4}}
[6,2,4,7,1,8,5,3]=>{{1,3,4,5,6,7,8},{2}}
[4,6,2,7,1,8,5,3]=>{{1,4,5,7},{2,3,6,8}}
[1,7,4,8,5,2,6,3]=>{{1},{2,6,7},{3,4,8},{5}}
[1,3,7,8,5,2,6,4]=>{{1},{2,3,6,7},{4,8},{5}}
[2,5,7,8,1,6,3,4]=>{{1,2,5},{3,7},{4,8},{6}}
[6,3,7,1,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,5,6,1,7,8,4,3]=>{{1,2,4,5,7},{3,6,8}}
[5,6,1,2,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,1,8,5,3,4]=>{{1,4,5,6,8},{2,3,7}}
[6,7,2,8,5,4,1,3]=>{{1,2,3,4,6,7,8},{5}}
[1,6,7,4,8,5,3,2]=>{{1},{2,5,6,8},{3,7},{4}}
[1,8,2,4,6,3,5,7]=>{{1},{2,3,5,6,7,8},{4}}
[1,5,7,4,3,6,2,8]=>{{1},{2,3,5,7},{4},{6},{8}}
[1,8,4,5,3,6,2,7]=>{{1},{2,7,8},{3,4,5},{6}}
[1,8,5,3,4,7,2,6]=>{{1},{2,6,7,8},{3,4,5}}
[1,8,2,4,6,3,7,5]=>{{1},{2,3,5,6,8},{4},{7}}
[1,8,2,5,4,6,7,3]=>{{1},{2,3,8},{4,5},{6},{7}}
[3,6,2,7,1,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[1,4,7,5,2,6,8,3]=>{{1},{2,4,5},{3,7,8},{6}}
[4,6,5,3,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[4,2,3,8,6,7,1,5]=>{{1,4,5,6,7,8},{2},{3}}
[5,2,4,8,1,3,7,6]=>{{1,5},{2},{3,4,6,8},{7}}
[6,2,5,4,8,3,7,1]=>{{1,3,5,6,8},{2},{4},{7}}
[6,4,3,5,8,2,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[5,2,3,4,8,1,6,7]=>{{1,5,6,7,8},{2},{3},{4}}
[3,5,2,4,7,1,6,8]=>{{1,2,3,5,6,7},{4},{8}}
[5,3,4,8,1,6,2,7]=>{{1,5},{2,3,4,7,8},{6}}
[4,5,3,7,1,6,2,8]=>{{1,2,4,5,7},{3},{6},{8}}
[7,6,3,8,5,1,2,4]=>{{1,2,6,7},{3},{4,8},{5}}
[4,2,6,7,3,8,1,5]=>{{1,4,7},{2},{3,5,6,8}}
[1,5,7,4,2,8,6,3]=>{{1},{2,5},{3,6,7,8},{4}}
[1,3,7,2,8,6,4,5]=>{{1},{2,3,4,7},{5,8},{6}}
[1,4,3,7,8,6,2,5]=>{{1},{2,4,7},{3},{5,8},{6}}
[1,5,3,6,8,2,7,4]=>{{1},{2,4,5,6,8},{3},{7}}
[4,3,6,5,7,8,1,2]=>{{1,4,5,7},{2,3,6,8}}
[4,2,3,5,6,8,1,7]=>{{1,4,5,6,7,8},{2},{3}}
[5,2,6,4,7,8,3,1]=>{{1,3,5,6,7,8},{2},{4}}
[4,2,6,7,3,8,5,1]=>{{1,3,4,5,6,7,8},{2}}
[3,2,5,6,8,1,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[6,4,5,2,3,8,7,1]=>{{1,6,8},{2,4},{3,5},{7}}
[6,4,2,5,3,8,7,1]=>{{1,6,8},{2,3,4,5},{7}}
[8,6,2,7,4,5,3,1]=>{{1,8},{2,3,4,5,6,7}}
[6,4,2,5,8,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[4,6,2,5,3,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,6,5,2,3,8,7,1]=>{{1,2,4,6,8},{3,5},{7}}
[6,8,2,7,4,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,2,4,5,3,1]=>{{1,2,4,5,6,8},{3,7}}
[2,6,4,5,8,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,6,4,8,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[8,2,4,6,7,5,3,1]=>{{1,8},{2},{3,4,5,6,7}}
[4,2,6,8,7,5,3,1]=>{{1,4,8},{2},{3,5,6,7}}
[4,2,6,5,8,7,3,1]=>{{1,4,5,8},{2},{3,6,7}}
[4,2,3,6,8,7,5,1]=>{{1,4,5,6,7,8},{2},{3}}
[6,4,8,7,2,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,7,5,2,3,1]=>{{1,2,3,4,6,7,8},{5}}
[4,6,5,8,7,2,3,1]=>{{1,4,8},{2,6},{3,5,7}}
[8,2,6,4,7,5,3,1]=>{{1,8},{2},{3,5,6,7},{4}}
[4,6,8,2,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,8,2,7,3,1]=>{{1,4,8},{2,3,5,6,7}}
[2,1,8,6,4,7,5,3]=>{{1,2},{3,8},{4,5,6,7}}
[6,8,7,4,2,5,3,1]=>{{1,2,5,6,8},{3,7},{4}}
[4,2,5,6,3,8,1,7]=>{{1,4,6,7,8},{2},{3,5}}
[6,2,5,7,4,8,3,1]=>{{1,6,8},{2},{3,4,5,7}}
[8,5,2,1,4,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[6,7,3,2,5,8,4,1]=>{{1,6,8},{2,4,7},{3},{5}}
[3,2,6,4,8,1,5,7]=>{{1,3,6},{2},{4},{5,7,8}}
[2,3,6,4,7,8,5,1]=>{{1,2,3,6,8},{4},{5,7}}
[7,5,1,8,3,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,2,6,3,4,1]=>{{1,3,5,6,8},{2,4,7}}
[7,1,6,3,5,8,4,2]=>{{1,2,3,4,6,7,8},{5}}
[6,3,1,7,8,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,7,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[7,3,1,2,5,8,6,4]=>{{1,2,3,4,6,7,8},{5}}
[1,6,3,5,2,4,8,7]=>{{1},{2,4,5,6},{3},{7,8}}
[3,4,8,2,7,5,1,6]=>{{1,3,5,6,7,8},{2,4}}
[6,3,2,8,5,7,4,1]=>{{1,4,6,7,8},{2,3},{5}}
[3,8,4,7,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,1,5,3,7,6]=>{{1,2,4},{3,6,8},{5},{7}}
[3,4,8,1,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[1,8,4,6,7,3,5,2]=>{{1},{2,8},{3,4,6},{5,7}}
[8,1,6,3,4,5,7,2]=>{{1,2,8},{3,4,5,6},{7}}
[7,6,5,4,1,2,8,3]=>{{1,3,5,7,8},{2,6},{4}}
[5,7,6,8,3,4,2,1]=>{{1,3,4,5,6,8},{2,7}}
[2,8,1,6,5,7,4,3]=>{{1,2,3,8},{4,6,7},{5}}
[4,6,8,2,5,3,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[5,2,3,7,6,1,8,4]=>{{1,5,6},{2},{3},{4,7,8}}
[8,1,2,4,6,7,3,5]=>{{1,2,3,5,6,7,8},{4}}
[5,2,3,7,4,8,6,1]=>{{1,4,5,6,7,8},{2},{3}}
[5,2,6,8,4,3,1,7]=>{{1,4,5,7,8},{2},{3,6}}
[7,8,1,5,4,3,6,2]=>{{1,3,6,7},{2,8},{4,5}}
[7,2,4,8,5,3,6,1]=>{{1,3,4,6,7,8},{2},{5}}
[3,7,5,1,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,5,4,6,1,3]=>{{1,2,7},{3,8},{4,5},{6}}
[5,7,4,3,8,6,2,1]=>{{1,5,8},{2,7},{3,4},{6}}
[4,8,1,6,3,5,2,7]=>{{1,3,4,5,6},{2,7,8}}
[8,3,1,7,4,2,5,6]=>{{1,2,3,6,8},{4,5,7}}
[3,1,8,2,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[8,1,3,7,6,2,4,5]=>{{1,2,5,6,8},{3},{4,7}}
[2,3,6,8,7,1,4,5]=>{{1,2,3,6},{4,5,7,8}}
[4,3,2,8,5,7,1,6]=>{{1,4,6,7,8},{2,3},{5}}
[3,6,4,2,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,7,3,2,5,1,8,6]=>{{1,2,4,6,7,8},{3},{5}}
[3,2,4,7,5,8,6,1]=>{{1,3,4,6,7,8},{2},{5}}
[4,2,3,8,6,5,1,7]=>{{1,4,7,8},{2},{3},{5,6}}
[2,4,3,5,1,8,6,7]=>{{1,2,4,5},{3},{6,7,8}}
[3,2,8,1,4,6,5,7]=>{{1,3,4,5,7,8},{2},{6}}
[4,7,8,3,1,2,6,5]=>{{1,3,4,5,8},{2,6,7}}
[4,7,8,2,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[4,1,6,8,2,3,7,5]=>{{1,2,4,5,8},{3,6},{7}}
[4,5,1,2,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,6,2,8,1,3,7,5]=>{{1,4,5,8},{2,3,6},{7}}
[3,6,2,8,4,7,1,5]=>{{1,2,3,6,7},{4,5,8}}
[3,2,6,8,4,7,1,5]=>{{1,3,6,7},{2},{4,5,8}}
[4,2,6,8,3,1,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[4,2,5,1,8,3,7,6]=>{{1,4},{2},{3,5,6,8},{7}}
[4,1,2,5,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,2,4,1,3,8,7,6]=>{{1,3,4,5},{2},{6,8},{7}}
[4,2,5,3,8,1,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[3,2,5,4,8,7,1,6]=>{{1,3,5,6,7,8},{2},{4}}
[5,1,4,2,3,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[5,4,1,3,2,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[5,4,3,1,2,8,7,6]=>{{1,2,4,5},{3},{6,8},{7}}
[3,5,1,4,8,7,2,6]=>{{1,3},{2,5,6,7,8},{4}}
[2,5,6,8,7,3,4,1]=>{{1,2,4,5,7,8},{3,6}}
[3,4,5,1,8,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,6,8,2,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,4,6,8,3,7,5,1]=>{{1,2,4,8},{3,5,6,7}}
[3,4,5,2,8,7,1,6]=>{{1,3,5,6,7,8},{2,4}}
[5,3,1,4,2,8,7,6]=>{{1,2,3,5},{4},{6,8},{7}}
[5,3,2,1,4,8,7,6]=>{{1,4,5},{2,3},{6,8},{7}}
[4,3,2,5,8,1,7,6]=>{{1,4,5,6,8},{2,3},{7}}
[3,2,4,5,8,7,1,6]=>{{1,3,4,5,6,7,8},{2}}
[5,2,1,3,4,8,7,6]=>{{1,3,4,5},{2},{6,8},{7}}
[5,1,2,3,4,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[8,6,2,5,4,1,3,7]=>{{1,2,3,6,7,8},{4,5}}
[6,5,7,4,2,8,3,1]=>{{1,6,8},{2,5},{3,7},{4}}
[6,7,5,3,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,6,3,4,5,7]=>{{1,3,5,7,8},{2},{4,6}}
[8,3,5,6,2,4,1,7]=>{{1,7,8},{2,3,5},{4,6}}
[8,6,2,1,3,5,4,7]=>{{1,4,7,8},{2,3,5,6}}
[8,1,2,3,4,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[6,2,3,7,8,4,5,1]=>{{1,4,5,6,7,8},{2},{3}}
[7,5,8,2,6,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[7,3,1,6,5,8,4,2]=>{{1,2,3,4,6,7,8},{5}}
[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,8,2,1,4,5,3]=>{{1,2,4,5,6,7},{3,8}}
[8,4,7,6,2,1,3,5]=>{{1,2,4,5,6,8},{3,7}}
[5,3,8,4,7,2,6,1]=>{{1,2,3,5,6,7,8},{4}}
[8,1,3,7,6,4,2,5]=>{{1,2,4,5,6,7,8},{3}}
[5,3,1,7,8,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[3,5,8,2,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,2,8,5,3,1,7,4]=>{{1,6},{2},{3,4,5,8},{7}}
[8,2,6,4,7,1,3,5]=>{{1,3,5,6,7,8},{2},{4}}
[3,4,2,8,5,1,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[3,8,6,5,2,1,7,4]=>{{1,3,6},{2,4,5,8},{7}}
[8,3,7,4,2,5,6,1]=>{{1,8},{2,3,5,6,7},{4}}
[4,8,5,7,2,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,8,2,6,7,5]=>{{1,3},{2,4,5,8},{6},{7}}
[8,4,6,3,7,1,5,2]=>{{1,2,3,4,6,8},{5,7}}
[6,8,3,4,1,5,7,2]=>{{1,5,6},{2,8},{3},{4},{7}}
[5,1,7,6,2,8,4,3]=>{{1,2,5},{3,4,6,7,8}}
[6,8,2,5,7,4,1,3]=>{{1,4,5,6,7},{2,3,8}}
[2,8,5,6,7,1,3,4]=>{{1,2,4,6,8},{3,5,7}}
[2,5,7,6,3,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[4,2,8,3,1,5,6,7]=>{{1,3,4,5,6,7,8},{2}}
[2,5,7,3,8,4,6,1]=>{{1,2,5,8},{3,4,6,7}}
[4,2,7,1,8,5,3,6]=>{{1,4},{2},{3,7},{5,6,8}}
[4,2,1,8,7,5,6,3]=>{{1,3,4,8},{2},{5,6,7}}
[8,3,6,7,1,5,4,2]=>{{1,2,3,5,6,8},{4,7}}
[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,7,8,4,3,1,6,2]=>{{1,2,3,5,6,7,8},{4}}
[2,7,4,5,8,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,1,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[7,2,8,5,1,4,6,3]=>{{1,4,5,6,7},{2},{3,8}}
[1,6,5,3,8,4,2,7]=>{{1},{2,3,4,5,6,7,8}}
[5,7,4,8,3,6,2,1]=>{{1,3,4,5,8},{2,7},{6}}
[4,8,6,1,3,5,2,7]=>{{1,4},{2,7,8},{3,5,6}}
[1,8,3,2,4,7,5,6]=>{{1},{2,4,5,6,7,8},{3}}
[8,4,3,2,5,7,1,6]=>{{1,6,7,8},{2,4},{3},{5}}
[3,6,4,8,2,5,7,1]=>{{1,3,4,8},{2,5,6},{7}}
[4,3,7,2,5,8,1,6]=>{{1,2,3,4,7},{5},{6,8}}
[3,2,4,7,8,5,6,1]=>{{1,3,4,5,6,7,8},{2}}
[2,6,4,3,8,5,1,7]=>{{1,2,5,6,7,8},{3,4}}
[3,8,2,1,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,3,4,5,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[4,6,8,3,2,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,2,6,8,5,4,1,7]=>{{1,3,4,6,7,8},{2},{5}}
[7,3,8,2,5,4,1,6]=>{{1,7},{2,3,4,6,8},{5}}
[4,2,5,3,8,7,6,1]=>{{1,3,4,5,8},{2},{6,7}}
[4,8,2,6,5,3,1,7]=>{{1,2,3,4,6,7,8},{5}}
[2,6,8,5,4,1,3,7]=>{{1,2,6},{3,7,8},{4,5}}
[3,1,8,6,5,4,2,7]=>{{1,2,3,7,8},{4,6},{5}}
[5,4,8,7,3,2,6,1]=>{{1,3,5,8},{2,4,6,7}}
[6,4,8,3,7,2,5,1]=>{{1,2,3,4,6,8},{5,7}}
[4,7,3,6,2,1,8,5]=>{{1,4,6},{2,5,7,8},{3}}
[5,4,3,7,1,8,2,6]=>{{1,5},{2,4,7},{3},{6,8}}
[7,3,8,5,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,7,6,2,1,3]=>{{1,2,4,5,6,7},{3,8}}
[3,8,1,5,7,4,6,2]=>{{1,3},{2,8},{4,5,6,7}}
[4,8,5,7,3,1,6,2]=>{{1,4,6,7},{2,8},{3,5}}
[1,5,4,8,3,7,6,2]=>{{1},{2,3,4,5,8},{6,7}}
[4,8,3,6,7,1,5,2]=>{{1,4,6},{2,8},{3},{5,7}}
[4,7,8,3,1,6,5,2]=>{{1,2,3,4,5,7,8},{6}}
[8,7,5,3,6,4,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[4,6,1,3,8,7,5,2]=>{{1,3,4},{2,5,6,7,8}}
[6,8,2,1,7,4,5,3]=>{{1,4,6},{2,3,8},{5,7}}
[3,7,1,6,4,2,8,5]=>{{1,3},{2,4,5,6,7,8}}
[3,1,2,7,5,6,8,4]=>{{1,2,3},{4,7,8},{5},{6}}
[3,6,1,2,7,5,8,4]=>{{1,3},{2,4,5,6,7,8}}
[3,7,6,2,5,8,1,4]=>{{1,2,3,4,6,7,8},{5}}
[3,6,2,5,8,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,3,6,7,4,1]=>{{1,8},{2,3,4,5,6,7}}
[4,7,2,6,3,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[6,3,2,4,8,7,5,1]=>{{1,5,6,7,8},{2,3},{4}}
[3,7,2,4,6,1,8,5]=>{{1,2,3,5,6,7,8},{4}}
[5,3,7,2,8,1,4,6]=>{{1,5,6,8},{2,3,4,7}}
[6,3,2,8,7,5,1,4]=>{{1,5,6,7},{2,3},{4,8}}
[7,3,8,2,6,5,1,4]=>{{1,7},{2,3,4,8},{5,6}}
[6,4,8,7,2,5,1,3]=>{{1,2,4,5,6,7},{3,8}}
[2,5,4,8,1,7,6,3]=>{{1,2,5},{3,4,8},{6,7}}
[5,2,8,1,7,6,3,4]=>{{1,3,4,5,7,8},{2},{6}}
[6,2,1,3,8,7,5,4]=>{{1,3,4,5,6,7,8},{2}}
[3,6,1,8,7,5,2,4]=>{{1,3},{2,5,6,7},{4,8}}
[5,6,1,2,8,7,4,3]=>{{1,3,5,8},{2,4,6,7}}
[7,5,2,8,1,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[2,7,6,8,1,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,1,6,2,4,3]=>{{1,4,7},{2,3,5,6,8}}
[7,4,8,6,1,2,5,3]=>{{1,5,7},{2,4,6},{3,8}}
[7,2,1,8,3,6,5,4]=>{{1,3,5,7},{2},{4,8},{6}}
[5,8,7,1,6,4,3,2]=>{{1,4,5,6},{2,8},{3,7}}
[8,5,4,3,7,2,1,6]=>{{1,2,5,6,7,8},{3,4}}
[6,5,4,8,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,6,4,3,2,8,5,1]=>{{1,2,5,6,7,8},{3,4}}
[7,3,1,4,8,2,5,6]=>{{1,2,3,5,6,7,8},{4}}
[7,4,1,2,5,8,3,6]=>{{1,3,7},{2,4},{5},{6,8}}
[6,7,4,2,5,1,3,8]=>{{1,6},{2,3,4,7},{5},{8}}
[5,7,2,4,6,8,1,3]=>{{1,2,3,5,6,7,8},{4}}
[4,7,5,1,6,2,8,3]=>{{1,4},{2,3,5,6,7,8}}
[5,7,4,6,3,1,8,2]=>{{1,3,4,5,6},{2,7,8}}
[7,5,1,4,3,2,8,6]=>{{1,2,3,5,6,7,8},{4}}
[8,6,4,2,3,7,5,1]=>{{1,8},{2,3,4,5,6,7}}
[6,4,7,1,3,8,5,2]=>{{1,2,4,6,8},{3,5,7}}
[5,4,2,7,3,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,1,2,7,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[5,4,6,8,3,1,2,7]=>{{1,3,5,6},{2,4,7,8}}
[6,4,8,1,3,7,2,5]=>{{1,2,4,6,7},{3,5,8}}
[4,6,1,3,8,5,2,7]=>{{1,3,4},{2,5,6,7,8}}
[1,3,8,4,5,7,2,6]=>{{1},{2,3,6,7,8},{4},{5}}
[2,6,7,4,5,3,1,8]=>{{1,2,3,6,7},{4},{5},{8}}
[2,6,8,4,3,5,1,7]=>{{1,2,3,5,6,7,8},{4}}
[1,3,7,4,2,8,5,6]=>{{1},{2,3,5,7},{4},{6,8}}
[4,6,1,3,7,2,5,8]=>{{1,3,4},{2,6},{5,7},{8}}
[7,5,8,6,2,1,3,4]=>{{1,3,4,6,7,8},{2,5}}
[2,8,1,3,6,5,4,7]=>{{1,2,3,4,7,8},{5,6}}
[2,8,7,3,5,4,1,6]=>{{1,2,3,4,6,7,8},{5}}
[3,4,2,6,8,7,1,5]=>{{1,2,3,4,6,7},{5,8}}
[7,4,2,3,6,1,8,5]=>{{1,5,6,7,8},{2,3,4}}
[8,4,2,3,6,5,7,1]=>{{1,8},{2,3,4},{5,6},{7}}
[7,3,8,4,1,2,6,5]=>{{1,2,3,5,6,7,8},{4}}
[6,8,3,2,7,1,5,4]=>{{1,6},{2,4,8},{3},{5,7}}
[2,8,5,6,3,7,1,4]=>{{1,2,4,6,7,8},{3,5}}
[7,4,2,5,8,1,6,3]=>{{1,6,7},{2,3,4,5,8}}
[2,7,8,3,4,5,1,6]=>{{1,2,7},{3,4,5,6,8}}
[3,7,1,2,4,6,5,8]=>{{1,3},{2,4,5,7},{6},{8}}
[7,5,6,8,2,1,4,3]=>{{1,3,4,6,7,8},{2,5}}
[3,1,6,5,2,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,8,6,5,3,4,1,7]=>{{1,2,7,8},{3,4,5,6}}
[1,7,2,3,5,6,8,4]=>{{1},{2,3,4,7,8},{5},{6}}
[3,7,4,2,1,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[3,4,6,2,8,5,7,1]=>{{1,3,5,6,8},{2,4},{7}}
[4,2,1,7,5,8,3,6]=>{{1,3,4,7},{2},{5},{6,8}}
[4,7,2,6,5,1,3,8]=>{{1,4,6},{2,3,7},{5},{8}}
[3,7,4,1,2,5,8,6]=>{{1,3,4},{2,5,6,7,8}}
[4,7,1,6,5,2,8,3]=>{{1,2,3,4,6,7,8},{5}}
[4,7,3,6,5,1,8,2]=>{{1,4,6},{2,7,8},{3},{5}}
[4,3,7,1,6,8,5,2]=>{{1,4},{2,3,5,6,7,8}}
[4,2,1,7,5,6,8,3]=>{{1,3,4,7,8},{2},{5},{6}}
[3,2,4,8,6,7,1,5]=>{{1,3,4,5,6,7,8},{2}}
[4,2,6,8,7,3,1,5]=>{{1,4,5,7,8},{2},{3,6}}
[3,4,6,1,8,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,6,7,5,8,2,3]=>{{1,2,4,7},{3,6,8},{5}}
[4,3,6,7,5,1,2,8]=>{{1,2,3,4,6,7},{5},{8}}
[4,3,7,1,6,8,2,5]=>{{1,4},{2,3,7},{5,6,8}}
[4,3,7,5,6,8,2,1]=>{{1,4,5,6,8},{2,3,7}}
[4,1,7,3,6,5,2,8]=>{{1,2,3,4,7},{5,6},{8}}
[2,8,7,4,5,3,1,6]=>{{1,2,3,6,7,8},{4},{5}}
[2,8,7,4,3,5,1,6]=>{{1,2,3,5,6,7,8},{4}}
[3,8,1,4,2,6,5,7]=>{{1,3},{2,5,7,8},{4},{6}}
[4,1,7,3,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[5,8,7,6,1,2,4,3]=>{{1,5},{2,3,4,6,7,8}}
[5,8,7,6,2,1,3,4]=>{{1,2,4,5,6,8},{3,7}}
[4,1,7,2,6,8,5,3]=>{{1,2,4},{3,5,6,7,8}}
[4,2,7,3,6,1,8,5]=>{{1,3,4,5,6,7,8},{2}}
[4,2,7,3,6,5,8,1]=>{{1,3,4,7,8},{2},{5,6}}
[3,8,2,4,5,6,7,1]=>{{1,2,3,8},{4},{5},{6},{7}}
[3,8,2,4,1,6,7,5]=>{{1,2,3,5,8},{4},{6},{7}}
[3,8,5,6,2,4,1,7]=>{{1,2,3,5,7,8},{4,6}}
[2,8,6,5,3,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,5,1,4,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[3,8,2,1,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[3,8,2,5,4,6,7,1]=>{{1,2,3,8},{4,5},{6},{7}}
[4,2,7,5,6,3,8,1]=>{{1,3,4,5,6,7,8},{2}}
[4,2,7,5,6,1,8,3]=>{{1,4,5,6},{2},{3,7,8}}
[4,2,6,7,5,3,1,8]=>{{1,4,7},{2},{3,6},{5},{8}}
[3,2,6,1,4,5,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[2,8,7,3,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[3,8,1,2,4,6,5,7]=>{{1,3},{2,4,5,7,8},{6}}
[5,8,7,6,1,3,4,2]=>{{1,5},{2,8},{3,4,6,7}}
[5,8,7,6,2,3,4,1]=>{{1,2,5,8},{3,4,6,7}}
[4,1,7,5,6,2,3,8]=>{{1,2,4,5,6},{3,7},{8}}
[3,8,1,5,2,6,4,7]=>{{1,3},{2,4,5,7,8},{6}}
[2,8,7,5,3,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,7,5,4,3,1,6]=>{{1,2,3,6,7,8},{4,5}}
[4,1,7,5,6,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[5,8,7,6,1,3,2,4]=>{{1,5},{2,3,4,6,7,8}}
[5,8,7,6,4,1,2,3]=>{{1,4,5,6},{2,3,7,8}}
[5,4,2,3,7,6,8,1]=>{{1,5,7,8},{2,3,4},{6}}
[7,4,3,5,2,8,1,6]=>{{1,7},{2,4,5},{3},{6,8}}
[8,4,3,7,5,1,6,2]=>{{1,2,4,6,7,8},{3},{5}}
[8,4,7,2,5,1,6,3]=>{{1,3,6,7,8},{2,4},{5}}
[7,4,6,2,3,5,8,1]=>{{1,7,8},{2,4},{3,5,6}}
[5,1,7,2,4,6,8,3]=>{{1,2,4,5},{3,7,8},{6}}
[4,5,7,1,2,6,8,3]=>{{1,4},{2,5},{3,7,8},{6}}
[5,4,1,7,3,6,8,2]=>{{1,3,5},{2,4,7,8},{6}}
[3,6,4,7,5,2,8,1]=>{{1,3,4,7,8},{2,6},{5}}
[3,4,7,6,2,5,8,1]=>{{1,3,7,8},{2,4,5,6}}
[4,7,5,6,1,3,8,2]=>{{1,3,4,5,6},{2,7,8}}
[5,7,6,4,3,1,8,2]=>{{1,3,5,6},{2,7,8},{4}}
[5,7,6,3,1,4,8,2]=>{{1,5},{2,7,8},{3,4,6}}
[7,5,2,3,4,8,1,6]=>{{1,7},{2,3,4,5},{6,8}}
[8,7,5,3,4,1,6,2]=>{{1,2,6,7,8},{3,4,5}}
[6,7,1,3,8,4,2,5]=>{{1,3,4,6},{2,7},{5,8}}
[7,6,1,3,4,8,5,2]=>{{1,3,4,5,7},{2,6,8}}
[3,6,5,2,7,8,1,4]=>{{1,3,5,7},{2,4,6,8}}
[3,2,8,6,7,1,4,5]=>{{1,3,4,5,6,7,8},{2}}
[4,8,3,6,5,2,1,7]=>{{1,2,4,6,7,8},{3},{5}}
[1,8,6,5,4,2,3,7]=>{{1},{2,3,6,7,8},{4,5}}
[1,8,7,2,3,5,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,2,5,3,4,6]=>{{1},{2,3,4,6,7,8},{5}}
[3,6,8,5,1,2,4,7]=>{{1,3,4,5,7,8},{2,6}}
[3,7,5,1,8,2,6,4]=>{{1,3,4,5,8},{2,6,7}}
[7,1,2,8,3,5,6,4]=>{{1,2,3,5,6,7},{4,8}}
[6,1,7,8,2,5,3,4]=>{{1,2,5,6},{3,7},{4,8}}
[6,7,5,2,8,1,4,3]=>{{1,6},{2,4,7},{3,5,8}}
[7,1,4,5,8,6,2,3]=>{{1,2,7},{3,4,5,8},{6}}
[5,7,6,4,2,8,1,3]=>{{1,2,5,7},{3,6,8},{4}}
[7,5,6,1,2,8,4,3]=>{{1,4,7},{2,5},{3,6,8}}
[4,1,3,7,8,6,2,5]=>{{1,2,4,7},{3},{5,8},{6}}
[5,1,4,3,6,8,7,2]=>{{1,2,5,6,8},{3,4},{7}}
[4,5,7,6,8,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,8,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,8,4,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[7,4,8,2,3,6,5,1]=>{{1,3,5,7,8},{2,4},{6}}
[5,6,8,4,7,3,2,1]=>{{1,2,3,5,6,7,8},{4}}
[6,4,7,8,5,2,1,3]=>{{1,2,3,4,6,7,8},{5}}
[3,6,4,8,5,1,2,7]=>{{1,2,3,4,6,7,8},{5}}
[3,7,4,8,1,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,3,8,2,6,5,1]=>{{1,2,4,5,7,8},{3},{6}}
[7,6,8,3,2,5,4,1]=>{{1,3,4,7,8},{2,5,6}}
[8,7,1,3,5,4,6,2]=>{{1,2,3,4,6,7,8},{5}}
[7,1,8,3,4,2,6,5]=>{{1,2,6,7},{3,4,5,8}}
[7,6,8,3,1,4,5,2]=>{{1,5,7},{2,3,4,6,8}}
[3,1,4,8,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,8,5,2,1,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,8,2,6,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[6,8,2,3,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,2,3,4,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[8,1,7,2,4,5,3,6]=>{{1,2,4,5,6,8},{3,7}}
[8,1,3,6,2,5,4,7]=>{{1,2,4,5,6,7,8},{3}}
[7,2,1,6,3,5,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[2,7,1,6,3,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,7,1,5,4,3,6,8]=>{{1,2,3,6,7},{4,5},{8}}
[7,2,1,5,4,3,6,8]=>{{1,3,6,7},{2},{4,5},{8}}
[8,1,3,5,4,2,6,7]=>{{1,2,6,7,8},{3},{4,5}}
[8,1,5,3,4,2,6,7]=>{{1,2,6,7,8},{3,4,5}}
[8,1,5,6,2,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[8,1,4,5,3,2,6,7]=>{{1,2,6,7,8},{3,4,5}}
[8,1,4,3,5,2,6,7]=>{{1,2,6,7,8},{3,4},{5}}
[7,2,1,4,5,3,6,8]=>{{1,3,6,7},{2},{4},{5},{8}}
[2,7,1,4,5,3,6,8]=>{{1,2,3,6,7},{4},{5},{8}}
[2,6,3,1,5,4,7,8]=>{{1,2,4,6},{3},{5},{7},{8}}
[6,3,2,1,5,4,7,8]=>{{1,4,6},{2,3},{5},{7},{8}}
[7,3,1,4,5,2,6,8]=>{{1,2,3,6,7},{4},{5},{8}}
[7,3,1,5,4,2,6,8]=>{{1,2,3,6,7},{4,5},{8}}
[7,3,1,6,2,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[3,7,1,6,2,5,4,8]=>{{1,3},{2,4,5,6,7},{8}}
[3,7,1,4,5,2,6,8]=>{{1,3},{2,6,7},{4},{5},{8}}
[3,6,2,1,5,4,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[2,3,6,1,5,4,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[3,5,2,4,1,6,7,8]=>{{1,2,3,5},{4},{6},{7},{8}}
[6,3,4,1,5,2,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[6,2,4,1,5,3,7,8]=>{{1,3,4,6},{2},{5},{7},{8}}
[2,6,4,1,5,3,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[2,6,5,1,3,7,4,8]=>{{1,2,4,6,7},{3,5},{8}}
[6,2,5,1,3,7,4,8]=>{{1,4,6,7},{2},{3,5},{8}}
[6,5,2,1,3,7,4,8]=>{{1,4,6,7},{2,3,5},{8}}
[7,6,1,2,4,5,3,8]=>{{1,3,7},{2,4,5,6},{8}}
[6,7,1,2,8,3,5,4]=>{{1,3,6},{2,4,5,7,8}}
[6,7,1,2,5,4,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[5,6,2,1,3,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[5,2,6,1,3,7,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[2,4,6,1,5,3,7,8]=>{{1,2,4},{3,6},{5},{7},{8}}
[4,7,1,3,5,2,6,8]=>{{1,3,4},{2,6,7},{5},{8}}
[4,7,1,5,3,2,6,8]=>{{1,3,4,5},{2,6,7},{8}}
[5,7,1,4,2,6,3,8]=>{{1,2,3,5,7},{4},{6},{8}}
[5,7,1,6,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,6,3,1,2,7,4,8]=>{{1,2,4,5,6,7},{3},{8}}
[4,2,5,3,1,6,7,8]=>{{1,3,4,5},{2},{6},{7},{8}}
[5,3,6,1,2,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[3,4,6,1,5,2,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[6,5,1,8,7,3,4,2]=>{{1,3,6},{2,4,5,7,8}}
[8,2,7,5,4,1,3,6]=>{{1,6,8},{2},{3,7},{4,5}}
[6,8,5,2,3,4,1,7]=>{{1,2,4,6,7,8},{3,5}}
[8,5,6,2,7,1,4,3]=>{{1,3,6,8},{2,4,5,7}}
[6,5,1,2,7,8,4,3]=>{{1,3,6,8},{2,4,5,7}}
[4,7,6,1,5,3,8,2]=>{{1,4},{2,7,8},{3,6},{5}}
[5,7,6,4,1,3,8,2]=>{{1,5},{2,7,8},{3,6},{4}}
[7,6,2,4,5,3,8,1]=>{{1,7,8},{2,3,6},{4},{5}}
[6,1,7,5,3,8,4,2]=>{{1,2,6,8},{3,4,5,7}}
[8,6,7,5,3,1,4,2]=>{{1,2,6,8},{3,4,5,7}}
[8,5,2,7,1,6,4,3]=>{{1,2,3,5,8},{4,7},{6}}
[7,6,1,5,3,8,4,2]=>{{1,3,4,5,7},{2,6,8}}
[5,6,2,4,7,8,1,3]=>{{1,5,7},{2,3,6,8},{4}}
[3,4,6,1,7,8,5,2]=>{{1,2,3,4,6,8},{5,7}}
[3,4,8,6,7,1,5,2]=>{{1,2,3,4,6,8},{5,7}}
[4,8,5,6,7,2,3,1]=>{{1,2,4,6,8},{3,5,7}}
[5,8,6,4,1,2,7,3]=>{{1,5},{2,3,6,8},{4},{7}}
[5,8,6,1,7,2,4,3]=>{{1,4,5,7},{2,3,6,8}}
[5,8,7,3,2,6,4,1]=>{{1,2,5,8},{3,4,7},{6}}
[5,8,1,7,2,6,4,3]=>{{1,2,3,5,8},{4,7},{6}}
[8,1,5,7,2,6,4,3]=>{{1,2,3,5,8},{4,7},{6}}
[8,1,7,2,5,6,3,4]=>{{1,2,4,8},{3,7},{5},{6}}
[6,8,7,2,5,1,3,4]=>{{1,6},{2,4,8},{3,7},{5}}
[5,8,7,2,1,6,3,4]=>{{1,5},{2,4,8},{3,7},{6}}
[4,8,1,5,2,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[3,7,8,5,1,6,2,4]=>{{1,3,4,5,8},{2,7},{6}}
[6,5,2,7,8,1,4,3]=>{{1,6},{2,3,5,8},{4,7}}
[7,1,2,8,5,6,3,4]=>{{1,2,3,7},{4,8},{5},{6}}
[8,7,2,1,5,6,3,4]=>{{1,4,8},{2,3,7},{5},{6}}
[8,6,7,1,5,2,3,4]=>{{1,4,8},{2,6},{3,7},{5}}
[6,1,7,8,5,2,3,4]=>{{1,2,6},{3,7},{4,8},{5}}
[7,5,6,2,1,8,4,3]=>{{1,2,4,5,7},{3,6,8}}
[8,7,5,2,1,6,4,3]=>{{1,3,5,8},{2,4,7},{6}}
[7,1,3,5,8,6,2,4]=>{{1,2,7},{3},{4,5,8},{6}}
[5,1,3,4,6,8,7,2]=>{{1,2,5,6,8},{3},{4},{7}}
[4,5,3,6,8,2,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[5,6,3,4,8,1,7,2]=>{{1,2,5,6,8},{3},{4},{7}}
[4,6,7,8,5,1,3,2]=>{{1,2,4,6,8},{3,7},{5}}
[8,4,3,1,2,6,7,5]=>{{1,2,4,5,8},{3},{6},{7}}
[8,5,1,6,3,4,7,2]=>{{1,2,3,5,8},{4,6},{7}}
[5,1,8,6,3,4,7,2]=>{{1,2,3,5,8},{4,6},{7}}
[4,6,8,1,5,3,7,2]=>{{1,4},{2,3,6,8},{5},{7}}
[6,4,5,8,3,2,7,1]=>{{1,2,4,6,8},{3,5},{7}}
[3,6,4,8,7,1,5,2]=>{{1,2,3,4,6,8},{5,7}}
[6,5,8,1,3,4,7,2]=>{{1,4,6},{2,3,5,8},{7}}
[5,6,8,3,1,2,7,4]=>{{1,5},{2,6},{3,4,8},{7}}
[6,1,8,3,5,2,7,4]=>{{1,2,6},{3,4,8},{5},{7}}
[7,6,8,3,5,2,1,4]=>{{1,7},{2,6},{3,4,8},{5}}
[8,6,1,3,5,2,7,4]=>{{1,3,4,8},{2,6},{5},{7}}
[8,7,1,3,5,6,2,4]=>{{1,3,4,8},{2,7},{5},{6}}
[6,7,8,3,5,1,2,4]=>{{1,6},{2,7},{3,4,8},{5}}
[3,4,8,1,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[5,8,2,4,3,6,7,1]=>{{1,2,3,5,8},{4},{6},{7}}
[5,8,2,3,1,6,7,4]=>{{1,5},{2,3,4,8},{6},{7}}
[6,8,2,3,5,1,7,4]=>{{1,6},{2,3,4,8},{5},{7}}
[7,8,2,3,5,6,1,4]=>{{1,7},{2,3,4,8},{5},{6}}
[8,6,5,1,4,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[2,6,5,4,1,3,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[4,1,7,6,3,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,2,5,7,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[3,4,6,5,1,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[2,6,5,3,4,1,8,7]=>{{1,2,6},{3,4,5},{7,8}}
[4,6,1,5,2,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[6,2,3,5,1,4,8,7]=>{{1,4,5,6},{2},{3},{7,8}}
[2,6,7,5,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[8,6,1,2,5,3,4,7]=>{{1,2,3,4,6,7,8},{5}}
[6,2,5,1,8,3,4,7]=>{{1,3,4,5,6,7,8},{2}}
[7,6,5,2,8,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,6,3,5,1,8,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[2,4,7,6,5,8,1,3]=>{{1,2,3,4,6,7,8},{5}}
[2,1,4,8,7,6,3,5]=>{{1,2},{3,4,5,7,8},{6}}
[7,4,6,8,5,3,2,1]=>{{1,2,4,7,8},{3,6},{5}}
[8,1,3,5,7,4,6,2]=>{{1,2,8},{3},{4,5,6,7}}
[3,2,8,7,5,1,6,4]=>{{1,3,4,6,7,8},{2},{5}}
[4,8,5,1,6,7,2,3]=>{{1,4},{2,3,5,6,7,8}}
[3,8,5,1,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,6,1,3,5,2,4]=>{{1,2,4,7,8},{3,5,6}}
[5,6,7,2,8,1,3,4]=>{{1,2,4,5,6,8},{3,7}}
[2,5,1,8,6,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,8,6,7,4,2]=>{{1,3},{2,4,5,6,7,8}}
[5,2,3,8,6,7,4,1]=>{{1,4,5,6,7,8},{2},{3}}
[8,3,5,4,6,7,1,2]=>{{1,2,3,5,6,7,8},{4}}
[5,1,3,8,6,7,4,2]=>{{1,2,4,5,6,7,8},{3}}
[3,2,5,8,6,7,4,1]=>{{1,3,4,5,6,7,8},{2}}
[6,2,1,5,3,8,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[5,6,3,2,8,1,4,7]=>{{1,2,4,5,6,7,8},{3}}
[8,1,6,3,5,2,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[8,7,6,2,5,3,1,4]=>{{1,2,4,7,8},{3,6},{5}}
[4,7,6,8,3,2,5,1]=>{{1,4,8},{2,3,5,6,7}}
[2,7,5,8,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,6,2,8,5,1,4,3]=>{{1,2,3,4,6,7,8},{5}}
[8,1,3,7,5,2,6,4]=>{{1,2,4,6,7,8},{3},{5}}
[3,4,8,7,5,1,6,2]=>{{1,2,3,4,6,7,8},{5}}
[6,3,8,1,4,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[6,3,8,5,7,4,1,2]=>{{1,4,5,6,7},{2,3,8}}
[7,4,6,8,5,1,3,2]=>{{1,3,6,7},{2,4,8},{5}}
[2,1,4,8,7,5,6,3]=>{{1,2},{3,4,8},{5,6,7}}
[7,1,5,8,2,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[3,6,8,2,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,5,8,2,6,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[5,2,8,1,6,7,3,4]=>{{1,3,4,5,6,7,8},{2}}
[2,5,8,4,6,7,3,1]=>{{1,2,3,5,6,7,8},{4}}
[5,8,3,4,6,7,2,1]=>{{1,2,5,6,7,8},{3},{4}}
[8,4,3,2,6,7,1,5]=>{{1,5,6,7,8},{2,4},{3}}
[4,2,8,1,6,7,3,5]=>{{1,4},{2},{3,5,6,7,8}}
[2,4,8,1,6,7,3,5]=>{{1,2,4},{3,5,6,7,8}}
[5,1,8,2,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[3,4,8,7,2,1,5,6]=>{{1,3,6,8},{2,4,5,7}}
[7,8,5,3,6,4,2,1]=>{{1,2,7,8},{3,4,5,6}}
[2,8,5,7,4,1,3,6]=>{{1,2,6,8},{3,4,5,7}}
[5,8,4,1,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,8,1,4,6,7,2,5]=>{{1,3},{2,5,6,7,8},{4}}
[8,2,3,4,6,7,1,5]=>{{1,5,6,7,8},{2},{3},{4}}
[6,2,7,3,8,4,1,5]=>{{1,3,4,6,7},{2},{5,8}}
[7,4,3,2,8,5,1,6]=>{{1,7},{2,4},{3},{5,6,8}}
[5,3,2,8,4,6,1,7]=>{{1,4,5,7,8},{2,3},{6}}
[8,4,2,6,5,3,1,7]=>{{1,7,8},{2,3,4,6},{5}}
[7,4,2,5,3,1,6,8]=>{{1,6,7},{2,3,4,5},{8}}
[8,3,6,2,5,4,1,7]=>{{1,7,8},{2,3,4,6},{5}}
[5,4,8,3,2,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[3,5,8,2,4,6,1,7]=>{{1,3,7,8},{2,4,5},{6}}
[6,4,7,8,2,3,1,5]=>{{1,3,6,7},{2,4,5,8}}
[5,8,3,6,4,2,1,7]=>{{1,2,4,5,6,7,8},{3}}
[4,8,6,2,5,3,1,7]=>{{1,2,4,7,8},{3,6},{5}}
[1,6,4,3,2,8,7,5]=>{{1},{2,5,6,8},{3,4},{7}}
[1,5,3,2,8,4,7,6]=>{{1},{2,4,5,6,8},{3},{7}}
[5,7,4,3,1,2,6,8]=>{{1,5},{2,6,7},{3,4},{8}}
[2,8,7,3,5,1,4,6]=>{{1,2,6,8},{3,4,7},{5}}
[7,3,8,6,4,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[6,1,2,7,3,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,4,3,8,6,5]=>{{1,2},{3,5,6,7,8},{4}}
[6,1,4,3,8,2,7,5]=>{{1,2,6},{3,4},{5,8},{7}}
[5,1,3,2,8,7,4,6]=>{{1,2,4,5,6,7,8},{3}}
[1,8,4,2,7,6,5,3]=>{{1},{2,3,4,8},{5,7},{6}}
[1,8,3,7,2,6,5,4]=>{{1},{2,4,5,7,8},{3},{6}}
[5,1,4,8,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,6,8,5,4,7,3]=>{{1,2},{3,4,6,8},{5},{7}}
[6,1,5,7,8,2,4,3]=>{{1,2,6},{3,5,8},{4,7}}
[8,3,1,6,7,2,5,4]=>{{1,2,3,4,6,8},{5,7}}
[7,4,8,6,1,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,7,6,1,2,5,3,8]=>{{1,4},{2,3,5,6,7},{8}}
[3,7,6,1,5,2,4,8]=>{{1,2,3,4,6,7},{5},{8}}
[1,5,4,8,3,2,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[7,3,6,1,2,5,4,8]=>{{1,4,7},{2,3,5,6},{8}}
[5,4,7,1,3,2,6,8]=>{{1,2,3,4,5,6,7},{8}}
[5,7,4,8,2,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[4,6,8,2,5,1,3,7]=>{{1,2,4,6},{3,7,8},{5}}
[7,4,6,2,1,5,3,8]=>{{1,3,5,6,7},{2,4},{8}}
[1,2,6,3,8,5,7,4]=>{{1},{2},{3,4,5,6,8},{7}}
[1,5,2,6,8,4,7,3]=>{{1},{2,3,5,8},{4,6},{7}}
[5,7,2,3,8,1,4,6]=>{{1,5,6,8},{2,3,4,7}}
[6,4,7,5,8,1,2,3]=>{{1,6},{2,3,4,5,7,8}}
[7,4,8,5,1,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[5,8,3,6,1,7,4,2]=>{{1,5},{2,8},{3},{4,6,7}}
[8,6,4,2,1,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,1,5,8,6,3]=>{{1,2,3,4,6,7,8},{5}}
[7,6,4,1,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,8,7,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,1,2,8,4,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[7,5,1,3,2,8,6,4]=>{{1,3,4,6,7,8},{2,5}}
[4,7,1,2,5,8,6,3]=>{{1,2,3,4,6,7,8},{5}}
[6,8,4,1,2,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,1,2,6,4,3]=>{{1,4,7},{2,5},{3,8},{6}}
[7,4,8,1,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[5,8,2,1,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,8,2,4,7,5]=>{{1,3},{2,4,5,6,8},{7}}
[1,3,8,7,6,2,5,4]=>{{1},{2,3,4,5,6,7,8}}
[5,4,1,8,7,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,8,7,2,4,6]=>{{1,3},{2,4,5,6,7,8}}
[4,6,1,8,3,7,2,5]=>{{1,3,4,5,8},{2,6,7}}
[4,7,1,2,8,6,3,5]=>{{1,2,3,4,7},{5,8},{6}}
[5,8,4,1,7,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[7,6,8,1,5,4,2,3]=>{{1,2,4,6,7},{3,8},{5}}
[8,6,1,7,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}
[7,1,5,8,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,7,3,6,4,2]=>{{1,2,3,5,8},{4,7},{6}}
[4,1,8,7,6,2,5,3]=>{{1,2,4,5,6,7},{3,8}}
[3,1,8,7,6,5,2,4]=>{{1,2,3,4,7,8},{5,6}}
[1,6,4,5,2,3,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,7,4,5,2,3,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,7,3,5,2,4,6,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,6,3,5,2,4,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[1,6,3,4,2,5,7,8]=>{{1},{2,5,6},{3},{4},{7},{8}}
[1,7,3,4,2,5,6,8]=>{{1},{2,5,6,7},{3},{4},{8}}
[1,8,6,7,3,4,2,5]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,7,3,4,2,6]=>{{1},{2,4,6,7,8},{3,5}}
[1,7,3,4,2,6,5,8]=>{{1},{2,5,7},{3},{4},{6},{8}}
[1,5,2,8,4,7,3,6]=>{{1},{2,3,4,5,6,7,8}}
[1,4,2,8,5,7,3,6]=>{{1},{2,3,4,6,7,8},{5}}
[1,7,3,5,2,6,4,8]=>{{1},{2,4,5,7},{3},{6},{8}}
[1,8,4,7,3,5,2,6]=>{{1},{2,3,4,5,6,7,8}}
[1,7,3,6,2,5,4,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,7,3,6,2,4,5,8]=>{{1},{2,5,7},{3},{4,6},{8}}
[1,7,4,6,2,3,5,8]=>{{1},{2,5,7},{3,4,6},{8}}
[1,8,5,6,2,3,4,7]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,6,2,4,3,7]=>{{1},{2,3,5,7,8},{4,6}}
[1,3,2,8,5,6,4,7]=>{{1},{2,3},{4,7,8},{5},{6}}
[1,4,2,8,5,6,3,7]=>{{1},{2,3,4,7,8},{5},{6}}
[1,5,2,8,4,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,6,2,8,4,5,3,7]=>{{1},{2,3,4,5,6,7,8}}
[8,1,2,4,5,3,6,7]=>{{1,2,3,6,7,8},{4},{5}}
[8,6,4,7,2,1,3,5]=>{{1,2,5,6,8},{3,4,7}}
[1,6,4,7,2,8,3,5]=>{{1},{2,5,6,8},{3,4,7}}
[1,4,7,3,5,8,2,6]=>{{1},{2,3,4,7},{5},{6,8}}
[8,4,6,2,3,5,1,7]=>{{1,7,8},{2,4},{3,5,6}}
[5,4,8,2,3,6,1,7]=>{{1,3,5,7,8},{2,4},{6}}
[7,4,8,5,2,3,1,6]=>{{1,7},{2,4,5},{3,6,8}}
[3,8,6,2,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,8,6,2,3,5,1,7]=>{{1,2,4,7,8},{3,5,6}}
[1,7,5,3,4,8,2,6]=>{{1},{2,7},{3,4,5},{6,8}}
[1,7,6,4,8,2,3,5]=>{{1},{2,3,6,7},{4},{5,8}}
[5,8,7,4,1,2,3,6]=>{{1,5},{2,6,8},{3,7},{4}}
[6,8,5,3,4,1,2,7]=>{{1,6},{2,7,8},{3,4,5}}
[6,8,3,7,2,1,4,5]=>{{1,6},{2,5,8},{3},{4,7}}
[8,5,1,6,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,1,3,7,4,8,2,5]=>{{1,2,4,5,6,7,8},{3}}
[4,1,7,3,5,8,2,6]=>{{1,2,3,4,7},{5},{6,8}}
[7,1,6,4,8,2,3,5]=>{{1,2,3,6,7},{4},{5,8}}
[1,8,5,7,2,3,4,6]=>{{1},{2,3,5,6,8},{4,7}}
[6,1,5,8,2,3,4,7]=>{{1,2,3,5,6},{4,7,8}}
[5,1,7,3,8,2,4,6]=>{{1,2,5,6,8},{3,4,7}}
[6,1,5,7,8,2,3,4]=>{{1,2,6},{3,4,5,7,8}}
[7,4,8,6,1,2,3,5]=>{{1,3,5,7,8},{2,4,6}}
[3,8,7,5,1,2,4,6]=>{{1,3,4,5,7},{2,6,8}}
[3,7,6,1,2,4,5,8]=>{{1,3,4,6},{2,5,7},{8}}
[4,7,6,1,2,3,5,8]=>{{1,4},{2,5,7},{3,6},{8}}
[1,6,5,8,2,3,4,7]=>{{1},{2,3,5,6},{4,7,8}}
[6,5,8,4,1,2,3,7]=>{{1,2,5,6},{3,7,8},{4}}
[8,5,7,4,1,2,3,6]=>{{1,2,5,6,8},{3,7},{4}}
[1,5,7,4,8,2,3,6]=>{{1},{2,5,6,8},{3,7},{4}}
[7,6,4,8,2,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,6,2,3,8,1,4,5]=>{{1,2,3,4,6,7},{5,8}}
[7,4,8,5,1,6,2,3]=>{{1,2,4,5,7},{3,8},{6}}
[8,6,2,3,1,7,4,5]=>{{1,5,8},{2,3,4,6,7}}
[8,6,4,1,2,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[1,7,2,8,6,3,4,5]=>{{1},{2,3,4,5,6,7,8}}
[7,6,1,3,8,2,4,5]=>{{1,3,4,7},{2,6},{5,8}}
[7,5,8,1,3,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[5,4,1,8,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,4,8,7,2,3,5,6]=>{{1},{2,4,5,7},{3,6,8}}
[1,5,8,7,2,3,4,6]=>{{1},{2,5},{3,6,8},{4,7}}
[6,5,1,8,2,3,4,7]=>{{1,3,6},{2,5},{4,7,8}}
[5,7,1,3,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,1,5,2,3,4]=>{{1,3,4,7,8},{2,6},{5}}
[7,1,5,8,6,2,3,4]=>{{1,2,3,5,6,7},{4,8}}
[6,1,8,2,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[4,1,8,7,2,3,5,6]=>{{1,2,4,5,7},{3,6,8}}
[5,1,8,7,2,3,4,6]=>{{1,2,5},{3,6,8},{4,7}}
[1,8,7,6,4,5,3,2]=>{{1},{2,8},{3,7},{4,5,6}}
[1,8,7,3,6,5,4,2]=>{{1},{2,8},{3,4,7},{5,6}}
[7,1,5,8,3,4,2,6]=>{{1,2,7},{3,5},{4,6,8}}
[7,1,4,3,2,5,6,8]=>{{1,2,5,6,7},{3,4},{8}}
[6,4,2,3,8,5,7,1]=>{{1,5,6,8},{2,3,4},{7}}
[6,4,2,7,5,8,3,1]=>{{1,6,8},{2,3,4,7},{5}}
[2,4,1,7,5,8,3,6]=>{{1,2,3,4,7},{5},{6,8}}
[7,1,4,6,5,2,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[7,1,4,6,5,8,2,3]=>{{1,2,7},{3,4,6,8},{5}}
[7,1,4,6,3,8,2,5]=>{{1,2,7},{3,4,5,6,8}}
[7,1,4,3,2,5,8,6]=>{{1,2,5,6,7,8},{3,4}}
[7,1,4,6,5,2,8,3]=>{{1,2,3,4,6,7,8},{5}}
[7,1,4,6,5,3,8,2]=>{{1,2,7,8},{3,4,6},{5}}
[7,1,4,6,5,3,2,8]=>{{1,2,7},{3,4,6},{5},{8}}
[6,4,2,7,5,3,8,1]=>{{1,2,3,4,6,7,8},{5}}
[3,4,7,2,6,8,5,1]=>{{1,3,5,6,7,8},{2,4}}
[3,4,7,1,6,8,2,5]=>{{1,2,3,4,7},{5,6,8}}
[3,4,7,1,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[2,4,1,7,5,3,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[3,4,1,7,8,6,2,5]=>{{1,3},{2,4,7},{5,8},{6}}
[6,4,2,3,8,5,1,7]=>{{1,5,6,7,8},{2,3,4}}
[6,4,2,7,5,8,1,3]=>{{1,2,3,4,6,7,8},{5}}
[6,4,2,7,5,3,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[3,4,7,2,6,8,1,5]=>{{1,3,7},{2,4},{5,6,8}}
[5,4,7,3,6,8,2,1]=>{{1,5,6,8},{2,3,4,7}}
[3,4,7,2,6,5,1,8]=>{{1,3,7},{2,4},{5,6},{8}}
[4,8,3,2,5,6,1,7]=>{{1,2,4,7,8},{3},{5},{6}}
[4,8,7,3,5,1,2,6]=>{{1,2,3,4,6,7,8},{5}}
[4,8,7,1,3,5,2,6]=>{{1,4},{2,3,5,6,7,8}}
[4,8,3,1,2,6,5,7]=>{{1,4},{2,5,7,8},{3},{6}}
[3,4,7,1,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,4,7,1,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,2,6,5,8,1]=>{{1,3,7,8},{2,4},{5,6}}
[4,8,3,1,2,6,7,5]=>{{1,4},{2,5,8},{3},{6},{7}}
[5,8,1,6,3,4,2,7]=>{{1,3,5},{2,7,8},{4,6}}
[6,8,5,1,3,7,2,4]=>{{1,2,4,6,7,8},{3,5}}
[6,8,5,1,3,4,7,2]=>{{1,4,6},{2,8},{3,5},{7}}
[5,8,3,4,2,6,7,1]=>{{1,2,5,8},{3},{4},{6},{7}}
[5,4,7,3,6,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,7,2,6,1,8,3]=>{{1,5,6},{2,4},{3,7,8}}
[6,4,3,7,5,1,2,8]=>{{1,6},{2,4,7},{3},{5},{8}}
[6,4,3,7,5,1,8,2]=>{{1,6},{2,4,7,8},{3},{5}}
[6,2,4,3,1,5,8,7]=>{{1,5,6},{2},{3,4},{7,8}}
[3,8,7,4,1,5,2,6]=>{{1,2,3,5,6,7,8},{4}}
[2,4,7,3,6,1,5,8]=>{{1,2,3,4,5,6,7},{8}}
[5,8,3,2,1,6,4,7]=>{{1,5},{2,4,7,8},{3},{6}}
[5,8,7,4,3,1,2,6]=>{{1,2,3,5,6,7,8},{4}}
[5,4,7,3,6,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[7,3,8,2,1,6,5,4]=>{{1,5,7},{2,3,4,8},{6}}
[7,4,3,8,5,2,1,6]=>{{1,7},{2,4,6,8},{3},{5}}
[6,5,2,8,4,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,2,8,6,5,1,7]=>{{1,4,7,8},{2,3},{5,6}}
[4,3,8,7,5,1,6,2]=>{{1,4,6,7},{2,3,8},{5}}
[3,2,5,8,6,1,4,7]=>{{1,3,5,6},{2},{4,7,8}}
[8,4,3,7,5,2,6,1]=>{{1,8},{2,4,6,7},{3},{5}}
[4,3,7,8,5,1,2,6]=>{{1,4,6,8},{2,3,7},{5}}
[5,3,7,8,4,1,2,6]=>{{1,4,5,6,8},{2,3,7}}
[6,2,5,8,3,1,4,7]=>{{1,6},{2},{3,5},{4,7,8}}
[6,2,4,8,3,1,5,7]=>{{1,6},{2},{3,4,5,7,8}}
[5,2,3,8,4,1,6,7]=>{{1,4,5,6,7,8},{2},{3}}
[5,3,8,7,4,1,6,2]=>{{1,4,5,6,7},{2,3,8}}
[5,3,2,8,6,4,1,7]=>{{1,4,5,6,7,8},{2,3}}
[7,5,3,8,4,2,1,6]=>{{1,7},{2,4,5,6,8},{3}}
[8,7,5,3,6,2,4,1]=>{{1,8},{2,3,4,5,6,7}}
[8,6,5,3,7,2,4,1]=>{{1,8},{2,6},{3,4,5,7}}
[7,5,4,3,8,2,6,1]=>{{1,2,5,6,7,8},{3,4}}
[6,4,5,3,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,4,6,3,8,2,5,1]=>{{1,5,7,8},{2,3,4,6}}
[7,5,6,3,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,3,7,2,4,1]=>{{1,8},{2,3,4,5,6,7}}
[7,4,6,3,5,2,8,1]=>{{1,7,8},{2,3,4,6},{5}}
[8,4,6,3,5,2,7,1]=>{{1,8},{2,3,4,6},{5},{7}}
[8,4,7,3,5,2,6,1]=>{{1,8},{2,3,4,6,7},{5}}
[8,5,7,3,4,2,6,1]=>{{1,8},{2,3,4,5,6,7}}
[7,5,8,4,3,2,6,1]=>{{1,2,3,5,6,7,8},{4}}
[6,5,8,4,3,2,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[6,5,8,3,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,5,8,3,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,4,6,2,3,1]=>{{1,3,7,8},{2,5,6},{4}}
[7,4,8,3,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,8,3,5,2,6,1]=>{{1,2,3,4,6,7,8},{5}}
[6,4,8,3,5,2,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[6,4,7,3,5,2,8,1]=>{{1,2,3,4,6,7,8},{5}}
[5,4,8,3,7,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,3,7,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,4,7,2,3,1]=>{{1,2,3,5,6,7,8},{4}}
[6,5,8,4,7,3,2,1]=>{{1,3,6,8},{2,5,7},{4}}
[6,4,7,3,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,7,3,8,2,6,1]=>{{1,5,8},{2,3,4,6,7}}
[5,4,6,3,8,2,7,1]=>{{1,5,8},{2,3,4,6},{7}}
[5,3,6,2,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,1,4,8,7,2]=>{{1,4,5},{2,3,6,8},{7}}
[5,3,7,2,4,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[4,3,1,5,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,2,1,5,8,6,3,7]=>{{1,3,4,5,7,8},{2},{6}}
[4,2,1,5,8,6,7,3]=>{{1,3,4,5,8},{2},{6},{7}}
[4,2,1,5,8,7,6,3]=>{{1,3,4,5,8},{2},{6,7}}
[4,3,1,5,7,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,7,5,8,6,2]=>{{1,2,3,4,6,7,8},{5}}
[6,7,3,1,4,8,2,5]=>{{1,4,5,6,8},{2,7},{3}}
[5,3,7,1,4,8,2,6]=>{{1,4,5},{2,3,7},{6,8}}
[4,3,1,5,7,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[3,2,1,8,5,4,6,7]=>{{1,3},{2},{4,6,7,8},{5}}
[3,2,1,8,5,7,4,6]=>{{1,3},{2},{4,6,7,8},{5}}
[3,2,1,8,7,5,4,6]=>{{1,3},{2},{4,5,6,7,8}}
[5,2,7,1,8,4,3,6]=>{{1,4,5,6,8},{2},{3,7}}
[6,7,2,1,8,4,3,5]=>{{1,4,6},{2,3,7},{5,8}}
[6,7,2,1,8,4,5,3]=>{{1,4,6},{2,3,5,7,8}}
[3,2,1,8,5,6,4,7]=>{{1,3},{2},{4,7,8},{5},{6}}
[3,2,1,8,6,5,4,7]=>{{1,3},{2},{4,7,8},{5,6}}
[4,3,1,6,7,8,5,2]=>{{1,2,3,4,6,8},{5,7}}
[4,2,1,6,8,7,5,3]=>{{1,3,4,5,6,7,8},{2}}
[4,2,1,6,8,5,7,3]=>{{1,3,4,5,6,8},{2},{7}}
[4,2,1,6,8,5,3,7]=>{{1,3,4,5,6,7,8},{2}}
[5,2,6,1,8,4,3,7]=>{{1,3,4,5,6,7,8},{2}}
[5,2,6,1,8,7,4,3]=>{{1,3,4,5,6,7,8},{2}}
[5,2,6,1,8,7,3,4]=>{{1,4,5,8},{2},{3,6,7}}
[5,2,6,1,8,3,4,7]=>{{1,4,5,7,8},{2},{3,6}}
[4,2,1,6,8,3,7,5]=>{{1,3,4,6},{2},{5,8},{7}}
[4,3,1,6,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,3,1,5,8,2,4]=>{{1,4,6,8},{2,7},{3},{5}}
[4,2,1,7,8,6,3,5]=>{{1,3,4,7},{2},{5,8},{6}}
[3,2,1,8,7,6,4,5]=>{{1,3},{2},{4,5,7,8},{6}}
[3,2,1,8,6,4,7,5]=>{{1,3},{2},{4,5,6,8},{7}}
[3,2,1,8,6,4,5,7]=>{{1,3},{2},{4,5,6,7,8}}
[3,2,1,8,4,6,5,7]=>{{1,3},{2},{4,5,7,8},{6}}
[3,2,1,8,4,6,7,5]=>{{1,3},{2},{4,5,8},{6},{7}}
[3,2,1,8,4,7,6,5]=>{{1,3},{2},{4,5,8},{6,7}}
[3,2,1,8,7,4,6,5]=>{{1,3},{2},{4,5,6,7,8}}
[4,2,1,7,8,3,6,5]=>{{1,3,4,6,7},{2},{5,8}}
[5,2,7,1,8,3,6,4]=>{{1,4,5,8},{2},{3,6,7}}
[6,7,2,1,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[5,2,7,1,8,3,4,6]=>{{1,3,4,5,6,7,8},{2}}
[4,2,1,7,8,3,5,6]=>{{1,3,4,5,6,7,8},{2}}
[3,2,1,8,4,5,7,6]=>{{1,3},{2},{4,5,6,8},{7}}
[7,5,2,8,6,3,4,1]=>{{1,4,7,8},{2,3,5,6}}
[7,4,8,6,2,5,3,1]=>{{1,3,7,8},{2,4,5,6}}
[7,3,8,6,2,4,5,1]=>{{1,2,3,5,7,8},{4,6}}
[7,4,3,1,8,2,5,6]=>{{1,2,4,5,6,7,8},{3}}
[7,4,2,8,5,6,1,3]=>{{1,7},{2,3,4,8},{5},{6}}
[7,3,8,5,2,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,4,5,6,2,1]=>{{1,2,3,7,8},{4},{5},{6}}
[6,3,8,2,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[6,3,8,2,5,7,4,1]=>{{1,2,3,4,6,7,8},{5}}
[6,4,3,8,1,5,2,7]=>{{1,5,6},{2,4,7,8},{3}}
[6,3,7,8,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,3,8,2,4,1]=>{{1,5,8},{2,6},{3,4,7}}
[5,4,7,2,6,8,1,3]=>{{1,3,5,6,7,8},{2,4}}
[5,3,8,2,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[6,3,8,2,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,2,6,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,2,7,5,1,3]=>{{1,5,6,7},{2,4},{3,8}}
[6,5,3,1,4,2,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[5,7,4,2,6,1,3,8]=>{{1,5,6},{2,3,4,7},{8}}
[5,6,4,2,3,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,3,7,8,2,4,1]=>{{1,5,8},{2,6},{3},{4,7}}
[5,6,3,8,2,4,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[6,3,7,2,4,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[6,3,7,2,5,8,4,1]=>{{1,6,8},{2,3,4,7},{5}}
[5,3,6,8,2,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,4,6,2,3,8,1,7]=>{{1,3,5,6,7,8},{2,4}}
[5,3,6,7,8,2,4,1]=>{{1,5,8},{2,3,6},{4,7}}
[3,6,4,2,1,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,5,8,6,4,2,1,7]=>{{1,3,7,8},{2,4,5,6}}
[5,8,6,3,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,3,4,2,1,8,7]=>{{1,2,5,6},{3},{4},{7,8}}
[6,3,4,2,1,5,8,7]=>{{1,5,6},{2,3,4},{7,8}}
[5,6,4,2,1,3,8,7]=>{{1,5},{2,3,4,6},{7,8}}
[2,5,4,1,7,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,5,4,1,6,3]=>{{1,2,6,7},{3,8},{4,5}}
[2,8,5,4,1,6,3,7]=>{{1,2,3,5,7,8},{4},{6}}
[2,6,3,8,5,4,1,7]=>{{1,2,4,6,7,8},{3},{5}}
[2,8,6,3,5,4,1,7]=>{{1,2,7,8},{3,4,6},{5}}
[5,8,6,4,2,1,3,7]=>{{1,2,3,5,6,7,8},{4}}
[4,2,1,5,7,8,6,3]=>{{1,3,4,5,6,7,8},{2}}
[2,7,8,6,3,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,5,7,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[7,6,2,1,8,4,3,5]=>{{1,2,3,4,6,7},{5,8}}
[2,1,8,5,6,4,3,7]=>{{1,2},{3,7,8},{4,5,6}}
[4,2,1,8,5,6,3,7]=>{{1,3,4,7,8},{2},{5},{6}}
[8,4,2,1,5,6,3,7]=>{{1,2,3,4,7,8},{5},{6}}
[2,5,6,3,8,4,1,7]=>{{1,2,5,7,8},{3,4,6}}
[6,3,4,2,1,8,5,7]=>{{1,5,6,7,8},{2,3,4}}
[3,7,8,5,6,4,2,1]=>{{1,3,8},{2,7},{4,5,6}}
[3,8,5,6,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,2,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,4,2,1,5,7]=>{{1,3,6},{2,5,7,8},{4}}
[3,7,8,6,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,7,6,2,4,1]=>{{1,8},{2,5,6},{3},{4,7}}
[7,6,2,4,1,8,5,3]=>{{1,5,7},{2,3,6,8},{4}}
[8,5,4,1,7,6,2,3]=>{{1,3,4,8},{2,5,7},{6}}
[7,6,2,3,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,8,6,4,3,5]=>{{1,2},{3,7},{4,5,6,8}}
[2,1,6,4,3,7,8,5]=>{{1,2},{3,5,6,7,8},{4}}
[6,4,2,1,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,8,4,2,1,5]=>{{1,2,3,6,7},{4,5,8}}
[7,8,4,2,1,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[5,7,6,2,3,8,4,1]=>{{1,3,5,6,8},{2,4,7}}
[2,6,1,8,4,3,7,5]=>{{1,2,3,6},{4,5,8},{7}}
[2,6,1,7,5,8,4,3]=>{{1,2,3,6,8},{4,7},{5}}
[8,4,2,3,7,5,6,1]=>{{1,8},{2,3,4},{5,6,7}}
[8,5,7,6,2,1,4,3]=>{{1,3,4,6,7,8},{2,5}}
[4,8,5,7,6,2,1,3]=>{{1,4,7},{2,3,5,6,8}}
[4,7,6,2,1,3,8,5]=>{{1,2,4,5,7,8},{3,6}}
[7,5,6,1,8,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,8,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,3,6,1,7,5]=>{{1,2,5,6,8},{3,4},{7}}
[6,4,7,8,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[6,4,3,7,5,2,1,8]=>{{1,2,4,6,7},{3},{5},{8}}
[6,5,3,2,8,4,1,7]=>{{1,2,4,5,6,7,8},{3}}
[6,5,2,7,8,4,1,3]=>{{1,4,6,7},{2,3,5,8}}
[6,4,3,2,5,8,1,7]=>{{1,6,7,8},{2,4},{3},{5}}
[6,3,7,2,5,4,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[6,3,2,7,5,4,1,8]=>{{1,4,6,7},{2,3},{5},{8}}
[8,4,2,6,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[1,5,3,7,4,2,8,6]=>{{1},{2,4,5,6,7,8},{3}}
[1,6,7,3,4,2,8,5]=>{{1},{2,6},{3,4,5,7,8}}
[8,6,5,2,3,1,7,4]=>{{1,2,4,6,8},{3,5},{7}}
[1,7,6,3,4,2,8,5]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,3,2,5,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[8,7,5,2,1,4,6,3]=>{{1,3,5,8},{2,4,6,7}}
[7,8,5,2,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,2,3,1,7,4]=>{{1,6},{2,4,8},{3,5},{7}}
[5,8,6,2,3,1,7,4]=>{{1,3,5,6},{2,4,8},{7}}
[4,8,2,6,3,1,7,5]=>{{1,4,6},{2,3,5,8},{7}}
[3,2,8,6,4,1,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[3,2,1,7,5,4,8,6]=>{{1,3},{2},{4,6,7,8},{5}}
[4,1,3,7,5,2,8,6]=>{{1,2,4,6,7,8},{3},{5}}
[5,1,7,3,4,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,3,2,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,2,7,4,3,6,8,5]=>{{1},{2},{3,5,7,8},{4},{6}}
[6,1,8,2,4,5,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[5,1,8,3,2,6,7,4]=>{{1,2,5},{3,4,8},{6},{7}}
[3,2,8,7,1,5,6,4]=>{{1,3,4,5,6,7,8},{2}}
[4,8,2,7,1,5,6,3]=>{{1,4,5,6,7},{2,3,8}}
[5,8,7,2,1,4,6,3]=>{{1,5},{2,3,4,6,7,8}}
[6,8,7,1,3,4,5,2]=>{{1,4,6},{2,8},{3,5,7}}
[7,8,6,1,3,4,5,2]=>{{1,3,4,5,6,7},{2,8}}
[1,7,8,2,4,5,6,3]=>{{1},{2,4,5,6,7},{3,8}}
[8,6,7,1,3,4,5,2]=>{{1,2,4,6,8},{3,5,7}}
[7,6,8,1,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,2,3,1,7,4]=>{{1,6},{2,3,4,5,8},{7}}
[1,6,8,3,2,5,7,4]=>{{1},{2,5,6},{3,4,8},{7}}
[1,5,3,8,2,6,7,4]=>{{1},{2,5},{3},{4,8},{6},{7}}
[8,4,2,7,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,8,1,5,6,3]=>{{1,5,6,7},{2,3,4,8}}
[6,4,2,8,3,1,7,5]=>{{1,6},{2,3,4,5,8},{7}}
[5,4,2,3,8,1,7,6]=>{{1,5,6,8},{2,3,4},{7}}
[4,5,2,3,1,6,8,7]=>{{1,2,3,4,5},{6},{7,8}}
[7,4,2,1,3,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[8,4,2,1,3,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[1,5,3,2,4,7,8,6]=>{{1},{2,4,5},{3},{6,7,8}}
[8,5,1,3,2,6,7,4]=>{{1,3,4,8},{2,5},{6},{7}}
[5,6,1,3,4,2,8,7]=>{{1,3,4,5},{2,6},{7,8}}
[4,6,2,1,5,3,8,7]=>{{1,4},{2,3,6},{5},{7,8}}
[4,7,2,1,3,6,8,5]=>{{1,4},{2,3,5,7,8},{6}}
[5,7,1,3,2,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[6,7,1,2,4,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[8,6,1,2,4,5,7,3]=>{{1,3,8},{2,4,5,6},{7}}
[1,8,2,3,5,6,7,4]=>{{1},{2,3,4,8},{5},{6},{7}}
[8,7,1,2,4,5,6,3]=>{{1,3,8},{2,4,5,6,7}}
[7,8,1,2,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,3,2,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[4,8,2,1,3,6,7,5]=>{{1,4},{2,3,5,8},{6},{7}}
[4,1,3,2,5,7,8,6]=>{{1,2,4},{3},{5},{6,7,8}}
[5,1,2,4,3,7,8,6]=>{{1,2,3,5},{4},{6,7,8}}
[5,4,8,1,2,3,7,6]=>{{1,2,4,5},{3,6,8},{7}}
[1,4,7,6,3,2,5,8]=>{{1},{2,4,6},{3,5,7},{8}}
[4,8,3,2,7,6,1,5]=>{{1,2,4,5,7,8},{3},{6}}
[4,3,8,2,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[4,3,2,8,1,7,6,5]=>{{1,4,5,8},{2,3},{6,7}}
[4,1,8,7,3,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,1,2,5,3,6]=>{{1,4},{2,3,5,6,7,8}}
[2,3,6,7,4,1,8,5]=>{{1,2,3,6},{4,5,7,8}}
[2,6,3,4,7,8,1,5]=>{{1,2,5,6,7,8},{3},{4}}
[3,1,7,8,4,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,2,6,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,7,2,4,8,6,1,5]=>{{1,2,3,7},{4},{5,8},{6}}
[1,3,6,4,7,2,5,8]=>{{1},{2,3,6},{4},{5,7},{8}}
[4,7,1,5,8,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,6,7,3,8,4,1,5]=>{{1,2,3,4,6,7},{5,8}}
[8,7,5,2,6,3,4,1]=>{{1,8},{2,4,7},{3,5,6}}
[8,6,5,2,7,3,4,1]=>{{1,8},{2,3,4,5,6,7}}
[7,4,8,5,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,4,6,7,8,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,2,6,4,7,5,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[3,1,7,5,4,2,6,8]=>{{1,2,3,6,7},{4,5},{8}}
[6,3,8,5,4,7,1,2]=>{{1,6,7},{2,3,8},{4,5}}
[1,6,2,5,4,7,8,3]=>{{1},{2,3,6,7,8},{4,5}}
[1,8,2,5,6,3,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[1,2,6,4,8,5,7,3]=>{{1},{2},{3,5,6,8},{4},{7}}
[7,8,3,1,4,2,5,6]=>{{1,4,5,7},{2,6,8},{3}}
[4,8,1,5,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,5,2,3,6,8]=>{{1,3,6,7},{2,4,5},{8}}
[5,6,1,8,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,6,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,3,8,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,1,2,5,8,3,7,4]=>{{1,2,3,6},{4,5,8},{7}}
[6,1,8,7,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[7,1,2,5,4,8,6,3]=>{{1,2,3,6,7,8},{4,5}}
[1,2,7,5,8,3,6,4]=>{{1},{2},{3,6,7},{4,5,8}}
[4,1,6,3,7,5,2,8]=>{{1,2,3,4,5,6,7},{8}}
[1,3,6,7,8,5,2,4]=>{{1},{2,3,4,5,6,7,8}}
[1,2,6,4,7,8,5,3]=>{{1},{2},{3,6,8},{4},{5,7}}
[4,1,6,3,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,6,4,8,2,7,5]=>{{1,2,3,6},{4},{5,8},{7}}
[7,8,4,1,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,1,6,3,8,7,2,5]=>{{1,2,3,4,6,7},{5,8}}
[7,5,1,8,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[6,5,1,7,4,3,2,8]=>{{1,3,6},{2,4,5,7},{8}}
[4,1,8,5,2,3,7,6]=>{{1,2,4,5},{3,6,8},{7}}
[4,1,6,8,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[5,4,6,1,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,1,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,3,5,4,7,2,6,8]=>{{1},{2,3,5,6,7},{4},{8}}
[1,3,5,4,7,2,8,6]=>{{1},{2,3,5,6,7,8},{4}}
[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,3,5,7,4,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,3,5,7,8,4,2,6]=>{{1},{2,3,4,5,6,7,8}}
[1,6,3,2,7,4,8,5]=>{{1},{2,4,6},{3},{5,7,8}}
[3,5,1,6,2,8,7,4]=>{{1,3},{2,5},{4,6,8},{7}}
[1,3,7,2,5,4,8,6]=>{{1},{2,3,4,6,7,8},{5}}
[1,3,7,5,2,4,8,6]=>{{1},{2,3,4,5,6,7,8}}
[2,5,7,4,3,8,1,6]=>{{1,2,3,5,7},{4},{6,8}}
[2,5,3,7,4,8,1,6]=>{{1,2,4,5,7},{3},{6,8}}
[3,2,6,7,8,1,5,4]=>{{1,3,6},{2},{4,5,7,8}}
[3,5,2,7,8,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[1,5,7,4,8,3,2,6]=>{{1},{2,3,5,6,7,8},{4}}
[3,5,2,6,8,4,7,1]=>{{1,2,3,5,8},{4,6},{7}}
[2,5,7,4,3,8,6,1]=>{{1,2,3,5,6,7,8},{4}}
[1,5,7,2,4,8,6,3]=>{{1},{2,4,5},{3,6,7,8}}
[4,6,3,7,2,8,5,1]=>{{1,2,4,5,6,7,8},{3}}
[1,4,7,3,8,6,2,5]=>{{1},{2,3,4,7},{5,8},{6}}
[5,1,6,8,2,4,3,7]=>{{1,2,5},{3,4,6,7,8}}
[5,3,7,8,2,4,1,6]=>{{1,2,3,5,7},{4,6,8}}
[8,5,3,7,2,4,1,6]=>{{1,4,6,7,8},{2,5},{3}}
[8,2,4,7,3,1,5,6]=>{{1,6,8},{2},{3,4,5,7}}
[2,4,7,8,3,1,5,6]=>{{1,2,4,6,8},{3,5,7}}
[6,3,1,5,8,2,4,7]=>{{1,2,3,6},{4,5,7,8}}
[6,5,3,4,2,8,1,7]=>{{1,6,7,8},{2,5},{3},{4}}
[5,2,4,3,8,1,6,7]=>{{1,5,6,7,8},{2},{3,4}}
[3,2,4,8,1,5,6,7]=>{{1,3,4,5,6,7,8},{2}}
[3,2,4,6,8,1,5,7]=>{{1,3,4,6},{2},{5,7,8}}
[8,1,5,7,3,2,4,6]=>{{1,2,6,8},{3,5},{4,7}}
[8,4,6,7,2,3,1,5]=>{{1,2,4,5,7,8},{3,6}}
[4,6,7,8,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,8,2,3,1,5]=>{{1,7},{2,4,5,8},{3,6}}
[7,2,4,8,3,1,5,6]=>{{1,3,4,5,6,7,8},{2}}
[5,3,8,7,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,7,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,6,8,7,2,3,1,5]=>{{1,4,7},{2,3,5,6,8}}
[8,7,4,6,2,3,1,5]=>{{1,2,5,7,8},{3,4,6}}
[5,6,8,7,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,7,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,4,2,8,6,5]=>{{1,2,3,5,6,7,8},{4}}
[3,2,8,4,1,7,6,5]=>{{1,3,5,8},{2},{4},{6,7}}
[7,6,4,8,2,3,1,5]=>{{1,7},{2,3,4,5,6,8}}
[5,7,6,8,2,3,1,4]=>{{1,2,5,7},{3,6},{4,8}}
[4,7,6,8,2,3,1,5]=>{{1,2,4,5,7,8},{3,6}}
[8,6,4,7,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,2,3,7,4,1,6,5]=>{{1,4,5,6,7,8},{2},{3}}
[2,3,7,8,4,1,6,5]=>{{1,2,3,6,7},{4,5,8}}
[3,7,4,8,2,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,7,4,1,6,8,5]=>{{1,2,3,5,7,8},{4},{6}}
[8,1,6,4,2,3,7,5]=>{{1,2,5,8},{3,6},{4},{7}}
[4,7,8,6,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,4,7,3,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,7,4,2,8,5]=>{{1,2,3,6},{4,5,7,8}}
[8,5,7,6,2,3,1,4]=>{{1,3,4,6,7,8},{2,5}}
[7,5,8,6,2,3,1,4]=>{{1,7},{2,5},{3,4,6,8}}
[7,1,6,4,2,3,8,5]=>{{1,2,5,7,8},{3,6},{4}}
[3,1,7,6,4,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,6,2,3,1,5]=>{{1,3,4,6,7},{2,5,8}}
[6,8,7,5,2,3,1,4]=>{{1,3,6,7},{2,4,5,8}}
[4,3,6,1,5,8,7,2]=>{{1,4},{2,3,6,8},{5},{7}}
[4,3,6,5,1,8,7,2]=>{{1,4,5},{2,3,6,8},{7}}
[4,6,3,5,1,8,7,2]=>{{1,4,5},{2,6,8},{3},{7}}
[4,6,3,1,5,8,7,2]=>{{1,4},{2,6,8},{3},{5},{7}}
[4,1,6,5,3,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,6,1,5,3,8,7,2]=>{{1,3,4,5},{2,6,8},{7}}
[2,6,5,3,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,6,5,1,8,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[2,6,5,8,1,7,3,4]=>{{1,2,3,5,6,7},{4,8}}
[2,6,5,8,1,3,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[2,6,5,8,3,1,7,4]=>{{1,2,6},{3,5},{4,8},{7}}
[2,6,5,3,8,1,7,4]=>{{1,2,6},{3,4,5,8},{7}}
[4,6,1,5,8,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,1,6,5,8,3,7,2]=>{{1,2,4,5,8},{3,6},{7}}
[1,4,6,5,8,3,7,2]=>{{1},{2,4,5,8},{3,6},{7}}
[4,1,6,5,8,7,3,2]=>{{1,2,4,5,8},{3,6,7}}
[2,6,5,3,8,7,1,4]=>{{1,2,6,7},{3,4,5,8}}
[6,4,3,8,7,1,5,2]=>{{1,6},{2,4,8},{3},{5,7}}
[6,4,8,3,7,1,5,2]=>{{1,6},{2,3,4,8},{5,7}}
[2,6,8,5,3,7,1,4]=>{{1,2,6,7},{3,4,5,8}}
[4,6,8,1,5,7,3,2]=>{{1,4},{2,3,6,7,8},{5}}
[4,6,1,8,5,7,3,2]=>{{1,2,3,4,6,7,8},{5}}
[4,1,6,8,5,7,3,2]=>{{1,2,4,8},{3,6,7},{5}}
[1,4,6,8,5,7,3,2]=>{{1},{2,4,8},{3,6,7},{5}}
[1,4,6,8,5,3,7,2]=>{{1},{2,4,8},{3,6},{5},{7}}
[4,6,1,8,5,3,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[2,6,8,5,3,1,7,4]=>{{1,2,6},{3,4,5,8},{7}}
[2,6,8,5,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[4,6,8,3,5,1,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[4,6,8,3,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,6,3,1,8,5,7,2]=>{{1,4},{2,5,6,8},{3},{7}}
[4,6,3,8,1,5,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[4,6,3,8,5,7,1,2]=>{{1,2,4,6,7,8},{3},{5}}
[4,3,6,8,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,3,6,1,8,5,7,2]=>{{1,4},{2,3,5,6,8},{7}}
[4,3,1,6,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,1,3,6,8,7,5,2]=>{{1,2,4,5,6,7,8},{3}}
[4,3,6,1,8,7,5,2]=>{{1,4},{2,3,5,6,7,8}}
[4,3,6,8,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,8,7,3,1,4]=>{{1,2,3,5,6,7},{4,8}}
[6,5,2,8,7,1,3,4]=>{{1,6},{2,3,5,7},{4,8}}
[6,2,5,8,7,1,3,4]=>{{1,6},{2},{3,5,7},{4,8}}
[6,2,5,8,7,3,1,4]=>{{1,3,5,6,7},{2},{4,8}}
[4,6,3,8,1,7,5,2]=>{{1,2,4,5,6,7,8},{3}}
[4,6,3,1,8,7,5,2]=>{{1,4},{2,5,6,7,8},{3}}
[4,1,6,3,8,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[1,4,6,3,8,7,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,6,8,3,7,5,2]=>{{1,2,4,8},{3,5,6,7}}
[4,6,1,8,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,6,8,1,3,7,5,2]=>{{1,4},{2,3,5,6,7,8}}
[6,2,8,5,7,3,1,4]=>{{1,3,4,5,6,7,8},{2}}
[6,2,8,5,7,1,3,4]=>{{1,6},{2},{3,4,5,7,8}}
[2,4,8,7,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[4,2,8,7,5,3,1,6]=>{{1,4,7},{2},{3,6,8},{5}}
[6,4,1,8,7,5,3,2]=>{{1,3,5,6,7},{2,4,8}}
[6,1,4,8,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,8,7,3,5,2]=>{{1},{2,3,4,6,8},{5,7}}
[6,4,1,8,7,3,5,2]=>{{1,3,6},{2,4,8},{5,7}}
[4,2,8,7,5,1,3,6]=>{{1,3,4,6,7,8},{2},{5}}
[2,4,8,7,3,5,1,6]=>{{1,2,4,7},{3,5,6,8}}
[2,3,4,7,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[2,3,7,1,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[2,6,1,3,7,8,5,4]=>{{1,2,3,4,6,8},{5,7}}
[1,5,3,2,6,4,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[1,5,3,2,6,7,4,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,7,3,2,8,5,4,6]=>{{1},{2,4,7},{3},{5,6,8}}
[1,3,2,7,5,4,8,6]=>{{1},{2,3},{4,6,7,8},{5}}
[6,5,2,4,3,7,1,8]=>{{1,6,7},{2,3,5},{4},{8}}
[6,4,2,5,3,7,1,8]=>{{1,6,7},{2,3,4,5},{8}}
[5,4,7,6,2,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[3,6,4,8,2,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,2,8,5,3,4,7]=>{{1},{2,3,6},{4,7,8},{5}}
[4,6,2,3,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,7,2,3,6,5,1,8]=>{{1,2,3,4,7},{5,6},{8}}
[4,7,2,3,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}
[5,3,2,7,4,6,1,8]=>{{1,4,5,7},{2,3},{6},{8}}
[5,3,2,6,4,7,1,8]=>{{1,4,5,6,7},{2,3},{8}}
[4,6,2,3,5,7,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[3,5,2,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,5,2,6,8,4,3,7]=>{{1},{2,3,5,7,8},{4,6}}
[1,5,7,2,8,4,3,6]=>{{1},{2,4,5,6,8},{3,7}}
[3,5,2,1,8,6,4,7]=>{{1,2,3,4,5,7,8},{6}}
[3,6,8,4,2,1,5,7]=>{{1,2,3,5,6,7,8},{4}}
[4,3,2,6,1,8,5,7]=>{{1,4,5,6,7,8},{2,3}}
[1,5,8,2,7,4,3,6]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,3,4,8,6,5]=>{{1},{2,3,4,5,6,7,8}}
[6,8,2,3,4,1,7,5]=>{{1,6},{2,3,4,5,8},{7}}
[4,1,8,2,3,5,7,6]=>{{1,2,4},{3,5,6,8},{7}}
[2,3,1,8,4,5,7,6]=>{{1,2,3},{4,5,6,8},{7}}
[7,3,2,1,4,5,8,6]=>{{1,4,5,6,7,8},{2,3}}
[7,8,1,4,3,5,2,6]=>{{1,2,3,5,6,7,8},{4}}
[7,1,2,3,4,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[6,1,2,3,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[1,8,2,3,4,7,6,5]=>{{1},{2,3,4,5,8},{6,7}}
[8,1,2,3,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[2,8,1,3,5,4,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[8,7,1,4,3,5,2,6]=>{{1,3,5,6,8},{2,7},{4}}
[8,3,2,1,4,5,7,6]=>{{1,4,5,6,8},{2,3},{7}}
[3,8,2,1,5,6,4,7]=>{{1,2,3,4,7,8},{5},{6}}
[3,8,2,1,6,5,4,7]=>{{1,2,3,4,7,8},{5,6}}
[1,7,8,3,5,4,2,6]=>{{1},{2,7},{3,4,6,8},{5}}
[7,4,1,8,3,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,7,3,5,2,6]=>{{1,3,5,6,8},{2,4,7}}
[3,8,4,6,2,1,5,7]=>{{1,3,4,6},{2,5,7,8}}
[8,4,2,5,3,1,6,7]=>{{1,6,7,8},{2,3,4,5}}
[8,5,2,4,3,1,6,7]=>{{1,6,7,8},{2,3,5},{4}}
[8,3,2,5,4,1,6,7]=>{{1,6,7,8},{2,3},{4,5}}
[4,3,2,5,1,8,6,7]=>{{1,4,5},{2,3},{6,7,8}}
[3,5,2,4,1,8,6,7]=>{{1,2,3,5},{4},{6,7,8}}
[2,4,7,8,1,5,3,6]=>{{1,2,4,5,6,8},{3,7}}
[1,8,7,3,5,4,2,6]=>{{1},{2,3,4,6,7,8},{5}}
[5,1,8,2,7,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[5,1,7,2,8,4,3,6]=>{{1,2,4,5,6,8},{3,7}}
[6,1,2,8,5,3,4,7]=>{{1,2,3,6},{4,7,8},{5}}
[6,3,2,1,8,4,5,7]=>{{1,4,6},{2,3},{5,7,8}}
[7,3,2,8,4,5,1,6]=>{{1,7},{2,3},{4,5,6,8}}
[2,7,8,4,3,5,1,6]=>{{1,2,7},{3,5,6,8},{4}}
[7,1,8,3,5,4,2,6]=>{{1,2,7},{3,4,6,8},{5}}
[7,8,2,3,4,6,1,5]=>{{1,7},{2,3,4,5,8},{6}}
[6,7,1,3,4,8,2,5]=>{{1,3,4,5,6,8},{2,7}}
[6,8,1,3,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[1,7,2,3,4,6,8,5]=>{{1},{2,3,4,5,7,8},{6}}
[1,6,2,3,4,8,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[7,6,2,3,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,3,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[8,1,7,3,5,4,2,6]=>{{1,2,3,4,6,7,8},{5}}
[8,3,2,7,4,5,1,6]=>{{1,4,5,6,7,8},{2,3}}
[6,7,2,3,4,1,8,5]=>{{1,6},{2,3,4,5,7,8}}
[7,6,2,3,4,8,1,5]=>{{1,7},{2,3,4,5,6,8}}
[8,6,2,3,4,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[6,3,4,8,7,5,1,2]=>{{1,5,6,7},{2,3,4,8}}
[4,8,7,3,5,6,1,2]=>{{1,3,4,7},{2,8},{5},{6}}
[4,8,7,5,3,6,1,2]=>{{1,3,4,5,7},{2,8},{6}}
[5,8,7,3,4,6,1,2]=>{{1,3,4,5,7},{2,8},{6}}
[5,8,4,2,1,6,7,3]=>{{1,5},{2,3,4,8},{6},{7}}
[5,8,4,1,2,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[5,3,7,2,6,1,8,4]=>{{1,5,6},{2,3,4,7,8}}
[5,2,8,1,6,3,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[5,8,2,1,4,7,6,3]=>{{1,4,5},{2,3,8},{6,7}}
[4,8,2,5,1,7,6,3]=>{{1,4,5},{2,3,8},{6,7}}
[7,8,4,1,2,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[4,8,1,5,2,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[5,8,1,2,4,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[5,2,8,3,6,7,1,4]=>{{1,5,6,7},{2},{3,4,8}}
[3,8,7,6,2,4,1,5]=>{{1,3,7},{2,5,8},{4,6}}
[2,8,7,6,4,1,3,5]=>{{1,2,4,5,6,8},{3,7}}
[7,8,2,6,5,1,3,4]=>{{1,2,3,4,6,7,8},{5}}
[1,8,7,6,4,2,3,5]=>{{1},{2,4,5,6,8},{3,7}}
[2,8,7,6,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,6,2,4,3,5]=>{{1},{2,5,8},{3,7},{4,6}}
[1,8,7,6,3,4,2,5]=>{{1},{2,3,5,7,8},{4,6}}
[2,8,1,4,5,6,7,3]=>{{1,2,3,8},{4},{5},{6},{7}}
[2,1,7,3,6,5,8,4]=>{{1,2},{3,4,7,8},{5,6}}
[3,1,7,2,6,5,8,4]=>{{1,2,3,4,7,8},{5,6}}
[3,2,7,1,6,5,8,4]=>{{1,3,4,7,8},{2},{5,6}}
[6,1,2,8,5,7,3,4]=>{{1,2,3,6,7},{4,8},{5}}
[6,2,1,8,5,7,3,4]=>{{1,3,6,7},{2},{4,8},{5}}
[6,3,1,8,5,7,2,4]=>{{1,2,3,6,7},{4,8},{5}}
[6,4,2,1,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[6,1,3,8,5,2,7,4]=>{{1,2,6},{3},{4,8},{5},{7}}
[2,3,7,1,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[1,3,7,2,6,8,5,4]=>{{1},{2,3,4,5,6,7,8}}
[7,8,2,6,5,3,1,4]=>{{1,7},{2,3,4,6,8},{5}}
[3,2,6,7,5,8,1,4]=>{{1,3,4,6,7,8},{2},{5}}
[1,2,7,5,6,3,8,4]=>{{1},{2},{3,4,5,6,7,8}}
[2,8,7,6,4,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,6,1,2,5,4]=>{{1,3,5,7},{2,4,6,8}}
[3,8,7,6,2,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,6,2,1,3,5]=>{{1,4,6},{2,5,8},{3,7}}
[4,8,7,6,1,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,6,4,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,3,6,5,1,2,4]=>{{1,2,4,6,7,8},{3},{5}}
[2,3,7,5,6,8,1,4]=>{{1,2,3,7},{4,5,6,8}}
[3,8,7,6,4,2,1,5]=>{{1,3,7},{2,4,5,6,8}}
[5,1,4,6,8,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,7,6,3,5,4,8,2]=>{{1},{2,7,8},{3,4,6},{5}}
[4,3,7,2,6,5,1,8]=>{{1,2,3,4,7},{5,6},{8}}
[3,4,6,1,5,7,2,8]=>{{1,2,3,4,6,7},{5},{8}}
[1,6,8,5,7,3,4,2]=>{{1},{2,3,6,8},{4,5,7}}
[2,4,1,5,8,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[4,6,1,2,5,8,3,7]=>{{1,2,3,4,6,7,8},{5}}
[5,6,7,2,1,4,8,3]=>{{1,5},{2,4,6},{3,7,8}}
[7,8,6,5,1,2,4,3]=>{{1,4,5,7},{2,3,6,8}}
[1,3,6,5,7,8,2,4]=>{{1},{2,3,4,5,6,7,8}}
[7,4,8,5,3,1,6,2]=>{{1,6,7},{2,3,4,5,8}}
[6,8,5,2,4,1,7,3]=>{{1,6},{2,3,4,5,8},{7}}
[2,3,1,6,8,5,7,4]=>{{1,2,3},{4,5,6,8},{7}}
[7,3,2,5,1,4,8,6]=>{{1,4,5,6,7,8},{2,3}}
[7,1,4,2,3,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[1,5,8,3,4,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[8,3,1,2,4,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[2,3,8,1,6,5,4,7]=>{{1,2,3,4,7,8},{5,6}}
[8,1,4,7,2,5,3,6]=>{{1,2,5,6,8},{3,4,7}}
[3,5,2,4,1,7,8,6]=>{{1,2,3,5},{4},{6,7,8}}
[3,4,7,8,6,2,1,5]=>{{1,3,7},{2,4,5,6,8}}
[3,4,8,6,2,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[5,8,2,1,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,7,2,8,6,4,3,1]=>{{1,4,5,6,8},{2,3,7}}
[6,1,2,7,5,3,8,4]=>{{1,2,3,6},{4,7,8},{5}}
[7,3,2,8,6,4,1,5]=>{{1,7},{2,3},{4,5,6,8}}
[2,7,8,4,6,3,1,5]=>{{1,2,7},{3,5,6,8},{4}}
[1,4,5,7,2,6,8,3]=>{{1},{2,3,4,5,7,8},{6}}
[7,3,5,2,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,3,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[8,1,6,3,5,7,2,4]=>{{1,2,3,4,6,7,8},{5}}
[2,8,6,4,3,7,1,5]=>{{1,2,3,5,6,7,8},{4}}
[8,3,2,6,4,7,1,5]=>{{1,4,5,6,7,8},{2,3}}
[2,3,8,7,6,5,1,4]=>{{1,2,3,4,7,8},{5,6}}
[1,2,8,7,3,6,5,4]=>{{1},{2},{3,4,5,7,8},{6}}
[4,2,8,7,3,6,1,5]=>{{1,4,7},{2},{3,5,8},{6}}
[4,5,8,7,1,2,6,3]=>{{1,2,4,5,6,7},{3,8}}
[1,5,8,7,3,2,6,4]=>{{1},{2,3,4,5,6,7,8}}
[4,5,8,7,3,2,1,6]=>{{1,4,7},{2,3,5,6,8}}
[2,6,8,1,7,5,4,3]=>{{1,2,4,5,6,7},{3,8}}
[3,6,8,4,7,2,1,5]=>{{1,3,5,7,8},{2,6},{4}}
[2,5,8,3,7,6,1,4]=>{{1,2,5,7},{3,4,8},{6}}
[3,2,8,4,7,6,1,5]=>{{1,3,5,7,8},{2},{4},{6}}
[1,5,8,3,7,2,6,4]=>{{1},{2,5,6,7},{3,4,8}}
[3,5,8,4,7,2,1,6]=>{{1,2,3,5,6,7,8},{4}}
[5,6,8,2,3,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[1,6,8,4,2,7,5,3]=>{{1},{2,5,6,7},{3,8},{4}}
[1,5,8,4,2,7,6,3]=>{{1},{2,5},{3,8},{4},{6,7}}
[1,5,8,2,3,7,6,4]=>{{1},{2,3,4,5,8},{6,7}}
[2,1,8,4,3,7,6,5]=>{{1,2},{3,5,8},{4},{6,7}}
[2,5,8,4,3,7,1,6]=>{{1,2,3,5,6,7,8},{4}}
[5,6,8,4,1,2,7,3]=>{{1,5},{2,6},{3,8},{4},{7}}
[5,6,8,1,3,2,7,4]=>{{1,3,4,5,8},{2,6},{7}}
[1,6,8,4,3,2,7,5]=>{{1},{2,6},{3,5,8},{4},{7}}
[5,6,8,4,3,2,1,7]=>{{1,3,5,7,8},{2,6},{4}}
[7,1,2,8,6,5,4,3]=>{{1,2,3,4,7,8},{5,6}}
[7,1,4,8,6,2,5,3]=>{{1,2,5,6,7},{3,4,8}}
[7,3,1,8,6,2,5,4]=>{{1,2,3,5,6,7},{4,8}}
[7,2,4,8,3,6,1,5]=>{{1,7},{2},{3,4,5,8},{6}}
[7,1,4,8,3,2,6,5]=>{{1,2,6,7},{3,4,5,8}}
[7,4,5,8,3,2,1,6]=>{{1,7},{2,4,6,8},{3,5}}
[1,6,2,8,7,5,4,3]=>{{1},{2,3,4,5,6,7,8}}
[1,6,4,8,7,2,5,3]=>{{1},{2,6},{3,4,8},{5,7}}
[3,6,4,8,7,2,1,5]=>{{1,3,4,5,7,8},{2,6}}
[3,2,5,8,7,6,1,4]=>{{1,3,5,7},{2},{4,8},{6}}
[3,2,4,8,7,6,1,5]=>{{1,3,4,5,7,8},{2},{6}}
[3,1,5,8,7,2,6,4]=>{{1,2,3,5,6,7},{4,8}}
[3,1,4,8,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,8,2,7,5,3]=>{{1},{2,5,6,7},{3,4,8}}
[1,4,5,8,2,7,6,3]=>{{1},{2,3,4,5,8},{6,7}}
[2,4,5,8,3,7,1,6]=>{{1,2,4,6,7,8},{3,5}}
[4,6,5,8,1,2,7,3]=>{{1,3,4,5,8},{2,6},{7}}
[1,6,4,8,3,2,7,5]=>{{1},{2,6},{3,4,5,8},{7}}
[1,4,5,8,3,2,7,6]=>{{1},{2,4,6,8},{3,5},{7}}
[7,6,1,4,8,2,5,3]=>{{1,3,5,7,8},{2,6},{4}}
[7,6,1,3,8,2,5,4]=>{{1,3,4,5,7,8},{2,6}}
[7,6,3,4,8,2,1,5]=>{{1,7},{2,6},{3},{4},{5,8}}
[7,2,5,1,8,6,4,3]=>{{1,4,7},{2},{3,5,8},{6}}
[7,2,5,3,8,6,1,4]=>{{1,7},{2},{3,4,5,8},{6}}
[7,2,1,4,8,6,5,3]=>{{1,3,5,7,8},{2},{4},{6}}
[7,2,1,3,8,6,5,4]=>{{1,3,4,5,7,8},{2},{6}}
[7,2,3,4,8,6,1,5]=>{{1,7},{2},{3},{4},{5,8},{6}}
[7,3,5,4,8,2,1,6]=>{{1,7},{2,3,5,6,8},{4}}
[2,6,5,1,8,7,4,3]=>{{1,2,4,6,7},{3,5,8}}
[2,3,5,4,8,7,1,6]=>{{1,2,3,5,6,7,8},{4}}
[1,6,5,4,8,2,7,3]=>{{1},{2,6},{3,5,8},{4},{7}}
[1,6,5,3,8,2,7,4]=>{{1},{2,6},{3,4,5,8},{7}}
[1,6,3,4,8,2,7,5]=>{{1},{2,6},{3},{4},{5,8},{7}}
[1,3,5,4,8,2,7,6]=>{{1},{2,3,5,6,8},{4},{7}}
[3,6,5,4,8,2,1,7]=>{{1,3,5,7,8},{2,6},{4}}
[7,6,5,2,3,8,1,4]=>{{1,7},{2,4,6,8},{3,5}}
[7,6,1,4,2,8,5,3]=>{{1,2,3,5,6,7,8},{4}}
[7,6,1,2,3,8,5,4]=>{{1,3,5,7},{2,4,6,8}}
[7,6,2,4,3,8,1,5]=>{{1,7},{2,3,5,6,8},{4}}
[7,1,5,4,2,8,6,3]=>{{1,2,3,5,6,7,8},{4}}
[7,1,5,2,3,8,6,4]=>{{1,2,4,6,7,8},{3,5}}
[7,1,2,4,3,8,6,5]=>{{1,2,3,5,6,7,8},{4}}
[2,6,5,4,3,8,1,7]=>{{1,2,6,7,8},{3,5},{4}}
[7,6,1,4,3,2,8,5]=>{{1,3,5,7,8},{2,6},{4}}
[7,1,5,4,3,2,8,6]=>{{1,2,6,7,8},{3,5},{4}}
[3,4,2,6,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,2,6,8,7,5]=>{{1,2,3,4},{5,6,8},{7}}
[8,3,4,2,6,1,7,5]=>{{1,5,6,8},{2,3,4},{7}}
[2,6,7,3,5,4,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,7,8,3,5,4,1,6]=>{{1,2,7},{3,4,6,8},{5}}
[2,6,8,3,5,4,1,7]=>{{1,2,3,4,6,7,8},{5}}
[4,7,1,2,8,5,3,6]=>{{1,2,3,4,7},{5,6,8}}
[4,8,1,2,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,6,3,7,5,4,8]=>{{1,2},{3,4,5,6,7},{8}}
[2,7,1,3,6,8,4,5]=>{{1,2,3,4,7},{5,6,8}}
[6,7,3,2,8,1,4,5]=>{{1,6},{2,4,7},{3},{5,8}}
[7,3,4,2,6,1,8,5]=>{{1,5,6,7,8},{2,3,4}}
[7,4,1,2,8,5,3,6]=>{{1,3,7},{2,4},{5,6,8}}
[8,7,4,2,1,5,3,6]=>{{1,5,6,8},{2,3,4,7}}
[7,4,1,2,6,5,3,8]=>{{1,3,7},{2,4},{5,6},{8}}
[7,4,3,1,5,6,8,2]=>{{1,2,4,7,8},{3},{5},{6}}
[6,7,4,1,5,8,3,2]=>{{1,2,3,4,6,7,8},{5}}
[4,7,5,1,6,8,3,2]=>{{1,4},{2,3,5,6,7,8}}
[4,5,3,1,7,6,8,2]=>{{1,4},{2,5,7,8},{3},{6}}
[4,6,1,2,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[2,7,1,3,6,5,4,8]=>{{1,2,3,4,7},{5,6},{8}}
[4,1,8,2,6,5,3,7]=>{{1,2,4},{3,7,8},{5,6}}
[4,6,1,2,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,3,1,5,6,7,2]=>{{1,2,4,8},{3},{5},{6},{7}}
[4,5,3,1,8,6,7,2]=>{{1,4},{2,5,8},{3},{6},{7}}
[4,8,5,6,3,1,7,2]=>{{1,4,6},{2,8},{3,5},{7}}
[5,1,3,4,8,6,7,2]=>{{1,2,5,8},{3},{4},{6},{7}}
[5,4,3,8,1,6,7,2]=>{{1,5},{2,4,8},{3},{6},{7}}
[8,5,3,4,1,6,7,2]=>{{1,2,5,8},{3},{4},{6},{7}}
[6,4,8,2,1,5,3,7]=>{{1,5,6},{2,4},{3,7,8}}
[6,7,3,2,5,1,4,8]=>{{1,6},{2,4,7},{3},{5},{8}}
[6,8,3,2,5,1,4,7]=>{{1,6},{2,4,7,8},{3},{5}}
[5,7,1,4,6,8,3,2]=>{{1,2,3,5,6,7,8},{4}}
[5,1,3,4,7,6,8,2]=>{{1,2,5,7,8},{3},{4},{6}}
[6,1,4,2,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,3,7,1,6,8,2]=>{{1,5},{2,4,7,8},{3},{6}}
[6,7,5,4,1,8,3,2]=>{{1,2,3,5,6,7,8},{4}}
[7,6,4,2,1,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[8,2,7,6,5,4,1,3]=>{{1,3,7,8},{2},{4,6},{5}}
[7,2,8,6,5,4,3,1]=>{{1,3,7,8},{2},{4,6},{5}}
[8,7,2,6,5,4,1,3]=>{{1,2,3,7,8},{4,6},{5}}
[3,2,8,7,6,5,1,4]=>{{1,3,4,7,8},{2},{5,6}}
[4,8,7,6,5,3,1,2]=>{{1,3,4,6,7},{2,8},{5}}
[7,8,6,1,5,4,3,2]=>{{1,3,4,6,7},{2,8},{5}}
[7,3,8,6,5,4,2,1]=>{{1,2,3,7,8},{4,6},{5}}
[4,8,5,7,6,3,2,1]=>{{1,2,4,7,8},{3,5,6}}
[8,5,6,1,3,2,4,7]=>{{1,4,7,8},{2,3,5,6}}
[8,6,1,5,3,2,4,7]=>{{1,3,4,5,7,8},{2,6}}
[7,8,1,5,3,2,4,6]=>{{1,3,4,5,7},{2,6,8}}
[8,1,7,5,3,2,4,6]=>{{1,2,6,8},{3,4,5,7}}
[8,6,1,4,5,2,3,7]=>{{1,3,7,8},{2,6},{4},{5}}
[8,6,3,1,5,2,4,7]=>{{1,4,7,8},{2,6},{3},{5}}
[8,4,6,1,5,2,3,7]=>{{1,2,3,4,6,7,8},{5}}
[8,6,2,1,5,4,3,7]=>{{1,2,3,4,6,7,8},{5}}
[8,5,2,6,1,4,3,7]=>{{1,2,3,5,7,8},{4,6}}
[8,5,2,1,7,4,3,6]=>{{1,4,6,8},{2,3,5,7}}
[7,8,2,1,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}
[7,8,3,1,5,2,4,6]=>{{1,4,7},{2,6,8},{3},{5}}
[8,2,7,5,1,3,4,6]=>{{1,3,4,5,6,7,8},{2}}
[8,4,1,7,5,2,3,6]=>{{1,2,3,4,6,7,8},{5}}
[8,2,7,1,5,4,3,6]=>{{1,4,6,8},{2},{3,7},{5}}
[8,2,6,1,7,4,3,5]=>{{1,3,4,5,6,7,8},{2}}
[8,1,7,4,3,2,6,5]=>{{1,2,3,5,6,7,8},{4}}
[8,1,5,7,3,2,6,4]=>{{1,2,4,6,7,8},{3,5}}
[5,7,8,1,3,2,6,4]=>{{1,3,4,5,8},{2,6,7}}
[8,2,6,1,5,7,3,4]=>{{1,4,8},{2},{3,6,7},{5}}
[5,8,1,6,7,2,3,4]=>{{1,3,5,7},{2,4,6,8}}
[5,7,6,1,8,2,3,4]=>{{1,4,5,8},{2,3,6,7}}
[6,7,2,5,1,8,3,4]=>{{1,4,5,6,8},{2,3,7}}
[7,5,1,6,8,2,3,4]=>{{1,3,7},{2,4,5,6,8}}
[6,5,7,1,8,2,3,4]=>{{1,2,4,5,6,8},{3,7}}
[6,7,3,8,1,2,4,5]=>{{1,2,4,5,6,7,8},{3}}
[7,5,4,1,8,2,3,6]=>{{1,3,4,7},{2,5,6,8}}
[7,6,1,4,8,2,3,5]=>{{1,3,7},{2,6},{4},{5,8}}
[8,1,6,4,7,2,3,5]=>{{1,2,3,5,6,7,8},{4}}
[7,5,8,1,3,2,4,6]=>{{1,4,7},{2,3,5,6,8}}
[7,8,4,1,3,2,5,6]=>{{1,3,4,5,7},{2,6,8}}
[8,3,7,4,1,2,5,6]=>{{1,2,3,5,6,7,8},{4}}
[8,5,1,7,3,2,4,6]=>{{1,2,3,5,6,8},{4,7}}
[6,8,1,7,3,2,4,5]=>{{1,2,3,5,6,8},{4,7}}
[7,1,8,4,3,6,2,5]=>{{1,2,7},{3,5,8},{4},{6}}
[7,3,1,8,6,4,2,5]=>{{1,2,3,7},{4,5,6,8}}
[8,3,1,7,4,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[8,4,5,1,7,2,3,6]=>{{1,2,4,6,8},{3,5,7}}
[5,6,8,1,7,2,3,4]=>{{1,3,4,5,7,8},{2,6}}
[6,5,8,1,2,7,3,4]=>{{1,3,4,6,7,8},{2,5}}
[7,3,1,8,5,6,2,4]=>{{1,2,3,7},{4,8},{5},{6}}
[6,2,7,8,3,1,5,4]=>{{1,6},{2},{3,5,7},{4,8}}
[5,8,1,7,3,2,6,4]=>{{1,3,5},{2,4,6,7,8}}
[8,4,1,7,3,2,6,5]=>{{1,3,5,8},{2,4,6,7}}
[8,3,4,7,1,2,6,5]=>{{1,5,8},{2,3,4,6,7}}
[8,2,7,4,1,3,6,5]=>{{1,5,8},{2},{3,6,7},{4}}
[7,4,8,2,1,3,6,5]=>{{1,3,5,6,7,8},{2,4}}
[7,4,3,8,1,2,6,5]=>{{1,2,4,5,6,7,8},{3}}
[8,2,3,6,7,1,5,4]=>{{1,4,6,8},{2},{3},{5,7}}
[7,8,5,2,3,6,4,1]=>{{1,2,4,7,8},{3,5},{6}}
[6,8,5,2,3,4,7,1]=>{{1,2,4,6,8},{3,5},{7}}
[3,5,2,6,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,4,6,8,1,7]=>{{1,2,3,5,6,7,8},{4}}
[2,4,5,7,3,6,8,1]=>{{1,2,4,7,8},{3,5},{6}}
[2,4,5,3,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,2,4,6,8,1,3,7]=>{{1,3,4,5,6,7,8},{2}}
[5,1,3,4,6,8,2,7]=>{{1,2,5,6,7,8},{3},{4}}
[4,3,5,2,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,5,7,2,8,1,6]=>{{1,4,7},{2,3,5},{6,8}}
[4,3,5,7,2,6,8,1]=>{{1,4,7,8},{2,3,5},{6}}
[4,6,3,7,2,5,8,1]=>{{1,4,7,8},{2,5,6},{3}}
[4,6,3,1,7,8,2,5]=>{{1,4},{2,5,6,7,8},{3}}
[4,3,5,1,7,8,2,6]=>{{1,4},{2,3,5,7},{6,8}}
[5,7,1,3,4,8,2,6]=>{{1,3,4,5},{2,7},{6,8}}
[5,7,1,3,4,6,8,2]=>{{1,3,4,5},{2,7,8},{6}}
[4,5,7,1,3,6,8,2]=>{{1,4},{2,3,5,7,8},{6}}
[4,3,6,7,1,5,8,2]=>{{1,2,3,4,5,6,7,8}}
[4,6,3,5,1,7,8,2]=>{{1,4,5},{2,6,7,8},{3}}
[4,6,3,5,7,2,8,1]=>{{1,4,5,7,8},{2,6},{3}}
[3,5,6,4,1,7,8,2]=>{{1,2,3,5,6,7,8},{4}}
[3,1,5,6,7,4,8,2]=>{{1,2,3,5,7,8},{4,6}}
[5,1,6,7,3,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,1,3,5,8,2]=>{{1,2,3,4,5,6,7,8}}
[1,6,7,3,4,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,7,4,5,8,1,3]=>{{1,2,3,6,7,8},{4},{5}}
[2,6,7,4,8,1,3,5]=>{{1,2,6},{3,7},{4},{5,8}}
[5,3,6,1,2,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,6,1,7,8,4]=>{{1,2,3,5},{4,6,7,8}}
[3,5,2,6,7,4,8,1]=>{{1,2,3,5,7,8},{4,6}}
[5,2,3,6,7,4,8,1]=>{{1,5,7,8},{2},{3},{4,6}}
[5,2,3,6,1,7,8,4]=>{{1,5},{2},{3},{4,6,7,8}}
[5,2,6,1,3,7,8,4]=>{{1,3,4,5,6,7,8},{2}}
[4,2,6,7,3,5,8,1]=>{{1,4,7,8},{2},{3,5,6}}
[6,3,7,2,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,2,8,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,2,4,8,1,5,6]=>{{1,2,3,5,6,7,8},{4}}
[7,2,4,6,8,1,3,5]=>{{1,3,4,6,7},{2},{5,8}}
[7,1,3,4,6,8,2,5]=>{{1,2,7},{3},{4},{5,6,8}}
[3,7,2,4,6,8,1,5]=>{{1,2,3,7},{4},{5,6,8}}
[3,5,7,2,6,8,1,4]=>{{1,3,7},{2,4,5,6,8}}
[6,3,7,2,5,8,1,4]=>{{1,2,3,4,6,7,8},{5}}
[6,3,5,7,2,8,1,4]=>{{1,4,6,7,8},{2,3,5}}
[6,3,5,7,2,4,8,1]=>{{1,4,6,7,8},{2,3,5}}
[6,2,4,5,7,3,8,1]=>{{1,3,4,5,6,7,8},{2}}
[6,2,4,5,1,7,8,3]=>{{1,3,4,5,6,7,8},{2}}
[4,7,1,2,5,6,8,3]=>{{1,2,3,4,7,8},{5},{6}}
[2,6,7,5,8,1,3,4]=>{{1,2,6},{3,7},{4,5,8}}
[4,6,7,1,2,5,8,3]=>{{1,4},{2,5,6},{3,7,8}}
[5,6,2,4,7,3,8,1]=>{{1,5,7,8},{2,3,6},{4}}
[5,4,2,6,7,3,8,1]=>{{1,5,7,8},{2,3,4,6}}
[5,4,2,6,1,7,8,3]=>{{1,5},{2,3,4,6,7,8}}
[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[5,6,4,1,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[6,4,5,1,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,1,7,8,2,4]=>{{1,4,6,8},{2,3,5,7}}
[6,5,7,2,8,1,3,4]=>{{1,6},{2,4,5,8},{3,7}}
[6,5,7,1,3,4,8,2]=>{{1,4,6},{2,3,5,7,8}}
[5,6,4,7,1,3,8,2]=>{{1,5},{2,3,4,6,7,8}}
[5,4,6,3,1,7,8,2]=>{{1,5},{2,3,4,6,7,8}}
[7,5,3,2,4,8,1,6]=>{{1,7},{2,4,5},{3},{6,8}}
[8,4,5,2,6,1,3,7]=>{{1,3,5,6,7,8},{2,4}}
[8,5,4,2,1,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[8,5,3,4,1,6,2,7]=>{{1,2,5,7,8},{3},{4},{6}}
[8,4,5,3,1,6,2,7]=>{{1,2,3,4,5,7,8},{6}}
[7,5,4,2,1,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[7,5,4,2,1,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[7,4,5,3,1,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[7,4,3,5,6,1,8,2]=>{{1,2,4,5,6,7,8},{3}}
[5,6,3,7,4,1,8,2]=>{{1,2,4,5,6,7,8},{3}}
[5,6,7,3,1,4,8,2]=>{{1,5},{2,3,4,6,7,8}}
[6,7,3,4,1,5,8,2]=>{{1,5,6},{2,7,8},{3},{4}}
[6,7,4,2,1,5,8,3]=>{{1,5,6},{2,3,4,7,8}}
[5,6,7,3,1,8,2,4]=>{{1,5},{2,3,4,6,7,8}}
[5,6,3,7,8,1,2,4]=>{{1,2,4,5,6,7,8},{3}}
[5,6,3,7,2,4,8,1]=>{{1,2,4,5,6,7,8},{3}}
[5,6,7,2,3,8,1,4]=>{{1,3,5,7},{2,4,6,8}}
[7,4,5,2,8,1,3,6]=>{{1,3,5,6,7,8},{2,4}}
[6,7,3,2,4,8,1,5]=>{{1,2,4,5,6,7,8},{3}}
[7,6,4,2,1,3,8,5]=>{{1,5,7,8},{2,3,4,6}}
[7,6,3,4,1,2,8,5]=>{{1,5,7,8},{2,6},{3},{4}}
[7,6,3,2,4,1,8,5]=>{{1,2,4,5,6,7,8},{3}}
[6,7,3,2,5,1,8,4]=>{{1,6},{2,4,7,8},{3},{5}}
[6,5,3,2,7,8,1,4]=>{{1,2,4,5,6,7,8},{3}}
[6,5,3,2,7,4,8,1]=>{{1,2,4,5,6,7,8},{3}}
[6,4,5,2,7,3,8,1]=>{{1,3,5,6,7,8},{2,4}}
[6,4,5,2,7,8,1,3]=>{{1,3,5,6,7,8},{2,4}}
[7,4,5,2,6,1,8,3]=>{{1,3,5,6,7,8},{2,4}}
[7,4,5,6,1,2,8,3]=>{{1,3,5,7,8},{2,4,6}}
[7,5,6,2,1,3,8,4]=>{{1,2,4,5,7,8},{3,6}}
[6,7,3,5,1,2,8,4]=>{{1,2,4,5,6,7,8},{3}}
[5,6,7,4,1,2,8,3]=>{{1,5},{2,6},{3,7,8},{4}}
[5,6,7,2,4,1,8,3]=>{{1,2,4,5,6},{3,7,8}}
[5,6,4,2,7,8,1,3]=>{{1,5,7},{2,3,4,6,8}}
[6,5,7,2,1,8,3,4]=>{{1,2,4,5,6,8},{3,7}}
[6,5,7,2,1,4,8,3]=>{{1,2,4,5,6},{3,7,8}}
[5,4,6,7,3,1,8,2]=>{{1,3,5,6},{2,4,7,8}}
[3,7,8,5,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[1,7,8,5,6,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,5,8,6,3,4,2]=>{{1},{2,4,7,8},{3,5,6}}
[3,7,5,8,6,1,4,2]=>{{1,3,5,6},{2,4,7,8}}
[5,7,3,8,6,4,1,2]=>{{1,2,4,5,6,7,8},{3}}
[1,5,7,8,6,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,7,8,3,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,3,7,8,1,6,4,2]=>{{1,5},{2,3,4,7,8},{6}}
[7,8,1,5,6,3,4,2]=>{{1,3,4,5,6,7},{2,8}}
[7,1,8,5,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,1,5,8,6,3,4,2]=>{{1,2,4,7,8},{3,5,6}}
[5,1,7,8,3,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[3,1,7,8,5,6,4,2]=>{{1,2,3,4,7,8},{5},{6}}
[1,3,7,8,5,6,4,2]=>{{1},{2,3,4,7,8},{5},{6}}
[3,1,7,5,8,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[5,1,7,3,8,6,4,2]=>{{1,2,5,8},{3,4,7},{6}}
[7,1,5,3,8,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[7,1,5,8,3,6,4,2]=>{{1,2,4,7,8},{3,5},{6}}
[7,3,5,8,1,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[5,3,7,1,8,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[3,5,7,1,8,6,4,2]=>{{1,3,4,7},{2,5,8},{6}}
[1,7,5,3,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,7,3,1,8,6,4,2]=>{{1,2,4,5,7,8},{3},{6}}
[5,7,3,8,6,1,4,2]=>{{1,5,6},{2,4,7,8},{3}}
[3,7,5,8,1,6,4,2]=>{{1,3,5},{2,4,7,8},{6}}
[1,7,5,8,3,6,4,2]=>{{1},{2,4,7,8},{3,5},{6}}
[1,7,8,5,3,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,7,8,6,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,6,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,1,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,1,5,6,4,2]=>{{1,2,3,4,7,8},{5},{6}}
[1,7,8,3,5,6,4,2]=>{{1},{2,3,4,7,8},{5},{6}}
[1,7,3,8,5,6,4,2]=>{{1},{2,4,7,8},{3},{5},{6}}
[3,7,1,8,5,6,4,2]=>{{1,3},{2,4,7,8},{5},{6}}
[5,7,1,8,3,6,4,2]=>{{1,3,5},{2,4,7,8},{6}}
[5,7,1,8,6,3,4,2]=>{{1,3,5,6},{2,4,7,8}}
[7,5,1,8,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,1,6,3,4,2]=>{{1,4,7},{2,3,5,6,8}}
[7,8,5,1,6,3,4,2]=>{{1,4,7},{2,8},{3,5,6}}
[7,5,8,1,3,6,4,2]=>{{1,4,7},{2,3,5,8},{6}}
[7,5,1,8,3,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[7,5,1,3,8,6,4,2]=>{{1,3,4,7},{2,5,8},{6}}
[5,7,1,3,8,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[3,7,1,5,8,6,4,2]=>{{1,3},{2,4,5,7,8},{6}}
[1,7,3,5,8,6,4,2]=>{{1},{2,4,5,7,8},{3},{6}}
[1,5,3,7,8,6,4,2]=>{{1},{2,5,8},{3},{4,7},{6}}
[3,5,1,7,8,6,4,2]=>{{1,3},{2,5,8},{4,7},{6}}
[5,3,1,7,8,6,4,2]=>{{1,2,3,5,8},{4,7},{6}}
[7,3,1,5,8,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[7,3,1,8,5,6,4,2]=>{{1,2,3,4,7,8},{5},{6}}
[7,8,3,1,5,6,4,2]=>{{1,4,7},{2,8},{3},{5},{6}}
[7,1,8,3,5,6,4,2]=>{{1,2,3,4,7,8},{5},{6}}
[7,1,3,8,5,6,4,2]=>{{1,2,4,7,8},{3},{5},{6}}
[7,1,3,5,8,6,4,2]=>{{1,2,4,5,7,8},{3},{6}}
[3,1,5,7,8,6,4,2]=>{{1,2,3,5,8},{4,7},{6}}
[5,7,3,4,8,6,1,2]=>{{1,2,5,7,8},{3},{4},{6}}
[5,7,3,4,8,1,6,2]=>{{1,2,5,6,7,8},{3},{4}}
[5,7,3,4,1,8,6,2]=>{{1,5},{2,6,7,8},{3},{4}}
[5,7,3,1,4,6,2,8]=>{{1,4,5},{2,7},{3},{6},{8}}
[5,7,3,1,4,8,6,2]=>{{1,4,5},{2,6,7,8},{3}}
[5,3,7,4,1,2,6,8]=>{{1,5},{2,3,6,7},{4},{8}}
[5,3,7,1,4,2,6,8]=>{{1,4,5},{2,3,6,7},{8}}
[5,3,7,1,4,2,8,6]=>{{1,4,5},{2,3,6,7,8}}
[3,7,5,1,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,3,5,1,2,6,4]=>{{1,2,4,5,6,7,8},{3}}
[7,3,5,8,1,2,6,4]=>{{1,2,3,5,6,7},{4,8}}
[3,7,5,1,2,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[6,1,4,3,5,2,8,7]=>{{1,2,6},{3,4},{5},{7,8}}
[2,5,7,3,8,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,4,7,8,6,1,3,2]=>{{1,5,6},{2,4,8},{3,7}}
[7,5,6,2,8,3,1,4]=>{{1,7},{2,4,5,8},{3,6}}
[4,7,2,5,8,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[6,2,4,5,1,3,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[5,1,4,6,3,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,5,6,2,4,1,8,7]=>{{1,3,6},{2,4,5},{7,8}}
[3,8,6,7,5,4,1,2]=>{{1,3,4,6,7},{2,8},{5}}
[6,2,7,8,3,4,1,5]=>{{1,3,4,5,6,7,8},{2}}
[2,5,3,4,8,1,7,6]=>{{1,2,5,6,8},{3},{4},{7}}
[8,7,1,2,5,3,4,6]=>{{1,3,6,8},{2,4,7},{5}}
[5,1,8,2,3,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,4,7,6,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,1,5,4,6,2]=>{{1,2,3,4,6,7,8},{5}}
[7,1,3,4,6,8,5,2]=>{{1,2,5,6,7,8},{3},{4}}
[8,3,6,5,7,1,4,2]=>{{1,2,3,6,8},{4,5,7}}
[5,8,7,1,4,6,2,3]=>{{1,4,5},{2,3,7,8},{6}}
[4,7,6,1,8,3,5,2]=>{{1,4},{2,5,7,8},{3,6}}
[4,7,2,6,3,8,5,1]=>{{1,4,6,8},{2,3,5,7}}
[2,1,8,4,6,7,3,5]=>{{1,2},{3,5,6,7,8},{4}}
[4,7,8,6,3,1,2,5]=>{{1,4,6},{2,7},{3,5,8}}
[3,8,1,5,6,7,2,4]=>{{1,3},{2,4,5,6,7,8}}
[6,7,2,4,8,5,3,1]=>{{1,5,6,8},{2,3,7},{4}}
[2,8,3,6,7,5,1,4]=>{{1,2,4,5,6,7,8},{3}}
[8,2,1,7,6,3,5,4]=>{{1,3,4,5,6,7,8},{2}}
[3,2,4,5,8,1,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[7,4,6,3,2,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[4,7,3,2,1,8,6,5]=>{{1,2,4,5,6,7,8},{3}}
[6,4,7,5,2,3,8,1]=>{{1,3,6,7,8},{2,4,5}}
[6,4,8,1,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,2,3,1,5,6]=>{{1,2,4,6,8},{3,5,7}}
[4,2,3,1,8,7,5,6]=>{{1,4},{2},{3},{5,6,7,8}}
[7,6,8,1,3,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,5,2,3,1,8,4]=>{{1,6},{2,4,7,8},{3,5}}
[4,7,2,6,5,1,8,3]=>{{1,4,6},{2,3,7,8},{5}}
[6,4,2,1,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[7,2,1,5,6,8,4,3]=>{{1,3,4,5,6,7,8},{2}}
[8,7,2,6,4,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,2,5,3,1,4]=>{{1,2,3,4,6,7,8},{5}}
[2,1,7,3,6,8,5,4]=>{{1,2},{3,4,5,6,7,8}}
[2,1,5,7,8,4,6,3]=>{{1,2},{3,5,8},{4,6,7}}
[2,5,7,8,3,6,1,4]=>{{1,2,3,5,7},{4,8},{6}}
[6,4,1,5,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,8,1,2,5,6,3]=>{{1,2,4,5,6,7},{3,8}}
[4,2,7,8,6,3,5,1]=>{{1,4,8},{2},{3,5,6,7}}
[6,1,7,4,3,2,8,5]=>{{1,2,6},{3,5,7,8},{4}}
[6,8,3,4,2,1,7,5]=>{{1,6},{2,5,8},{3},{4},{7}}
[4,2,6,1,5,7,8,3]=>{{1,4},{2},{3,6,7,8},{5}}
[2,4,6,7,3,5,8,1]=>{{1,2,4,7,8},{3,5,6}}
[6,5,8,3,7,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[7,1,4,8,3,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,5,3,4,1,2]=>{{1,3,4,5,6,7},{2,8}}
[4,8,6,3,1,5,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[3,4,8,2,5,7,6,1]=>{{1,3,8},{2,4},{5},{6,7}}
[2,5,7,4,8,6,1,3]=>{{1,2,3,5,7,8},{4},{6}}
[2,6,3,7,5,1,8,4]=>{{1,2,6},{3},{4,7,8},{5}}
[2,6,4,8,7,5,1,3]=>{{1,2,5,6,7},{3,4,8}}
[6,3,7,2,8,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[3,6,2,5,8,7,1,4]=>{{1,2,3,6,7},{4,5,8}}
[5,2,8,4,7,6,1,3]=>{{1,5,7},{2},{3,8},{4},{6}}
[7,2,4,8,6,5,1,3]=>{{1,7},{2},{3,4,8},{5,6}}
[6,2,4,8,7,5,1,3]=>{{1,5,6,7},{2},{3,4,8}}
[2,4,5,8,7,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[4,2,7,3,8,1,6,5]=>{{1,3,4,6,7},{2},{5,8}}
[2,5,1,4,7,3,8,6]=>{{1,2,3,5,6,7,8},{4}}
[6,1,3,8,7,2,5,4]=>{{1,2,6},{3},{4,8},{5,7}}
[3,1,5,6,2,8,7,4]=>{{1,2,3,5},{4,6,8},{7}}
[1,2,4,6,3,8,7,5]=>{{1},{2},{3,4,5,6,8},{7}}
[4,1,5,2,8,7,6,3]=>{{1,2,4},{3,5,8},{6,7}}
[4,1,5,3,2,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[7,2,3,5,1,8,6,4]=>{{1,4,5,6,7,8},{2},{3}}
[3,4,5,1,8,7,6,2]=>{{1,2,3,4,5,8},{6,7}}
[1,6,4,2,8,7,5,3]=>{{1},{2,3,4,5,6,7,8}}
[7,4,2,5,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[4,6,2,7,5,1,8,3]=>{{1,2,3,4,6,7,8},{5}}
[1,5,3,6,2,8,7,4]=>{{1},{2,5},{3},{4,6,8},{7}}
[1,5,8,3,2,7,6,4]=>{{1},{2,5},{3,4,8},{6,7}}
[4,5,8,2,1,7,6,3]=>{{1,2,4,5},{3,8},{6,7}}
[3,6,2,5,1,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,4,8,7,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[1,3,8,2,4,7,6,5]=>{{1},{2,3,4,5,8},{6,7}}
[3,5,2,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,7,2,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,2,8,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[1,5,2,3,8,7,6,4]=>{{1},{2,3,4,5,8},{6,7}}
[6,4,1,2,8,7,5,3]=>{{1,3,5,6,7,8},{2,4}}
[5,2,8,1,3,7,6,4]=>{{1,3,4,5,8},{2},{6,7}}
[4,7,5,6,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[8,6,4,7,5,3,1,2]=>{{1,2,3,4,6,7,8},{5}}
[7,5,2,6,4,1,3,8]=>{{1,2,3,4,5,6,7},{8}}
[1,6,3,7,5,8,4,2]=>{{1},{2,6,8},{3},{4,7},{5}}
[1,3,7,4,5,8,6,2]=>{{1},{2,3,6,7,8},{4},{5}}
[7,2,6,3,4,1,5,8]=>{{1,3,4,5,6,7},{2},{8}}
[8,3,7,4,6,5,1,2]=>{{1,2,3,7,8},{4},{5,6}}
[6,8,4,7,5,3,1,2]=>{{1,3,4,6,7},{2,8},{5}}
[4,8,7,5,6,3,1,2]=>{{1,3,4,5,6,7},{2,8}}
[3,8,7,6,4,5,1,2]=>{{1,3,7},{2,8},{4,5,6}}
[1,6,5,2,8,3,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[8,6,5,2,1,4,3,7]=>{{1,3,5,7,8},{2,4,6}}
[2,7,6,3,1,4,5,8]=>{{1,2,5,7},{3,4,6},{8}}
[6,8,5,3,2,1,4,7]=>{{1,6},{2,3,4,5,7,8}}
[2,7,6,4,5,1,3,8]=>{{1,2,3,6,7},{4},{5},{8}}
[5,7,2,6,4,1,3,8]=>{{1,4,5,6},{2,3,7},{8}}
[6,1,3,7,5,8,4,2]=>{{1,2,6,8},{3},{4,7},{5}}
[4,1,7,3,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,4,3,7,5,2]=>{{1,2,8},{3,5,6,7},{4}}
[2,1,7,4,8,6,3,5]=>{{1,2},{3,7},{4},{5,8},{6}}
[1,8,6,3,7,5,4,2]=>{{1},{2,8},{3,4,5,6,7}}
[1,8,2,7,3,6,5,4]=>{{1},{2,3,4,5,7,8},{6}}
[2,1,3,8,4,7,5,6]=>{{1,2},{3},{4,5,6,7,8}}
[8,1,2,7,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,6,8,4,7,2]=>{{1,2,3,5,8},{4,6},{7}}
[6,2,8,7,1,4,3,5]=>{{1,3,4,5,6,7,8},{2}}
[8,7,2,1,5,4,3,6]=>{{1,4,6,8},{2,3,7},{5}}
[8,2,3,1,4,6,5,7]=>{{1,4,5,7,8},{2},{3},{6}}
[2,4,8,3,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,4,2,7,1,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[4,7,3,8,2,1,5,6]=>{{1,4,6,8},{2,5,7},{3}}
[5,2,7,3,1,4,6,8]=>{{1,5},{2},{3,4,6,7},{8}}
[8,3,7,2,1,5,4,6]=>{{1,5,6,8},{2,3,4,7}}
[1,3,7,2,8,4,6,5]=>{{1},{2,3,4,6,7},{5,8}}
[1,4,2,5,8,6,7,3]=>{{1},{2,3,4,5,8},{6},{7}}
[6,5,3,8,2,1,4,7]=>{{1,6},{2,5},{3},{4,7,8}}
[2,6,4,5,7,1,3,8]=>{{1,2,6},{3,4,5,7},{8}}
[5,4,6,2,7,1,3,8]=>{{1,3,5,6,7},{2,4},{8}}
[7,6,3,1,8,4,5,2]=>{{1,2,4,5,6,7,8},{3}}
[7,6,2,1,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,7,5,8,6,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,1,2,8,3,7,4]=>{{1,3,6},{2,4,5,8},{7}}
[8,6,1,4,3,7,5,2]=>{{1,2,3,5,6,7,8},{4}}
[6,8,4,1,3,7,5,2]=>{{1,3,4,5,6,7},{2,8}}
[6,5,7,1,3,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[5,8,3,1,7,4,6,2]=>{{1,4,5,6,7},{2,8},{3}}
[8,3,1,7,5,4,6,2]=>{{1,2,3,8},{4,6,7},{5}}
[1,3,8,7,4,6,5,2]=>{{1},{2,3,8},{4,5,7},{6}}
[1,2,8,7,6,3,5,4]=>{{1},{2},{3,4,5,6,7,8}}
[8,2,1,7,6,4,3,5]=>{{1,3,4,5,6,7,8},{2}}
[2,3,1,8,7,4,5,6]=>{{1,2,3},{4,6,8},{5,7}}
[2,4,1,8,5,7,3,6]=>{{1,2,3,4,6,7,8},{5}}
[5,8,2,1,7,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[6,2,7,1,8,5,3,4]=>{{1,4,5,6,8},{2},{3,7}}
[8,7,1,6,5,4,3,2]=>{{1,2,3,7,8},{4,6},{5}}
[7,1,8,3,6,5,4,2]=>{{1,2,3,4,7,8},{5,6}}
[4,1,8,7,5,6,3,2]=>{{1,2,3,4,7,8},{5},{6}}
[3,5,8,7,2,6,4,1]=>{{1,3,8},{2,5},{4,7},{6}}
[5,8,2,7,1,6,4,3]=>{{1,5},{2,3,8},{4,7},{6}}
[2,1,6,4,5,8,3,7]=>{{1,2},{3,6,7,8},{4},{5}}
[8,6,3,7,5,2,1,4]=>{{1,4,7,8},{2,6},{3},{5}}
[4,6,3,8,5,2,1,7]=>{{1,4,7,8},{2,6},{3},{5}}
[4,6,3,7,5,2,8,1]=>{{1,4,7,8},{2,6},{3},{5}}
[3,5,7,8,2,6,1,4]=>{{1,3,7},{2,5},{4,8},{6}}
[8,2,3,4,6,1,5,7]=>{{1,5,6,7,8},{2},{3},{4}}
[7,2,3,4,6,8,5,1]=>{{1,5,6,7,8},{2},{3},{4}}
[4,8,3,7,5,1,6,2]=>{{1,4,6,7},{2,8},{3},{5}}
[5,2,3,4,8,7,1,6]=>{{1,5,6,7,8},{2},{3},{4}}
[5,2,3,4,6,8,1,7]=>{{1,5,6,7,8},{2},{3},{4}}
[4,2,8,5,7,6,1,3]=>{{1,4,5,7},{2},{3,8},{6}}
[3,7,6,4,5,1,8,2]=>{{1,3,6},{2,7,8},{4},{5}}
[4,8,3,7,5,2,1,6]=>{{1,4,7},{2,6,8},{3},{5}}
[8,7,3,6,5,1,2,4]=>{{1,4,6,8},{2,7},{3},{5}}
[4,2,7,5,8,6,3,1]=>{{1,4,5,8},{2},{3,7},{6}}
[5,8,1,7,3,6,4,2]=>{{1,3,5},{2,8},{4,7},{6}}
[5,2,7,8,4,6,3,1]=>{{1,4,5,8},{2},{3,7},{6}}
[5,2,8,3,7,6,1,4]=>{{1,5,7},{2},{3,4,8},{6}}
[8,2,7,3,1,6,4,5]=>{{1,5,8},{2},{3,4,7},{6}}
[6,2,3,4,8,5,1,7]=>{{1,5,6,7,8},{2},{3},{4}}
[6,2,3,4,1,8,5,7]=>{{1,5,6,7,8},{2},{3},{4}}
[7,2,3,4,1,8,6,5]=>{{1,5,6,7,8},{2},{3},{4}}
[7,2,3,4,1,5,8,6]=>{{1,5,6,7,8},{2},{3},{4}}
[1,2,3,4,8,7,5,6]=>{{1},{2},{3},{4},{5,6,7,8}}
[1,2,8,5,3,4,6,7]=>{{1},{2},{3,4,5,6,7,8}}
[1,8,4,2,3,5,6,7]=>{{1},{2,3,4,5,6,7,8}}
[8,6,7,4,1,5,3,2]=>{{1,2,5,6,8},{3,7},{4}}
[4,8,6,7,5,1,3,2]=>{{1,3,4,6,7},{2,8},{5}}
[7,1,8,4,6,5,2,3]=>{{1,2,7},{3,8},{4},{5,6}}
[8,7,1,5,4,6,2,3]=>{{1,3,8},{2,7},{4,5},{6}}
[8,5,7,1,4,6,3,2]=>{{1,2,4,5,8},{3,7},{6}}
[6,4,8,5,1,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,7,1,6,3,2]=>{{1,3,4,5,7},{2,8},{6}}
[8,4,7,1,5,6,3,2]=>{{1,2,4,8},{3,7},{5},{6}}
[8,7,1,4,5,6,3,2]=>{{1,2,3,7,8},{4},{5},{6}}
[8,7,4,5,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,1,4,6,2,3]=>{{1,3,4,5,8},{2,7},{6}}
[8,7,2,5,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,2,5,1,6,3]=>{{1,2,3,4,6,7,8},{5}}
[1,6,4,8,5,2,7,3]=>{{1},{2,6},{3,4,8},{5},{7}}
[8,7,1,4,2,5,6,3]=>{{1,3,8},{2,5,6,7},{4}}
[8,7,5,1,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,5,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,1,2,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[3,5,8,7,1,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,5,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,1,5,6,2,4]=>{{1,2,3,4,7,8},{5},{6}}
[3,5,8,7,1,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[2,3,8,6,7,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[3,2,8,6,7,5,1,4]=>{{1,3,4,5,6,7,8},{2}}
[4,1,8,6,2,7,5,3]=>{{1,2,4,5,6,7},{3,8}}
[8,7,4,1,2,6,5,3]=>{{1,3,4,8},{2,5,7},{6}}
[1,3,8,6,7,5,2,4]=>{{1},{2,3,4,5,6,7,8}}
[5,7,1,8,2,6,3,4]=>{{1,2,3,5,7},{4,8},{6}}
[2,8,7,1,5,6,3,4]=>{{1,2,4,8},{3,7},{5},{6}}
[8,7,1,5,2,4,6,3]=>{{1,3,8},{2,4,5,6,7}}
[7,1,8,2,4,6,5,3]=>{{1,2,4,5,7},{3,8},{6}}
[1,6,2,8,4,7,5,3]=>{{1},{2,3,4,5,6,7,8}}
[1,3,8,5,7,2,6,4]=>{{1},{2,3,4,5,6,7,8}}
[1,8,3,7,2,5,6,4]=>{{1},{2,4,5,6,7,8},{3}}
[2,8,7,1,3,5,6,4]=>{{1,2,4,8},{3,5,6,7}}
[5,7,1,8,2,3,6,4]=>{{1,2,3,5,6,7},{4,8}}
[7,1,8,2,3,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,6,3,7,4,1,5,2]=>{{1,2,6,8},{3},{4,5,7}}
[4,2,8,6,7,5,1,3]=>{{1,4,5,6,7},{2},{3,8}}
[8,4,2,7,5,6,1,3]=>{{1,2,3,4,7,8},{5},{6}}
[4,8,3,6,1,7,5,2]=>{{1,4,5,6,7},{2,8},{3}}
[8,3,4,7,5,1,6,2]=>{{1,2,3,4,6,7,8},{5}}
[8,3,7,4,5,1,6,2]=>{{1,2,3,6,7,8},{4},{5}}
[8,7,4,2,5,6,1,3]=>{{1,2,3,4,7,8},{5},{6}}
[8,7,5,1,6,2,3,4]=>{{1,4,8},{2,3,5,6,7}}
[8,7,2,4,1,5,6,3]=>{{1,2,3,5,6,7,8},{4}}
[4,8,6,1,7,2,5,3]=>{{1,4},{2,3,6,8},{5,7}}
[4,7,1,8,2,6,5,3]=>{{1,3,4,8},{2,5,7},{6}}
[4,2,8,6,7,1,5,3]=>{{1,4,6},{2},{3,8},{5,7}}
[8,7,4,1,2,5,6,3]=>{{1,3,4,8},{2,5,6,7}}
[8,2,7,1,6,3,4,5]=>{{1,3,4,5,6,7,8},{2}}
[8,2,7,1,3,6,4,5]=>{{1,3,4,5,7,8},{2},{6}}
[2,8,3,6,7,1,5,4]=>{{1,2,4,6,8},{3},{5,7}}
[8,7,2,1,3,5,6,4]=>{{1,4,8},{2,3,5,6,7}}
[1,8,7,2,3,6,4,5]=>{{1},{2,3,4,5,7,8},{6}}
[1,8,7,2,6,3,4,5]=>{{1},{2,3,4,5,6,7,8}}
[8,2,7,3,6,1,4,5]=>{{1,5,6,8},{2},{3,4,7}}
[1,8,7,3,6,2,4,5]=>{{1},{2,5,6,8},{3,4,7}}
[1,8,2,7,6,3,4,5]=>{{1},{2,3,5,6,8},{4,7}}
[8,2,7,4,1,5,6,3]=>{{1,3,5,6,7,8},{2},{4}}
[8,2,1,7,5,6,3,4]=>{{1,3,4,7,8},{2},{5},{6}}
[8,7,3,1,5,6,2,4]=>{{1,4,8},{2,7},{3},{5},{6}}
[2,8,7,3,5,6,1,4]=>{{1,2,3,4,7,8},{5},{6}}
[8,3,1,6,7,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,1,6,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[1,5,2,8,6,7,4,3]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,6,7,5,3,4]=>{{1},{2},{3,4,5,6,7,8}}
[1,8,3,6,7,5,2,4]=>{{1},{2,4,5,6,7,8},{3}}
[8,2,3,6,7,5,1,4]=>{{1,4,5,6,7,8},{2},{3}}
[8,3,7,2,5,6,1,4]=>{{1,2,3,4,7,8},{5},{6}}
[8,1,3,7,5,6,2,4]=>{{1,2,4,7,8},{3},{5},{6}}
[8,4,1,2,7,5,6,3]=>{{1,3,8},{2,4},{5,6,7}}
[8,1,4,2,6,7,5,3]=>{{1,2,3,4,8},{5,6,7}}
[1,2,8,6,7,3,5,4]=>{{1},{2},{3,4,6,8},{5,7}}
[8,1,2,7,3,6,4,5]=>{{1,2,3,5,8},{4,7},{6}}
[8,1,7,3,6,2,4,5]=>{{1,2,5,6,8},{3,4,7}}
[8,1,7,2,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,2,3,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[8,1,3,7,2,5,6,4]=>{{1,2,4,5,6,7,8},{3}}
[1,8,3,6,7,2,5,4]=>{{1},{2,4,6,8},{3},{5,7}}
[1,7,8,2,3,6,5,4]=>{{1},{2,3,4,5,7,8},{6}}
[8,3,7,1,2,5,6,4]=>{{1,4,8},{2,3,5,6,7}}
[8,7,1,2,3,6,4,5]=>{{1,3,5,8},{2,4,7},{6}}
[2,8,5,7,4,6,3,1]=>{{1,2,8},{3,4,5,7},{6}}
[3,1,8,5,7,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,5,7,4,2,6,1]=>{{1,8},{2,3,4,5,6,7}}
[8,3,6,2,4,5,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[2,8,6,4,3,5,7,1]=>{{1,2,8},{3,5,6},{4},{7}}
[2,6,8,3,5,4,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[2,7,5,8,4,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[8,4,2,7,6,1,3,5]=>{{1,5,6,8},{2,3,4,7}}
[4,8,1,7,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,1,7,6,2,3,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,7,1,8,6,2,5,4]=>{{1,3},{2,5,6,7},{4,8}}
[3,1,7,6,4,5,2,8]=>{{1,2,3,7},{4,5,6},{8}}
[3,1,7,5,8,4,2,6]=>{{1,2,3,7},{4,5,6,8}}
[3,1,6,8,7,5,2,4]=>{{1,2,3,5,6,7},{4,8}}
[6,3,8,7,5,2,4,1]=>{{1,2,3,6,8},{4,7},{5}}
[7,3,5,8,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,3,6,4,2,8,5,1]=>{{1,2,3,5,6,7,8},{4}}
[7,8,3,6,2,5,4,1]=>{{1,2,4,5,6,7,8},{3}}
[7,4,8,2,1,6,3,5]=>{{1,3,5,7,8},{2,4},{6}}
[8,7,4,6,3,2,5,1]=>{{1,8},{2,3,4,5,6,7}}
[7,8,5,2,1,4,3,6]=>{{1,3,5,7},{2,4,6,8}}
[7,5,2,3,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,2,3,8,1,5]=>{{1,7},{2,4},{3,5,6,8}}
[6,4,2,5,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,6,5,8,1,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[4,7,1,5,3,8,2,6]=>{{1,3,4,5},{2,7},{6,8}}
[4,7,8,1,3,6,2,5]=>{{1,4},{2,7},{3,5,8},{6}}
[5,7,1,3,4,6,2,8]=>{{1,3,4,5},{2,7},{6},{8}}
[5,7,1,4,2,3,6,8]=>{{1,2,3,5,6,7},{4},{8}}
[5,8,1,3,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,8,6,1,3,2,7,5]=>{{1,4},{2,3,5,6,8},{7}}
[8,4,6,2,1,3,7,5]=>{{1,5,8},{2,4},{3,6},{7}}
[5,4,8,7,2,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,7,3,1,2,6]=>{{1,3,5,6,8},{2,4,7}}
[6,8,3,7,2,5,4,1]=>{{1,2,5,6,8},{3},{4,7}}
[5,4,6,8,2,3,7,1]=>{{1,2,4,5,8},{3,6},{7}}
[5,7,4,2,8,3,6,1]=>{{1,5,8},{2,3,4,6,7}}
[6,4,7,2,1,8,3,5]=>{{1,5,6,8},{2,4},{3,7}}
[6,5,3,4,1,2,8,7]=>{{1,2,5,6},{3},{4},{7,8}}
[6,8,5,4,1,3,2,7]=>{{1,3,5,6},{2,7,8},{4}}
[6,4,3,7,1,5,2,8]=>{{1,5,6},{2,4,7},{3},{8}}
[7,4,2,6,1,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[7,4,2,5,6,1,3,8]=>{{1,2,3,4,5,6,7},{8}}
[6,4,2,8,1,5,7,3]=>{{1,5,6},{2,3,4,8},{7}}
[6,3,7,8,2,5,1,4]=>{{1,2,3,5,6,7},{4,8}}
[7,3,5,6,4,2,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[7,4,3,1,5,6,2,8]=>{{1,2,4,7},{3},{5},{6},{8}}
[7,4,5,2,6,1,3,8]=>{{1,3,5,6,7},{2,4},{8}}
[5,3,7,2,8,6,4,1]=>{{1,5,8},{2,3,4,7},{6}}
[5,3,8,2,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,8,2,5,4,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[6,4,8,2,1,5,7,3]=>{{1,5,6},{2,4},{3,8},{7}}
[6,4,3,1,8,2,7,5]=>{{1,2,4,6},{3},{5,8},{7}}
[5,3,7,8,2,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[4,7,8,5,6,3,2,1]=>{{1,3,4,5,6,8},{2,7}}
[5,3,7,6,8,2,4,1]=>{{1,5,8},{2,3,4,6,7}}
[5,7,8,4,6,2,1,3]=>{{1,2,5,6,7},{3,8},{4}}
[5,8,4,3,6,7,1,2]=>{{1,5,6,7},{2,8},{3,4}}
[5,8,6,4,7,2,1,3]=>{{1,5,7},{2,3,6,8},{4}}
[5,3,8,6,2,7,4,1]=>{{1,2,3,5,8},{4,6,7}}
[4,7,5,8,6,3,2,1]=>{{1,4,8},{2,7},{3,5,6}}
[4,8,6,7,5,3,2,1]=>{{1,2,4,7,8},{3,6},{5}}
[6,3,8,7,2,4,1,5]=>{{1,4,6,7},{2,3,5,8}}
[5,3,8,7,2,6,4,1]=>{{1,2,3,5,8},{4,7},{6}}
[5,3,8,6,7,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,8,6,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,4,8,2,1,3]=>{{1,2,3,5,6,7,8},{4}}
[5,8,4,6,7,2,1,3]=>{{1,5,7},{2,3,4,6,8}}
[6,4,2,8,1,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,4,3,7,8,1]=>{{1,6,7,8},{2,3,5},{4}}
[5,4,6,2,8,7,1,3]=>{{1,3,5,6,7,8},{2,4}}
[5,6,3,8,7,2,4,1]=>{{1,4,5,7,8},{2,6},{3}}
[6,7,4,3,1,8,2,5]=>{{1,5,6,8},{2,7},{3,4}}
[5,7,4,3,6,8,1,2]=>{{1,2,5,6,7,8},{3,4}}
[5,7,3,8,6,2,4,1]=>{{1,2,4,5,6,7,8},{3}}
[4,5,8,6,7,3,2,1]=>{{1,3,4,6,8},{2,5,7}}
[4,6,8,5,7,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,6,8,3,7,2,4,1]=>{{1,3,4,5,7,8},{2,6}}
[5,4,6,8,2,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,2,6,4,1,3]=>{{1,2,4,5,6,7},{3,8}}
[3,6,8,5,7,1,4,2]=>{{1,2,3,6,8},{4,5,7}}
[1,7,4,8,6,2,3,5]=>{{1},{2,3,4,5,6,7,8}}
[3,6,2,5,7,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,2,7,4,6,8,1,3]=>{{1,3,5,6,7,8},{2},{4}}
[5,3,6,7,1,8,4,2]=>{{1,5},{2,3,6,8},{4,7}}
[4,2,5,6,7,1,8,3]=>{{1,4,6},{2},{3,5,7,8}}
[8,1,3,6,7,2,4,5]=>{{1,2,4,5,6,7,8},{3}}
[8,1,4,2,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[6,1,3,8,2,7,4,5]=>{{1,2,4,5,6,7,8},{3}}
[1,7,5,2,8,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}
[3,6,4,8,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[1,5,8,4,2,6,3,7]=>{{1},{2,5},{3,7,8},{4},{6}}
[3,5,7,4,1,6,8,2]=>{{1,2,3,5,7,8},{4},{6}}
[3,5,7,1,2,6,4,8]=>{{1,3,4,7},{2,5},{6},{8}}
[4,5,1,8,2,3,7,6]=>{{1,3,4,6,8},{2,5},{7}}
[4,7,1,8,2,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[7,5,1,2,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,2,6,1,3,4,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[7,8,4,5,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,3,2,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,7,1,4,3,5,2,8]=>{{1,3,5,6},{2,7},{4},{8}}
[7,8,2,3,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,8,2,4,3,5,1,6]=>{{1,7},{2,3,5,6,8},{4}}
[7,8,2,4,1,5,3,6]=>{{1,2,3,5,6,7,8},{4}}
[1,4,2,6,5,7,3,8]=>{{1},{2,3,4,6,7},{5},{8}}
[5,6,1,4,2,7,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[6,7,2,4,1,5,3,8]=>{{1,5,6},{2,3,7},{4},{8}}
[6,7,2,4,3,5,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[6,7,2,3,1,5,4,8]=>{{1,5,6},{2,3,4,7},{8}}
[6,7,3,5,4,8,1,2]=>{{1,2,6,7,8},{3},{4,5}}
[2,4,1,6,5,7,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[1,5,2,6,4,7,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,5,1,6,4,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[3,6,5,7,4,8,1,2]=>{{1,3,4,5,7},{2,6,8}}
[5,6,2,4,3,7,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[4,5,2,6,1,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,1,6,3,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,3,6,1,7,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,6,3,4,1,7,2,8]=>{{1,5},{2,6,7},{3},{4},{8}}
[5,6,1,4,3,7,2,8]=>{{1,3,5},{2,6,7},{4},{8}}
[5,6,1,3,2,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[5,6,4,7,1,3,2,8]=>{{1,5},{2,3,4,6,7},{8}}
[6,7,4,5,1,3,2,8]=>{{1,3,4,5,6},{2,7},{8}}
[6,7,5,8,1,3,2,4]=>{{1,3,5,6},{2,7},{4,8}}
[4,5,1,3,2,7,6,8]=>{{1,3,4},{2,5},{6,7},{8}}
[4,6,5,7,1,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,1,3,2,7,5,8]=>{{1,3,4},{2,5,6,7},{8}}
[1,4,3,6,2,7,5,8]=>{{1},{2,4,5,6,7},{3},{8}}
[3,4,1,6,5,7,2,8]=>{{1,3},{2,4,6,7},{5},{8}}
[4,5,2,3,1,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[4,5,3,7,6,8,1,2]=>{{1,4,7},{2,5,6,8},{3}}
[4,6,5,7,3,8,1,2]=>{{1,4,7},{2,6,8},{3,5}}
[4,6,5,7,2,3,1,8]=>{{1,4,7},{2,3,5,6},{8}}
[3,5,4,6,1,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,1,6,4,7,2,8]=>{{1,3},{2,4,5,6,7},{8}}
[1,5,3,6,4,7,2,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,5,3,6,2,7,4,8]=>{{1},{2,5},{3},{4,6,7},{8}}
[3,5,2,6,1,7,4,8]=>{{1,2,3,5},{4,6,7},{8}}
[3,5,2,6,4,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[3,4,2,6,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,2,3,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[2,4,3,6,1,7,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[2,5,3,6,4,7,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[2,5,3,6,1,7,4,8]=>{{1,2,5},{3},{4,6,7},{8}}
[3,6,2,7,5,4,8,1]=>{{1,2,3,4,6,7,8},{5}}
[4,6,1,7,3,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[5,2,6,7,4,3,8,1]=>{{1,4,5,7,8},{2},{3,6}}
[3,5,2,7,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[1,5,7,2,8,3,6,4]=>{{1},{2,4,5,8},{3,6,7}}
[2,5,7,3,1,8,4,6]=>{{1,2,5},{3,4,7},{6,8}}
[2,1,5,6,8,4,3,7]=>{{1,2},{3,5,7,8},{4,6}}
[1,3,7,2,8,5,4,6]=>{{1},{2,3,4,7},{5,6,8}}
[4,6,2,7,1,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[1,5,4,3,6,8,2,7]=>{{1},{2,5,6,7,8},{3,4}}
[1,6,4,5,7,8,3,2]=>{{1},{2,6,8},{3,4,5,7}}
[2,1,5,6,8,4,7,3]=>{{1,2},{3,5,8},{4,6},{7}}
[2,1,5,6,8,7,3,4]=>{{1,2},{3,4,5,6,7,8}}
[3,6,5,2,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,2,4,7,5,8,3,1]=>{{1,6,8},{2},{3,4,7},{5}}
[1,5,7,8,4,2,6,3]=>{{1},{2,3,4,5,6,7,8}}
[3,7,4,1,8,6,2,5]=>{{1,3,4},{2,7},{5,8},{6}}
[3,4,6,8,5,7,2,1]=>{{1,2,3,4,6,7,8},{5}}
[4,2,5,7,3,1,8,6]=>{{1,4,6,7,8},{2},{3,5}}
[4,5,6,2,8,7,3,1]=>{{1,2,4,5,8},{3,6,7}}
[2,5,6,8,1,7,4,3]=>{{1,2,5},{3,4,6,7,8}}
[4,5,6,1,8,7,3,2]=>{{1,4},{2,5,8},{3,6,7}}
[4,5,6,3,1,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,3,6,2,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,3,2,1,7,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[4,6,3,1,7,5,2,8]=>{{1,4},{2,5,6,7},{3},{8}}
[4,5,3,7,6,1,8,2]=>{{1,2,4,5,6,7,8},{3}}
[4,5,1,7,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,1,4,3,8,6]=>{{1,2,4,5},{3,6,7,8}}
[4,3,5,7,6,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[4,3,6,1,7,5,2,8]=>{{1,4},{2,3,5,6,7},{8}}
[4,3,2,6,1,7,5,8]=>{{1,4,5,6,7},{2,3},{8}}
[5,3,2,1,6,4,7,8]=>{{1,4,5,6},{2,3},{7},{8}}
[5,3,1,6,2,7,4,8]=>{{1,2,3,5},{4,6,7},{8}}
[5,1,6,3,2,7,4,8]=>{{1,2,5},{3,4,6,7},{8}}
[2,6,1,4,7,5,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[3,6,1,7,4,2,5,8]=>{{1,3},{2,6},{4,5,7},{8}}
[4,6,1,7,5,3,2,8]=>{{1,2,3,4,6,7},{5},{8}}
[5,1,6,3,7,4,2,8]=>{{1,2,5,7},{3,4,6},{8}}
[5,3,6,4,2,1,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[5,3,2,6,4,1,7,8]=>{{1,4,5,6},{2,3},{7},{8}}
[5,2,1,6,3,7,4,8]=>{{1,3,5},{2},{4,6,7},{8}}
[5,2,6,3,1,7,4,8]=>{{1,5},{2},{3,4,6,7},{8}}
[4,2,6,3,1,7,8,5]=>{{1,3,4,5,6,7,8},{2}}
[3,6,2,1,7,4,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[3,6,2,7,4,1,5,8]=>{{1,2,3,6},{4,5,7},{8}}
[3,5,7,2,8,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[2,4,7,1,3,6,5,8]=>{{1,2,4},{3,5,7},{6},{8}}
[2,6,1,3,7,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[3,6,1,7,5,2,4,8]=>{{1,3},{2,6},{4,7},{5},{8}}
[5,1,6,2,7,4,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,2,6,4,3,1,7,8]=>{{1,3,5,6},{2},{4},{7},{8}}
[5,2,1,6,4,3,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[5,4,2,1,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,4,2,6,3,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,4,1,6,2,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,1,6,4,2,7,3,8]=>{{1,2,5},{3,6,7},{4},{8}}
[3,6,1,7,5,4,8,2]=>{{1,3},{2,4,6,7,8},{5}}
[2,6,1,5,4,3,7,8]=>{{1,2,3,6},{4,5},{7},{8}}
[3,1,6,2,5,4,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[5,1,6,4,3,2,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[5,4,1,6,3,2,7,8]=>{{1,3,5},{2,4,6},{7},{8}}
[5,4,3,1,6,2,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[7,3,1,6,5,4,8,2]=>{{1,2,3,7,8},{4,6},{5}}
[7,2,8,1,5,4,3,6]=>{{1,3,4,6,7,8},{2},{5}}
[4,2,7,6,5,8,1,3]=>{{1,3,4,6,7,8},{2},{5}}
[3,8,2,6,5,4,1,7]=>{{1,2,3,7,8},{4,6},{5}}
[7,3,2,1,5,4,6,8]=>{{1,4,6,7},{2,3},{5},{8}}
[7,2,8,6,1,4,3,5]=>{{1,3,5,7,8},{2},{4,6}}
[5,2,7,6,8,4,1,3]=>{{1,3,5,7,8},{2},{4,6}}
[3,8,7,2,5,4,1,6]=>{{1,3,7},{2,4,6,8},{5}}
[7,5,1,6,8,4,3,2]=>{{1,3,7},{2,5,8},{4,6}}
[7,4,2,1,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}
[7,2,8,6,5,1,3,4]=>{{1,3,4,6,7,8},{2},{5}}
[5,3,2,6,7,4,1,8]=>{{1,5,7},{2,3},{4,6},{8}}
[4,3,7,2,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}
[6,7,1,4,3,2,5,8]=>{{1,2,3,5,6,7},{4},{8}}
[3,4,2,6,7,1,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[3,7,1,6,5,2,4,8]=>{{1,3},{2,4,6,7},{5},{8}}
[3,5,6,2,4,7,1,8]=>{{1,3,6,7},{2,4,5},{8}}
[3,5,8,7,2,4,6,1]=>{{1,3,8},{2,5},{4,6,7}}
[1,7,8,2,5,4,3,6]=>{{1},{2,3,4,6,7,8},{5}}
[8,7,2,5,4,3,6,1]=>{{1,8},{2,3,6,7},{4,5}}
[2,5,6,4,7,1,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[4,7,1,6,3,5,2,8]=>{{1,3,4,5,6},{2,7},{8}}
[4,5,3,8,7,2,6,1]=>{{1,4,8},{2,5,6,7},{3}}
[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,4,8,2,7,6,3,5]=>{{1},{2,4},{3,5,7,8},{6}}
[4,7,3,5,1,8,6,2]=>{{1,4,5},{2,6,7,8},{3}}
[8,7,3,6,1,5,4,2]=>{{1,2,4,5,6,7,8},{3}}
[2,5,8,7,4,6,1,3]=>{{1,2,4,5,7},{3,8},{6}}
[5,4,2,1,7,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[4,7,8,3,5,2,1,6]=>{{1,2,3,4,6,7,8},{5}}
[4,7,6,2,1,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[1,4,6,7,3,5,8,2]=>{{1},{2,4,7,8},{3,5,6}}
[8,3,6,2,1,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,6,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,3,1,8,4,7,6,5]=>{{1,2,3},{4,5,8},{6,7}}
[2,7,4,8,6,5,1,3]=>{{1,2,7},{3,4,8},{5,6}}
[8,6,5,1,4,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,1,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,2,8,5,4,1]=>{{1,5,6,8},{2,3,4,7}}
[1,6,3,8,2,7,5,4]=>{{1},{2,5,6,7},{3},{4,8}}
[1,7,5,3,8,2,6,4]=>{{1},{2,6,7},{3,4,5,8}}
[6,2,7,4,1,8,5,3]=>{{1,3,5,6,7,8},{2},{4}}
[8,6,3,2,7,5,1,4]=>{{1,2,4,5,6,7,8},{3}}
[2,7,5,1,3,8,6,4]=>{{1,2,4,6,7,8},{3,5}}
[1,7,6,4,3,8,2,5]=>{{1},{2,7},{3,5,6,8},{4}}
[3,7,2,4,8,6,5,1]=>{{1,2,3,5,7,8},{4},{6}}
[3,4,2,8,7,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[5,1,4,3,2,7,8,6]=>{{1,2,5},{3,4},{6,7,8}}
[3,7,8,5,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,2,4,1,8,5]=>{{1,3,6},{2,4,5,7,8}}
[1,6,8,2,5,7,4,3]=>{{1},{2,4,6,7},{3,8},{5}}
[6,7,2,5,8,4,3,1]=>{{1,4,5,6,8},{2,3,7}}
[5,2,7,8,4,3,1,6]=>{{1,3,4,5,6,7,8},{2}}
[5,3,1,7,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,4,1,3,8,5]=>{{1,2,5,7,8},{3,6},{4}}
[4,1,7,6,3,2,8,5]=>{{1,2,4,6},{3,5,7,8}}
[8,4,2,7,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,7,5,2,8,4]=>{{1,2,3,6},{4,7,8},{5}}
[6,2,7,5,3,1,8,4]=>{{1,6},{2},{3,4,5,7,8}}
[1,5,8,2,7,4,6,3]=>{{1},{2,4,5,6,7},{3,8}}
[5,7,2,8,4,6,3,1]=>{{1,4,5,8},{2,3,7},{6}}
[5,7,3,1,8,4,6,2]=>{{1,2,4,5,6,7,8},{3}}
[8,4,7,3,1,6,5,2]=>{{1,2,3,4,5,7,8},{6}}
[2,6,8,5,7,4,1,3]=>{{1,2,4,5,6,7},{3,8}}
[6,5,2,1,7,4,8,3]=>{{1,4,6},{2,3,5,7,8}}
[5,7,4,6,2,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[5,6,4,8,3,7,2,1]=>{{1,3,4,5,8},{2,6,7}}
[6,7,1,8,3,4,2,5]=>{{1,3,4,5,6,8},{2,7}}
[7,8,3,5,1,4,2,6]=>{{1,2,4,5,6,7,8},{3}}
[5,6,2,7,1,8,3,4]=>{{1,5},{2,3,4,6,7,8}}
[6,7,2,4,3,8,1,5]=>{{1,2,3,5,6,7,8},{4}}
[2,4,3,8,6,7,1,5]=>{{1,2,4,5,6,7,8},{3}}
[1,8,2,7,4,5,3,6]=>{{1},{2,3,4,5,6,7,8}}
[2,5,4,8,3,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[2,3,1,8,5,6,4,7]=>{{1,2,3},{4,7,8},{5},{6}}
[3,8,5,6,4,7,1,2]=>{{1,3,4,5,6,7},{2,8}}
[5,7,3,6,4,8,1,2]=>{{1,2,4,5,6,7,8},{3}}
[5,7,2,3,1,6,4,8]=>{{1,5},{2,3,4,7},{6},{8}}
[5,7,2,4,3,6,1,8]=>{{1,2,3,5,7},{4},{6},{8}}
[4,6,2,7,1,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,7,1,6,2,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,7,1,5,3,6,2,8]=>{{1,3,4,5},{2,7},{6},{8}}
[4,6,3,5,1,7,2,8]=>{{1,4,5},{2,6,7},{3},{8}}
[6,7,3,5,1,4,2,8]=>{{1,4,5,6},{2,7},{3},{8}}
[5,6,3,7,1,4,2,8]=>{{1,5},{2,4,6,7},{3},{8}}
[5,7,1,6,3,4,2,8]=>{{1,3,5},{2,7},{4,6},{8}}
[1,8,5,6,3,4,2,7]=>{{1},{2,7,8},{3,5},{4,6}}
[1,8,5,6,4,7,2,3]=>{{1},{2,3,4,5,6,7,8}}
[5,7,1,6,4,8,2,3]=>{{1,3,4,5,6,8},{2,7}}
[4,6,5,8,1,7,2,3]=>{{1,3,4,5,8},{2,6,7}}
[3,7,1,4,2,8,5,6]=>{{1,3},{2,5,7},{4},{6,8}}
[3,5,1,4,2,8,6,7]=>{{1,3},{2,5},{4},{6,7,8}}
[4,6,5,8,3,7,1,2]=>{{1,2,4,6,7,8},{3,5}}
[4,6,5,8,2,3,1,7]=>{{1,4,7,8},{2,3,5,6}}
[3,4,2,6,5,8,1,7]=>{{1,2,3,4,6,7,8},{5}}
[3,5,4,6,2,8,1,7]=>{{1,3,4,6,7,8},{2,5}}
[1,8,3,5,4,7,2,6]=>{{1},{2,6,7,8},{3},{4,5}}
[3,4,2,7,1,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[4,7,2,3,1,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[2,4,3,8,1,7,5,6]=>{{1,2,4,5,6,7,8},{3}}
[2,5,3,8,4,7,1,6]=>{{1,2,4,5,6,7,8},{3}}
[2,6,3,8,1,7,4,5]=>{{1,2,4,5,6,7,8},{3}}
[2,7,1,8,3,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[4,5,1,8,7,6,2,3]=>{{1,3,4,8},{2,5,7},{6}}
[5,2,6,8,3,7,4,1]=>{{1,3,4,5,6,7,8},{2}}
[3,1,6,8,7,4,5,2]=>{{1,2,3,4,6,8},{5,7}}
[6,1,4,8,7,2,5,3]=>{{1,2,6},{3,4,8},{5,7}}
[6,1,8,4,7,3,5,2]=>{{1,2,3,6,8},{4},{5,7}}
[6,8,3,5,7,1,4,2]=>{{1,6},{2,8},{3},{4,5,7}}
[4,6,7,8,2,5,3,1]=>{{1,4,8},{2,5,6},{3,7}}
[7,4,5,2,8,6,3,1]=>{{1,3,5,7,8},{2,4},{6}}
[6,8,2,5,3,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,8,4,2,7,5,1]=>{{1,2,3,5,6,7,8},{4}}
[3,4,7,5,8,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[6,7,4,2,8,5,3,1]=>{{1,5,6,8},{2,3,4,7}}
[2,7,5,3,8,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[5,6,2,8,3,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[1,5,8,2,7,3,6,4]=>{{1},{2,3,4,5,6,7,8}}
[6,7,4,8,1,5,3,2]=>{{1,5,6},{2,3,4,7,8}}
[1,7,4,8,6,2,5,3]=>{{1},{2,5,6,7},{3,4,8}}
[6,8,5,3,7,2,4,1]=>{{1,2,6,8},{3,4,5,7}}
[6,8,5,2,3,7,4,1]=>{{1,2,4,6,7,8},{3,5}}
[7,5,3,8,2,6,4,1]=>{{1,4,7,8},{2,5},{3},{6}}
[7,5,2,3,8,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[6,7,3,4,8,5,2,1]=>{{1,5,6,8},{2,7},{3},{4}}
[3,6,4,7,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,5,8,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[7,4,5,8,1,6,3,2]=>{{1,3,5,7},{2,4,8},{6}}
[6,3,4,7,8,5,2,1]=>{{1,5,6,8},{2,3,4,7}}
[6,1,2,7,4,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,8,3,4,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,2,7,4,3,8,1]=>{{1,4,5,7,8},{2,3,6}}
[4,6,7,3,2,5,8,1]=>{{1,3,4,7,8},{2,5,6}}
[2,6,7,3,8,5,4,1]=>{{1,2,5,6,8},{3,4,7}}
[2,6,1,8,4,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,8,4,3,6,1]=>{{1,2,4,5,8},{3,6,7}}
[3,6,8,4,5,7,1,2]=>{{1,2,3,6,7,8},{4},{5}}
[1,6,8,4,7,2,3,5]=>{{1},{2,6},{3,5,7,8},{4}}
[1,4,5,7,8,2,6,3]=>{{1},{2,4,6,7},{3,5,8}}
[3,4,5,7,8,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[3,4,5,7,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,4,8,5,1,2]=>{{1,3,7},{2,5,6,8},{4}}
[3,4,5,6,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,4,5,8,7,2,3,6]=>{{1},{2,4,6,8},{3,5,7}}
[1,2,5,8,3,6,4,7]=>{{1},{2},{3,5},{4,7,8},{6}}
[1,4,5,8,6,2,3,7]=>{{1},{2,3,4,5,6,7,8}}
[7,8,1,4,6,2,3,5]=>{{1,3,7},{2,5,6,8},{4}}
[1,6,7,4,8,2,5,3]=>{{1},{2,6},{3,5,7,8},{4}}
[1,4,5,6,8,2,7,3]=>{{1},{2,4,6},{3,5,8},{7}}
[1,4,5,8,6,2,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[1,2,5,8,3,4,7,6]=>{{1},{2},{3,5},{4,6,8},{7}}
[1,6,7,2,3,5,8,4]=>{{1},{2,3,4,5,6,7,8}}
[7,8,1,2,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[1,6,7,2,3,5,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,4,5,7,6,2,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,2,5,7,3,6,4,8]=>{{1},{2},{3,5},{4,7},{6},{8}}
[1,2,5,7,3,6,8,4]=>{{1},{2},{3,5},{4,7,8},{6}}
[1,6,8,2,3,5,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,8,4,5,2,3,7]=>{{1},{2,6},{3,7,8},{4},{5}}
[1,6,8,4,5,2,7,3]=>{{1},{2,6},{3,8},{4},{5},{7}}
[1,6,8,2,3,4,7,5]=>{{1},{2,4,6},{3,5,8},{7}}
[1,6,8,2,3,7,4,5]=>{{1},{2,4,6,7},{3,5,8}}
[1,4,5,7,6,2,8,3]=>{{1},{2,3,4,5,6,7,8}}
[7,8,1,4,5,2,6,3]=>{{1,2,3,6,7,8},{4},{5}}
[7,8,1,2,3,4,6,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,2,3,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[1,6,7,2,3,8,5,4]=>{{1},{2,4,6,8},{3,5,7}}
[1,2,5,6,3,8,7,4]=>{{1},{2},{3,5},{4,6,8},{7}}
[4,2,1,6,5,3,8,7]=>{{1,3,4,6},{2},{5},{7,8}}
[6,8,2,1,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[8,6,2,4,3,1,5,7]=>{{1,2,3,5,6,7,8},{4}}
[4,6,5,2,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,6,4,5,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[8,4,2,6,3,5,1,7]=>{{1,7,8},{2,3,4,5,6}}
[4,2,6,3,5,8,7,1]=>{{1,3,4,6,8},{2},{5},{7}}
[6,2,4,3,8,5,7,1]=>{{1,5,6,8},{2},{3,4},{7}}
[8,2,4,3,6,5,1,7]=>{{1,7,8},{2},{3,4},{5,6}}
[6,2,1,8,4,3,7,5]=>{{1,3,6},{2},{4,5,8},{7}}
[2,6,8,7,4,5,1,3]=>{{1,2,4,5,6,7},{3,8}}
[4,2,8,6,5,7,1,3]=>{{1,4,6,7},{2},{3,8},{5}}
[8,2,6,4,5,1,3,7]=>{{1,3,6,7,8},{2},{4},{5}}
[2,8,5,3,1,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,7,4,8,3,5,1,6]=>{{1,2,7},{3,4,5,6,8}}
[2,7,4,8,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,2,8,4,3,5,1,6]=>{{1,7},{2},{3,5,6,8},{4}}
[8,4,2,1,5,3,6,7]=>{{1,2,3,4,6,7,8},{5}}
[8,5,1,4,2,3,6,7]=>{{1,3,6,7,8},{2,5},{4}}
[8,4,1,5,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[6,7,3,8,4,2,5,1]=>{{1,2,4,5,6,7,8},{3}}
[6,7,3,8,4,2,1,5]=>{{1,2,6,7},{3},{4,5,8}}
[7,1,8,4,3,5,2,6]=>{{1,2,7},{3,5,6,8},{4}}
[1,7,8,4,3,5,2,6]=>{{1},{2,7},{3,5,6,8},{4}}
[7,1,4,8,3,5,2,6]=>{{1,2,7},{3,4,5,6,8}}
[7,4,8,1,5,6,2,3]=>{{1,2,4,7},{3,8},{5},{6}}
[7,1,8,4,3,5,6,2]=>{{1,2,3,5,6,7,8},{4}}
[6,7,3,1,8,4,5,2]=>{{1,4,6},{2,5,7,8},{3}}
[6,7,3,8,4,5,2,1]=>{{1,4,5,6,8},{2,7},{3}}
[6,7,1,4,8,3,5,2]=>{{1,3,6},{2,5,7,8},{4}}
[6,7,4,1,3,8,2,5]=>{{1,3,4,5,6,8},{2,7}}
[1,6,7,8,4,3,2,5]=>{{1},{2,3,6,7},{4,5,8}}
[7,2,1,8,4,5,3,6]=>{{1,3,7},{2},{4,5,6,8}}
[6,2,7,1,8,4,3,5]=>{{1,4,6},{2},{3,7},{5,8}}
[6,2,7,8,4,3,1,5]=>{{1,3,6,7},{2},{4,5,8}}
[6,2,7,8,4,3,5,1]=>{{1,3,4,5,6,7,8},{2}}
[2,6,7,4,8,3,5,1]=>{{1,2,3,5,6,7,8},{4}}
[2,6,7,4,8,3,1,5]=>{{1,2,3,6,7},{4},{5,8}}
[7,8,1,3,6,2,4,5]=>{{1,3,4,7},{2,5,6,8}}
[1,2,7,8,6,3,4,5]=>{{1},{2},{3,4,5,6,7,8}}
[2,6,7,1,8,5,3,4]=>{{1,2,4,5,6,8},{3,7}}
[2,6,7,8,5,3,1,4]=>{{1,2,3,6,7},{4,8},{5}}
[2,6,7,8,5,3,4,1]=>{{1,2,3,4,6,7,8},{5}}
[6,2,7,8,4,5,3,1]=>{{1,4,5,6,8},{2},{3,7}}
[7,2,1,8,4,5,6,3]=>{{1,3,4,5,6,7,8},{2}}
[1,7,2,8,4,5,6,3]=>{{1},{2,3,4,5,6,7,8}}
[3,7,8,1,5,6,2,4]=>{{1,3,4,8},{2,7},{5},{6}}
[6,3,7,8,1,5,2,4]=>{{1,5,6},{2,3,7},{4,8}}
[6,7,1,2,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,6,7,8,4,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,1,2,7,6,5,8,4]=>{{1,2,3},{4,7,8},{5,6}}
[6,1,2,4,7,3,8,5]=>{{1,2,3,6},{4},{5,7,8}}
[1,7,5,3,6,4,8,2]=>{{1},{2,7,8},{3,4,5,6}}
[5,1,2,6,7,4,8,3]=>{{1,2,3,5,7,8},{4,6}}
[4,1,5,7,3,2,6,8]=>{{1,2,4,6,7},{3,5},{8}}
[4,6,1,7,3,2,5,8]=>{{1,3,4,5,7},{2,6},{8}}
[4,6,1,8,3,2,5,7]=>{{1,3,4,5,7,8},{2,6}}
[4,7,1,8,3,5,2,6]=>{{1,3,4,5,6,8},{2,7}}
[4,1,7,8,6,2,3,5]=>{{1,2,4,5,6,8},{3,7}}
[1,6,5,7,8,3,4,2]=>{{1},{2,3,5,6,8},{4,7}}
[1,6,5,8,7,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,8,7,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,7,3,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,6,3,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,7,1,6,3,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[6,1,2,3,7,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,8,1,5,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,2,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[1,5,7,3,4,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,8,3,4,7,6,2]=>{{1},{2,3,4,5,8},{6,7}}
[7,8,5,2,4,1,6,3]=>{{1,6,7},{2,3,4,5,8}}
[7,1,2,3,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}
[8,1,2,3,5,6,4,7]=>{{1,2,3,4,7,8},{5},{6}}
[8,1,2,3,5,4,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[7,1,8,4,6,3,2,5]=>{{1,2,7},{3,5,6,8},{4}}
[6,8,2,4,3,1,5,7]=>{{1,6},{2,3,5,7,8},{4}}
[6,7,2,4,3,1,5,8]=>{{1,6},{2,3,5,7},{4},{8}}
[3,8,1,2,4,5,7,6]=>{{1,3},{2,4,5,6,8},{7}}
[3,7,1,8,6,4,2,5]=>{{1,3},{2,7},{4,5,6,8}}
[1,6,4,3,7,5,8,2]=>{{1},{2,5,6,7,8},{3,4}}
[3,1,2,6,7,5,8,4]=>{{1,2,3},{4,5,6,7,8}}
[3,8,1,7,6,4,2,5]=>{{1,3},{2,4,5,6,7,8}}
[7,6,2,4,3,1,5,8]=>{{1,2,3,5,6,7},{4},{8}}
[8,7,2,4,3,5,1,6]=>{{1,2,3,5,6,7,8},{4}}
[8,1,7,4,6,3,2,5]=>{{1,2,3,5,6,7,8},{4}}
[8,1,7,6,5,3,2,4]=>{{1,2,3,4,6,7,8},{5}}
[1,5,7,3,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[8,7,2,5,3,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[7,1,2,3,5,4,8,6]=>{{1,2,3,4,6,7,8},{5}}
[6,1,2,3,5,8,4,7]=>{{1,2,3,4,6,7,8},{5}}
[6,1,2,3,5,7,4,8]=>{{1,2,3,4,6,7},{5},{8}}
[5,1,2,3,7,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}
[5,1,2,3,8,6,4,7]=>{{1,2,3,4,5,7,8},{6}}
[1,5,6,3,4,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,5,2,4,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[7,6,2,5,3,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,2,3,8,6,1]=>{{1,6,7,8},{2,4},{3,5}}
[8,2,3,7,4,5,1,6]=>{{1,4,5,6,7,8},{2},{3}}
[8,4,7,3,2,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,4,6,3,1,2,8,7]=>{{1,5},{2,3,4,6},{7,8}}
[4,6,2,3,1,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[7,2,3,4,5,8,6,1]=>{{1,6,7,8},{2},{3},{4},{5}}
[8,2,3,4,5,7,1,6]=>{{1,6,7,8},{2},{3},{4},{5}}
[7,3,4,6,8,5,1,2]=>{{1,7},{2,3,4,5,6,8}}
[4,7,3,2,8,6,1,5]=>{{1,2,4,7},{3},{5,8},{6}}
[3,7,4,5,1,8,6,2]=>{{1,3,4,5},{2,6,7,8}}
[3,8,2,6,7,4,5,1]=>{{1,2,3,8},{4,6},{5,7}}
[4,8,1,5,6,7,3,2]=>{{1,3,4,5,6,7},{2,8}}
[5,8,2,4,6,7,1,3]=>{{1,5,6,7},{2,3,8},{4}}
[6,8,1,3,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[5,8,2,4,3,1,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[2,1,7,6,8,5,3,4]=>{{1,2},{3,7},{4,5,6,8}}
[3,7,6,1,8,5,2,4]=>{{1,3,4,5,6,8},{2,7}}
[4,7,2,3,8,5,1,6]=>{{1,2,3,4,7},{5,6,8}}
[7,1,3,6,4,8,5,2]=>{{1,2,4,5,6,7,8},{3}}
[7,6,1,4,8,5,2,3]=>{{1,2,3,5,6,7,8},{4}}
[6,2,3,7,8,5,4,1]=>{{1,5,6,8},{2},{3},{4,7}}
[6,2,3,8,4,5,1,7]=>{{1,4,5,6,7,8},{2},{3}}
[7,2,3,6,8,4,1,5]=>{{1,7},{2},{3},{4,6},{5,8}}
[8,2,3,5,7,1,4,6]=>{{1,6,8},{2},{3},{4,5,7}}
[6,4,8,3,5,1,7,2]=>{{1,6},{2,3,4,8},{5},{7}}
[5,4,8,3,6,7,1,2]=>{{1,5,6,7},{2,3,4,8}}
[3,5,1,8,4,6,7,2]=>{{1,3},{2,4,5,8},{6},{7}}
[3,6,1,8,4,5,2,7]=>{{1,3},{2,4,5,6,7,8}}
[4,6,8,3,5,2,7,1]=>{{1,3,4,8},{2,6},{5},{7}}
[5,7,8,3,2,4,1,6]=>{{1,2,5,7},{3,4,6,8}}
[4,8,2,3,5,6,1,7]=>{{1,2,3,4,7,8},{5},{6}}
[6,8,2,3,1,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[5,2,7,4,8,3,1,6]=>{{1,3,5,6,7,8},{2},{4}}
[3,7,8,2,1,4,6,5]=>{{1,3,5,8},{2,4,6,7}}
[3,7,5,2,8,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[6,3,2,4,1,8,7,5]=>{{1,5,6,8},{2,3},{4},{7}}
[7,2,3,4,8,5,1,6]=>{{1,7},{2},{3},{4},{5,6,8}}
[5,7,3,1,4,2,6,8]=>{{1,4,5},{2,6,7},{3},{8}}
[3,7,4,1,8,2,5,6]=>{{1,3,4},{2,5,6,7,8}}
[6,3,7,4,8,1,2,5]=>{{1,6},{2,3,7},{4},{5,8}}
[8,3,7,4,2,6,1,5]=>{{1,2,3,5,7,8},{4},{6}}
[3,7,4,1,5,6,2,8]=>{{1,3,4},{2,7},{5},{6},{8}}
[1,8,3,2,4,5,7,6]=>{{1},{2,4,5,6,8},{3},{7}}
[8,4,1,6,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,2,1,6,3,5]=>{{1,5,8},{2,3,4,7},{6}}
[8,3,5,2,7,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[1,5,3,8,7,6,4,2]=>{{1},{2,4,5,7,8},{3},{6}}
[7,2,4,8,1,3,6,5]=>{{1,3,4,5,6,7,8},{2}}
[1,2,8,7,5,6,3,4]=>{{1},{2},{3,4,7,8},{5},{6}}
[3,1,8,6,7,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[1,4,8,6,5,7,2,3]=>{{1},{2,4,6,7},{3,8},{5}}
[1,6,5,4,8,2,3,7]=>{{1},{2,6},{3,5,7,8},{4}}
[5,1,6,8,3,4,2,7]=>{{1,2,3,4,5,6,7,8}}
[6,2,5,1,7,4,3,8]=>{{1,4,6},{2},{3,5,7},{8}}
[5,2,1,8,7,4,3,6]=>{{1,3,5,7},{2},{4,6,8}}
[5,2,6,3,8,1,4,7]=>{{1,3,4,5,6,7,8},{2}}
[5,2,8,3,4,6,1,7]=>{{1,3,4,5,7,8},{2},{6}}
[6,2,8,4,3,1,7,5]=>{{1,6},{2},{3,5,8},{4},{7}}
[7,2,8,1,3,6,5,4]=>{{1,3,4,5,7,8},{2},{6}}
[7,3,8,1,4,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[1,7,8,5,4,6,3,2]=>{{1},{2,3,7,8},{4,5},{6}}
[1,5,8,4,6,3,7,2]=>{{1},{2,3,5,6,8},{4},{7}}
[5,3,8,4,1,2,7,6]=>{{1,5},{2,3,6,8},{4},{7}}
[5,8,4,3,6,2,1,7]=>{{1,2,5,6,7,8},{3,4}}
[1,8,3,6,5,2,7,4]=>{{1},{2,4,6,8},{3},{5},{7}}
[1,8,2,4,7,6,5,3]=>{{1},{2,3,8},{4},{5,7},{6}}
[3,8,1,4,6,7,5,2]=>{{1,3},{2,8},{4},{5,6,7}}
[3,8,2,5,1,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[4,3,8,2,5,1,6,7]=>{{1,2,3,4,6,7,8},{5}}
[8,2,4,3,5,1,7,6]=>{{1,6,8},{2},{3,4},{5},{7}}
[8,2,1,4,6,5,7,3]=>{{1,3,8},{2},{4},{5,6},{7}}
[8,1,3,4,5,7,6,2]=>{{1,2,8},{3},{4},{5},{6,7}}
[6,1,5,2,4,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[4,1,8,5,2,7,6,3]=>{{1,2,4,5},{3,8},{6,7}}
[4,1,8,2,3,7,5,6]=>{{1,2,4},{3,5,6,7,8}}
[5,3,8,7,2,1,4,6]=>{{1,2,3,5,6,8},{4,7}}
[6,7,3,5,1,4,8,2]=>{{1,4,5,6},{2,7,8},{3}}
[6,4,7,5,8,2,3,1]=>{{1,2,4,5,6,8},{3,7}}
[5,7,8,4,2,6,3,1]=>{{1,2,3,5,7,8},{4},{6}}
[5,4,7,6,2,8,3,1]=>{{1,2,4,5,6,8},{3,7}}
[5,7,4,1,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,5,7,1,3,2]=>{{1,6},{2,8},{3,4,5,7}}
[5,8,4,6,1,7,3,2]=>{{1,5},{2,8},{3,4,6,7}}
[5,6,1,4,7,8,3,2]=>{{1,3,5,7},{2,6,8},{4}}
[5,6,7,2,4,8,3,1]=>{{1,2,4,5,6,8},{3,7}}
[5,6,3,7,4,8,2,1]=>{{1,2,4,5,6,7,8},{3}}
[5,3,6,7,4,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,3,2,8,6,7,4,1]=>{{1,4,5,6,7,8},{2,3}}
[5,4,8,2,6,7,3,1]=>{{1,3,5,6,7,8},{2,4}}
[5,4,8,6,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,5,7,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,8,5,6,2,1,3]=>{{1,7},{2,4,5,6},{3,8}}
[4,6,8,5,7,2,3,1]=>{{1,3,4,5,7,8},{2,6}}
[5,6,8,2,4,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[5,6,3,8,4,7,2,1]=>{{1,4,5,8},{2,6,7},{3}}
[4,6,3,5,8,7,2,1]=>{{1,4,5,8},{2,6,7},{3}}
[4,6,3,2,8,7,5,1]=>{{1,2,4,5,6,7,8},{3}}
[5,6,3,8,2,7,4,1]=>{{1,2,4,5,6,7,8},{3}}
[3,6,5,8,7,2,4,1]=>{{1,3,4,5,7,8},{2,6}}
[5,3,6,8,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,2,8,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[5,4,7,2,6,8,3,1]=>{{1,5,6,8},{2,4},{3,7}}
[5,3,2,7,6,8,4,1]=>{{1,5,6,8},{2,3},{4,7}}
[6,7,3,8,5,2,4,1]=>{{1,2,4,6,7,8},{3},{5}}
[6,3,2,7,5,4,8,1]=>{{1,4,6,7,8},{2,3},{5}}
[6,4,7,2,5,3,8,1]=>{{1,3,6,7,8},{2,4},{5}}
[6,2,7,5,1,4,8,3]=>{{1,4,5,6},{2},{3,7,8}}
[2,7,8,5,3,6,1,4]=>{{1,2,7},{3,4,5,8},{6}}
[6,3,7,8,4,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,8,4,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[5,3,7,8,4,6,2,1]=>{{1,4,5,8},{2,3,7},{6}}
[5,7,8,2,4,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[2,5,8,4,3,7,6,1]=>{{1,2,3,5,8},{4},{6,7}}
[2,6,8,4,7,3,5,1]=>{{1,2,3,6,8},{4},{5,7}}
[3,7,4,8,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,8,7,2,5,1]=>{{1,3,4,8},{2,6},{5,7}}
[3,5,4,8,2,7,6,1]=>{{1,3,4,8},{2,5},{6,7}}
[4,3,7,5,8,6,2,1]=>{{1,4,5,8},{2,3,7},{6}}
[4,5,7,3,8,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[3,5,6,8,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,8,7,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,1,7,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[8,5,4,1,7,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[1,8,2,5,6,3,4,7]=>{{1},{2,3,4,5,6,7,8}}
[7,2,8,4,5,1,3,6]=>{{1,3,6,7,8},{2},{4},{5}}
[1,3,7,5,6,2,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,7,4,3,5,2,8]=>{{1},{2,3,5,6,7},{4},{8}}
[1,8,5,2,3,7,4,6]=>{{1},{2,4,6,7,8},{3,5}}
[1,8,2,5,3,6,7,4]=>{{1},{2,3,4,5,8},{6},{7}}
[2,6,8,4,3,5,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[7,5,8,3,2,1,6,4]=>{{1,6,7},{2,5},{3,4,8}}
[7,2,8,4,1,5,6,3]=>{{1,5,6,7},{2},{3,8},{4}}
[7,5,8,1,2,6,3,4]=>{{1,3,4,7,8},{2,5},{6}}
[1,6,7,4,3,2,8,5]=>{{1},{2,6},{3,5,7,8},{4}}
[1,5,2,6,4,7,8,3]=>{{1},{2,3,4,5,6,7,8}}
[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[6,2,5,7,1,4,8,3]=>{{1,3,4,5,6,7,8},{2}}
[6,5,4,3,8,1,7,2]=>{{1,6},{2,5,8},{3,4},{7}}
[7,3,6,8,5,2,4,1]=>{{1,4,7,8},{2,3,6},{5}}
[2,7,8,3,6,5,1,4]=>{{1,2,7},{3,4,8},{5,6}}
[2,7,8,5,4,6,3,1]=>{{1,2,3,7,8},{4,5},{6}}
[2,6,5,8,3,4,1,7]=>{{1,2,4,6,7,8},{3,5}}
[2,6,5,7,3,4,1,8]=>{{1,2,4,6,7},{3,5},{8}}
[6,2,5,7,4,1,3,8]=>{{1,6},{2},{3,4,5,7},{8}}
[6,2,5,8,4,1,3,7]=>{{1,6},{2},{3,4,5,7,8}}
[2,7,8,4,6,1,3,5]=>{{1,2,3,5,6,7,8},{4}}
[6,1,2,8,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[6,1,2,8,5,4,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[6,2,5,7,8,1,3,4]=>{{1,6},{2},{3,4,5,7,8}}
[1,5,4,2,6,7,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,6,5,7,3,8,1,4]=>{{1,2,4,6,7,8},{3,5}}
[1,6,2,7,5,8,4,3]=>{{1},{2,3,6,8},{4,7},{5}}
[1,3,2,7,8,5,6,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,6,2,4,8,7,3,5]=>{{1},{2,3,6,7},{4},{5,8}}
[6,5,2,1,8,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[2,6,5,3,7,8,4,1]=>{{1,2,6,8},{3,4,5,7}}
[6,2,5,3,8,4,7,1]=>{{1,3,4,5,6,8},{2},{7}}
[6,5,2,3,8,7,1,4]=>{{1,6,7},{2,3,4,5,8}}
[5,4,1,2,3,8,6,7]=>{{1,3,5},{2,4},{6,7,8}}
[5,1,4,2,3,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[1,5,4,2,6,3,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[5,1,6,3,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[1,8,7,6,2,5,4,3]=>{{1},{2,3,4,5,6,7,8}}
[5,2,7,4,1,6,3,8]=>{{1,5},{2},{3,7},{4},{6},{8}}
[4,7,3,1,5,6,2,8]=>{{1,4},{2,7},{3},{5},{6},{8}}
[5,8,3,4,1,6,7,2]=>{{1,5},{2,8},{3},{4},{6},{7}}
[1,7,8,4,5,6,2,3]=>{{1},{2,7},{3,8},{4},{5},{6}}
[1,5,8,4,2,6,7,3]=>{{1},{2,5},{3,8},{4},{6},{7}}
[1,6,3,8,5,2,7,4]=>{{1},{2,6},{3},{4,8},{5},{7}}
[5,2,3,7,1,6,4,8]=>{{1,5},{2},{3},{4,7},{6},{8}}
[6,2,3,7,5,1,4,8]=>{{1,6},{2},{3},{4,7},{5},{8}}
[1,7,3,4,8,6,2,5]=>{{1},{2,7},{3},{4},{5,8},{6}}
[6,2,3,4,8,1,7,5]=>{{1,6},{2},{3},{4},{5,8},{7}}
[8,7,3,2,1,6,5,4]=>{{1,2,4,5,7,8},{3},{6}}
[8,7,6,3,1,5,2,4]=>{{1,3,4,5,6,8},{2,7}}
[8,5,1,7,2,3,4,6]=>{{1,3,6,8},{2,5},{4,7}}
[2,4,8,5,3,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[2,4,1,8,5,3,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[2,4,8,6,3,1,7,5]=>{{1,2,4,6},{3,5,8},{7}}
[3,4,6,8,2,1,7,5]=>{{1,3,6},{2,4,5,8},{7}}
[3,4,1,5,8,2,7,6]=>{{1,3},{2,4,5,6,8},{7}}
[8,1,4,5,3,2,7,6]=>{{1,2,6,8},{3,4,5},{7}}
[3,4,1,5,2,8,7,6]=>{{1,3},{2,4,5},{6,8},{7}}
[3,4,6,2,1,8,7,5]=>{{1,3,5,6,8},{2,4},{7}}
[3,5,6,2,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[3,4,6,2,7,8,1,5]=>{{1,3,5,6,7,8},{2,4}}
[8,1,4,6,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,6,3,7,5,2]=>{{1,2,8},{3,4,5,6,7}}
[3,5,6,2,1,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[8,1,5,6,7,3,4,2]=>{{1,2,8},{3,4,5,6,7}}
[8,1,5,6,7,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,6,8,7,2,5]=>{{1,3},{2,4,6,7},{5,8}}
[3,5,6,1,8,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[2,1,3,8,6,7,4,5]=>{{1,2},{3},{4,5,6,7,8}}
[8,1,3,2,6,7,5,4]=>{{1,2,4,8},{3},{5,6,7}}
[2,3,8,6,7,1,5,4]=>{{1,2,3,4,6,8},{5,7}}
[2,4,1,8,6,7,5,3]=>{{1,2,3,4,8},{5,6,7}}
[2,5,8,6,1,7,4,3]=>{{1,2,5},{3,8},{4,6,7}}
[3,5,6,1,8,7,4,2]=>{{1,3,4,6,7},{2,5,8}}
[3,4,1,6,8,7,5,2]=>{{1,3},{2,4,5,6,7,8}}
[3,4,6,8,7,1,5,2]=>{{1,3,6},{2,4,8},{5,7}}
[8,1,4,6,2,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,6,7,8,4,2]=>{{1,3},{2,4,5,6,7,8}}
[4,5,6,1,7,8,3,2]=>{{1,4},{2,3,5,6,7,8}}
[4,5,6,1,7,3,8,2]=>{{1,4},{2,5,7,8},{3,6}}
[3,5,1,6,7,4,8,2]=>{{1,3},{2,5,7,8},{4,6}}
[8,1,5,6,7,4,2,3]=>{{1,2,3,5,7,8},{4,6}}
[8,1,5,6,7,4,3,2]=>{{1,2,8},{3,5,7},{4,6}}
[3,5,1,6,7,4,2,8]=>{{1,3},{2,5,7},{4,6},{8}}
[4,5,6,1,7,3,2,8]=>{{1,4},{2,5,7},{3,6},{8}}
[6,5,8,7,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,4,2,7,8,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,1,4,8,7,5,2,3]=>{{1,2,5,6,7},{3,4,8}}
[1,6,4,8,7,5,2,3]=>{{1},{2,5,6,7},{3,4,8}}
[1,8,6,2,4,7,3,5]=>{{1},{2,4,5,8},{3,6,7}}
[8,1,6,2,4,7,3,5]=>{{1,2,4,5,8},{3,6,7}}
[7,6,2,1,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,7,8,5,2,3]=>{{1,3,5,6,8},{2,4,7}}
[7,6,1,2,4,8,3,5]=>{{1,3,7},{2,4,5,6,8}}
[7,6,1,3,4,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,3,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[1,8,6,3,4,7,2,5]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,5,4,8,3,6]=>{{1},{2,3,7},{4,5},{6,8}}
[7,1,2,5,4,8,3,6]=>{{1,2,3,7},{4,5},{6,8}}
[2,7,1,5,4,8,3,6]=>{{1,2,3,7},{4,5},{6,8}}
[2,8,6,3,4,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,8,6,1,4,7,3,5]=>{{1,2,4,5,8},{3,6,7}}
[7,2,1,5,4,8,3,6]=>{{1,3,7},{2},{4,5},{6,8}}
[1,2,7,5,4,8,3,6]=>{{1},{2},{3,7},{4,5},{6,8}}
[3,2,7,5,4,8,1,6]=>{{1,3,7},{2},{4,5},{6,8}}
[2,5,8,4,7,3,1,6]=>{{1,2,5,7},{3,6,8},{4}}
[2,3,7,5,4,8,1,6]=>{{1,2,3,7},{4,5},{6,8}}
[6,8,3,2,4,7,1,5]=>{{1,6,7},{2,4,5,8},{3}}
[3,7,2,5,4,8,1,6]=>{{1,2,3,7},{4,5},{6,8}}
[3,1,7,5,4,8,2,6]=>{{1,2,3,7},{4,5},{6,8}}
[1,3,7,5,4,8,2,6]=>{{1},{2,3,7},{4,5},{6,8}}
[1,5,8,4,7,3,2,6]=>{{1},{2,5,7},{3,6,8},{4}}
[5,1,8,4,7,3,2,6]=>{{1,2,5,7},{3,6,8},{4}}
[5,8,2,4,7,3,1,6]=>{{1,5,7},{2,3,6,8},{4}}
[6,8,4,3,7,5,1,2]=>{{1,5,6,7},{2,8},{3,4}}
[8,7,5,6,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,4,7,3,1,6]=>{{1,2,3,5,6,7,8},{4}}
[8,1,5,4,7,3,2,6]=>{{1,2,3,5,6,7,8},{4}}
[1,8,5,4,7,3,2,6]=>{{1},{2,3,5,6,7,8},{4}}
[1,7,3,5,4,8,2,6]=>{{1},{2,7},{3},{4,5},{6,8}}
[8,6,3,1,4,7,2,5]=>{{1,4,5,8},{2,6,7},{3}}
[8,6,4,2,7,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[8,6,4,1,7,2,5,3]=>{{1,3,4,8},{2,6},{5,7}}
[5,3,7,4,6,8,2,1]=>{{1,5,6,8},{2,3,7},{4}}
[4,1,3,2,7,8,5,6]=>{{1,2,4},{3},{5,7},{6,8}}
[1,4,3,2,7,8,5,6]=>{{1},{2,4},{3},{5,7},{6,8}}
[2,4,3,1,7,8,5,6]=>{{1,2,4},{3},{5,7},{6,8}}
[2,7,3,5,4,8,1,6]=>{{1,2,7},{3},{4,5},{6,8}}
[2,8,5,4,7,3,1,6]=>{{1,2,3,5,6,7,8},{4}}
[5,7,3,4,6,8,2,1]=>{{1,5,6,8},{2,7},{3},{4}}
[8,2,5,4,7,3,1,6]=>{{1,3,5,6,7,8},{2},{4}}
[7,2,3,5,4,8,1,6]=>{{1,7},{2},{3},{4,5},{6,8}}
[3,2,1,4,7,8,5,6]=>{{1,3},{2},{4},{5,7},{6,8}}
[8,1,7,6,4,3,5,2]=>{{1,2,8},{3,4,5,6,7}}
[8,6,4,5,2,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,6,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,5,1,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[7,3,6,5,2,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[8,3,6,5,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[7,3,6,5,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,6,4,2,1,3]=>{{1,7},{2,4,5,6},{3,8}}
[5,4,2,8,1,3,7,6]=>{{1,5},{2,3,4,6,8},{7}}
[5,8,2,6,4,1,3,7]=>{{1,4,5,6},{2,3,7,8}}
[6,4,2,5,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,2,1,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,5,8,6,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,8,1,4,7,6]=>{{1,2,3,5},{4,6,8},{7}}
[2,3,6,8,1,5,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[6,3,8,5,2,7,1,4]=>{{1,6,7},{2,3,4,5,8}}
[6,3,7,5,2,1,4,8]=>{{1,6},{2,3,4,5,7},{8}}
[2,5,7,6,3,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,8,7,6,3,1,5,4]=>{{1,2,4,6,8},{3,5,7}}
[2,5,8,7,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,1,6,5,7,3]=>{{1,2,4},{3,8},{5,6},{7}}
[2,8,7,3,6,1,4,5]=>{{1,2,5,6,8},{3,4,7}}
[7,3,5,2,1,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[8,4,2,5,1,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,3,6,8,1,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,7,8,6,3,1,4,5]=>{{1,2,4,6,7},{3,5,8}}
[7,3,8,5,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[2,3,6,1,8,4,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[2,8,6,3,1,4,5,7]=>{{1,2,5,7,8},{3,4,6}}
[8,3,5,2,1,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,1,3,7,5,6]=>{{1,2,4},{3,5,6,7,8}}
[2,5,8,1,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,5,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,1,4,7,5,2]=>{{1,3,4,5,6,7},{2,8}}
[2,6,8,1,5,7,3,4]=>{{1,2,3,4,6,7,8},{5}}
[2,7,1,5,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,5,8,1,2,6,4]=>{{1,3,5},{2,6,7},{4,8}}
[7,3,6,1,2,8,4,5]=>{{1,4,7},{2,3,5,6,8}}
[7,4,8,1,6,5,2,3]=>{{1,2,4,7},{3,8},{5,6}}
[7,4,5,8,6,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,5,1,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,7,6,2,3,4]=>{{1,2,5,6},{3,4,7,8}}
[8,5,1,6,2,7,3,4]=>{{1,3,4,6,7,8},{2,5}}
[4,5,1,8,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,8,7,1,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,7,1,2,5,3]=>{{1,2,4,5,6,7},{3,8}}
[5,6,8,3,7,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,1,2,8,5,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,1,2,7,3,8,4]=>{{1,3,6},{2,4,5,7,8}}
[6,5,1,8,2,7,3,4]=>{{1,3,6,7},{2,5},{4,8}}
[6,5,1,8,7,2,3,4]=>{{1,2,3,5,6,7},{4,8}}
[6,5,1,7,2,8,3,4]=>{{1,3,4,6,7,8},{2,5}}
[6,5,1,7,2,3,8,4]=>{{1,3,6},{2,5},{4,7,8}}
[5,6,8,7,4,1,2,3]=>{{1,2,4,5,6,7},{3,8}}
[6,8,5,7,4,1,2,3]=>{{1,6},{2,3,4,5,7,8}}
[7,3,8,1,5,2,4,6]=>{{1,4,7},{2,3,6,8},{5}}
[4,1,7,5,3,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}
[1,8,4,2,3,6,7,5]=>{{1},{2,3,4,5,8},{6},{7}}
[2,5,8,3,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[4,1,7,2,3,6,8,5]=>{{1,2,4},{3,5,7,8},{6}}
[4,6,2,1,5,7,8,3]=>{{1,4},{2,3,6,7,8},{5}}
[4,5,2,3,1,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[3,2,6,7,4,1,8,5]=>{{1,3,6},{2},{4,5,7,8}}
[5,6,2,7,1,4,8,3]=>{{1,5},{2,3,4,6,7,8}}
[6,2,3,8,1,7,4,5]=>{{1,4,5,6,7,8},{2},{3}}
[2,6,8,3,4,7,1,5]=>{{1,2,6,7},{3,4,5,8}}
[4,6,2,7,5,1,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,6,3,1,8,4,5,7]=>{{1,2,4,6},{3},{5,7,8}}
[2,4,3,7,8,1,5,6]=>{{1,2,4,5,6,7,8},{3}}
[5,3,2,7,4,8,1,6]=>{{1,4,5,7},{2,3},{6,8}}
[5,1,2,7,6,8,4,3]=>{{1,2,3,5,6,8},{4,7}}
[2,6,3,1,8,7,4,5]=>{{1,2,4,6,7},{3},{5,8}}
[3,5,6,4,7,8,1,2]=>{{1,2,3,5,6,7,8},{4}}
[5,3,6,4,2,8,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[5,4,2,3,7,8,6,1]=>{{1,5,6,7,8},{2,3,4}}
[4,1,8,2,5,7,3,6]=>{{1,2,4},{3,6,7,8},{5}}
[3,1,8,4,7,2,5,6]=>{{1,2,3,6,8},{4},{5,7}}
[6,2,3,8,4,1,7,5]=>{{1,6},{2},{3},{4,5,8},{7}}
[2,6,4,1,5,3,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[3,2,7,6,4,1,8,5]=>{{1,3,4,5,6,7,8},{2}}
[2,5,4,1,7,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[6,2,1,4,7,8,3,5]=>{{1,3,5,6,7,8},{2},{4}}
[2,6,5,1,7,8,3,4]=>{{1,2,4,6,8},{3,5,7}}
[4,7,5,2,1,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,2,3,7,8,1,6,5]=>{{1,4,6,7},{2},{3},{5,8}}
[5,8,3,1,7,2,4,6]=>{{1,4,5,7},{2,6,8},{3}}
[6,8,3,1,5,2,4,7]=>{{1,2,4,6,7,8},{3},{5}}
[5,1,7,4,2,6,3,8]=>{{1,2,5},{3,7},{4},{6},{8}}
[6,8,3,2,5,1,7,4]=>{{1,6},{2,4,8},{3},{5},{7}}
[6,8,4,3,1,5,7,2]=>{{1,5,6},{2,8},{3,4},{7}}
[6,8,4,2,1,5,7,3]=>{{1,5,6},{2,3,4,8},{7}}
[5,1,7,3,2,4,6,8]=>{{1,2,5},{3,4,6,7},{8}}
[5,2,1,8,3,6,7,4]=>{{1,3,5},{2},{4,8},{6},{7}}
[4,3,8,1,6,2,7,5]=>{{1,4},{2,3,5,6,8},{7}}
[4,2,1,8,5,7,3,6]=>{{1,3,4,6,7,8},{2},{5}}
[6,3,2,1,7,4,5,8]=>{{1,4,6},{2,3},{5,7},{8}}
[6,4,2,1,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,2,1,8,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[5,3,2,7,6,1,4,8]=>{{1,5,6},{2,3},{4,7},{8}}
[5,3,2,8,6,1,4,7]=>{{1,5,6},{2,3},{4,7,8}}
[6,3,2,8,7,1,4,5]=>{{1,6},{2,3},{4,5,7,8}}
[4,2,8,1,7,3,5,6]=>{{1,4},{2},{3,6,8},{5,7}}
[4,3,8,7,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,8,4,7,3,6]=>{{1,2},{3,4,5,6,7,8}}
[4,3,1,6,2,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,1,7,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,3,1,7,8,4,2]=>{{1,2,4,5,6,7,8},{3}}
[5,4,2,1,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[6,4,2,1,7,8,5,3]=>{{1,2,3,4,6,8},{5,7}}
[5,3,2,1,6,7,8,4]=>{{1,4,5,6,7,8},{2,3}}
[8,6,1,4,5,7,2,3]=>{{1,3,8},{2,6,7},{4},{5}}
[5,2,8,3,7,4,6,1]=>{{1,3,4,5,6,7,8},{2}}
[6,2,8,5,4,7,3,1]=>{{1,3,6,7,8},{2},{4,5}}
[1,8,6,3,7,4,2,5]=>{{1},{2,5,7,8},{3,4,6}}
[1,8,6,5,7,2,3,4]=>{{1},{2,3,4,5,6,7,8}}
[5,2,8,4,3,6,7,1]=>{{1,3,5,8},{2},{4},{6},{7}}
[5,4,2,7,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[5,4,2,8,3,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[6,5,3,8,4,7,2,1]=>{{1,2,4,5,6,7,8},{3}}
[5,2,8,4,3,7,1,6]=>{{1,3,5,6,7,8},{2},{4}}
[6,2,8,3,7,4,1,5]=>{{1,3,4,5,6,7,8},{2}}
[5,4,2,7,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[6,4,3,7,1,2,8,5]=>{{1,2,4,5,6,7,8},{3}}
[6,4,3,8,1,2,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[7,6,3,8,4,2,1,5]=>{{1,7},{2,6},{3},{4,5,8}}
[7,2,8,5,1,6,3,4]=>{{1,3,4,5,7,8},{2},{6}}
[7,2,8,4,3,1,5,6]=>{{1,3,5,6,7,8},{2},{4}}
[7,5,3,8,4,2,6,1]=>{{1,2,4,5,6,7,8},{3}}
[6,4,2,7,3,1,5,8]=>{{1,6},{2,3,4,5,7},{8}}
[7,6,4,8,2,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,1,2,5,3,4]=>{{1,3,4,7,8},{2,5,6}}
[5,3,1,7,8,4,6,2]=>{{1,2,3,5,8},{4,6,7}}
[5,3,2,7,8,4,6,1]=>{{1,5,8},{2,3},{4,6,7}}
[5,4,1,6,3,8,7,2]=>{{1,3,5},{2,4,6,8},{7}}
[6,5,1,7,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,7,8,4,2,5]=>{{1,2,3,4,6,7},{5,8}}
[5,4,1,7,3,8,2,6]=>{{1,3,5},{2,4,7},{6,8}}
[6,3,2,7,8,4,1,5]=>{{1,4,6,7},{2,3},{5,8}}
[6,1,5,4,3,2,8,7]=>{{1,2,6},{3,5},{4},{7,8}}
[8,7,6,1,3,5,2,4]=>{{1,4,8},{2,7},{3,5,6}}
[8,1,6,5,7,3,4,2]=>{{1,2,8},{3,6},{4,5,7}}
[8,4,1,5,7,6,2,3]=>{{1,3,8},{2,4,5,7},{6}}
[7,8,6,2,5,3,1,4]=>{{1,7},{2,4,8},{3,6},{5}}
[6,1,3,5,2,8,4,7]=>{{1,2,4,5,6,7,8},{3}}
[8,1,3,7,4,2,5,6]=>{{1,2,6,8},{3},{4,5,7}}
[4,3,8,7,5,2,1,6]=>{{1,4,7},{2,3,6,8},{5}}
[6,7,1,8,5,3,4,2]=>{{1,3,6},{2,4,7,8},{5}}
[2,7,6,4,8,3,5,1]=>{{1,2,5,7,8},{3,6},{4}}
[6,5,2,7,1,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,1,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[7,5,2,1,3,8,4,6]=>{{1,4,7},{2,3,5},{6,8}}
[8,4,7,6,3,1,5,2]=>{{1,2,4,6,8},{3,5,7}}
[7,4,1,5,6,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,5,6,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[2,4,7,5,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,1,7,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,7,1,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,1,3,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,7,2,1,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[4,7,2,5,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,5,7,1,4,3]=>{{1,2,3,6,8},{4,5,7}}
[2,7,4,5,3,8,1,6]=>{{1,2,7},{3,4,5},{6,8}}
[6,8,7,1,3,2,5,4]=>{{1,2,4,6,8},{3,5,7}}
[2,8,6,5,7,1,4,3]=>{{1,2,3,6,8},{4,5,7}}
[5,8,4,3,2,6,7,1]=>{{1,2,5,8},{3,4},{6},{7}}
[1,8,5,6,2,4,7,3]=>{{1},{2,3,5,8},{4,6},{7}}
[8,1,5,6,2,4,7,3]=>{{1,2,3,5,8},{4,6},{7}}
[6,4,8,1,3,2,7,5]=>{{1,2,4,6},{3,5,8},{7}}
[1,4,5,2,8,6,7,3]=>{{1},{2,4},{3,5,8},{6},{7}}
[2,3,1,7,8,6,4,5]=>{{1,2,3},{4,7},{5,8},{6}}
[3,5,7,6,2,8,1,4]=>{{1,3,7},{2,5},{4,6,8}}
[4,5,6,1,2,8,7,3]=>{{1,4},{2,5},{3,6,8},{7}}
[5,4,1,2,8,6,7,3]=>{{1,3,5,8},{2,4},{6},{7}}
[8,4,5,2,1,6,7,3]=>{{1,3,5,8},{2,4},{6},{7}}
[3,1,2,6,8,4,7,5]=>{{1,2,3},{4,6},{5,8},{7}}
[5,1,3,2,7,8,4,6]=>{{1,2,4,5,7},{3},{6,8}}
[1,5,4,2,7,8,3,6]=>{{1},{2,3,4,5,7},{6,8}}
[4,6,7,8,3,1,5,2]=>{{1,2,4,6,8},{3,5,7}}
[7,6,2,8,4,3,1,5]=>{{1,7},{2,3,6},{4,5,8}}
[5,2,8,6,3,4,7,1]=>{{1,3,5,8},{2},{4,6},{7}}
[5,6,8,4,3,2,7,1]=>{{1,3,5,8},{2,6},{4},{7}}
[5,3,8,1,7,2,4,6]=>{{1,4,5,7},{2,3,6,8}}
[3,6,7,8,4,2,1,5]=>{{1,3,7},{2,6},{4,5,8}}
[6,5,1,8,4,3,7,2]=>{{1,3,6},{2,4,5,8},{7}}
[6,3,8,4,2,1,7,5]=>{{1,6},{2,3,5,8},{4},{7}}
[2,5,8,3,1,6,7,4]=>{{1,2,5},{3,4,8},{6},{7}}
[3,5,8,1,2,6,7,4]=>{{1,3,4,8},{2,5},{6},{7}}
[3,2,8,1,5,6,7,4]=>{{1,3,4,8},{2},{5},{6},{7}}
[1,5,8,3,2,6,7,4]=>{{1},{2,5},{3,4,8},{6},{7}}
[1,3,8,6,2,4,7,5]=>{{1},{2,3,5,8},{4,6},{7}}
[3,2,7,8,4,6,1,5]=>{{1,3,7},{2},{4,5,8},{6}}
[5,1,8,3,4,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[4,8,7,2,1,6,3,5]=>{{1,2,4,5,8},{3,7},{6}}
[2,8,1,6,3,4,7,5]=>{{1,2,3,5,8},{4,6},{7}}
[8,3,4,2,1,6,5,7]=>{{1,5,7,8},{2,3,4},{6}}
[6,4,7,2,5,8,1,3]=>{{1,3,6,7,8},{2,4},{5}}
[8,4,5,2,6,3,1,7]=>{{1,7,8},{2,4},{3,5,6}}
[2,4,5,8,3,6,1,7]=>{{1,2,4,7,8},{3,5},{6}}
[3,5,8,1,2,6,4,7]=>{{1,3,4,7,8},{2,5},{6}}
[8,6,1,3,5,2,4,7]=>{{1,3,4,7,8},{2,6},{5}}
[8,5,1,2,6,4,3,7]=>{{1,3,7,8},{2,4,5,6}}
[5,8,6,1,3,4,2,7]=>{{1,3,4,5,6},{2,7,8}}
[5,8,4,6,1,3,2,7]=>{{1,5},{2,7,8},{3,4,6}}
[7,3,4,5,2,8,1,6]=>{{1,7},{2,3,4,5},{6,8}}
[5,7,4,3,6,1,8,2]=>{{1,5,6},{2,7,8},{3,4}}
[2,6,4,3,7,8,5,1]=>{{1,2,6,8},{3,4},{5,7}}
[7,4,1,8,3,2,5,6]=>{{1,3,5,7},{2,4,6,8}}
[6,2,1,7,8,4,5,3]=>{{1,3,4,5,6,7,8},{2}}
[7,6,3,1,5,4,8,2]=>{{1,2,4,6,7,8},{3},{5}}
[2,4,6,5,1,7,8,3]=>{{1,2,4,5},{3,6,7,8}}
[1,4,7,5,6,8,2,3]=>{{1},{2,3,4,5,6,7,8}}
[1,4,7,6,5,8,2,3]=>{{1},{2,3,4,6,7,8},{5}}
[3,7,5,2,4,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[5,6,1,7,4,2,8,3]=>{{1,3,4,5,7,8},{2,6}}
[3,7,4,8,1,2,6,5]=>{{1,3,4,5,8},{2,6,7}}
[6,3,5,7,8,1,4,2]=>{{1,6},{2,3,5,8},{4,7}}
[3,6,5,7,1,8,4,2]=>{{1,3,5},{2,6,8},{4,7}}
[6,4,7,8,2,1,3,5]=>{{1,6},{2,4,5,8},{3,7}}
[6,7,3,8,4,1,2,5]=>{{1,6},{2,7},{3},{4,5,8}}
[2,7,8,3,4,6,1,5]=>{{1,2,7},{3,4,5,8},{6}}
[7,5,8,4,1,3,2,6]=>{{1,2,5,7},{3,6,8},{4}}
[4,7,5,8,3,1,2,6]=>{{1,4,6,8},{2,7},{3,5}}
[3,6,7,4,8,1,2,5]=>{{1,2,3,6,7},{4},{5,8}}
[5,7,3,1,6,8,4,2]=>{{1,2,4,5,6,7,8},{3}}
[2,7,3,1,8,6,4,5]=>{{1,2,4,7},{3},{5,8},{6}}
[2,8,4,3,1,5,7,6]=>{{1,2,5,6,8},{3,4},{7}}
[4,8,1,2,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[7,6,8,1,2,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,5,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,5,4,6,1,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[8,4,5,2,7,6,1,3]=>{{1,3,5,7,8},{2,4},{6}}
[8,7,6,4,1,2,5,3]=>{{1,2,3,5,6,7,8},{4}}
[6,7,1,3,5,2,8,4]=>{{1,2,3,4,6,7,8},{5}}
[5,7,2,3,6,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,2,7,6,1,4]=>{{1,2,4,5,7,8},{3},{6}}
[3,4,6,7,5,8,1,2]=>{{1,2,3,4,6,7,8},{5}}
[3,4,5,7,6,1,8,2]=>{{1,3,5,6},{2,4,7,8}}
[2,6,4,5,7,8,3,1]=>{{1,2,6,8},{3,4,5,7}}
[3,8,5,1,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,5,1,3,6,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[5,4,6,1,3,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,7,1,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[7,3,4,6,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,4,1,5,6,2]=>{{1,2,3,5,6,7,8},{4}}
[8,7,5,4,2,1,6,3]=>{{1,2,3,5,6,7,8},{4}}
[6,7,2,5,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,2,5,8,4,7]=>{{1,3},{2,4,6,7,8},{5}}
[1,4,5,8,2,3,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,2,6,4,5,8,3,7]=>{{1},{2},{3,6,7,8},{4},{5}}
[1,5,2,4,6,8,3,7]=>{{1},{2,3,5,6,7,8},{4}}
[3,6,1,5,8,2,4,7]=>{{1,3},{2,6},{4,5,7,8}}
[2,6,5,1,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[5,2,6,1,4,8,3,7]=>{{1,4,5},{2},{3,6,7,8}}
[2,5,1,8,4,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,7,1,4,3,6,8,5]=>{{1,2,3,5,7,8},{4},{6}}
[1,3,7,5,8,2,4,6]=>{{1},{2,3,4,5,6,7,8}}
[8,2,1,5,7,3,4,6]=>{{1,3,6,8},{2},{4,5,7}}
[2,5,4,8,1,3,7,6]=>{{1,2,5},{3,4,6,8},{7}}
[2,4,1,3,8,6,7,5]=>{{1,2,3,4},{5,8},{6},{7}}
[8,4,3,7,1,2,6,5]=>{{1,5,8},{2,4,6,7},{3}}
[1,7,3,5,8,2,6,4]=>{{1},{2,6,7},{3},{4,5,8}}
[1,8,4,2,6,7,3,5]=>{{1},{2,3,4,5,6,7,8}}
[3,1,6,8,7,2,4,5]=>{{1,2,3,6},{4,5,7,8}}
[7,2,1,6,8,3,4,5]=>{{1,3,4,6,7},{2},{5,8}}
[3,1,7,6,8,2,4,5]=>{{1,2,3,4,6,7},{5,8}}
[4,1,7,2,6,8,3,5]=>{{1,2,4},{3,7},{5,6,8}}
[5,1,7,2,3,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[7,2,1,6,3,5,8,4]=>{{1,3,4,5,6,7,8},{2}}
[2,6,1,7,3,5,8,4]=>{{1,2,3,5,6},{4,7,8}}
[7,1,2,5,3,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[5,4,1,2,7,8,3,6]=>{{1,3,5,7},{2,4},{6,8}}
[8,1,3,2,4,6,7,5]=>{{1,2,4,5,8},{3},{6},{7}}
[7,3,1,2,4,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[1,8,3,4,7,2,5,6]=>{{1},{2,6,8},{3},{4},{5,7}}
[3,5,8,1,2,7,4,6]=>{{1,3,4,6,7,8},{2,5}}
[3,6,8,1,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,1,3,8,7,2,6,5]=>{{1,2,4,5,6,7,8},{3}}
[1,3,7,4,8,2,6,5]=>{{1},{2,3,6,7},{4},{5,8}}
[1,4,6,8,2,3,7,5]=>{{1},{2,4,5,8},{3,6},{7}}
[3,5,8,1,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[2,6,8,1,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[6,1,5,8,2,3,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[1,8,3,2,7,5,6,4]=>{{1},{2,4,8},{3},{5,6,7}}
[3,1,7,2,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[2,6,7,3,8,1,5,4]=>{{1,2,6},{3,4,5,7,8}}
[8,4,1,7,3,6,2,5]=>{{1,3,5,8},{2,4,7},{6}}
[3,7,2,8,6,1,5,4]=>{{1,2,3,5,6,7},{4,8}}
[6,2,3,8,7,1,5,4]=>{{1,6},{2},{3},{4,8},{5,7}}
[5,1,7,8,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,7,4,2,6,3]=>{{1,2,4,5,6,7},{3,8}}
[4,7,2,8,3,6,5,1]=>{{1,4,8},{2,3,5,7},{6}}
[4,1,7,8,5,3,6,2]=>{{1,2,4,8},{3,6,7},{5}}
[5,1,7,4,8,3,6,2]=>{{1,2,5,8},{3,6,7},{4}}
[4,1,8,7,5,3,6,2]=>{{1,2,3,4,6,7,8},{5}}
[4,8,2,7,3,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[4,7,2,6,3,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,8,2,4,3,7,5,1]=>{{1,2,3,5,6,7,8},{4}}
[6,7,2,4,3,8,5,1]=>{{1,6,8},{2,3,5,7},{4}}
[6,8,2,7,3,5,4,1]=>{{1,2,3,5,6,8},{4,7}}
[3,8,7,2,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,2,4,1,5,6]=>{{1,3,6,8},{2,4,5,7}}
[3,6,8,2,4,5,7,1]=>{{1,3,8},{2,4,5,6},{7}}
[3,6,7,2,4,5,8,1]=>{{1,3,7,8},{2,4,5,6}}
[6,5,1,4,2,3,8,7]=>{{1,3,6},{2,5},{4},{7,8}}
[8,6,1,7,2,5,4,3]=>{{1,3,8},{2,5,6},{4,7}}
[8,7,6,1,2,3,5,4]=>{{1,4,8},{2,5,7},{3,6}}
[5,4,3,1,6,2,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[8,3,4,7,1,6,2,5]=>{{1,5,8},{2,3,4,7},{6}}
[6,3,4,1,8,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[3,8,5,2,7,1,6,4]=>{{1,3,5,6,7},{2,4,8}}
[2,8,6,7,5,3,4,1]=>{{1,2,8},{3,6},{4,7},{5}}
[2,1,8,7,3,6,4,5]=>{{1,2},{3,5,8},{4,7},{6}}
[3,6,5,8,2,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,2,1,8,7,3,4,6]=>{{1,3,4,5,6,7,8},{2}}
[6,5,2,7,4,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,2,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,2,7,1,8,3,5,4]=>{{1,3,4,5,6,7,8},{2}}
[2,7,5,4,8,3,6,1]=>{{1,2,3,5,6,7,8},{4}}
[8,7,5,1,2,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[8,4,3,2,7,1,6,5]=>{{1,5,6,7,8},{2,4},{3}}
[7,1,6,2,3,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,3,2,7,5,6]=>{{1,3,4},{2,5,6,7,8}}
[3,8,1,4,7,5,2,6]=>{{1,3},{2,5,6,7,8},{4}}
[6,3,8,7,4,5,1,2]=>{{1,4,5,6,7},{2,3,8}}
[6,1,4,8,5,2,3,7]=>{{1,2,6},{3,4,7,8},{5}}
[8,5,7,4,6,2,1,3]=>{{1,3,7,8},{2,5,6},{4}}
[4,6,7,8,2,3,5,1]=>{{1,4,8},{2,3,5,6,7}}
[8,7,4,6,2,1,5,3]=>{{1,3,4,6,8},{2,5,7}}
[7,6,1,3,5,2,8,4]=>{{1,3,4,7,8},{2,6},{5}}
[5,8,3,2,4,6,1,7]=>{{1,2,4,5,7,8},{3},{6}}
[8,2,6,5,3,1,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[4,8,7,6,5,2,3,1]=>{{1,2,4,6,8},{3,7},{5}}
[2,1,8,6,4,3,7,5]=>{{1,2},{3,4,5,6,8},{7}}
[2,1,7,6,5,3,8,4]=>{{1,2},{3,4,6,7,8},{5}}
[2,7,6,1,3,5,8,4]=>{{1,2,4,7,8},{3,5,6}}
[7,2,5,4,6,1,8,3]=>{{1,3,5,6,7,8},{2},{4}}
[4,7,6,1,2,5,8,3]=>{{1,4},{2,3,5,6,7,8}}
[2,4,1,7,6,8,5,3]=>{{1,2,3,4,5,6,7,8}}
[3,4,1,7,8,5,6,2]=>{{1,3},{2,4,5,6,7,8}}
[7,5,4,3,1,8,6,2]=>{{1,2,5,6,7,8},{3,4}}
[8,5,6,2,7,3,1,4]=>{{1,2,4,5,7,8},{3,6}}
[8,4,2,5,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,3,5,4,1,7,8,2]=>{{1,2,3,5,6,7,8},{4}}
[4,1,3,6,7,5,8,2]=>{{1,2,4,5,6,7,8},{3}}
[1,7,2,4,5,8,3,6]=>{{1},{2,3,7},{4},{5},{6,8}}
[1,7,4,5,8,3,2,6]=>{{1},{2,7},{3,4,5,6,8}}
[2,6,4,7,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[1,2,6,4,7,8,3,5]=>{{1},{2},{3,5,6,7,8},{4}}
[6,1,4,7,8,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,7,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,3,6,7,1,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,7,8,1,2,5]=>{{1,2,3,4,6,7},{5,8}}
[4,7,2,1,5,3,8,6]=>{{1,4},{2,3,6,7,8},{5}}
[1,3,6,4,7,2,8,5]=>{{1},{2,3,6},{4},{5,7,8}}
[3,6,4,7,2,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[5,1,3,4,2,7,8,6]=>{{1,2,5},{3},{4},{6,7,8}}
[5,4,2,1,3,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[1,6,7,3,8,2,5,4]=>{{1},{2,6},{3,4,5,7,8}}
[6,1,4,7,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,2,1,7,8,5,4]=>{{1,4,6,8},{2,3},{5,7}}
[8,6,5,1,3,2,4,7]=>{{1,4,7,8},{2,6},{3,5}}
[6,4,7,8,3,2,5,1]=>{{1,2,4,6,8},{3,5,7}}
[3,8,4,7,1,2,5,6]=>{{1,3,4,5,7},{2,6,8}}
[8,6,1,2,5,4,3,7]=>{{1,3,7,8},{2,4,6},{5}}
[4,8,6,1,5,3,2,7]=>{{1,4},{2,7,8},{3,6},{5}}
[5,8,6,4,1,3,2,7]=>{{1,5},{2,7,8},{3,6},{4}}
[8,3,6,4,5,2,1,7]=>{{1,7,8},{2,3,6},{4},{5}}
[6,8,5,7,4,2,3,1]=>{{1,2,6,8},{3,4,5,7}}
[2,3,8,7,1,6,4,5]=>{{1,2,3,5,8},{4,7},{6}}
[4,3,7,8,1,6,2,5]=>{{1,4,5,8},{2,3,7},{6}}
[3,5,8,7,4,1,2,6]=>{{1,3,6,8},{2,4,5,7}}
[7,3,8,4,1,2,5,6]=>{{1,5,7},{2,3,6,8},{4}}
[4,8,1,2,7,3,5,6]=>{{1,2,3,4,6,8},{5,7}}
[6,8,1,2,7,4,5,3]=>{{1,2,3,4,6,8},{5,7}}
[5,6,8,4,1,3,7,2]=>{{1,5},{2,3,6,8},{4},{7}}
[8,5,4,7,1,6,3,2]=>{{1,2,5,8},{3,4,7},{6}}
[2,5,8,7,3,6,4,1]=>{{1,2,3,5,8},{4,7},{6}}
[2,4,8,7,5,6,1,3]=>{{1,2,4,7},{3,8},{5},{6}}
[3,7,4,8,5,6,2,1]=>{{1,3,4,8},{2,7},{5},{6}}
[6,4,8,7,5,1,2,3]=>{{1,6},{2,4,7},{3,8},{5}}
[3,8,5,2,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[5,7,1,8,4,6,2,3]=>{{1,3,4,5,8},{2,7},{6}}
[6,3,8,7,2,1,4,5]=>{{1,6},{2,3,5,8},{4,7}}
[2,3,7,8,5,6,1,4]=>{{1,2,3,7},{4,8},{5},{6}}
[3,7,6,8,5,1,2,4]=>{{1,3,6},{2,7},{4,8},{5}}
[2,6,7,8,5,1,3,4]=>{{1,2,6},{3,7},{4,8},{5}}
[2,4,7,8,1,6,3,5]=>{{1,2,4,5,8},{3,7},{6}}
[5,4,7,8,2,6,3,1]=>{{1,2,4,5,8},{3,7},{6}}
[2,8,3,4,1,5,7,6]=>{{1,2,5,6,8},{3},{4},{7}}
[6,8,3,4,1,2,7,5]=>{{1,2,5,6,8},{3},{4},{7}}
[6,8,7,1,5,2,3,4]=>{{1,2,4,6,8},{3,7},{5}}
[5,8,3,2,7,6,1,4]=>{{1,5,7},{2,4,8},{3},{6}}
[2,5,3,1,8,6,7,4]=>{{1,2,4,5,8},{3},{6},{7}}
[4,5,3,2,8,6,7,1]=>{{1,2,4,5,8},{3},{6},{7}}
[3,5,8,6,1,4,7,2]=>{{1,2,3,5,8},{4,6},{7}}
[2,8,5,6,1,4,7,3]=>{{1,2,3,5,8},{4,6},{7}}
[4,8,6,1,5,2,7,3]=>{{1,4},{2,3,6,8},{5},{7}}
[5,8,2,3,7,6,1,4]=>{{1,5,7},{2,3,4,8},{6}}
[4,6,8,5,3,2,7,1]=>{{1,3,4,5,8},{2,6},{7}}
[2,6,4,8,5,1,7,3]=>{{1,2,6},{3,4,8},{5},{7}}
[7,6,4,8,5,2,1,3]=>{{1,7},{2,6},{3,4,8},{5}}
[3,4,8,6,5,2,7,1]=>{{1,3,8},{2,4,6},{5},{7}}
[3,4,8,7,5,6,2,1]=>{{1,3,8},{2,4,7},{5},{6}}
[7,5,3,2,8,6,1,4]=>{{1,7},{2,4,5,8},{3},{6}}
[2,5,1,3,8,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[4,5,1,2,8,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[5,4,8,1,3,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[8,3,5,4,1,6,7,2]=>{{1,2,3,5,8},{4},{6},{7}}
[7,3,4,8,5,6,1,2]=>{{1,7},{2,3,4,8},{5},{6}}
[6,1,5,7,2,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,1,2,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,3,1,2,8,5,6]=>{{1,2,4,5,7},{3},{6,8}}
[8,4,7,6,2,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[8,4,6,5,7,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,2,1,4,5,8,3,6]=>{{1,3,7},{2},{4},{5},{6,8}}
[7,4,1,6,3,5,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,6,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,2,1,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[5,7,2,3,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,3,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[5,7,2,4,8,3,6,1]=>{{1,5,8},{2,3,6,7},{4}}
[1,7,2,4,8,6,3,5]=>{{1},{2,3,7},{4},{5,8},{6}}
[7,6,1,5,4,8,3,2]=>{{1,3,7},{2,6,8},{4,5}}
[4,7,3,2,1,8,5,6]=>{{1,2,4,5,7},{3},{6,8}}
[3,1,7,2,5,8,4,6]=>{{1,2,3,4,7},{5},{6,8}}
[4,8,7,6,1,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,8,6,1,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,6,7,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,4,2,3,1,7]=>{{1,2,5,7,8},{3,6},{4}}
[2,8,3,1,6,5,4,7]=>{{1,2,4,7,8},{3},{5,6}}
[3,8,1,2,5,7,4,6]=>{{1,3},{2,4,6,7,8},{5}}
[6,8,5,4,2,7,3,1]=>{{1,2,3,5,6,7,8},{4}}
[6,8,3,1,2,4,5,7]=>{{1,4,6},{2,5,7,8},{3}}
[4,6,8,7,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,3,7,8,4,1,2]=>{{1,4,6,7},{2,5,8},{3}}
[4,1,3,8,7,5,6,2]=>{{1,2,4,8},{3},{5,6,7}}
[6,2,7,4,8,1,3,5]=>{{1,6},{2},{3,7},{4},{5,8}}
[8,4,5,2,1,6,3,7]=>{{1,3,5,7,8},{2,4},{6}}
[4,3,2,6,8,1,7,5]=>{{1,4,6},{2,3},{5,8},{7}}
[7,1,5,6,3,8,2,4]=>{{1,2,7},{3,5},{4,6,8}}
[5,1,2,4,7,8,3,6]=>{{1,2,3,5,7},{4},{6,8}}
[3,5,4,2,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,1,3,8,4,2,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[6,2,8,7,3,5,4,1]=>{{1,3,5,6,8},{2},{4,7}}
[7,1,8,4,3,6,5,2]=>{{1,2,3,5,7,8},{4},{6}}
[3,6,8,7,4,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[5,6,8,1,7,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[3,1,6,8,7,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,8,2,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,4,3,1,2,7]=>{{1,6},{2,3,5,7,8},{4}}
[2,5,8,3,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,5,1,3,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[1,5,8,3,7,4,2,6]=>{{1},{2,5,7},{3,4,6,8}}
[3,8,2,7,1,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,2,3,6,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[6,8,2,3,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,8,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,6,8,5,2,7,4,1]=>{{1,3,8},{2,4,5,6,7}}
[2,1,6,5,4,8,3,7]=>{{1,2},{3,6,7,8},{4,5}}
[2,1,7,8,4,6,5,3]=>{{1,2},{3,4,5,7,8},{6}}
[2,1,7,4,3,5,8,6]=>{{1,2},{3,5,6,7,8},{4}}
[3,5,7,8,4,6,1,2]=>{{1,3,7},{2,4,5,8},{6}}
[7,5,2,8,4,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[7,8,2,4,3,1,5,6]=>{{1,2,3,5,6,7,8},{4}}
[7,6,3,8,1,5,4,2]=>{{1,2,4,5,6,7,8},{3}}
[7,2,4,1,6,3,8,5]=>{{1,3,4,5,6,7,8},{2}}
[8,4,3,1,7,5,2,6]=>{{1,2,4,5,6,7,8},{3}}
[7,3,1,4,6,8,5,2]=>{{1,2,3,5,6,7,8},{4}}
[4,3,8,7,1,6,5,2]=>{{1,4,5,7},{2,3,8},{6}}
[5,2,4,3,6,8,1,7]=>{{1,5,6,7,8},{2},{3,4}}
[3,8,6,5,4,1,2,7]=>{{1,3,6},{2,7,8},{4,5}}
[4,7,5,6,3,8,2,1]=>{{1,4,6,8},{2,7},{3,5}}
[4,2,7,5,8,3,6,1]=>{{1,4,5,8},{2},{3,6,7}}
[5,8,2,7,3,4,6,1]=>{{1,2,3,5,8},{4,6,7}}
[6,7,2,4,5,3,8,1]=>{{1,2,3,6,7,8},{4},{5}}
[6,3,2,1,4,8,5,7]=>{{1,4,5,6,7,8},{2,3}}
[6,2,3,1,4,7,8,5]=>{{1,4,5,6,7,8},{2},{3}}
[5,2,1,3,6,4,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[7,1,8,3,5,4,6,2]=>{{1,2,3,4,6,7,8},{5}}
[7,1,2,4,8,5,6,3]=>{{1,2,3,5,6,7,8},{4}}
[7,2,1,3,4,5,8,6]=>{{1,3,4,5,6,7,8},{2}}
[8,7,3,5,4,2,1,6]=>{{1,2,6,7,8},{3},{4,5}}
[8,4,6,5,3,2,1,7]=>{{1,7,8},{2,3,4,5,6}}
[5,1,6,4,3,2,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[8,3,7,1,4,6,5,2]=>{{1,2,3,4,5,7,8},{6}}
[2,8,3,6,4,7,5,1]=>{{1,2,8},{3},{4,5,6,7}}
[6,2,1,7,5,8,3,4]=>{{1,3,4,6,7,8},{2},{5}}
[6,3,8,7,5,2,1,4]=>{{1,2,3,4,6,7,8},{5}}
[6,7,2,1,5,8,4,3]=>{{1,2,3,4,6,7,8},{5}}
[7,6,8,1,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}
[5,4,8,7,6,1,3,2]=>{{1,5,6},{2,3,4,7,8}}
[7,6,1,8,5,4,3,2]=>{{1,3,7},{2,4,6,8},{5}}
[6,5,8,1,7,4,3,2]=>{{1,4,6},{2,3,5,7,8}}
[6,5,8,7,4,1,3,2]=>{{1,6},{2,3,4,5,7,8}}
[1,6,4,8,3,2,5,7]=>{{1},{2,6},{3,4,5,7,8}}
[1,8,3,5,6,2,4,7]=>{{1},{2,4,5,6,7,8},{3}}
[1,4,8,5,6,2,3,7]=>{{1},{2,4,5,6},{3,7,8}}
[1,2,8,5,3,7,4,6]=>{{1},{2},{3,4,5,6,7,8}}
[6,1,4,8,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,7,2,5,6,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[1,8,2,5,4,7,3,6]=>{{1},{2,3,6,7,8},{4,5}}
[5,7,4,1,2,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,7,4,2,5,3,8,6]=>{{1},{2,3,4,6,7,8},{5}}
[6,7,4,2,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,4,3,8,5,7,1,2]=>{{1,6,7},{2,4,8},{3},{5}}
[7,4,3,6,2,1,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,2,5,3,4,1,6,8]=>{{1,6,7},{2},{3,4,5},{8}}
[8,3,7,4,5,6,1,2]=>{{1,2,3,7,8},{4},{5},{6}}
[2,7,4,3,1,5,6,8]=>{{1,2,5,6,7},{3,4},{8}}
[6,8,4,2,3,1,5,7]=>{{1,6},{2,3,4,5,7,8}}
[3,7,5,2,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[7,1,3,2,8,4,5,6]=>{{1,2,4,5,6,7,8},{3}}
[2,1,7,4,8,3,5,6]=>{{1,2},{3,5,6,7,8},{4}}
[5,2,8,6,1,3,4,7]=>{{1,5},{2},{3,4,6,7,8}}
[2,8,3,1,4,5,6,7]=>{{1,2,4,5,6,7,8},{3}}
[7,4,8,2,3,1,5,6]=>{{1,3,5,6,7,8},{2,4}}
[4,2,7,3,1,5,6,8]=>{{1,3,4,5,6,7},{2},{8}}
[8,3,7,2,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,4,7,1,3,8]=>{{1,6},{2,3,5,7},{4},{8}}
[6,5,7,4,1,8,2,3]=>{{1,2,3,5,6,7,8},{4}}
[7,6,4,5,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,6,4,1,3,7,2,5]=>{{1,3,4,5,8},{2,6,7}}
[6,4,3,1,8,2,5,7]=>{{1,2,4,6},{3},{5,7,8}}
[7,4,1,2,8,3,5,6]=>{{1,3,5,6,7,8},{2,4}}
[4,8,1,3,5,7,2,6]=>{{1,3,4},{2,6,7,8},{5}}
[7,8,4,1,3,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[6,5,8,1,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,1,8,2,4,7]=>{{1,4,5,7,8},{2,3,6}}
[4,7,3,1,8,2,5,6]=>{{1,4},{2,5,6,7,8},{3}}
[8,3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,1,4,7,3,5,6]=>{{1,2,3,6,8},{4},{5,7}}
[4,1,5,8,3,7,6,2]=>{{1,2,4,8},{3,5},{6,7}}
[4,5,1,8,2,7,6,3]=>{{1,3,4,8},{2,5},{6,7}}
[4,5,2,1,8,7,6,3]=>{{1,4},{2,3,5,8},{6,7}}
[5,6,2,7,8,1,4,3]=>{{1,2,3,5,6,8},{4,7}}
[4,6,2,8,7,1,5,3]=>{{1,2,3,4,6,8},{5,7}}
[4,8,6,3,7,5,1,2]=>{{1,3,4,5,6,7},{2,8}}
[5,6,2,7,4,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,2,3,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,7,8,3,4,2]=>{{1,2,5,8},{3,6},{4,7}}
[4,1,6,8,7,3,5,2]=>{{1,2,4,8},{3,6},{5,7}}
[4,1,6,8,7,5,3,2]=>{{1,2,4,8},{3,5,6,7}}
[4,6,8,1,7,5,2,3]=>{{1,4},{2,5,6,7},{3,8}}
[5,6,7,1,8,3,2,4]=>{{1,4,5,8},{2,3,6,7}}
[5,6,7,3,8,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,3,8,2,1,4]=>{{1,3,4,5,7,8},{2,6}}
[7,4,6,2,3,5,1,8]=>{{1,7},{2,4},{3,5,6},{8}}
[1,4,8,6,3,2,5,7]=>{{1},{2,4,6},{3,5,7,8}}
[7,4,1,6,3,8,5,2]=>{{1,3,5,7},{2,4,6,8}}
[7,6,3,1,5,8,4,2]=>{{1,4,7},{2,6,8},{3},{5}}
[6,4,2,5,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,2,5,7,6,3,1,8]=>{{1,4,7},{2},{3,5,6},{8}}
[7,4,5,6,1,8,3,2]=>{{1,3,5,7},{2,4,6,8}}
[4,1,5,8,6,3,2,7]=>{{1,2,4,7,8},{3,5,6}}
[3,2,7,6,1,8,5,4]=>{{1,3,5,7},{2},{4,6,8}}
[4,7,5,1,6,8,2,3]=>{{1,4},{2,7},{3,5,6,8}}
[8,6,5,1,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[3,2,5,1,4,8,7,6]=>{{1,3,4,5},{2},{6,8},{7}}
[8,5,4,1,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[1,4,2,3,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[5,4,8,3,7,1,6,2]=>{{1,5,6,7},{2,3,4,8}}
[4,7,1,8,2,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,8,5,3,7,2]=>{{1,3,6},{2,4,8},{5},{7}}
[8,4,6,1,3,5,2,7]=>{{1,2,4,7,8},{3,5,6}}
[3,2,5,4,7,8,1,6]=>{{1,3,5,7},{2},{4},{6,8}}
[5,2,4,3,7,8,1,6]=>{{1,5,7},{2},{3,4},{6,8}}
[8,1,6,7,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,6,5,8,2,4]=>{{1,2,3,7},{4,6,8},{5}}
[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[6,1,4,7,2,8,3,5]=>{{1,2,5,6,8},{3,4,7}}
[3,2,1,7,6,8,4,5]=>{{1,3},{2},{4,7},{5,6,8}}
[3,2,8,6,4,7,1,5]=>{{1,3,4,5,6,7,8},{2}}
[7,8,4,6,3,2,1,5]=>{{1,7},{2,3,4,5,6,8}}
[1,8,6,5,3,7,2,4]=>{{1},{2,3,4,5,6,7,8}}
[8,2,5,3,6,7,1,4]=>{{1,3,4,5,6,7,8},{2}}
[3,8,5,2,7,6,1,4]=>{{1,3,5,7},{2,4,8},{6}}
[4,7,5,3,1,8,6,2]=>{{1,3,4,5},{2,6,7,8}}
[4,5,3,6,8,1,7,2]=>{{1,4,6},{2,5,8},{3},{7}}
[3,5,2,6,1,8,7,4]=>{{1,2,3,5},{4,6,8},{7}}
[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[8,4,6,5,7,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,2,6,8,1,3]=>{{1,7},{2,4},{3,5,6,8}}
[5,4,2,6,8,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,1,4,3,2,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[3,6,4,5,2,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[7,5,4,2,3,8,1,6]=>{{1,7},{2,3,4,5},{6,8}}
[7,8,1,3,5,6,2,4]=>{{1,2,3,4,7,8},{5},{6}}
[1,7,8,3,5,6,2,4]=>{{1},{2,7},{3,4,8},{5},{6}}
[3,1,7,8,5,2,6,4]=>{{1,2,3,6,7},{4,8},{5}}
[1,3,7,5,8,2,6,4]=>{{1},{2,3,6,7},{4,5,8}}
[3,1,7,5,8,2,6,4]=>{{1,2,3,6,7},{4,5,8}}
[3,5,7,1,8,4,6,2]=>{{1,3,4,6,7},{2,5,8}}
[3,5,7,8,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,8,4,6,1,2]=>{{1,2,3,4,5,7,8},{6}}
[5,3,7,1,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,1,3,7,8,4,2,6]=>{{1,2,4,5,6,7,8},{3}}
[3,6,2,1,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,6,2,5,1,3,8,7]=>{{1,4,5},{2,3,6},{7,8}}
[6,4,2,5,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[8,6,1,7,3,2,4,5]=>{{1,3,5,8},{2,6},{4,7}}
[2,5,8,1,7,3,4,6]=>{{1,2,4,5,7},{3,6,8}}
[6,8,2,7,3,1,4,5]=>{{1,6},{2,3,5,8},{4,7}}
[6,8,2,3,7,1,4,5]=>{{1,6},{2,3,4,5,7,8}}
[8,6,2,7,4,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,2,8,1,7,3,4,6]=>{{1,4,5,7},{2},{3,6,8}}
[4,2,3,8,1,5,6,7]=>{{1,4,5,6,7,8},{2},{3}}
[5,2,8,3,7,1,4,6]=>{{1,3,4,5,6,7,8},{2}}
[5,2,8,4,6,1,3,7]=>{{1,5,6},{2},{3,7,8},{4}}
[2,1,5,8,4,3,6,7]=>{{1,2},{3,4,5,6,7,8}}
[5,8,3,2,7,1,4,6]=>{{1,2,4,5,6,7,8},{3}}
[4,1,3,8,2,5,6,7]=>{{1,2,4,5,6,7,8},{3}}
[3,5,8,2,7,1,4,6]=>{{1,3,6,8},{2,4,5,7}}
[4,5,8,2,6,1,3,7]=>{{1,2,4,5,6},{3,7,8}}
[2,6,8,3,7,1,4,5]=>{{1,2,6},{3,4,5,7,8}}
[5,1,8,3,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,4,6,2,3,7]=>{{1,2,5,6},{3,7,8},{4}}
[5,8,4,1,6,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,8,1,6,2,3,7]=>{{1,4},{2,5,6},{3,7,8}}
[5,4,8,1,6,2,3,7]=>{{1,2,4,5,6},{3,7,8}}
[4,8,5,1,6,2,3,7]=>{{1,4},{2,3,5,6,7,8}}
[2,1,5,4,8,3,6,7]=>{{1,2},{3,5,6,7,8},{4}}
[2,4,3,8,1,5,6,7]=>{{1,2,4,5,6,7,8},{3}}
[3,1,8,4,2,5,6,7]=>{{1,2,3,5,6,7,8},{4}}
[3,8,4,2,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,4,1,5,6,7]=>{{1,2,3,5,6,7,8},{4}}
[3,4,2,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,8,5,2,7,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,2,6,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[2,1,4,8,5,3,6,7]=>{{1,2},{3,4,6,7,8},{5}}
[3,2,8,4,1,5,6,7]=>{{1,3,5,6,7,8},{2},{4}}
[2,8,4,3,1,5,6,7]=>{{1,2,5,6,7,8},{3,4}}
[4,1,7,5,6,2,8,3]=>{{1,2,4,5,6},{3,7,8}}
[5,7,4,3,8,1,6,2]=>{{1,2,5,6,7,8},{3,4}}
[5,7,4,3,8,2,6,1]=>{{1,5,8},{2,6,7},{3,4}}
[3,8,4,2,6,7,5,1]=>{{1,2,3,4,8},{5,6,7}}
[3,8,4,1,6,7,5,2]=>{{1,3,4},{2,8},{5,6,7}}
[6,1,7,5,2,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,6,4,3,2,8,1,7]=>{{1,2,5,6,7,8},{3,4}}
[2,6,7,5,3,8,4,1]=>{{1,2,6,8},{3,4,5,7}}
[6,7,4,8,2,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,1,6,7,5,3,8,4]=>{{1,2},{3,6},{4,7,8},{5}}
[3,8,4,2,1,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[5,7,4,3,8,2,1,6]=>{{1,2,5,6,7,8},{3,4}}
[6,7,4,8,1,2,5,3]=>{{1,2,5,6,7},{3,4,8}}
[6,7,5,8,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,8,3,1,2,5]=>{{1,6},{2,7},{3,4,5,8}}
[3,4,8,1,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[6,1,3,4,8,2,5,7]=>{{1,2,6},{3},{4},{5,7,8}}
[6,2,3,4,8,1,5,7]=>{{1,6},{2},{3},{4},{5,7,8}}
[3,4,8,2,1,5,7,6]=>{{1,3,5,6,8},{2,4},{7}}
[6,7,5,8,2,4,3,1]=>{{1,4,6,8},{2,3,5,7}}
[6,7,5,8,3,1,4,2]=>{{1,6},{2,4,7,8},{3,5}}
[3,4,8,1,5,7,6,2]=>{{1,2,3,4,8},{5},{6,7}}
[2,5,7,6,1,4,8,3]=>{{1,2,5},{3,7,8},{4,6}}
[6,7,4,8,2,3,5,1]=>{{1,3,4,6,8},{2,5,7}}
[6,7,4,8,1,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[2,6,7,5,1,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,4,8,2,5,7]=>{{1,2,3,6},{4},{5,7,8}}
[6,7,4,8,1,3,2,5]=>{{1,3,4,5,6,8},{2,7}}
[6,7,5,8,4,1,3,2]=>{{1,6},{2,3,4,5,7,8}}
[6,7,4,8,2,1,3,5]=>{{1,6},{2,3,4,5,7,8}}
[6,7,4,8,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[1,5,6,3,4,8,2,7]=>{{1},{2,3,4,5,6,7,8}}
[1,4,3,6,5,8,2,7]=>{{1},{2,4,6,7,8},{3},{5}}
[8,1,3,4,7,2,6,5]=>{{1,2,5,6,7,8},{3},{4}}
[5,1,7,3,4,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[6,7,8,2,3,5,4,1]=>{{1,3,5,6,8},{2,4,7}}
[5,8,6,2,3,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,8,3,4,7,5,6,1]=>{{1,2,8},{3},{4},{5,6,7}}
[1,8,3,4,7,6,2,5]=>{{1},{2,5,7,8},{3},{4},{6}}
[8,7,2,3,6,5,4,1]=>{{1,8},{2,3,4,7},{5,6}}
[3,8,1,7,5,2,6,4]=>{{1,3},{2,4,6,7,8},{5}}
[4,8,1,6,7,2,5,3]=>{{1,2,3,4,6,8},{5,7}}
[2,1,3,8,4,6,5,7]=>{{1,2},{3},{4,5,7,8},{6}}
[8,2,1,7,4,3,6,5]=>{{1,3,4,5,6,7,8},{2}}
[1,3,2,8,5,4,6,7]=>{{1},{2,3},{4,6,7,8},{5}}
[8,3,1,5,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,4,5,1,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[1,5,6,8,7,4,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[8,4,5,7,6,3,2,1]=>{{1,8},{2,4,7},{3,5,6}}
[1,4,8,5,7,6,2,3]=>{{1},{2,4,5,7},{3,8},{6}}
[2,4,8,5,7,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,6,5,7,2,1]=>{{1,2,3,4,6,7,8},{5}}
[6,7,2,8,5,3,4,1]=>{{1,2,3,4,6,7,8},{5}}
[5,2,7,8,6,3,4,1]=>{{1,3,4,5,6,7,8},{2}}
[4,2,8,6,7,3,5,1]=>{{1,3,4,6,8},{2},{5,7}}
[3,2,8,7,5,4,6,1]=>{{1,3,8},{2},{4,6,7},{5}}
[3,1,8,7,5,6,2,4]=>{{1,2,3,4,7,8},{5},{6}}
[4,1,8,6,7,5,2,3]=>{{1,2,4,5,6,7},{3,8}}
[5,1,7,8,6,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,8,5,4,2,3]=>{{1,3,4,6,8},{2,7},{5}}
[7,8,3,2,6,1,4,5]=>{{1,2,4,5,6,7,8},{3}}
[3,4,8,2,6,1,7,5]=>{{1,3,5,6,8},{2,4},{7}}
[7,8,4,1,5,6,3,2]=>{{1,3,4,7},{2,8},{5},{6}}
[7,8,1,4,5,6,3,2]=>{{1,3,7},{2,8},{4},{5},{6}}
[7,8,1,2,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,1,4,6,3,2]=>{{1,3,4,5,7},{2,8},{6}}
[7,8,4,5,1,6,3,2]=>{{1,3,4,5,7},{2,8},{6}}
[5,3,8,4,1,6,7,2]=>{{1,5},{2,3,8},{4},{6},{7}}
[6,2,4,8,1,5,3,7]=>{{1,5,6},{2},{3,4,7,8}}
[3,4,8,5,1,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[3,5,8,1,4,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[1,4,8,2,6,3,7,5]=>{{1},{2,4},{3,5,6,8},{7}}
[5,3,8,1,4,6,7,2]=>{{1,4,5},{2,3,8},{6},{7}}
[4,2,6,8,1,5,3,7]=>{{1,3,4,5,6,7,8},{2}}
[7,4,2,8,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[6,1,7,5,8,4,3,2]=>{{1,2,4,5,6,8},{3,7}}
[6,2,1,8,4,5,3,7]=>{{1,3,4,5,6,7,8},{2}}
[1,2,7,8,5,3,4,6]=>{{1},{2},{3,4,6,7,8},{5}}
[6,3,7,8,5,4,1,2]=>{{1,2,3,4,6,7,8},{5}}
[6,1,5,7,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[1,7,5,6,8,4,3,2]=>{{1},{2,3,5,7,8},{4,6}}
[3,1,8,4,5,6,7,2]=>{{1,2,3,8},{4},{5},{6},{7}}
[2,1,4,8,6,5,3,7]=>{{1,2},{3,4,7,8},{5,6}}
[2,4,1,8,6,5,3,7]=>{{1,2,3,4,7,8},{5,6}}
[4,2,1,8,6,5,3,7]=>{{1,3,4,7,8},{2},{5,6}}
[3,2,7,8,5,1,4,6]=>{{1,3,4,6,7,8},{2},{5}}
[2,3,7,8,5,1,4,6]=>{{1,2,3,4,6,7,8},{5}}
[2,7,3,8,5,1,4,6]=>{{1,2,4,6,7,8},{3},{5}}
[3,6,2,8,5,1,4,7]=>{{1,2,3,6},{4,7,8},{5}}
[4,1,2,8,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[1,4,2,8,7,5,3,6]=>{{1},{2,3,4,5,6,7,8}}
[7,3,6,8,5,4,1,2]=>{{1,7},{2,3,4,6,8},{5}}
[7,2,1,8,5,3,4,6]=>{{1,3,4,6,7,8},{2},{5}}
[1,2,6,8,4,5,3,7]=>{{1},{2},{3,4,5,6,7,8}}
[7,1,6,5,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,7,1,8,4,3,2]=>{{1,4,6},{2,5,8},{3,7}}
[5,7,6,1,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,5,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,3,8,5,4,1,2]=>{{1,2,4,6,7,8},{3},{5}}
[7,1,2,8,4,5,3,6]=>{{1,2,3,7},{4,5,6,8}}
[7,6,1,5,8,4,3,2]=>{{1,3,7},{2,4,5,6,8}}
[7,5,6,1,8,4,3,2]=>{{1,3,4,6,7},{2,5,8}}
[7,1,6,5,3,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[1,8,7,5,3,2,4,6]=>{{1},{2,6,8},{3,4,5,7}}
[1,8,7,4,2,5,3,6]=>{{1},{2,5,6,8},{3,7},{4}}
[8,7,4,2,5,3,6,1]=>{{1,8},{2,3,4,6,7},{5}}
[7,1,6,4,2,5,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[2,6,5,4,7,1,3,8]=>{{1,2,6},{3,5,7},{4},{8}}
[7,1,5,3,6,4,2,8]=>{{1,2,7},{3,4,5,6},{8}}
[5,3,7,1,6,4,2,8]=>{{1,4,5,6},{2,3,7},{8}}
[5,3,6,4,2,7,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[1,5,3,8,7,4,2,6]=>{{1},{2,5,7},{3},{4,6,8}}
[7,4,2,8,6,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,1,8,7,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,1,5,3,8,7,4,2]=>{{1,2,3,4,5,6,7,8}}
[2,8,7,5,4,6,1,3]=>{{1,2,3,7,8},{4,5},{6}}
[2,3,1,8,7,5,4,6]=>{{1,2,3},{4,5,6,7,8}}
[5,3,8,7,4,2,1,6]=>{{1,4,5,7},{2,3,6,8}}
[7,4,2,1,8,6,3,5]=>{{1,2,3,4,7},{5,8},{6}}
[8,6,3,5,7,4,2,1]=>{{1,8},{2,4,5,6,7},{3}}
[1,8,6,3,5,7,4,2]=>{{1},{2,8},{3,4,6,7},{5}}
[6,3,8,5,2,1,7,4]=>{{1,6},{2,3,4,5,8},{7}}
[8,6,3,7,4,2,1,5]=>{{1,4,5,7,8},{2,6},{3}}
[2,8,6,4,7,5,1,3]=>{{1,2,3,5,6,7,8},{4}}
[5,1,8,6,3,7,4,2]=>{{1,2,3,5,8},{4,6,7}}
[6,3,7,4,1,8,5,2]=>{{1,2,3,5,6,7,8},{4}}
[8,5,2,6,3,7,4,1]=>{{1,8},{2,3,5},{4,6,7}}
[6,1,8,7,4,2,5,3]=>{{1,2,6},{3,8},{4,5,7}}
[8,6,3,7,4,2,5,1]=>{{1,8},{2,6},{3},{4,5,7}}
[1,8,6,3,2,4,7,5]=>{{1},{2,5,8},{3,4,6},{7}}
[8,6,3,2,4,7,5,1]=>{{1,8},{2,4,5,6,7},{3}}
[7,5,1,8,6,3,2,4]=>{{1,2,3,5,6,7},{4,8}}
[6,1,8,7,5,3,2,4]=>{{1,2,3,4,6,7,8},{5}}
[4,3,2,8,7,6,1,5]=>{{1,4,5,7,8},{2,3},{6}}
[2,4,5,1,3,8,7,6]=>{{1,2,4},{3,5},{6,8},{7}}
[7,5,8,6,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[1,7,5,8,6,3,2,4]=>{{1},{2,7},{3,5,6},{4,8}}
[1,7,4,2,5,8,6,3]=>{{1},{2,3,4,6,7,8},{5}}
[8,6,3,1,7,4,2,5]=>{{1,2,4,5,6,7,8},{3}}
[8,7,4,2,5,3,1,6]=>{{1,2,3,4,6,7,8},{5}}
[5,3,1,8,7,4,2,6]=>{{1,2,3,5,7},{4,6,8}}
[4,1,8,7,5,3,2,6]=>{{1,2,4,7},{3,6,8},{5}}
[2,8,6,4,1,3,7,5]=>{{1,2,5,8},{3,6},{4},{7}}
[4,1,8,6,3,2,7,5]=>{{1,2,4,6},{3,5,8},{7}}
[7,4,2,8,6,3,1,5]=>{{1,7},{2,3,4,5,6,8}}
[6,3,1,8,5,2,7,4]=>{{1,2,3,6},{4,8},{5},{7}}
[8,5,2,6,3,1,7,4]=>{{1,4,6,8},{2,3,5},{7}}
[7,4,8,5,2,6,3,1]=>{{1,3,7,8},{2,4,5},{6}}
[1,8,5,2,7,4,6,3]=>{{1},{2,3,4,5,6,7,8}}
[8,5,2,7,4,6,3,1]=>{{1,8},{2,3,4,5,7},{6}}
[7,4,6,3,1,8,5,2]=>{{1,5,7},{2,3,4,6,8}}
[6,3,1,7,4,8,5,2]=>{{1,2,3,6,8},{4,5,7}}
[8,6,3,1,5,7,4,2]=>{{1,2,4,6,7,8},{3},{5}}
[4,1,7,5,8,6,3,2]=>{{1,2,4,5,8},{3,7},{6}}
[2,3,1,7,5,8,6,4]=>{{1,2,3},{4,6,7,8},{5}}
[7,4,8,5,2,1,6,3]=>{{1,6,7},{2,4,5},{3,8}}
[8,5,2,1,7,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[1,7,4,6,3,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,8,5,7,3,2,6]=>{{1,2,4,5,7},{3,6,8}}
[2,1,5,7,8,4,3,6]=>{{1,2},{3,4,5,6,7,8}}
[5,1,7,4,8,3,2,6]=>{{1,2,3,5,6,7,8},{4}}
[4,7,2,8,3,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[4,6,2,7,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,2,8,4,1,7,3,5]=>{{1,3,5,6,7,8},{2},{4}}
[6,3,4,8,1,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[1,8,5,4,2,3,7,6]=>{{1},{2,3,5,6,8},{4},{7}}
[3,5,4,8,1,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,6,3,8,7,1,2,4]=>{{1,2,5,6,7},{3},{4,8}}
[2,6,8,4,1,7,3,5]=>{{1,2,3,5,6,7,8},{4}}
[1,8,7,4,2,6,3,5]=>{{1},{2,5,8},{3,7},{4},{6}}
[6,3,5,8,7,1,2,4]=>{{1,6},{2,3,5,7},{4,8}}
[5,2,8,6,7,1,3,4]=>{{1,3,4,5,6,7,8},{2}}
[6,2,8,7,5,1,3,4]=>{{1,6},{2},{3,4,7,8},{5}}
[1,8,5,7,6,2,3,4]=>{{1},{2,3,4,5,6,7,8}}
[3,6,7,8,5,1,2,4]=>{{1,2,3,6,7},{4,8},{5}}
[1,8,6,7,5,2,3,4]=>{{1},{2,3,4,6,7,8},{5}}
[5,7,6,4,8,1,2,3]=>{{1,3,5,6,8},{2,7},{4}}
[6,3,8,7,5,1,2,4]=>{{1,6},{2,3,4,7,8},{5}}
[2,8,7,4,1,3,5,6]=>{{1,2,3,5,6,7,8},{4}}
[5,4,8,7,1,3,2,6]=>{{1,5},{2,4,7},{3,6,8}}
[4,8,6,1,3,2,5,7]=>{{1,4},{2,3,5,6,7,8}}
[5,4,2,7,6,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[2,8,7,1,4,5,3,6]=>{{1,2,4,5,6,8},{3,7}}
[4,2,1,8,7,3,5,6]=>{{1,3,4,6,8},{2},{5,7}}
[5,1,6,3,2,8,7,4]=>{{1,2,5},{3,4,6,8},{7}}
[4,6,1,8,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,2,3,5,4,1,6]=>{{1,2,3,4,6,7,8},{5}}
[5,3,1,4,8,7,2,6]=>{{1,2,3,5,6,7,8},{4}}
[4,3,5,2,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,2,8,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,8,1,5,2,4]=>{{1,3,5,6},{2,7},{4,8}}
[8,1,4,2,3,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[3,7,2,1,8,6,4,5]=>{{1,2,3,4,7},{5,8},{6}}
[2,8,6,1,7,3,5,4]=>{{1,2,4,8},{3,6},{5,7}}
[1,7,6,3,5,8,2,4]=>{{1},{2,7},{3,4,6,8},{5}}
[3,7,5,1,6,8,2,4]=>{{1,3,4,5,6,8},{2,7}}
[3,6,5,8,1,4,7,2]=>{{1,3,5},{2,4,6,8},{7}}
[8,1,5,6,4,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,4,1,8,2,5]=>{{1,2,3,5,6,7,8},{4}}
[1,7,4,6,8,2,5,3]=>{{1},{2,3,4,5,6,7,8}}
[7,5,8,2,6,3,1,4]=>{{1,7},{2,3,4,5,6,8}}
[2,7,1,6,5,4,8,3]=>{{1,2,3,7,8},{4,6},{5}}
[7,3,2,6,1,8,5,4]=>{{1,5,7},{2,3},{4,6,8}}
[6,4,7,2,3,1,8,5]=>{{1,6},{2,4},{3,5,7,8}}
[5,3,1,8,4,6,2,7]=>{{1,2,3,4,5,7,8},{6}}
[3,8,1,6,7,4,2,5]=>{{1,3},{2,5,7,8},{4,6}}
[2,7,4,3,6,8,1,5]=>{{1,2,7},{3,4},{5,6,8}}
[2,8,4,6,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,6,3,2,5,7]=>{{1,3,5,7,8},{2,4,6}}
[4,7,3,8,5,2,1,6]=>{{1,2,4,6,7,8},{3},{5}}
[3,1,7,4,8,5,2,6]=>{{1,2,3,7},{4},{5,6,8}}
[7,4,1,6,3,2,8,5]=>{{1,3,5,7,8},{2,4,6}}
[3,8,6,2,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[7,3,1,4,5,2,8,6]=>{{1,2,3,6,7,8},{4},{5}}
[6,1,4,8,5,3,2,7]=>{{1,2,3,4,6,7,8},{5}}
[8,1,2,4,6,7,5,3]=>{{1,2,3,8},{4},{5,6,7}}
[8,1,3,6,7,5,4,2]=>{{1,2,8},{3},{4,5,6,7}}
[7,5,2,3,8,6,1,4]=>{{1,7},{2,3,4,5,8},{6}}
[8,6,2,4,1,3,7,5]=>{{1,5,8},{2,3,6},{4},{7}}
[4,7,5,1,8,6,3,2]=>{{1,4},{2,3,5,7,8},{6}}
[4,7,3,2,8,5,6,1]=>{{1,2,4,5,6,7,8},{3}}
[8,4,5,7,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,4,2,3,6,1]=>{{1,3,6,7,8},{2,5},{4}}
[3,8,4,6,1,7,5,2]=>{{1,3,4,5,6,7},{2,8}}
[3,7,4,6,5,2,8,1]=>{{1,2,3,4,6,7,8},{5}}
[4,2,7,6,1,5,8,3]=>{{1,4,5,6},{2},{3,7,8}}
[8,3,1,4,5,7,6,2]=>{{1,2,3,8},{4},{5},{6,7}}
[3,5,1,6,8,4,7,2]=>{{1,3},{2,5,8},{4,6},{7}}
[6,1,5,7,3,8,4,2]=>{{1,2,6,8},{3,5},{4,7}}
[5,8,4,7,3,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,2,6,5,8,4,1,3]=>{{1,7},{2},{3,4,5,6,8}}
[8,3,2,5,1,6,7,4]=>{{1,4,5,8},{2,3},{6},{7}}
[2,6,8,3,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,5,6,4,7,3,2]=>{{1,2,8},{3,4,5,6,7}}
[2,5,8,1,6,4,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[7,4,1,8,3,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,4,2,1,6,5]=>{{1,2,3,5,6,7,8},{4}}
[5,2,6,8,3,1,7,4]=>{{1,3,5,6},{2},{4,8},{7}}
[3,6,5,8,4,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[7,3,6,1,8,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,2,7,3,4,6,5,1]=>{{1,8},{2},{3,4,5,7},{6}}
[7,3,8,2,5,6,4,1]=>{{1,2,3,4,7,8},{5},{6}}
[5,7,3,1,6,4,8,2]=>{{1,4,5,6},{2,7,8},{3}}
[6,1,3,2,4,8,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[8,7,4,2,3,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[8,7,1,5,4,2,3,6]=>{{1,2,3,6,7,8},{4,5}}
[3,7,1,5,2,8,6,4]=>{{1,3},{2,4,5,6,7,8}}
[8,7,2,5,4,1,3,6]=>{{1,6,8},{2,3,7},{4,5}}
[8,7,2,5,3,1,4,6]=>{{1,6,8},{2,3,4,5,7}}
[5,2,8,7,1,4,3,6]=>{{1,5},{2},{3,4,6,7,8}}
[7,1,8,6,2,4,3,5]=>{{1,2,3,5,7,8},{4,6}}
[8,1,6,2,7,5,3,4]=>{{1,2,4,8},{3,5,6,7}}
[7,1,6,2,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,3,4,1,7,2,8,5]=>{{1,2,3,4,6},{5,7,8}}
[7,2,4,3,5,1,8,6]=>{{1,6,7,8},{2},{3,4},{5}}
[5,1,7,2,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,2,3,5,1,7,6,4]=>{{1,4,5,8},{2},{3},{6,7}}
[7,6,3,1,4,8,2,5]=>{{1,2,4,5,6,7,8},{3}}
[6,1,8,2,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,2,8,1,6,5,3,4]=>{{1,3,4,7,8},{2},{5,6}}
[7,2,6,4,3,8,1,5]=>{{1,7},{2},{3,5,6,8},{4}}
[5,1,7,4,3,8,2,6]=>{{1,2,3,5,7},{4},{6,8}}
[5,3,1,7,4,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[7,4,8,2,1,5,3,6]=>{{1,3,5,6,7,8},{2,4}}
[8,2,4,1,6,3,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[8,2,7,5,1,6,4,3]=>{{1,3,4,5,7,8},{2},{6}}
[6,1,7,3,2,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[4,7,2,1,6,3,8,5]=>{{1,4},{2,3,5,6,7,8}}
[6,2,1,5,3,8,4,7]=>{{1,3,4,5,6,7,8},{2}}
[5,3,1,6,2,8,4,7]=>{{1,2,3,5},{4,6,7,8}}
[6,1,5,2,8,4,3,7]=>{{1,2,4,6},{3,5,7,8}}
[7,4,3,8,1,5,2,6]=>{{1,2,4,5,6,7,8},{3}}
[7,4,8,1,5,3,2,6]=>{{1,2,4,7},{3,6,8},{5}}
[6,1,5,3,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[6,3,2,8,4,1,5,7]=>{{1,6},{2,3},{4,5,7,8}}
[7,3,4,2,8,5,1,6]=>{{1,7},{2,3,4},{5,6,8}}
[7,1,6,3,4,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[8,5,1,3,7,4,2,6]=>{{1,3,4,6,8},{2,5,7}}
[3,8,6,1,5,2,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[8,6,1,3,7,5,2,4]=>{{1,3,4,8},{2,5,6,7}}
[4,8,5,6,1,7,3,2]=>{{1,3,4,5,6,7},{2,8}}
[6,7,1,3,8,5,2,4]=>{{1,3,4,5,6,8},{2,7}}
[3,6,7,1,5,2,8,4]=>{{1,3,4,7,8},{2,6},{5}}
[7,1,3,8,4,2,6,5]=>{{1,2,6,7},{3},{4,5,8}}
[5,6,2,7,1,3,8,4]=>{{1,5},{2,3,6},{4,7,8}}
[5,6,2,8,1,3,7,4]=>{{1,5},{2,3,6},{4,8},{7}}
[6,1,8,3,7,5,2,4]=>{{1,2,5,6,7},{3,4,8}}
[7,4,2,1,5,8,3,6]=>{{1,2,3,4,7},{5},{6,8}}
[7,4,1,5,8,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[7,3,2,6,4,8,1,5]=>{{1,7},{2,3},{4,5,6,8}}
[6,4,2,7,3,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,3,7,4,2,6]=>{{1,2,5,7},{3,4,6,8}}
[7,4,8,3,1,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[5,2,1,7,4,8,3,6]=>{{1,3,4,5,7},{2},{6,8}}
[6,1,8,4,5,2,7,3]=>{{1,2,6},{3,8},{4},{5},{7}}
[7,1,6,4,5,2,8,3]=>{{1,2,3,6,7,8},{4},{5}}
[3,5,2,7,1,6,8,4]=>{{1,2,3,5},{4,7,8},{6}}
[4,5,7,3,1,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[4,5,7,2,8,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[3,5,1,7,2,6,8,4]=>{{1,3},{2,5},{4,7,8},{6}}
[4,5,7,2,8,1,3,6]=>{{1,2,4,5,6,8},{3,7}}
[4,6,7,2,1,5,8,3]=>{{1,2,4,5,6},{3,7,8}}
[4,6,7,1,3,8,5,2]=>{{1,4},{2,6,8},{3,5,7}}
[3,6,1,5,7,8,4,2]=>{{1,3},{2,6,8},{4,5,7}}
[4,6,7,1,5,8,3,2]=>{{1,4},{2,6,8},{3,7},{5}}
[6,1,3,7,4,8,5,2]=>{{1,2,6,8},{3},{4,5,7}}
[3,2,1,7,4,8,5,6]=>{{1,3},{2},{4,5,7},{6,8}}
[4,1,5,2,7,6,3,8]=>{{1,2,4},{3,5,7},{6},{8}}
[2,5,1,3,7,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}
[2,5,1,4,3,8,6,7]=>{{1,2,3,5},{4},{6,7,8}}
[3,7,2,1,5,8,6,4]=>{{1,2,3,4,6,7,8},{5}}
[6,2,7,1,4,8,5,3]=>{{1,3,4,5,6,7,8},{2}}
[3,7,4,2,1,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[7,2,5,3,1,8,6,4]=>{{1,3,4,5,6,7,8},{2}}
[7,5,1,4,2,8,6,3]=>{{1,3,6,7,8},{2,5},{4}}
[7,5,4,1,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,2,1,7,6,4,8]=>{{1,4,5,7},{2,3},{6},{8}}
[6,3,2,8,1,5,7,4]=>{{1,5,6},{2,3},{4,8},{7}}
[7,4,3,2,8,1,6,5]=>{{1,6,7},{2,4},{3},{5,8}}
[7,6,2,4,8,3,5,1]=>{{1,5,7,8},{2,3,6},{4}}
[7,3,6,4,8,1,5,2]=>{{1,2,3,5,6,7,8},{4}}
[2,7,5,3,8,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[1,8,5,3,6,4,2,7]=>{{1},{2,7,8},{3,4,5,6}}
[8,6,2,3,7,5,4,1]=>{{1,8},{2,3,4,5,6,7}}
[8,6,3,2,7,5,4,1]=>{{1,8},{2,4,5,6,7},{3}}
[8,3,2,7,1,6,4,5]=>{{1,5,8},{2,3},{4,7},{6}}
[7,2,6,1,5,4,3,8]=>{{1,3,4,6,7},{2},{5},{8}}
[8,5,7,4,3,6,2,1]=>{{1,8},{2,3,5,7},{4},{6}}
[8,5,7,2,4,6,3,1]=>{{1,8},{2,4,5},{3,7},{6}}
[8,4,6,7,1,3,2,5]=>{{1,5,8},{2,4,7},{3,6}}
[2,8,5,6,1,4,3,7]=>{{1,2,3,5,7,8},{4,6}}
[7,2,6,8,4,1,5,3]=>{{1,3,4,5,6,7,8},{2}}
[7,6,4,8,3,2,5,1]=>{{1,3,4,5,7,8},{2,6}}
[6,5,8,1,4,2,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[6,5,8,4,1,3,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[5,4,8,3,2,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,3,7,2,1,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[2,5,8,1,4,3,7,6]=>{{1,2,4,5},{3,6,8},{7}}
[3,6,8,2,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[5,7,4,8,1,3,6,2]=>{{1,5},{2,3,4,6,7,8}}
[5,7,1,4,8,2,6,3]=>{{1,3,5,8},{2,6,7},{4}}
[2,7,4,1,8,3,6,5]=>{{1,2,3,4,6,7},{5,8}}
[3,5,1,8,4,2,7,6]=>{{1,3},{2,4,5,6,8},{7}}
[4,1,5,7,3,6,2,8]=>{{1,2,4,7},{3,5},{6},{8}}
[4,2,5,8,3,1,7,6]=>{{1,4,6,8},{2},{3,5},{7}}
[6,1,2,7,8,3,5,4]=>{{1,2,3,6},{4,5,7,8}}
[5,3,1,8,6,4,2,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,4,7,5,2,6]=>{{1,2,3,5,6,7,8},{4}}
[4,2,8,7,3,5,1,6]=>{{1,4,7},{2},{3,5,6,8}}
[4,8,1,7,6,2,3,5]=>{{1,3,4,7},{2,5,6,8}}
[6,8,1,4,7,5,2,3]=>{{1,2,3,5,6,7,8},{4}}
[7,3,8,1,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,1,5,3,2,6]=>{{1,4},{2,7},{3,6,8},{5}}
[7,1,8,6,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,1,3,6,4,2]=>{{1,3,4,5,7},{2,8},{6}}
[3,8,7,2,1,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[2,8,7,1,6,3,5,4]=>{{1,2,4,8},{3,5,6,7}}
[3,7,6,1,5,4,2,8]=>{{1,3,4,6},{2,7},{5},{8}}
[4,8,7,6,1,3,5,2]=>{{1,3,4,5,6,7},{2,8}}
[5,8,7,2,6,1,4,3]=>{{1,5,6},{2,3,4,7,8}}
[6,8,1,7,5,2,4,3]=>{{1,2,3,6,8},{4,7},{5}}
[7,3,8,6,5,1,2,4]=>{{1,2,3,4,6,7,8},{5}}
[5,7,8,4,3,1,2,6]=>{{1,3,5,6,8},{2,7},{4}}
[5,8,6,4,3,2,1,7]=>{{1,2,3,5,6,7,8},{4}}
[8,7,3,6,4,2,1,5]=>{{1,2,4,5,6,7,8},{3}}
[6,1,4,2,5,3,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[1,3,7,5,4,2,8,6]=>{{1},{2,3,6,7,8},{4,5}}
[6,1,3,5,4,2,7,8]=>{{1,2,6},{3},{4,5},{7},{8}}
[6,1,2,5,4,7,3,8]=>{{1,2,3,6,7},{4,5},{8}}
[5,1,6,3,4,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[5,2,6,3,4,7,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,4,7,5,8,6,1,2]=>{{1,3,7},{2,4,5,8},{6}}
[2,4,7,1,5,3,8,6]=>{{1,2,4},{3,6,7,8},{5}}
[2,3,6,7,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[1,3,6,7,4,8,5,2]=>{{1},{2,3,6,8},{4,5,7}}
[2,7,6,5,3,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,2,6,1,4,7,8,3]=>{{1,4,5},{2},{3,6,7,8}}
[4,7,6,5,2,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,2,4,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,7,4,2,1,3,6,8]=>{{1,5},{2,3,4,6,7},{8}}
[6,3,1,5,4,7,8,2]=>{{1,2,3,6,7,8},{4,5}}
[5,3,6,1,4,2,7,8]=>{{1,4,5},{2,3,6},{7},{8}}
[1,7,4,2,6,3,8,5]=>{{1},{2,3,4,5,6,7,8}}
[5,7,4,1,2,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[6,4,1,2,5,3,7,8]=>{{1,3,6},{2,4},{5},{7},{8}}
[4,7,6,3,8,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,5,2,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,5,1,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[4,7,2,6,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,7,1,6,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,5,8,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,2,8,7,6,4,3,1]=>{{1,3,4,5,6,7,8},{2}}
[8,2,7,6,1,5,4,3]=>{{1,3,4,5,6,7,8},{2}}
[8,4,1,7,6,5,3,2]=>{{1,2,3,4,7,8},{5,6}}
[4,5,6,2,3,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,3,2,7,8,1,6]=>{{1,2,4,5,7},{3},{6,8}}
[6,5,7,3,8,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,2,4,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,2,7,4,5,8,1,6]=>{{1,3,7},{2},{4},{5},{6,8}}
[6,8,1,5,2,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,6,1,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,4,7,5,8,1,6]=>{{1,2,3,4,7},{5},{6,8}}
[6,3,4,7,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,4,8,6,1,2]=>{{1,2,3,5,7,8},{4},{6}}
[8,3,6,4,1,7,2,5]=>{{1,5,8},{2,3,6,7},{4}}
[1,3,7,4,8,6,2,5]=>{{1},{2,3,7},{4},{5,8},{6}}
[3,7,8,5,4,1,2,6]=>{{1,3,6,8},{2,7},{4,5}}
[5,4,3,1,7,8,2,6]=>{{1,2,4,5,7},{3},{6,8}}
[5,7,6,2,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,1,7,5,8,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,6,4,1,3,8,2]=>{{1,2,5,7,8},{3,6},{4}}
[1,5,6,8,4,7,3,2]=>{{1},{2,4,5,8},{3,6,7}}
[4,1,3,7,6,5,8,2]=>{{1,2,4,7,8},{3},{5,6}}
[3,4,1,7,5,8,6,2]=>{{1,3},{2,4,6,7,8},{5}}
[8,5,7,4,3,1,6,2]=>{{1,2,3,5,6,7,8},{4}}
[6,8,5,1,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[8,2,4,1,3,7,6,5]=>{{1,3,4,5,8},{2},{6,7}}
[7,8,3,6,2,1,4,5]=>{{1,4,6,7},{2,5,8},{3}}
[8,1,7,4,2,3,6,5]=>{{1,2,5,8},{3,6,7},{4}}
[1,8,7,2,3,5,6,4]=>{{1},{2,4,8},{3,5,6,7}}
[2,8,3,1,6,7,5,4]=>{{1,2,4,8},{3},{5,6,7}}
[8,2,3,1,5,7,6,4]=>{{1,4,8},{2},{3},{5},{6,7}}
[3,8,4,1,2,7,6,5]=>{{1,3,4},{2,5,8},{6,7}}
[5,4,7,2,3,6,8,1]=>{{1,3,5,7,8},{2,4},{6}}
[6,3,2,1,8,4,7,5]=>{{1,4,6},{2,3},{5,8},{7}}
[2,3,7,4,1,8,5,6]=>{{1,2,3,5,7},{4},{6,8}}
[6,4,1,3,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,5,1,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,2,5,6,7,1,3,4]=>{{1,4,6,8},{2},{3,5,7}}
[2,8,5,4,7,6,1,3]=>{{1,2,3,5,7,8},{4},{6}}
[6,7,1,5,8,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,6,2,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,5,3,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,7,3,8,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,7,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[7,3,4,6,1,5,8,2]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,5,7,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,2,6,8,3,1,5,7]=>{{1,3,4,5,6,7,8},{2}}
[3,7,6,2,4,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[2,3,6,5,8,1,4,7]=>{{1,2,3,6},{4,5,7,8}}
[2,3,5,8,6,1,4,7]=>{{1,2,3,5,6},{4,7,8}}
[4,2,3,8,6,1,5,7]=>{{1,4,5,6,7,8},{2},{3}}
[6,4,1,2,8,3,5,7]=>{{1,3,6},{2,4},{5,7,8}}
[1,2,3,7,4,6,8,5]=>{{1},{2},{3},{4,5,7,8},{6}}
[3,2,7,1,4,5,8,6]=>{{1,3,4,5,6,7,8},{2}}
[2,1,5,3,8,7,4,6]=>{{1,2},{3,4,5,6,7,8}}
[5,8,3,2,4,1,6,7]=>{{1,2,4,5,6,7,8},{3}}
[4,2,7,1,8,3,5,6]=>{{1,4},{2},{3,5,6,7,8}}
[4,1,8,2,7,3,5,6]=>{{1,2,4},{3,6,8},{5,7}}
[1,2,7,5,3,8,4,6]=>{{1},{2},{3,4,5,7},{6,8}}
[3,2,7,1,4,8,5,6]=>{{1,3,4,5,7},{2},{6,8}}
[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[1,2,3,6,8,7,4,5]=>{{1},{2},{3},{4,6,7},{5,8}}
[1,2,3,7,8,4,6,5]=>{{1},{2},{3},{4,6,7},{5,8}}
[1,2,3,6,8,4,7,5]=>{{1},{2},{3},{4,6},{5,8},{7}}
[1,2,3,7,8,6,4,5]=>{{1},{2},{3},{4,7},{5,8},{6}}
[6,2,8,3,7,5,1,4]=>{{1,5,6,7},{2},{3,4,8}}
[4,2,8,3,7,5,6,1]=>{{1,3,4,8},{2},{5,6,7}}
[7,3,4,8,6,5,1,2]=>{{1,7},{2,3,4,8},{5,6}}
[5,3,4,8,7,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,5,8,7,2,6,1]=>{{1,4,8},{2,3,5,6,7}}
[4,6,3,8,5,7,2,1]=>{{1,4,8},{2,6,7},{3},{5}}
[7,5,3,8,6,2,4,1]=>{{1,4,7,8},{2,5,6},{3}}
[2,6,8,3,7,4,5,1]=>{{1,2,3,4,6,8},{5,7}}
[1,8,4,3,7,5,6,2]=>{{1},{2,8},{3,4},{5,6,7}}
[2,5,8,3,7,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,3,8,6,2,5,1]=>{{1,2,4,5,6,7,8},{3}}
[3,5,4,8,7,2,6,1]=>{{1,3,4,8},{2,5,6,7}}
[4,5,3,8,6,7,2,1]=>{{1,4,8},{2,5,6,7},{3}}
[3,6,7,8,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[2,6,8,5,4,7,3,1]=>{{1,2,3,6,7,8},{4,5}}
[1,8,5,6,4,7,3,2]=>{{1},{2,8},{3,4,5,6,7}}
[2,5,8,6,4,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,5,8,3,2,1]=>{{1,2,4,5,7,8},{3,6}}
[6,3,7,8,4,5,2,1]=>{{1,4,5,6,8},{2,3,7}}
[4,3,7,8,5,6,2,1]=>{{1,4,8},{2,3,7},{5},{6}}
[5,2,8,6,4,7,3,1]=>{{1,3,4,5,6,7,8},{2}}
[4,2,8,6,5,7,3,1]=>{{1,3,4,6,7,8},{2},{5}}
[3,2,8,6,7,4,5,1]=>{{1,3,8},{2},{4,6},{5,7}}
[2,3,8,7,5,4,6,1]=>{{1,2,3,8},{4,6,7},{5}}
[1,8,2,7,4,5,6,3]=>{{1},{2,3,8},{4,5,6,7}}
[7,2,8,6,3,4,5,1]=>{{1,3,5,7,8},{2},{4,6}}
[6,2,8,4,5,7,3,1]=>{{1,3,6,7,8},{2},{4},{5}}
[5,2,8,4,6,7,3,1]=>{{1,3,5,6,7,8},{2},{4}}
[4,2,8,5,6,7,3,1]=>{{1,3,4,5,6,7,8},{2}}
[4,3,6,8,5,7,2,1]=>{{1,4,8},{2,3,6,7},{5}}
[3,4,6,8,7,2,5,1]=>{{1,2,3,4,6,8},{5,7}}
[7,3,5,8,6,2,4,1]=>{{1,4,7,8},{2,3,5,6}}
[1,8,3,5,7,4,6,2]=>{{1},{2,8},{3},{4,5,6,7}}
[2,7,8,4,5,6,3,1]=>{{1,2,3,7,8},{4},{5},{6}}
[3,7,5,8,4,6,2,1]=>{{1,3,4,5,8},{2,7},{6}}
[5,7,4,6,8,3,2,1]=>{{1,5,8},{2,7},{3,4,6}}
[3,6,5,8,4,7,2,1]=>{{1,3,4,5,8},{2,6,7}}
[2,6,8,4,5,7,3,1]=>{{1,2,3,6,7,8},{4},{5}}
[4,2,7,1,3,8,5,6]=>{{1,4},{2},{3,5,7},{6,8}}
[4,2,5,1,3,8,6,7]=>{{1,4},{2},{3,5},{6,7,8}}
[5,3,6,1,7,2,4,8]=>{{1,4,5,7},{2,3,6},{8}}
[3,7,1,2,5,8,6,4]=>{{1,3},{2,4,6,7,8},{5}}
[3,7,4,1,2,8,5,6]=>{{1,3,4},{2,5,7},{6,8}}
[7,5,1,3,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,2,4,8,6,3]=>{{1,3,6,7,8},{2,4,5}}
[6,4,2,3,7,1,5,8]=>{{1,6},{2,3,4},{5,7},{8}}
[7,6,3,8,1,2,5,4]=>{{1,5,7},{2,6},{3},{4,8}}
[7,4,2,3,8,1,6,5]=>{{1,6,7},{2,3,4},{5,8}}
[4,7,5,2,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[8,2,6,3,7,1,4,5]=>{{1,3,4,5,6,7,8},{2}}
[8,6,1,2,7,4,5,3]=>{{1,3,8},{2,4,6},{5,7}}
[8,4,7,1,2,3,6,5]=>{{1,2,4,5,8},{3,6,7}}
[8,5,7,1,2,4,6,3]=>{{1,3,4,6,7,8},{2,5}}
[8,5,7,1,3,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,7,1,3,5,4]=>{{1,4,5,7,8},{2,3,6}}
[3,8,5,6,1,2,4,7]=>{{1,3,5},{2,4,6,7,8}}
[3,7,5,8,1,2,4,6]=>{{1,3,5},{2,4,6,7,8}}
[7,6,4,8,1,3,5,2]=>{{1,5,7},{2,3,4,6,8}}
[6,5,8,1,2,4,7,3]=>{{1,4,6},{2,5},{3,8},{7}}
[3,6,8,1,2,5,7,4]=>{{1,3,4,8},{2,5,6},{7}}
[3,7,2,4,8,1,6,5]=>{{1,2,3,6,7},{4},{5,8}}
[4,6,3,8,1,2,5,7]=>{{1,4,5,7,8},{2,6},{3}}
[4,6,3,7,1,2,5,8]=>{{1,4,5,7},{2,6},{3},{8}}
[4,1,7,8,2,3,6,5]=>{{1,2,4,5,8},{3,6,7}}
[5,1,2,8,6,3,4,7]=>{{1,2,3,5,6},{4,7,8}}
[5,3,8,1,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[6,1,8,5,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[6,1,7,5,2,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,8,1,3,7,4,5,2]=>{{1,3,4,6},{2,8},{5,7}}
[7,2,8,1,6,3,4,5]=>{{1,4,7},{2},{3,5,6,8}}
[4,7,8,2,5,1,3,6]=>{{1,2,3,4,6,7,8},{5}}
[6,8,2,7,1,4,5,3]=>{{1,4,5,6,7},{2,3,8}}
[4,8,7,1,3,5,6,2]=>{{1,4},{2,8},{3,5,6,7}}
[3,8,7,1,2,4,6,5]=>{{1,3,4,6,7},{2,5,8}}
[4,8,7,1,2,3,6,5]=>{{1,4},{2,5,8},{3,6,7}}
[5,8,7,1,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,1,3,4,6,2]=>{{1,3,4,5,6,7},{2,8}}
[7,1,8,6,2,3,5,4]=>{{1,2,5,7},{3,4,6,8}}
[5,8,6,4,1,2,3,7]=>{{1,5},{2,3,6,7,8},{4}}
[7,8,4,1,2,5,3,6]=>{{1,3,4,7},{2,5,6,8}}
[7,8,1,2,6,5,3,4]=>{{1,3,7},{2,4,8},{5,6}}
[1,4,8,2,7,5,3,6]=>{{1},{2,4},{3,5,6,7,8}}
[6,1,3,4,7,2,5,8]=>{{1,2,6},{3},{4},{5,7},{8}}
[7,8,2,1,6,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[6,1,2,7,5,4,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[1,2,8,7,5,4,3,6]=>{{1},{2},{3,4,6,7,8},{5}}
[5,1,7,3,6,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[6,2,1,5,7,4,3,8]=>{{1,3,4,5,6,7},{2},{8}}
[6,2,3,7,4,1,5,8]=>{{1,6},{2},{3},{4,5,7},{8}}
[3,4,8,7,5,6,1,2]=>{{1,2,3,4,7,8},{5},{6}}
[2,3,8,7,4,1,5,6]=>{{1,2,3,6,8},{4,5,7}}
[2,7,3,8,6,4,1,5]=>{{1,2,7},{3},{4,5,6,8}}
[1,8,3,7,6,4,5,2]=>{{1},{2,8},{3},{4,5,6,7}}
[5,2,7,1,4,6,8,3]=>{{1,4,5},{2},{3,7,8},{6}}
[4,6,7,5,2,1,8,3]=>{{1,2,4,5,6},{3,7,8}}
[6,3,1,4,5,7,8,2]=>{{1,2,3,6,7,8},{4},{5}}
[5,3,1,4,6,2,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[5,1,2,4,7,6,8,3]=>{{1,2,3,5,7,8},{4},{6}}
[5,7,4,1,2,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,8,1,2,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[4,1,7,8,2,6,3,5]=>{{1,2,4,5,8},{3,7},{6}}
[1,2,8,7,6,5,3,4]=>{{1},{2},{3,4,7,8},{5,6}}
[3,1,2,4,6,8,7,5]=>{{1,2,3},{4},{5,6,8},{7}}
[3,1,8,4,5,7,6,2]=>{{1,2,3,8},{4},{5},{6,7}}
[3,2,8,5,4,7,1,6]=>{{1,3,6,7,8},{2},{4,5}}
[4,2,8,1,5,3,7,6]=>{{1,4},{2},{3,6,8},{5},{7}}
[4,3,8,5,7,6,1,2]=>{{1,4,5,7},{2,3,8},{6}}
[4,8,2,1,6,3,7,5]=>{{1,4},{2,3,5,6,8},{7}}
[3,8,6,5,2,7,1,4]=>{{1,3,6,7},{2,4,5,8}}
[3,8,5,6,1,7,4,2]=>{{1,3,5},{2,8},{4,6,7}}
[3,5,7,8,1,2,6,4]=>{{1,2,3,5,6,7},{4,8}}
[3,7,8,5,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[3,7,2,8,4,1,6,5]=>{{1,2,3,6,7},{4,5,8}}
[2,8,1,7,4,6,5,3]=>{{1,2,3,8},{4,5,7},{6}}
[2,8,7,5,1,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[2,8,6,7,5,1,4,3]=>{{1,2,3,6,8},{4,7},{5}}
[5,1,3,4,6,7,2,8]=>{{1,2,5,6,7},{3},{4},{8}}
[1,3,4,8,7,5,2,6]=>{{1},{2,3,4,5,6,7,8}}
[8,2,4,1,7,3,5,6]=>{{1,3,4,6,8},{2},{5,7}}
[8,6,1,4,2,3,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[3,6,1,4,2,8,7,5]=>{{1,3},{2,5,6,8},{4},{7}}
[1,6,8,4,3,7,2,5]=>{{1},{2,6,7},{3,5,8},{4}}
[3,1,4,7,8,5,2,6]=>{{1,2,3,4,7},{5,6,8}}
[6,1,7,4,3,8,2,5]=>{{1,2,3,5,6,7,8},{4}}
[1,8,7,4,3,6,2,5]=>{{1},{2,3,5,7,8},{4},{6}}
[7,4,1,3,8,2,6,5]=>{{1,2,3,4,6,7},{5,8}}
[4,8,2,3,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,8,6,2,1,3,7,5]=>{{1,2,4,5,8},{3,6},{7}}
[2,7,4,1,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[1,7,8,4,2,3,6,5]=>{{1},{2,3,5,6,7,8},{4}}
[4,7,1,3,8,2,6,5]=>{{1,3,4},{2,6,7},{5,8}}
[8,7,1,3,4,2,6,5]=>{{1,3,4,5,8},{2,6,7}}
[1,7,4,3,6,2,8,5]=>{{1},{2,5,6,7,8},{3,4}}
[3,8,6,4,5,2,1,7]=>{{1,2,3,6,7,8},{4},{5}}
[3,8,4,6,5,2,1,7]=>{{1,2,3,4,6,7,8},{5}}
[2,4,3,7,5,8,1,6]=>{{1,2,4,7},{3},{5},{6,8}}
[1,4,7,3,6,2,8,5]=>{{1},{2,3,4,5,6,7,8}}
[1,8,3,4,2,6,7,5]=>{{1},{2,5,8},{3},{4},{6},{7}}
[6,4,1,3,7,2,8,5]=>{{1,2,3,4,6},{5,7,8}}
[8,1,4,3,6,2,7,5]=>{{1,2,5,6,8},{3,4},{7}}
[4,2,3,8,5,7,1,6]=>{{1,4,6,7,8},{2},{3},{5}}
[2,8,5,7,3,4,1,6]=>{{1,2,4,6,7,8},{3,5}}
[5,8,2,6,4,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[7,2,5,8,4,3,1,6]=>{{1,7},{2},{3,4,5,6,8}}
[4,2,3,5,8,7,1,6]=>{{1,4,5,6,7,8},{2},{3}}
[8,2,3,5,4,7,1,6]=>{{1,6,7,8},{2},{3},{4,5}}
[6,1,8,3,4,2,7,5]=>{{1,2,6},{3,4,5,8},{7}}
[1,8,6,4,2,3,7,5]=>{{1},{2,5,8},{3,6},{4},{7}}
[3,8,4,5,6,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,3,5,7,8,1,6]=>{{1,2,4,5,7},{3},{6,8}}
[3,8,6,5,4,2,1,7]=>{{1,2,3,6,7,8},{4,5}}
[6,3,1,4,2,8,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[7,3,8,1,2,6,4,5]=>{{1,4,7},{2,3,5,8},{6}}
[7,1,4,5,3,2,6,8]=>{{1,2,6,7},{3,4,5},{8}}
[1,8,4,2,6,5,3,7]=>{{1},{2,3,4,7,8},{5,6}}
[5,1,4,8,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,8,4,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,1,5,7,2,6]=>{{1,4},{2,3,6,7,8},{5}}
[6,3,1,2,5,7,4,8]=>{{1,2,3,4,6,7},{5},{8}}
[7,1,4,2,6,5,3,8]=>{{1,2,3,4,7},{5,6},{8}}
[3,8,4,1,6,5,2,7]=>{{1,3,4},{2,7,8},{5,6}}
[7,3,6,4,5,8,2,1]=>{{1,2,3,6,7,8},{4},{5}}
[8,7,2,4,5,1,6,3]=>{{1,2,3,6,7,8},{4},{5}}
[7,1,5,4,8,6,3,2]=>{{1,2,3,5,7,8},{4},{6}}
[2,1,8,7,5,3,6,4]=>{{1,2},{3,4,6,7,8},{5}}
[5,8,3,7,4,1,6,2]=>{{1,4,5,6,7},{2,8},{3}}
[5,7,1,4,8,6,3,2]=>{{1,2,3,5,7,8},{4},{6}}
[3,5,7,4,8,6,2,1]=>{{1,2,3,5,7,8},{4},{6}}
[5,3,7,4,8,6,2,1]=>{{1,5,8},{2,3,7},{4},{6}}
[6,5,3,7,4,8,2,1]=>{{1,6,8},{2,4,5,7},{3}}
[7,5,8,4,1,6,3,2]=>{{1,2,3,5,7,8},{4},{6}}
[2,7,8,4,5,1,6,3]=>{{1,2,6,7},{3,8},{4},{5}}
[5,7,3,8,4,1,6,2]=>{{1,2,4,5,6,7,8},{3}}
[5,6,3,8,1,4,7,2]=>{{1,5},{2,4,6,8},{3},{7}}
[3,7,8,4,1,6,5,2]=>{{1,2,3,5,7,8},{4},{6}}
[8,7,3,1,5,4,2,6]=>{{1,4,6,8},{2,7},{3},{5}}
[3,6,2,1,5,4,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[5,4,2,6,1,3,8,7]=>{{1,5},{2,3,4,6},{7,8}}
[3,2,6,5,1,4,8,7]=>{{1,3,4,5,6},{2},{7,8}}
[2,5,8,1,7,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[6,8,2,7,4,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[6,8,2,3,7,5,1,4]=>{{1,5,6,7},{2,3,4,8}}
[7,6,2,5,4,8,1,3]=>{{1,7},{2,3,6,8},{4,5}}
[2,6,5,1,8,4,3,7]=>{{1,2,4,6},{3,5,7,8}}
[4,2,7,3,1,8,5,6]=>{{1,3,4,5,7},{2},{6,8}}
[4,2,3,7,1,5,8,6]=>{{1,4,5,6,7,8},{2},{3}}
[5,2,7,3,8,6,1,4]=>{{1,3,4,5,7,8},{2},{6}}
[2,1,5,8,4,3,7,6]=>{{1,2},{3,4,5,6,8},{7}}
[5,8,4,2,6,7,1,3]=>{{1,5,6,7},{2,3,4,8}}
[3,2,4,8,1,5,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[2,4,8,3,1,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,3,2,1,7,6,5]=>{{1,2,4,5,8},{3},{6,7}}
[4,1,3,7,2,6,8,5]=>{{1,2,4,5,7,8},{3},{6}}
[3,4,8,2,1,6,5,7]=>{{1,3,5,7,8},{2,4},{6}}
[6,8,3,7,2,1,5,4]=>{{1,6},{2,4,5,7,8},{3}}
[3,5,8,1,7,2,6,4]=>{{1,3,4,8},{2,5,6,7}}
[5,1,7,4,6,8,3,2]=>{{1,2,5,6,8},{3,7},{4}}
[7,6,4,8,1,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,1,8,2,6,4]=>{{1,4,5,8},{2,3,6,7}}
[2,7,6,3,8,1,4,5]=>{{1,2,3,4,6,7},{5,8}}
[2,1,7,6,4,8,3,5]=>{{1,2},{3,7},{4,5,6,8}}
[2,1,5,4,8,7,3,6]=>{{1,2},{3,5,6,7,8},{4}}
[5,4,8,7,2,6,1,3]=>{{1,2,4,5,7},{3,8},{6}}
[2,4,3,8,7,1,5,6]=>{{1,2,4,6,8},{3},{5,7}}
[3,4,1,8,6,2,7,5]=>{{1,3},{2,4,5,6,8},{7}}
[3,8,5,4,2,1,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[4,8,6,5,2,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[3,2,8,7,5,4,1,6]=>{{1,3,4,6,7,8},{2},{5}}
[2,8,6,5,4,3,1,7]=>{{1,2,7,8},{3,6},{4,5}}
[5,4,2,6,3,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[7,3,6,5,2,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,2,3,4,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,3,1,4,2,6]=>{{1,3,4,5,6,8},{2,7}}
[7,1,5,3,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,4,2,8,5,1]=>{{1,3,6,8},{2,5,7},{4}}
[2,1,8,7,4,3,5,6]=>{{1,2},{3,6,8},{4,5,7}}
[3,8,7,4,2,1,5,6]=>{{1,2,3,5,6,7,8},{4}}
[8,5,2,6,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,4,2,6,8,3,7,1]=>{{1,5,8},{2,3,4,6},{7}}
[6,5,2,8,1,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,4,5,1,3,6]=>{{1,2,3,6,7,8},{4},{5}}
[3,4,8,1,5,2,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[4,8,1,2,5,3,6,7]=>{{1,2,3,4,6,7,8},{5}}
[8,1,2,4,3,5,6,7]=>{{1,2,3,5,6,7,8},{4}}
[5,8,7,4,6,3,2,1]=>{{1,2,3,5,6,7,8},{4}}
[4,8,7,6,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,6,5,2,4,1]=>{{1,2,3,4,6,7,8},{5}}
[5,8,4,7,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,4,7,3,2,1]=>{{1,2,3,5,6,7,8},{4}}
[3,8,7,6,2,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,6,3,2,5,1]=>{{1,2,4,6,8},{3,5,7}}
[3,8,7,6,5,2,1,4]=>{{1,3,7},{2,4,6,8},{5}}
[7,5,8,4,6,3,1,2]=>{{1,7},{2,3,5,6,8},{4}}
[7,6,8,2,5,1,4,3]=>{{1,2,4,6,7},{3,8},{5}}
[3,5,2,4,7,6,1,8]=>{{1,2,3,5,7},{4},{6},{8}}
[3,5,4,7,2,6,1,8]=>{{1,3,4,7},{2,5},{6},{8}}
[3,5,4,7,6,1,2,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,4,7,6,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,4,6,1,8,2]=>{{1,2,3,5,6,7,8},{4}}
[3,5,7,4,6,1,2,8]=>{{1,2,3,5,6,7},{4},{8}}
[3,5,7,4,6,2,1,8]=>{{1,3,7},{2,5,6},{4},{8}}
[3,2,5,7,4,6,1,8]=>{{1,3,4,5,7},{2},{6},{8}}
[3,5,2,7,6,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,7,2,6,4,1,8]=>{{1,3,7},{2,4,5,6},{8}}
[5,3,7,6,2,4,1,8]=>{{1,2,3,5,7},{4,6},{8}}
[5,3,7,6,1,2,8,4]=>{{1,5},{2,3,4,6,7,8}}
[5,3,7,6,1,4,2,8]=>{{1,5},{2,3,7},{4,6},{8}}
[5,3,7,6,4,1,2,8]=>{{1,4,5,6},{2,3,7},{8}}
[3,5,7,2,6,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,2,7,6,1,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[5,3,7,6,4,1,8,2]=>{{1,4,5,6},{2,3,7,8}}
[3,7,5,4,1,8,2,6]=>{{1,3,5},{2,7},{4},{6,8}}
[3,7,5,4,1,8,6,2]=>{{1,3,5},{2,6,7,8},{4}}
[3,7,5,1,4,8,6,2]=>{{1,3,4,5},{2,6,7,8}}
[3,7,5,1,4,8,2,6]=>{{1,3,4,5},{2,7},{6,8}}
[3,5,7,1,2,6,8,4]=>{{1,3,4,7,8},{2,5},{6}}
[3,5,7,2,1,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[3,5,2,7,1,6,4,8]=>{{1,2,3,5},{4,7},{6},{8}}
[3,5,7,2,1,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}
[5,3,7,1,6,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,7,1,4,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[3,5,7,1,4,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}
[3,5,7,1,4,2,6,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,7,2,1,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,2,7,1,4,6,8]=>{{1,2,3,5},{4,6,7},{8}}
[3,2,5,7,4,1,6,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,5,2,7,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,7,4,2,1,6,8]=>{{1,3,6,7},{2,5},{4},{8}}
[3,5,7,4,1,2,6,8]=>{{1,2,3,5,6,7},{4},{8}}
[3,5,4,7,1,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[3,5,4,7,1,2,6,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,4,7,2,1,6,8]=>{{1,3,4,6,7},{2,5},{8}}
[3,5,4,2,7,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[3,2,5,4,7,1,6,8]=>{{1,3,5,6,7},{2},{4},{8}}
[3,5,4,7,2,1,8,6]=>{{1,3,4,6,7,8},{2,5}}
[3,5,4,7,1,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,3,1,8,4,2]=>{{1,5},{2,3,4,6,7,8}}
[5,7,6,3,1,8,2,4]=>{{1,5},{2,7},{3,4,6,8}}
[3,5,7,4,1,2,8,6]=>{{1,2,3,5,6,7,8},{4}}
[3,5,7,4,2,1,8,6]=>{{1,3,6,7,8},{2,5},{4}}
[3,2,5,7,4,1,8,6]=>{{1,3,4,5,6,7,8},{2}}
[3,2,5,7,1,4,8,6]=>{{1,3,5},{2},{4,6,7,8}}
[3,5,2,7,1,4,8,6]=>{{1,2,3,5},{4,6,7,8}}
[3,5,7,2,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,1,4,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,5,2,1,8,6,4]=>{{1,3,5},{2,4,6,7,8}}
[3,7,2,5,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[3,2,7,5,1,8,6,4]=>{{1,3,4,5,6,7,8},{2}}
[3,2,7,5,1,8,4,6]=>{{1,3,4,5,7},{2},{6,8}}
[3,7,2,5,1,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[3,7,5,2,1,8,4,6]=>{{1,3,5},{2,4,7},{6,8}}
[2,1,7,5,8,4,6,3]=>{{1,2},{3,4,5,6,7,8}}
[5,8,3,4,1,7,6,2]=>{{1,5},{2,8},{3},{4},{6,7}}
[5,8,7,2,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,4,1,7,5,2]=>{{1,3,5,6,7},{2,8},{4}}
[4,3,5,6,8,1,7,2]=>{{1,4,6},{2,3,5,8},{7}}
[3,7,6,4,1,8,5,2]=>{{1,2,3,5,6,7,8},{4}}
[3,7,4,1,8,6,5,2]=>{{1,3,4},{2,5,7,8},{6}}
[3,8,4,1,7,6,5,2]=>{{1,3,4},{2,8},{5,7},{6}}
[3,2,7,6,1,5,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,2,8,7,6,1,5,4]=>{{1,3,4,5,6,7,8},{2}}
[5,7,8,2,4,1,6,3]=>{{1,2,4,5,6,7},{3,8}}
[4,2,5,8,1,6,7,3]=>{{1,3,4,5,8},{2},{6},{7}}
[4,2,5,8,1,7,3,6]=>{{1,3,4,5,6,7,8},{2}}
[5,8,2,4,1,6,3,7]=>{{1,5},{2,3,7,8},{4},{6}}
[8,4,2,6,5,1,3,7]=>{{1,2,3,4,6,7,8},{5}}
[3,2,6,8,1,5,4,7]=>{{1,3,5,6},{2},{4,7,8}}
[8,3,2,5,6,1,4,7]=>{{1,4,5,6,7,8},{2,3}}
[3,2,8,6,7,1,5,4]=>{{1,3,4,6,8},{2},{5,7}}
[3,2,6,8,7,1,5,4]=>{{1,3,6},{2},{4,8},{5,7}}
[3,2,6,7,1,5,4,8]=>{{1,3,5,6},{2},{4,7},{8}}
[8,7,3,2,5,6,1,4]=>{{1,2,4,7,8},{3},{5},{6}}
[7,2,8,1,5,3,6,4]=>{{1,3,4,6,7,8},{2},{5}}
[8,4,2,7,5,1,3,6]=>{{1,6,8},{2,3,4,7},{5}}
[7,4,2,8,5,1,3,6]=>{{1,2,3,4,6,7,8},{5}}
[7,2,4,1,8,3,6,5]=>{{1,3,4,6,7},{2},{5,8}}
[3,2,8,5,7,1,4,6]=>{{1,3,6,8},{2},{4,5,7}}
[2,6,5,7,1,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,1,8,7,4,3,6]=>{{1,2,3,5,7},{4,6,8}}
[8,1,4,6,3,5,2,7]=>{{1,2,7,8},{3,4,5,6}}
[8,3,5,4,1,6,2,7]=>{{1,2,3,5,7,8},{4},{6}}
[8,6,3,4,1,5,2,7]=>{{1,2,5,6,7,8},{3},{4}}
[5,4,7,6,8,2,3,1]=>{{1,5,8},{2,4,6},{3,7}}
[4,1,8,2,3,7,6,5]=>{{1,2,4},{3,5,8},{6,7}}
[2,1,8,5,3,4,7,6]=>{{1,2},{3,4,5,6,8},{7}}
[5,2,4,6,8,7,3,1]=>{{1,5,8},{2},{3,4,6,7}}
[1,6,8,3,4,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[5,7,4,8,6,1,3,2]=>{{1,5,6},{2,3,4,7,8}}
[5,4,2,6,7,8,1,3]=>{{1,5,7},{2,3,4,6,8}}
[6,4,2,7,3,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,8,3,5,6,2]=>{{1,3,5,6,7},{2,4,8}}
[6,5,4,8,7,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,2,1,3,6,5]=>{{1,5,8},{2,3,4,6,7}}
[8,7,1,3,2,5,6,4]=>{{1,3,4,8},{2,5,6,7}}
[6,8,2,3,1,7,5,4]=>{{1,5,6,7},{2,3,4,8}}
[7,4,3,2,6,8,5,1]=>{{1,5,6,7,8},{2,4},{3}}
[2,7,4,3,8,5,6,1]=>{{1,2,5,6,7,8},{3,4}}
[8,3,7,2,1,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,2,4,3,1,6]=>{{1,2,4,5,7},{3,6,8}}
[8,4,7,3,2,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[8,3,1,6,7,4,2,5]=>{{1,2,3,5,7,8},{4,6}}
[3,2,5,7,4,8,1,6]=>{{1,3,4,5,7},{2},{6,8}}
[8,2,7,3,4,1,5,6]=>{{1,6,8},{2},{3,4,5,7}}
[7,1,6,3,5,8,2,4]=>{{1,2,7},{3,4,6,8},{5}}
[2,8,5,6,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[1,5,2,7,8,6,4,3]=>{{1},{2,3,5,8},{4,7},{6}}
[2,6,8,5,1,4,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[1,4,2,8,6,5,7,3]=>{{1},{2,3,4,8},{5,6},{7}}
[3,5,1,6,8,7,2,4]=>{{1,3},{2,4,5,6,7,8}}
[5,7,6,2,1,3,8,4]=>{{1,5},{2,4,7,8},{3,6}}
[2,5,8,7,4,1,6,3]=>{{1,2,4,5,6,7},{3,8}}
[4,1,7,5,2,6,8,3]=>{{1,2,4,5},{3,7,8},{6}}
[7,6,2,4,5,1,8,3]=>{{1,2,3,6,7,8},{4},{5}}
[7,3,4,2,5,8,6,1]=>{{1,6,7,8},{2,3,4},{5}}
[8,7,4,2,5,1,6,3]=>{{1,2,3,4,6,7,8},{5}}
[8,1,4,5,2,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[5,2,4,8,6,7,1,3]=>{{1,5,6,7},{2},{3,4,8}}
[8,5,6,2,1,3,7,4]=>{{1,2,4,5,8},{3,6},{7}}
[4,2,1,5,6,7,8,3]=>{{1,3,4,5,6,7,8},{2}}
[3,4,6,5,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[7,3,5,2,4,6,1,8]=>{{1,7},{2,3,4,5},{6},{8}}
[5,3,7,2,4,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[3,7,5,2,4,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[5,7,3,2,4,6,1,8]=>{{1,2,4,5,7},{3},{6},{8}}
[1,5,3,2,4,7,6,8]=>{{1},{2,4,5},{3},{6,7},{8}}
[1,5,3,2,7,4,6,8]=>{{1},{2,4,5,6,7},{3},{8}}
[5,7,3,2,1,4,6,8]=>{{1,5},{2,4,6,7},{3},{8}}
[5,7,3,2,4,1,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[3,7,2,5,4,1,6,8]=>{{1,2,3,6,7},{4,5},{8}}
[5,1,3,2,4,7,6,8]=>{{1,2,4,5},{3},{6,7},{8}}
[5,1,3,2,7,4,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,1,3,2,5,4,6,8]=>{{1,2,4,6,7},{3},{5},{8}}
[1,7,3,2,5,4,6,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[7,1,3,5,2,4,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,1,3,7,2,4,6,8]=>{{1,2,5},{3},{4,6,7},{8}}
[3,2,7,5,1,4,6,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,7,5,1,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[5,7,3,1,2,4,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[1,5,3,7,2,4,6,8]=>{{1},{2,5},{3},{4,6,7},{8}}
[5,3,2,7,4,1,6,8]=>{{1,4,5,6,7},{2,3},{8}}
[5,3,2,4,7,1,6,8]=>{{1,5,6,7},{2,3},{4},{8}}
[5,3,2,1,4,7,6,8]=>{{1,4,5},{2,3},{6,7},{8}}
[5,3,2,1,7,4,6,8]=>{{1,4,5,6,7},{2,3},{8}}
[1,3,2,7,5,4,6,8]=>{{1},{2,3},{4,6,7},{5},{8}}
[1,3,7,2,5,4,6,8]=>{{1},{2,3,4,6,7},{5},{8}}
[7,3,1,2,5,4,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[5,3,1,2,7,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[5,3,1,2,4,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[3,2,5,1,4,7,6,8]=>{{1,3,4,5},{2},{6,7},{8}}
[7,3,1,5,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[1,3,7,5,2,4,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,5,1,3,2,4,6,8]=>{{1,3,4,6,7},{2,5},{8}}
[5,7,1,3,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[3,7,1,5,2,4,6,8]=>{{1,3},{2,4,5,6,7},{8}}
[3,7,1,2,5,4,6,8]=>{{1,3},{2,4,6,7},{5},{8}}
[3,7,2,1,5,4,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[3,2,1,7,5,4,6,8]=>{{1,3},{2},{4,6,7},{5},{8}}
[3,1,2,7,5,4,6,8]=>{{1,2,3},{4,6,7},{5},{8}}
[3,1,7,2,5,4,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[3,1,7,5,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[7,1,5,3,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[1,7,5,3,2,4,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,7,4,2,6,5,3]=>{{1},{2,3,5,7,8},{4},{6}}
[2,8,5,1,7,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[6,8,5,1,2,7,4,3]=>{{1,4,6,7},{2,3,5,8}}
[2,8,1,4,7,6,5,3]=>{{1,2,3,8},{4},{5,7},{6}}
[1,8,7,4,3,2,6,5]=>{{1},{2,3,5,6,7,8},{4}}
[1,8,5,4,2,7,6,3]=>{{1},{2,3,5,8},{4},{6,7}}
[7,5,3,4,2,8,1,6]=>{{1,7},{2,5},{3},{4},{6,8}}
[8,5,3,6,2,4,7,1]=>{{1,8},{2,5},{3},{4,6},{7}}
[8,5,6,3,7,4,2,1]=>{{1,8},{2,5,7},{3,4,6}}
[8,5,6,2,7,4,3,1]=>{{1,8},{2,3,4,5,6,7}}
[8,7,6,3,4,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[1,7,2,3,6,8,5,4]=>{{1},{2,3,4,5,6,7,8}}
[3,5,6,4,8,2,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[3,5,1,4,8,2,7,6]=>{{1,3},{2,5,6,8},{4},{7}}
[1,7,5,4,8,2,6,3]=>{{1},{2,6,7},{3,5,8},{4}}
[3,7,5,1,6,4,8,2]=>{{1,3,4,5,6},{2,7,8}}
[2,7,5,4,8,1,3,6]=>{{1,2,3,5,6,7,8},{4}}
[2,7,5,4,8,6,1,3]=>{{1,2,7},{3,5,8},{4},{6}}
[1,7,5,4,8,6,3,2]=>{{1},{2,3,5,7,8},{4},{6}}
[2,5,1,4,8,7,3,6]=>{{1,2,3,5,6,7,8},{4}}
[3,6,4,2,8,7,1,5]=>{{1,2,3,4,6,7},{5,8}}
[3,5,2,4,8,1,6,7]=>{{1,2,3,5,6,7,8},{4}}
[3,5,6,4,8,1,2,7]=>{{1,3,6},{2,5,7,8},{4}}
[1,5,6,4,8,7,2,3]=>{{1},{2,3,5,6,7,8},{4}}
[3,6,4,1,8,7,2,5]=>{{1,3,4},{2,6,7},{5,8}}
[3,6,4,5,8,7,2,1]=>{{1,3,4,5,8},{2,6,7}}
[1,6,4,3,8,5,2,7]=>{{1},{2,5,6,7,8},{3,4}}
[7,1,3,4,5,8,2,6]=>{{1,2,7},{3},{4},{5},{6,8}}
[7,6,1,4,5,3,8,2]=>{{1,2,3,6,7,8},{4},{5}}
[7,6,1,3,5,4,8,2]=>{{1,2,3,4,6,7,8},{5}}
[7,1,3,2,5,8,4,6]=>{{1,2,4,7},{3},{5},{6,8}}
[1,6,4,2,8,5,3,7]=>{{1},{2,3,4,5,6,7,8}}
[7,6,5,8,2,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,5,8,3,1,4,2]=>{{1,2,4,6,7,8},{3,5}}
[2,6,4,3,8,1,7,5]=>{{1,2,6},{3,4},{5,8},{7}}
[2,6,4,3,8,5,7,1]=>{{1,2,5,6,8},{3,4},{7}}
[7,2,3,1,5,8,6,4]=>{{1,4,6,7,8},{2},{3},{5}}
[7,1,5,6,3,8,4,2]=>{{1,2,4,6,7,8},{3,5}}
[7,3,6,5,1,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[7,2,6,5,3,8,1,4]=>{{1,7},{2},{3,4,5,6,8}}
[7,2,3,1,4,8,6,5]=>{{1,4,5,6,7,8},{2},{3}}
[7,2,3,5,4,8,6,1]=>{{1,6,7,8},{2},{3},{4,5}}
[2,6,4,5,8,1,7,3]=>{{1,2,6},{3,4,5,8},{7}}
[1,5,6,4,8,3,7,2]=>{{1},{2,5,8},{3,6},{4},{7}}
[2,5,6,4,8,3,1,7]=>{{1,2,5,7,8},{3,6},{4}}
[3,5,6,1,4,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,1,3,4,5,8,2]=>{{1,2,3,4,5,6,7,8}}
[7,1,3,2,4,8,5,6]=>{{1,2,4,5,7},{3},{6,8}}
[7,6,1,5,3,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,1,5,4,3,8,2]=>{{1,2,3,6,7,8},{4,5}}
[1,6,4,5,8,3,2,7]=>{{1},{2,3,4,5,6,7,8}}
[7,6,5,8,1,3,2,4]=>{{1,2,3,5,6,7},{4,8}}
[3,4,6,8,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,8,2,1,7,4]=>{{1,3,6},{2,5},{4,8},{7}}
[4,2,1,5,3,7,8,6]=>{{1,3,4,5},{2},{6,7,8}}
[4,2,5,6,3,1,8,7]=>{{1,4,6},{2},{3,5},{7,8}}
[3,5,6,8,1,7,2,4]=>{{1,2,3,5,6,7},{4,8}}
[4,1,5,6,3,2,8,7]=>{{1,2,4,6},{3,5},{7,8}}
[4,5,3,1,7,2,8,6]=>{{1,4},{2,5,6,7,8},{3}}
[4,1,3,5,2,7,8,6]=>{{1,2,4,5},{3},{6,7,8}}
[2,5,4,7,3,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,1,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,1,5,3,2,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[4,5,3,7,1,2,8,6]=>{{1,2,4,5,6,7,8},{3}}
[4,3,6,1,2,7,5,8]=>{{1,4},{2,3,5,6,7},{8}}
[5,1,3,2,4,6,7,8]=>{{1,2,4,5},{3},{6},{7},{8}}
[3,6,1,7,4,5,2,8]=>{{1,3},{2,4,5,6,7},{8}}
[5,1,3,4,2,6,7,8]=>{{1,2,5},{3},{4},{6},{7},{8}}
[5,3,1,4,2,6,7,8]=>{{1,2,3,5},{4},{6},{7},{8}}
[4,5,2,3,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,2,6,1,3,7,5,8]=>{{1,4},{2},{3,5,6,7},{8}}
[4,6,2,1,3,7,5,8]=>{{1,4},{2,3,5,6,7},{8}}
[3,6,2,1,7,4,8,5]=>{{1,2,3,4,6},{5,7,8}}
[3,1,4,7,6,5,2,8]=>{{1,2,3,4,7},{5,6},{8}}
[3,6,2,7,1,5,8,4]=>{{1,2,3,5,6},{4,7,8}}
[4,6,2,7,1,3,5,8]=>{{1,4,5,7},{2,3,6},{8}}
[3,5,7,1,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,4,2,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[3,6,1,7,2,5,8,4]=>{{1,3},{2,5,6},{4,7,8}}
[2,6,5,3,4,7,8,1]=>{{1,2,6,7,8},{3,4,5}}
[3,6,1,7,5,4,2,8]=>{{1,3},{2,4,6,7},{5},{8}}
[5,1,4,3,2,6,7,8]=>{{1,2,5},{3,4},{6},{7},{8}}
[5,4,1,3,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[6,2,4,5,1,8,3,7]=>{{1,3,4,5,6,7,8},{2}}
[2,1,4,8,6,3,7,5]=>{{1,2},{3,4,5,6,8},{7}}
[6,4,8,2,5,3,7,1]=>{{1,3,6,8},{2,4},{5},{7}}
[8,6,2,4,7,5,1,3]=>{{1,2,3,5,6,7,8},{4}}
[4,6,8,2,3,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,6,8,1,4,5,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[8,4,2,6,7,3,1,5]=>{{1,5,7,8},{2,3,4,6}}
[7,6,4,5,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[1,6,7,5,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,2,3,8,4,1,5]=>{{1,7},{2,3,4,6},{5,8}}
[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[6,2,5,8,3,4,7,1]=>{{1,4,6,8},{2},{3,5},{7}}
[6,2,3,8,7,4,1,5]=>{{1,4,5,6,7,8},{2},{3}}
[2,4,7,3,5,8,6,1]=>{{1,2,3,4,6,7,8},{5}}
[2,5,3,7,1,8,4,6]=>{{1,2,5},{3},{4,7},{6,8}}
[5,2,8,3,1,4,6,7]=>{{1,5},{2},{3,4,6,7,8}}
[4,8,2,3,6,5,7,1]=>{{1,2,3,4,8},{5,6},{7}}
[5,8,1,3,6,4,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[5,8,1,4,3,6,2,7]=>{{1,3,5},{2,7,8},{4},{6}}
[5,8,4,1,3,7,6,2]=>{{1,3,4,5},{2,8},{6,7}}
[6,4,5,3,8,1,7,2]=>{{1,6},{2,3,4,5,8},{7}}
[4,6,5,3,7,1,2,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,1,3,6,2,8,7]=>{{1,3,4},{2,5,6},{7,8}}
[4,2,6,5,1,7,3,8]=>{{1,4,5},{2},{3,6,7},{8}}
[4,3,5,7,2,1,6,8]=>{{1,4,6,7},{2,3,5},{8}}
[3,4,7,6,8,1,2,5]=>{{1,2,3,4,6,7},{5,8}}
[3,4,6,2,5,8,7,1]=>{{1,3,6,8},{2,4},{5},{7}}
[3,5,2,4,6,1,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[4,2,5,1,6,8,3,7]=>{{1,4},{2},{3,5,6,7,8}}
[1,8,2,3,6,5,7,4]=>{{1},{2,3,4,8},{5,6},{7}}
[4,2,8,3,5,7,1,6]=>{{1,3,4,6,7,8},{2},{5}}
[4,3,8,6,5,7,1,2]=>{{1,4,6,7},{2,3,8},{5}}
[1,3,7,2,6,5,8,4]=>{{1},{2,3,4,7,8},{5,6}}
[1,3,6,4,2,5,8,7]=>{{1},{2,3,5,6},{4},{7,8}}
[1,5,4,7,3,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,2,3,8,4,1,7,6]=>{{1,4,5,6,8},{2},{3},{7}}
[7,5,3,4,8,2,1,6]=>{{1,7},{2,5,6,8},{3},{4}}
[7,2,8,3,4,1,5,6]=>{{1,3,4,5,6,7,8},{2}}
[7,4,3,8,5,2,6,1]=>{{1,2,4,6,7,8},{3},{5}}
[4,6,2,7,3,1,5,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,3,8,2,4,5,1]=>{{1,2,4,5,6,7,8},{3}}
[7,2,8,5,1,3,4,6]=>{{1,4,5,7},{2},{3,6,8}}
[1,5,3,7,6,8,4,2]=>{{1},{2,5,6,8},{3},{4,7}}
[1,6,3,7,8,2,4,5]=>{{1},{2,6},{3},{4,7},{5,8}}
[1,4,3,7,8,5,2,6]=>{{1},{2,4,7},{3},{5,6,8}}
[4,2,6,5,7,8,3,1]=>{{1,3,4,5,6,7,8},{2}}
[4,2,6,7,5,8,1,3]=>{{1,4,7},{2},{3,6,8},{5}}
[3,2,4,7,8,5,1,6]=>{{1,3,4,7},{2},{5,6,8}}
[3,2,6,7,8,1,4,5]=>{{1,3,6},{2},{4,7},{5,8}}
[5,1,8,3,6,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[3,8,5,6,1,7,2,4]=>{{1,3,5},{2,4,6,7,8}}
[3,4,8,1,7,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[4,7,6,8,5,1,3,2]=>{{1,2,3,4,6,7,8},{5}}
[6,7,4,8,5,1,3,2]=>{{1,6},{2,3,4,7,8},{5}}
[6,4,8,3,1,7,5,2]=>{{1,5,6,7},{2,3,4,8}}
[3,6,5,8,7,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,8,2,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[5,6,4,8,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[5,6,8,3,1,7,4,2]=>{{1,5},{2,3,4,6,7,8}}
[5,3,8,1,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,3,8,2,7,4,1]=>{{1,4,6,7,8},{2,5},{3}}
[6,4,8,1,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,3,1,4,2,5,8]=>{{1,4,5,7},{2,6},{3},{8}}
[1,5,4,3,7,8,2,6]=>{{1},{2,5,7},{3,4},{6,8}}
[7,8,4,2,5,3,1,6]=>{{1,7},{2,3,4,6,8},{5}}
[4,2,7,8,5,3,1,6]=>{{1,3,4,6,7,8},{2},{5}}
[4,2,5,3,1,7,8,6]=>{{1,3,4,5},{2},{6,7,8}}
[4,2,8,7,6,3,1,5]=>{{1,4,7},{2},{3,5,6,8}}
[4,2,7,6,3,1,5,8]=>{{1,4,6},{2},{3,5,7},{8}}
[6,3,1,7,5,2,4,8]=>{{1,2,3,6},{4,7},{5},{8}}
[6,3,1,8,7,5,2,4]=>{{1,2,3,5,6,7},{4,8}}
[8,6,3,1,7,5,2,4]=>{{1,4,8},{2,5,6,7},{3}}
[4,2,7,6,3,1,8,5]=>{{1,4,6},{2},{3,5,7,8}}
[7,6,3,1,8,4,2,5]=>{{1,2,4,6,7},{3},{5,8}}
[7,6,4,2,1,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[1,8,2,7,6,4,3,5]=>{{1},{2,3,4,5,6,7,8}}
[8,3,5,7,6,4,2,1]=>{{1,8},{2,3,4,5,6,7}}
[8,4,2,5,7,6,3,1]=>{{1,8},{2,3,4,5,7},{6}}
[7,5,2,4,8,6,3,1]=>{{1,2,3,5,7,8},{4},{6}}
[8,7,5,2,4,6,3,1]=>{{1,8},{2,3,4,5,7},{6}}
[7,5,2,4,6,3,1,8]=>{{1,7},{2,3,5,6},{4},{8}}
[5,2,8,6,3,7,4,1]=>{{1,3,5,8},{2},{4,6,7}}
[8,4,7,5,2,6,3,1]=>{{1,8},{2,4,5},{3,7},{6}}
[8,3,6,4,7,5,2,1]=>{{1,8},{2,3,5,6,7},{4}}
[1,8,2,7,5,3,6,4]=>{{1},{2,3,4,6,7,8},{5}}
[7,5,2,1,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,2,6,3,1,8,4]=>{{1,4,6,7,8},{2,3,5}}
[5,2,7,4,1,8,6,3]=>{{1,5},{2},{3,6,7,8},{4}}
[5,2,8,7,4,1,6,3]=>{{1,4,5,6,7},{2},{3,8}}
[8,7,4,1,5,2,6,3]=>{{1,3,4,8},{2,6,7},{5}}
[7,4,1,5,2,8,6,3]=>{{1,3,6,7,8},{2,4,5}}
[7,6,3,1,4,2,8,5]=>{{1,4,5,7,8},{2,6},{3}}
[7,5,2,8,6,3,1,4]=>{{1,7},{2,3,5,6},{4,8}}
[8,7,5,2,6,3,1,4]=>{{1,2,4,7,8},{3,5,6}}
[7,5,2,1,3,6,4,8]=>{{1,4,7},{2,3,5},{6},{8}}
[8,7,5,2,1,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,2,1,3,8,6,4]=>{{1,4,6,7,8},{2,3,5}}
[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[8,6,4,7,5,2,1,3]=>{{1,3,4,7,8},{2,6},{5}}
[6,4,8,7,5,2,1,3]=>{{1,2,4,6,7},{3,8},{5}}
[6,4,7,5,2,1,3,8]=>{{1,6},{2,4,5},{3,7},{8}}
[6,3,1,4,7,5,2,8]=>{{1,2,3,5,6,7},{4},{8}}
[6,3,1,4,8,7,5,2]=>{{1,2,3,5,6,7,8},{4}}
[8,6,3,1,4,7,5,2]=>{{1,2,4,5,6,7,8},{3}}
[8,5,7,6,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[1,8,2,5,7,6,4,3]=>{{1},{2,3,8},{4,5,7},{6}}
[1,8,2,6,4,7,5,3]=>{{1},{2,3,8},{4,5,6,7}}
[7,5,2,1,6,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,8,7,4,1,5,2]=>{{1,6},{2,3,8},{4,5,7}}
[6,3,7,4,1,5,2,8]=>{{1,5,6},{2,3,7},{4},{8}}
[7,4,1,6,3,5,2,8]=>{{1,2,3,4,5,6,7},{8}}
[7,4,1,8,6,3,5,2]=>{{1,3,5,6,7},{2,4,8}}
[8,4,6,3,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,5,2,1,8,3]=>{{1,6},{2,4,5},{3,7,8}}
[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[8,6,3,5,2,7,4,1]=>{{1,8},{2,4,5,6,7},{3}}
[6,3,5,2,8,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,2,7,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[1,4,7,3,5,2,6,8]=>{{1},{2,3,4,6,7},{5},{8}}
[5,7,4,2,6,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,2,6,3,5,7,1,8]=>{{1,3,4,6,7},{2},{5},{8}}
[2,4,5,8,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[6,1,3,7,4,2,5,8]=>{{1,2,6},{3},{4,5,7},{8}}
[3,2,6,8,1,5,7,4]=>{{1,3,5,6},{2},{4,8},{7}}
[8,2,6,1,5,4,7,3]=>{{1,3,4,6,8},{2},{5},{7}}
[8,6,2,7,1,5,4,3]=>{{1,2,3,5,6,8},{4,7}}
[7,6,8,3,1,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,2,8,1,5,4]=>{{1,6},{2,3,4,5,7,8}}
[7,5,2,8,6,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[2,7,3,8,1,5,6,4]=>{{1,2,5,6,7},{3},{4,8}}
[1,6,8,5,2,4,3,7]=>{{1},{2,4,5,6},{3,7,8}}
[4,5,7,2,8,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,4,6,5,3,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,5,3,1,7,2,6,8]=>{{1,4},{2,5,6,7},{3},{8}}
[7,8,1,2,4,3,6,5]=>{{1,3,6,7},{2,4,5,8}}
[8,4,1,6,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[6,1,3,4,2,8,5,7]=>{{1,2,5,6,7,8},{3},{4}}
[8,1,4,3,5,7,6,2]=>{{1,2,8},{3,4},{5},{6,7}}
[5,2,4,1,3,7,8,6]=>{{1,3,4,5},{2},{6,7,8}}
[8,7,1,3,6,5,4,2]=>{{1,2,3,4,7,8},{5,6}}
[1,8,5,7,4,2,6,3]=>{{1},{2,3,4,5,6,7,8}}
[4,7,5,3,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,5,4,7,2,6,3]=>{{1,2,3,5,6,7,8},{4}}
[6,3,5,8,7,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[4,7,2,8,5,6,3,1]=>{{1,4,8},{2,3,7},{5},{6}}
[1,4,8,7,3,5,6,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,7,6,3,5,4,2]=>{{1,2,8},{3,4,5,6,7}}
[3,6,8,5,7,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[4,7,6,8,5,3,1,2]=>{{1,2,4,7,8},{3,6},{5}}
[3,8,7,5,6,4,2,1]=>{{1,2,3,7,8},{4,5,6}}
[2,8,7,6,4,5,3,1]=>{{1,2,8},{3,7},{4,5,6}}
[1,8,7,6,5,3,4,2]=>{{1},{2,8},{3,4,6,7},{5}}
[4,6,7,2,5,3,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,4,7,8,1,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[4,2,6,8,7,1,5,3]=>{{1,3,4,6,8},{2},{5,7}}
[5,1,8,4,2,7,6,3]=>{{1,2,5},{3,8},{4},{6,7}}
[2,7,3,8,1,6,5,4]=>{{1,2,5,7},{3},{4,8},{6}}
[2,6,8,4,1,7,5,3]=>{{1,2,5,6,7},{3,8},{4}}
[4,6,7,1,2,8,5,3]=>{{1,4},{2,3,5,6,7,8}}
[3,6,1,8,2,7,5,4]=>{{1,3},{2,5,6,7},{4,8}}
[5,7,4,1,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,1,2,8,5,4]=>{{1,4,6,8},{2,3,5,7}}
[1,7,8,5,4,3,2,6]=>{{1},{2,7},{3,6,8},{4,5}}
[1,2,6,7,8,4,3,5]=>{{1},{2},{3,4,6,7},{5,8}}
[8,1,4,6,7,3,5,2]=>{{1,2,8},{3,4,6},{5,7}}
[4,7,1,3,6,8,2,5]=>{{1,3,4},{2,7},{5,6,8}}
[3,7,5,4,2,1,8,6]=>{{1,2,3,5,6,7,8},{4}}
[1,3,6,7,4,2,8,5]=>{{1},{2,3,6},{4,5,7,8}}
[3,6,4,8,2,7,5,1]=>{{1,3,4,8},{2,5,6,7}}
[8,1,6,7,5,3,2,4]=>{{1,2,4,7,8},{3,6},{5}}
[8,7,2,4,6,5,3,1]=>{{1,8},{2,3,7},{4},{5,6}}
[1,7,8,2,6,4,5,3]=>{{1},{2,4,5,6,7},{3,8}}
[8,7,2,5,4,6,1,3]=>{{1,2,3,7,8},{4,5},{6}}
[8,7,3,2,1,5,6,4]=>{{1,2,4,5,6,7,8},{3}}
[3,7,8,2,1,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[8,7,6,1,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,2,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[1,8,2,3,6,5,4,7]=>{{1},{2,3,4,7,8},{5,6}}
[3,5,8,4,7,2,6,1]=>{{1,3,8},{2,5,6,7},{4}}
[1,8,5,4,6,2,3,7]=>{{1},{2,3,5,6,7,8},{4}}
[3,8,5,4,6,1,2,7]=>{{1,3,5,6},{2,7,8},{4}}
[3,8,5,1,6,4,2,7]=>{{1,3,4,5,6},{2,7,8}}
[2,8,5,4,6,1,3,7]=>{{1,2,3,5,6,7,8},{4}}
[2,8,5,4,6,3,1,7]=>{{1,2,7,8},{3,5,6},{4}}
[1,8,5,4,6,3,2,7]=>{{1},{2,7,8},{3,5,6},{4}}
[2,5,8,4,7,3,6,1]=>{{1,2,3,5,6,7,8},{4}}
[3,6,4,2,7,8,5,1]=>{{1,2,3,4,6,8},{5,7}}
[3,5,4,1,6,2,7,8]=>{{1,3,4},{2,5,6},{7},{8}}
[4,5,8,1,7,6,2,3]=>{{1,4},{2,5,7},{3,8},{6}}
[3,5,8,4,7,1,6,2]=>{{1,2,3,5,6,7,8},{4}}
[1,5,8,4,7,3,6,2]=>{{1},{2,3,5,6,7,8},{4}}
[3,6,4,1,7,8,5,2]=>{{1,3,4},{2,6,8},{5,7}}
[3,6,4,8,7,5,2,1]=>{{1,3,4,8},{2,5,6,7}}
[1,6,4,3,7,8,5,2]=>{{1},{2,6,8},{3,4},{5,7}}
[7,1,3,4,8,6,5,2]=>{{1,2,5,7,8},{3},{4},{6}}
[7,6,1,3,8,4,2,5]=>{{1,2,3,4,6,7},{5,8}}
[1,6,4,2,7,8,3,5]=>{{1},{2,3,4,5,6,7,8}}
[2,6,4,3,7,1,8,5]=>{{1,2,6},{3,4},{5,7,8}}
[2,6,4,1,7,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,2,3,4,8,6,5,1]=>{{1,5,7,8},{2},{3},{4},{6}}
[7,2,3,1,8,6,4,5]=>{{1,4,7},{2},{3},{5,8},{6}}
[7,2,3,4,1,6,8,5]=>{{1,5,7,8},{2},{3},{4},{6}}
[1,2,4,3,8,5,7,6]=>{{1},{2},{3,4},{5,6,8},{7}}
[7,3,8,6,1,4,2,5]=>{{1,2,3,5,7,8},{4,6}}
[7,2,8,6,3,4,1,5]=>{{1,7},{2},{3,5,8},{4,6}}
[7,2,3,1,5,6,8,4]=>{{1,4,7,8},{2},{3},{5},{6}}
[7,2,3,8,1,6,5,4]=>{{1,5,7},{2},{3},{4,8},{6}}
[7,2,3,8,5,6,4,1]=>{{1,4,7,8},{2},{3},{5},{6}}
[2,6,4,8,7,1,5,3]=>{{1,2,6},{3,4,8},{5,7}}
[1,5,8,4,7,6,2,3]=>{{1},{2,5,7},{3,8},{4},{6}}
[3,5,8,1,6,7,2,4]=>{{1,3,4,8},{2,5,6,7}}
[7,6,1,3,5,8,2,4]=>{{1,2,3,4,6,7,8},{5}}
[7,1,3,2,5,6,8,4]=>{{1,2,4,7,8},{3},{5},{6}}
[7,1,3,8,2,6,5,4]=>{{1,2,5,7},{3},{4,8},{6}}
[7,6,1,8,5,4,2,3]=>{{1,2,3,4,6,7,8},{5}}
[3,2,6,5,8,4,7,1]=>{{1,3,4,5,6,8},{2},{7}}
[4,3,7,1,6,5,8,2]=>{{1,4},{2,3,7,8},{5,6}}
[5,2,6,4,8,3,7,1]=>{{1,5,8},{2},{3,6},{4},{7}}
[5,2,6,4,8,1,7,3]=>{{1,3,5,6,8},{2},{4},{7}}
[4,3,7,5,8,2,6,1]=>{{1,4,5,8},{2,3,6,7}}
[5,3,7,4,8,2,6,1]=>{{1,5,8},{2,3,6,7},{4}}
[5,3,7,4,8,1,6,2]=>{{1,2,3,5,6,7,8},{4}}
[4,3,7,1,5,2,8,6]=>{{1,4},{2,3,6,7,8},{5}}
[4,3,7,1,6,2,8,5]=>{{1,4},{2,3,5,6,7,8}}
[5,4,8,2,6,3,7,1]=>{{1,3,5,6,8},{2,4},{7}}
[5,4,8,1,6,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,1,7,5,2,3,6,8]=>{{1,2,4,5},{3,6,7},{8}}
[4,1,7,8,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[1,2,6,8,3,7,4,5]=>{{1},{2},{3,4,5,6,7,8}}
[6,8,3,2,1,4,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[7,2,4,1,6,5,8,3]=>{{1,3,4,7,8},{2},{5,6}}
[7,5,8,4,3,1,6,2]=>{{1,6,7},{2,3,5,8},{4}}
[6,8,2,4,1,3,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[2,8,4,7,6,3,5,1]=>{{1,2,8},{3,4,5,6,7}}
[6,1,2,7,5,8,4,3]=>{{1,2,3,6,8},{4,7},{5}}
[4,2,7,3,8,5,6,1]=>{{1,3,4,5,6,7,8},{2}}
[4,5,2,6,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,8,3,2,5,7,6,1]=>{{1,2,4,8},{3},{5},{6,7}}
[6,8,5,3,4,7,2,1]=>{{1,2,6,7,8},{3,4,5}}
[6,8,4,1,5,3,7,2]=>{{1,3,4,6},{2,8},{5},{7}}
[8,3,4,7,6,2,5,1]=>{{1,8},{2,3,4,5,6,7}}
[1,8,3,5,2,6,7,4]=>{{1},{2,4,5,8},{3},{6},{7}}
[6,8,3,5,1,4,7,2]=>{{1,4,5,6},{2,8},{3},{7}}
[6,8,5,4,2,3,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[5,8,2,4,3,7,6,1]=>{{1,2,3,5,8},{4},{6,7}}
[8,1,3,4,2,6,5,7]=>{{1,2,5,7,8},{3},{4},{6}}
[8,1,3,2,5,6,4,7]=>{{1,2,4,7,8},{3},{5},{6}}
[8,1,2,4,5,3,7,6]=>{{1,2,3,6,8},{4},{5},{7}}
[6,5,3,8,4,2,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[7,4,5,1,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,3,5,6,2,8,1]=>{{1,2,4,5,6,7,8},{3}}
[6,7,8,4,1,3,5,2]=>{{1,2,3,5,6,7,8},{4}}
[3,1,6,8,4,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,3,6,1,5,7,4,2]=>{{1,2,3,4,6,7,8},{5}}
[3,2,7,5,8,6,1,4]=>{{1,3,7},{2},{4,5,8},{6}}
[2,5,4,7,8,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,7,8,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,8,1,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,3,8,6,2,1,5]=>{{1,7},{2,4,5,6,8},{3}}
[2,4,7,8,3,5,6,1]=>{{1,2,4,8},{3,5,6,7}}
[3,2,7,6,1,8,4,5]=>{{1,3,4,5,6,7,8},{2}}
[3,2,6,8,1,7,4,5]=>{{1,3,4,5,6,7,8},{2}}
[4,3,6,2,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,6,2,3,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,2,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[8,4,5,3,2,1,7,6]=>{{1,6,8},{2,3,4,5},{7}}
[5,8,3,4,2,1,7,6]=>{{1,2,5,6,8},{3},{4},{7}}
[6,8,4,2,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,3,2,7,1,5]=>{{1,6,7},{2,3,4,5,8}}
[5,8,3,7,2,1,6,4]=>{{1,2,4,5,6,7,8},{3}}
[2,5,6,4,7,1,8,3]=>{{1,2,3,5,6,7,8},{4}}
[6,4,7,3,8,2,1,5]=>{{1,2,3,4,6,7},{5,8}}
[6,7,4,3,2,1,8,5]=>{{1,6},{2,5,7,8},{3,4}}
[8,4,3,7,2,1,5,6]=>{{1,6,8},{2,4,5,7},{3}}
[1,2,6,5,8,7,3,4]=>{{1},{2},{3,6,7},{4,5,8}}
[1,5,2,8,4,6,7,3]=>{{1},{2,3,4,5,8},{6},{7}}
[1,5,2,7,4,6,8,3]=>{{1},{2,3,4,5,7,8},{6}}
[5,1,2,7,3,6,8,4]=>{{1,2,3,5},{4,7,8},{6}}
[5,1,2,8,3,6,7,4]=>{{1,2,3,5},{4,8},{6},{7}}
[5,6,3,4,8,7,2,1]=>{{1,5,8},{2,6,7},{3},{4}}
[6,5,3,4,8,7,2,1]=>{{1,2,5,6,7,8},{3},{4}}
[4,1,2,8,3,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[4,1,2,7,3,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[7,5,3,8,4,6,2,1]=>{{1,2,4,5,7,8},{3},{6}}
[8,5,3,7,4,6,2,1]=>{{1,8},{2,4,5,7},{3},{6}}
[5,8,1,2,3,4,7,6]=>{{1,3,5},{2,4,6,8},{7}}
[7,1,2,8,3,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[6,1,8,2,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[6,1,7,2,3,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,6,8,2,4,5,7,3]=>{{1},{2,4,5,6},{3,8},{7}}
[4,3,8,7,5,6,2,1]=>{{1,2,3,4,7,8},{5},{6}}
[1,8,2,7,4,6,5,3]=>{{1},{2,3,8},{4,5,7},{6}}
[7,1,6,2,3,5,8,4]=>{{1,2,4,7,8},{3,5,6}}
[8,1,6,2,3,5,7,4]=>{{1,2,4,8},{3,5,6},{7}}
[8,1,7,2,3,5,6,4]=>{{1,2,4,8},{3,5,6,7}}
[5,8,3,7,4,6,2,1]=>{{1,2,4,5,7,8},{3},{6}}
[6,8,7,3,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,2,4,5,3,6]=>{{1},{2,4,5,6,8},{3,7}}
[8,7,1,2,3,4,6,5]=>{{1,3,5,8},{2,4,6,7}}
[8,6,1,2,3,4,7,5]=>{{1,3,5,8},{2,4,6},{7}}
[8,1,6,2,3,5,4,7]=>{{1,2,4,7,8},{3,5,6}}
[1,7,6,2,4,5,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,7,4,6,3,5,2]=>{{1},{2,8},{3,5,6,7},{4}}
[1,8,3,5,7,2,6,4]=>{{1},{2,4,5,6,7,8},{3}}
[2,3,4,6,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,3,5,7,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,3,7,8,5,1]=>{{1,2,3,4,6,8},{5,7}}
[2,5,7,1,8,6,3,4]=>{{1,2,4,5,8},{3,7},{6}}
[8,2,4,5,1,3,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[2,6,7,1,8,4,5,3]=>{{1,2,4,6},{3,5,7,8}}
[5,8,3,1,4,2,6,7]=>{{1,4,5},{2,6,7,8},{3}}
[3,8,4,2,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,4,1,8,5,6,3,7]=>{{1,2,3,4,7,8},{5},{6}}
[1,6,2,7,8,5,3,4]=>{{1},{2,3,4,5,6,7,8}}
[3,5,2,6,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,6,7,3,8,2]=>{{1,3,4,6},{2,5,7,8}}
[2,8,4,1,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,1,7,4,2,6]=>{{1,4,6,8},{2,5,7},{3}}
[4,2,8,7,1,5,3,6]=>{{1,3,4,5,6,7,8},{2}}
[5,2,6,8,1,7,4,3]=>{{1,5},{2},{3,4,6,7,8}}
[5,7,3,2,6,8,1,4]=>{{1,2,4,5,6,7,8},{3}}
[8,4,7,3,1,6,2,5]=>{{1,5,8},{2,3,4,7},{6}}
[6,7,1,2,3,5,8,4]=>{{1,3,5,6},{2,4,7,8}}
[3,1,6,7,8,4,2,5]=>{{1,2,3,4,6,7},{5,8}}
[3,1,4,8,5,6,2,7]=>{{1,2,3,4,7,8},{5},{6}}
[8,3,1,4,5,7,2,6]=>{{1,2,3,6,7,8},{4},{5}}
[8,6,2,3,5,1,4,7]=>{{1,2,3,4,6,7,8},{5}}
[8,2,4,5,7,3,1,6]=>{{1,3,4,5,6,7,8},{2}}
[2,6,3,8,7,5,4,1]=>{{1,2,4,5,6,7,8},{3}}
[8,2,3,7,5,4,1,6]=>{{1,4,6,7,8},{2},{3},{5}}
[8,2,6,3,5,4,1,7]=>{{1,7,8},{2},{3,4,6},{5}}
[8,6,1,5,2,4,3,7]=>{{1,3,7,8},{2,4,5,6}}
[8,6,2,4,1,5,3,7]=>{{1,2,3,5,6,7,8},{4}}
[8,4,1,6,5,3,2,7]=>{{1,2,3,4,6,7,8},{5}}
[8,3,6,1,5,4,2,7]=>{{1,2,3,4,6,7,8},{5}}
[8,3,2,6,5,4,1,7]=>{{1,7,8},{2,3},{4,6},{5}}
[8,3,2,5,7,4,1,6]=>{{1,4,5,6,7,8},{2,3}}
[8,3,1,7,5,4,2,6]=>{{1,2,3,4,6,7,8},{5}}
[8,2,7,4,1,5,3,6]=>{{1,5,6,8},{2},{3,7},{4}}
[6,1,3,8,7,5,4,2]=>{{1,2,4,5,6,7,8},{3}}
[3,6,1,8,7,5,4,2]=>{{1,3},{2,4,5,6,7,8}}
[3,8,1,5,7,6,4,2]=>{{1,3},{2,8},{4,5,7},{6}}
[3,5,2,8,7,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[3,4,8,2,7,6,5,1]=>{{1,3,8},{2,4},{5,7},{6}}
[3,4,8,7,1,6,5,2]=>{{1,2,3,4,5,7,8},{6}}
[8,1,3,5,7,6,4,2]=>{{1,2,8},{3},{4,5,7},{6}}
[4,1,8,5,7,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[8,2,7,1,4,5,6,3]=>{{1,3,4,5,6,7,8},{2}}
[8,1,7,3,4,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[8,3,1,7,2,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[3,8,2,4,7,6,5,1]=>{{1,2,3,8},{4},{5,7},{6}}
[2,8,3,7,4,6,5,1]=>{{1,2,8},{3},{4,5,7},{6}}
[8,2,3,7,1,6,5,4]=>{{1,4,5,7,8},{2},{3},{6}}
[8,2,7,1,3,6,5,4]=>{{1,4,8},{2},{3,5,7},{6}}
[8,1,7,2,6,4,3,5]=>{{1,2,4,5,6,8},{3,7}}
[8,1,7,5,2,4,3,6]=>{{1,2,4,5,6,8},{3,7}}
[8,2,3,7,4,6,1,5]=>{{1,4,5,7,8},{2},{3},{6}}
[2,4,8,5,7,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[8,2,4,3,7,6,1,5]=>{{1,5,7,8},{2},{3,4},{6}}
[8,2,7,3,5,1,4,6]=>{{1,6,8},{2},{3,4,7},{5}}
[8,2,7,4,3,1,5,6]=>{{1,6,8},{2},{3,5,7},{4}}
[8,2,7,3,1,5,6,4]=>{{1,3,4,5,6,7,8},{2}}
[8,2,1,5,7,6,4,3]=>{{1,3,8},{2},{4,5,7},{6}}
[6,2,1,8,7,5,4,3]=>{{1,3,4,5,6,7,8},{2}}
[6,1,8,2,7,5,4,3]=>{{1,2,4,5,6,7},{3,8}}
[8,1,7,3,5,2,6,4]=>{{1,2,3,4,6,7,8},{5}}
[8,1,5,2,7,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[8,1,7,2,4,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[8,2,4,1,7,6,5,3]=>{{1,3,4,8},{2},{5,7},{6}}
[4,2,8,3,7,6,5,1]=>{{1,3,4,8},{2},{5,7},{6}}
[4,8,2,1,7,6,5,3]=>{{1,4},{2,3,8},{5,7},{6}}
[5,1,8,7,2,6,4,3]=>{{1,2,5},{3,8},{4,7},{6}}
[5,8,1,3,7,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[8,2,5,4,1,7,6,3]=>{{1,3,5,8},{2},{4},{6,7}}
[5,1,4,8,7,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[8,1,4,3,7,6,5,2]=>{{1,2,8},{3,4},{5,7},{6}}
[4,8,1,3,7,6,5,2]=>{{1,3,4},{2,8},{5,7},{6}}
[4,3,8,1,7,6,5,2]=>{{1,4},{2,3,8},{5,7},{6}}
[5,8,6,3,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[5,7,6,3,2,4,1,8]=>{{1,2,5,7},{3,4,6},{8}}
[6,5,7,2,4,3,1,8]=>{{1,3,6,7},{2,4,5},{8}}
[5,7,1,3,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,3,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,5,1,3,2,4,6,7]=>{{1,3,4,6,7,8},{2,5}}
[7,5,8,2,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,2,5,4,8,3]=>{{1,2,3,4,6,7,8},{5}}
[6,8,1,2,5,7,4,3]=>{{1,2,3,4,6,7,8},{5}}
[8,1,6,4,2,3,5,7]=>{{1,2,5,7,8},{3,6},{4}}
[1,5,4,8,2,3,7,6]=>{{1},{2,5},{3,4,6,8},{7}}
[1,7,8,2,3,5,6,4]=>{{1},{2,3,4,5,6,7,8}}
[7,5,8,2,3,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,2,6,8,3,5]=>{{1,3,7},{2,4},{5,6,8}}
[6,2,8,1,5,7,3,4]=>{{1,3,4,6,7,8},{2},{5}}
[7,3,5,4,2,1,8,6]=>{{1,6,7,8},{2,3,5},{4}}
[7,3,2,8,5,6,1,4]=>{{1,7},{2,3},{4,8},{5},{6}}
[1,7,4,3,6,8,5,2]=>{{1},{2,5,6,7,8},{3,4}}
[4,7,6,5,2,3,8,1]=>{{1,2,4,5,7,8},{3,6}}
[4,7,6,5,1,3,8,2]=>{{1,4,5},{2,7,8},{3,6}}
[6,7,4,2,1,8,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,7,6,3,2,8,4,5]=>{{1},{2,3,4,5,6,7,8}}
[5,4,2,1,7,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[6,5,8,1,7,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,2,3,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,8,5,3,6,7]=>{{1,2,3,4,6,7,8},{5}}
[3,5,8,2,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[3,7,6,1,5,2,8,4]=>{{1,2,3,4,6,7,8},{5}}
[1,7,6,2,5,8,4,3]=>{{1},{2,4,7},{3,6,8},{5}}
[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,7,6,5,8,1,2,4]=>{{1,3,6},{2,7},{4,5,8}}
[3,7,6,2,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,6,8,5,1,2,7]=>{{1,2,3,4,6,7,8},{5}}
[2,7,1,5,8,4,3,6]=>{{1,2,3,7},{4,5,6,8}}
[2,7,6,1,8,4,3,5]=>{{1,2,3,4,6,7},{5,8}}
[7,1,2,6,3,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[7,2,6,3,4,5,1,8]=>{{1,7},{2},{3,4,5,6},{8}}
[6,7,8,4,2,5,3,1]=>{{1,2,3,5,6,7,8},{4}}
[6,1,2,5,7,8,4,3]=>{{1,2,3,6,8},{4,5,7}}
[4,1,2,7,8,5,3,6]=>{{1,2,3,4,7},{5,6,8}}
[4,7,3,1,2,6,8,5]=>{{1,4},{2,5,7,8},{3},{6}}
[3,7,6,1,5,8,2,4]=>{{1,3,4,6,8},{2,7},{5}}
[3,8,5,6,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[3,2,6,4,7,8,5,1]=>{{1,3,6,8},{2},{4},{5,7}}
[4,2,7,5,8,3,1,6]=>{{1,3,4,5,6,7,8},{2}}
[4,2,7,1,3,8,6,5]=>{{1,4},{2},{3,5,6,7,8}}
[5,2,1,4,7,8,3,6]=>{{1,3,5,7},{2},{4},{6,8}}
[5,6,2,7,3,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,1,3,8,5,4,7,2]=>{{1,2,4,6,8},{3},{5},{7}}
[2,7,6,8,5,1,3,4]=>{{1,2,3,6,7},{4,8},{5}}
[1,5,8,6,4,2,3,7]=>{{1},{2,4,5,6},{3,7,8}}
[2,5,8,6,4,1,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[1,6,2,3,5,8,7,4]=>{{1},{2,3,4,6,8},{5},{7}}
[4,7,2,3,1,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[6,7,3,1,5,4,8,2]=>{{1,4,6},{2,7,8},{3},{5}}
[7,4,6,2,8,3,5,1]=>{{1,5,7,8},{2,4},{3,6}}
[7,3,5,1,4,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[3,4,6,5,1,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[7,5,4,3,8,6,2,1]=>{{1,2,5,7,8},{3,4},{6}}
[4,3,8,2,6,7,5,1]=>{{1,2,3,4,8},{5,6,7}}
[4,3,8,2,5,7,1,6]=>{{1,2,3,4,6,7,8},{5}}
[5,1,8,6,4,7,2,3]=>{{1,2,4,5,6,7},{3,8}}
[4,2,6,1,5,3,8,7]=>{{1,4},{2},{3,6},{5},{7,8}}
[6,7,2,3,1,5,8,4]=>{{1,5,6},{2,3,4,7,8}}
[7,5,2,3,8,1,6,4]=>{{1,6,7},{2,3,4,5,8}}
[7,5,2,3,8,4,1,6]=>{{1,7},{2,3,4,5,6,8}}
[4,5,1,7,6,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,5,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,6,3,1,4,2,5,7]=>{{1,4,5,7,8},{2,6},{3}}
[4,5,1,6,2,8,7,3]=>{{1,3,4,6,8},{2,5},{7}}
[4,8,3,6,1,7,2,5]=>{{1,2,4,5,6,7,8},{3}}
[6,2,7,8,3,4,5,1]=>{{1,4,6,8},{2},{3,5,7}}
[1,2,4,6,8,5,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[2,1,7,5,8,6,3,4]=>{{1,2},{3,7},{4,5,8},{6}}
[7,3,8,4,6,5,1,2]=>{{1,7},{2,3,8},{4},{5,6}}
[6,3,8,7,5,1,4,2]=>{{1,6},{2,3,8},{4,7},{5}}
[5,3,6,4,1,2,8,7]=>{{1,5},{2,3,6},{4},{7,8}}
[3,2,4,5,1,8,6,7]=>{{1,3,4,5},{2},{6,7,8}}
[4,2,5,1,7,8,3,6]=>{{1,4},{2},{3,5,7},{6,8}}
[2,5,4,1,3,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[1,4,5,3,8,2,6,7]=>{{1},{2,3,4,5,6,7,8}}
[5,1,8,2,4,3,6,7]=>{{1,2,4,5},{3,6,7,8}}
[1,5,4,8,2,3,6,7]=>{{1},{2,5},{3,4,6,7,8}}
[4,8,3,1,6,7,2,5]=>{{1,4},{2,5,6,7,8},{3}}
[3,4,8,2,6,5,7,1]=>{{1,3,8},{2,4},{5,6},{7}}
[3,6,2,4,8,7,1,5]=>{{1,2,3,6,7},{4},{5,8}}
[4,7,3,2,6,8,1,5]=>{{1,2,4,7},{3},{5,6,8}}
[7,3,4,6,8,1,2,5]=>{{1,2,3,4,6,7},{5,8}}
[3,6,7,2,5,8,1,4]=>{{1,3,7},{2,4,6,8},{5}}
[1,5,6,8,3,7,2,4]=>{{1},{2,3,5,6,7},{4,8}}
[6,1,5,8,3,4,7,2]=>{{1,2,4,6,8},{3,5},{7}}
[5,6,8,1,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[2,8,5,6,3,4,7,1]=>{{1,2,8},{3,5},{4,6},{7}}
[6,8,1,3,5,4,7,2]=>{{1,3,4,6},{2,8},{5},{7}}
[8,1,6,3,5,4,7,2]=>{{1,2,8},{3,4,6},{5},{7}}
[7,1,2,5,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[6,2,4,8,1,7,3,5]=>{{1,3,4,5,6,7,8},{2}}
[3,1,7,8,5,4,6,2]=>{{1,2,3,4,6,7,8},{5}}
[1,6,2,7,4,8,5,3]=>{{1},{2,3,6,8},{4,5,7}}
[2,7,1,8,4,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,8,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,3,5,8,1,4]=>{{1,2,7},{3,4,6,8},{5}}
[2,7,5,6,8,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,8,1,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[5,1,6,8,7,2,3,4]=>{{1,2,3,5,6,7},{4,8}}
[1,5,7,6,8,2,3,4]=>{{1},{2,4,5,6,8},{3,7}}
[3,8,6,7,5,1,2,4]=>{{1,3,6},{2,4,7,8},{5}}
[4,7,5,8,6,3,1,2]=>{{1,2,4,7,8},{3,5,6}}
[1,6,8,3,2,5,4,7]=>{{1},{2,5,6},{3,4,7,8}}
[2,6,8,1,5,4,7,3]=>{{1,2,4,6},{3,8},{5},{7}}
[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[2,3,7,6,5,1,8,4]=>{{1,2,3,4,6,7,8},{5}}
[6,1,5,8,3,2,7,4]=>{{1,2,6},{3,5},{4,8},{7}}
[3,1,2,4,8,5,7,6]=>{{1,2,3},{4},{5,6,8},{7}}
[2,5,8,4,6,3,1,7]=>{{1,2,3,5,6,7,8},{4}}
[7,1,5,4,8,3,2,6]=>{{1,2,7},{3,5,6,8},{4}}
[6,4,1,7,5,3,2,8]=>{{1,3,6},{2,4,7},{5},{8}}
[2,7,6,4,8,1,5,3]=>{{1,2,3,5,6,7,8},{4}}
[7,2,5,4,8,1,6,3]=>{{1,6,7},{2},{3,5,8},{4}}
[1,7,2,5,3,8,6,4]=>{{1},{2,3,4,5,6,7,8}}
[7,2,3,8,6,1,5,4]=>{{1,5,6,7},{2},{3},{4,8}}
[7,3,2,5,8,1,6,4]=>{{1,6,7},{2,3},{4,5,8}}
[5,3,8,4,1,2,6,7]=>{{1,5},{2,3,6,7,8},{4}}
[2,4,8,3,7,1,5,6]=>{{1,2,3,4,6,8},{5,7}}
[5,2,8,4,1,6,3,7]=>{{1,5},{2},{3,7,8},{4},{6}}
[7,6,5,2,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,1,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,7,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,2,4,6,1,5]=>{{1,3,7},{2,4,5,8},{6}}
[5,7,1,3,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,2,7,6,3,5,8,1]=>{{1,3,4,5,6,7,8},{2}}
[8,4,7,6,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,4,2,3,5,6]=>{{1,2,3,5,6,7,8},{4}}
[6,5,1,3,8,7,4,2]=>{{1,3,4,6,7},{2,5,8}}
[4,7,8,3,2,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[6,1,8,5,3,7,2,4]=>{{1,2,6,7},{3,4,5,8}}
[5,1,6,8,3,7,4,2]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,1,7,4,3,2]=>{{1,2,4,6,8},{3,5,7}}
[7,6,4,1,3,5,8,2]=>{{1,2,3,4,5,6,7,8}}
[8,2,3,7,1,4,5,6]=>{{1,4,5,6,7,8},{2},{3}}
[2,8,3,7,1,4,5,6]=>{{1,2,4,5,6,7,8},{3}}
[5,6,2,7,4,3,1,8]=>{{1,4,5,7},{2,3,6},{8}}
[8,6,2,7,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,5,2,1,4,6]=>{{1,3,6,8},{2,4,5,7}}
[6,8,4,7,3,1,5,2]=>{{1,6},{2,8},{3,4,5,7}}
[4,8,6,5,1,2,7,3]=>{{1,4,5},{2,3,6,8},{7}}
[4,8,6,5,1,2,3,7]=>{{1,4,5},{2,3,6,7,8}}
[3,4,5,1,7,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[3,8,7,6,5,1,2,4]=>{{1,2,3,4,6,7,8},{5}}
[8,4,6,7,1,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,2,6,1,8,4,3]=>{{1,5},{2,3,4,6,7,8}}
[5,7,2,6,1,3,8,4]=>{{1,5},{2,3,4,6,7,8}}
[5,8,2,6,1,4,7,3]=>{{1,5},{2,3,8},{4,6},{7}}
[3,8,7,5,6,1,4,2]=>{{1,3,4,5,6,7},{2,8}}
[6,8,4,7,2,1,5,3]=>{{1,6},{2,3,4,5,7,8}}
[7,4,6,5,1,3,8,2]=>{{1,2,4,5,7,8},{3,6}}
[1,7,3,4,5,2,8,6]=>{{1},{2,6,7,8},{3},{4},{5}}
[4,8,2,1,3,5,6,7]=>{{1,4},{2,3,5,6,7,8}}
[1,7,2,5,4,3,8,6]=>{{1},{2,3,6,7,8},{4,5}}
[2,6,7,3,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,7,4,3,8,6]=>{{1,2},{3,4,5,6,7,8}}
[4,1,8,7,5,6,2,3]=>{{1,2,4,7},{3,8},{5},{6}}
[1,5,8,7,4,3,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,1,3,8,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,4,6,8,3,5]=>{{1,2},{3,7},{4},{5,6,8}}
[1,7,2,4,6,8,3,5]=>{{1},{2,3,7},{4},{5,6,8}}
[8,6,4,2,7,3,5,1]=>{{1,8},{2,3,4,6},{5,7}}
[7,4,6,1,2,3,8,5]=>{{1,2,4,5,7,8},{3,6}}
[1,8,6,2,7,3,5,4]=>{{1},{2,4,8},{3,6},{5,7}}
[1,7,8,6,2,3,5,4]=>{{1},{2,5,7},{3,4,6,8}}
[2,1,8,3,5,7,6,4]=>{{1,2},{3,4,8},{5},{6,7}}
[3,5,8,1,7,6,2,4]=>{{1,3,4,8},{2,5,7},{6}}
[2,8,1,3,6,7,5,4]=>{{1,2,3,4,8},{5,6,7}}
[7,2,4,8,6,1,5,3]=>{{1,5,6,7},{2},{3,4,8}}
[6,4,3,2,8,1,7,5]=>{{1,6},{2,4},{3},{5,8},{7}}
[6,2,4,3,8,1,7,5]=>{{1,6},{2},{3,4},{5,8},{7}}
[5,8,4,3,1,6,7,2]=>{{1,5},{2,8},{3,4},{6},{7}}
[4,2,8,1,5,7,6,3]=>{{1,4},{2},{3,8},{5},{6,7}}
[6,3,7,2,5,4,8,1]=>{{1,2,3,4,6,7,8},{5}}
[5,4,7,3,2,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[5,7,2,6,3,4,8,1]=>{{1,2,3,5,7,8},{4,6}}
[3,7,5,4,6,2,8,1]=>{{1,2,3,5,6,7,8},{4}}
[6,8,3,2,1,7,4,5]=>{{1,2,4,5,6,7,8},{3}}
[4,8,1,7,5,3,2,6]=>{{1,2,3,4,6,7,8},{5}}
[5,4,3,7,2,8,6,1]=>{{1,2,4,5,6,7,8},{3}}
[3,6,5,7,2,8,4,1]=>{{1,2,3,5,6,8},{4,7}}
[4,6,5,3,8,2,1,7]=>{{1,3,4,5,7,8},{2,6}}
[2,6,5,8,7,3,1,4]=>{{1,2,3,5,6,7},{4,8}}
[6,3,8,4,1,7,2,5]=>{{1,2,3,5,6,7,8},{4}}
[7,2,8,1,6,4,3,5]=>{{1,3,4,5,6,7,8},{2}}
[8,2,6,4,3,5,1,7]=>{{1,7,8},{2},{3,5,6},{4}}
[5,4,2,8,6,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,8,7,5,3,1,4,6]=>{{1,2,6,8},{3,4,5,7}}
[2,5,6,3,1,4,8,7]=>{{1,2,5},{3,4,6},{7,8}}
[2,4,7,8,5,3,1,6]=>{{1,2,3,4,6,7,8},{5}}
[6,5,3,2,4,1,8,7]=>{{1,6},{2,4,5},{3},{7,8}}
[6,5,8,7,3,2,4,1]=>{{1,2,3,5,6,8},{4,7}}
[2,1,4,7,8,5,3,6]=>{{1,2},{3,4,7},{5,6,8}}
[8,3,1,6,5,7,4,2]=>{{1,2,3,8},{4,6,7},{5}}
[8,5,6,7,3,1,4,2]=>{{1,2,3,5,6,8},{4,7}}
[8,7,5,3,2,6,4,1]=>{{1,8},{2,3,4,5,7},{6}}
[8,5,3,1,4,6,7,2]=>{{1,2,4,5,8},{3},{6},{7}}
[8,5,1,6,4,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[6,1,4,3,7,8,2,5]=>{{1,2,5,6,7,8},{3,4}}
[6,1,2,7,5,8,3,4]=>{{1,2,3,4,6,7,8},{5}}
[2,7,3,1,4,6,8,5]=>{{1,2,4,5,7,8},{3},{6}}
[2,8,3,1,6,5,7,4]=>{{1,2,4,8},{3},{5,6},{7}}
[3,8,5,6,7,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,1,2,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,5,8,1,4,6,7,3]=>{{1,2,4,5},{3,8},{6},{7}}
[2,1,8,7,5,4,6,3]=>{{1,2},{3,8},{4,6,7},{5}}
[7,8,3,4,1,6,5,2]=>{{1,5,7},{2,8},{3},{4},{6}}
[8,7,3,4,2,6,5,1]=>{{1,8},{2,5,7},{3},{4},{6}}
[8,4,5,2,3,7,1,6]=>{{1,6,7,8},{2,4},{3,5}}
[4,7,2,8,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,2,3,8,1,6]=>{{1,2,4,7},{3,5},{6,8}}
[6,4,7,5,2,8,3,1]=>{{1,6,8},{2,4,5},{3,7}}
[7,5,1,3,6,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,3,7,8,4,1]=>{{1,6,8},{2,3,4,5,7}}
[7,2,6,3,1,5,8,4]=>{{1,3,4,5,6,7,8},{2}}
[4,6,3,8,7,5,1,2]=>{{1,2,4,5,6,7,8},{3}}
[2,8,4,1,5,7,6,3]=>{{1,2,3,4,8},{5},{6,7}}
[1,8,4,2,5,7,6,3]=>{{1},{2,3,4,8},{5},{6,7}}
[2,8,5,4,1,7,6,3]=>{{1,2,3,5,8},{4},{6,7}}
[2,5,8,3,7,1,6,4]=>{{1,2,5,6,7},{3,4,8}}
[1,8,5,2,4,7,6,3]=>{{1},{2,3,4,5,8},{6,7}}
[1,4,6,2,8,7,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[7,8,2,4,1,6,5,3]=>{{1,5,7},{2,3,8},{4},{6}}
[2,4,6,1,8,7,5,3]=>{{1,2,4},{3,5,6,7,8}}
[2,8,4,5,1,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[3,5,8,2,7,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[2,1,6,8,7,5,3,4]=>{{1,2},{3,5,6,7},{4,8}}
[1,8,2,4,5,7,6,3]=>{{1},{2,3,8},{4},{5},{6,7}}
[1,2,8,3,5,7,6,4]=>{{1},{2},{3,4,8},{5},{6,7}}
[1,3,8,2,5,7,6,4]=>{{1},{2,3,4,8},{5},{6,7}}
[2,3,8,1,5,7,6,4]=>{{1,2,3,4,8},{5},{6,7}}
[2,6,1,8,7,5,3,4]=>{{1,2,3,5,6,7},{4,8}}
[1,6,2,8,7,5,3,4]=>{{1},{2,3,5,6,7},{4,8}}
[1,6,3,8,7,5,2,4]=>{{1},{2,5,6,7},{3},{4,8}}
[2,6,3,8,7,5,1,4]=>{{1,2,5,6,7},{3},{4,8}}
[3,2,8,1,5,7,6,4]=>{{1,3,4,8},{2},{5},{6,7}}
[3,1,8,2,5,7,6,4]=>{{1,2,3,4,8},{5},{6,7}}
[2,8,1,4,5,7,6,3]=>{{1,2,3,8},{4},{5},{6,7}}
[7,8,2,1,4,6,5,3]=>{{1,4,5,7},{2,3,8},{6}}
[2,3,6,8,7,5,1,4]=>{{1,2,3,5,6,7},{4,8}}
[3,1,6,8,7,2,5,4]=>{{1,2,3,6},{4,8},{5,7}}
[3,8,4,5,1,6,2,7]=>{{1,3,4,5},{2,7,8},{6}}
[6,1,4,5,7,2,3,8]=>{{1,2,6},{3,4,5,7},{8}}
[8,1,4,7,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,6,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,6,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,3,6,1,5,7,2,4]=>{{1,4,8},{2,3,6,7},{5}}
[8,4,6,3,1,2,5,7]=>{{1,5,7,8},{2,3,4,6}}
[6,8,1,4,5,2,3,7]=>{{1,2,3,6,7,8},{4},{5}}
[1,5,8,4,6,2,3,7]=>{{1},{2,5,6},{3,7,8},{4}}
[2,1,6,5,3,8,4,7]=>{{1,2},{3,4,5,6,7,8}}
[5,6,8,1,4,2,3,7]=>{{1,4,5},{2,6},{3,7,8}}
[5,7,4,8,1,2,3,6]=>{{1,5},{2,3,4,6,7,8}}
[8,2,1,5,3,7,4,6]=>{{1,3,4,5,6,7,8},{2}}
[4,7,8,1,2,6,3,5]=>{{1,4},{2,3,5,7,8},{6}}
[8,7,1,5,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,6,5,8,7,2,3,4]=>{{1},{2,6},{3,5,7},{4,8}}
[3,7,1,6,2,4,8,5]=>{{1,3},{2,5,7,8},{4,6}}
[5,1,2,7,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,1,7,2,5,8,3,4]=>{{1,2,4,6,8},{3,7},{5}}
[1,7,6,5,8,2,3,4]=>{{1},{2,3,6,7},{4,5,8}}
[1,6,8,5,7,2,3,4]=>{{1},{2,6},{3,4,5,7,8}}
[7,5,1,2,6,8,3,4]=>{{1,3,7},{2,4,5,6,8}}
[6,1,5,2,7,8,3,4]=>{{1,2,4,6,8},{3,5,7}}
[1,6,3,8,7,2,4,5]=>{{1},{2,6},{3},{4,5,7,8}}
[1,7,3,2,4,6,8,5]=>{{1},{2,4,5,7,8},{3},{6}}
[8,3,1,4,2,5,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[3,1,2,7,8,4,6,5]=>{{1,2,3},{4,6,7},{5,8}}
[5,1,2,6,8,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,8,6,2,5,7,3,4]=>{{1},{2,4,8},{3,6,7},{5}}
[5,7,8,1,2,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[8,1,5,7,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,8,5,2,3,4]=>{{1,2,3,6,7},{4,8},{5}}
[3,7,1,2,8,4,6,5]=>{{1,3},{2,4,6,7},{5,8}}
[8,3,1,2,7,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[1,5,8,7,6,2,3,4]=>{{1},{2,5,6},{3,4,7,8}}
[7,8,6,1,5,2,3,4]=>{{1,2,3,4,6,7,8},{5}}
[7,8,6,3,1,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,3,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[1,7,4,8,2,5,3,6]=>{{1},{2,3,4,5,6,7,8}}
[3,8,6,1,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[7,1,8,2,4,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[7,6,8,4,1,5,3,2]=>{{1,2,3,5,6,7,8},{4}}
[7,3,2,8,1,5,4,6]=>{{1,4,5,6,7,8},{2,3}}
[3,5,4,1,7,2,6,8]=>{{1,3,4},{2,5,6,7},{8}}
[6,4,7,3,2,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,5,3,8,4,1,2]=>{{1,7},{2,3,4,5,6,8}}
[6,4,5,7,8,1,3,2]=>{{1,6},{2,3,4,5,7,8}}
[3,7,4,1,6,8,5,2]=>{{1,3,4},{2,5,6,7,8}}
[3,1,2,7,6,8,5,4]=>{{1,2,3},{4,5,6,7,8}}
[6,3,2,8,4,5,1,7]=>{{1,4,5,6,7,8},{2,3}}
[6,1,8,3,5,4,2,7]=>{{1,2,3,4,6,7,8},{5}}
[3,8,5,2,4,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[1,6,4,8,3,5,2,7]=>{{1},{2,3,4,5,6,7,8}}
[1,5,4,8,6,3,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[4,8,2,5,3,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[3,8,4,5,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[4,1,8,6,5,3,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[5,7,8,4,6,3,2,1]=>{{1,3,5,6,8},{2,7},{4}}
[5,3,2,8,6,4,7,1]=>{{1,4,5,6,8},{2,3},{7}}
[6,8,1,2,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,3,6,2,4,1]=>{{1,2,5,6,8},{3,4,7}}
[7,5,2,3,4,8,6,1]=>{{1,6,7,8},{2,3,4,5}}
[7,3,5,4,2,8,6,1]=>{{1,6,7,8},{2,3,5},{4}}
[5,6,1,3,2,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,5,1,3,7,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,2,1,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,2,1,3,5,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,2,3,1,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[3,6,4,2,5,1,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[3,1,6,4,7,5,2,8]=>{{1,2,3,5,6,7},{4},{8}}
[3,6,2,7,5,4,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,4,7,5,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[2,5,7,3,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[2,3,5,8,6,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,4,7,3,8,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[3,4,2,7,5,8,6,1]=>{{1,2,3,4,6,7,8},{5}}
[3,1,5,4,7,8,6,2]=>{{1,2,3,5,6,7,8},{4}}
[4,5,7,2,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,1,4,6,5,2]=>{{1,2,3,4,5,7,8},{6}}
[2,5,8,7,4,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,6,4,7,5,3,8,1]=>{{1,2,3,4,6,7,8},{5}}
[6,2,4,7,1,3,8,5]=>{{1,3,4,5,6,7,8},{2}}
[7,3,5,1,4,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[5,4,7,1,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[6,1,4,7,5,3,8,2]=>{{1,2,3,4,6,7,8},{5}}
[8,7,4,3,1,5,6,2]=>{{1,2,5,6,7,8},{3,4}}
[8,7,1,4,3,5,6,2]=>{{1,2,3,5,6,7,8},{4}}
[6,1,8,4,7,3,2,5]=>{{1,2,3,5,6,7,8},{4}}
[4,7,3,6,1,2,8,5]=>{{1,2,4,5,6,7,8},{3}}
[5,2,1,7,4,3,8,6]=>{{1,3,4,5,6,7,8},{2}}
[4,7,6,2,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,2,5,3,4,1]=>{{1,2,3,4,6,7,8},{5}}
[2,3,6,1,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[2,6,8,7,5,3,1,4]=>{{1,2,3,4,6,7,8},{5}}
[6,4,1,7,5,2,8,3]=>{{1,2,3,4,6,7,8},{5}}
[5,7,8,2,3,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[4,8,7,1,2,5,6,3]=>{{1,4},{2,3,5,6,7,8}}
[2,8,7,4,1,5,6,3]=>{{1,2,3,5,6,7,8},{4}}
[8,6,2,1,5,7,4,3]=>{{1,2,3,4,6,7,8},{5}}
[3,8,6,7,5,2,1,4]=>{{1,2,3,4,6,7,8},{5}}
[6,1,3,7,5,8,2,4]=>{{1,2,4,6,7,8},{3},{5}}
[4,7,3,1,8,5,6,2]=>{{1,4},{2,5,6,7,8},{3}}
[2,6,7,5,3,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,6,4,5,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,1,4,5,8,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[6,1,8,5,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,1,5,6,8,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[6,4,1,8,7,2,5,3]=>{{1,2,3,4,6,8},{5,7}}
[1,3,8,5,2,7,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,3,8,6,7,2,4,5]=>{{1},{2,3,4,5,6,7,8}}
[2,8,3,7,6,1,4,5]=>{{1,2,5,6,8},{3},{4,7}}
[4,2,7,8,6,1,3,5]=>{{1,4,5,6,8},{2},{3,7}}
[1,3,8,7,6,2,4,5]=>{{1},{2,3,5,6,8},{4,7}}
[7,4,6,8,5,2,3,1]=>{{1,2,3,4,6,7,8},{5}}
[5,2,6,7,8,1,3,4]=>{{1,3,4,5,6,7,8},{2}}
[4,5,6,8,1,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[3,5,8,6,1,2,7,4]=>{{1,2,3,4,5,6,8},{7}}
[4,2,6,8,7,1,3,5]=>{{1,3,4,5,6,7,8},{2}}
[1,4,6,8,7,2,3,5]=>{{1},{2,3,4,5,6,7,8}}
[4,5,3,8,1,7,2,6]=>{{1,2,4,5,6,7,8},{3}}
[3,5,8,4,1,7,2,6]=>{{1,2,3,5,6,7,8},{4}}
[1,6,5,7,8,2,3,4]=>{{1},{2,6},{3,4,5,7,8}}
[6,5,4,8,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[7,6,4,8,5,1,3,2]=>{{1,2,3,4,6,7,8},{5}}
[6,3,7,5,2,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,7,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,4,6,1,3,8]=>{{1,2,5,6},{3,7},{4},{8}}
[6,1,7,4,5,3,8,2]=>{{1,2,3,6,7,8},{4},{5}}
[8,2,7,3,1,5,4,6]=>{{1,5,6,8},{2},{3,4,7}}
[2,6,4,8,3,1,7,5]=>{{1,2,6},{3,4,5,8},{7}}
[8,1,3,7,5,6,4,2]=>{{1,2,8},{3},{4,7},{5},{6}}
[1,2,5,3,8,6,7,4]=>{{1},{2},{3,4,5,8},{6},{7}}
[4,1,6,5,7,8,2,3]=>{{1,2,4,5,7},{3,6,8}}
[6,1,3,7,4,2,8,5]=>{{1,2,6},{3},{4,5,7,8}}
[6,7,2,4,1,3,8,5]=>{{1,2,3,5,6,7,8},{4}}
[7,3,8,4,2,6,5,1]=>{{1,2,3,5,7,8},{4},{6}}
[8,5,3,4,2,7,1,6]=>{{1,6,7,8},{2,5},{3},{4}}
[1,3,8,2,5,6,7,4]=>{{1},{2,3,4,8},{5},{6},{7}}
[1,8,6,7,2,5,4,3]=>{{1},{2,3,5,6,8},{4,7}}
[7,6,8,3,5,4,2,1]=>{{1,2,3,4,6,7,8},{5}}
[1,6,7,3,8,5,4,2]=>{{1},{2,5,6,8},{3,4,7}}
[8,7,2,4,6,1,5,3]=>{{1,2,3,5,6,7,8},{4}}
[7,8,6,5,2,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,5,2,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,6,7,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,7,8,1,4,2]=>{{1,2,3,5,6,8},{4,7}}
[5,3,7,6,8,4,1,2]=>{{1,2,3,5,7,8},{4,6}}
[7,5,3,2,8,6,4,1]=>{{1,2,4,5,7,8},{3},{6}}
[5,4,8,6,7,2,3,1]=>{{1,3,5,7,8},{2,4,6}}
[5,4,8,6,3,1,2,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,7,3,6,2,8,1]=>{{1,3,4,7,8},{2,5,6}}
[4,5,6,3,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,4,8,7,2,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,7,8,1,3,6]=>{{1,2,5,6,8},{3,4,7}}
[5,3,6,4,8,2,7,1]=>{{1,5,8},{2,3,6},{4},{7}}
[5,3,7,4,6,2,8,1]=>{{1,2,3,5,6,7,8},{4}}
[8,2,6,3,7,4,5,1]=>{{1,8},{2},{3,4,6},{5,7}}
[8,2,4,7,3,5,6,1]=>{{1,8},{2},{3,4,5,6,7}}
[8,2,6,5,7,3,4,1]=>{{1,8},{2},{3,6},{4,5,7}}
[4,5,6,2,7,3,8,1]=>{{1,2,4,5,7,8},{3,6}}
[5,4,6,2,8,3,7,1]=>{{1,5,8},{2,4},{3,6},{7}}
[8,4,6,1,7,2,5,3]=>{{1,2,3,4,6,8},{5,7}}
[5,2,1,6,3,8,7,4]=>{{1,3,5},{2},{4,6,8},{7}}
[4,5,6,3,7,1,8,2]=>{{1,3,4,6},{2,5,7,8}}
[6,3,2,8,5,4,1,7]=>{{1,4,6,7,8},{2,3},{5}}
[4,3,1,5,2,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[8,5,4,1,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,8,4,1,5,2,6,7]=>{{1,3,4},{2,6,7,8},{5}}
[2,5,4,3,8,1,6,7]=>{{1,2,5,6,7,8},{3,4}}
[2,5,7,4,3,1,6,8]=>{{1,2,3,5,6,7},{4},{8}}
[5,3,4,2,7,1,6,8]=>{{1,5,6,7},{2,3,4},{8}}
[3,7,5,4,1,2,6,8]=>{{1,3,5},{2,6,7},{4},{8}}
[4,2,5,1,3,8,7,6]=>{{1,4},{2},{3,5},{6,8},{7}}
[4,3,5,1,2,7,6,8]=>{{1,4},{2,3,5},{6,7},{8}}
[4,1,6,3,5,2,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[4,2,1,8,6,3,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[3,1,7,2,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}
[3,7,5,4,2,1,6,8]=>{{1,2,3,5,6,7},{4},{8}}
[3,7,2,4,1,6,5,8]=>{{1,2,3,5,7},{4},{6},{8}}
[7,3,2,1,6,4,5,8]=>{{1,4,5,6,7},{2,3},{8}}
[2,8,6,1,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,6,1,3,7,8]=>{{1,2,5},{3,4,6},{7},{8}}
[2,5,6,4,1,3,7,8]=>{{1,2,5},{3,6},{4},{7},{8}}
[8,5,2,6,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[7,1,5,6,3,2,4,8]=>{{1,2,4,6,7},{3,5},{8}}
[7,1,2,5,4,6,3,8]=>{{1,2,3,7},{4,5},{6},{8}}
[2,4,1,6,5,3,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[4,1,2,7,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}
[7,1,2,6,5,4,3,8]=>{{1,2,3,7},{4,6},{5},{8}}
[8,2,1,5,6,3,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[2,8,5,1,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,1,4,5,3,2,7,8]=>{{1,2,6},{3,4,5},{7},{8}}
[3,1,6,5,4,2,7,8]=>{{1,2,3,6},{4,5},{7},{8}}
[3,1,4,6,5,2,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[2,1,8,6,3,7,5,4]=>{{1,2},{3,4,5,6,7,8}}
[5,8,3,1,7,6,4,2]=>{{1,4,5,7},{2,8},{3},{6}}
[7,6,3,2,8,5,1,4]=>{{1,7},{2,4,5,6,8},{3}}
[5,6,3,8,7,4,1,2]=>{{1,5,7},{2,4,6,8},{3}}
[5,2,6,8,7,4,1,3]=>{{1,5,7},{2},{3,4,6,8}}
[4,3,8,5,7,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,8,5,4,1,2,7]=>{{1,6},{2,3,7,8},{4,5}}
[6,3,8,4,5,1,2,7]=>{{1,6},{2,3,7,8},{4},{5}}
[5,2,3,1,4,8,6,7]=>{{1,4,5},{2},{3},{6,7,8}}
[5,4,1,3,2,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[5,1,3,4,2,8,6,7]=>{{1,2,5},{3},{4},{6,7,8}}
[5,2,1,4,3,8,6,7]=>{{1,3,5},{2},{4},{6,7,8}}
[4,2,7,3,8,5,1,6]=>{{1,3,4,7},{2},{5,6,8}}
[4,7,3,2,8,5,1,6]=>{{1,2,4,7},{3},{5,6,8}}
[4,3,7,2,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,2,4,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[5,4,3,1,2,8,6,7]=>{{1,2,4,5},{3},{6,7,8}}
[5,3,4,1,2,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[5,2,3,4,1,8,6,7]=>{{1,5},{2},{3},{4},{6,7,8}}
[5,1,7,3,4,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[5,8,7,4,3,1,6,2]=>{{1,3,5,6,7},{2,8},{4}}
[6,8,1,3,4,5,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[3,1,7,8,2,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[6,2,3,7,4,1,8,5]=>{{1,6},{2},{3},{4,5,7,8}}
[6,3,7,4,1,2,5,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,2,6,8,4,3,1,5]=>{{1,7},{2},{3,6},{4,5,8}}
[3,7,2,8,6,5,1,4]=>{{1,2,3,7},{4,8},{5,6}}
[3,6,7,5,1,2,4,8]=>{{1,3,4,5,7},{2,6},{8}}
[7,4,5,1,8,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,2,3,1,8,4,5,6]=>{{1,4,5,6,7,8},{2},{3}}
[2,1,4,8,3,7,5,6]=>{{1,2},{3,4,5,6,7,8}}
[4,8,1,6,7,3,2,5]=>{{1,3,4,6},{2,5,7,8}}
[1,2,7,8,4,3,6,5]=>{{1},{2},{3,6,7},{4,5,8}}
[4,8,1,3,5,6,2,7]=>{{1,3,4},{2,7,8},{5},{6}}
[5,3,7,8,4,2,6,1]=>{{1,4,5,8},{2,3,6,7}}
[6,3,7,8,2,4,5,1]=>{{1,4,6,8},{2,3,5,7}}
[8,5,2,4,3,1,7,6]=>{{1,6,8},{2,3,5},{4},{7}}
[7,5,4,2,3,1,8,6]=>{{1,6,7,8},{2,3,4,5}}
[3,5,4,6,7,1,8,2]=>{{1,3,4,6},{2,5,7,8}}
[1,4,2,6,5,8,7,3]=>{{1},{2,3,4,6,8},{5},{7}}
[1,3,2,6,4,8,7,5]=>{{1},{2,3},{4,5,6,8},{7}}
[1,4,2,5,3,8,7,6]=>{{1},{2,3,4,5},{6,8},{7}}
[1,5,2,6,4,8,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,2,5,3,8,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[2,5,1,4,3,8,7,6]=>{{1,2,3,5},{4},{6,8},{7}}
[1,7,3,5,4,8,6,2]=>{{1},{2,6,7,8},{3},{4,5}}
[1,8,2,6,3,7,5,4]=>{{1},{2,3,4,5,6,7,8}}
[1,8,3,6,4,7,5,2]=>{{1},{2,8},{3},{4,5,6,7}}
[1,7,2,6,4,8,5,3]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,6,3,8,5,4]=>{{1},{2,3,5,7},{4,6,8}}
[1,5,2,7,4,8,6,3]=>{{1},{2,3,4,5,6,7,8}}
[1,4,2,8,5,7,6,3]=>{{1},{2,3,4,8},{5},{6,7}}
[4,8,1,3,2,6,5,7]=>{{1,3,4},{2,5,7,8},{6}}
[1,5,3,8,4,7,6,2]=>{{1},{2,4,5,8},{3},{6,7}}
[1,8,4,7,3,6,5,2]=>{{1},{2,8},{3,4,5,7},{6}}
[2,6,3,8,1,5,4,7]=>{{1,2,5,6},{3},{4,7,8}}
[8,3,1,4,2,6,5,7]=>{{1,2,3,5,7,8},{4},{6}}
[4,8,7,3,5,2,1,6]=>{{1,3,4,7},{2,6,8},{5}}
[6,8,7,3,5,2,4,1]=>{{1,2,6,8},{3,4,7},{5}}
[8,3,5,1,2,6,4,7]=>{{1,4,7,8},{2,3,5},{6}}
[8,6,3,1,5,4,2,7]=>{{1,2,4,6,7,8},{3},{5}}
[8,6,4,1,5,3,2,7]=>{{1,2,3,4,6,7,8},{5}}
[8,6,5,4,1,3,2,7]=>{{1,2,3,5,6,7,8},{4}}
[5,3,8,7,4,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[2,3,8,7,4,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[8,3,5,7,4,1,2,6]=>{{1,6,8},{2,3,4,5,7}}
[4,8,5,3,1,2,7,6]=>{{1,3,4,5},{2,6,8},{7}}
[6,8,7,3,1,5,4,2]=>{{1,5,6},{2,8},{3,4,7}}
[6,8,5,4,1,3,7,2]=>{{1,3,5,6},{2,8},{4},{7}}
[2,5,8,7,4,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[4,8,7,6,5,1,3,2]=>{{1,4,6},{2,8},{3,7},{5}}
[3,8,7,5,1,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[2,3,8,7,5,6,1,4]=>{{1,2,3,4,7,8},{5},{6}}
[2,8,7,1,3,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[8,5,4,7,2,1,3,6]=>{{1,6,8},{2,5},{3,4,7}}
[6,8,7,3,5,2,1,4]=>{{1,2,3,4,6,7,8},{5}}
[3,5,8,6,4,2,7,1]=>{{1,3,8},{2,4,5,6},{7}}
[6,8,4,1,5,2,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[6,8,2,1,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,6,1,2,7,3]=>{{1,5},{2,3,4,6,8},{7}}
[2,4,8,6,5,1,7,3]=>{{1,2,4,6},{3,8},{5},{7}}
[4,8,7,6,5,2,1,3]=>{{1,2,3,4,6,7,8},{5}}
[4,8,7,5,1,6,2,3]=>{{1,4,5},{2,3,7,8},{6}}
[4,5,2,1,8,6,7,3]=>{{1,4},{2,3,5,8},{6},{7}}
[4,5,8,3,1,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[5,7,2,8,4,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[6,7,3,2,4,8,5,1]=>{{1,6,8},{2,4,5,7},{3}}
[7,2,8,6,4,5,1,3]=>{{1,7},{2},{3,8},{4,5,6}}
[8,7,2,6,5,1,3,4]=>{{1,4,6,8},{2,3,7},{5}}
[5,2,7,8,4,1,3,6]=>{{1,4,5,6,8},{2},{3,7}}
[2,7,8,6,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,6,3,5,2,8,4,1]=>{{1,2,4,5,6,7,8},{3}}
[6,2,7,4,8,5,3,1]=>{{1,5,6,8},{2},{3,7},{4}}
[8,6,5,1,7,2,4,3]=>{{1,3,4,5,7,8},{2,6}}
[6,8,5,1,7,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[1,6,8,3,7,4,2,5]=>{{1},{2,3,4,5,6,7,8}}
[5,1,6,3,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,6,4,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,4,8,1,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[6,3,8,2,4,1,7,5]=>{{1,6},{2,3,4,5,8},{7}}
[4,6,3,8,7,5,2,1]=>{{1,4,8},{2,5,6,7},{3}}
[6,3,8,7,5,4,2,1]=>{{1,2,3,4,6,7,8},{5}}
[6,8,4,2,1,7,5,3]=>{{1,5,6,7},{2,3,4,8}}
[5,2,6,4,3,8,1,7]=>{{1,3,5,6,7,8},{2},{4}}
[6,5,3,1,4,8,2,7]=>{{1,2,4,5,6,7,8},{3}}
[3,1,7,8,6,4,2,5]=>{{1,2,3,7},{4,5,6,8}}
[3,8,1,7,6,2,5,4]=>{{1,3},{2,4,5,6,7,8}}
[8,1,7,6,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,2,6,3,8,5,4,1]=>{{1,3,4,5,6,7,8},{2}}
[7,3,8,6,4,1,5,2]=>{{1,4,5,6,7},{2,3,8}}
[1,7,5,8,2,4,3,6]=>{{1},{2,3,5,7},{4,6,8}}
[6,1,5,2,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,5,6,3,8,2,4,7]=>{{1},{2,3,4,5,6,7,8}}
[8,7,1,3,6,5,2,4]=>{{1,3,4,8},{2,7},{5,6}}
[2,6,7,4,3,8,5,1]=>{{1,2,6,8},{3,5,7},{4}}
[5,2,4,7,3,8,6,1]=>{{1,3,4,5,6,7,8},{2}}
[1,5,8,7,2,4,6,3]=>{{1},{2,5},{3,8},{4,6,7}}
[1,4,8,7,3,6,5,2]=>{{1},{2,3,4,5,7,8},{6}}
[8,3,7,2,5,1,6,4]=>{{1,2,3,4,6,7,8},{5}}
[3,7,2,8,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,2,6,1,5,8,4,7]=>{{1,3,4,6,7,8},{2},{5}}
[7,2,1,5,8,4,3,6]=>{{1,3,7},{2},{4,5,6,8}}
[7,2,8,1,4,3,6,5]=>{{1,3,4,5,6,7,8},{2}}
[1,7,8,3,2,6,5,4]=>{{1},{2,5,7},{3,4,8},{6}}
[1,7,4,8,3,2,6,5]=>{{1},{2,6,7},{3,4,5,8}}
[1,7,5,4,8,3,2,6]=>{{1},{2,7},{3,5,6,8},{4}}
[6,1,5,4,3,8,2,7]=>{{1,2,6,7,8},{3,5},{4}}
[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,6,4,2,3,5,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,8,7,2,3,4,5,6]=>{{1},{2,4,6,8},{3,5,7}}
[1,5,8,6,2,3,4,7]=>{{1},{2,5},{3,4,6,7,8}}
[1,6,5,7,2,3,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[1,7,5,6,2,3,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,2,7,6,4,5,8]=>{{1},{2,3},{4,5,6,7},{8}}
[1,2,3,7,6,4,5,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[1,5,4,2,3,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[1,5,4,2,3,8,6,7]=>{{1},{2,3,4,5},{6,7,8}}
[1,3,2,8,6,4,5,7]=>{{1},{2,3},{4,5,6,7,8}}
[1,7,5,8,2,3,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,5,2,3,4,6]=>{{1},{2,3,4,5,6,7,8}}
[2,1,5,8,6,3,7,4]=>{{1,2},{3,5,6},{4,8},{7}}
[2,5,8,4,6,1,7,3]=>{{1,2,5,6},{3,8},{4},{7}}
[5,8,4,6,1,3,7,2]=>{{1,5},{2,8},{3,4,6},{7}}
[2,4,6,8,5,3,7,1]=>{{1,2,4,8},{3,6},{5},{7}}
[2,4,8,1,7,6,5,3]=>{{1,2,4},{3,8},{5,7},{6}}
[4,3,8,1,5,7,6,2]=>{{1,4},{2,3,8},{5},{6,7}}
[4,3,6,8,5,2,7,1]=>{{1,4,8},{2,3,6},{5},{7}}
[3,6,8,5,4,2,7,1]=>{{1,3,8},{2,6},{4,5},{7}}
[3,6,4,1,8,2,7,5]=>{{1,3,4},{2,6},{5,8},{7}}
[3,6,4,1,5,2,8,7]=>{{1,3,4},{2,6},{5},{7,8}}
[4,8,6,5,1,3,7,2]=>{{1,4,5},{2,8},{3,6},{7}}
[2,8,3,5,6,7,1,4]=>{{1,2,4,5,6,7,8},{3}}
[5,6,2,4,7,1,8,3]=>{{1,2,3,5,6,7,8},{4}}
[2,7,5,4,6,1,8,3]=>{{1,2,3,5,6,7,8},{4}}
[2,3,7,4,6,1,8,5]=>{{1,2,3,5,6,7,8},{4}}
[2,6,7,4,1,3,8,5]=>{{1,2,3,5,6,7,8},{4}}
[6,5,7,4,1,3,8,2]=>{{1,2,3,5,6,7,8},{4}}
[2,4,6,3,5,7,8,1]=>{{1,2,3,4,6,7,8},{5}}
[4,1,6,3,5,7,8,2]=>{{1,2,3,4,6,7,8},{5}}
[3,6,4,2,5,7,8,1]=>{{1,2,3,4,6,7,8},{5}}
[2,3,6,1,5,7,8,4]=>{{1,2,3,4,6,7,8},{5}}
[4,3,6,2,5,7,8,1]=>{{1,2,3,4,6,7,8},{5}}
[4,6,1,2,5,7,8,3]=>{{1,2,3,4,6,7,8},{5}}
[2,6,4,1,5,7,8,3]=>{{1,2,3,4,6,7,8},{5}}
[2,4,1,6,5,7,8,3]=>{{1,2,3,4,6,7,8},{5}}
[7,5,4,2,6,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,3,1,8,6,5,2]=>{{1,4},{2,5,7,8},{3},{6}}
[5,6,4,2,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[4,2,7,5,3,1,8,6]=>{{1,3,4,5,6,7,8},{2}}
[5,3,6,4,8,2,1,7]=>{{1,5,7,8},{2,3,6},{4}}
[7,3,2,5,4,1,8,6]=>{{1,6,7,8},{2,3},{4,5}}
[7,3,2,5,1,8,6,4]=>{{1,4,5,6,7,8},{2,3}}
[4,6,3,8,7,2,1,5]=>{{1,4,5,7,8},{2,6},{3}}
[4,7,6,3,8,2,1,5]=>{{1,2,3,4,6,7},{5,8}}
[4,7,3,8,6,2,1,5]=>{{1,2,4,5,6,7,8},{3}}
[5,7,3,2,6,1,8,4]=>{{1,5,6},{2,4,7,8},{3}}
[5,7,3,2,6,4,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[2,7,5,3,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,2,8,4,3,1,6]=>{{1,7},{2,3,4,5,6,8}}
[7,3,2,4,1,8,6,5]=>{{1,5,6,7,8},{2,3},{4}}
[8,4,3,2,7,5,1,6]=>{{1,5,6,7,8},{2,4},{3}}
[4,3,7,5,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,5,2,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[8,4,5,3,7,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[4,3,5,2,8,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[1,2,8,6,4,5,7,3]=>{{1},{2},{3,8},{4,5,6},{7}}
[1,8,5,3,4,6,7,2]=>{{1},{2,8},{3,4,5},{6},{7}}
[7,8,4,1,6,3,5,2]=>{{1,3,4,5,6,7},{2,8}}
[8,7,5,6,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[3,2,6,4,1,8,5,7]=>{{1,3,5,6,7,8},{2},{4}}
[2,8,6,5,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,6,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,5,2,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,2,4,7,6,8,3,1]=>{{1,5,6,8},{2},{3,4,7}}
[3,4,2,8,7,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,6,3,2,4,1]=>{{1,8},{2,3,4,5,6,7}}
[6,4,1,8,7,3,2,5]=>{{1,3,6},{2,4,5,7,8}}
[1,8,5,4,2,7,3,6]=>{{1},{2,3,5,6,7,8},{4}}
[3,7,6,1,5,8,4,2]=>{{1,2,3,4,6,7,8},{5}}
[3,6,5,8,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,3,2,7,4,6,5,1]=>{{1,8},{2,3},{4,5,7},{6}}
[7,5,8,4,1,3,6,2]=>{{1,2,3,5,6,7,8},{4}}
[7,1,6,2,3,8,4,5]=>{{1,2,4,7},{3,5,6,8}}
[6,4,7,1,3,2,8,5]=>{{1,2,4,6},{3,5,7,8}}
[5,1,3,8,7,2,6,4]=>{{1,2,5,6,7},{3},{4,8}}
[8,7,1,6,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[3,8,5,2,4,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[7,1,5,2,4,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[3,8,5,1,4,7,2,6]=>{{1,3,4,5},{2,6,7,8}}
[7,2,5,4,1,3,8,6]=>{{1,3,5,6,7,8},{2},{4}}
[7,5,8,1,6,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,1,3,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[1,4,5,8,6,3,2,7]=>{{1},{2,4,7,8},{3,5,6}}
[8,4,5,7,2,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[4,5,2,6,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[8,1,7,5,3,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[5,2,8,3,6,1,4,7]=>{{1,5,6},{2},{3,4,7,8}}
[5,2,6,3,1,7,8,4]=>{{1,5},{2},{3,4,6,7,8}}
[4,3,5,1,6,7,8,2]=>{{1,4},{2,3,5,6,7,8}}
[5,7,6,1,2,3,8,4]=>{{1,2,4,5,7,8},{3,6}}
[3,6,7,5,1,2,8,4]=>{{1,3,4,5,7,8},{2,6}}
[1,7,6,8,5,2,4,3]=>{{1},{2,3,4,6,7,8},{5}}
[5,7,6,8,1,2,4,3]=>{{1,5},{2,3,4,6,7,8}}
[5,6,3,7,1,4,8,2]=>{{1,5},{2,4,6,7,8},{3}}
[5,3,2,1,8,6,4,7]=>{{1,4,5,7,8},{2,3},{6}}
[7,8,6,1,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,3,7,2,1,4]=>{{1,2,5,6,7},{3,4,8}}
[7,8,5,3,6,2,1,4]=>{{1,7},{2,3,4,5,6,8}}
[7,8,5,3,6,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,3,2,6,5,1]=>{{1,2,5,7,8},{3,4},{6}}
[1,8,4,3,2,6,7,5]=>{{1},{2,5,8},{3,4},{6},{7}}
[5,4,3,8,2,1,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[6,4,8,3,2,1,7,5]=>{{1,6},{2,3,4,5,8},{7}}
[1,8,4,3,2,7,6,5]=>{{1},{2,5,8},{3,4},{6,7}}
[1,8,6,7,3,2,4,5]=>{{1},{2,3,5,6,8},{4,7}}
[7,8,6,1,3,2,4,5]=>{{1,4,7},{2,3,5,6,8}}
[1,8,4,3,2,7,5,6]=>{{1},{2,5,6,7,8},{3,4}}
[5,4,3,8,2,1,6,7]=>{{1,2,4,5,6,7,8},{3}}
[1,8,4,3,2,5,7,6]=>{{1},{2,5,6,8},{3,4},{7}}
[5,4,3,8,2,6,7,1]=>{{1,2,4,5,8},{3},{6},{7}}
[6,4,2,3,5,1,8,7]=>{{1,6},{2,3,4},{5},{7,8}}
[5,2,3,6,1,4,8,7]=>{{1,5},{2},{3},{4,6},{7,8}}
[5,2,3,8,6,4,7,1]=>{{1,4,5,6,8},{2},{3},{7}}
[5,2,3,7,4,8,1,6]=>{{1,4,5,7},{2},{3},{6,8}}
[8,6,3,2,5,4,7,1]=>{{1,8},{2,4,6},{3},{5},{7}}
[7,2,3,4,5,8,1,6]=>{{1,7},{2},{3},{4},{5},{6,8}}
[7,2,8,1,5,3,4,6]=>{{1,4,7},{2},{3,6,8},{5}}
[3,8,6,4,7,2,5,1]=>{{1,2,3,6,8},{4},{5,7}}
[2,1,8,6,4,5,7,3]=>{{1,2},{3,8},{4,5,6},{7}}
[4,8,2,5,7,3,1,6]=>{{1,4,5,7},{2,3,6,8}}
[5,8,2,3,4,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[6,3,4,7,8,2,1,5]=>{{1,2,3,4,6,7},{5,8}}
[3,8,5,1,4,7,6,2]=>{{1,3,4,5},{2,8},{6,7}}
[4,8,5,1,3,6,7,2]=>{{1,4},{2,8},{3,5},{6},{7}}
[4,6,8,5,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,5,2,6,4,1]=>{{1,3,8},{2,4,5,7},{6}}
[3,8,6,2,7,4,5,1]=>{{1,2,3,4,6,8},{5,7}}
[8,5,4,7,1,3,6,2]=>{{1,2,5,8},{3,4,6,7}}
[7,3,6,2,8,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,5,2,3,7,6,4]=>{{1,2,4,8},{3,5},{6,7}}
[6,4,2,3,7,8,5,1]=>{{1,6,8},{2,3,4},{5,7}}
[8,4,2,3,6,7,1,5]=>{{1,5,6,7,8},{2,3,4}}
[4,5,8,3,7,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,2,8,4,5,1,6]=>{{1,2,3,7},{4,5,6,8}}
[3,5,1,8,4,6,2,7]=>{{1,3},{2,4,5,7,8},{6}}
[4,2,1,5,6,8,3,7]=>{{1,3,4,5,6,7,8},{2}}
[4,1,2,6,5,8,3,7]=>{{1,2,3,4,6,7,8},{5}}
[4,1,8,3,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[4,2,7,5,8,1,3,6]=>{{1,4,5,6,8},{2},{3,7}}
[4,6,2,7,8,3,1,5]=>{{1,4,7},{2,3,6},{5,8}}
[4,6,1,3,8,2,5,7]=>{{1,3,4},{2,6},{5,7,8}}
[4,3,6,2,1,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,7,4,5,1,6,2,8]=>{{1,3,4,5},{2,7},{6},{8}}
[3,6,4,5,8,2,1,7]=>{{1,3,4,5,7,8},{2,6}}
[6,1,4,5,2,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[7,2,4,5,1,6,3,8]=>{{1,3,4,5,7},{2},{6},{8}}
[7,5,4,1,6,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[1,5,4,8,6,3,2,7]=>{{1},{2,3,4,5,6,7,8}}
[7,5,4,8,6,3,1,2]=>{{1,7},{2,3,4,5,6,8}}
[1,8,7,5,3,6,4,2]=>{{1},{2,8},{3,4,5,7},{6}}
[8,3,7,4,1,6,2,5]=>{{1,5,8},{2,3,7},{4},{6}}
[8,5,4,1,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,7,4,2,6,5,3,8]=>{{1},{2,3,4,7},{5,6},{8}}
[8,2,1,5,6,7,3,4]=>{{1,3,4,5,6,7,8},{2}}
[6,3,1,8,4,7,2,5]=>{{1,2,3,6,7},{4,5,8}}
[7,1,4,8,6,3,2,5]=>{{1,2,7},{3,4,5,6,8}}
[4,1,8,5,6,7,2,3]=>{{1,2,4,5,6,7},{3,8}}
[5,7,4,8,6,2,1,3]=>{{1,2,5,6,7},{3,4,8}}
[5,3,6,8,2,7,1,4]=>{{1,2,3,5,6,7},{4,8}}
[6,3,7,4,8,2,1,5]=>{{1,2,3,6,7},{4},{5,8}}
[5,3,6,1,4,7,2,8]=>{{1,4,5},{2,3,6,7},{8}}
[4,3,6,8,2,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,4,8,2,1,6]=>{{1,2,3,5,6,7,8},{4}}
[5,3,8,4,1,6,2,7]=>{{1,5},{2,3,7,8},{4},{6}}
[5,3,8,1,4,7,2,6]=>{{1,4,5},{2,3,6,7,8}}
[5,8,4,1,6,3,2,7]=>{{1,3,4,5,6},{2,7,8}}
[7,3,8,4,1,6,2,5]=>{{1,2,3,5,7,8},{4},{6}}
[1,5,8,3,6,7,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,5,6,7,3,4]=>{{1},{2,3,4,5,6,7,8}}
[7,8,4,1,6,5,2,3]=>{{1,2,3,4,7,8},{5,6}}
[6,3,8,1,5,7,2,4]=>{{1,2,3,4,6,7,8},{5}}
[8,3,1,2,5,7,4,6]=>{{1,2,3,4,6,7,8},{5}}
[8,1,4,2,6,5,3,7]=>{{1,2,3,4,7,8},{5,6}}
[5,1,3,7,4,8,2,6]=>{{1,2,4,5,7},{3},{6,8}}
[5,1,3,4,7,8,2,6]=>{{1,2,5,7},{3},{4},{6,8}}
[2,5,8,7,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[5,1,7,8,3,4,2,6]=>{{1,2,3,5,7},{4,6,8}}
[2,5,4,8,3,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[5,6,8,2,3,4,1,7]=>{{1,3,5,7,8},{2,4,6}}
[2,3,5,7,4,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[4,5,2,3,8,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[3,7,4,5,8,1,2,6]=>{{1,3,4,5,6,8},{2,7}}
[3,7,8,1,4,5,2,6]=>{{1,3,4,5,6,8},{2,7}}
[5,8,2,1,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,3,7,5,2,6]=>{{1,3,4},{2,5,6,7,8}}
[2,4,7,8,5,3,6,1]=>{{1,2,4,8},{3,6,7},{5}}
[5,3,1,4,7,2,8,6]=>{{1,2,3,5,6,7,8},{4}}
[2,4,7,5,8,3,6,1]=>{{1,2,4,5,8},{3,6,7}}
[4,3,5,8,2,1,7,6]=>{{1,4,6,8},{2,3,5},{7}}
[4,8,5,3,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,7,3,1,2,6]=>{{1,2,4,6,7,8},{3,5}}
[4,8,7,5,1,3,2,6]=>{{1,4,5},{2,3,6,7,8}}
[3,7,8,4,1,5,2,6]=>{{1,3,5,6,8},{2,7},{4}}
[1,8,5,7,2,4,3,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,4,2,3,6,7]=>{{1},{2,3,5,6,7,8},{4}}
[1,3,6,8,5,4,2,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,6,3,8,2,7,4,5]=>{{1},{2,4,5,6,7,8},{3}}
[1,4,2,7,5,8,3,6]=>{{1},{2,3,4,7},{5},{6,8}}
[1,8,2,3,6,7,5,4]=>{{1},{2,3,4,8},{5,6,7}}
[1,3,6,8,2,7,5,4]=>{{1},{2,3,5,6,7},{4,8}}
[1,6,5,4,3,8,2,7]=>{{1},{2,6,7,8},{3,5},{4}}
[1,8,3,4,5,6,2,7]=>{{1},{2,7,8},{3},{4},{5},{6}}
[1,8,3,6,2,4,5,7]=>{{1},{2,5,7,8},{3},{4,6}}
[1,4,5,8,3,6,2,7]=>{{1},{2,4,7,8},{3,5},{6}}
[1,2,7,8,4,5,3,6]=>{{1},{2},{3,7},{4,5,6,8}}
[7,2,8,5,6,3,4,1]=>{{1,3,4,5,6,7,8},{2}}
[7,6,3,8,5,4,2,1]=>{{1,2,4,6,7,8},{3},{5}}
[6,2,8,7,5,4,1,3]=>{{1,4,6,7},{2},{3,8},{5}}
[6,2,8,4,3,7,1,5]=>{{1,6,7},{2},{3,5,8},{4}}
[5,2,8,4,3,1,7,6]=>{{1,3,5,6,8},{2},{4},{7}}
[1,2,5,4,8,3,7,6]=>{{1},{2},{3,5,6,8},{4},{7}}
[1,4,3,6,8,7,2,5]=>{{1},{2,4,6,7},{3},{5,8}}
[3,2,5,7,6,8,1,4]=>{{1,3,4,5,6,7,8},{2}}
[5,3,2,6,8,4,7,1]=>{{1,5,8},{2,3},{4,6},{7}}
[3,1,8,6,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,6,8,5,4,2,7]=>{{1,2,3,4,6,7,8},{5}}
[5,3,2,8,7,6,4,1]=>{{1,4,5,7,8},{2,3},{6}}
[5,3,8,2,7,6,1,4]=>{{1,5,7},{2,3,4,8},{6}}
[6,5,4,8,3,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,1,3,7,2,6]=>{{1,4},{2,6,7,8},{3,5}}
[4,3,8,7,2,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[2,7,5,1,8,4,6,3]=>{{1,2,4,6,7},{3,5,8}}
[7,8,5,2,1,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[7,6,4,8,1,2,5,3]=>{{1,5,7},{2,6},{3,4,8}}
[7,5,4,8,3,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,5,6,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,8,7,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,8,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,5,6,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,1,5,8,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,6,1,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,6,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,5,6,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,8,6,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[3,4,5,8,6,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,8,6,7,4,3]=>{{1,2},{3,4,5,6,7,8}}
[3,4,5,8,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,7,1,5,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[2,6,4,7,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,6,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,5,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,7,2,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,4,6,1,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,5,6,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,4,5,6,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,5,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,5,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,5,1,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,7,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,1,4,6,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,7,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[2,1,6,5,3,7,8,4]=>{{1,2},{3,4,5,6,7,8}}
[6,1,4,7,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,6,2,5,4,8,3,7]=>{{1},{2,3,6,7,8},{4,5}}
[4,1,2,7,5,8,3,6]=>{{1,2,3,4,7},{5},{6,8}}
[6,1,3,5,8,2,4,7]=>{{1,2,6},{3},{4,5,7,8}}
[5,6,4,3,1,8,2,7]=>{{1,5},{2,6,7,8},{3,4}}
[6,2,3,5,8,1,4,7]=>{{1,6},{2},{3},{4,5,7,8}}
[6,7,2,3,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,1,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,1,8,3,2,6]=>{{1,3,4,5,6,8},{2,7}}
[4,1,7,5,8,3,6,2]=>{{1,2,4,5,8},{3,6,7}}
[6,7,1,3,8,4,5,2]=>{{1,3,4,6},{2,5,7,8}}
[1,6,7,4,3,8,5,2]=>{{1},{2,6,8},{3,5,7},{4}}
[6,1,7,4,2,8,5,3]=>{{1,2,3,5,6,7,8},{4}}
[2,1,6,7,4,3,8,5]=>{{1,2},{3,6},{4,5,7,8}}
[6,7,3,2,1,8,4,5]=>{{1,5,6,8},{2,4,7},{3}}
[2,5,7,3,1,4,8,6]=>{{1,2,5},{3,4,6,7,8}}
[6,7,3,2,8,4,5,1]=>{{1,2,4,5,6,7,8},{3}}
[1,2,6,7,4,3,8,5]=>{{1},{2},{3,6},{4,5,7,8}}
[2,7,1,8,4,6,3,5]=>{{1,2,3,7},{4,5,8},{6}}
[2,7,5,8,1,6,3,4]=>{{1,2,3,5,7},{4,8},{6}}
[6,7,1,8,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,6,1,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,4,6,2,5,1]=>{{1,8},{2,5,6,7},{3},{4}}
[8,2,5,7,1,4,6,3]=>{{1,3,5,8},{2},{4,6,7}}
[8,2,4,7,1,5,6,3]=>{{1,3,4,5,6,7,8},{2}}
[8,2,3,4,7,1,5,6]=>{{1,6,8},{2},{3},{4},{5,7}}
[8,7,3,5,6,2,4,1]=>{{1,8},{2,4,5,6,7},{3}}
[8,7,4,6,5,2,3,1]=>{{1,8},{2,3,4,6,7},{5}}
[8,4,6,7,5,1,2,3]=>{{1,3,6,8},{2,4,7},{5}}
[8,4,6,7,5,1,3,2]=>{{1,2,3,4,6,7,8},{5}}
[8,3,5,7,6,1,4,2]=>{{1,2,3,5,6,8},{4,7}}
[8,7,3,6,2,1,5,4]=>{{1,4,6,8},{2,5,7},{3}}
[8,7,3,4,6,2,1,5]=>{{1,2,5,6,7,8},{3},{4}}
[8,7,4,6,5,2,1,3]=>{{1,2,3,4,6,7,8},{5}}
[8,6,5,2,7,4,3,1]=>{{1,8},{2,4,6},{3,5,7}}
[8,4,3,7,6,5,1,2]=>{{1,2,4,7,8},{3},{5,6}}
[8,5,6,7,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,6,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,7,5,1,6,3]=>{{1,2,3,4,6,7,8},{5}}
[8,3,4,2,7,5,6,1]=>{{1,8},{2,3,4},{5,6,7}}
[8,4,7,6,5,1,2,3]=>{{1,2,3,4,6,7,8},{5}}
[8,3,5,2,7,4,6,1]=>{{1,8},{2,3,4,5,6,7}}
[8,5,2,6,7,4,1,3]=>{{1,2,3,5,7,8},{4,6}}
[8,5,3,7,6,4,1,2]=>{{1,2,4,5,6,7,8},{3}}
[8,6,2,5,7,3,1,4]=>{{1,4,5,7,8},{2,3,6}}
[8,6,2,4,7,3,1,5]=>{{1,5,7,8},{2,3,6},{4}}
[8,5,2,3,7,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,2,7,6,4,1]=>{{1,8},{2,4,5,7},{3},{6}}
[8,6,1,5,4,3,2,7]=>{{1,2,3,6,7,8},{4,5}}
[2,4,5,8,3,1,6,7]=>{{1,2,4,6,7,8},{3,5}}
[2,7,4,6,1,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[2,4,3,8,5,1,6,7]=>{{1,2,4,6,7,8},{3},{5}}
[7,8,3,2,5,4,6,1]=>{{1,2,4,6,7,8},{3},{5}}
[1,5,6,7,3,8,2,4]=>{{1},{2,3,4,5,6,7,8}}
[1,6,5,4,8,3,2,7]=>{{1},{2,3,5,6,7,8},{4}}
[1,7,3,5,8,4,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,2,1,6,4,8,5,3]=>{{1,3,4,5,6,7,8},{2}}
[7,5,8,3,2,4,6,1]=>{{1,3,4,6,7,8},{2,5}}
[3,8,7,2,4,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[1,3,7,6,4,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,1,8,7,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,7,5,4,2,6]=>{{1,2,3,4,6,7,8},{5}}
[3,1,7,6,5,4,2,8]=>{{1,2,3,7},{4,6},{5},{8}}
[4,7,1,6,5,3,2,8]=>{{1,3,4,6},{2,7},{5},{8}}
[4,8,1,6,5,3,2,7]=>{{1,3,4,6},{2,7,8},{5}}
[8,4,1,7,6,3,2,5]=>{{1,3,5,6,8},{2,4,7}}
[5,4,1,8,6,3,2,7]=>{{1,3,5,6},{2,4,7,8}}
[5,4,1,7,6,3,2,8]=>{{1,3,5,6},{2,4,7},{8}}
[6,4,1,8,5,3,2,7]=>{{1,3,6},{2,4,7,8},{5}}
[8,4,1,7,5,3,2,6]=>{{1,3,6,8},{2,4,7},{5}}
[7,4,1,6,5,3,2,8]=>{{1,2,3,4,6,7},{5},{8}}
[7,5,6,1,4,3,2,8]=>{{1,2,4,5,7},{3,6},{8}}
[8,5,6,1,4,3,2,7]=>{{1,2,4,5,7,8},{3,6}}
[8,5,7,1,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,1,4,3,2,8]=>{{1,4,5},{2,7},{3,6},{8}}
[5,8,6,1,4,3,2,7]=>{{1,4,5},{2,7,8},{3,6}}
[6,7,5,1,4,3,2,8]=>{{1,3,4,5,6},{2,7},{8}}
[8,7,5,1,4,3,2,6]=>{{1,3,4,5,6,8},{2,7}}
[8,6,5,1,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,1,7,2,5,3,4]=>{{1,3,4,7,8},{2,5,6}}
[1,8,6,3,4,2,5,7]=>{{1},{2,3,4,5,6,7,8}}
[3,1,6,4,5,8,7,2]=>{{1,2,3,6,8},{4},{5},{7}}
[3,1,6,4,5,8,2,7]=>{{1,2,3,6,7,8},{4},{5}}
[4,6,8,7,2,5,1,3]=>{{1,4,7},{2,5,6},{3,8}}
[7,6,3,8,4,5,2,1]=>{{1,2,4,5,6,7,8},{3}}
[8,2,7,6,1,4,3,5]=>{{1,5,8},{2},{3,7},{4,6}}
[5,2,7,8,1,4,3,6]=>{{1,5},{2},{3,7},{4,6,8}}
[5,6,3,8,4,1,2,7]=>{{1,2,4,5,6,7,8},{3}}
[8,2,7,6,1,4,5,3]=>{{1,3,5,7,8},{2},{4,6}}
[5,2,3,4,7,1,6,8]=>{{1,5,6,7},{2},{3},{4},{8}}
[5,2,3,7,1,6,8,4]=>{{1,5},{2},{3},{4,7,8},{6}}
[8,7,5,3,1,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[1,4,7,8,5,2,3,6]=>{{1},{2,4,6,8},{3,7},{5}}
[3,2,6,7,4,1,5,8]=>{{1,3,6},{2},{4,5,7},{8}}
[5,8,3,7,6,4,1,2]=>{{1,4,5,6,7},{2,8},{3}}
[6,5,1,7,2,4,8,3]=>{{1,3,4,6,7,8},{2,5}}
[3,6,7,1,4,2,5,8]=>{{1,3,4,5,7},{2,6},{8}}
[4,7,5,8,2,1,3,6]=>{{1,4,6,8},{2,3,5,7}}
[8,1,2,7,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}
[6,5,1,8,3,7,2,4]=>{{1,2,3,5,6,7},{4,8}}
[1,8,7,5,3,2,6,4]=>{{1},{2,3,4,5,6,7,8}}
[7,8,1,5,4,2,3,6]=>{{1,3,7},{2,6,8},{4,5}}
[3,4,6,8,1,5,7,2]=>{{1,3,5,6},{2,4,8},{7}}
[6,8,1,7,5,4,2,3]=>{{1,2,3,4,6,7,8},{5}}
[7,6,3,1,2,8,5,4]=>{{1,2,4,5,6,7,8},{3}}
[6,3,5,7,1,4,2,8]=>{{1,2,3,4,5,6,7},{8}}
[1,7,5,2,6,4,8,3]=>{{1},{2,3,4,5,6,7,8}}
[7,1,3,6,8,2,4,5]=>{{1,2,4,6,7},{3},{5,8}}
[1,2,5,7,8,4,6,3]=>{{1},{2},{3,5,8},{4,6,7}}
[3,1,2,7,5,4,8,6]=>{{1,2,3},{4,6,7,8},{5}}
[6,7,4,1,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,7,2,8,4,3,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,6,3,5,7,8,2,4]=>{{1},{2,4,5,6,7,8},{3}}
[8,6,1,7,5,2,4,3]=>{{1,3,8},{2,6},{4,7},{5}}
[7,6,4,1,8,3,2,5]=>{{1,2,3,4,6,7},{5,8}}
[8,4,1,6,5,2,7,3]=>{{1,3,8},{2,4,6},{5},{7}}
[1,5,3,4,7,8,2,6]=>{{1},{2,5,7},{3},{4},{6,8}}
[4,2,1,5,7,8,3,6]=>{{1,3,4,5,7},{2},{6,8}}
[5,4,1,6,7,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,1,4,6,7,8,2,3]=>{{1,2,5,7},{3,4,6,8}}
[4,1,5,3,7,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[8,1,4,6,5,2,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[7,1,5,4,6,3,2,8]=>{{1,2,7},{3,5,6},{4},{8}}
[8,2,1,6,7,5,4,3]=>{{1,3,8},{2},{4,5,6,7}}
[1,2,4,7,6,3,8,5]=>{{1},{2},{3,4,5,6,7,8}}
[6,7,4,1,8,5,2,3]=>{{1,3,4,5,6,8},{2,7}}
[8,6,4,1,5,7,3,2]=>{{1,2,3,4,6,7,8},{5}}
[5,2,4,3,7,1,6,8]=>{{1,5,6,7},{2},{3,4},{8}}
[6,1,5,4,8,3,2,7]=>{{1,2,3,5,6,7,8},{4}}
[1,2,8,7,4,3,6,5]=>{{1},{2},{3,4,5,6,7,8}}
[3,2,1,7,5,8,4,6]=>{{1,3},{2},{4,7},{5},{6,8}}
[1,3,6,4,7,8,2,5]=>{{1},{2,3,5,6,7,8},{4}}
[4,5,1,3,7,8,2,6]=>{{1,3,4},{2,5,7},{6,8}}
[5,2,3,1,7,8,4,6]=>{{1,4,5,7},{2},{3},{6,8}}
[1,6,4,3,7,8,2,5]=>{{1},{2,5,6,7,8},{3,4}}
[7,6,4,3,1,5,2,8]=>{{1,2,5,6,7},{3,4},{8}}
[7,5,4,6,1,3,2,8]=>{{1,2,5,7},{3,4,6},{8}}
[8,4,6,5,1,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[1,5,6,3,7,8,2,4]=>{{1},{2,5,7},{3,4,6,8}}
[1,5,2,4,3,8,7,6]=>{{1},{2,3,5},{4},{6,8},{7}}
[8,6,5,7,2,1,4,3]=>{{1,2,3,5,6,8},{4,7}}
[1,6,3,8,4,5,7,2]=>{{1},{2,4,5,6,8},{3},{7}}
[7,5,4,2,6,3,8,1]=>{{1,7,8},{2,3,4,5,6}}
[2,3,8,4,7,5,6,1]=>{{1,2,3,8},{4},{5,6,7}}
[3,7,2,8,6,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,5,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,8,6,2,5,1]=>{{1,4,8},{2,3,5,6,7}}
[3,8,1,7,5,2,4,6]=>{{1,3},{2,6,8},{4,7},{5}}
[2,4,7,8,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,5,1,7,3,6]=>{{1,2,4,5},{3,6,7,8}}
[2,8,3,5,1,6,4,7]=>{{1,2,4,5,7,8},{3},{6}}
[8,2,4,6,3,7,5,1]=>{{1,8},{2},{3,4,5,6,7}}
[4,5,3,8,2,1,7,6]=>{{1,4,6,8},{2,5},{3},{7}}
[1,4,6,2,7,5,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[8,2,1,4,5,6,7,3]=>{{1,3,8},{2},{4},{5},{6},{7}}
[7,3,1,2,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}
[7,8,2,1,5,4,6,3]=>{{1,4,6,7},{2,3,8},{5}}
[1,4,8,5,2,6,3,7]=>{{1},{2,4,5},{3,7,8},{6}}
[5,2,3,7,8,1,6,4]=>{{1,4,5,6,7,8},{2},{3}}
[1,2,8,4,3,6,7,5]=>{{1},{2},{3,5,8},{4},{6},{7}}
[1,2,7,5,3,4,6,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,7,3,2,6,8,4,5]=>{{1},{2,4,7},{3},{5,6,8}}
[7,2,1,3,6,8,4,5]=>{{1,3,4,7},{2},{5,6,8}}
[4,7,8,1,6,5,3,2]=>{{1,4},{2,3,7,8},{5,6}}
[3,5,8,6,1,4,2,7]=>{{1,2,3,5,7,8},{4,6}}
[1,8,4,2,7,6,3,5]=>{{1},{2,3,4,5,7,8},{6}}
[7,3,8,1,6,5,4,2]=>{{1,4,7},{2,3,8},{5,6}}
[7,3,8,2,6,5,4,1]=>{{1,2,3,4,7,8},{5,6}}
[7,1,3,8,6,5,4,2]=>{{1,2,4,7,8},{3},{5,6}}
[8,1,3,7,6,5,4,2]=>{{1,2,8},{3},{4,7},{5,6}}
[2,4,1,8,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,6,1,5,4,2]=>{{1,4,5,6,7},{2,3,8}}
[3,5,1,7,8,2,6,4]=>{{1,3},{2,4,5,6,7,8}}
[5,4,7,8,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,8,7,1,5,4,2]=>{{1,5,6},{2,3,8},{4,7}}
[8,6,4,7,1,5,3,2]=>{{1,2,5,6,8},{3,4,7}}
[6,4,7,1,5,3,2,8]=>{{1,2,3,4,6,7},{5},{8}}
[3,4,6,2,1,8,5,7]=>{{1,3,5,6,7,8},{2,4}}
[4,5,7,2,1,6,3,8]=>{{1,2,4,5},{3,7},{6},{8}}
[5,6,4,8,3,2,1,7]=>{{1,3,4,5,7,8},{2,6}}
[5,7,4,8,2,1,6,3]=>{{1,2,5,6,7},{3,4,8}}
[4,7,5,8,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,2,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,1,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,1,7,3,2,4]=>{{1,4,8},{2,5,7},{3,6}}
[4,5,1,6,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[4,5,2,6,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[8,4,6,7,2,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[7,1,4,6,8,3,5,2]=>{{1,2,5,7,8},{3,4,6}}
[6,7,1,2,4,8,5,3]=>{{1,3,6,8},{2,4,5,7}}
[1,6,3,4,7,8,5,2]=>{{1},{2,6,8},{3},{4},{5,7}}
[2,3,6,4,7,5,8,1]=>{{1,2,3,5,6,7,8},{4}}
[7,8,1,3,4,5,6,2]=>{{1,3,4,5,6,7},{2,8}}
[1,8,2,6,7,3,4,5]=>{{1},{2,3,4,5,6,7,8}}
[4,7,3,2,8,1,5,6]=>{{1,2,4,5,6,7,8},{3}}
[7,1,2,6,3,8,5,4]=>{{1,2,3,5,7},{4,6,8}}
[8,1,2,6,3,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,7,6,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,3,1,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[4,7,8,3,1,6,2,5]=>{{1,3,4,5,8},{2,7},{6}}
[7,4,3,1,6,2,8,5]=>{{1,2,4,5,6,7,8},{3}}
[7,4,3,1,8,6,2,5]=>{{1,2,4,7},{3},{5,8},{6}}
[3,7,6,2,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,2,8,6,1,5]=>{{1,2,3,4,7},{5,8},{6}}
[6,1,2,7,4,3,8,5]=>{{1,2,3,6},{4,5,7,8}}
[5,1,2,6,3,8,7,4]=>{{1,2,3,5},{4,6,8},{7}}
[5,1,2,7,3,8,6,4]=>{{1,2,3,5},{4,6,7,8}}
[6,1,2,7,3,5,8,4]=>{{1,2,3,5,6},{4,7,8}}
[7,5,3,2,1,8,6,4]=>{{1,2,4,5,6,7,8},{3}}
[4,2,1,5,3,6,7,8]=>{{1,3,4,5},{2},{6},{7},{8}}
[6,2,5,4,1,8,7,3]=>{{1,3,5,6,8},{2},{4},{7}}
[4,6,3,2,1,8,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[6,5,3,2,1,8,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[8,4,3,2,7,6,1,5]=>{{1,5,7,8},{2,4},{3},{6}}
[1,5,8,4,7,6,3,2]=>{{1},{2,3,5,7,8},{4},{6}}
[3,2,7,4,8,6,1,5]=>{{1,3,7},{2},{4},{5,8},{6}}
[7,4,3,2,8,6,1,5]=>{{1,7},{2,4},{3},{5,8},{6}}
[6,8,3,7,5,2,1,4]=>{{1,2,4,6,7,8},{3},{5}}
[5,7,8,4,3,2,1,6]=>{{1,2,3,5,6,7,8},{4}}
[6,4,3,8,5,2,1,7]=>{{1,2,4,6,7,8},{3},{5}}
[8,2,5,4,7,6,1,3]=>{{1,3,5,7,8},{2},{4},{6}}
[7,2,5,4,8,6,1,3]=>{{1,7},{2},{3,5,8},{4},{6}}
[4,5,3,2,8,6,1,7]=>{{1,2,4,5,7,8},{3},{6}}
[3,2,5,4,8,6,1,7]=>{{1,3,5,7,8},{2},{4},{6}}
[3,2,8,6,5,4,1,7]=>{{1,3,7,8},{2},{4,6},{5}}
[8,4,3,6,5,2,1,7]=>{{1,7,8},{2,4,6},{3},{5}}
[8,4,3,7,5,2,1,6]=>{{1,2,4,6,7,8},{3},{5}}
[3,2,7,8,5,4,1,6]=>{{1,3,7},{2},{4,6,8},{5}}
[6,8,7,4,3,2,1,5]=>{{1,2,3,5,6,7,8},{4}}
[5,8,1,3,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,1,8,2,6,3]=>{{1,4},{2,6,7},{3,5,8}}
[6,3,2,1,8,7,4,5]=>{{1,4,6,7},{2,3},{5,8}}
[6,2,3,1,8,7,4,5]=>{{1,4,6,7},{2},{3},{5,8}}
[3,4,8,1,7,5,6,2]=>{{1,2,3,4,8},{5,6,7}}
[7,2,5,1,8,3,6,4]=>{{1,3,4,5,6,7,8},{2}}
[7,2,1,5,8,4,6,3]=>{{1,3,4,5,6,7,8},{2}}
[4,2,8,1,7,5,6,3]=>{{1,4},{2},{3,8},{5,6,7}}
[7,3,1,5,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,4,2,8,5,3]=>{{1,2,5,7},{3,6,8},{4}}
[3,7,4,1,5,8,6,2]=>{{1,3,4},{2,6,7,8},{5}}
[5,8,6,1,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,1,4,3,7,5,2]=>{{1,3,5,6,7},{2,8},{4}}
[6,7,1,4,3,8,5,2]=>{{1,2,3,5,6,7,8},{4}}
[4,7,1,5,3,8,6,2]=>{{1,3,4,5},{2,6,7,8}}
[6,8,1,2,4,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,4,8,3,5,2]=>{{1,2,5,7,8},{3,6},{4}}
[8,6,4,1,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,6,1,7,4,2]=>{{1,2,5,8},{3},{4,6,7}}
[7,2,1,4,5,8,6,3]=>{{1,3,6,7,8},{2},{4},{5}}
[8,5,6,1,2,7,4,3]=>{{1,3,4,6,7,8},{2,5}}
[8,6,2,5,4,7,3,1]=>{{1,8},{2,3,6,7},{4,5}}
[8,5,7,3,2,4,6,1]=>{{1,8},{2,5},{3,4,6,7}}
[8,5,2,1,4,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,1,3,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[8,1,2,4,5,6,7,3]=>{{1,2,3,8},{4},{5},{6},{7}}
[6,1,4,3,2,7,8,5]=>{{1,2,5,6,7,8},{3,4}}
[1,8,3,6,7,2,4,5]=>{{1},{2,4,5,6,7,8},{3}}
[1,2,8,3,7,4,6,5]=>{{1},{2},{3,4,5,6,7,8}}
[8,2,6,5,4,3,1,7]=>{{1,7,8},{2},{3,6},{4,5}}
[8,2,7,6,4,5,3,1]=>{{1,8},{2},{3,7},{4,5,6}}
[8,7,3,5,4,2,6,1]=>{{1,8},{2,6,7},{3},{4,5}}
[4,6,7,2,1,8,3,5]=>{{1,2,4,5,6,8},{3,7}}
[3,7,1,8,2,5,4,6]=>{{1,3},{2,4,5,6,7,8}}
[4,5,8,6,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,5,8,6,2,7,3,1]=>{{1,3,4,6,7,8},{2,5}}
[4,6,7,1,5,3,8,2]=>{{1,4},{2,3,6,7,8},{5}}
[4,6,7,2,1,8,5,3]=>{{1,2,3,4,5,6,7,8}}
[4,2,5,6,7,8,3,1]=>{{1,4,6,8},{2},{3,5,7}}
[4,1,3,5,6,7,8,2]=>{{1,2,4,5,6,7,8},{3}}
[3,7,8,4,5,1,6,2]=>{{1,2,3,6,7,8},{4},{5}}
[4,6,8,3,2,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,8,2,3,7,1,5]=>{{1,2,4,6,7},{3,5,8}}
[3,8,1,7,4,5,2,6]=>{{1,3},{2,4,5,6,7,8}}
[4,5,8,3,7,1,2,6]=>{{1,3,4,6,8},{2,5,7}}
[3,7,8,4,6,2,5,1]=>{{1,3,8},{2,5,6,7},{4}}
[3,6,1,5,7,8,2,4]=>{{1,3},{2,4,5,6,7,8}}
[3,8,2,5,4,7,1,6]=>{{1,2,3,6,7,8},{4,5}}
[3,8,6,2,5,1,7,4]=>{{1,3,6},{2,4,8},{5},{7}}
[4,5,8,6,2,1,7,3]=>{{1,4,6},{2,5},{3,8},{7}}
[4,5,8,6,1,2,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[4,6,8,5,2,7,1,3]=>{{1,2,4,5,6,7},{3,8}}
[3,7,8,5,2,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[3,7,8,5,4,1,6,2]=>{{1,2,3,6,7,8},{4,5}}
[4,6,8,5,3,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[7,8,2,3,5,4,1,6]=>{{1,7},{2,3,4,6,8},{5}}
[4,6,5,2,7,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[1,6,5,2,3,4,8,7]=>{{1},{2,4,6},{3,5},{7,8}}
[4,6,5,1,7,3,8,2]=>{{1,4},{2,3,5,6,7,8}}
[5,7,3,1,2,4,8,6]=>{{1,2,4,5,6,7,8},{3}}
[6,3,2,5,1,7,4,8]=>{{1,4,5,6,7},{2,3},{8}}
[6,1,2,4,8,5,3,7]=>{{1,2,3,5,6,7,8},{4}}
[6,3,1,7,2,5,8,4]=>{{1,2,3,5,6},{4,7,8}}
[3,6,5,8,1,7,2,4]=>{{1,3,5},{2,6,7},{4,8}}
[5,2,7,3,4,6,1,8]=>{{1,3,4,5,7},{2},{6},{8}}
[1,3,5,8,6,4,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[1,3,5,8,6,7,2,4]=>{{1},{2,3,5,6,7},{4,8}}
[6,1,7,4,8,5,3,2]=>{{1,2,5,6,8},{3,7},{4}}
[5,7,4,1,3,6,8,2]=>{{1,3,4,5},{2,7,8},{6}}
[7,4,3,1,6,5,8,2]=>{{1,2,4,7,8},{3},{5,6}}
[8,6,1,7,5,3,2,4]=>{{1,2,3,4,6,7,8},{5}}
[7,8,1,4,6,5,3,2]=>{{1,3,7},{2,8},{4},{5,6}}
[7,8,6,1,4,5,3,2]=>{{1,3,4,5,6,7},{2,8}}
[6,2,7,3,8,5,4,1]=>{{1,5,6,8},{2},{3,4,7}}
[1,2,7,5,3,4,8,6]=>{{1},{2},{3,4,5,6,7,8}}
[7,2,8,3,6,4,5,1]=>{{1,3,4,5,6,7,8},{2}}
[6,2,7,8,3,1,4,5]=>{{1,6},{2},{3,4,5,7,8}}
[1,7,8,2,5,3,4,6]=>{{1},{2,4,7},{3,6,8},{5}}
[1,2,8,7,3,4,6,5]=>{{1},{2},{3,5,8},{4,6,7}}
[8,2,7,4,5,1,6,3]=>{{1,3,6,7,8},{2},{4},{5}}
[3,8,1,5,7,2,6,4]=>{{1,3},{2,4,5,6,7,8}}
[7,5,4,8,6,1,2,3]=>{{1,2,5,6,7},{3,4,8}}
[7,1,8,6,4,5,2,3]=>{{1,2,7},{3,8},{4,5,6}}
[8,7,5,1,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,3,1,7,2,5]=>{{1,2,5,6,7,8},{3,4}}
[8,4,1,3,7,5,6,2]=>{{1,2,3,4,8},{5,6,7}}
[4,8,1,3,7,5,6,2]=>{{1,3,4},{2,8},{5,6,7}}
[2,1,6,8,5,3,4,7]=>{{1,2},{3,6},{4,7,8},{5}}
[4,5,1,3,8,6,7,2]=>{{1,3,4},{2,5,8},{6},{7}}
[1,2,6,8,5,3,4,7]=>{{1},{2},{3,6},{4,7,8},{5}}
[5,6,8,7,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,5,3,8,1,2,4]=>{{1,6},{2,7},{3,4,5,8}}
[6,8,5,7,3,1,2,4]=>{{1,6},{2,4,7,8},{3,5}}
[5,1,4,2,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,3,2,4,7,1,8,5]=>{{1,6},{2,3},{4},{5,7,8}}
[1,5,8,6,2,4,3,7]=>{{1},{2,5},{3,7,8},{4,6}}
[5,1,8,6,2,4,3,7]=>{{1,2,5},{3,7,8},{4,6}}
[5,8,6,3,7,1,2,4]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,3,8,1,2,4]=>{{1,3,4,5,6,8},{2,7}}
[6,8,7,5,3,1,2,4]=>{{1,6},{2,3,4,5,7,8}}
[1,2,5,3,6,8,7,4]=>{{1},{2},{3,4,5,6,8},{7}}
[6,8,7,2,1,5,3,4]=>{{1,5,6},{2,4,8},{3,7}}
[7,3,6,1,4,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,6,5,3,4,2]=>{{1,3,4,6,7},{2,8},{5}}
[8,7,3,2,1,4,6,5]=>{{1,5,8},{2,4,6,7},{3}}
[8,3,5,1,7,4,2,6]=>{{1,4,6,8},{2,3,5,7}}
[3,5,6,8,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,8,2,6,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,8,6,3,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[1,7,2,3,5,8,6,4]=>{{1},{2,3,4,6,7,8},{5}}
[2,8,3,7,5,1,6,4]=>{{1,2,4,6,7,8},{3},{5}}
[6,4,8,7,2,1,5,3]=>{{1,6},{2,4,5,7},{3,8}}
[2,8,4,3,6,7,1,5]=>{{1,2,5,6,7,8},{3,4}}
[7,3,2,5,6,1,8,4]=>{{1,4,5,6,7,8},{2,3}}
[1,6,7,8,2,4,3,5]=>{{1},{2,4,5,6,8},{3,7}}
[4,1,2,8,5,3,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[3,8,4,2,5,1,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[1,8,5,6,4,3,2,7]=>{{1},{2,7,8},{3,4,5,6}}
[2,8,3,5,6,4,1,7]=>{{1,2,7,8},{3},{4,5,6}}
[7,6,8,3,2,5,1,4]=>{{1,7},{2,5,6},{3,4,8}}
[2,7,1,4,5,3,8,6]=>{{1,2,3,6,7,8},{4},{5}}
[1,5,2,7,4,3,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,1,3,8,4,6,2,7]=>{{1,2,4,5,7,8},{3},{6}}
[6,5,8,7,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[2,7,3,5,1,6,8,4]=>{{1,2,4,5,7,8},{3},{6}}
[5,7,6,8,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[1,3,6,5,2,7,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,2,6,5,3,4,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[1,7,2,5,6,8,3,4]=>{{1},{2,3,7},{4,5,6,8}}
[1,7,2,4,8,3,5,6]=>{{1},{2,3,5,6,7,8},{4}}
[1,6,2,4,5,3,7,8]=>{{1},{2,3,6},{4},{5},{7},{8}}
[1,3,2,8,4,5,7,6]=>{{1},{2,3},{4,5,6,8},{7}}
[1,6,8,2,4,3,5,7]=>{{1},{2,3,4,5,6,7,8}}
[1,6,7,2,5,3,4,8]=>{{1},{2,3,4,6,7},{5},{8}}
[1,2,8,3,6,7,4,5]=>{{1},{2},{3,4,5,6,7,8}}
[1,7,2,5,3,4,8,6]=>{{1},{2,3,4,5,6,7,8}}
[7,1,5,6,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,4,6,7,3,5]=>{{1,3,5,6,7,8},{2},{4}}
[7,2,6,1,3,4,8,5]=>{{1,3,4,5,6,7,8},{2}}
[4,1,3,7,2,5,8,6]=>{{1,2,4,5,6,7,8},{3}}
[6,2,7,5,1,3,8,4]=>{{1,3,4,5,6,7,8},{2}}
[1,7,5,6,2,3,8,4]=>{{1},{2,3,4,5,6,7,8}}
[3,7,6,1,2,4,8,5]=>{{1,3,4,6},{2,5,7,8}}
[8,6,1,3,5,7,2,4]=>{{1,3,4,8},{2,6,7},{5}}
[1,7,4,3,8,2,5,6]=>{{1},{2,5,6,7,8},{3,4}}
[6,1,5,3,4,8,2,7]=>{{1,2,6,7,8},{3,4,5}}
[3,6,7,5,2,8,1,4]=>{{1,3,7},{2,4,5,6,8}}
[7,8,4,1,5,6,2,3]=>{{1,2,3,4,7,8},{5},{6}}
[5,8,1,3,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,3,7,1,5,6]=>{{1,2,6,8},{3,4},{5,7}}
[3,8,4,6,7,1,2,5]=>{{1,3,4,6},{2,5,7,8}}
[6,3,8,4,7,1,2,5]=>{{1,6},{2,3,5,7,8},{4}}
[1,2,5,4,8,3,6,7]=>{{1},{2},{3,5,6,7,8},{4}}
[7,1,3,8,2,4,5,6]=>{{1,2,5,7},{3},{4,6,8}}
[8,1,3,7,2,4,5,6]=>{{1,2,4,5,6,7,8},{3}}
[3,5,4,7,8,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,4,7,2,5,6]=>{{1,2,3,6,8},{4},{5,7}}
[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[5,2,3,6,7,8,1,4]=>{{1,5,7},{2},{3},{4,6,8}}
[6,2,7,3,8,5,1,4]=>{{1,3,4,5,6,7,8},{2}}
[1,3,7,8,5,6,2,4]=>{{1},{2,3,7},{4,8},{5},{6}}
[8,2,6,7,5,1,3,4]=>{{1,3,4,6,7,8},{2},{5}}
[8,1,7,4,6,2,3,5]=>{{1,2,5,6,8},{3,7},{4}}
[2,5,8,4,7,1,3,6]=>{{1,2,3,5,6,7,8},{4}}
[4,5,8,7,1,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[4,1,8,5,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,4,6,2,3,5]=>{{1},{2,5,6,8},{3,7},{4}}
[2,6,5,4,1,8,3,7]=>{{1,2,3,5,6,7,8},{4}}
[6,2,5,1,4,8,3,7]=>{{1,3,4,5,6,7,8},{2}}
[6,5,4,1,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[6,3,5,4,2,8,1,7]=>{{1,6,7,8},{2,3,5},{4}}
[1,3,8,7,4,2,6,5]=>{{1},{2,3,4,5,6,7,8}}
[8,7,4,3,1,5,2,6]=>{{1,5,6,8},{2,7},{3,4}}
[8,2,5,1,4,6,7,3]=>{{1,3,4,5,8},{2},{6},{7}}
[3,8,4,5,1,6,7,2]=>{{1,3,4,5},{2,8},{6},{7}}
[8,5,4,1,3,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[8,3,1,7,5,6,4,2]=>{{1,2,3,8},{4,7},{5},{6}}
[8,4,7,6,5,3,1,2]=>{{1,2,3,4,6,7,8},{5}}
[8,1,4,5,7,6,3,2]=>{{1,2,8},{3,4,5,7},{6}}
[2,4,1,8,5,7,6,3]=>{{1,2,3,4,8},{5},{6,7}}
[8,2,1,4,7,6,3,5]=>{{1,3,5,7,8},{2},{4},{6}}
[8,3,1,7,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,2,7,3,1,6,5,4]=>{{1,3,4,5,7,8},{2},{6}}
[1,8,4,2,3,7,6,5]=>{{1},{2,3,4,5,8},{6,7}}
[3,1,2,8,7,4,6,5]=>{{1,2,3},{4,5,6,7,8}}
[8,5,1,2,4,3,7,6]=>{{1,3,6,8},{2,4,5},{7}}
[2,8,3,7,4,1,6,5]=>{{1,2,4,5,6,7,8},{3}}
[8,4,5,7,6,2,3,1]=>{{1,8},{2,3,4,5,6,7}}
[2,3,1,8,7,6,4,5]=>{{1,2,3},{4,5,7,8},{6}}
[4,2,8,7,3,1,5,6]=>{{1,3,4,5,6,7,8},{2}}
[1,3,4,8,7,2,5,6]=>{{1},{2,3,4,6,8},{5,7}}
[8,1,3,4,6,7,2,5]=>{{1,2,5,6,7,8},{3},{4}}
[3,4,8,2,6,7,1,5]=>{{1,3,5,6,7,8},{2,4}}
[3,6,8,2,5,1,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[3,8,2,5,7,4,6,1]=>{{1,2,3,8},{4,5,6,7}}
[8,4,2,1,7,5,6,3]=>{{1,2,3,4,8},{5,6,7}}
[8,2,7,5,6,4,1,3]=>{{1,3,7,8},{2},{4,5,6}}
[6,2,8,5,4,1,7,3]=>{{1,6},{2},{3,8},{4,5},{7}}
[6,8,5,4,1,7,2,3]=>{{1,2,3,5,6,7,8},{4}}
[2,8,1,5,7,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[3,1,8,2,7,5,6,4]=>{{1,2,3,4,8},{5,6,7}}
[8,5,7,1,6,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,7,3,6,5,1]=>{{1,2,8},{3,4,5,7},{6}}
[8,4,7,2,1,6,5,3]=>{{1,3,5,7,8},{2,4},{6}}
[1,8,4,7,6,5,2,3]=>{{1},{2,3,4,7,8},{5,6}}
[3,5,8,1,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,1,3,6,5,2]=>{{1,2,4,8},{3,5,7},{6}}
[2,3,4,7,6,8,1,5]=>{{1,2,3,4,7},{5,6,8}}
[3,8,1,2,5,6,4,7]=>{{1,3},{2,4,7,8},{5},{6}}
[3,7,1,2,5,6,4,8]=>{{1,3},{2,4,7},{5},{6},{8}}
[8,5,2,1,4,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[4,8,1,6,5,2,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[4,2,6,3,8,5,7,1]=>{{1,3,4,5,6,8},{2},{7}}
[4,5,2,6,7,1,8,3]=>{{1,4,6},{2,3,5,7,8}}
[8,3,5,4,2,7,1,6]=>{{1,6,7,8},{2,3,5},{4}}
[2,8,6,4,7,3,1,5]=>{{1,2,5,7,8},{3,6},{4}}
[3,1,8,6,5,2,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[8,3,1,5,2,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[3,8,2,4,1,5,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[5,8,3,2,4,1,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[7,2,6,8,4,3,5,1]=>{{1,4,5,7,8},{2},{3,6}}
[6,5,3,2,4,8,1,7]=>{{1,6,7,8},{2,4,5},{3}}
[5,2,4,6,1,3,8,7]=>{{1,5},{2},{3,4,6},{7,8}}
[7,2,3,4,6,8,1,5]=>{{1,7},{2},{3},{4},{5,6,8}}
[8,3,4,6,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,8,3,4,7,5,2,1]=>{{1,2,5,6,7,8},{3},{4}}
[5,8,6,1,3,4,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[4,8,1,5,7,6,3,2]=>{{1,3,4,5,7},{2,8},{6}}
[3,7,4,6,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,7,1,6,8,3,2,5]=>{{1,3,4,6},{2,7},{5,8}}
[4,5,2,8,1,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,5,2,8,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[4,8,5,2,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,6,1,2,7,3]=>{{1,5},{2,4,6},{3,8},{7}}
[8,4,6,5,2,7,3,1]=>{{1,8},{2,4,5},{3,6,7}}
[8,1,6,4,7,5,2,3]=>{{1,2,3,5,6,7,8},{4}}
[5,2,7,6,4,8,1,3]=>{{1,3,4,5,6,7,8},{2}}
[8,6,2,3,5,1,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[8,2,5,7,4,1,3,6]=>{{1,6,8},{2},{3,4,5,7}}
[7,2,4,5,6,8,1,3]=>{{1,7},{2},{3,4,5,6,8}}
[7,1,3,5,6,2,8,4]=>{{1,2,4,5,6,7,8},{3}}
[7,1,5,8,4,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[6,3,8,4,7,1,5,2]=>{{1,6},{2,3,8},{4},{5,7}}
[7,1,4,3,2,8,5,6]=>{{1,2,5,7},{3,4},{6,8}}
[5,3,6,1,4,2,8,7]=>{{1,4,5},{2,3,6},{7,8}}
[5,7,2,1,4,3,8,6]=>{{1,4,5},{2,3,6,7,8}}
[7,1,8,3,5,2,4,6]=>{{1,2,3,4,6,7,8},{5}}
[7,2,4,8,1,5,6,3]=>{{1,5,6,7},{2},{3,4,8}}
[7,1,8,4,2,5,6,3]=>{{1,2,5,6,7},{3,8},{4}}
[6,4,2,5,8,1,7,3]=>{{1,6},{2,3,4,5,8},{7}}
[2,1,7,5,8,3,6,4]=>{{1,2},{3,6,7},{4,5,8}}
[7,3,8,5,6,2,1,4]=>{{1,7},{2,3,4,5,6,8}}
[2,7,4,8,1,5,6,3]=>{{1,2,5,6,7},{3,4,8}}
[7,4,8,3,1,5,6,2]=>{{1,5,6,7},{2,3,4,8}}
[6,1,5,8,3,7,4,2]=>{{1,2,4,6,7,8},{3,5}}
[2,6,3,5,8,7,4,1]=>{{1,2,4,5,6,7,8},{3}}
[8,6,5,3,7,2,1,4]=>{{1,3,4,5,7,8},{2,6}}
[4,8,5,3,7,2,1,6]=>{{1,3,4,5,7},{2,6,8}}
[7,4,8,6,5,3,2,1]=>{{1,2,3,4,6,7,8},{5}}
[7,4,8,5,6,3,1,2]=>{{1,7},{2,3,4,5,6,8}}
[7,8,4,1,3,5,6,2]=>{{1,3,4,5,6,7},{2,8}}
[7,8,3,4,1,5,6,2]=>{{1,5,6,7},{2,8},{3},{4}}
[7,3,1,8,2,5,6,4]=>{{1,2,3,5,6,7},{4,8}}
[7,2,3,8,1,5,6,4]=>{{1,5,6,7},{2},{3},{4,8}}
[6,4,8,7,3,2,1,5]=>{{1,2,4,6,7},{3,5,8}}
[2,7,4,8,6,3,1,5]=>{{1,2,7},{3,4,5,6,8}}
[6,4,8,2,3,1,7,5]=>{{1,6},{2,4},{3,5,8},{7}}
[7,2,1,8,3,5,6,4]=>{{1,3,5,6,7},{2},{4,8}}
[5,1,6,3,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,6,5,1,4,8,7,2]=>{{1,3,4,5},{2,6,8},{7}}
[7,3,6,2,8,4,1,5]=>{{1,7},{2,3,4,6},{5,8}}
[7,5,4,8,1,6,2,3]=>{{1,2,5,7},{3,4,8},{6}}
[4,3,5,8,7,1,2,6]=>{{1,4,6,8},{2,3,5,7}}
[3,5,6,8,1,4,2,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,5,8,2,1,6,7]=>{{1,4,6,7,8},{2,3,5}}
[6,4,7,2,3,1,5,8]=>{{1,6},{2,4},{3,5,7},{8}}
[6,8,1,5,4,2,7,3]=>{{1,2,3,6,8},{4,5},{7}}
[7,8,6,3,1,4,2,5]=>{{1,2,5,7,8},{3,4,6}}
[7,8,6,3,5,1,2,4]=>{{1,2,3,4,6,7,8},{5}}
[7,2,8,5,4,6,3,1]=>{{1,3,7,8},{2},{4,5},{6}}
[6,1,8,4,7,2,3,5]=>{{1,2,6},{3,5,7,8},{4}}
[5,6,4,3,7,1,8,2]=>{{1,2,5,6,7,8},{3,4}}
[6,5,3,7,2,4,8,1]=>{{1,4,6,7,8},{2,5},{3}}
[5,6,2,8,4,3,7,1]=>{{1,4,5,8},{2,3,6},{7}}
[7,1,3,6,5,8,4,2]=>{{1,2,4,6,7,8},{3},{5}}
[5,7,4,3,6,8,2,1]=>{{1,5,6,8},{2,7},{3,4}}
[4,6,2,7,8,3,5,1]=>{{1,4,5,7,8},{2,3,6}}
[5,1,2,4,6,7,8,3]=>{{1,2,3,5,6,7,8},{4}}
[4,6,3,5,2,8,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[5,6,3,4,8,2,7,1]=>{{1,5,8},{2,6},{3},{4},{7}}
[5,2,6,4,1,7,8,3]=>{{1,5},{2},{3,6,7,8},{4}}
[5,8,4,6,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,4,3,8,6,2,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[5,7,8,2,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[5,6,2,4,8,3,7,1]=>{{1,5,8},{2,3,6},{4},{7}}
[6,4,7,8,2,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,7,5,2,4,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[4,7,5,2,3,8,6,1]=>{{1,2,4,6,7,8},{3,5}}
[6,4,7,3,2,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,3,2,8,4,6,1]=>{{1,5,8},{2,4,6,7},{3}}
[5,3,7,2,8,4,6,1]=>{{1,5,8},{2,3,4,6,7}}
[4,3,7,2,5,8,6,1]=>{{1,2,3,4,6,7,8},{5}}
[4,7,3,2,5,8,6,1]=>{{1,2,4,6,7,8},{3},{5}}
[4,7,3,2,6,8,5,1]=>{{1,2,4,5,6,7,8},{3}}
[7,5,3,2,6,4,8,1]=>{{1,7,8},{2,4,5,6},{3}}
[8,5,2,6,7,3,4,1]=>{{1,8},{2,3,4,5,6,7}}
[8,4,2,6,3,7,5,1]=>{{1,8},{2,3,4,5,6,7}}
[7,4,6,2,3,8,5,1]=>{{1,3,5,6,7,8},{2,4}}
[7,5,6,2,8,3,4,1]=>{{1,2,4,5,7,8},{3,6}}
[5,7,6,2,8,3,4,1]=>{{1,5,8},{2,4,7},{3,6}}
[4,7,6,2,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,3,2,5,8,1,4]=>{{1,7},{2,4,6,8},{3},{5}}
[7,6,4,2,5,8,3,1]=>{{1,2,3,4,6,7,8},{5}}
[6,3,8,5,4,7,2,1]=>{{1,2,3,6,7,8},{4,5}}
[2,4,6,3,8,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[2,4,3,6,8,7,1,5]=>{{1,2,4,6,7},{3},{5,8}}
[2,4,6,3,8,7,1,5]=>{{1,2,3,4,6,7},{5,8}}
[2,4,6,5,8,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,8,5,7,3,1]=>{{1,2,4,8},{3,6,7},{5}}
[2,4,6,8,5,7,1,3]=>{{1,2,3,4,6,7,8},{5}}
[2,4,6,8,3,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,8,1,7,3,5]=>{{1,2,4,5,8},{3,6,7}}
[2,4,6,5,8,3,7,1]=>{{1,2,4,5,8},{3,6},{7}}
[2,4,6,5,8,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,4,6,8,5,1,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[2,4,6,8,7,3,5,1]=>{{1,2,4,8},{3,6},{5,7}}
[2,4,6,8,7,1,5,3]=>{{1,2,3,4,6,8},{5,7}}
[2,4,6,8,7,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,8,5,1,3,7]=>{{1,2,3,4,6,7,8},{5}}
[2,4,6,5,1,8,3,7]=>{{1,2,4,5},{3,6,7,8}}
[2,4,6,5,3,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,5,8,3,1,7]=>{{1,2,4,5,7,8},{3,6}}
[2,4,6,8,5,3,1,7]=>{{1,2,4,7,8},{3,6},{5}}
[2,4,6,8,7,3,1,5]=>{{1,2,4,5,7,8},{3,6}}
[2,4,6,8,7,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,5,2,1,3,6]=>{{1,2,4,5,6,8},{3,7}}
[6,1,4,7,5,8,2,3]=>{{1,2,3,4,6,7,8},{5}}
[1,8,6,5,3,2,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,3,5,8,2,4,7]=>{{1},{2,6},{3},{4,5,7,8}}
[4,6,1,7,8,5,3,2]=>{{1,3,4,7},{2,5,6,8}}
[6,1,2,7,8,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[6,1,3,2,7,8,5,4]=>{{1,2,4,6,8},{3},{5,7}}
[5,6,3,1,7,4,8,2]=>{{1,2,4,5,6,7,8},{3}}
[4,8,3,7,1,6,5,2]=>{{1,4,5,7},{2,8},{3},{6}}
[8,7,2,6,5,1,4,3]=>{{1,2,3,4,6,7,8},{5}}
[5,8,3,2,1,7,6,4]=>{{1,5},{2,4,8},{3},{6,7}}
[5,4,3,8,1,7,6,2]=>{{1,5},{2,4,8},{3},{6,7}}
[6,5,3,8,7,1,4,2]=>{{1,6},{2,4,5,7,8},{3}}
[4,3,8,2,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}
[4,8,2,7,6,5,3,1]=>{{1,2,3,4,7,8},{5,6}}
[7,8,2,6,5,4,1,3]=>{{1,7},{2,3,8},{4,6},{5}}
[3,8,7,6,2,5,1,4]=>{{1,3,7},{2,4,5,6,8}}
[4,8,3,7,2,1,6,5]=>{{1,4,6,7},{2,5,8},{3}}
[8,6,3,1,7,5,4,2]=>{{1,2,4,5,6,7,8},{3}}
[8,6,3,7,1,5,4,2]=>{{1,2,5,6,8},{3},{4,7}}
[4,8,3,7,6,2,5,1]=>{{1,2,4,5,6,7,8},{3}}
[5,8,2,7,6,4,1,3]=>{{1,4,5,6,7},{2,3,8}}
[8,4,2,1,7,6,5,3]=>{{1,2,3,4,8},{5,7},{6}}
[1,6,4,2,5,3,7,8]=>{{1},{2,3,4,6},{5},{7},{8}}
[1,8,6,2,7,3,4,5]=>{{1},{2,4,5,7,8},{3,6}}
[1,6,3,2,4,5,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[1,5,2,6,4,3,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,5,2,4,6,3,7,8]=>{{1},{2,3,5,6},{4},{7},{8}}
[1,8,6,2,3,7,4,5]=>{{1},{2,3,4,5,6,7,8}}
[1,5,2,8,6,3,4,7]=>{{1},{2,3,5,6},{4,7,8}}
[1,3,6,8,2,7,4,5]=>{{1},{2,3,4,5,6,7,8}}
[1,4,3,8,2,5,6,7]=>{{1},{2,4,5,6,7,8},{3}}
[1,7,2,3,8,5,4,6]=>{{1},{2,3,4,7},{5,6,8}}
[1,3,8,4,2,5,6,7]=>{{1},{2,3,5,6,7,8},{4}}
[1,6,2,8,5,4,3,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,7,2,3,8,6,4,5]=>{{1},{2,3,4,7},{5,8},{6}}
[1,5,3,8,2,7,4,6]=>{{1},{2,5},{3},{4,6,7,8}}
[1,4,8,2,5,6,3,7]=>{{1},{2,4},{3,7,8},{5},{6}}
[1,5,7,3,2,8,4,6]=>{{1},{2,5},{3,4,7},{6,8}}
[1,2,7,3,6,8,4,5]=>{{1},{2},{3,4,7},{5,6,8}}
[1,7,2,3,6,8,4,5]=>{{1},{2,3,4,7},{5,6,8}}
[1,4,8,3,2,5,6,7]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,5,8,3,4,6]=>{{1},{2,3,4,5,6,7,8}}
[6,2,3,5,8,1,7,4]=>{{1,6},{2},{3},{4,5,8},{7}}
[5,2,4,8,1,6,7,3]=>{{1,5},{2},{3,4,8},{6},{7}}
[2,6,4,5,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,3,6,7,4,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,6,3,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,5,3,6,4,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[1,5,3,7,4,6,2,8]=>{{1},{2,4,5,7},{3},{6},{8}}
[1,5,7,3,6,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,5,7,4,1,3,8,6]=>{{1,2,5},{3,6,7,8},{4}}
[6,7,3,1,8,5,2,4]=>{{1,4,5,6,8},{2,7},{3}}
[4,6,3,5,8,2,1,7]=>{{1,4,5,7,8},{2,6},{3}}
[7,2,4,8,6,3,1,5]=>{{1,7},{2},{3,4,5,6,8}}
[7,4,5,2,1,8,6,3]=>{{1,3,5,6,7,8},{2,4}}
[4,7,5,2,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,6,2,1,7,4]=>{{1,4,6,8},{2,5},{3},{7}}
[4,5,7,3,1,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,8,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,7,4,6,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[3,6,1,2,4,8,7,5]=>{{1,3},{2,4,5,6,8},{7}}
[2,5,3,8,4,1,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[7,5,2,3,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,2,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,7,5,2,3,6,1,8]=>{{1,2,4,7},{3,5},{6},{8}}
[3,6,8,4,5,1,2,7]=>{{1,2,3,6,7,8},{4},{5}}
[5,2,3,7,6,4,1,8]=>{{1,4,5,6,7},{2},{3},{8}}
[6,2,7,3,5,4,1,8]=>{{1,3,4,6,7},{2},{5},{8}}
[7,2,6,5,3,4,1,8]=>{{1,7},{2},{3,4,5,6},{8}}
[8,2,6,5,4,1,3,7]=>{{1,3,6,7,8},{2},{4,5}}
[6,2,8,4,5,1,3,7]=>{{1,6},{2},{3,7,8},{4},{5}}
[2,3,1,7,8,5,6,4]=>{{1,2,3},{4,5,6,7,8}}
[7,2,8,5,1,4,3,6]=>{{1,3,4,5,6,7,8},{2}}
[8,6,7,1,4,2,3,5]=>{{1,4,5,8},{2,6},{3,7}}
[6,8,7,1,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[6,8,2,5,3,1,4,7]=>{{1,6},{2,3,4,5,7,8}}
[3,7,8,5,1,4,2,6]=>{{1,3,4,5,6,8},{2,7}}
[4,8,7,3,1,2,5,6]=>{{1,3,4,5,7},{2,6,8}}
[4,8,6,2,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,8,5,4,2,1,6,7]=>{{1,2,3,5,6,7,8},{4}}
[4,5,3,8,2,1,6,7]=>{{1,4,6,7,8},{2,5},{3}}
[3,7,4,1,8,2,6,5]=>{{1,3,4},{2,6,7},{5,8}}
[3,8,4,1,7,6,2,5]=>{{1,3,4},{2,5,7,8},{6}}
[3,7,2,1,8,4,6,5]=>{{1,2,3,4,6,7},{5,8}}
[8,7,1,6,5,2,3,4]=>{{1,2,3,4,6,7,8},{5}}
[8,5,1,2,7,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[3,8,2,1,7,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[3,5,7,8,2,4,6,1]=>{{1,3,4,6,7,8},{2,5}}
[7,8,2,5,4,3,6,1]=>{{1,2,3,6,7,8},{4,5}}
[4,5,3,7,8,2,6,1]=>{{1,2,4,5,6,7,8},{3}}
[1,5,4,7,3,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,7,3,6,8,4,5,2]=>{{1},{2,5,7,8},{3},{4,6}}
[4,6,8,2,7,3,5,1]=>{{1,2,3,4,6,8},{5,7}}
[4,7,6,3,5,1,8,2]=>{{1,3,4,6},{2,7,8},{5}}
[7,8,3,6,1,5,4,2]=>{{1,4,5,6,7},{2,8},{3}}
[2,5,7,8,4,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[3,7,5,6,2,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,2,1,7,4,5,3,8]=>{{1,3,4,5,6,7},{2},{8}}
[1,2,6,4,7,5,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[7,5,6,3,8,4,2,1]=>{{1,2,5,7,8},{3,4,6}}
[8,5,4,2,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[2,6,8,4,7,5,1,3]=>{{1,2,5,6,7},{3,8},{4}}
[6,7,5,1,4,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,6,5,3,8,2]=>{{1,2,3,4,6,7,8},{5}}
[5,8,2,7,3,6,4,1]=>{{1,2,3,5,8},{4,7},{6}}
[1,6,5,7,3,8,4,2]=>{{1},{2,6,8},{3,5},{4,7}}
[1,5,6,8,4,2,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[7,5,4,1,8,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,8,2,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,3,2,6,1,4]=>{{1,7},{2,3,4,5,8},{6}}
[8,2,5,1,7,6,4,3]=>{{1,3,4,5,7,8},{2},{6}}
[6,7,4,3,8,2,5,1]=>{{1,2,5,6,7,8},{3,4}}
[3,4,2,7,8,6,1,5]=>{{1,2,3,4,7},{5,8},{6}}
[7,8,6,1,4,3,2,5]=>{{1,2,4,5,7,8},{3,6}}
[2,4,7,8,6,1,3,5]=>{{1,2,4,5,6,8},{3,7}}
[3,7,8,6,5,2,4,1]=>{{1,3,8},{2,4,6,7},{5}}
[4,5,2,7,8,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[4,6,2,5,3,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[4,1,5,6,3,2,7,8]=>{{1,2,4,6},{3,5},{7},{8}}
[2,6,7,5,4,1,3,8]=>{{1,2,6},{3,7},{4,5},{8}}
[4,1,6,7,5,3,2,8]=>{{1,2,4,7},{3,6},{5},{8}}
[6,7,4,3,1,5,2,8]=>{{1,5,6},{2,7},{3,4},{8}}
[1,7,5,6,4,3,2,8]=>{{1},{2,7},{3,4,5,6},{8}}
[7,6,5,3,1,8,4,2]=>{{1,3,4,5,7},{2,6,8}}
[7,8,6,4,3,1,5,2]=>{{1,3,5,6,7},{2,8},{4}}
[4,1,7,8,6,5,3,2]=>{{1,2,4,8},{3,7},{5,6}}
[4,5,7,3,8,6,1,2]=>{{1,3,4,7},{2,5,8},{6}}
[6,8,5,3,7,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[4,7,1,5,8,2,6,3]=>{{1,3,4,5,8},{2,6,7}}
[2,7,5,8,3,6,4,1]=>{{1,2,4,7,8},{3,5},{6}}
[7,4,8,2,6,5,3,1]=>{{1,3,7,8},{2,4},{5,6}}
[7,5,4,8,2,6,3,1]=>{{1,3,4,7,8},{2,5},{6}}
[4,3,8,1,6,5,2,7]=>{{1,4},{2,3,7,8},{5,6}}
[2,3,6,5,7,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,1,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[7,3,4,8,5,2,1,6]=>{{1,7},{2,3,4,6,8},{5}}
[7,3,8,4,1,5,6,2]=>{{1,5,6,7},{2,3,8},{4}}
[7,2,4,5,1,8,3,6]=>{{1,3,4,5,7},{2},{6,8}}
[7,3,1,2,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[4,8,2,3,5,7,6,1]=>{{1,2,3,4,8},{5},{6,7}}
[4,5,2,3,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[6,7,4,8,5,3,2,1]=>{{1,3,4,6,8},{2,7},{5}}
[4,3,5,6,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,6,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,8,5,7,6,3]=>{{1,2,3,4,8},{5},{6,7}}
[3,1,5,6,4,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,1,4,6,7,5,8,2]=>{{1,2,3,4,5,6,7,8}}
[2,6,4,5,8,1,3,7]=>{{1,2,6},{3,4,5,7,8}}
[6,4,1,3,5,8,2,7]=>{{1,2,3,4,6,7,8},{5}}
[3,4,1,7,2,6,8,5]=>{{1,3},{2,4,5,7,8},{6}}
[2,4,7,5,8,1,3,6]=>{{1,2,4,5,6,8},{3,7}}
[3,1,6,4,8,7,5,2]=>{{1,2,3,5,6,7,8},{4}}
[3,7,6,2,1,5,8,4]=>{{1,3,5,6},{2,4,7,8}}
[4,2,6,1,3,7,8,5]=>{{1,4},{2},{3,5,6,7,8}}
[8,5,4,2,7,6,3,1]=>{{1,8},{2,3,4,5,7},{6}}
[2,8,4,6,7,1,3,5]=>{{1,2,3,4,5,6,7,8}}
[5,8,2,1,4,6,7,3]=>{{1,4,5},{2,3,8},{6},{7}}
[8,4,6,1,2,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[3,7,8,4,2,6,5,1]=>{{1,3,8},{2,5,7},{4},{6}}
[5,6,2,8,7,1,3,4]=>{{1,2,3,5,6,7},{4,8}}
[7,1,3,8,4,5,6,2]=>{{1,2,4,5,6,7,8},{3}}
[7,8,1,4,3,5,6,2]=>{{1,3,5,6,7},{2,8},{4}}
[3,6,7,2,8,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[2,6,7,1,3,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,1,8,2,5,4]=>{{1,3,4,5,7,8},{2,6}}
[3,4,1,8,7,2,6,5]=>{{1,3},{2,4,5,6,7,8}}
[3,1,5,7,2,8,6,4]=>{{1,2,3,5},{4,6,7,8}}
[3,8,1,4,7,2,6,5]=>{{1,3},{2,5,6,7,8},{4}}
[4,8,1,3,2,7,6,5]=>{{1,3,4},{2,5,8},{6,7}}
[4,1,8,3,2,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[4,3,8,1,2,7,6,5]=>{{1,4},{2,3,5,8},{6,7}}
[3,8,4,2,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,3,7,6,1,5]=>{{1,2,5,7,8},{3,4},{6}}
[3,8,2,4,7,1,6,5]=>{{1,2,3,5,6,7,8},{4}}
[3,2,4,8,7,1,6,5]=>{{1,3,4,5,6,7,8},{2}}
[3,2,5,7,1,8,6,4]=>{{1,3,5},{2},{4,6,7,8}}
[4,2,8,3,1,7,6,5]=>{{1,3,4,5,8},{2},{6,7}}
[4,8,2,1,3,7,6,5]=>{{1,4},{2,3,5,8},{6,7}}
[4,2,8,1,3,7,6,5]=>{{1,4},{2},{3,5,8},{6,7}}
[2,3,4,6,8,7,1,5]=>{{1,2,3,4,6,7},{5,8}}
[5,6,4,7,1,2,8,3]=>{{1,5},{2,6},{3,4,7,8}}
[4,6,7,5,8,2,3,1]=>{{1,4,5,8},{2,6},{3,7}}
[4,5,7,1,6,8,3,2]=>{{1,4},{2,5,6,8},{3,7}}
[3,2,7,6,8,1,4,5]=>{{1,3,4,6,7},{2},{5,8}}
[4,5,1,7,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,8,3,1,4,5]=>{{1,6},{2,3,4,5,7,8}}
[7,6,3,1,2,8,4,5]=>{{1,4,7},{2,5,6,8},{3}}
[6,2,7,8,4,1,3,5]=>{{1,6},{2},{3,7},{4,5,8}}
[6,3,7,8,4,1,2,5]=>{{1,6},{2,3,7},{4,5,8}}
[7,8,5,2,4,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,6,2,3,1,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[4,2,5,1,3,7,8,6]=>{{1,4},{2},{3,5},{6,7,8}}
[3,4,1,7,8,5,2,6]=>{{1,3},{2,4,7},{5,6,8}}
[4,1,3,7,8,5,2,6]=>{{1,2,4,7},{3},{5,6,8}}
[4,3,1,8,5,2,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[7,6,3,5,8,4,2,1]=>{{1,2,4,5,6,7,8},{3}}
[4,5,1,3,2,7,8,6]=>{{1,3,4},{2,5},{6,7,8}}
[5,1,3,2,4,7,8,6]=>{{1,2,4,5},{3},{6,7,8}}
[2,3,7,8,5,4,1,6]=>{{1,2,3,7},{4,6,8},{5}}
[8,3,5,6,1,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[4,5,8,1,2,6,7,3]=>{{1,4},{2,5},{3,8},{6},{7}}
[5,3,6,7,8,2,1,4]=>{{1,4,5,7,8},{2,3,6}}
[1,3,4,8,6,2,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[7,2,4,1,3,8,5,6]=>{{1,3,4,5,7},{2},{6,8}}
[8,4,5,2,6,1,7,3]=>{{1,3,5,6,8},{2,4},{7}}
[4,6,8,2,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,7,2,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[2,7,3,4,1,5,6,8]=>{{1,2,5,6,7},{3},{4},{8}}
[6,7,2,3,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,4,6,7,8,1]=>{{1,2,3,5,6,7,8},{4}}
[4,2,6,3,5,7,8,1]=>{{1,3,4,6,7,8},{2},{5}}
[1,4,8,5,6,2,7,3]=>{{1},{2,4,5,6},{3,8},{7}}
[2,8,7,4,5,1,6,3]=>{{1,2,3,6,7,8},{4},{5}}
[1,3,8,5,2,6,7,4]=>{{1},{2,3,4,5,8},{6},{7}}
[7,2,8,4,5,1,6,3]=>{{1,6,7},{2},{3,8},{4},{5}}
[8,6,2,4,1,5,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[1,6,4,3,2,7,8,5]=>{{1},{2,5,6,7,8},{3,4}}
[8,5,3,2,1,6,7,4]=>{{1,2,4,5,8},{3},{6},{7}}
[1,7,5,2,3,6,8,4]=>{{1},{2,4,7,8},{3,5},{6}}
[7,1,5,2,3,6,8,4]=>{{1,2,4,7,8},{3,5},{6}}
[8,1,2,5,3,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[8,4,1,6,3,7,2,5]=>{{1,3,5,8},{2,4,6,7}}
[6,7,5,3,8,2,1,4]=>{{1,2,6,7},{3,4,5,8}}
[5,2,6,8,3,7,1,4]=>{{1,3,5,6,7},{2},{4,8}}
[4,2,5,8,6,7,1,3]=>{{1,3,4,5,6,7,8},{2}}
[5,8,6,3,4,1,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[3,7,2,4,1,8,6,5]=>{{1,2,3,5,6,7,8},{4}}
[2,4,7,8,5,1,3,6]=>{{1,2,4,6,8},{3,7},{5}}
[2,5,3,8,4,1,6,7]=>{{1,2,4,5,6,7,8},{3}}
[3,1,7,4,5,6,2,8]=>{{1,2,3,7},{4},{5},{6},{8}}
[2,4,8,3,5,7,1,6]=>{{1,2,3,4,6,7,8},{5}}
[8,1,7,2,4,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[1,3,8,2,4,7,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,3,7,2,4,6,5,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,7,3,2,4,6,5,8]=>{{1},{2,4,5,7},{3},{6},{8}}
[1,8,3,7,4,2,5,6]=>{{1},{2,6,8},{3},{4,5,7}}
[8,7,3,1,4,2,5,6]=>{{1,2,4,5,6,7,8},{3}}
[2,8,4,3,5,7,1,6]=>{{1,2,6,7,8},{3,4},{5}}
[3,2,8,7,4,1,5,6]=>{{1,3,6,8},{2},{4,5,7}}
[3,2,1,7,4,6,5,8]=>{{1,3},{2},{4,5,7},{6},{8}}
[3,2,6,5,1,7,8,4]=>{{1,3,4,5,6,7,8},{2}}
[5,3,2,6,7,1,8,4]=>{{1,4,5,6,7,8},{2,3}}
[3,2,8,6,7,4,1,5]=>{{1,3,5,7,8},{2},{4,6}}
[8,4,6,2,7,3,1,5]=>{{1,5,7,8},{2,4},{3,6}}
[4,3,8,6,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,3,6,2,8,7,1,5]=>{{1,2,3,4,6,7},{5,8}}
[3,8,4,7,6,5,1,2]=>{{1,3,4,7},{2,8},{5,6}}
[7,8,4,2,6,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,2,7,8,6,4,5,1]=>{{1,3,4,5,6,7,8},{2}}
[3,2,7,5,6,8,4,1]=>{{1,3,4,5,6,7,8},{2}}
[5,7,8,6,3,2,4,1]=>{{1,3,5,8},{2,4,6,7}}
[6,5,4,2,1,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[5,4,2,1,7,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,1,6,5,2,7,8,3]=>{{1,2,4,5},{3,6,7,8}}
[5,4,1,6,7,2,8,3]=>{{1,3,5,7,8},{2,4,6}}
[6,8,5,3,1,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[5,2,6,3,8,7,1,4]=>{{1,3,4,5,6,7,8},{2}}
[8,6,1,7,3,4,2,5]=>{{1,3,5,8},{2,4,6,7}}
[1,8,3,6,7,4,2,5]=>{{1},{2,5,7,8},{3},{4,6}}
[1,6,3,5,2,7,8,4]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,7,3,2,6,4,8]=>{{1},{2,5},{3,4,7},{6},{8}}
[5,1,3,7,2,6,4,8]=>{{1,2,5},{3},{4,7},{6},{8}}
[8,1,6,7,2,4,3,5]=>{{1,2,5,8},{3,4,6,7}}
[6,1,4,8,2,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,2,4,8,3,7,1,5]=>{{1,6,7},{2},{3,4,5,8}}
[8,7,2,6,3,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,6,5,2,3,4]=>{{1,2,4,6,8},{3,7},{5}}
[7,1,5,6,8,2,4,3]=>{{1,2,4,6,7},{3,5,8}}
[6,7,1,5,2,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,6,1,5,2,4,3,8]=>{{1,3,7},{2,4,5,6},{8}}
[7,1,6,3,5,4,2,8]=>{{1,2,7},{3,4,6},{5},{8}}
[1,6,7,3,5,4,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,7,8,3,6,4,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,6,4,5,2,3]=>{{1},{2,3,7,8},{4,5,6}}
[8,2,7,4,6,5,1,3]=>{{1,3,7,8},{2},{4},{5,6}}
[2,8,5,7,6,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,1,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[4,1,7,5,6,8,3,2]=>{{1,2,4,5,6,8},{3,7}}
[5,6,7,4,3,1,8,2]=>{{1,2,3,5,6,7,8},{4}}
[6,7,8,5,3,1,4,2]=>{{1,6},{2,3,4,5,7,8}}
[1,4,6,2,5,3,7,8]=>{{1},{2,4},{3,6},{5},{7},{8}}
[1,6,3,2,5,4,7,8]=>{{1},{2,4,6},{3},{5},{7},{8}}
[1,6,8,2,5,4,7,3]=>{{1},{2,4,6},{3,8},{5},{7}}
[1,5,4,2,6,3,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,2,6,4,3,5,7,8]=>{{1},{2},{3,5,6},{4},{7},{8}}
[1,6,8,2,7,5,4,3]=>{{1},{2,4,5,6,7},{3,8}}
[1,7,4,3,2,6,8,5]=>{{1},{2,5,7,8},{3,4},{6}}
[1,5,4,7,2,6,8,3]=>{{1},{2,5},{3,4,7,8},{6}}
[1,3,7,6,2,8,5,4]=>{{1},{2,3,5,7},{4,6,8}}
[1,7,6,2,8,4,3,5]=>{{1},{2,3,4,6,7},{5,8}}
[1,5,2,8,4,3,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,2,8,4,3,6,5,7]=>{{1},{2},{3,5,7,8},{4},{6}}
[1,2,8,5,6,3,4,7]=>{{1},{2},{3,4,5,6,7,8}}
[1,7,3,5,2,8,6,4]=>{{1},{2,4,5,6,7,8},{3}}
[1,6,7,2,5,8,4,3]=>{{1},{2,3,4,6,7,8},{5}}
[1,5,8,3,2,7,4,6]=>{{1},{2,5},{3,4,6,7,8}}
[1,4,5,8,2,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,6,4,8,2,5,3]=>{{1},{2,3,5,6,7,8},{4}}
[1,4,8,6,5,2,7,3]=>{{1},{2,4,6},{3,8},{5},{7}}
[1,3,8,2,6,5,4,7]=>{{1},{2,3,4,7,8},{5,6}}
[1,7,6,3,8,2,4,5]=>{{1},{2,3,4,6,7},{5,8}}
[1,5,2,7,6,4,8,3]=>{{1},{2,3,4,5,6,7,8}}
[1,2,4,3,8,7,5,6]=>{{1},{2},{3,4},{5,6,7,8}}
[1,4,3,8,7,2,5,6]=>{{1},{2,4,6,8},{3},{5,7}}
[1,3,8,6,2,4,5,7]=>{{1},{2,3,5,7,8},{4,6}}
[1,3,8,5,4,2,6,7]=>{{1},{2,3,6,7,8},{4,5}}
[1,7,2,4,8,6,5,3]=>{{1},{2,3,5,7,8},{4},{6}}
[1,6,5,3,2,8,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[1,3,2,8,7,5,4,6]=>{{1},{2,3},{4,5,6,7,8}}
[1,2,8,6,5,4,3,7]=>{{1},{2},{3,7,8},{4,6},{5}}
[8,1,3,4,6,5,2,7]=>{{1,2,7,8},{3},{4},{5,6}}
[8,3,1,4,6,5,2,7]=>{{1,2,3,7,8},{4},{5,6}}
[5,8,3,1,2,6,4,7]=>{{1,2,4,5,7,8},{3},{6}}
[4,8,1,7,5,2,3,6]=>{{1,3,4,7},{2,6,8},{5}}
[4,8,1,7,5,2,6,3]=>{{1,2,3,4,6,7,8},{5}}
[8,5,1,4,2,6,3,7]=>{{1,3,7,8},{2,5},{4},{6}}
[8,4,1,3,5,6,2,7]=>{{1,2,3,4,7,8},{5},{6}}
[8,5,3,2,1,6,4,7]=>{{1,2,4,5,7,8},{3},{6}}
[8,1,5,4,2,6,3,7]=>{{1,2,3,5,7,8},{4},{6}}
[8,5,2,4,1,6,3,7]=>{{1,2,3,5,7,8},{4},{6}}
[4,8,7,1,5,2,6,3]=>{{1,4},{2,3,6,7,8},{5}}
[4,8,7,1,5,2,3,6]=>{{1,4},{2,6,8},{3,7},{5}}
[7,6,8,4,1,3,2,5]=>{{1,2,3,5,6,7,8},{4}}
[7,6,8,4,1,3,5,2]=>{{1,5,7},{2,3,6,8},{4}}
[3,8,7,5,4,1,2,6]=>{{1,2,3,6,7,8},{4,5}}
[4,8,2,7,5,1,3,6]=>{{1,2,3,4,6,7,8},{5}}
[7,6,8,4,1,5,2,3]=>{{1,2,5,6,7},{3,8},{4}}
[8,7,6,1,5,2,3,4]=>{{1,4,8},{2,3,6,7},{5}}
[7,1,4,8,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,5,3,4,7,2]=>{{1,2,8},{3,4,5,6},{7}}
[8,6,2,5,3,4,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[8,6,5,1,3,4,7,2]=>{{1,2,4,6,8},{3,5},{7}}
[8,7,5,1,3,6,2,4]=>{{1,4,8},{2,7},{3,5},{6}}
[8,7,1,5,3,6,2,4]=>{{1,3,4,5,8},{2,7},{6}}
[8,6,1,3,5,4,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[7,1,4,8,3,6,5,2]=>{{1,2,3,4,5,7,8},{6}}
[7,8,5,2,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,2,5,4,6,1]=>{{1,2,3,4,6,7,8},{5}}
[8,4,2,5,3,7,6,1]=>{{1,8},{2,3,4,5},{6,7}}
[4,8,1,5,3,7,6,2]=>{{1,3,4,5},{2,8},{6,7}}
[7,4,8,2,6,3,5,1]=>{{1,3,5,6,7,8},{2,4}}
[7,4,8,2,6,3,1,5]=>{{1,7},{2,4},{3,5,6,8}}
[8,7,3,1,6,4,2,5]=>{{1,4,5,6,8},{2,7},{3}}
[8,7,3,1,6,4,5,2]=>{{1,2,4,5,6,7,8},{3}}
[8,7,3,1,4,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}
[8,4,3,2,7,5,6,1]=>{{1,8},{2,4},{3},{5,6,7}}
[6,4,1,7,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,3,4,1,8,5,2]=>{{1,5,7},{2,6,8},{3},{4}}
[8,7,3,1,6,2,5,4]=>{{1,4,8},{2,5,6,7},{3}}
[7,8,6,4,2,5,1,3]=>{{1,7},{2,3,5,6,8},{4}}
[7,8,2,4,6,5,1,3]=>{{1,7},{2,3,8},{4},{5,6}}
[8,1,7,3,5,6,2,4]=>{{1,2,3,4,7,8},{5},{6}}
[8,7,5,2,4,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[8,1,7,5,4,6,2,3]=>{{1,2,3,7,8},{4,5},{6}}
[8,7,3,2,6,1,5,4]=>{{1,2,4,5,6,7,8},{3}}
[5,3,1,7,6,4,2,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,3,2,1,6,4,8]=>{{1,2,4,5,7},{3},{6},{8}}
[7,6,5,3,1,4,2,8]=>{{1,2,3,4,5,6,7},{8}}
[1,8,6,4,3,2,7,5]=>{{1},{2,3,5,6,8},{4},{7}}
[1,8,7,6,4,2,5,3]=>{{1},{2,3,4,5,6,7,8}}
[1,4,8,6,7,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,2,5,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[1,7,3,6,8,5,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[8,6,2,5,7,4,3,1]=>{{1,8},{2,3,4,5,6,7}}
[7,1,3,6,8,5,4,2]=>{{1,2,4,5,6,7,8},{3}}
[1,8,3,6,7,5,4,2]=>{{1},{2,8},{3},{4,5,6,7}}
[8,1,7,6,4,5,3,2]=>{{1,2,8},{3,7},{4,5,6}}
[7,1,8,6,4,5,3,2]=>{{1,2,3,7,8},{4,5,6}}
[1,6,2,7,4,5,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,2,6,4,3,5,7]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,6,4,3,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,7,2,5,4,6,3,8]=>{{1},{2,3,7},{4,5},{6},{8}}
[6,5,7,2,8,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,2,7,5,8,1,4,3]=>{{1,6},{2},{3,4,5,7,8}}
[6,7,2,5,8,1,4,3]=>{{1,6},{2,3,4,5,7,8}}
[6,5,7,3,8,1,4,2]=>{{1,6},{2,5,8},{3,4,7}}
[6,3,7,4,8,2,5,1]=>{{1,2,3,5,6,7,8},{4}}
[6,3,7,4,8,1,5,2]=>{{1,6},{2,3,5,7,8},{4}}
[6,2,7,4,8,1,5,3]=>{{1,6},{2},{3,5,7,8},{4}}
[6,7,5,1,4,3,8,2]=>{{1,3,4,5,6},{2,7,8}}
[7,8,5,1,4,3,6,2]=>{{1,3,4,5,6,7},{2,8}}
[7,2,1,5,3,8,6,4]=>{{1,3,4,5,6,7,8},{2}}
[5,8,2,7,6,1,3,4]=>{{1,5,6},{2,3,4,7,8}}
[5,1,8,7,3,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[8,2,3,6,7,1,4,5]=>{{1,4,5,6,7,8},{2},{3}}
[4,2,3,1,5,8,6,7]=>{{1,4},{2},{3},{5},{6,7,8}}
[2,4,8,7,5,3,1,6]=>{{1,2,4,7},{3,6,8},{5}}
[2,6,8,7,5,3,4,1]=>{{1,2,3,6,8},{4,7},{5}}
[2,6,5,1,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[6,5,1,2,4,3,8,7]=>{{1,3,6},{2,4,5},{7,8}}
[4,6,5,3,1,2,8,7]=>{{1,3,4,5},{2,6},{7,8}}
[4,8,7,5,3,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,6,8,7,5,3,1,2]=>{{1,4,7},{2,3,6,8},{5}}
[6,8,7,5,3,1,4,2]=>{{1,6},{2,8},{3,4,5,7}}
[8,7,5,6,3,1,4,2]=>{{1,2,4,6,7,8},{3,5}}
[8,7,3,4,6,5,1,2]=>{{1,2,7,8},{3},{4},{5,6}}
[2,1,4,8,7,3,6,5]=>{{1,2},{3,4,5,6,7,8}}
[4,8,7,3,1,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,4,1,2,6,5]=>{{1,5,8},{2,6,7},{3},{4}}
[8,7,3,1,6,5,2,4]=>{{1,4,8},{2,7},{3},{5,6}}
[8,7,3,2,6,5,1,4]=>{{1,2,4,7,8},{3},{5,6}}
[2,8,7,3,4,6,5,1]=>{{1,2,8},{3,4,5,7},{6}}
[2,8,7,3,6,5,1,4]=>{{1,2,3,4,7,8},{5,6}}
[2,8,7,1,6,5,3,4]=>{{1,2,4,8},{3,7},{5,6}}
[8,7,1,2,6,5,3,4]=>{{1,2,3,4,7,8},{5,6}}
[8,7,1,2,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[2,1,8,7,3,4,6,5]=>{{1,2},{3,5,8},{4,6,7}}
[8,7,5,1,2,4,3,6]=>{{1,4,6,8},{2,3,5,7}}
[2,8,7,1,4,3,6,5]=>{{1,2,4,5,8},{3,6,7}}
[2,8,7,3,4,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[2,8,7,5,6,3,4,1]=>{{1,2,8},{3,4,5,6,7}}
[2,4,8,7,3,1,6,5]=>{{1,2,4,6,7},{3,5,8}}
[2,8,7,3,1,4,6,5]=>{{1,2,5,8},{3,4,6,7}}
[2,4,3,1,8,7,5,6]=>{{1,2,4},{3},{5,6,7,8}}
[4,3,1,2,6,8,7,5]=>{{1,2,3,4},{5,6,8},{7}}
[2,8,7,5,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,7,5,3,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,7,5,3,6,4,1]=>{{1,2,8},{3,4,5,7},{6}}
[2,8,7,5,6,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[2,6,8,7,5,1,4,3]=>{{1,2,6},{3,8},{4,7},{5}}
[6,8,7,5,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,6,1,2,4,3]=>{{1,3,5,8},{2,4,6,7}}
[8,7,1,2,4,6,5,3]=>{{1,3,8},{2,4,5,7},{6}}
[2,4,8,7,3,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[8,7,2,4,3,6,5,1]=>{{1,8},{2,3,5,7},{4},{6}}
[4,8,7,1,2,6,5,3]=>{{1,4},{2,3,5,7,8},{6}}
[8,7,5,3,1,2,6,4]=>{{1,3,4,5,8},{2,6,7}}
[8,7,5,3,6,4,1,2]=>{{1,2,7,8},{3,4,5,6}}
[8,7,1,4,3,6,5,2]=>{{1,2,3,5,7,8},{4},{6}}
[8,7,3,4,1,6,5,2]=>{{1,2,5,7,8},{3},{4},{6}}
[7,1,2,6,4,5,3,8]=>{{1,2,3,7},{4,5,6},{8}}
[4,7,3,6,5,1,2,8]=>{{1,4,6},{2,7},{3},{5},{8}}
[7,5,4,2,8,3,1,6]=>{{1,7},{2,3,4,5,6,8}}
[8,3,6,1,5,2,4,7]=>{{1,4,7,8},{2,3,6},{5}}
[3,1,6,8,5,7,2,4]=>{{1,2,3,6,7},{4,8},{5}}
[5,7,2,1,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[7,2,8,6,4,3,1,5]=>{{1,7},{2},{3,4,5,6,8}}
[6,3,8,7,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[7,6,3,2,8,4,1,5]=>{{1,7},{2,4,6},{3},{5,8}}
[8,6,1,3,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[5,8,3,7,4,2,1,6]=>{{1,4,5,7},{2,6,8},{3}}
[4,1,7,3,5,8,6,2]=>{{1,2,3,4,6,7,8},{5}}
[8,4,7,3,5,2,1,6]=>{{1,2,3,4,6,7,8},{5}}
[5,4,8,1,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,8,2,1,3,6,7]=>{{1,2,4,5},{3,6,7,8}}
[8,1,3,5,2,4,6,7]=>{{1,2,4,5,6,7,8},{3}}
[1,8,3,5,7,2,4,6]=>{{1},{2,6,8},{3},{4,5,7}}
[8,1,4,2,7,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[1,5,7,3,6,8,2,4]=>{{1},{2,3,4,5,6,7,8}}
[8,4,6,2,5,7,1,3]=>{{1,3,6,7,8},{2,4},{5}}
[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[8,1,3,6,7,4,2,5]=>{{1,2,5,7,8},{3},{4,6}}
[1,2,4,7,8,5,3,6]=>{{1},{2},{3,4,7},{5,6,8}}
[3,1,4,7,6,8,2,5]=>{{1,2,3,4,7},{5,6,8}}
[4,1,3,7,6,8,2,5]=>{{1,2,4,7},{3},{5,6,8}}
[5,1,7,3,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,2,4,5,1,3]=>{{1,2,4,5,6,7},{3,8}}
[5,8,6,2,4,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[3,8,2,6,5,7,1,4]=>{{1,2,3,4,6,7,8},{5}}
[2,8,3,6,7,4,1,5]=>{{1,2,5,7,8},{3},{4,6}}
[8,7,2,5,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,1,6,4,3,2,5]=>{{1,3,4,5,6,8},{2,7}}
[1,8,2,7,5,4,3,6]=>{{1},{2,3,4,6,7,8},{5}}
[3,8,1,7,5,4,2,6]=>{{1,3},{2,4,6,7,8},{5}}
[5,8,6,1,7,3,2,4]=>{{1,2,4,5,7,8},{3,6}}
[6,7,1,2,8,4,3,5]=>{{1,2,3,4,6,7},{5,8}}
[2,1,3,8,6,5,4,7]=>{{1,2},{3},{4,7,8},{5,6}}
[8,2,1,7,5,4,3,6]=>{{1,3,4,6,7,8},{2},{5}}
[1,3,2,8,6,5,4,7]=>{{1},{2,3},{4,7,8},{5,6}}
[3,4,1,7,6,8,2,5]=>{{1,3},{2,4,7},{5,6,8}}
[2,5,7,1,8,4,3,6]=>{{1,2,4,5,6,8},{3,7}}
[3,5,7,1,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}
[4,5,7,6,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,4,7,6,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,5,7,8,6,3,2,4]=>{{1},{2,3,5,6,7},{4,8}}
[8,4,6,7,5,2,1,3]=>{{1,2,3,4,6,7,8},{5}}
[8,3,7,5,6,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[1,4,8,6,7,3,2,5]=>{{1},{2,3,4,5,6,7,8}}
[2,4,8,6,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[5,2,7,8,6,3,1,4]=>{{1,3,5,6,7},{2},{4,8}}
[2,3,8,7,5,4,1,6]=>{{1,2,3,4,6,7,8},{5}}
[1,3,8,7,5,4,2,6]=>{{1},{2,3,4,6,7,8},{5}}
[8,2,7,6,4,3,1,5]=>{{1,3,4,5,6,7,8},{2}}
[8,1,7,6,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,1,8,6,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,5,6,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[1,5,8,4,3,7,6,2]=>{{1},{2,3,5,8},{4},{6,7}}
[8,1,7,2,5,6,4,3]=>{{1,2,3,4,7,8},{5},{6}}
[8,1,3,5,2,7,6,4]=>{{1,2,4,5,8},{3},{6,7}}
[2,7,1,5,4,8,6,3]=>{{1,2,3,6,7,8},{4,5}}
[8,6,2,4,3,7,5,1]=>{{1,8},{2,3,5,6,7},{4}}
[2,4,1,6,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,5,6,3,7,2]=>{{1,2,8},{3,4,5,6},{7}}
[8,1,4,5,6,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[8,1,4,7,6,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,1,7,8,6,4,3]=>{{1,2,3,5,8},{4,7},{6}}
[3,5,6,2,8,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,1,7,6,3,8]=>{{1,2,4},{3,5,7},{6},{8}}
[7,3,1,5,6,4,2,8]=>{{1,2,3,7},{4,5,6},{8}}
[8,3,2,5,6,7,1,4]=>{{1,4,5,6,7,8},{2,3}}
[8,4,5,3,7,6,2,1]=>{{1,8},{2,3,4,5,7},{6}}
[3,4,5,6,2,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[3,7,4,2,8,5,1,6]=>{{1,2,3,4,7},{5,6,8}}
[7,3,4,1,6,8,2,5]=>{{1,2,3,4,7},{5,6,8}}
[2,6,3,1,4,7,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,2,1,6,3,4,8,5]=>{{1,3,5,7,8},{2},{4,6}}
[7,3,4,1,6,5,8,2]=>{{1,2,3,4,7,8},{5,6}}
[3,7,4,2,5,8,6,1]=>{{1,2,3,4,6,7,8},{5}}
[2,3,5,1,4,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[2,7,1,3,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[2,7,1,3,8,4,6,5]=>{{1,2,3,4,6,7},{5,8}}
[3,8,7,1,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,1,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,4,2,1,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,7,2,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[8,4,5,7,3,2,6,1]=>{{1,8},{2,4,6,7},{3,5}}
[8,3,7,2,4,1,5,6]=>{{1,6,8},{2,3,4,5,7}}
[8,6,7,2,1,4,3,5]=>{{1,5,8},{2,4,6},{3,7}}
[8,3,7,5,1,2,6,4]=>{{1,4,5,8},{2,3,6,7}}
[7,3,4,6,2,1,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,7,4,6,1,5,2,8]=>{{1,3,4,5,6},{2,7},{8}}
[3,4,7,6,1,2,8,5]=>{{1,3,5,7,8},{2,4,6}}
[4,5,8,7,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,5,6,1,4,2]=>{{1,2,4,5,6,7,8},{3}}
[8,5,2,7,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,2,1,5,8,3]=>{{1,5,6},{2,4},{3,7,8}}
[8,4,2,5,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[8,5,3,1,6,4,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[8,7,3,1,4,5,6,2]=>{{1,2,4,5,6,7,8},{3}}
[8,6,4,1,7,5,2,3]=>{{1,3,4,8},{2,5,6,7}}
[8,5,3,7,1,6,4,2]=>{{1,2,5,8},{3},{4,7},{6}}
[7,6,3,8,1,4,2,5]=>{{1,2,4,5,6,7,8},{3}}
[7,4,8,2,6,1,5,3]=>{{1,5,6,7},{2,4},{3,8}}
[6,4,7,3,1,5,2,8]=>{{1,5,6},{2,3,4,7},{8}}
[8,5,3,1,6,4,2,7]=>{{1,2,4,5,6,7,8},{3}}
[8,7,5,1,2,6,3,4]=>{{1,4,8},{2,3,5,7},{6}}
[8,6,4,1,2,7,5,3]=>{{1,3,4,8},{2,5,6,7}}
[8,7,4,1,2,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[6,5,3,7,4,2,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[1,6,3,8,4,2,5,7]=>{{1},{2,6},{3},{4,5,7,8}}
[4,7,2,5,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[1,8,3,4,5,2,6,7]=>{{1},{2,6,7,8},{3},{4},{5}}
[1,8,6,4,2,5,3,7]=>{{1},{2,3,5,6,7,8},{4}}
[8,2,6,4,1,5,7,3]=>{{1,3,5,6,8},{2},{4},{7}}
[7,8,3,4,6,1,5,2]=>{{1,5,6,7},{2,8},{3},{4}}
[4,8,7,5,3,1,6,2]=>{{1,3,4,5,6,7},{2,8}}
[6,1,4,8,3,2,5,7]=>{{1,2,6},{3,4,5,7,8}}
[4,1,8,5,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,4,2,7,3,5]=>{{1,2,5,8},{3,6,7},{4}}
[3,1,7,4,2,5,8,6]=>{{1,2,3,5,6,7,8},{4}}
[1,2,7,4,3,5,6,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[6,1,8,5,2,4,3,7]=>{{1,2,4,5,6},{3,7,8}}
[6,8,2,5,1,4,7,3]=>{{1,4,5,6},{2,3,8},{7}}
[4,5,2,1,6,8,7,3]=>{{1,4},{2,3,5,6,8},{7}}
[7,2,8,6,5,1,4,3]=>{{1,4,6,7},{2},{3,8},{5}}
[7,4,8,6,1,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,2,6,1,4,5,3]=>{{1,2,3,5,7,8},{4,6}}
[1,7,8,6,2,4,3,5]=>{{1},{2,3,5,7,8},{4,6}}
[7,6,3,1,2,5,4,8]=>{{1,4,7},{2,5,6},{3},{8}}
[8,5,3,1,2,4,7,6]=>{{1,4,6,8},{2,5},{3},{7}}
[8,2,1,6,5,3,4,7]=>{{1,3,4,6,7,8},{2},{5}}
[3,8,1,5,6,2,4,7]=>{{1,3},{2,4,5,6,7,8}}
[6,8,4,1,5,2,3,7]=>{{1,2,3,4,6,7,8},{5}}
[3,2,8,1,6,4,5,7]=>{{1,3,4,5,6,7,8},{2}}
[5,2,1,3,7,6,4,8]=>{{1,3,4,5,7},{2},{6},{8}}
[5,4,1,2,8,3,7,6]=>{{1,3,5,6,8},{2,4},{7}}
[5,8,4,1,2,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[7,1,2,5,3,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[1,6,7,3,2,8,4,5]=>{{1},{2,5,6,8},{3,4,7}}
[1,8,6,3,2,7,4,5]=>{{1},{2,5,8},{3,4,6,7}}
[1,5,3,7,2,8,4,6]=>{{1},{2,5},{3},{4,7},{6,8}}
[1,4,6,2,8,5,3,7]=>{{1},{2,4},{3,5,6,7,8}}
[1,5,6,2,8,4,3,7]=>{{1},{2,3,4,5,6,7,8}}
[3,4,8,6,5,7,2,1]=>{{1,3,8},{2,4,6,7},{5}}
[1,2,5,7,4,6,8,3]=>{{1},{2},{3,4,5,7,8},{6}}
[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[3,5,8,6,1,7,2,4]=>{{1,2,3,4,5,6,7,8}}
[2,3,7,1,8,6,4,5]=>{{1,2,3,4,7},{5,8},{6}}
[2,6,1,7,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[3,2,1,6,8,4,7,5]=>{{1,3},{2},{4,6},{5,8},{7}}
[4,8,3,1,6,5,7,2]=>{{1,4},{2,8},{3},{5,6},{7}}
[1,6,8,5,4,2,7,3]=>{{1},{2,6},{3,8},{4,5},{7}}
[6,5,8,4,2,1,7,3]=>{{1,6},{2,5},{3,8},{4},{7}}
[1,7,8,6,5,4,2,3]=>{{1},{2,7},{3,8},{4,6},{5}}
[6,8,7,4,5,1,3,2]=>{{1,6},{2,8},{3,7},{4},{5}}
[3,6,4,2,5,1,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[2,1,5,8,6,4,7,3]=>{{1,2},{3,4,5,6,8},{7}}
[4,2,8,5,6,3,7,1]=>{{1,3,4,5,6,8},{2},{7}}
[5,7,2,3,4,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[1,8,7,3,2,5,6,4]=>{{1},{2,3,4,5,6,7,8}}
[5,7,1,2,3,8,6,4]=>{{1,3,5},{2,4,6,7,8}}
[7,8,6,2,4,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,2,8,4,6,1,5,3]=>{{1,5,6,7},{2},{3,8},{4}}
[7,4,6,2,8,1,5,3]=>{{1,3,5,6,7,8},{2,4}}
[7,1,5,8,2,3,6,4]=>{{1,2,3,5,6,7},{4,8}}
[7,6,4,8,2,1,5,3]=>{{1,2,5,6,7},{3,4,8}}
[6,1,8,4,2,3,5,7]=>{{1,2,3,5,6,7,8},{4}}
[7,3,6,2,1,8,5,4]=>{{1,5,7},{2,3,4,6,8}}
[1,8,6,4,2,5,7,3]=>{{1},{2,3,5,6,8},{4},{7}}
[5,6,2,1,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,8,1,6,5,7,3,4]=>{{1,2,3,4,6,7,8},{5}}
[5,1,6,4,3,8,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[3,7,1,6,4,5,8,2]=>{{1,3},{2,7,8},{4,5,6}}
[3,5,2,1,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[1,3,8,7,5,4,6,2]=>{{1},{2,3,8},{4,6,7},{5}}
[6,7,3,4,8,5,1,2]=>{{1,2,5,6,7,8},{3},{4}}
[7,4,1,8,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,2,5,6,8,4]=>{{1,2,3,4,7,8},{5},{6}}
[4,1,5,7,3,2,8,6]=>{{1,2,4,6,7,8},{3,5}}
[6,4,1,7,2,8,5,3]=>{{1,3,6,8},{2,4,5,7}}
[7,3,1,6,2,8,5,4]=>{{1,2,3,5,7},{4,6,8}}
[4,8,2,5,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[5,1,3,4,8,2,6,7]=>{{1,2,5,6,7,8},{3},{4}}
[6,1,4,5,7,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,4,7,1,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[7,8,5,1,3,4,6,2]=>{{1,4,6,7},{2,8},{3,5}}
[7,1,3,4,5,6,8,2]=>{{1,2,7,8},{3},{4},{5},{6}}
[8,5,2,7,6,3,1,4]=>{{1,4,7,8},{2,3,5,6}}
[1,8,3,5,6,2,7,4]=>{{1},{2,4,5,6,8},{3},{7}}
[8,3,2,5,6,1,7,4]=>{{1,4,5,6,8},{2,3},{7}}
[4,2,5,1,6,8,7,3]=>{{1,4},{2},{3,5,6,8},{7}}
[5,4,2,7,8,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[6,8,7,2,1,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,8,5,2,4,1]=>{{1,2,3,4,6,7,8},{5}}
[1,7,8,5,2,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}
[7,6,1,2,5,3,8,4]=>{{1,2,3,4,6,7,8},{5}}
[7,6,2,4,8,1,5,3]=>{{1,2,3,5,6,7,8},{4}}
[1,5,7,3,8,6,2,4]=>{{1},{2,3,4,5,7,8},{6}}
[6,7,5,1,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,6,1,2,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,1,5,3,8,4]=>{{1,2,3,4,6,7,8},{5}}
[4,3,2,8,7,1,6,5]=>{{1,4,5,6,7,8},{2,3}}
[4,8,3,1,7,6,5,2]=>{{1,4},{2,8},{3},{5,7},{6}}
[5,3,8,7,1,6,4,2]=>{{1,5},{2,3,8},{4,7},{6}}
[5,8,7,3,1,6,4,2]=>{{1,5},{2,8},{3,4,7},{6}}
[5,3,8,2,1,7,6,4]=>{{1,5},{2,3,4,8},{6,7}}
[3,8,7,2,6,5,1,4]=>{{1,3,7},{2,4,8},{5,6}}
[7,4,1,8,6,5,3,2]=>{{1,3,7},{2,4,8},{5,6}}
[5,4,2,8,1,7,6,3]=>{{1,5},{2,3,4,8},{6,7}}
[5,8,4,2,1,7,6,3]=>{{1,5},{2,3,4,8},{6,7}}
[5,8,4,7,1,6,3,2]=>{{1,5},{2,8},{3,4,7},{6}}
[5,4,8,3,1,7,6,2]=>{{1,5},{2,3,4,8},{6,7}}
[8,5,6,1,4,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,1,2,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[1,6,7,4,2,5,8,3]=>{{1},{2,5,6},{3,7,8},{4}}
[3,6,7,5,8,1,2,4]=>{{1,2,3,6,7},{4,5,8}}
[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[3,8,6,5,7,4,1,2]=>{{1,3,4,5,6,7},{2,8}}
[5,2,1,6,8,4,7,3]=>{{1,3,5,8},{2},{4,6},{7}}
[6,5,8,7,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,7,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,3,6,1,2,8]=>{{1,3,4,5,6},{2,7},{8}}
[4,7,5,3,1,6,2,8]=>{{1,3,4,5},{2,7},{6},{8}}
[2,7,5,3,6,4,8,1]=>{{1,2,7,8},{3,4,5,6}}
[4,7,5,3,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,8,6,3,4,1]=>{{1,2,4,7,8},{3,5,6}}
[2,7,5,6,8,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,6,8,3,1,4]=>{{1,2,7},{3,4,5,6,8}}
[4,7,5,3,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,6,3,8,4,1]=>{{1,2,4,6,7,8},{3,5}}
[8,7,5,3,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,3,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,2,8,3,1,4]=>{{1,2,4,5,7,8},{3,6}}
[5,1,6,3,2,4,8,7]=>{{1,2,5},{3,4,6},{7,8}}
[5,7,6,1,8,3,2,4]=>{{1,4,5,8},{2,7},{3,6}}
[3,8,7,2,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[6,1,7,2,8,4,3,5]=>{{1,2,4,6},{3,7},{5,8}}
[3,7,6,2,8,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[6,1,7,3,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,3,2,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,3,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,2,7,4,1,3]=>{{1,5,7},{2,3,4,6,8}}
[2,4,6,7,8,5,1,3]=>{{1,2,4,7},{3,5,6,8}}
[2,4,6,7,8,3,1,5]=>{{1,2,4,7},{3,6},{5,8}}
[4,7,6,2,8,5,1,3]=>{{1,2,4,7},{3,5,6,8}}
[5,8,7,3,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,8,7,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,7,2,6,4,5]=>{{1,2,3,5,8},{4,7},{6}}
[4,5,1,2,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[5,6,1,2,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[5,8,7,1,6,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[8,4,5,1,7,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[6,3,1,4,8,2,7,5]=>{{1,2,3,6},{4},{5,8},{7}}
[8,5,6,1,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,6,1,3,8,4,2]=>{{1,4,7},{2,3,5,6,8}}
[5,7,6,1,3,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,4,2,8,5,3]=>{{1,3,6,8},{2,5,7},{4}}
[2,1,6,4,8,3,7,5]=>{{1,2},{3,6},{4},{5,8},{7}}
[7,4,5,1,3,8,6,2]=>{{1,2,4,6,7,8},{3,5}}
[1,5,7,8,4,2,3,6]=>{{1},{2,4,5,6,8},{3,7}}
[1,3,6,4,2,5,7,8]=>{{1},{2,3,5,6},{4},{7},{8}}
[1,4,5,7,8,3,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,7,8,3,6,2,4]=>{{1},{2,3,5,7},{4,8},{6}}
[1,5,7,8,2,4,3,6]=>{{1},{2,5},{3,7},{4,6,8}}
[6,8,4,7,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,4,2,7,1,3]=>{{1,6,7},{2,3,5,8},{4}}
[1,8,4,6,3,2,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[6,4,8,5,3,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,1,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[1,6,3,8,4,2,7,5]=>{{1},{2,6},{3},{4,5,8},{7}}
[7,1,3,2,4,6,8,5]=>{{1,2,4,5,7,8},{3},{6}}
[2,6,5,7,8,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[4,1,8,2,6,7,5,3]=>{{1,2,4},{3,8},{5,6,7}}
[3,6,7,8,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,1,6,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[4,2,8,3,6,5,1,7]=>{{1,3,4,7,8},{2},{5,6}}
[6,3,8,7,2,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,1,8,2,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,3,4,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,2,4,7,8,6,1,3]=>{{1,3,4,5,7,8},{2},{6}}
[7,2,1,3,4,8,5,6]=>{{1,3,4,5,7},{2},{6,8}}
[2,4,5,7,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,2,3,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[6,1,4,2,5,7,8,3]=>{{1,2,3,4,6,7,8},{5}}
[1,8,3,4,5,2,7,6]=>{{1},{2,6,8},{3},{4},{5},{7}}
[1,8,3,6,4,7,2,5]=>{{1},{2,4,5,6,7,8},{3}}
[1,4,7,2,5,6,3,8]=>{{1},{2,4},{3,7},{5},{6},{8}}
[3,4,8,6,7,2,1,5]=>{{1,3,5,7,8},{2,4,6}}
[3,4,8,2,5,1,7,6]=>{{1,3,6,8},{2,4},{5},{7}}
[1,7,2,5,8,4,3,6]=>{{1},{2,3,7},{4,5,6,8}}
[1,4,6,7,8,3,5,2]=>{{1},{2,4,5,7,8},{3,6}}
[4,1,5,3,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[5,8,7,4,6,2,3,1]=>{{1,2,5,6,8},{3,7},{4}}
[6,4,8,1,5,7,3,2]=>{{1,2,3,4,6,7,8},{5}}
[1,6,8,3,5,2,7,4]=>{{1},{2,6},{3,4,8},{5},{7}}
[7,2,1,8,6,4,5,3]=>{{1,3,4,5,6,7,8},{2}}
[2,4,7,8,5,6,1,3]=>{{1,2,3,4,7,8},{5},{6}}
[2,6,3,8,5,1,7,4]=>{{1,2,6},{3},{4,8},{5},{7}}
[2,8,5,4,1,3,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[5,4,6,3,1,7,2,8]=>{{1,5},{2,3,4,6,7},{8}}
[4,3,6,5,1,8,2,7]=>{{1,4,5},{2,3,6,7,8}}
[1,5,6,8,7,3,2,4]=>{{1},{2,5,7},{3,6},{4,8}}
[1,4,8,3,6,5,2,7]=>{{1},{2,3,4,7,8},{5,6}}
[1,3,8,6,4,7,2,5]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,6,4,3,7,5]=>{{1},{2},{3,4,5,6,8},{7}}
[4,1,7,6,8,3,2,5]=>{{1,2,3,4,6,7},{5,8}}
[1,8,4,7,6,2,3,5]=>{{1},{2,5,6,8},{3,4,7}}
[7,2,3,8,4,5,6,1]=>{{1,4,5,6,7,8},{2},{3}}
[6,5,1,8,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,3,7,2,1,6]=>{{1,5,7},{2,6,8},{3,4}}
[6,1,2,8,7,3,4,5]=>{{1,2,3,6},{4,5,7,8}}
[4,5,1,7,6,2,8,3]=>{{1,3,4,7,8},{2,5,6}}
[6,5,1,8,7,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,8,6,4,3,2]=>{{1,3,7},{2,4,5,6,8}}
[8,5,1,7,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,3,7,6,1,4,2]=>{{1,2,5,6,8},{3},{4,7}}
[3,8,7,6,1,5,4,2]=>{{1,3,4,5,6,7},{2,8}}
[8,3,7,5,4,1,6,2]=>{{1,2,3,6,7,8},{4,5}}
[4,5,3,1,8,7,2,6]=>{{1,4},{2,5,6,7,8},{3}}
[3,4,8,1,5,2,6,7]=>{{1,2,3,4,6,7,8},{5}}
[8,6,5,7,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[1,5,8,6,2,7,4,3]=>{{1},{2,5},{3,8},{4,6,7}}
[3,1,8,5,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,3,4,2,1,7]=>{{1,2,6,7,8},{3,4,5}}
[8,5,2,6,4,3,1,7]=>{{1,7,8},{2,3,4,5,6}}
[8,5,2,6,1,4,7,3]=>{{1,2,3,5,8},{4,6},{7}}
[2,7,5,8,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,2,6,7,1,8,5,4]=>{{1,3,4,5,6,7,8},{2}}
[3,4,6,7,8,2,1,5]=>{{1,2,3,4,6,7},{5,8}}
[3,2,6,7,8,4,1,5]=>{{1,3,4,6,7},{2},{5,8}}
[6,2,7,4,8,5,1,3]=>{{1,3,5,6,7,8},{2},{4}}
[6,7,1,3,8,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,1,8,5,2,4,3]=>{{1,2,3,4,6,7,8},{5}}
[1,2,6,7,8,5,3,4]=>{{1},{2},{3,4,5,6,7,8}}
[1,6,7,4,8,3,2,5]=>{{1},{2,3,6,7},{4},{5,8}}
[1,4,6,7,8,3,2,5]=>{{1},{2,4,7},{3,6},{5,8}}
[8,7,2,1,5,4,6,3]=>{{1,2,3,4,6,7,8},{5}}
[2,7,4,8,6,5,3,1]=>{{1,2,3,4,7,8},{5,6}}
[7,6,5,2,4,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,6,4,3,1,5,8,2]=>{{1,2,5,6,7,8},{3,4}}
[6,1,8,7,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,6,1,2,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,8,2,7,1,5,4]=>{{1,2,3,4,6,8},{5,7}}
[2,8,6,1,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,8,7,2,5,4,1,3]=>{{1,2,3,4,6,7,8},{5}}
[3,2,6,4,8,7,5,1]=>{{1,3,5,6,7,8},{2},{4}}
[4,7,2,8,6,5,1,3]=>{{1,2,3,4,7,8},{5,6}}
[4,7,1,8,6,5,3,2]=>{{1,2,3,4,7,8},{5,6}}
[2,7,4,8,3,6,1,5]=>{{1,2,7},{3,4,5,8},{6}}
[4,7,3,8,6,1,5,2]=>{{1,2,4,5,6,7,8},{3}}
[4,3,6,8,7,2,5,1]=>{{1,4,8},{2,3,6},{5,7}}
[4,3,8,2,5,7,6,1]=>{{1,2,3,4,8},{5},{6,7}}
[4,1,2,6,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[3,1,6,4,8,7,2,5]=>{{1,2,3,6,7},{4},{5,8}}
[4,1,6,8,7,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,8,1,4,5,7,2,6]=>{{1,3},{2,6,7,8},{4},{5}}
[3,8,1,4,2,5,7,6]=>{{1,3},{2,5,6,8},{4},{7}}
[4,1,8,3,5,2,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[3,8,1,2,5,4,7,6]=>{{1,3},{2,4,6,8},{5},{7}}
[4,2,3,6,8,7,1,5]=>{{1,4,6,7},{2},{3},{5,8}}
[4,2,8,3,5,1,7,6]=>{{1,3,4,6,8},{2},{5},{7}}
[4,2,8,3,5,7,6,1]=>{{1,3,4,8},{2},{5},{6,7}}
[3,8,2,4,5,7,6,1]=>{{1,2,3,8},{4},{5},{6,7}}
[3,8,2,5,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,2,8,5,7,1,3,6]=>{{1,3,4,5,6,7,8},{2}}
[3,8,1,5,2,4,7,6]=>{{1,3},{2,4,5,6,8},{7}}
[7,5,6,4,1,3,2,8]=>{{1,2,5,7},{3,6},{4},{8}}
[7,8,6,4,1,3,2,5]=>{{1,2,5,7,8},{3,6},{4}}
[7,1,4,2,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}
[7,3,2,1,4,6,5,8]=>{{1,4,5,7},{2,3},{6},{8}}
[7,6,1,4,3,2,5,8]=>{{1,3,5,7},{2,6},{4},{8}}
[7,4,1,3,5,6,2,8]=>{{1,2,3,4,7},{5},{6},{8}}
[2,7,1,3,5,6,8,4]=>{{1,2,3,4,7,8},{5},{6}}
[3,6,2,1,5,8,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[2,3,6,1,5,8,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[3,4,7,1,5,6,8,2]=>{{1,2,3,4,7,8},{5},{6}}
[3,6,7,4,1,2,8,5]=>{{1,3,5,7,8},{2,6},{4}}
[4,3,2,7,1,6,8,5]=>{{1,4,5,7,8},{2,3},{6}}
[7,3,2,8,1,6,4,5]=>{{1,4,5,7,8},{2,3},{6}}
[7,4,8,1,5,6,3,2]=>{{1,2,3,4,7,8},{5},{6}}
[2,6,8,1,5,3,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[6,8,2,1,5,3,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[4,8,2,5,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[4,5,8,2,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[2,4,8,5,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[5,3,2,6,4,8,7,1]=>{{1,4,5,6,8},{2,3},{7}}
[2,4,5,3,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[4,3,5,2,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[4,8,5,3,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[3,5,4,2,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[4,1,2,7,5,6,8,3]=>{{1,2,3,4,7,8},{5},{6}}
[5,6,7,4,2,8,3,1]=>{{1,2,5,6,8},{3,7},{4}}
[2,5,7,4,6,8,3,1]=>{{1,2,5,6,8},{3,7},{4}}
[7,5,2,4,3,8,6,1]=>{{1,6,7,8},{2,3,5},{4}}
[6,8,1,2,5,4,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[6,4,1,8,5,2,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[2,6,1,8,5,4,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[7,1,2,8,5,6,4,3]=>{{1,2,3,4,7,8},{5},{6}}
[4,3,2,6,8,5,7,1]=>{{1,4,5,6,8},{2,3},{7}}
[3,7,6,4,8,5,2,1]=>{{1,3,5,6,8},{2,7},{4}}
[3,1,6,8,5,4,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[2,3,5,8,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[3,5,2,8,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[3,4,5,8,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[5,4,2,8,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[5,3,4,8,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[2,5,4,8,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[6,3,2,5,8,4,7,1]=>{{1,4,5,6,8},{2,3},{7}}
[6,1,8,3,5,4,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[5,4,8,3,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[5,8,2,3,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[6,2,1,7,8,5,4,3]=>{{1,3,5,6,8},{2},{4,7}}
[7,4,6,8,3,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,4,5,2,7,1,6,8]=>{{1,3,5,6,7},{2,4},{8}}
[7,5,6,1,2,3,8,4]=>{{1,4,7,8},{2,5},{3,6}}
[1,5,7,6,3,2,8,4]=>{{1},{2,3,4,5,6,7,8}}
[8,4,6,7,3,2,5,1]=>{{1,8},{2,3,4,5,6,7}}
[8,4,6,2,3,1,5,7]=>{{1,3,5,6,7,8},{2,4}}
[7,5,2,1,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,8,5,4,2,6]=>{{1,2,3,7},{4,6,8},{5}}
[3,4,5,2,1,8,6,7]=>{{1,3,5},{2,4},{6,7,8}}
[7,6,4,8,3,1,2,5]=>{{1,2,6,7},{3,4,5,8}}
[7,4,8,5,6,1,2,3]=>{{1,2,4,5,6,7},{3,8}}
[6,2,8,5,1,3,4,7]=>{{1,3,4,5,6,7,8},{2}}
[3,2,7,8,6,1,4,5]=>{{1,3,4,5,6,7,8},{2}}
[6,8,2,5,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[6,7,4,2,1,5,3,8]=>{{1,5,6},{2,3,4,7},{8}}
[5,7,4,1,3,6,2,8]=>{{1,3,4,5},{2,7},{6},{8}}
[4,2,7,5,1,8,3,6]=>{{1,4,5},{2},{3,7},{6,8}}
[4,1,6,5,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,5,4,6,3,8,2,7]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,4,7,3,2,5]=>{{1},{2,5,7,8},{3,6},{4}}
[4,7,1,8,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,1,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,6,2,1,7,5]=>{{1,4,6},{2,3,5,8},{7}}
[8,3,6,2,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[7,8,3,2,4,6,5,1]=>{{1,2,4,5,7,8},{3},{6}}
[7,2,8,5,3,1,6,4]=>{{1,6,7},{2},{3,4,5,8}}
[2,5,4,8,7,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,2,8,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,8,1,7,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,6,3,1,4,5,2]=>{{1,5,7},{2,8},{3,4,6}}
[3,8,6,1,7,5,2,4]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,4,8,3,1,6]=>{{1,2,7},{3,5,6,8},{4}}
[6,8,7,5,2,1,3,4]=>{{1,6},{2,4,5,8},{3,7}}
[7,6,2,8,5,1,3,4]=>{{1,2,3,6,7},{4,8},{5}}
[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,6,5,2,7,8,4,3]=>{{1},{2,3,4,5,6,7,8}}
[4,7,8,5,6,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,5,6,1,4,3]=>{{1,2,4,5,6,7},{3,8}}
[6,7,8,4,2,1,5,3]=>{{1,6},{2,5,7},{3,8},{4}}
[4,7,8,1,2,5,6,3]=>{{1,4},{2,5,6,7},{3,8}}
[8,6,4,1,2,5,7,3]=>{{1,3,4,8},{2,5,6},{7}}
[6,1,4,7,2,5,8,3]=>{{1,2,5,6},{3,4,7,8}}
[6,7,8,3,5,4,2,1]=>{{1,3,4,6,8},{2,7},{5}}
[6,7,8,2,1,5,3,4]=>{{1,5,6},{2,3,4,7,8}}
[5,6,3,2,7,4,1,8]=>{{1,5,7},{2,4,6},{3},{8}}
[2,6,4,3,7,5,8,1]=>{{1,2,5,6,7,8},{3,4}}
[7,2,3,6,1,8,4,5]=>{{1,4,5,6,7,8},{2},{3}}
[3,4,6,5,7,1,2,8]=>{{1,3,6},{2,4,5,7},{8}}
[7,6,2,3,5,4,8,1]=>{{1,7,8},{2,3,4,6},{5}}
[8,5,2,4,3,6,1,7]=>{{1,7,8},{2,3,5},{4},{6}}
[8,5,7,2,4,1,6,3]=>{{1,3,6,7,8},{2,4,5}}
[7,4,8,2,1,5,6,3]=>{{1,5,6,7},{2,4},{3,8}}
[2,3,6,7,8,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,1,6,4,2,5]=>{{1,4,5,6,8},{2,3,7}}
[8,2,1,7,6,5,3,4]=>{{1,3,4,7,8},{2},{5,6}}
[5,7,4,1,6,8,2,3]=>{{1,3,4,5,6,8},{2,7}}
[6,5,1,2,8,3,4,7]=>{{1,3,6},{2,4,5,7,8}}
[5,6,8,1,3,7,2,4]=>{{1,3,4,5,8},{2,6,7}}
[3,7,4,8,6,1,2,5]=>{{1,3,4,5,6,8},{2,7}}
[1,6,8,5,3,2,4,7]=>{{1},{2,6},{3,4,5,7,8}}
[5,8,1,6,7,4,2,3]=>{{1,2,3,5,7,8},{4,6}}
[7,2,8,4,6,1,3,5]=>{{1,3,5,6,7,8},{2},{4}}
[6,2,7,4,3,8,1,5]=>{{1,3,5,6,7,8},{2},{4}}
[1,7,8,4,6,2,3,5]=>{{1},{2,3,5,6,7,8},{4}}
[7,1,8,4,6,2,3,5]=>{{1,2,3,5,6,7,8},{4}}
[8,1,6,5,4,7,2,3]=>{{1,2,3,6,7,8},{4,5}}
[4,1,6,8,7,3,2,5]=>{{1,2,4,5,7,8},{3,6}}
[5,1,4,6,7,3,8,2]=>{{1,2,5,7,8},{3,4,6}}
[7,1,3,4,6,2,8,5]=>{{1,2,5,6,7,8},{3},{4}}
[8,7,1,4,6,3,2,5]=>{{1,3,5,6,8},{2,7},{4}}
[1,4,7,5,8,6,3,2]=>{{1},{2,4,5,8},{3,7},{6}}
[6,1,8,3,4,7,2,5]=>{{1,2,6,7},{3,4,5,8}}
[1,8,6,3,5,2,7,4]=>{{1},{2,3,4,6,8},{5},{7}}
[4,7,1,6,8,3,5,2]=>{{1,3,4,6},{2,5,7,8}}
[3,6,5,2,8,4,1,7]=>{{1,3,5,7,8},{2,4,6}}
[7,1,8,4,2,5,3,6]=>{{1,2,3,5,6,7,8},{4}}
[1,4,8,7,5,2,6,3]=>{{1},{2,4,6,7},{3,8},{5}}
[1,5,6,4,2,3,7,8]=>{{1},{2,5},{3,6},{4},{7},{8}}
[5,7,3,6,8,4,2,1]=>{{1,5,8},{2,7},{3},{4,6}}
[5,8,7,4,2,1,3,6]=>{{1,2,5,6,8},{3,7},{4}}
[1,8,7,3,2,5,4,6]=>{{1},{2,5,6,8},{3,4,7}}
[1,2,5,4,8,7,3,6]=>{{1},{2},{3,5,6,7,8},{4}}
[1,2,4,8,6,3,5,7]=>{{1},{2},{3,4,5,6,7,8}}
[1,5,2,4,7,3,8,6]=>{{1},{2,3,5,6,7,8},{4}}
[8,6,3,5,7,4,1,2]=>{{1,2,4,5,6,7,8},{3}}
[8,5,3,2,1,4,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[1,2,7,6,8,4,3,5]=>{{1},{2},{3,7},{4,6},{5,8}}
[1,6,3,2,5,7,8,4]=>{{1},{2,4,6,7,8},{3},{5}}
[1,7,3,4,2,6,8,5]=>{{1},{2,5,7,8},{3},{4},{6}}
[1,6,3,5,8,4,2,7]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,6,3,2,8,4,7]=>{{1},{2,5},{3,4,6,7,8}}
[1,2,5,8,4,6,3,7]=>{{1},{2},{3,4,5,7,8},{6}}
[1,5,3,2,7,8,4,6]=>{{1},{2,4,5,7},{3},{6,8}}
[4,1,8,6,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[7,5,8,6,2,3,4,1]=>{{1,3,4,6,7,8},{2,5}}
[1,7,6,4,3,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[1,8,5,7,6,3,2,4]=>{{1},{2,4,7,8},{3,5,6}}
[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,3,5,7,8,4,2]=>{{1},{2,6,8},{3},{4,5,7}}
[1,5,6,3,2,7,8,4]=>{{1},{2,5},{3,4,6,7,8}}
[1,2,7,6,8,4,5,3]=>{{1},{2},{3,5,7,8},{4,6}}
[1,8,4,7,5,3,2,6]=>{{1},{2,3,4,6,7,8},{5}}
[6,8,5,2,1,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[1,2,6,8,4,3,7,5]=>{{1},{2},{3,6},{4,5,8},{7}}
[5,3,7,2,6,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[7,6,2,5,3,4,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[7,6,2,4,5,3,1,8]=>{{1,7},{2,3,6},{4},{5},{8}}
[7,6,2,4,3,5,1,8]=>{{1,7},{2,3,5,6},{4},{8}}
[7,6,2,3,5,4,1,8]=>{{1,7},{2,3,4,6},{5},{8}}
[8,4,2,7,1,6,3,5]=>{{1,5,8},{2,3,4,7},{6}}
[8,7,6,1,5,3,2,4]=>{{1,4,8},{2,7},{3,6},{5}}
[8,7,6,1,4,3,5,2]=>{{1,2,4,5,7,8},{3,6}}
[8,7,6,1,3,5,4,2]=>{{1,2,4,7,8},{3,5,6}}
[8,7,6,1,5,4,2,3]=>{{1,3,4,6,8},{2,7},{5}}
[8,6,2,7,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,2,8,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,3,5,4,2,1,6,7]=>{{1,6,7,8},{2,3,5},{4}}
[7,8,4,3,1,5,2,6]=>{{1,2,5,6,7,8},{3,4}}
[8,7,6,1,2,5,3,4]=>{{1,4,8},{2,3,5,6,7}}
[8,7,6,1,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,1,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,8,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,7,3,8,4,1,2]=>{{1,3,4,6,7},{2,5,8}}
[8,7,5,4,1,2,6,3]=>{{1,3,5,8},{2,6,7},{4}}
[8,6,7,1,5,3,2,4]=>{{1,4,8},{2,3,6,7},{5}}
[5,7,1,3,4,2,8,6]=>{{1,3,4,5},{2,6,7,8}}
[7,3,5,6,4,8,1,2]=>{{1,7},{2,3,4,5,6,8}}
[1,5,3,7,8,4,6,2]=>{{1},{2,5,8},{3},{4,6,7}}
[1,5,7,3,8,2,6,4]=>{{1},{2,3,4,5,6,7,8}}
[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[3,7,5,8,4,1,2,6]=>{{1,3,4,5,6,8},{2,7}}
[5,3,7,6,8,1,2,4]=>{{1,4,5,6,8},{2,3,7}}
[3,1,2,7,5,8,4,6]=>{{1,2,3},{4,7},{5},{6,8}}
[3,1,2,5,7,8,6,4]=>{{1,2,3},{4,5,6,7,8}}
[3,7,1,2,8,5,6,4]=>{{1,3},{2,4,5,6,7,8}}
[5,3,1,7,4,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[2,4,7,3,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}
[5,7,6,4,2,3,1,8]=>{{1,2,5,7},{3,6},{4},{8}}
[7,4,8,2,5,6,1,3]=>{{1,7},{2,4},{3,8},{5},{6}}
[5,8,2,4,6,1,3,7]=>{{1,5,6},{2,3,7,8},{4}}
[6,1,4,8,5,2,7,3]=>{{1,2,6},{3,4,8},{5},{7}}
[3,4,5,8,1,6,7,2]=>{{1,3,5},{2,4,8},{6},{7}}
[5,6,8,4,7,3,1,2]=>{{1,5,7},{2,3,6,8},{4}}
[3,1,6,8,5,2,7,4]=>{{1,2,3,6},{4,8},{5},{7}}
[2,3,8,1,5,6,4,7]=>{{1,2,3,4,7,8},{5},{6}}
[5,4,8,1,2,6,7,3]=>{{1,2,4,5},{3,8},{6},{7}}
[4,1,8,2,3,6,7,5]=>{{1,2,4},{3,5,8},{6},{7}}
[5,2,3,8,1,7,4,6]=>{{1,5},{2},{3},{4,6,7,8}}
[1,5,3,8,2,4,6,7]=>{{1},{2,5},{3},{4,6,7,8}}
[8,6,2,7,5,1,4,3]=>{{1,2,3,6,8},{4,7},{5}}
[2,7,1,8,6,3,5,4]=>{{1,2,3,5,6,7},{4,8}}
[5,7,6,1,3,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[3,5,4,6,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[8,1,5,4,6,3,7,2]=>{{1,2,8},{3,5,6},{4},{7}}
[2,7,1,5,6,4,3,8]=>{{1,2,3,7},{4,5,6},{8}}
[8,4,6,3,1,7,2,5]=>{{1,5,8},{2,3,4,6,7}}
[8,4,2,5,6,3,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[5,4,7,2,8,6,1,3]=>{{1,3,5,7,8},{2,4},{6}}
[3,5,6,4,1,7,2,8]=>{{1,2,3,5,6,7},{4},{8}}
[2,5,6,1,7,4,3,8]=>{{1,2,3,4,5,6,7},{8}}
[2,7,1,8,6,5,4,3]=>{{1,2,3,4,7,8},{5,6}}
[3,7,6,1,8,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,2,8,3,1,4,5,7]=>{{1,3,4,5,6,7,8},{2}}
[2,7,8,3,1,4,5,6]=>{{1,2,5,7},{3,4,6,8}}
[1,5,3,2,8,6,7,4]=>{{1},{2,4,5,8},{3},{6},{7}}
[1,8,5,3,2,6,7,4]=>{{1},{2,3,4,5,8},{6},{7}}
[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[1,7,5,2,3,4,8,6]=>{{1},{2,4,6,7,8},{3,5}}
[1,7,5,2,4,8,6,3]=>{{1},{2,3,4,5,6,7,8}}
[1,6,7,8,3,2,4,5]=>{{1},{2,6},{3,4,5,7,8}}
[1,4,8,6,2,3,5,7]=>{{1},{2,3,4,5,6,7,8}}
[1,8,4,5,6,7,2,3]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,6,3,5,7,4]=>{{1},{2},{3,4,5,6,8},{7}}
[1,2,7,8,4,3,5,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,8,6,7,4,2,3,5]=>{{1},{2,3,4,5,6,7,8}}
[1,6,7,8,4,2,3,5]=>{{1},{2,6},{3,7},{4,5,8}}
[1,6,7,8,3,4,2,5]=>{{1},{2,3,4,5,6,7,8}}
[1,7,4,2,3,8,5,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,7,8,4,2,3,5,6]=>{{1},{2,5,7},{3,6,8},{4}}
[1,7,3,5,6,2,8,4]=>{{1},{2,4,5,6,7,8},{3}}
[1,7,8,3,4,2,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,2,3,7,8,5,4,6]=>{{1},{2},{3},{4,7},{5,6,8}}
[1,2,7,4,6,3,8,5]=>{{1},{2},{3,5,6,7,8},{4}}
[1,7,8,4,5,2,3,6]=>{{1},{2,3,6,7,8},{4},{5}}
[1,7,8,3,4,5,2,6]=>{{1},{2,7},{3,4,5,6,8}}
[1,2,8,4,5,6,3,7]=>{{1},{2},{3,7,8},{4},{5},{6}}
[1,8,4,5,6,2,3,7]=>{{1},{2,3,4,5,6,7,8}}
[5,8,2,7,3,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,2,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,5,2,6,1,4]=>{{1,3,7},{2,4,5,8},{6}}
[4,8,7,3,2,5,1,6]=>{{1,3,4,7},{2,5,6,8}}
[5,3,8,1,6,7,4,2]=>{{1,4,5,6,7},{2,3,8}}
[5,8,2,1,3,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[5,1,8,3,6,7,4,2]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,4,6,2,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[8,4,1,6,5,2,3,7]=>{{1,3,7,8},{2,4,6},{5}}
[1,8,7,6,4,3,5,2]=>{{1},{2,8},{3,4,5,6,7}}
[6,1,8,7,5,3,4,2]=>{{1,2,3,6,8},{4,7},{5}}
[6,8,7,3,2,4,1,5]=>{{1,3,4,6,7},{2,5,8}}
[2,3,7,5,6,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[3,2,4,7,5,8,1,6]=>{{1,3,4,7},{2},{5},{6,8}}
[2,8,7,6,4,5,1,3]=>{{1,2,3,7,8},{4,5,6}}
[4,8,7,6,3,1,5,2]=>{{1,4,6},{2,8},{3,5,7}}
[3,5,2,4,7,6,8,1]=>{{1,2,3,5,7,8},{4},{6}}
[5,3,2,6,4,7,8,1]=>{{1,4,5,6,7,8},{2,3}}
[5,3,2,6,7,4,8,1]=>{{1,5,7,8},{2,3},{4,6}}
[5,3,2,7,6,4,8,1]=>{{1,4,5,6,7,8},{2,3}}
[7,3,5,2,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,7,4,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[3,2,5,7,4,6,8,1]=>{{1,3,4,5,7,8},{2},{6}}
[3,2,7,5,4,8,6,1]=>{{1,3,6,7,8},{2},{4,5}}
[3,7,5,2,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[2,3,7,5,4,8,6,1]=>{{1,2,3,6,7,8},{4,5}}
[3,4,7,6,8,2,5,1]=>{{1,3,5,7,8},{2,4,6}}
[5,2,8,4,1,3,6,7]=>{{1,5},{2},{3,6,7,8},{4}}
[3,8,5,2,1,4,6,7]=>{{1,3,5},{2,4,6,7,8}}
[7,6,4,1,8,2,5,3]=>{{1,3,4,5,7,8},{2,6}}
[7,5,4,2,1,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[8,1,6,7,3,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,6,7,4,3,5]=>{{1,3,5,7,8},{2},{4,6}}
[5,2,8,6,3,7,1,4]=>{{1,3,4,5,6,7,8},{2}}
[7,6,8,1,2,5,4,3]=>{{1,4,7},{2,5,6},{3,8}}
[2,1,3,4,8,5,7,6]=>{{1,2},{3},{4},{5,6,8},{7}}
[5,7,1,2,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,5,2,3,6,8,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[3,5,7,4,1,8,2,6]=>{{1,2,3,5,7},{4},{6,8}}
[8,6,4,7,5,1,2,3]=>{{1,2,3,4,6,7,8},{5}}
[8,6,4,1,2,5,3,7]=>{{1,3,4,7,8},{2,5,6}}
[2,8,4,3,1,6,5,7]=>{{1,2,5,7,8},{3,4},{6}}
[3,8,4,6,1,5,2,7]=>{{1,3,4,5,6},{2,7,8}}
[8,3,5,6,1,4,7,2]=>{{1,2,3,5,8},{4,6},{7}}
[6,8,7,3,5,4,2,1]=>{{1,2,3,4,6,7,8},{5}}
[3,1,2,8,5,7,4,6]=>{{1,2,3},{4,6,7,8},{5}}
[7,3,1,2,5,8,4,6]=>{{1,2,3,4,7},{5},{6,8}}
[8,3,5,7,2,1,4,6]=>{{1,6,8},{2,3,5},{4,7}}
[2,1,3,8,5,7,4,6]=>{{1,2},{3},{4,6,7,8},{5}}
[7,3,1,2,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,1,4,7,6,3,5,8]=>{{1,2},{3,4,5,6,7},{8}}
[7,2,4,5,3,8,1,6]=>{{1,7},{2},{3,4,5},{6,8}}
[8,4,2,5,6,7,3,1]=>{{1,8},{2,3,4,5,6,7}}
[5,4,1,6,3,7,8,2]=>{{1,3,5},{2,4,6,7,8}}
[4,5,1,3,6,7,8,2]=>{{1,3,4},{2,5,6,7,8}}
[5,1,7,6,3,4,8,2]=>{{1,2,3,5,7,8},{4,6}}
[6,1,7,5,4,8,2,3]=>{{1,2,3,6,7,8},{4,5}}
[3,7,2,1,6,8,4,5]=>{{1,2,3,4,7},{5,6,8}}
[1,5,8,2,4,7,6,3]=>{{1},{2,4,5},{3,8},{6,7}}
[5,8,1,6,4,7,3,2]=>{{1,3,4,5,6,7},{2,8}}
[3,8,6,5,7,2,4,1]=>{{1,2,3,6,8},{4,5,7}}
[6,8,1,4,7,3,5,2]=>{{1,3,6},{2,8},{4},{5,7}}
[1,6,8,2,7,4,5,3]=>{{1},{2,4,6},{3,8},{5,7}}
[5,7,2,1,8,4,3,6]=>{{1,4,5,6,8},{2,3,7}}
[5,7,1,6,8,3,2,4]=>{{1,3,4,5,6,8},{2,7}}
[5,6,2,1,8,3,4,7]=>{{1,4,5,7,8},{2,3,6}}
[6,4,1,7,3,8,2,5]=>{{1,3,5,6,8},{2,4,7}}
[8,2,5,6,7,1,4,3]=>{{1,3,4,5,6,7,8},{2}}
[7,2,4,6,8,3,1,5]=>{{1,7},{2},{3,4,6},{5,8}}
[6,2,4,7,8,1,3,5]=>{{1,6},{2},{3,4,7},{5,8}}
[6,1,4,3,2,8,5,7]=>{{1,2,5,6,7,8},{3,4}}
[2,7,4,8,6,1,5,3]=>{{1,2,5,6,7},{3,4,8}}
[2,4,8,6,5,7,3,1]=>{{1,2,3,4,6,7,8},{5}}
[3,7,8,6,4,2,5,1]=>{{1,3,8},{2,4,5,6,7}}
[6,2,8,4,7,5,1,3]=>{{1,5,6,7},{2},{3,8},{4}}
[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[4,2,8,5,1,6,3,7]=>{{1,4,5},{2},{3,7,8},{6}}
[6,5,8,1,4,2,3,7]=>{{1,2,4,5,6},{3,7,8}}
[2,3,8,4,1,6,5,7]=>{{1,2,3,5,7,8},{4},{6}}
[4,5,7,3,1,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}
[5,1,8,7,4,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[2,4,8,7,5,1,3,6]=>{{1,2,3,4,6,7,8},{5}}
[3,5,7,6,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,6,2,8,4,1]=>{{1,3,4,6,7,8},{2,5}}
[1,5,3,2,8,7,6,4]=>{{1},{2,4,5,8},{3},{6,7}}
[6,1,4,3,8,7,5,2]=>{{1,2,5,6,7,8},{3,4}}
[6,3,1,8,7,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,2,8,7,4,1]=>{{1,5,8},{2,3,4,6,7}}
[6,3,5,2,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[2,8,4,1,3,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[3,8,1,4,7,6,5,2]=>{{1,3},{2,8},{4},{5,7},{6}}
[6,2,3,8,7,5,4,1]=>{{1,4,5,6,7,8},{2},{3}}
[4,1,3,5,8,7,6,2]=>{{1,2,4,5,8},{3},{6,7}}
[3,4,7,5,8,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,3,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,6,7,5,4,3,1]=>{{1,2,8},{3,4,6,7},{5}}
[7,2,6,8,1,4,3,5]=>{{1,3,4,5,6,7,8},{2}}
[5,3,6,2,8,4,7,1]=>{{1,5,8},{2,3,4,6},{7}}
[8,1,6,3,7,4,5,2]=>{{1,2,8},{3,4,6},{5,7}}
[2,4,3,7,1,8,6,5]=>{{1,2,4,5,6,7,8},{3}}
[2,6,5,7,3,8,4,1]=>{{1,2,6,8},{3,5},{4,7}}
[6,8,2,7,4,1,5,3]=>{{1,6},{2,3,8},{4,5,7}}
[6,1,7,8,5,3,2,4]=>{{1,2,3,6,7},{4,8},{5}}
[2,6,5,4,7,1,8,3]=>{{1,2,6},{3,5,7,8},{4}}
[5,8,3,4,6,1,7,2]=>{{1,5,6},{2,8},{3},{4},{7}}
[6,1,7,4,2,5,8,3]=>{{1,2,5,6},{3,7,8},{4}}
[6,8,7,1,5,4,2,3]=>{{1,4,6},{2,3,7,8},{5}}
[4,8,3,1,5,7,6,2]=>{{1,4},{2,8},{3},{5},{6,7}}
[5,3,8,2,7,1,6,4]=>{{1,5,6,7},{2,3,4,8}}
[8,3,4,5,2,7,1,6]=>{{1,6,7,8},{2,3,4,5}}
[7,1,5,2,6,3,4,8]=>{{1,2,4,7},{3,5,6},{8}}
[3,7,1,5,2,6,8,4]=>{{1,3},{2,4,5,7,8},{6}}
[6,7,1,8,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[3,7,1,6,8,4,5,2]=>{{1,3},{2,5,7,8},{4,6}}
[3,8,5,2,6,7,1,4]=>{{1,3,5,6,7},{2,4,8}}
[3,6,5,2,7,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,8,3,4,7,1,5,2]=>{{1,6},{2,8},{3},{4},{5,7}}
[3,7,1,6,5,2,8,4]=>{{1,3},{2,4,6,7,8},{5}}
[8,3,5,2,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,4,6,3,5,2]=>{{1,2,3,5,6,7,8},{4}}
[3,7,1,4,8,6,5,2]=>{{1,3},{2,5,7,8},{4},{6}}
[3,7,1,4,5,2,8,6]=>{{1,3},{2,6,7,8},{4},{5}}
[2,3,7,6,5,8,1,4]=>{{1,2,3,7},{4,6,8},{5}}
[3,5,7,6,8,2,1,4]=>{{1,3,7},{2,4,5,6,8}}
[4,2,5,3,7,6,1,8]=>{{1,3,4,5,7},{2},{6},{8}}
[6,2,4,3,7,5,1,8]=>{{1,5,6,7},{2},{3,4},{8}}
[1,3,6,4,7,5,2,8]=>{{1},{2,3,5,6,7},{4},{8}}
[8,2,5,3,6,4,1,7]=>{{1,7,8},{2},{3,4,5,6}}
[7,2,5,3,6,4,1,8]=>{{1,7},{2},{3,4,5,6},{8}}
[6,2,5,3,7,4,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[4,2,6,3,7,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[5,2,7,3,6,4,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[7,3,6,2,5,4,1,8]=>{{1,7},{2,3,4,6},{5},{8}}
[6,3,8,2,5,4,1,7]=>{{1,2,3,4,6,7,8},{5}}
[7,3,1,4,6,5,2,8]=>{{1,2,3,7},{4},{5,6},{8}}
[8,3,7,2,5,4,1,6]=>{{1,2,3,4,6,7,8},{5}}
[5,2,8,3,6,4,1,7]=>{{1,3,4,5,6,7,8},{2}}
[3,2,8,4,6,5,1,7]=>{{1,3,7,8},{2},{4},{5,6}}
[1,4,7,3,6,5,2,8]=>{{1},{2,3,4,7},{5,6},{8}}
[8,2,5,4,1,6,3,7]=>{{1,3,5,7,8},{2},{4},{6}}
[8,2,6,4,1,5,3,7]=>{{1,3,5,6,7,8},{2},{4}}
[1,4,8,3,7,5,2,6]=>{{1},{2,3,4,5,6,7,8}}
[6,2,1,4,8,5,3,7]=>{{1,3,5,6,7,8},{2},{4}}
[5,2,1,4,8,6,3,7]=>{{1,3,5,7,8},{2},{4},{6}}
[3,2,1,5,8,6,4,7]=>{{1,3},{2},{4,5,7,8},{6}}
[4,2,8,3,7,5,1,6]=>{{1,3,4,5,6,7,8},{2}}
[5,2,8,3,7,4,1,6]=>{{1,5,7},{2},{3,4,6,8}}
[8,3,7,2,6,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[7,3,1,4,8,5,2,6]=>{{1,2,3,7},{4},{5,6,8}}
[1,3,7,4,8,5,2,6]=>{{1},{2,3,7},{4},{5,6,8}}
[8,2,6,3,7,4,1,5]=>{{1,5,7,8},{2},{3,4,6}}
[7,2,6,3,8,4,1,5]=>{{1,7},{2},{3,4,6},{5,8}}
[5,2,7,3,8,4,1,6]=>{{1,3,4,5,6,7,8},{2}}
[3,2,7,4,8,5,1,6]=>{{1,3,7},{2},{4},{5,6,8}}
[5,2,6,3,8,4,1,7]=>{{1,5,7,8},{2},{3,4,6}}
[6,2,5,3,8,4,1,7]=>{{1,3,4,5,6,7,8},{2}}
[7,2,5,3,8,4,1,6]=>{{1,7},{2},{3,4,5,6,8}}
[8,2,5,3,7,4,1,6]=>{{1,3,4,5,6,7,8},{2}}
[1,3,6,4,8,5,2,7]=>{{1},{2,3,5,6,7,8},{4}}
[1,3,5,4,8,6,2,7]=>{{1},{2,3,5,7,8},{4},{6}}
[8,2,4,3,7,5,1,6]=>{{1,5,6,7,8},{2},{3,4}}
[7,2,4,3,8,5,1,6]=>{{1,7},{2},{3,4},{5,6,8}}
[6,2,4,3,8,5,1,7]=>{{1,5,6,7,8},{2},{3,4}}
[5,2,4,3,8,6,1,7]=>{{1,5,7,8},{2},{3,4},{6}}
[4,2,5,3,8,6,1,7]=>{{1,3,4,5,7,8},{2},{6}}
[4,2,5,3,1,7,6,8]=>{{1,3,4,5},{2},{6,7},{8}}
[6,2,4,3,1,7,5,8]=>{{1,5,6,7},{2},{3,4},{8}}
[7,2,4,3,1,6,5,8]=>{{1,5,7},{2},{3,4},{6},{8}}
[8,5,1,3,6,4,2,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,3,6,5,2,7]=>{{1,2,3,4,7,8},{5,6}}
[1,5,2,4,7,6,3,8]=>{{1},{2,3,5,7},{4},{6},{8}}
[7,2,5,3,1,6,4,8]=>{{1,3,4,5,7},{2},{6},{8}}
[6,2,5,3,1,7,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[4,2,6,3,1,7,5,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,2,6,4,1,7,5,8]=>{{1,3,5,6,7},{2},{4},{8}}
[3,2,7,4,1,6,5,8]=>{{1,3,5,7},{2},{4},{6},{8}}
[4,2,7,3,1,6,5,8]=>{{1,3,4,5,7},{2},{6},{8}}
[5,2,7,3,1,6,4,8]=>{{1,5},{2},{3,4,7},{6},{8}}
[6,2,7,3,1,5,4,8]=>{{1,5,6},{2},{3,4,7},{8}}
[7,2,6,3,1,5,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[1,5,2,4,8,6,3,7]=>{{1},{2,3,5,7,8},{4},{6}}
[8,4,1,3,7,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[6,2,1,5,3,7,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,2,1,6,4,7,5,8]=>{{1,3},{2},{4,5,6,7},{8}}
[3,2,8,5,1,6,4,7]=>{{1,3,4,5,7,8},{2},{6}}
[6,2,8,4,1,5,3,7]=>{{1,5,6},{2},{3,7,8},{4}}
[8,3,7,4,1,5,2,6]=>{{1,5,6,8},{2,3,7},{4}}
[7,1,3,2,5,6,4,8]=>{{1,2,4,7},{3},{5},{6},{8}}
[6,3,5,2,4,8,1,7]=>{{1,6,7,8},{2,3,4,5}}
[1,5,2,8,7,4,3,6]=>{{1},{2,3,5,7},{4,6,8}}
[5,7,2,8,1,4,3,6]=>{{1,5},{2,3,7},{4,6,8}}
[5,8,2,7,1,4,3,6]=>{{1,5},{2,3,4,6,7,8}}
[4,8,3,1,5,2,7,6]=>{{1,4},{2,6,8},{3},{5},{7}}
[7,1,5,3,2,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[8,6,2,3,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[1,4,2,7,3,6,8,5]=>{{1},{2,3,4,5,7,8},{6}}
[3,2,1,7,8,5,4,6]=>{{1,3},{2},{4,7},{5,6,8}}
[7,3,4,2,1,5,8,6]=>{{1,5,6,7,8},{2,3,4}}
[1,7,6,3,2,4,8,5]=>{{1},{2,5,7,8},{3,4,6}}
[2,1,6,4,7,8,5,3]=>{{1,2},{3,6,8},{4},{5,7}}
[1,6,3,2,4,7,8,5]=>{{1},{2,4,5,6,7,8},{3}}
[1,2,3,7,5,8,4,6]=>{{1},{2},{3},{4,7},{5},{6,8}}
[1,8,5,3,2,4,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[4,7,8,1,5,6,2,3]=>{{1,4},{2,7},{3,8},{5},{6}}
[3,6,7,1,8,4,2,5]=>{{1,2,3,4,6,7},{5,8}}
[1,3,7,6,2,4,5,8]=>{{1},{2,3,5,7},{4,6},{8}}
[2,7,3,8,4,5,6,1]=>{{1,2,4,5,6,7,8},{3}}
[7,1,4,3,8,5,6,2]=>{{1,2,5,6,7,8},{3,4}}
[5,6,2,7,8,3,4,1]=>{{1,5,8},{2,3,6},{4,7}}
[7,4,1,8,5,6,2,3]=>{{1,2,3,4,7,8},{5},{6}}
[7,2,5,8,1,6,3,4]=>{{1,3,5,7},{2},{4,8},{6}}
[6,4,8,1,5,7,2,3]=>{{1,2,4,6,7},{3,8},{5}}
[2,7,4,1,3,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[6,2,1,4,7,5,8,3]=>{{1,3,5,6,7,8},{2},{4}}
[2,6,1,5,4,7,3,8]=>{{1,2,3,6,7},{4,5},{8}}
[2,3,6,8,4,1,7,5]=>{{1,2,3,6},{4,5,8},{7}}
[1,7,2,8,6,3,5,4]=>{{1},{2,3,5,6,7},{4,8}}
[8,4,2,3,7,1,6,5]=>{{1,5,6,7,8},{2,3,4}}
[5,2,4,8,7,3,1,6]=>{{1,5,7},{2},{3,4,6,8}}
[8,3,2,6,7,4,1,5]=>{{1,5,7,8},{2,3},{4,6}}
[3,2,4,6,7,8,1,5]=>{{1,3,4,5,6,7,8},{2}}
[5,2,6,8,1,3,7,4]=>{{1,5},{2},{3,6},{4,8},{7}}
[4,8,1,6,3,7,5,2]=>{{1,3,4,5,6,7},{2,8}}
[7,1,5,2,6,4,3,8]=>{{1,2,3,4,5,6,7},{8}}
[8,3,5,2,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,8,5,6,2,7,4,3]=>{{1},{2,3,5,8},{4,6,7}}
[8,3,2,4,6,7,1,5]=>{{1,5,6,7,8},{2,3},{4}}
[4,2,7,6,1,8,5,3]=>{{1,3,4,5,6,7,8},{2}}
[7,2,4,8,6,3,5,1]=>{{1,3,4,5,6,7,8},{2}}
[7,3,2,1,8,5,4,6]=>{{1,4,7},{2,3},{5,6,8}}
[7,3,2,1,6,4,8,5]=>{{1,4,5,6,7,8},{2,3}}
[3,6,5,2,1,8,4,7]=>{{1,3,5},{2,4,6,7,8}}
[6,7,2,4,3,5,8,1]=>{{1,2,3,5,6,7,8},{4}}
[4,3,8,2,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,3,2,8,1,6,7,5]=>{{1,4,5,8},{2,3},{6},{7}}
[4,5,8,3,2,7,1,6]=>{{1,3,4,6,7,8},{2,5}}
[6,8,5,2,7,3,4,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,7,8,2,3,6,1]=>{{1,2,4,5,8},{3,6,7}}
[4,3,8,2,1,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[3,5,7,4,6,2,8,1]=>{{1,3,7,8},{2,5,6},{4}}
[5,3,7,6,2,4,8,1]=>{{1,2,3,5,7,8},{4,6}}
[4,6,7,2,5,3,8,1]=>{{1,2,3,4,6,7,8},{5}}
[6,4,7,8,3,1,5,2]=>{{1,6},{2,4,8},{3,5,7}}
[8,4,7,3,1,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,7,6,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,6,7,1,8,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,6,2,5,4,3]=>{{1,2,4,5,6,7},{3,8}}
[8,5,1,7,6,4,2,3]=>{{1,3,8},{2,4,5,6,7}}
[1,5,8,2,6,4,7,3]=>{{1},{2,4,5,6},{3,8},{7}}
[1,5,7,4,6,8,3,2]=>{{1},{2,5,6,8},{3,7},{4}}
[1,4,7,5,6,8,3,2]=>{{1},{2,4,5,6,8},{3,7}}
[5,6,7,4,8,1,3,2]=>{{1,2,5,6,8},{3,7},{4}}
[8,1,2,6,4,5,7,3]=>{{1,2,3,8},{4,5,6},{7}}
[4,8,1,7,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[2,6,7,1,5,4,8,3]=>{{1,2,4,6},{3,7,8},{5}}
[1,7,3,4,5,8,2,6]=>{{1},{2,7},{3},{4},{5},{6,8}}
[7,1,8,4,5,6,3,2]=>{{1,2,3,7,8},{4},{5},{6}}
[1,2,7,4,5,8,3,6]=>{{1},{2},{3,7},{4},{5},{6,8}}
[6,7,3,2,5,8,1,4]=>{{1,2,4,6,7,8},{3},{5}}
[6,1,8,4,5,3,7,2]=>{{1,2,3,6,8},{4},{5},{7}}
[4,6,2,5,1,8,7,3]=>{{1,4,5},{2,3,6,8},{7}}
[5,1,4,6,2,8,7,3]=>{{1,2,5},{3,4,6,8},{7}}
[7,3,5,2,1,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[8,5,1,2,6,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[1,5,8,7,4,6,3,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,7,2,1,3,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[3,7,2,6,8,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[7,4,8,6,5,1,3,2]=>{{1,2,3,4,6,7,8},{5}}
[2,7,6,8,5,1,4,3]=>{{1,2,3,4,6,7,8},{5}}
[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,4,7,8,6,2,3]=>{{1},{2,3,4,5,7,8},{6}}
[7,3,1,6,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,8,5,2,4,3]=>{{1,2,3,4,6,7,8},{5}}
[3,5,8,7,6,4,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,5,7,8,6,2,4,3]=>{{1},{2,5,6},{3,4,7,8}}
[3,6,2,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,8,2,7,5,4,3,1]=>{{1,2,3,4,6,7,8},{5}}
[5,8,1,7,6,4,3,2]=>{{1,3,4,5,6,7},{2,8}}
[8,6,3,2,1,5,4,7]=>{{1,2,4,5,6,7,8},{3}}
[8,5,3,2,4,1,7,6]=>{{1,6,8},{2,4,5},{3},{7}}
[7,5,2,4,3,6,8,1]=>{{1,7,8},{2,3,5},{4},{6}}
[8,5,1,4,6,3,2,7]=>{{1,2,3,5,6,7,8},{4}}
[8,5,1,6,3,4,2,7]=>{{1,2,3,5,7,8},{4,6}}
[8,4,3,6,1,5,2,7]=>{{1,2,4,5,6,7,8},{3}}
[8,4,3,5,2,1,7,6]=>{{1,6,8},{2,4,5},{3},{7}}
[6,4,3,2,8,7,1,5]=>{{1,6,7},{2,4},{3},{5,8}}
[8,5,1,4,3,7,2,6]=>{{1,2,3,5,6,7,8},{4}}
[8,5,4,2,1,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,7,3,6,1,8,5,2]=>{{1,2,4,5,6,7,8},{3}}
[7,6,2,4,1,5,8,3]=>{{1,2,3,5,6,7,8},{4}}
[8,1,6,3,7,4,2,5]=>{{1,2,5,7,8},{3,4,6}}
[5,3,8,2,6,7,1,4]=>{{1,5,6,7},{2,3,4,8}}
[8,2,5,1,7,6,3,4]=>{{1,4,8},{2},{3,5,7},{6}}
[8,2,4,6,3,7,1,5]=>{{1,3,4,5,6,7,8},{2}}
[7,2,6,4,3,5,8,1]=>{{1,7,8},{2},{3,5,6},{4}}
[7,3,6,2,4,5,8,1]=>{{1,7,8},{2,3,4,5,6}}
[8,3,7,2,1,4,6,5]=>{{1,5,8},{2,3,4,6,7}}
[7,6,4,1,3,2,8,5]=>{{1,3,4,5,7,8},{2,6}}
[7,3,8,2,1,5,6,4]=>{{1,5,6,7},{2,3,4,8}}
[6,2,5,7,4,3,8,1]=>{{1,3,4,5,6,7,8},{2}}
[6,2,5,4,8,7,1,3]=>{{1,6,7},{2},{3,5,8},{4}}
[7,2,4,8,5,1,6,3]=>{{1,6,7},{2},{3,4,8},{5}}
[4,2,7,6,8,5,1,3]=>{{1,3,4,5,6,7,8},{2}}
[7,1,6,2,8,5,4,3]=>{{1,2,4,7},{3,5,6,8}}
[7,1,6,3,8,5,2,4]=>{{1,2,7},{3,4,5,6,8}}
[7,2,6,8,1,3,5,4]=>{{1,5,7},{2},{3,6},{4,8}}
[7,2,8,5,1,3,6,4]=>{{1,3,4,5,6,7,8},{2}}
[7,1,8,5,3,2,6,4]=>{{1,2,6,7},{3,4,5,8}}
[7,1,8,2,5,6,4,3]=>{{1,2,4,7},{3,8},{5},{6}}
[6,1,5,8,7,2,4,3]=>{{1,2,6},{3,4,5,7,8}}
[6,1,5,7,4,8,3,2]=>{{1,2,6,8},{3,4,5,7}}
[6,1,5,7,8,3,4,2]=>{{1,2,3,5,6,8},{4,7}}
[4,6,7,3,1,8,5,2]=>{{1,3,4,5,7},{2,6,8}}
[4,2,6,3,1,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[6,1,4,2,5,8,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[1,5,3,8,4,6,2,7]=>{{1},{2,4,5,7,8},{3},{6}}
[7,2,3,5,8,4,1,6]=>{{1,7},{2},{3},{4,5,6,8}}
[7,6,4,2,8,5,1,3]=>{{1,7},{2,3,4,5,6,8}}
[1,7,6,4,8,5,3,2]=>{{1},{2,3,5,6,7,8},{4}}
[8,7,4,2,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,2,3,5,1,4,6,7]=>{{1,4,5,6,7,8},{2},{3}}
[8,7,4,1,3,2,6,5]=>{{1,3,4,5,8},{2,6,7}}
[7,1,4,8,3,6,2,5]=>{{1,2,7},{3,4,5,8},{6}}
[4,1,8,5,7,6,2,3]=>{{1,2,4,5,7},{3,8},{6}}
[3,7,5,8,4,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[6,1,5,8,3,4,2,7]=>{{1,2,4,6,7,8},{3,5}}
[6,7,5,1,3,2,4,8]=>{{1,2,4,6,7},{3,5},{8}}
[5,2,6,1,7,3,4,8]=>{{1,4,5,7},{2},{3,6},{8}}
[4,2,6,8,3,7,1,5]=>{{1,3,4,5,6,7,8},{2}}
[6,8,5,1,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[7,8,4,5,1,3,6,2]=>{{1,3,4,5,6,7},{2,8}}
[1,7,8,5,3,4,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,8,3,6,4,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[6,3,8,1,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[4,8,1,5,6,3,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[1,8,2,6,5,3,7,4]=>{{1},{2,3,4,6,8},{5},{7}}
[3,8,1,7,2,6,5,4]=>{{1,3},{2,4,5,7,8},{6}}
[7,3,8,1,2,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[8,1,4,2,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[8,1,2,4,6,5,7,3]=>{{1,2,3,8},{4},{5,6},{7}}
[5,1,8,3,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,1,5,4,6,2]=>{{1,2,3,4,6,7,8},{5}}
[8,4,7,1,5,3,6,2]=>{{1,2,4,8},{3,6,7},{5}}
[7,2,5,3,4,6,1,8]=>{{1,7},{2},{3,4,5},{6},{8}}
[7,6,4,2,5,3,1,8]=>{{1,7},{2,3,4,6},{5},{8}}
[5,8,4,3,6,2,7,1]=>{{1,2,5,6,8},{3,4},{7}}
[1,7,2,6,3,4,8,5]=>{{1},{2,3,5,7,8},{4,6}}
[7,5,1,6,3,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[7,1,2,6,3,4,5,8]=>{{1,2,3,5,7},{4,6},{8}}
[7,3,1,4,6,2,5,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,1,6,5,4,2,3,8]=>{{1,2,3,6,7},{4,5},{8}}
[5,8,4,3,1,7,2,6]=>{{1,5},{2,6,7,8},{3,4}}
[3,6,8,5,2,4,7,1]=>{{1,3,8},{2,4,5,6},{7}}
[5,7,8,4,3,2,6,1]=>{{1,3,5,8},{2,6,7},{4}}
[1,3,8,4,7,2,6,5]=>{{1},{2,3,5,6,7,8},{4}}
[6,7,1,3,2,8,5,4]=>{{1,3,4,6,8},{2,5,7}}
[1,5,3,2,6,8,4,7]=>{{1},{2,4,5,6,7,8},{3}}
[5,4,3,1,7,2,8,6]=>{{1,2,4,5,6,7,8},{3}}
[3,7,6,5,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,2,8,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[5,4,3,7,8,2,6,1]=>{{1,5,8},{2,4,6,7},{3}}
[3,8,5,7,6,2,4,1]=>{{1,2,3,5,6,8},{4,7}}
[1,3,6,8,7,2,5,4]=>{{1},{2,3,6},{4,8},{5,7}}
[5,8,7,1,4,2,3,6]=>{{1,4,5},{2,6,8},{3,7}}
[2,6,3,7,1,4,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[7,6,8,4,3,1,5,2]=>{{1,2,3,5,6,7,8},{4}}
[1,7,6,5,3,2,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,7,6,5,4,1,3,8]=>{{1,2,3,6,7},{4,5},{8}}
[6,2,3,5,8,4,1,7]=>{{1,4,5,6,7,8},{2},{3}}
[4,7,6,1,5,8,3,2]=>{{1,4},{2,3,6,7,8},{5}}
[6,8,7,1,5,4,3,2]=>{{1,4,6},{2,8},{3,7},{5}}
[8,7,4,6,5,1,3,2]=>{{1,2,3,4,6,7,8},{5}}
[7,2,6,1,5,8,3,4]=>{{1,3,4,6,7,8},{2},{5}}
[4,7,3,8,6,2,5,1]=>{{1,4,8},{2,5,6,7},{3}}
[4,7,3,6,8,2,1,5]=>{{1,2,4,6,7},{3},{5,8}}
[5,4,7,3,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,2,4,6,3,5,1]=>{{1,8},{2,3,5,6,7},{4}}
[4,3,5,7,2,6,1,8]=>{{1,4,7},{2,3,5},{6},{8}}
[1,7,2,8,5,4,3,6]=>{{1},{2,3,7},{4,6,8},{5}}
[5,4,8,3,6,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[6,8,2,5,7,1,4,3]=>{{1,6},{2,3,8},{4,5,7}}
[3,8,6,2,7,5,1,4]=>{{1,3,5,6,7},{2,4,8}}
[5,8,4,2,7,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[8,2,7,3,4,5,1,6]=>{{1,3,4,5,6,7,8},{2}}
[8,1,5,2,4,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[8,6,1,3,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[8,5,1,2,4,6,7,3]=>{{1,3,8},{2,4,5},{6},{7}}
[2,6,8,7,3,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[1,7,8,5,6,4,2,3]=>{{1},{2,7},{3,8},{4,5,6}}
[8,3,1,2,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[3,1,7,5,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,1,3,2,4,6,5,7]=>{{1,2,4,5,7,8},{3},{6}}
[8,1,5,6,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,5,4,3,2,7]=>{{1,2,7,8},{3,6},{4,5}}
[2,6,8,1,5,4,3,7]=>{{1,2,4,6},{3,7,8},{5}}
[3,5,8,2,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,2,8,5,3,7,6,1]=>{{1,3,4,5,8},{2},{6,7}}
[4,2,7,5,3,8,6,1]=>{{1,3,4,5,6,7,8},{2}}
[6,4,5,1,8,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[5,4,7,8,3,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[4,5,8,1,3,7,2,6]=>{{1,4},{2,3,5,6,7,8}}
[1,5,3,6,8,7,2,4]=>{{1},{2,4,5,6,7,8},{3}}
[7,6,2,8,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[4,7,2,6,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[6,3,2,8,7,4,5,1]=>{{1,4,6,8},{2,3},{5,7}}
[7,4,3,8,5,6,2,1]=>{{1,2,4,7,8},{3},{5},{6}}
[3,1,5,8,7,6,2,4]=>{{1,2,3,5,7},{4,8},{6}}
[8,2,1,6,5,7,3,4]=>{{1,3,4,6,7,8},{2},{5}}
[3,1,8,6,5,7,2,4]=>{{1,2,3,4,6,7,8},{5}}
[1,2,7,6,4,5,8,3]=>{{1},{2},{3,7,8},{4,5,6}}
[7,2,6,5,1,8,3,4]=>{{1,3,4,5,6,7,8},{2}}
[4,2,8,5,6,3,1,7]=>{{1,3,4,5,6,7,8},{2}}
[4,7,3,2,5,1,6,8]=>{{1,2,4,6,7},{3},{5},{8}}
[4,2,5,3,8,7,1,6]=>{{1,3,4,5,6,7,8},{2}}
[7,2,5,3,8,4,6,1]=>{{1,3,4,5,6,7,8},{2}}
[8,7,3,2,5,4,6,1]=>{{1,8},{2,4,6,7},{3},{5}}
[7,5,6,1,8,3,2,4]=>{{1,2,4,5,7,8},{3,6}}
[4,5,6,2,7,3,1,8]=>{{1,2,4,5,7},{3,6},{8}}
[3,5,1,4,6,8,2,7]=>{{1,3},{2,5,6,7,8},{4}}
[8,5,7,4,2,1,3,6]=>{{1,6,8},{2,5},{3,7},{4}}
[4,6,2,7,5,8,1,3]=>{{1,4,7},{2,3,6,8},{5}}
[7,8,1,4,2,3,5,6]=>{{1,2,3,5,6,7,8},{4}}
[6,5,2,4,8,7,1,3]=>{{1,6,7},{2,3,5,8},{4}}
[8,5,2,4,1,3,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[5,1,2,4,3,6,8,7]=>{{1,2,3,5},{4},{6},{7,8}}
[8,6,2,7,5,3,1,4]=>{{1,4,7,8},{2,3,6},{5}}
[4,3,8,1,5,2,6,7]=>{{1,4},{2,3,6,7,8},{5}}
[4,1,3,6,7,2,8,5]=>{{1,2,4,6},{3},{5,7,8}}
[7,8,1,6,5,2,4,3]=>{{1,2,3,4,6,7,8},{5}}
[7,4,8,6,5,1,2,3]=>{{1,2,4,6,7},{3,8},{5}}
[3,7,8,6,5,1,2,4]=>{{1,3,4,6,8},{2,7},{5}}
[8,4,5,7,2,6,3,1]=>{{1,8},{2,3,4,5,7},{6}}
[4,5,8,2,7,3,1,6]=>{{1,2,4,5,7},{3,6,8}}
[6,5,8,2,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,2,7,3,1,5]=>{{1,3,5,6,7,8},{2,4}}
[7,8,1,3,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,5,7,8,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,7,3,4,2,6,8,1]=>{{1,2,5,7,8},{3},{4},{6}}
[5,7,4,2,3,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[5,4,7,3,2,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[6,8,3,2,4,5,1,7]=>{{1,2,4,5,6,7,8},{3}}
[5,8,3,4,6,1,2,7]=>{{1,5,6},{2,7,8},{3},{4}}
[6,4,3,8,5,1,2,7]=>{{1,6},{2,4,7,8},{3},{5}}
[6,4,8,2,3,5,1,7]=>{{1,3,5,6,7,8},{2,4}}
[5,4,6,8,2,3,1,7]=>{{1,2,4,5,7,8},{3,6}}
[5,6,8,4,1,2,3,7]=>{{1,5},{2,6},{3,7,8},{4}}
[6,4,8,5,1,2,3,7]=>{{1,2,4,5,6},{3,7,8}}
[7,4,8,3,1,2,5,6]=>{{1,5,7},{2,3,4,6,8}}
[5,7,8,2,3,1,4,6]=>{{1,3,5,6,8},{2,4,7}}
[5,4,7,8,2,1,3,6]=>{{1,2,4,5,6,8},{3,7}}
[5,8,6,3,1,2,4,7]=>{{1,5},{2,3,4,6,7,8}}
[6,8,5,2,1,3,4,7]=>{{1,3,5,6},{2,4,7,8}}
[5,6,1,3,2,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,3,8,1,2,5,7,6]=>{{1,4},{2,3,5,6,8},{7}}
[4,6,3,2,8,5,7,1]=>{{1,2,4,5,6,8},{3},{7}}
[5,3,7,2,1,8,6,4]=>{{1,5},{2,3,4,6,7,8}}
[5,4,8,3,7,2,1,6]=>{{1,5,7},{2,3,4,6,8}}
[3,6,8,5,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[6,1,5,4,7,2,8,3]=>{{1,2,6},{3,5,7,8},{4}}
[5,4,8,3,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,7,2,1,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,4,3,7,8,2,1,6]=>{{1,2,4,5,6,7,8},{3}}
[1,4,8,6,3,2,7,5]=>{{1},{2,4,6},{3,5,8},{7}}
[4,1,8,6,2,5,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[6,7,2,5,3,8,4,1]=>{{1,6,8},{2,3,4,5,7}}
[6,3,4,8,1,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[2,6,3,1,5,8,7,4]=>{{1,2,4,6,8},{3},{5},{7}}
[7,1,3,2,6,5,8,4]=>{{1,2,4,7,8},{3},{5,6}}
[6,1,3,5,8,7,4,2]=>{{1,2,4,5,6,7,8},{3}}
[3,5,8,7,4,6,2,1]=>{{1,3,8},{2,4,5,7},{6}}
[6,8,5,7,3,4,2,1]=>{{1,2,4,6,7,8},{3,5}}
[5,3,6,8,4,2,1,7]=>{{1,4,5,7,8},{2,3,6}}
[5,1,6,8,4,7,3,2]=>{{1,2,4,5,8},{3,6,7}}
[6,2,8,3,4,1,5,7]=>{{1,6},{2},{3,4,5,7,8}}
[2,4,1,8,7,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[1,3,5,8,4,7,2,6]=>{{1},{2,3,4,5,6,7,8}}
[2,3,8,7,5,1,6,4]=>{{1,2,3,4,6,7,8},{5}}
[8,5,4,7,6,1,3,2]=>{{1,2,5,6,8},{3,4,7}}
[5,8,7,2,4,1,3,6]=>{{1,2,4,5,6,8},{3,7}}
[4,1,3,5,6,2,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[6,3,8,5,1,7,4,2]=>{{1,4,5,6,7},{2,3,8}}
[8,2,4,6,1,3,7,5]=>{{1,5,8},{2},{3,4,6},{7}}
[6,4,8,7,3,5,2,1]=>{{1,3,5,6,8},{2,4,7}}
[8,2,3,5,6,1,4,7]=>{{1,4,5,6,7,8},{2},{3}}
[4,3,5,6,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[8,2,3,4,6,1,7,5]=>{{1,5,6,8},{2},{3},{4},{7}}
[1,7,4,3,5,2,8,6]=>{{1},{2,6,7,8},{3,4},{5}}
[2,7,4,3,8,1,5,6]=>{{1,2,5,6,7,8},{3,4}}
[3,8,2,7,6,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,2,1,8,4,7]=>{{1,5},{2,3,4,6,7,8}}
[4,3,8,6,2,7,1,5]=>{{1,4,6,7},{2,3,5,8}}
[8,2,1,4,6,3,7,5]=>{{1,3,5,6,8},{2},{4},{7}}
[3,1,6,8,2,7,5,4]=>{{1,2,3,5,6,7},{4,8}}
[5,3,8,6,7,2,1,4]=>{{1,5,7},{2,3,4,6,8}}
[5,8,7,2,4,6,1,3]=>{{1,2,3,4,5,7,8},{6}}
[1,5,2,8,7,6,4,3]=>{{1},{2,3,4,5,7,8},{6}}
[2,7,1,4,6,5,3,8]=>{{1,2,3,7},{4},{5,6},{8}}
[4,7,1,2,6,5,8,3]=>{{1,2,3,4,7,8},{5,6}}
[4,2,5,6,8,7,3,1]=>{{1,3,4,5,6,7,8},{2}}
[6,5,8,3,7,4,2,1]=>{{1,3,4,6,8},{2,5,7}}
[8,2,5,1,6,3,7,4]=>{{1,4,8},{2},{3,5,6},{7}}
[8,3,4,5,1,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[7,8,1,3,5,4,6,2]=>{{1,3,4,6,7},{2,8},{5}}
[3,5,7,6,4,8,1,2]=>{{1,3,7},{2,4,5,6,8}}
[1,3,7,8,5,4,6,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,3,2,7,8,5,4,6]=>{{1},{2,3},{4,7},{5,6,8}}
[1,5,7,6,8,3,4,2]=>{{1},{2,5,8},{3,4,6,7}}
[6,5,8,4,3,7,1,2]=>{{1,6,7},{2,3,5,8},{4}}
[6,7,3,1,5,2,4,8]=>{{1,2,4,6,7},{3},{5},{8}}
[5,2,4,1,8,3,6,7]=>{{1,3,4,5,6,7,8},{2}}
[2,1,7,4,3,8,5,6]=>{{1,2},{3,5,7},{4},{6,8}}
[7,2,3,8,5,4,1,6]=>{{1,7},{2},{3},{4,6,8},{5}}
[4,1,5,7,6,3,8,2]=>{{1,2,4,7,8},{3,5,6}}
[1,4,8,2,3,6,5,7]=>{{1},{2,4},{3,5,7,8},{6}}
[1,4,6,7,3,5,2,8]=>{{1},{2,4,7},{3,5,6},{8}}
[1,7,3,2,4,5,6,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,7,3,2,4,5,8,6]=>{{1},{2,4,5,6,7,8},{3}}
[1,6,4,3,2,5,7,8]=>{{1},{2,5,6},{3,4},{7},{8}}
[4,2,6,5,3,1,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[5,2,1,6,8,7,4,3]=>{{1,3,5,8},{2},{4,6,7}}
[1,3,5,8,6,2,7,4]=>{{1},{2,3,5,6},{4,8},{7}}
[3,7,8,5,4,2,6,1]=>{{1,3,8},{2,6,7},{4,5}}
[8,3,2,7,5,6,1,4]=>{{1,4,7,8},{2,3},{5},{6}}
[1,3,8,5,7,4,2,6]=>{{1},{2,3,4,5,6,7,8}}
[1,2,3,7,5,4,6,8]=>{{1},{2},{3},{4,6,7},{5},{8}}
[1,4,2,8,6,3,5,7]=>{{1},{2,3,4,5,6,7,8}}
[2,8,6,3,5,7,4,1]=>{{1,2,8},{3,4,6,7},{5}}
[6,1,8,2,5,3,4,7]=>{{1,2,3,4,6,7,8},{5}}
[1,5,4,2,3,6,8,7]=>{{1},{2,3,4,5},{6},{7,8}}
[6,1,5,2,3,4,8,7]=>{{1,2,4,6},{3,5},{7,8}}
[3,1,2,4,8,6,7,5]=>{{1,2,3},{4},{5,8},{6},{7}}
[3,1,2,5,8,7,4,6]=>{{1,2,3},{4,5,6,7,8}}
[6,5,2,1,8,4,7,3]=>{{1,4,6},{2,3,5,8},{7}}
[5,6,2,4,3,8,1,7]=>{{1,2,3,5,6,7,8},{4}}
[3,7,5,2,8,1,4,6]=>{{1,3,5,6,8},{2,4,7}}
[5,1,4,7,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,1,5,8,6,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,6,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,3,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[6,4,7,5,3,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,8,3,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,3,5,1,8,7,2,6]=>{{1,4},{2,3,5,6,7,8}}
[2,5,3,6,1,8,4,7]=>{{1,2,5},{3},{4,6,7,8}}
[2,5,6,8,3,1,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[7,1,4,5,3,6,2,8]=>{{1,2,7},{3,4,5},{6},{8}}
[1,7,2,4,5,3,6,8]=>{{1},{2,3,6,7},{4},{5},{8}}
[1,7,4,5,3,2,6,8]=>{{1},{2,6,7},{3,4,5},{8}}
[1,6,4,7,3,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,5,6,4,8,2,1,7]=>{{1,2,3,5,6,7,8},{4}}
[1,6,4,7,5,2,3,8]=>{{1},{2,6},{3,4,7},{5},{8}}
[1,5,2,6,7,4,3,8]=>{{1},{2,3,5,7},{4,6},{8}}
[8,5,6,1,4,3,7,2]=>{{1,2,4,5,8},{3,6},{7}}
[2,5,4,7,8,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[6,4,5,8,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,1,3,2,5,7,4]=>{{1,3,4,8},{2,5,6},{7}}
[7,5,8,1,4,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[4,2,6,7,8,1,5,3]=>{{1,3,4,5,6,7,8},{2}}
[3,4,6,7,8,1,5,2]=>{{1,3,6},{2,4,5,7,8}}
[4,7,3,8,5,1,6,2]=>{{1,2,4,6,7,8},{3},{5}}
[4,3,2,7,5,8,1,6]=>{{1,4,7},{2,3},{5},{6,8}}
[4,8,5,3,2,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[2,8,4,5,3,6,1,7]=>{{1,2,7,8},{3,4,5},{6}}
[8,1,5,3,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[7,8,4,1,3,6,5,2]=>{{1,3,4,5,7},{2,8},{6}}
[8,6,1,3,2,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,2,4,1,6,5]=>{{1,6,7},{2,3,4,5,8}}
[6,2,3,7,8,1,5,4]=>{{1,6},{2},{3},{4,5,7,8}}
[6,3,7,8,1,5,4,2]=>{{1,5,6},{2,3,4,7,8}}
[2,6,3,7,8,1,5,4]=>{{1,2,6},{3},{4,5,7,8}}
[7,5,8,1,6,4,2,3]=>{{1,2,4,5,6,7},{3,8}}
[8,1,4,3,7,5,6,2]=>{{1,2,8},{3,4},{5,6,7}}
[1,4,8,5,3,2,6,7]=>{{1},{2,3,4,5,6,7,8}}
[8,2,7,6,4,1,5,3]=>{{1,3,4,5,6,7,8},{2}}
[2,7,4,3,8,5,1,6]=>{{1,2,7},{3,4},{5,6,8}}
[6,8,2,7,3,1,5,4]=>{{1,6},{2,3,4,5,7,8}}
[8,2,6,3,4,1,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[6,1,2,8,5,3,7,4]=>{{1,2,3,6},{4,8},{5},{7}}
[4,1,5,8,3,6,7,2]=>{{1,2,4,8},{3,5},{6},{7}}
[7,5,2,8,1,6,3,4]=>{{1,2,3,5,7},{4,8},{6}}
[4,8,5,7,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,2,1,5,8,6]=>{{1,3,5,6,7,8},{2,4}}
[4,8,2,7,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,7,4,6,3,5]=>{{1,3,4,5,7,8},{2},{6}}
[4,2,5,8,3,6,7,1]=>{{1,4,8},{2},{3,5},{6},{7}}
[5,1,6,8,3,2,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[4,1,5,6,8,2,7,3]=>{{1,2,4,6},{3,5,8},{7}}
[4,5,2,8,7,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,3,1,6,7,2]=>{{1,3,4,5},{2,8},{6},{7}}
[6,2,3,1,7,8,5,4]=>{{1,4,6,8},{2},{3},{5,7}}
[5,2,3,6,8,4,7,1]=>{{1,5,8},{2},{3},{4,6},{7}}
[6,2,1,7,8,4,3,5]=>{{1,3,4,6,7},{2},{5,8}}
[5,2,1,3,8,4,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[5,2,7,8,4,1,6,3]=>{{1,3,4,5,6,7,8},{2}}
[6,2,7,8,3,5,4,1]=>{{1,3,4,5,6,7,8},{2}}
[5,2,8,6,4,1,7,3]=>{{1,4,5,6},{2},{3,8},{7}}
[5,1,2,8,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[6,7,8,3,2,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,2,6,4,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,2,3,4,7,8,5,1]=>{{1,6,8},{2},{3},{4},{5,7}}
[7,2,1,8,4,3,5,6]=>{{1,3,4,5,6,7,8},{2}}
[6,2,1,3,7,5,8,4]=>{{1,3,4,5,6,7,8},{2}}
[6,8,7,3,4,5,1,2]=>{{1,3,4,5,6,7},{2,8}}
[6,2,3,7,8,1,4,5]=>{{1,6},{2},{3},{4,7},{5,8}}
[7,4,3,2,5,8,1,6]=>{{1,7},{2,4},{3},{5},{6,8}}
[7,2,4,3,5,8,1,6]=>{{1,7},{2},{3,4},{5},{6,8}}
[1,7,6,4,2,3,5,8]=>{{1},{2,5,7},{3,6},{4},{8}}
[1,3,2,5,8,6,4,7]=>{{1},{2,3},{4,5,7,8},{6}}
[6,1,4,7,2,8,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,6,7,2,4,8,5,3]=>{{1},{2,3,4,5,6,7,8}}
[5,7,2,4,3,6,8,1]=>{{1,2,3,5,7,8},{4},{6}}
[5,7,3,4,6,2,8,1]=>{{1,2,5,6,7,8},{3},{4}}
[2,8,3,6,1,7,4,5]=>{{1,2,5,8},{3},{4,6,7}}
[4,3,1,8,5,2,6,7]=>{{1,2,3,4,6,7,8},{5}}
[1,8,4,5,6,2,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[7,3,8,2,1,4,5,6]=>{{1,5,7},{2,3,4,6,8}}
[8,2,5,3,1,7,4,6]=>{{1,3,4,5,6,7,8},{2}}
[6,3,5,8,1,7,4,2]=>{{1,2,3,4,5,6,7,8}}
[3,5,4,8,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[7,5,2,3,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,1,4,8,3,6]=>{{1,2,3,4,5,7},{6,8}}
[5,7,6,1,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,5,1,8,2,3]=>{{1,2,4,5,7},{3,6,8}}
[7,1,3,2,6,8,4,5]=>{{1,2,4,7},{3},{5,6,8}}
[4,3,5,2,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,7,3,8,2,4,6,5]=>{{1},{2,4,5,6,7,8},{3}}
[2,7,4,8,5,3,1,6]=>{{1,2,7},{3,4,6,8},{5}}
[6,1,3,8,4,2,7,5]=>{{1,2,6},{3},{4,5,8},{7}}
[5,4,1,8,6,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[5,4,6,8,1,3,2,7]=>{{1,5},{2,4,7,8},{3,6}}
[3,6,1,5,8,4,7,2]=>{{1,3},{2,4,5,6,8},{7}}
[6,4,8,3,5,7,2,1]=>{{1,2,3,4,6,7,8},{5}}
[3,5,8,2,4,1,7,6]=>{{1,3,6,8},{2,4,5},{7}}
[7,2,8,4,1,3,6,5]=>{{1,3,5,6,7,8},{2},{4}}
[5,8,1,2,4,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,3,5,7,2,6,1]=>{{1,8},{2,4,5,6,7},{3}}
[4,1,5,2,3,8,7,6]=>{{1,2,4},{3,5},{6,8},{7}}
[6,3,5,8,2,4,7,1]=>{{1,4,6,8},{2,3,5},{7}}
[2,8,7,1,4,6,3,5]=>{{1,2,4,5,8},{3,7},{6}}
[1,8,5,3,7,4,2,6]=>{{1},{2,3,4,5,6,7,8}}
[7,5,6,2,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,2,8,1,4,3]=>{{1,3,5,6,8},{2,4,7}}
[6,3,8,1,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[7,6,4,8,5,3,2,1]=>{{1,2,3,4,6,7,8},{5}}
[1,5,7,2,4,3,6,8]=>{{1},{2,4,5},{3,6,7},{8}}
[1,6,5,3,2,4,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,7,2,4,6,5,3,8]=>{{1},{2,3,7},{4},{5,6},{8}}
[1,4,7,2,6,5,3,8]=>{{1},{2,4},{3,7},{5,6},{8}}
[1,2,6,8,7,4,3,5]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,7,4,3,5,8,6]=>{{1},{2},{3,5,6,7,8},{4}}
[1,6,2,8,7,4,3,5]=>{{1},{2,3,4,5,6,7,8}}
[1,7,4,2,3,5,8,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,2,3,6,4,7]=>{{1},{2,4,7,8},{3,5},{6}}
[1,7,4,8,5,2,3,6]=>{{1},{2,3,4,6,7,8},{5}}
[1,4,7,5,2,8,6,3]=>{{1},{2,4,5},{3,6,7,8}}
[1,6,3,7,4,2,8,5]=>{{1},{2,6},{3},{4,5,7,8}}
[1,8,5,2,7,4,3,6]=>{{1},{2,4,6,8},{3,5,7}}
[1,4,8,7,5,3,2,6]=>{{1},{2,4,7},{3,6,8},{5}}
[1,2,5,8,6,3,7,4]=>{{1},{2},{3,5,6},{4,8},{7}}
[1,2,4,7,5,8,6,3]=>{{1},{2},{3,4,6,7,8},{5}}
[1,5,8,7,6,2,4,3]=>{{1},{2,5,6},{3,8},{4,7}}
[1,3,5,8,7,6,2,4]=>{{1},{2,3,5,7},{4,8},{6}}
[1,5,2,4,3,6,8,7]=>{{1},{2,3,5},{4},{6},{7,8}}
[1,6,8,7,5,3,2,4]=>{{1},{2,3,4,6,7,8},{5}}
[1,2,5,7,4,3,8,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,5,3,2,6,8,7,4]=>{{1},{2,4,5,6,8},{3},{7}}
[1,4,2,6,8,7,5,3]=>{{1},{2,3,4,5,6,7,8}}
[1,5,8,6,3,2,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[1,8,5,2,6,3,4,7]=>{{1},{2,4,7,8},{3,5,6}}
[1,7,4,6,3,2,8,5]=>{{1},{2,3,4,5,6,7,8}}
[1,6,3,2,8,5,4,7]=>{{1},{2,4,5,6,7,8},{3}}
[1,3,8,6,4,2,5,7]=>{{1},{2,3,4,5,6,7,8}}
[1,5,7,4,2,3,8,6]=>{{1},{2,5},{3,6,7,8},{4}}
[6,3,7,5,4,2,8,1]=>{{1,2,3,6,7,8},{4,5}}
[7,5,2,6,3,4,8,1]=>{{1,7,8},{2,3,5},{4,6}}
[3,8,2,7,5,4,1,6]=>{{1,2,3,4,6,7,8},{5}}
[5,4,8,6,7,1,2,3]=>{{1,2,4,5,6,7},{3,8}}
[2,7,3,6,8,5,4,1]=>{{1,2,4,5,6,7,8},{3}}
[3,7,2,8,1,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[8,5,2,4,6,7,3,1]=>{{1,8},{2,3,5,6,7},{4}}
[2,5,8,7,1,4,3,6]=>{{1,2,5},{3,4,6,7,8}}
[3,4,6,5,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,2,4,1,6,7,8,3]=>{{1,3,4,5,6,7,8},{2}}
[5,2,8,6,4,7,1,3]=>{{1,4,5,6,7},{2},{3,8}}
[6,1,3,4,7,2,8,5]=>{{1,2,6},{3},{4},{5,7,8}}
[8,4,7,2,5,3,1,6]=>{{1,3,6,7,8},{2,4},{5}}
[8,3,4,5,2,1,7,6]=>{{1,6,8},{2,3,4,5},{7}}
[8,6,1,4,7,3,5,2]=>{{1,2,3,6,8},{4},{5,7}}
[5,3,6,7,2,8,4,1]=>{{1,2,3,5,6,8},{4,7}}
[5,3,6,7,2,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[8,6,1,4,7,5,2,3]=>{{1,3,8},{2,5,6,7},{4}}
[1,5,8,2,6,7,4,3]=>{{1},{2,4,5,6,7},{3,8}}
[7,1,3,6,5,2,8,4]=>{{1,2,4,6,7,8},{3},{5}}
[8,2,1,4,5,7,6,3]=>{{1,3,8},{2},{4},{5},{6,7}}
[1,4,7,5,2,3,8,6]=>{{1},{2,4,5},{3,6,7,8}}
[6,1,7,5,4,2,8,3]=>{{1,2,6},{3,7,8},{4,5}}
[2,7,3,6,5,1,8,4]=>{{1,2,4,6,7,8},{3},{5}}
[8,6,5,1,3,7,4,2]=>{{1,2,4,6,7,8},{3,5}}
[5,7,6,2,4,8,1,3]=>{{1,2,4,5,7},{3,6,8}}
[3,7,5,6,4,8,1,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,1,3,5,4,2]=>{{1,4,7},{2,3,5,6,8}}
[2,8,4,6,1,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[2,8,6,4,7,3,5,1]=>{{1,2,8},{3,6},{4},{5,7}}
[8,7,1,4,6,5,3,2]=>{{1,2,3,7,8},{4},{5,6}}
[3,5,8,6,7,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[1,2,4,6,8,5,3,7]=>{{1},{2},{3,4,5,6,7,8}}
[3,1,5,8,6,2,4,7]=>{{1,2,3,5,6},{4,7,8}}
[2,5,4,6,8,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,4,7,8,1,3]=>{{1,2,3,5,6,7,8},{4}}
[7,2,5,8,6,4,1,3]=>{{1,7},{2},{3,4,5,6,8}}
[5,2,8,3,4,7,6,1]=>{{1,3,4,5,8},{2},{6,7}}
[2,4,3,8,7,1,6,5]=>{{1,2,4,5,6,7,8},{3}}
[1,5,8,7,4,2,6,3]=>{{1},{2,4,5,6,7},{3,8}}
[6,8,7,5,4,3,1,2]=>{{1,3,6,7},{2,8},{4,5}}
[5,3,4,8,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[3,4,5,8,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[5,4,2,3,6,1,8,7]=>{{1,5,6},{2,3,4},{7,8}}
[5,1,7,4,3,6,8,2]=>{{1,2,3,5,7,8},{4},{6}}
[4,3,7,6,8,2,1,5]=>{{1,2,3,4,6,7},{5,8}}
[8,1,4,7,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[6,1,8,5,2,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,2,6,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,7,1,6,4,5,2,3]=>{{1,3,8},{2,7},{4,5,6}}
[5,4,1,3,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,4,7,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,7,5,2,4,6]=>{{1,2,3,6,8},{4,7},{5}}
[6,5,8,7,2,4,3,1]=>{{1,3,4,6,7,8},{2,5}}
[4,3,6,5,8,2,1,7]=>{{1,4,5,7,8},{2,3,6}}
[7,6,3,2,8,5,4,1]=>{{1,2,4,5,6,7,8},{3}}
[4,3,7,1,8,5,2,6]=>{{1,4},{2,3,7},{5,6,8}}
[3,2,8,5,6,7,1,4]=>{{1,3,4,5,6,7,8},{2}}
[8,3,2,1,4,7,5,6]=>{{1,4,5,6,7,8},{2,3}}
[4,7,3,1,8,5,2,6]=>{{1,4},{2,7},{3},{5,6,8}}
[3,7,8,2,5,6,1,4]=>{{1,2,3,4,7,8},{5},{6}}
[7,5,1,4,2,3,6,8]=>{{1,3,6,7},{2,5},{4},{8}}
[7,8,6,1,2,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,5,3,4,7,8,6,2]=>{{1},{2,5,6,7,8},{3},{4}}
[5,1,2,4,7,8,6,3]=>{{1,2,3,5,6,7,8},{4}}
[5,1,7,8,6,2,3,4]=>{{1,2,5,6},{3,7},{4,8}}
[8,5,1,6,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,2,4,6,8,3]=>{{1,3,7,8},{2,4,5},{6}}
[6,1,5,2,7,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[7,1,2,6,4,5,8,3]=>{{1,2,3,7,8},{4,5,6}}
[1,7,3,6,4,5,8,2]=>{{1},{2,7,8},{3},{4,5,6}}
[1,8,3,6,4,5,7,2]=>{{1},{2,8},{3},{4,5,6},{7}}
[8,1,6,2,7,3,4,5]=>{{1,2,4,5,7,8},{3,6}}
[7,1,6,2,5,3,4,8]=>{{1,2,4,7},{3,6},{5},{8}}
[8,1,6,2,5,3,4,7]=>{{1,2,4,7,8},{3,6},{5}}
[8,1,7,2,5,3,4,6]=>{{1,2,3,4,6,7,8},{5}}
[8,1,2,7,4,5,6,3]=>{{1,2,3,8},{4,5,6,7}}
[1,8,3,7,4,5,6,2]=>{{1},{2,8},{3},{4,5,6,7}}
[8,1,6,7,5,2,3,4]=>{{1,2,3,4,6,7,8},{5}}
[7,3,1,2,6,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[3,1,2,8,5,6,7,4]=>{{1,2,3},{4,8},{5},{6},{7}}
[6,3,1,2,7,4,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[6,1,7,4,2,3,5,8]=>{{1,2,3,5,6,7},{4},{8}}
[1,7,3,4,6,8,5,2]=>{{1},{2,5,6,7,8},{3},{4}}
[1,7,3,8,4,5,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,1,8,2,5,3,4,6]=>{{1,2,4,7},{3,6,8},{5}}
[6,1,7,2,5,3,4,8]=>{{1,2,3,4,6,7},{5},{8}}
[5,1,7,2,6,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[5,1,8,2,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,3,7,4,5,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,4,7,3,5,1,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,4,8,6,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,7,5,4,1,6,8]=>{{1,2,3,6,7},{4,5},{8}}
[3,4,6,2,1,5,8,7]=>{{1,3,5,6},{2,4},{7,8}}
[3,4,7,2,1,6,5,8]=>{{1,3,5,7},{2,4},{6},{8}}
[2,6,8,3,5,1,4,7]=>{{1,2,6},{3,4,7,8},{5}}
[2,3,6,1,5,8,4,7]=>{{1,2,3,4,6,7,8},{5}}
[2,3,7,1,6,5,8,4]=>{{1,2,3,4,7,8},{5,6}}
[2,4,7,1,3,6,8,5]=>{{1,2,4},{3,5,7,8},{6}}
[5,4,7,8,1,3,2,6]=>{{1,5},{2,3,4,6,7,8}}
[2,5,7,1,4,6,3,8]=>{{1,2,4,5},{3,7},{6},{8}}
[2,4,7,1,6,3,5,8]=>{{1,2,4},{3,5,6,7},{8}}
[2,3,7,1,6,5,4,8]=>{{1,2,3,4,7},{5,6},{8}}
[2,5,7,1,4,3,6,8]=>{{1,2,4,5},{3,6,7},{8}}
[2,5,7,3,1,4,6,8]=>{{1,2,5},{3,4,6,7},{8}}
[3,4,7,2,1,6,8,5]=>{{1,3,5,7,8},{2,4},{6}}
[4,6,3,7,1,5,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,7,3,2,8,1,4,6]=>{{1,5,6,8},{2,4,7},{3}}
[2,6,5,7,1,8,4,3]=>{{1,2,3,5,6,8},{4,7}}
[3,6,8,5,4,1,7,2]=>{{1,2,3,6,8},{4,5},{7}}
[5,4,7,8,1,3,6,2]=>{{1,5},{2,4,8},{3,6,7}}
[2,5,7,1,4,6,8,3]=>{{1,2,4,5},{3,7,8},{6}}
[2,4,7,1,6,3,8,5]=>{{1,2,4},{3,5,6,7,8}}
[2,4,7,1,6,8,3,5]=>{{1,2,4},{3,7},{5,6,8}}
[8,6,5,1,2,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[7,6,1,4,2,3,5,8]=>{{1,2,3,5,6,7},{4},{8}}
[6,5,1,4,8,3,2,7]=>{{1,3,6},{2,5,7,8},{4}}
[8,7,5,1,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,2,5,3,6,7]=>{{1,3,6,7,8},{2,4},{5}}
[8,7,5,1,4,2,6,3]=>{{1,3,4,5,8},{2,6,7}}
[8,6,1,4,2,5,3,7]=>{{1,3,7,8},{2,5,6},{4}}
[8,7,1,4,3,2,6,5]=>{{1,3,5,8},{2,6,7},{4}}
[2,8,3,7,4,5,6,1]=>{{1,2,8},{3},{4,5,6,7}}
[8,7,5,2,4,3,6,1]=>{{1,8},{2,3,4,5,6,7}}
[4,2,5,7,3,1,6,8]=>{{1,4,6,7},{2},{3,5},{8}}
[8,2,4,5,3,1,6,7]=>{{1,6,7,8},{2},{3,4,5}}
[8,4,5,1,3,2,6,7]=>{{1,2,4,6,7,8},{3,5}}
[4,3,7,5,2,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[1,6,7,4,3,2,5,8]=>{{1},{2,6},{3,5,7},{4},{8}}
[1,4,5,7,3,2,6,8]=>{{1},{2,4,6,7},{3,5},{8}}
[3,5,1,4,7,2,6,8]=>{{1,3},{2,5,6,7},{4},{8}}
[2,5,1,4,7,8,3,6]=>{{1,2,3,5,7},{4},{6,8}}
[4,3,7,1,5,2,6,8]=>{{1,4},{2,3,6,7},{5},{8}}
[3,5,1,6,4,2,7,8]=>{{1,3},{2,4,5,6},{7},{8}}
[6,4,3,1,7,2,5,8]=>{{1,2,4,6},{3},{5,7},{8}}
[6,2,7,4,3,1,5,8]=>{{1,6},{2},{3,5,7},{4},{8}}
[2,6,4,1,7,3,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[6,3,2,7,4,5,1,8]=>{{1,4,5,6,7},{2,3},{8}}
[7,2,4,1,3,6,8,5]=>{{1,3,4,5,7,8},{2},{6}}
[6,3,2,5,7,1,4,8]=>{{1,6},{2,3},{4,5,7},{8}}
[3,2,6,5,7,1,4,8]=>{{1,3,6},{2},{4,5,7},{8}}
[1,7,3,2,5,6,4,8]=>{{1},{2,4,7},{3},{5},{6},{8}}
[2,1,7,3,5,6,8,4]=>{{1,2},{3,4,7,8},{5},{6}}
[2,1,6,3,5,7,8,4]=>{{1,2},{3,4,6,7,8},{5}}
[1,6,3,2,5,7,4,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[1,4,6,5,2,7,3,8]=>{{1},{2,4,5},{3,6,7},{8}}
[5,6,2,1,4,3,7,8]=>{{1,4,5},{2,3,6},{7},{8}}
[2,5,1,6,4,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,5,4,1,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[4,6,1,5,2,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[1,6,5,3,7,2,4,8]=>{{1},{2,6},{3,4,5,7},{8}}
[1,2,5,3,4,8,7,6]=>{{1},{2},{3,4,5},{6,8},{7}}
[5,2,7,6,1,8,4,3]=>{{1,5},{2},{3,4,6,7,8}}
[5,8,2,6,1,7,4,3]=>{{1,5},{2,3,8},{4,6,7}}
[1,5,8,3,6,2,7,4]=>{{1},{2,5,6},{3,4,8},{7}}
[1,2,6,4,7,3,8,5]=>{{1},{2},{3,6},{4},{5,7,8}}
[1,2,7,8,3,5,6,4]=>{{1},{2},{3,5,6,7},{4,8}}
[2,7,4,5,8,1,6,3]=>{{1,2,6,7},{3,4,5,8}}
[2,6,1,8,5,4,3,7]=>{{1,2,3,4,6,7,8},{5}}
[5,8,6,2,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,2,1,4,3,7]=>{{1,5},{2,3,4,6,7,8}}
[4,5,8,6,2,1,3,7]=>{{1,4,6},{2,5},{3,7,8}}
[6,4,7,5,8,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,4,2,5,8,1]=>{{1,2,3,5,6,7,8},{4}}
[7,5,6,2,4,3,8,1]=>{{1,7,8},{2,4,5},{3,6}}
[4,6,2,5,7,3,8,1]=>{{1,4,5,7,8},{2,3,6}}
[4,2,8,5,3,6,1,7]=>{{1,3,4,5,7,8},{2},{6}}
[8,1,7,4,5,6,2,3]=>{{1,2,3,7,8},{4},{5},{6}}
[2,1,7,8,4,5,6,3]=>{{1,2},{3,4,5,6,7,8}}
[8,2,1,4,3,7,6,5]=>{{1,3,5,8},{2},{4},{6,7}}
[7,6,5,3,1,2,8,4]=>{{1,3,4,5,7,8},{2,6}}
[5,4,1,6,2,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[6,2,3,1,7,8,4,5]=>{{1,4,5,6,7,8},{2},{3}}
[3,1,8,6,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[4,2,5,1,8,6,7,3]=>{{1,4},{2},{3,5,8},{6},{7}}
[4,5,3,7,1,6,8,2]=>{{1,2,4,5,7,8},{3},{6}}
[4,2,8,5,3,6,7,1]=>{{1,3,4,5,8},{2},{6},{7}}
[2,8,6,3,5,4,7,1]=>{{1,2,8},{3,4,6},{5},{7}}
[3,5,2,8,6,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,3,5,1,6,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[5,1,4,7,2,6,8,3]=>{{1,2,5},{3,4,7,8},{6}}
[1,8,2,5,6,4,7,3]=>{{1},{2,3,8},{4,5,6},{7}}
[2,7,1,4,8,5,6,3]=>{{1,2,3,5,6,7,8},{4}}
[2,8,4,6,1,3,7,5]=>{{1,2,5,8},{3,4,6},{7}}
[8,4,6,2,5,3,7,1]=>{{1,8},{2,4},{3,6},{5},{7}}
[8,3,7,6,2,1,5,4]=>{{1,4,6,8},{2,3,5,7}}
[8,5,2,7,6,1,4,3]=>{{1,2,3,5,6,8},{4,7}}
[5,8,2,7,6,1,4,3]=>{{1,5,6},{2,3,8},{4,7}}
[8,3,7,6,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,6,5,1,4,2]=>{{1,4,6,7},{2,3,8},{5}}
[2,6,3,7,5,4,8,1]=>{{1,2,4,6,7,8},{3},{5}}
[5,4,7,1,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[2,8,5,1,4,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,2,6,5,8,4,3,1]=>{{1,3,4,5,6,7,8},{2}}
[5,8,2,3,4,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[6,1,3,4,2,5,7,8]=>{{1,2,5,6},{3},{4},{7},{8}}
[1,5,6,3,2,4,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[6,3,5,2,4,1,7,8]=>{{1,6},{2,3,4,5},{7},{8}}
[7,8,3,5,2,4,6,1]=>{{1,2,4,5,6,7,8},{3}}
[2,4,5,7,3,6,1,8]=>{{1,2,4,7},{3,5},{6},{8}}
[2,5,3,1,6,4,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[6,5,1,3,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,7,4,3,2,6,1,8]=>{{1,2,5,7},{3,4},{6},{8}}
[6,8,7,4,3,5,1,2]=>{{1,3,5,6,7},{2,8},{4}}
[2,6,7,8,4,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[1,7,8,4,5,3,6,2]=>{{1},{2,3,6,7,8},{4},{5}}
[7,1,8,5,3,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,2,1,6,3,8]=>{{1,5},{2,3,4,7},{6},{8}}
[5,1,4,7,3,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}
[7,4,8,6,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[4,7,6,3,5,2,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[1,6,5,8,7,4,2,3]=>{{1},{2,3,4,5,6,7,8}}
[6,1,3,8,7,5,2,4]=>{{1,2,5,6,7},{3},{4,8}}
[7,6,2,1,8,3,5,4]=>{{1,4,5,7,8},{2,3,6}}
[7,1,3,6,8,2,5,4]=>{{1,2,4,5,6,7,8},{3}}
[1,7,5,6,8,2,4,3]=>{{1},{2,4,6,7},{3,5,8}}
[3,6,7,5,8,2,4,1]=>{{1,3,4,5,7,8},{2,6}}
[1,7,4,5,2,8,6,3]=>{{1},{2,3,4,5,6,7,8}}
[7,5,4,2,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,6,7,4,2,8,5,1]=>{{1,2,3,5,6,7,8},{4}}
[4,6,3,2,7,8,5,1]=>{{1,2,4,6,8},{3},{5,7}}
[7,6,1,3,4,2,5,8]=>{{1,3,4,5,7},{2,6},{8}}
[7,8,2,6,4,5,3,1]=>{{1,2,3,7,8},{4,5,6}}
[7,2,5,4,6,1,3,8]=>{{1,3,5,6,7},{2},{4},{8}}
[7,1,2,4,5,6,3,8]=>{{1,2,3,7},{4},{5},{6},{8}}
[7,3,2,1,5,6,4,8]=>{{1,4,7},{2,3},{5},{6},{8}}
[3,6,2,1,7,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,6,7,3,1,5,4,8]=>{{1,2,5,6},{3,4,7},{8}}
[2,1,6,4,7,5,3,8]=>{{1,2},{3,5,6,7},{4},{8}}
[7,2,8,5,6,4,3,1]=>{{1,3,7,8},{2},{4,5,6}}
[7,6,8,5,4,1,3,2]=>{{1,2,3,6,7,8},{4,5}}
[7,1,8,4,6,5,3,2]=>{{1,2,3,7,8},{4},{5,6}}
[7,8,6,3,1,5,4,2]=>{{1,3,4,5,6,7},{2,8}}
[7,6,1,4,5,3,2,8]=>{{1,2,3,6,7},{4},{5},{8}}
[7,1,5,6,4,3,2,8]=>{{1,2,7},{3,4,5,6},{8}}
[4,1,3,8,6,2,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[5,6,3,2,8,1,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[8,2,6,3,1,5,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[8,2,5,6,7,4,3,1]=>{{1,8},{2},{3,5,7},{4,6}}
[8,2,5,3,4,7,6,1]=>{{1,8},{2},{3,4,5},{6,7}}
[7,5,3,2,4,1,8,6]=>{{1,6,7,8},{2,4,5},{3}}
[7,1,2,3,6,8,4,5]=>{{1,2,3,4,7},{5,6,8}}
[6,7,2,8,3,4,5,1]=>{{1,4,6,8},{2,3,5,7}}
[3,1,8,4,6,5,7,2]=>{{1,2,3,8},{4},{5,6},{7}}
[6,1,2,3,8,4,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[8,1,6,7,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,4,5,2,3,7]=>{{1,2,3,6,7,8},{4},{5}}
[8,6,4,1,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[8,6,1,4,2,5,7,3]=>{{1,3,8},{2,5,6},{4},{7}}
[8,6,4,2,5,3,7,1]=>{{1,8},{2,3,4,6},{5},{7}}
[8,6,4,1,5,7,2,3]=>{{1,3,4,8},{2,6,7},{5}}
[8,6,1,4,7,2,5,3]=>{{1,3,8},{2,6},{4},{5,7}}
[8,6,4,1,5,2,3,7]=>{{1,3,4,7,8},{2,6},{5}}
[8,6,7,1,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,5,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[8,7,1,4,6,5,2,3]=>{{1,3,8},{2,7},{4},{5,6}}
[8,3,7,6,4,5,1,2]=>{{1,2,3,7,8},{4,5,6}}
[5,3,8,6,4,1,7,2]=>{{1,4,5,6},{2,3,8},{7}}
[7,4,5,1,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,1,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,2,3,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,2,5,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,2,3,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,2,1,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,6,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,5,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,8,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,3,1,6,8,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,7,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[7,3,1,8,6,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,6,4,1,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,8,3,7,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,8,4,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,3,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,6,2,8,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,2,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,8,5,1,2,6]=>{{1,2,3,4,6,7,8},{5}}
[4,7,3,2,5,6,8,1]=>{{1,2,4,7,8},{3},{5},{6}}
[3,2,7,6,4,5,8,1]=>{{1,3,7,8},{2},{4,5,6}}
[1,7,3,6,8,4,2,5]=>{{1},{2,7},{3},{4,6},{5,8}}
[2,3,6,5,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[8,3,1,2,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[1,7,8,2,4,3,5,6]=>{{1},{2,4,5,7},{3,6,8}}
[3,6,4,7,1,2,8,5]=>{{1,3,4,5,7,8},{2,6}}
[5,7,4,8,1,3,2,6]=>{{1,5},{2,7},{3,4,6,8}}
[4,3,7,8,1,5,2,6]=>{{1,4,5,6,8},{2,3,7}}
[8,5,4,2,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[3,2,6,8,7,4,1,5]=>{{1,3,4,5,6,7,8},{2}}
[2,3,7,5,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,2,8,7,4,5]=>{{1,2,3,4,6,7},{5,8}}
[5,2,1,3,8,7,6,4]=>{{1,3,4,5,8},{2},{6,7}}
[7,2,1,5,3,8,4,6]=>{{1,3,4,5,7},{2},{6,8}}
[1,5,8,2,4,3,6,7]=>{{1},{2,4,5},{3,6,7,8}}
[4,3,6,8,1,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[5,4,6,8,3,1,7,2]=>{{1,3,5,6},{2,4,8},{7}}
[3,6,8,4,5,1,7,2]=>{{1,2,3,6,8},{4},{5},{7}}
[8,6,1,7,2,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,3,1,2,8,6,4,5]=>{{1,2,3,4,7},{5,8},{6}}
[2,3,7,6,1,8,5,4]=>{{1,2,3,5,7},{4,6,8}}
[3,2,7,8,6,4,1,5]=>{{1,3,7},{2},{4,5,6,8}}
[6,2,8,3,1,4,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[3,1,2,8,7,4,5,6]=>{{1,2,3},{4,6,8},{5,7}}
[2,1,3,8,7,4,6,5]=>{{1,2},{3},{4,5,6,7,8}}
[2,1,3,8,7,4,5,6]=>{{1,2},{3},{4,6,8},{5,7}}
[1,6,8,3,2,4,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[8,5,1,7,2,4,3,6]=>{{1,3,4,6,7,8},{2,5}}
[8,4,1,7,3,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,1,6,2,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[1,3,2,8,7,6,4,5]=>{{1},{2,3},{4,5,7,8},{6}}
[2,1,3,8,7,6,4,5]=>{{1,2},{3},{4,5,7,8},{6}}
[1,6,3,7,2,5,4,8]=>{{1},{2,5,6},{3},{4,7},{8}}
[1,7,2,4,6,3,5,8]=>{{1},{2,3,5,6,7},{4},{8}}
[5,6,2,8,4,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,8,4,2,1,6,7]=>{{1,3,6,7,8},{2,5},{4}}
[2,5,8,3,1,4,6,7]=>{{1,2,5},{3,4,6,7,8}}
[2,8,1,3,5,7,4,6]=>{{1,2,3,4,6,7,8},{5}}
[5,4,7,8,3,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,4,8,5,7,1,2,6]=>{{1,3,6,8},{2,4,5,7}}
[3,6,8,2,5,1,4,7]=>{{1,2,3,4,6,7,8},{5}}
[3,6,8,7,2,5,4,1]=>{{1,3,8},{2,5,6},{4,7}}
[3,4,6,5,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,6,7,8,3,5,1]=>{{1,2,4,5,7,8},{3,6}}
[1,4,2,5,7,6,3,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,4,2,6,8,5,3,7]=>{{1},{2,3,4,5,6,7,8}}
[1,2,6,8,3,5,4,7]=>{{1},{2},{3,5,6},{4,7,8}}
[1,6,8,3,5,4,2,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,5,3,2,4,6,8,7]=>{{1},{2,4,5},{3},{6},{7,8}}
[1,5,8,7,6,3,2,4]=>{{1},{2,3,4,5,6,7,8}}
[1,5,7,6,3,2,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,3,2,4,7,5,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,6,3,2,4,8,7,5]=>{{1},{2,4,5,6,8},{3},{7}}
[1,2,7,6,4,3,5,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,8,7,5,2,4,6,3]=>{{1},{2,3,4,5,6,7,8}}
[1,7,5,2,4,6,3,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,7,4,2,5,3,6,8]=>{{1},{2,3,4,6,7},{5},{8}}
[1,8,4,7,5,2,6,3]=>{{1},{2,3,4,6,7,8},{5}}
[1,7,5,2,3,6,4,8]=>{{1},{2,4,7},{3,5},{6},{8}}
[1,7,5,2,6,3,4,8]=>{{1},{2,4,7},{3,5,6},{8}}
[1,6,3,7,4,2,5,8]=>{{1},{2,6},{3},{4,5,7},{8}}
[1,6,3,2,7,5,4,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,4,7,5,2,6,3,8]=>{{1},{2,4,5},{3,7},{6},{8}}
[1,3,6,4,8,7,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[1,3,7,6,4,2,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,2,4,8,5,7,6]=>{{1},{2,3},{4},{5,6,8},{7}}
[1,3,8,7,5,2,4,6]=>{{1},{2,3,6,8},{4,7},{5}}
[1,4,6,3,2,7,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,4,6,3,2,8,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[1,5,7,6,4,2,3,8]=>{{1},{2,4,5,6},{3,7},{8}}
[1,6,3,2,8,4,7,5]=>{{1},{2,4,6},{3},{5,8},{7}}
[1,6,3,5,2,7,4,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,6,3,5,2,8,7,4]=>{{1},{2,4,5,6,8},{3},{7}}
[1,8,3,7,5,2,4,6]=>{{1},{2,6,8},{3},{4,7},{5}}
[6,4,7,1,5,3,8,2]=>{{1,2,3,4,6,7,8},{5}}
[5,3,8,2,6,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,3,8,2,6,5,7,1]=>{{1,2,3,4,8},{5,6},{7}}
[5,7,1,4,8,2,3,6]=>{{1,2,3,5,6,7,8},{4}}
[6,5,7,1,4,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,1,2,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[4,8,3,5,7,6,2,1]=>{{1,2,4,5,7,8},{3},{6}}
[1,3,4,2,8,5,7,6]=>{{1},{2,3,4},{5,6,8},{7}}
[5,7,6,2,4,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,5,2,3,8,4,1]=>{{1,6,8},{2,4,7},{3,5}}
[6,7,5,3,8,4,2,1]=>{{1,3,4,5,6,8},{2,7}}
[3,2,1,4,8,5,7,6]=>{{1,3},{2},{4},{5,6,8},{7}}
[7,3,1,4,2,6,5,8]=>{{1,2,3,5,7},{4},{6},{8}}
[7,4,1,6,2,5,3,8]=>{{1,3,7},{2,4,5,6},{8}}
[5,4,1,8,2,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[5,3,1,8,2,6,4,7]=>{{1,2,3,5},{4,7,8},{6}}
[4,7,1,5,2,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[6,5,1,4,2,7,3,8]=>{{1,3,6,7},{2,5},{4},{8}}
[1,8,7,3,4,5,2,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,4,5,2,3,6]=>{{1},{2,6,8},{3,7},{4},{5}}
[1,2,6,8,7,3,4,5]=>{{1},{2},{3,6},{4,5,7,8}}
[1,3,7,8,4,5,6,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,2,3,1,6,5,7]=>{{1,5,7,8},{2,3,4},{6}}
[6,4,5,2,8,1,7,3]=>{{1,6},{2,4},{3,5,8},{7}}
[4,8,6,2,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[6,4,2,1,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[6,4,2,3,5,8,1,7]=>{{1,6,7,8},{2,3,4},{5}}
[2,8,6,4,5,1,7,3]=>{{1,2,3,6,8},{4},{5},{7}}
[8,2,4,6,7,1,5,3]=>{{1,3,4,6,8},{2},{5,7}}
[2,6,3,1,7,4,8,5]=>{{1,2,4,6},{3},{5,7,8}}
[6,5,1,8,3,2,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[1,4,3,7,2,8,6,5]=>{{1},{2,4,5,6,7,8},{3}}
[1,8,7,4,5,3,2,6]=>{{1},{2,3,6,7,8},{4},{5}}
[2,8,3,1,4,5,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[6,1,7,2,8,4,5,3]=>{{1,2,4,6},{3,5,7,8}}
[8,3,2,1,5,6,7,4]=>{{1,4,8},{2,3},{5},{6},{7}}
[3,2,6,7,8,4,5,1]=>{{1,3,4,5,6,7,8},{2}}
[1,7,4,6,3,8,2,5]=>{{1},{2,7},{3,4,5,6,8}}
[5,6,4,1,3,8,2,7]=>{{1,3,4,5},{2,6,7,8}}
[4,5,3,1,8,7,6,2]=>{{1,4},{2,5,8},{3},{6,7}}
[6,3,4,2,7,8,5,1]=>{{1,6,8},{2,3,4},{5,7}}
[8,7,4,5,1,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[6,2,7,8,1,3,5,4]=>{{1,3,5,6,7},{2},{4,8}}
[5,1,8,4,3,7,2,6]=>{{1,2,3,5,6,7,8},{4}}
[7,2,8,1,4,5,6,3]=>{{1,4,5,6,7},{2},{3,8}}
[1,4,8,2,5,6,7,3]=>{{1},{2,4},{3,8},{5},{6},{7}}
[8,1,6,7,2,5,4,3]=>{{1,2,3,5,6,8},{4,7}}
[7,5,2,3,6,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,6,5,3,2,7]=>{{1,2,7,8},{3,4,6},{5}}
[8,1,4,7,6,5,2,3]=>{{1,2,3,4,7,8},{5,6}}
[8,1,2,7,6,5,4,3]=>{{1,2,3,8},{4,7},{5,6}}
[4,5,8,1,6,7,2,3]=>{{1,4},{2,5,6,7},{3,8}}
[3,2,8,6,1,5,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[3,7,2,5,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,8,4,1,5,2,3]=>{{1,5,6},{2,7},{3,8},{4}}
[6,2,8,3,5,1,4,7]=>{{1,6},{2},{3,4,7,8},{5}}
[6,2,7,4,5,3,1,8]=>{{1,3,6,7},{2},{4},{5},{8}}
[6,8,2,5,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,5,4,1,2,3]=>{{1,6},{2,3,7,8},{4,5}}
[7,4,5,6,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,1,8,7,4,5,2,3]=>{{1,2,4,5,6,7},{3,8}}
[4,8,7,1,6,3,2,5]=>{{1,4},{2,3,5,6,7,8}}
[4,8,2,7,5,3,6,1]=>{{1,2,3,4,6,7,8},{5}}
[1,3,2,6,8,7,4,5]=>{{1},{2,3},{4,6,7},{5,8}}
[1,3,8,2,5,4,6,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,6,2,5,8,7,3,4]=>{{1},{2,3,6,7},{4,5,8}}
[1,6,8,7,2,3,5,4]=>{{1},{2,3,4,5,6,7,8}}
[1,6,8,7,2,5,3,4]=>{{1},{2,5,6},{3,4,7,8}}
[1,5,2,4,8,3,6,7]=>{{1},{2,3,5,6,7,8},{4}}
[1,2,4,5,8,6,3,7]=>{{1},{2},{3,4,5,7,8},{6}}
[1,2,8,3,5,4,7,6]=>{{1},{2},{3,4,6,8},{5},{7}}
[1,3,8,2,5,4,7,6]=>{{1},{2,3,4,6,8},{5},{7}}
[1,6,7,5,2,4,8,3]=>{{1},{2,4,5,6},{3,7,8}}
[1,5,6,4,7,2,3,8]=>{{1},{2,3,5,6,7},{4},{8}}
[1,7,4,2,5,8,3,6]=>{{1},{2,3,4,7},{5},{6,8}}
[1,6,4,3,7,5,2,8]=>{{1},{2,5,6,7},{3,4},{8}}
[1,6,5,4,7,2,3,8]=>{{1},{2,6},{3,5,7},{4},{8}}
[1,7,3,2,6,4,8,5]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,8,2,3,6,7,4]=>{{1},{2,3,4,5,8},{6},{7}}
[1,3,2,6,8,5,4,7]=>{{1},{2,3},{4,5,6,7,8}}
[1,6,3,2,7,4,5,8]=>{{1},{2,4,6},{3},{5,7},{8}}
[1,7,8,5,4,2,3,6]=>{{1},{2,3,6,7,8},{4,5}}
[1,8,4,2,3,6,5,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,4,2,7,5,3,8,6]=>{{1},{2,3,4,6,7,8},{5}}
[1,5,7,6,2,4,3,8]=>{{1},{2,5},{3,7},{4,6},{8}}
[1,8,4,7,3,2,6,5]=>{{1},{2,3,4,5,6,7,8}}
[1,3,8,4,2,6,5,7]=>{{1},{2,3,5,7,8},{4},{6}}
[1,7,4,2,6,5,8,3]=>{{1},{2,3,4,7,8},{5,6}}
[1,6,5,8,3,7,4,2]=>{{1},{2,4,6,7,8},{3,5}}
[1,7,4,8,3,2,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,4,8,3,2,7,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,3,6,4,5,2,7]=>{{1},{2,7,8},{3},{4,5,6}}
[1,6,4,7,3,2,8,5]=>{{1},{2,6},{3,4,5,7,8}}
[8,2,3,7,4,5,6,1]=>{{1,8},{2},{3},{4,5,6,7}}
[8,5,7,2,3,6,4,1]=>{{1,8},{2,3,4,5,7},{6}}
[7,5,2,1,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[7,6,1,5,4,8,2,3]=>{{1,2,3,6,7,8},{4,5}}
[7,6,3,2,1,8,4,5]=>{{1,2,4,5,6,7,8},{3}}
[2,8,7,3,4,6,1,5]=>{{1,2,3,4,5,7,8},{6}}
[6,5,1,3,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,3,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,3,4,5,2,6]=>{{1,2,7},{3,4,5,6,8}}
[6,8,7,3,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,1,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[1,8,5,3,4,6,2,7]=>{{1},{2,7,8},{3,4,5},{6}}
[7,1,6,5,4,3,8,2]=>{{1,2,7,8},{3,6},{4,5}}
[7,1,3,6,4,5,8,2]=>{{1,2,7,8},{3},{4,5,6}}
[7,1,5,3,6,4,8,2]=>{{1,2,7,8},{3,4,5,6}}
[6,1,5,3,7,8,2,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,1,2,6,3,4]=>{{1,2,4,5,8},{3,7},{6}}
[6,8,2,3,4,7,1,5]=>{{1,6,7},{2,3,4,5,8}}
[5,1,7,3,8,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[6,1,3,2,4,7,8,5]=>{{1,2,4,5,6,7,8},{3}}
[6,2,1,3,4,7,8,5]=>{{1,3,4,5,6,7,8},{2}}
[3,2,5,8,7,4,1,6]=>{{1,3,5,7},{2},{4,6,8}}
[4,2,5,8,7,3,1,6]=>{{1,3,4,5,6,7,8},{2}}
[8,3,4,1,6,5,2,7]=>{{1,2,3,4,7,8},{5,6}}
[3,4,8,5,7,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[3,6,4,8,5,7,2,1]=>{{1,3,4,8},{2,6,7},{5}}
[5,8,4,7,3,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[4,2,8,7,3,1,6,5]=>{{1,4,6,7},{2},{3,5,8}}
[6,5,8,2,1,7,4,3]=>{{1,2,4,5,6,7},{3,8}}
[6,1,4,3,8,7,2,5]=>{{1,2,6,7},{3,4},{5,8}}
[5,1,3,2,6,8,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[6,1,3,8,7,2,4,5]=>{{1,2,6},{3},{4,5,7,8}}
[1,2,8,4,5,7,3,6]=>{{1},{2},{3,6,7,8},{4},{5}}
[4,2,1,8,7,6,3,5]=>{{1,3,4,5,7,8},{2},{6}}
[3,2,5,8,7,1,4,6]=>{{1,3,4,5,6,7,8},{2}}
[5,6,3,8,7,2,1,4]=>{{1,5,7},{2,6},{3},{4,8}}
[2,5,8,4,7,1,6,3]=>{{1,2,5,6,7},{3,8},{4}}
[1,6,2,4,8,5,7,3]=>{{1},{2,3,5,6,8},{4},{7}}
[3,1,6,5,8,7,2,4]=>{{1,2,3,6,7},{4,5,8}}
[4,8,5,3,6,7,1,2]=>{{1,3,4,5,6,7},{2,8}}
[1,8,5,3,4,7,6,2]=>{{1},{2,8},{3,4,5},{6,7}}
[2,7,1,3,6,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[8,1,7,3,5,4,6,2]=>{{1,2,8},{3,4,6,7},{5}}
[1,8,6,3,2,5,4,7]=>{{1},{2,3,4,5,6,7,8}}
[3,2,4,8,5,7,1,6]=>{{1,3,4,6,7,8},{2},{5}}
[8,1,2,4,7,5,6,3]=>{{1,2,3,8},{4},{5,6,7}}
[8,6,2,1,5,7,3,4]=>{{1,4,8},{2,3,6,7},{5}}
[4,6,2,8,5,3,7,1]=>{{1,4,8},{2,3,6},{5},{7}}
[8,7,2,4,1,5,3,6]=>{{1,5,6,8},{2,3,7},{4}}
[7,5,3,4,8,6,2,1]=>{{1,2,5,7,8},{3},{4},{6}}
[2,8,3,1,4,6,7,5]=>{{1,2,4,5,8},{3},{6},{7}}
[4,3,6,5,1,2,7,8]=>{{1,4,5},{2,3,6},{7},{8}}
[5,8,3,7,6,4,2,1]=>{{1,2,4,5,6,7,8},{3}}
[1,3,8,7,6,5,2,4]=>{{1},{2,3,4,7,8},{5,6}}
[4,8,7,2,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,2,6,3,5,4]=>{{1},{2,4,8},{3,5,6,7}}
[8,7,2,1,4,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,7,1,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}
[4,2,8,7,6,5,1,3]=>{{1,4,7},{2},{3,8},{5,6}}
[1,2,5,7,4,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,2,1,8,7,5,3,4]=>{{1,3,5,6,7},{2},{4,8}}
[6,3,8,7,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[2,8,3,4,1,5,6,7]=>{{1,2,5,6,7,8},{3},{4}}
[1,3,7,5,4,8,6,2]=>{{1},{2,3,6,7,8},{4,5}}
[4,5,6,3,1,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,5,6,3,8,4,2,7]=>{{1},{2,5,7,8},{3,4,6}}
[2,6,5,3,8,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,7,3,8,4,2,6,1]=>{{1,4,5,8},{2,6,7},{3}}
[5,3,6,2,8,4,1,7]=>{{1,5,7,8},{2,3,4,6}}
[2,3,6,5,4,8,1,7]=>{{1,2,3,6,7,8},{4,5}}
[3,7,5,4,8,2,6,1]=>{{1,3,5,8},{2,6,7},{4}}
[5,3,7,1,2,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[6,3,8,7,2,5,4,1]=>{{1,2,3,5,6,8},{4,7}}
[6,8,4,1,7,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,6,7,5,2,3]=>{{1,2,3,4,5,6,7,8}}
[2,6,8,1,4,7,5,3]=>{{1,2,4,5,6,7},{3,8}}
[6,4,8,1,2,7,5,3]=>{{1,2,4,5,6,7},{3,8}}
[8,2,1,6,7,4,5,3]=>{{1,3,8},{2},{4,6},{5,7}}
[4,2,8,1,6,7,5,3]=>{{1,4},{2},{3,8},{5,6,7}}
[8,1,2,6,4,7,5,3]=>{{1,2,3,8},{4,5,6,7}}
[8,4,1,6,2,7,5,3]=>{{1,3,8},{2,4,5,6,7}}
[4,8,1,2,6,7,5,3]=>{{1,2,3,4,8},{5,6,7}}
[4,8,2,1,6,7,5,3]=>{{1,4},{2,3,8},{5,6,7}}
[8,2,4,6,1,7,5,3]=>{{1,3,4,5,6,7,8},{2}}
[5,4,7,6,3,1,2,8]=>{{1,2,3,4,5,6,7},{8}}
[3,6,4,8,1,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[3,6,8,4,1,5,2,7]=>{{1,2,3,5,6,7,8},{4}}
[8,7,1,4,2,3,5,6]=>{{1,3,6,8},{2,5,7},{4}}
[3,8,6,4,1,5,2,7]=>{{1,3,5,6},{2,7,8},{4}}
[8,2,6,5,7,1,3,4]=>{{1,3,4,5,6,7,8},{2}}
[4,6,1,3,2,8,7,5]=>{{1,3,4},{2,5,6,8},{7}}
[7,1,4,8,2,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[4,5,3,6,7,1,8,2]=>{{1,4,6},{2,5,7,8},{3}}
[1,4,7,8,3,5,2,6]=>{{1},{2,3,4,5,6,7,8}}
[4,6,1,3,5,2,8,7]=>{{1,3,4},{2,6},{5},{7,8}}
[2,5,1,4,8,3,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[6,1,2,5,4,8,7,3]=>{{1,2,3,6,8},{4,5},{7}}
[8,4,1,7,3,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,2,5,7,3,6]=>{{1,3,6,7,8},{2,4},{5}}
[2,4,5,6,8,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[3,4,5,8,6,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,1,8,6,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[8,3,7,2,1,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[8,4,7,6,2,5,1,3]=>{{1,3,7,8},{2,4,5,6}}
[8,4,7,3,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,7,5,6,4,1,2]=>{{1,3,7},{2,8},{4,5,6}}
[3,8,7,5,6,2,1,4]=>{{1,3,7},{2,4,5,6,8}}
[3,8,7,5,6,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,8,7,5,6,4,1,3]=>{{1,2,3,7,8},{4,5,6}}
[1,5,6,3,8,2,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[2,6,3,8,4,7,1,5]=>{{1,2,6,7},{3},{4,5,8}}
[2,6,3,5,7,8,1,4]=>{{1,2,4,5,6,7,8},{3}}
[1,5,6,3,7,2,8,4]=>{{1},{2,3,4,5,6,7,8}}
[1,7,5,3,6,2,8,4]=>{{1},{2,3,4,5,6,7,8}}
[1,5,7,3,4,2,8,6]=>{{1},{2,3,4,5,6,7,8}}
[1,5,8,3,4,2,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,4,5,3,7,2,8,6]=>{{1},{2,3,4,5,6,7,8}}
[1,4,5,3,8,2,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[6,5,1,4,2,7,8,3]=>{{1,3,6,7,8},{2,5},{4}}
[6,5,1,4,2,8,7,3]=>{{1,3,6,8},{2,5},{4},{7}}
[1,7,5,4,2,8,6,3]=>{{1},{2,3,5,6,7,8},{4}}
[5,1,6,8,3,7,2,4]=>{{1,2,3,5,6,7},{4,8}}
[5,4,7,1,8,6,3,2]=>{{1,2,4,5,8},{3,7},{6}}
[1,4,8,2,6,5,3,7]=>{{1},{2,4},{3,7,8},{5,6}}
[8,5,1,3,6,2,4,7]=>{{1,3,4,7,8},{2,5,6}}
[7,5,1,8,3,4,2,6]=>{{1,2,3,5,7},{4,6,8}}
[5,2,8,1,7,4,3,6]=>{{1,3,4,5,6,7,8},{2}}
[1,2,5,6,8,7,3,4]=>{{1},{2},{3,4,5,6,7,8}}
[1,5,6,8,2,7,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[2,6,7,3,4,1,8,5]=>{{1,2,6},{3,4,5,7,8}}
[1,6,5,7,8,2,4,3]=>{{1},{2,6},{3,5,8},{4,7}}
[1,5,6,7,2,8,4,3]=>{{1},{2,5},{3,6,8},{4,7}}
[3,7,6,1,8,2,4,5]=>{{1,2,3,4,6,7},{5,8}}
[1,3,7,2,6,4,8,5]=>{{1},{2,3,4,5,6,7,8}}
[1,5,8,6,7,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,5,8,7,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[1,2,5,8,6,7,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[1,7,5,8,6,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,6,5,8,1,2,7,4]=>{{1,3,5},{2,6},{4,8},{7}}
[5,4,7,8,1,6,3,2]=>{{1,5},{2,4,8},{3,7},{6}}
[4,6,5,8,3,2,7,1]=>{{1,4,8},{2,6},{3,5},{7}}
[4,7,5,8,3,6,2,1]=>{{1,4,8},{2,7},{3,5},{6}}
[7,3,6,8,5,2,1,4]=>{{1,7},{2,3,6},{4,8},{5}}
[2,4,7,8,5,6,3,1]=>{{1,2,4,8},{3,7},{5},{6}}
[6,8,4,7,5,1,3,2]=>{{1,6},{2,8},{3,4,7},{5}}
[7,6,1,2,3,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[2,8,7,5,1,6,3,4]=>{{1,2,4,5,8},{3,7},{6}}
[8,7,6,4,2,1,5,3]=>{{1,3,6,8},{2,5,7},{4}}
[3,8,7,5,2,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[3,8,7,5,1,2,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,3,7,1,4,6,2]=>{{1,5},{2,8},{3},{4,6,7}}
[3,8,7,4,2,6,5,1]=>{{1,2,3,5,7,8},{4},{6}}
[5,8,3,2,4,7,6,1]=>{{1,2,4,5,8},{3},{6,7}}
[5,3,8,2,4,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[4,5,8,3,2,6,1,7]=>{{1,3,4,7,8},{2,5},{6}}
[5,8,2,1,4,6,3,7]=>{{1,4,5},{2,3,7,8},{6}}
[4,1,5,8,3,6,2,7]=>{{1,2,4,7,8},{3,5},{6}}
[4,5,8,3,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}
[3,2,7,1,8,5,4,6]=>{{1,3,4,7},{2},{5,6,8}}
[4,7,8,5,2,3,1,6]=>{{1,2,4,5,7},{3,6,8}}
[6,2,7,8,1,5,3,4]=>{{1,5,6},{2},{3,7},{4,8}}
[2,7,1,3,8,5,4,6]=>{{1,2,3,4,7},{5,6,8}}
[2,6,7,8,4,1,3,5]=>{{1,2,6},{3,7},{4,5,8}}
[2,6,7,8,4,3,1,5]=>{{1,2,3,6,7},{4,5,8}}
[7,1,2,6,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,6,5,3,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[8,5,4,6,1,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[7,4,1,8,2,5,3,6]=>{{1,3,7},{2,4,5,6,8}}
[7,4,8,3,1,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,4,5,3,1,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[8,2,3,1,6,7,4,5]=>{{1,4,5,6,7,8},{2},{3}}
[8,2,1,7,4,3,5,6]=>{{1,3,6,8},{2},{4,5,7}}
[7,2,6,8,4,1,3,5]=>{{1,3,6,7},{2},{4,5,8}}
[7,2,5,1,6,8,3,4]=>{{1,3,4,5,6,7,8},{2}}
[6,2,1,7,4,8,3,5]=>{{1,3,4,5,6,7,8},{2}}
[1,7,4,3,2,5,6,8]=>{{1},{2,5,6,7},{3,4},{8}}
[1,7,4,3,6,2,5,8]=>{{1},{2,5,6,7},{3,4},{8}}
[3,7,5,8,2,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[5,2,1,6,3,4,8,7]=>{{1,3,5},{2},{4,6},{7,8}}
[5,1,3,4,6,2,8,7]=>{{1,2,5,6},{3},{4},{7,8}}
[3,8,4,5,7,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,4,7,5,6,2,1]=>{{1,2,3,4,7,8},{5},{6}}
[4,2,8,6,3,7,5,1]=>{{1,3,4,5,6,7,8},{2}}
[4,1,7,6,3,8,5,2]=>{{1,2,4,6,8},{3,5,7}}
[7,4,1,8,5,3,6,2]=>{{1,3,6,7},{2,4,8},{5}}
[3,5,6,8,4,7,1,2]=>{{1,3,6,7},{2,4,5,8}}
[5,4,1,8,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,2,8,4,5,3,7,1]=>{{1,3,6,8},{2},{4},{5},{7}}
[4,5,2,1,8,7,3,6]=>{{1,4},{2,3,5,6,7,8}}
[4,7,3,8,2,6,5,1]=>{{1,4,8},{2,5,7},{3},{6}}
[4,7,3,1,8,6,2,5]=>{{1,4},{2,7},{3},{5,8},{6}}
[6,2,1,3,7,4,8,5]=>{{1,3,4,6},{2},{5,7,8}}
[6,3,7,1,2,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,4,7,8,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[7,2,5,8,1,3,6,4]=>{{1,3,5,6,7},{2},{4,8}}
[8,3,6,7,2,4,5,1]=>{{1,8},{2,3,4,5,6,7}}
[3,8,7,5,2,1,6,4]=>{{1,3,6,7},{2,4,5,8}}
[3,8,5,6,2,7,4,1]=>{{1,2,3,5,8},{4,6,7}}
[3,6,5,8,4,2,7,1]=>{{1,3,4,5,8},{2,6},{7}}
[6,8,3,2,5,7,4,1]=>{{1,2,4,6,7,8},{3},{5}}
[4,1,5,6,8,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,3,6,7,5,1]=>{{1,8},{2,3,4},{5,6,7}}
[6,1,2,4,5,7,8,3]=>{{1,2,3,6,7,8},{4},{5}}
[4,5,1,3,7,6,8,2]=>{{1,3,4},{2,5,7,8},{6}}
[3,5,4,8,6,2,7,1]=>{{1,3,4,8},{2,5,6},{7}}
[3,6,2,4,5,8,7,1]=>{{1,2,3,6,8},{4},{5},{7}}
[8,1,3,7,4,5,6,2]=>{{1,2,8},{3},{4,5,6,7}}
[8,1,5,3,6,4,7,2]=>{{1,2,8},{3,4,5,6},{7}}
[2,6,4,8,3,1,5,7]=>{{1,2,6},{3,4,5,7,8}}
[2,6,4,1,5,8,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[3,6,4,5,2,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,5,4,7,3,6,2]=>{{1,2,8},{3,5,6,7},{4}}
[7,6,5,4,1,8,2,3]=>{{1,2,3,5,6,7,8},{4}}
[8,1,5,4,7,6,3,2]=>{{1,2,8},{3,5,7},{4},{6}}
[2,5,1,4,6,7,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[3,6,4,1,5,7,8,2]=>{{1,3,4},{2,6,7,8},{5}}
[7,6,5,2,8,4,1,3]=>{{1,7},{2,4,6},{3,5,8}}
[3,1,6,5,2,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[1,7,2,4,3,5,8,6]=>{{1},{2,3,5,6,7,8},{4}}
[3,8,1,7,4,2,6,5]=>{{1,3},{2,4,5,6,7,8}}
[8,1,7,4,3,5,6,2]=>{{1,2,8},{3,5,6,7},{4}}
[6,8,2,4,5,3,7,1]=>{{1,2,3,6,8},{4},{5},{7}}
[4,8,5,3,6,1,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[2,8,3,1,4,7,5,6]=>{{1,2,4,5,6,7,8},{3}}
[8,6,3,2,7,4,1,5]=>{{1,5,7,8},{2,4,6},{3}}
[2,7,3,1,8,4,5,6]=>{{1,2,4,5,6,7,8},{3}}
[1,2,8,3,5,6,4,7]=>{{1},{2},{3,4,7,8},{5},{6}}
[3,5,7,4,8,1,6,2]=>{{1,3,6,7},{2,5,8},{4}}
[2,8,1,3,5,4,6,7]=>{{1,2,3,4,6,7,8},{5}}
[1,5,2,8,6,4,3,7]=>{{1},{2,3,4,5,6,7,8}}
[7,4,8,6,3,1,2,5]=>{{1,2,4,6,7},{3,5,8}}
[3,6,8,4,1,2,5,7]=>{{1,3,5,7,8},{2,6},{4}}
[4,7,8,5,2,1,3,6]=>{{1,2,3,4,5,6,7,8}}
[6,1,5,2,8,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,3,5,7,4,2,6]=>{{1,2,4,5,6,7,8},{3}}
[3,1,8,5,4,7,2,6]=>{{1,2,3,6,7,8},{4,5}}
[3,1,6,4,8,5,2,7]=>{{1,2,3,5,6,7,8},{4}}
[5,1,3,4,2,6,8,7]=>{{1,2,5},{3},{4},{6},{7,8}}
[3,2,6,4,1,5,7,8]=>{{1,3,5,6},{2},{4},{7},{8}}
[5,4,2,1,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,2,5,1,8,7,3,6]=>{{1,4},{2},{3,5,6,7,8}}
[6,8,2,7,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[1,8,4,7,3,2,5,6]=>{{1},{2,6,8},{3,4,5,7}}
[8,6,3,1,5,7,2,4]=>{{1,4,8},{2,6,7},{3},{5}}
[5,8,3,1,4,7,6,2]=>{{1,4,5},{2,8},{3},{6,7}}
[1,2,5,4,7,8,3,6]=>{{1},{2},{3,5,7},{4},{6,8}}
[1,8,3,2,6,4,7,5]=>{{1},{2,4,5,6,8},{3},{7}}
[4,7,1,2,5,3,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[6,8,4,1,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[3,2,6,1,7,8,5,4]=>{{1,3,4,6,8},{2},{5,7}}
[7,6,4,1,8,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,1,6,7,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[7,4,1,6,5,8,2,3]=>{{1,2,3,4,6,7,8},{5}}
[8,5,4,1,6,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[5,2,1,6,4,7,8,3]=>{{1,3,4,5,6,7,8},{2}}
[1,6,2,3,5,7,8,4]=>{{1},{2,3,4,6,7,8},{5}}
[1,3,4,8,5,2,6,7]=>{{1},{2,3,4,6,7,8},{5}}
[8,2,4,6,1,7,3,5]=>{{1,5,8},{2},{3,4,6,7}}
[1,5,7,2,3,6,8,4]=>{{1},{2,3,4,5,7,8},{6}}
[7,3,1,4,2,5,8,6]=>{{1,2,3,5,6,7,8},{4}}
[3,2,5,7,8,4,1,6]=>{{1,3,4,5,6,7,8},{2}}
[4,3,5,1,6,2,7,8]=>{{1,4},{2,3,5,6},{7},{8}}
[8,6,3,5,4,1,2,7]=>{{1,2,6,7,8},{3},{4,5}}
[8,3,2,6,1,5,4,7]=>{{1,4,5,6,7,8},{2,3}}
[8,5,1,7,4,6,2,3]=>{{1,3,8},{2,4,5,7},{6}}
[4,8,1,7,6,3,5,2]=>{{1,3,4,5,6,7},{2,8}}
[8,5,1,7,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,7,6,2,1,3,4]=>{{1,4,6,8},{2,5},{3,7}}
[5,4,8,3,1,7,2,6]=>{{1,5},{2,3,4,6,7,8}}
[5,1,4,8,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[4,8,1,7,6,5,2,3]=>{{1,2,3,4,7,8},{5,6}}
[4,3,8,7,2,6,1,5]=>{{1,4,7},{2,3,5,8},{6}}
[3,8,7,2,6,4,1,5]=>{{1,3,7},{2,4,5,6,8}}
[8,2,5,7,4,3,6,1]=>{{1,8},{2},{3,4,5,6,7}}
[3,8,7,4,6,1,2,5]=>{{1,2,3,5,6,7,8},{4}}
[8,7,6,3,5,4,1,2]=>{{1,2,7,8},{3,4,6},{5}}
[2,8,4,7,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,8,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,4,8,2,1,3,7,6]=>{{1,5},{2,4},{3,6,8},{7}}
[3,8,7,2,6,1,5,4]=>{{1,3,5,6,7},{2,4,8}}
[1,8,4,7,6,3,5,2]=>{{1},{2,8},{3,4,5,6,7}}
[1,8,3,7,6,5,2,4]=>{{1},{2,4,7,8},{3},{5,6}}
[1,4,3,8,7,2,6,5]=>{{1},{2,4,5,6,7,8},{3}}
[7,1,5,4,6,2,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,4,1,3,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,3,1,7,6,2,8]=>{{1,2,4,5,7},{3},{6},{8}}
[2,6,8,3,1,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,8,1,7,3,6]=>{{1,2,5},{3,4,6,7,8}}
[7,5,2,4,8,3,6,1]=>{{1,2,3,5,6,7,8},{4}}
[7,8,2,6,3,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[7,2,6,5,8,3,4,1]=>{{1,4,5,7,8},{2},{3,6}}
[5,6,3,1,4,2,7,8]=>{{1,4,5},{2,6},{3},{7},{8}}
[2,6,5,3,4,8,7,1]=>{{1,2,6,8},{3,4,5},{7}}
[2,6,1,5,3,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[3,4,7,8,5,1,6,2]=>{{1,3,6,7},{2,4,8},{5}}
[3,6,2,4,7,8,5,1]=>{{1,2,3,6,8},{4},{5,7}}
[5,3,6,4,8,7,2,1]=>{{1,5,8},{2,3,6,7},{4}}
[1,5,4,8,6,2,7,3]=>{{1},{2,5,6},{3,4,8},{7}}
[4,5,2,7,6,3,8,1]=>{{1,4,7,8},{2,3,5,6}}
[5,8,3,1,2,7,6,4]=>{{1,2,4,5,8},{3},{6,7}}
[7,6,2,5,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,4,6,1,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,1,2,3,6,7]=>{{1,4},{2,3,5,6,7,8}}
[8,6,2,4,5,1,3,7]=>{{1,2,3,6,7,8},{4},{5}}
[4,5,1,3,8,6,2,7]=>{{1,3,4},{2,5,7,8},{6}}
[7,4,2,3,6,8,5,1]=>{{1,5,6,7,8},{2,3,4}}
[2,1,6,7,4,8,3,5]=>{{1,2},{3,4,5,6,7,8}}
[7,8,1,3,6,4,5,2]=>{{1,3,4,5,6,7},{2,8}}
[7,2,6,8,4,5,3,1]=>{{1,3,4,5,6,7,8},{2}}
[7,3,6,8,5,1,4,2]=>{{1,2,3,4,6,7,8},{5}}
[7,5,8,1,6,2,4,3]=>{{1,4,7},{2,5,6},{3,8}}
[5,7,8,1,6,3,2,4]=>{{1,3,4,5,6,8},{2,7}}
[7,2,6,8,5,1,4,3]=>{{1,3,4,6,7,8},{2},{5}}
[7,5,2,4,8,3,1,6]=>{{1,7},{2,3,5,6,8},{4}}
[7,8,3,1,6,2,5,4]=>{{1,2,4,5,6,7,8},{3}}
[6,7,8,4,3,1,5,2]=>{{1,6},{2,3,5,7,8},{4}}
[7,8,3,6,4,1,5,2]=>{{1,4,5,6,7},{2,8},{3}}
[7,3,8,1,6,4,5,2]=>{{1,4,5,6,7},{2,3,8}}
[1,7,5,8,2,4,6,3]=>{{1},{2,3,4,5,6,7,8}}
[7,5,2,8,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,2,6,5,1,4]=>{{1,2,3,4,7,8},{5,6}}
[3,7,8,2,1,6,4,5]=>{{1,3,5,8},{2,4,7},{6}}
[7,8,1,6,3,5,4,2]=>{{1,3,4,5,6,7},{2,8}}
[6,7,8,2,5,4,3,1]=>{{1,2,3,4,6,7,8},{5}}
[6,7,8,3,1,5,4,2]=>{{1,5,6},{2,3,4,7,8}}
[7,8,1,6,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,6,1,4,3,8,2,7]=>{{1,3,5},{2,6,7,8},{4}}
[5,1,6,8,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[7,1,6,8,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}
[5,6,8,1,2,3,7,4]=>{{1,2,3,4,5,6,8},{7}}
[4,8,1,2,7,6,5,3]=>{{1,2,3,4,8},{5,7},{6}}
[4,6,1,2,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,4,7,3,5,2,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[5,7,8,4,2,1,3,6]=>{{1,2,3,5,6,7,8},{4}}
[3,1,6,2,5,7,8,4]=>{{1,2,3,4,6,7,8},{5}}
[1,6,4,5,2,7,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,2,1,4,5,3,7,8]=>{{1,3,6},{2},{4},{5},{7},{8}}
[6,2,1,5,7,3,4,8]=>{{1,3,6},{2},{4,5,7},{8}}
[1,2,4,6,8,3,7,5]=>{{1},{2},{3,4,6},{5,8},{7}}
[1,3,5,8,2,6,7,4]=>{{1},{2,3,5},{4,8},{6},{7}}
[6,1,3,7,2,8,5,4]=>{{1,2,4,5,6,7,8},{3}}
[6,4,5,8,3,7,1,2]=>{{1,6,7},{2,4,8},{3,5}}
[8,1,4,3,6,7,2,5]=>{{1,2,5,6,7,8},{3,4}}
[2,6,8,4,3,1,7,5]=>{{1,2,6},{3,5,8},{4},{7}}
[8,1,5,2,6,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,7,4,2,8,3,5]=>{{1},{2,5,6,8},{3,7},{4}}
[1,7,8,4,3,6,2,5]=>{{1},{2,7},{3,5,8},{4},{6}}
[1,4,7,2,3,6,8,5]=>{{1},{2,4},{3,5,7,8},{6}}
[3,1,2,6,7,8,5,4]=>{{1,2,3},{4,6,8},{5,7}}
[3,8,1,6,4,2,7,5]=>{{1,3},{2,4,5,6,8},{7}}
[1,6,3,4,7,8,2,5]=>{{1},{2,5,6,7,8},{3},{4}}
[3,1,5,7,6,2,8,4]=>{{1,2,3,5,6},{4,7,8}}
[6,3,1,4,2,7,8,5]=>{{1,2,3,5,6,7,8},{4}}
[2,4,3,7,6,1,8,5]=>{{1,2,4,5,6,7,8},{3}}
[3,1,7,6,5,2,8,4]=>{{1,2,3,4,6,7,8},{5}}
[1,4,7,6,8,3,2,5]=>{{1},{2,3,4,6,7},{5,8}}
[7,2,1,5,6,3,8,4]=>{{1,3,4,5,6,7,8},{2}}
[4,3,1,8,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,1,5,2,8,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[1,2,8,4,3,7,6,5]=>{{1},{2},{3,5,8},{4},{6,7}}
[2,6,1,8,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,8,3,2,6,4]=>{{1,2,3,5,6,7},{4,8}}
[4,7,6,3,1,8,2,5]=>{{1,3,4,5,6,8},{2,7}}
[5,3,1,8,6,2,4,7]=>{{1,2,3,5,6},{4,7,8}}
[5,1,8,6,3,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,5,4,2,8,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,4,2,8,5,3,7,6]=>{{1},{2,3,4,6,8},{5},{7}}
[8,3,1,6,4,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,7,4,8,3,5,2,6]=>{{1},{2,7},{3,4,5,6,8}}
[7,3,2,4,8,5,1,6]=>{{1,7},{2,3},{4},{5,6,8}}
[5,7,8,1,4,2,6,3]=>{{1,4,5},{2,6,7},{3,8}}
[2,6,3,8,1,7,5,4]=>{{1,2,5,6,7},{3},{4,8}}
[2,5,1,8,6,3,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[2,8,6,4,1,7,3,5]=>{{1,2,5,8},{3,6,7},{4}}
[1,8,4,2,7,5,3,6]=>{{1},{2,3,4,5,6,7,8}}
[6,5,1,7,2,8,4,3]=>{{1,3,6,8},{2,5},{4,7}}
[2,8,1,7,5,3,6,4]=>{{1,2,3,4,6,7,8},{5}}
[1,2,8,7,6,4,3,5]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,7,8,6,3,5,2]=>{{1,2,4,8},{3,5,6,7}}
[1,6,5,7,8,4,2,3]=>{{1},{2,4,6,7},{3,5,8}}
[4,1,8,7,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,8,2,6,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,5,7,1,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,1,8,5,3,6,2,7]=>{{1,2,3,4,5,7,8},{6}}
[6,4,2,5,3,1,7,8]=>{{1,6},{2,3,4,5},{7},{8}}
[3,1,5,8,2,7,4,6]=>{{1,2,3,5},{4,6,7,8}}
[6,4,1,5,3,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[6,2,1,5,4,3,7,8]=>{{1,3,6},{2},{4,5},{7},{8}}
[3,1,8,5,4,6,2,7]=>{{1,2,3,7,8},{4,5},{6}}
[6,1,8,4,5,3,2,7]=>{{1,2,3,6,7,8},{4},{5}}
[4,5,2,7,1,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,3,5,7,1,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[4,1,8,5,3,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[6,3,8,4,5,1,7,2]=>{{1,6},{2,3,8},{4},{5},{7}}
[3,1,6,8,5,7,4,2]=>{{1,2,3,4,6,7,8},{5}}
[2,6,1,8,5,7,4,3]=>{{1,2,3,4,6,7,8},{5}}
[6,3,8,4,5,2,1,7]=>{{1,2,3,6,7,8},{4},{5}}
[6,5,8,7,2,3,4,1]=>{{1,3,6,8},{2,5},{4,7}}
[6,3,8,4,5,2,7,1]=>{{1,2,3,6,8},{4},{5},{7}}
[2,1,6,8,5,3,7,4]=>{{1,2},{3,6},{4,8},{5},{7}}
[3,2,6,8,5,4,7,1]=>{{1,3,4,6,8},{2},{5},{7}}
[4,1,8,5,2,6,3,7]=>{{1,2,4,5},{3,7,8},{6}}
[3,1,6,8,5,2,4,7]=>{{1,2,3,6},{4,7,8},{5}}
[6,5,8,7,4,1,2,3]=>{{1,6},{2,4,5,7},{3,8}}
[6,5,8,7,4,2,1,3]=>{{1,2,4,5,6,7},{3,8}}
[6,5,8,7,2,4,1,3]=>{{1,4,6,7},{2,5},{3,8}}
[6,2,8,4,5,7,1,3]=>{{1,6,7},{2},{3,8},{4},{5}}
[6,1,8,4,5,7,3,2]=>{{1,2,3,6,7,8},{4},{5}}
[4,2,7,3,5,8,6,1]=>{{1,3,4,6,7,8},{2},{5}}
[3,6,2,4,8,5,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[3,5,1,8,4,7,6,2]=>{{1,3},{2,4,5,8},{6,7}}
[3,6,1,8,5,4,7,2]=>{{1,3},{2,4,6,8},{5},{7}}
[2,4,8,3,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}
[3,6,8,2,5,7,4,1]=>{{1,3,8},{2,4,6,7},{5}}
[2,6,8,5,4,3,7,1]=>{{1,2,3,6,8},{4,5},{7}}
[3,6,8,2,5,4,7,1]=>{{1,3,8},{2,4,6},{5},{7}}
[4,6,8,3,2,5,7,1]=>{{1,3,4,8},{2,5,6},{7}}
[4,6,2,8,3,5,7,1]=>{{1,4,8},{2,3,5,6},{7}}
[3,6,1,8,5,7,4,2]=>{{1,3},{2,4,6,7,8},{5}}
[5,2,6,8,4,1,7,3]=>{{1,3,4,5,6,8},{2},{7}}
[4,6,3,8,7,2,5,1]=>{{1,4,8},{2,6},{3},{5,7}}
[3,5,8,2,7,4,6,1]=>{{1,3,8},{2,4,5,6,7}}
[2,6,8,5,7,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,4,8,7,6,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,6,3,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,3,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,3,1,2,8,4]=>{{1,5},{2,3,4,6,7,8}}
[4,8,2,1,7,5,6,3]=>{{1,4},{2,3,8},{5,6,7}}
[6,3,8,5,7,2,4,1]=>{{1,2,3,6,8},{4,5,7}}
[1,5,4,8,6,2,3,7]=>{{1},{2,5,6},{3,4,7,8}}
[8,2,1,7,5,3,6,4]=>{{1,3,4,6,7,8},{2},{5}}
[8,2,1,6,7,3,5,4]=>{{1,3,4,6,8},{2},{5,7}}
[6,2,8,1,7,5,3,4]=>{{1,3,4,5,6,7,8},{2}}
[5,6,2,7,8,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,3,5,6,1,2]=>{{1,2,3,4,7,8},{5},{6}}
[8,4,5,2,6,3,7,1]=>{{1,8},{2,4},{3,5,6},{7}}
[4,7,3,1,6,8,2,5]=>{{1,4},{2,7},{3},{5,6,8}}
[1,7,4,6,8,3,2,5]=>{{1},{2,7},{3,4,6},{5,8}}
[4,7,2,5,6,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,1,3,7,8,2,6]=>{{1,2,3,4,5,7},{6,8}}
[6,1,5,8,3,7,2,4]=>{{1,2,6,7},{3,5},{4,8}}
[7,2,1,6,8,3,5,4]=>{{1,3,4,5,6,7,8},{2}}
[5,6,4,1,8,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[4,5,2,1,7,8,3,6]=>{{1,4},{2,3,5,7},{6,8}}
[2,3,7,8,5,1,6,4]=>{{1,2,3,6,7},{4,8},{5}}
[1,2,6,7,4,3,5,8]=>{{1},{2},{3,6},{4,5,7},{8}}
[5,8,6,3,4,1,2,7]=>{{1,3,4,5,6},{2,7,8}}
[6,2,3,1,8,5,4,7]=>{{1,4,5,6,7,8},{2},{3}}
[5,1,2,6,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,3,7,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[4,5,2,8,6,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[3,4,8,2,5,6,1,7]=>{{1,3,7,8},{2,4},{5},{6}}
[6,8,2,7,5,3,1,4]=>{{1,2,3,4,6,7,8},{5}}
[6,3,2,5,8,4,1,7]=>{{1,4,5,6,7,8},{2,3}}
[5,6,7,2,8,4,1,3]=>{{1,3,5,7,8},{2,4,6}}
[5,8,3,6,4,1,7,2]=>{{1,4,5,6},{2,8},{3},{7}}
[4,3,8,5,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,5,1,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[3,2,5,8,4,7,1,6]=>{{1,3,4,5,6,7,8},{2}}
[2,5,8,1,3,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[3,5,1,8,7,4,2,6]=>{{1,3},{2,5,7},{4,6,8}}
[4,6,1,3,8,2,7,5]=>{{1,3,4},{2,6},{5,8},{7}}
[8,6,1,2,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[5,1,7,8,3,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,1,7,6,2,8,5,4]=>{{1,2,3,5,7},{4,6,8}}
[5,3,6,7,4,2,8,1]=>{{1,4,5,7,8},{2,3,6}}
[5,4,2,8,6,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,1,4,2,8,7,3,5]=>{{1,2,3,4,6,7},{5,8}}
[3,7,2,6,8,4,5,1]=>{{1,2,3,5,7,8},{4,6}}
[4,6,5,2,7,8,3,1]=>{{1,2,4,6,8},{3,5,7}}
[5,4,6,2,7,8,3,1]=>{{1,3,5,6,7,8},{2,4}}
[5,1,8,6,4,2,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[6,2,1,8,5,7,4,3]=>{{1,3,4,6,7,8},{2},{5}}
[5,4,6,2,3,1,8,7]=>{{1,3,5,6},{2,4},{7,8}}
[6,5,7,8,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[2,1,7,6,8,4,5,3]=>{{1,2},{3,5,7,8},{4,6}}
[6,4,7,2,8,3,1,5]=>{{1,3,6,7},{2,4},{5,8}}
[6,3,2,7,8,4,5,1]=>{{1,4,5,6,7,8},{2,3}}
[4,7,3,1,5,2,8,6]=>{{1,4},{2,6,7,8},{3},{5}}
[4,7,6,3,1,5,8,2]=>{{1,3,4,5,6},{2,7,8}}
[2,4,7,3,8,5,1,6]=>{{1,2,3,4,7},{5,6,8}}
[2,7,3,1,8,5,4,6]=>{{1,2,4,7},{3},{5,6,8}}
[2,8,3,1,7,4,5,6]=>{{1,2,4,6,8},{3},{5,7}}
[1,2,6,8,3,4,7,5]=>{{1},{2},{3,4,5,6,8},{7}}
[1,8,2,7,3,5,6,4]=>{{1},{2,3,4,5,6,7,8}}
[1,7,4,8,6,5,3,2]=>{{1},{2,3,4,7,8},{5,6}}
[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,4,7,2,8,3,6]=>{{1},{2,5},{3,4,7},{6,8}}
[3,8,5,2,6,1,7,4]=>{{1,3,5,6},{2,4,8},{7}}
[3,7,4,8,5,2,6,1]=>{{1,3,4,8},{2,6,7},{5}}
[8,1,2,6,5,3,4,7]=>{{1,2,3,4,6,7,8},{5}}
[3,7,4,2,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}
[6,8,7,1,3,4,2,5]=>{{1,4,6},{2,3,5,7,8}}
[3,4,2,8,6,7,5,1]=>{{1,2,3,4,8},{5,6,7}}
[3,7,8,6,1,4,2,5]=>{{1,3,5,8},{2,7},{4,6}}
[3,6,1,5,2,7,8,4]=>{{1,3},{2,4,5,6,7,8}}
[7,1,6,8,3,4,2,5]=>{{1,2,7},{3,4,5,6,8}}
[8,1,2,6,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[6,2,8,4,7,1,3,5]=>{{1,6},{2},{3,5,7,8},{4}}
[3,7,8,4,2,5,6,1]=>{{1,3,8},{2,5,6,7},{4}}
[3,4,2,8,5,1,6,7]=>{{1,2,3,4,6,7,8},{5}}
[6,8,2,7,5,4,1,3]=>{{1,4,6,7},{2,3,8},{5}}
[1,8,4,3,7,6,2,5]=>{{1},{2,5,7,8},{3,4},{6}}
[4,3,8,7,1,2,6,5]=>{{1,2,3,4,5,6,7,8}}
[1,8,4,5,7,6,2,3]=>{{1},{2,3,4,5,7,8},{6}}
[4,3,8,5,7,1,6,2]=>{{1,4,5,6,7},{2,3,8}}
[6,3,4,8,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,4,7,1,6,2]=>{{1,5,6,7},{2,3,8},{4}}
[5,2,8,7,1,4,6,3]=>{{1,5},{2},{3,8},{4,6,7}}
[3,2,8,7,1,6,4,5]=>{{1,3,5,8},{2},{4,7},{6}}
[2,7,8,3,1,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[2,7,8,5,1,4,6,3]=>{{1,2,4,5,6,7},{3,8}}
[3,5,8,7,4,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,8,3,5,1,2]=>{{1,7},{2,4,8},{3,5,6}}
[2,7,8,1,3,6,4,5]=>{{1,2,4,7},{3,5,8},{6}}
[2,7,8,1,5,4,6,3]=>{{1,2,4,6,7},{3,8},{5}}
[2,7,8,1,4,5,6,3]=>{{1,2,4,5,6,7},{3,8}}
[3,6,7,8,2,4,1,5]=>{{1,3,7},{2,4,5,6,8}}
[4,5,7,8,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,6,8,7,3,1,2]=>{{1,5,7},{2,4,8},{3,6}}
[4,5,8,6,7,1,3,2]=>{{1,4,6},{2,3,5,7,8}}
[5,7,6,8,2,1,3,4]=>{{1,2,3,5,6,7},{4,8}}
[3,7,6,8,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[5,4,7,8,6,3,1,2]=>{{1,3,5,6,7},{2,4,8}}
[4,5,7,8,2,6,1,3]=>{{1,3,4,7,8},{2,5},{6}}
[4,5,6,8,7,3,1,2]=>{{1,2,4,5,7,8},{3,6}}
[6,1,5,3,8,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[1,8,6,2,5,4,7,3]=>{{1},{2,3,4,6,8},{5},{7}}
[3,8,4,1,7,5,2,6]=>{{1,3,4},{2,5,6,7,8}}
[6,2,7,4,8,3,1,5]=>{{1,3,6,7},{2},{4},{5,8}}
[2,8,5,1,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[6,8,2,7,5,1,4,3]=>{{1,6},{2,3,8},{4,7},{5}}
[8,3,4,5,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[5,3,6,4,7,2,1,8]=>{{1,5,7},{2,3,6},{4},{8}}
[4,2,6,5,7,3,1,8]=>{{1,4,5,7},{2},{3,6},{8}}
[5,4,6,2,7,3,1,8]=>{{1,5,7},{2,4},{3,6},{8}}
[3,2,6,5,8,4,1,7]=>{{1,3,4,5,6,7,8},{2}}
[3,2,6,5,8,7,1,4]=>{{1,3,6,7},{2},{4,5,8}}
[4,2,6,5,8,7,1,3]=>{{1,3,4,5,6,7,8},{2}}
[5,2,6,4,8,7,1,3]=>{{1,3,5,6,7,8},{2},{4}}
[5,4,7,6,8,2,1,3]=>{{1,3,5,7,8},{2,4,6}}
[6,4,7,5,8,3,1,2]=>{{1,3,6,7},{2,4,5,8}}
[4,2,7,5,8,6,1,3]=>{{1,3,4,5,7,8},{2},{6}}
[3,2,7,5,8,4,1,6]=>{{1,3,7},{2},{4,5,6,8}}
[4,3,7,2,8,5,1,6]=>{{1,2,3,4,7},{5,6,8}}
[4,3,6,2,8,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,6,8,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,6,8,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,2,8,6,1,4]=>{{1,2,3,4,5,7,8},{6}}
[3,2,6,4,8,7,1,5]=>{{1,3,6,7},{2},{4},{5,8}}
[4,2,7,3,8,6,1,5]=>{{1,3,4,7},{2},{5,8},{6}}
[5,2,7,6,8,3,1,4]=>{{1,3,4,5,6,7,8},{2}}
[3,2,7,6,8,4,1,5]=>{{1,3,7},{2},{4,6},{5,8}}
[3,2,7,6,8,5,1,4]=>{{1,3,7},{2},{4,5,6,8}}
[6,2,7,5,8,4,1,3]=>{{1,3,4,5,6,7,8},{2}}
[4,8,1,7,3,2,5,6]=>{{1,3,4,5,7},{2,6,8}}
[3,7,4,8,2,1,5,6]=>{{1,3,4,6,8},{2,5,7}}
[3,7,8,2,5,4,6,1]=>{{1,3,8},{2,4,6,7},{5}}
[4,7,5,8,3,2,6,1]=>{{1,4,8},{2,6,7},{3,5}}
[6,7,1,3,2,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,4,1,5,3,2]=>{{1,2,3,5,6,7,8},{4}}
[3,8,5,2,6,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,2,5,3,4,8,1,6]=>{{1,7},{2},{3,4,5},{6,8}}
[4,2,5,3,7,8,6,1]=>{{1,3,4,5,6,7,8},{2}}
[5,3,6,2,4,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[7,8,6,2,3,5,4,1]=>{{1,2,4,7,8},{3,5,6}}
[5,8,2,6,3,7,4,1]=>{{1,2,3,5,8},{4,6,7}}
[4,8,2,3,7,5,6,1]=>{{1,2,3,4,8},{5,6,7}}
[7,5,6,2,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,6,4,3,8,1]=>{{1,2,7,8},{3,4,5,6}}
[2,8,4,3,7,5,6,1]=>{{1,2,8},{3,4},{5,6,7}}
[3,8,5,7,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,8,6,3,5,4,2,1]=>{{1,2,7,8},{3,4,6},{5}}
[2,7,6,3,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,5,6,3,8,1]=>{{1,7,8},{2,3,4,5,6}}
[6,2,7,5,3,8,4,1]=>{{1,6,8},{2},{3,4,5,7}}
[2,4,8,3,7,5,6,1]=>{{1,2,3,4,8},{5,6,7}}
[4,8,3,7,5,6,2,1]=>{{1,2,4,7,8},{3},{5},{6}}
[6,2,5,8,3,7,4,1]=>{{1,4,6,7,8},{2},{3,5}}
[4,7,3,8,2,5,6,1]=>{{1,4,8},{2,5,6,7},{3}}
[8,2,5,6,3,7,4,1]=>{{1,8},{2},{3,5},{4,6,7}}
[4,5,3,7,1,2,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[8,5,6,4,1,3,2,7]=>{{1,2,5,7,8},{3,6},{4}}
[6,7,2,8,4,3,1,5]=>{{1,2,3,6,7},{4,5,8}}
[6,7,3,2,8,4,1,5]=>{{1,2,4,6,7},{3},{5,8}}
[4,7,8,3,1,5,2,6]=>{{1,3,4,5,6,8},{2,7}}
[4,5,8,1,3,2,6,7]=>{{1,4},{2,3,5,6,7,8}}
[4,7,8,1,6,3,2,5]=>{{1,4},{2,7},{3,5,6,8}}
[4,7,1,3,8,6,5,2]=>{{1,3,4},{2,5,7,8},{6}}
[5,7,2,8,3,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,7,2,8,5,6,4,1]=>{{1,2,3,4,7,8},{5},{6}}
[3,1,5,8,6,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[2,3,8,6,4,5,7,1]=>{{1,2,3,8},{4,5,6},{7}}
[2,5,6,1,8,7,3,4]=>{{1,2,4,5,8},{3,6,7}}
[3,6,2,8,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}
[2,3,8,6,7,5,4,1]=>{{1,2,3,8},{4,5,6,7}}
[8,5,6,3,1,4,2,7]=>{{1,2,5,7,8},{3,4,6}}
[5,7,8,3,4,6,2,1]=>{{1,3,4,5,8},{2,7},{6}}
[3,5,1,8,6,4,2,7]=>{{1,3},{2,4,5,6,7,8}}
[7,5,3,8,6,4,2,1]=>{{1,2,4,5,6,7,8},{3}}
[5,1,3,8,6,4,2,7]=>{{1,2,4,5,6,7,8},{3}}
[1,5,8,3,6,4,2,7]=>{{1},{2,3,4,5,6,7,8}}
[7,5,8,3,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[1,5,8,6,3,4,2,7]=>{{1},{2,3,5,7,8},{4,6}}
[3,7,5,8,2,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[5,7,8,1,4,6,2,3]=>{{1,4,5},{2,7},{3,8},{6}}
[1,3,7,8,4,2,6,5]=>{{1},{2,3,6,7},{4,5,8}}
[6,1,2,5,3,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[1,4,6,5,7,2,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,7,3,5,4,1,2,8]=>{{1,6},{2,7},{3},{4,5},{8}}
[8,1,6,7,3,5,4,2]=>{{1,2,8},{3,5,6},{4,7}}
[7,2,4,1,6,5,3,8]=>{{1,3,4,7},{2},{5,6},{8}}
[4,2,5,1,3,7,6,8]=>{{1,4},{2},{3,5},{6,7},{8}}
[1,3,2,6,8,4,7,5]=>{{1},{2,3},{4,6},{5,8},{7}}
[8,1,7,5,4,2,6,3]=>{{1,2,3,6,7,8},{4,5}}
[1,2,6,4,7,3,5,8]=>{{1},{2},{3,6},{4},{5,7},{8}}
[1,6,4,3,7,2,5,8]=>{{1},{2,6},{3,4},{5,7},{8}}
[5,7,8,3,2,6,1,4]=>{{1,2,5,7},{3,4,8},{6}}
[8,4,5,1,3,7,6,2]=>{{1,2,4,8},{3,5},{6,7}}
[8,6,4,3,7,1,5,2]=>{{1,2,6,8},{3,4},{5,7}}
[7,3,1,8,6,5,2,4]=>{{1,2,3,7},{4,8},{5,6}}
[2,7,3,1,4,8,6,5]=>{{1,2,4,5,6,7,8},{3}}
[3,1,6,5,7,8,4,2]=>{{1,2,3,6,8},{4,5,7}}
[4,3,1,5,8,7,6,2]=>{{1,2,3,4,5,8},{6,7}}
[4,7,1,3,2,5,6,8]=>{{1,3,4},{2,5,6,7},{8}}
[1,7,2,5,6,8,4,3]=>{{1},{2,3,4,5,6,7,8}}
[4,7,6,8,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[3,5,4,7,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[7,1,5,4,2,3,6,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,1,3,6,4,5,2,8]=>{{1,2,7},{3},{4,5,6},{8}}
[6,1,3,8,4,5,2,7]=>{{1,2,4,5,6,7,8},{3}}
[2,1,8,7,3,6,5,4]=>{{1,2},{3,4,5,7,8},{6}}
[5,8,6,3,1,2,7,4]=>{{1,5},{2,3,4,6,8},{7}}
[5,8,2,7,1,3,6,4]=>{{1,5},{2,3,4,6,7,8}}
[2,6,5,4,1,3,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[4,1,5,7,6,3,2,8]=>{{1,2,4,7},{3,5,6},{8}}
[4,5,1,7,6,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,2,1,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[6,2,1,5,4,3,8,7]=>{{1,3,6},{2},{4,5},{7,8}}
[1,4,2,6,7,8,5,3]=>{{1},{2,3,4,6,8},{5,7}}
[1,4,2,5,6,8,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[2,5,3,6,7,8,4,1]=>{{1,2,4,5,6,7,8},{3}}
[1,8,6,2,4,3,5,7]=>{{1},{2,4,5,7,8},{3,6}}
[3,2,4,5,7,8,1,6]=>{{1,3,4,5,7},{2},{6,8}}
[2,3,4,7,5,8,6,1]=>{{1,2,3,4,6,7,8},{5}}
[6,5,2,8,7,4,3,1]=>{{1,4,6,8},{2,3,5,7}}
[7,8,5,4,2,1,6,3]=>{{1,6,7},{2,3,5,8},{4}}
[7,5,2,8,6,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[7,8,3,2,6,5,4,1]=>{{1,2,4,7,8},{3},{5,6}}
[8,2,6,3,7,5,1,4]=>{{1,3,4,5,6,7,8},{2}}
[8,6,7,2,5,3,1,4]=>{{1,2,3,4,6,7,8},{5}}
[1,6,2,7,8,4,5,3]=>{{1},{2,3,4,5,6,7,8}}
[8,6,2,7,5,4,1,3]=>{{1,2,3,4,6,7,8},{5}}
[1,6,8,2,7,5,3,4]=>{{1},{2,3,4,5,6,7,8}}
[7,6,3,2,8,1,5,4]=>{{1,2,4,5,6,7,8},{3}}
[5,1,7,4,3,8,6,2]=>{{1,2,3,5,6,7,8},{4}}
[8,6,3,7,2,4,1,5]=>{{1,2,4,5,6,7,8},{3}}
[1,7,8,6,4,2,3,5]=>{{1},{2,3,4,5,6,7,8}}
[7,2,8,6,4,1,3,5]=>{{1,3,4,5,6,7,8},{2}}
[1,5,3,7,4,2,6,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,7,6,4,3,2,8,5]=>{{1},{2,3,5,6,7,8},{4}}
[1,7,6,3,4,2,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,2,7,4,3,8,6,5]=>{{1},{2},{3,5,6,7,8},{4}}
[1,5,4,2,3,8,7,6]=>{{1},{2,3,4,5},{6,8},{7}}
[1,5,3,2,4,6,7,8]=>{{1},{2,4,5},{3},{6},{7},{8}}
[1,5,4,2,3,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[1,2,7,6,3,5,8,4]=>{{1},{2},{3,4,5,6,7,8}}
[8,1,3,2,6,5,7,4]=>{{1,2,4,8},{3},{5,6},{7}}
[3,2,7,5,6,1,8,4]=>{{1,3,4,5,6,7,8},{2}}
[7,4,5,1,6,3,8,2]=>{{1,2,4,7,8},{3,5,6}}
[7,5,6,1,4,3,8,2]=>{{1,2,4,5,7,8},{3,6}}
[3,2,6,4,8,5,7,1]=>{{1,3,5,6,8},{2},{4},{7}}
[8,1,4,3,5,2,7,6]=>{{1,2,6,8},{3,4},{5},{7}}
[7,2,8,1,6,3,5,4]=>{{1,3,4,5,6,7,8},{2}}
[8,3,6,5,4,1,2,7]=>{{1,2,3,6,7,8},{4,5}}
[1,7,5,8,4,6,3,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,5,7,1,2,8,3,4]=>{{1,4,6,8},{2,5},{3,7}}
[7,1,4,2,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,5,3,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[8,6,5,2,4,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[3,6,5,2,4,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[6,8,5,2,4,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[3,4,2,8,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,2,5,1,8,3]=>{{1,2,4,6},{3,7,8},{5}}
[3,6,2,5,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[3,4,2,7,8,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,1,4,2,5,8,6,3]=>{{1,2,3,4,6,7,8},{5}}
[7,8,5,1,2,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,4,3,6,7,2]=>{{1,3,5},{2,8},{4},{6},{7}}
[7,2,3,8,6,4,1,5]=>{{1,7},{2},{3},{4,5,6,8}}
[5,2,3,8,7,4,1,6]=>{{1,5,7},{2},{3},{4,6,8}}
[5,7,6,3,1,2,4,8]=>{{1,5},{2,3,4,6,7},{8}}
[4,6,2,7,8,1,3,5]=>{{1,2,3,4,6,7},{5,8}}
[6,2,3,7,1,4,5,8]=>{{1,4,5,6,7},{2},{3},{8}}
[4,6,7,8,2,1,3,5]=>{{1,2,4,5,6,8},{3,7}}
[8,6,3,2,1,7,5,4]=>{{1,2,4,5,6,7,8},{3}}
[6,1,3,4,2,5,8,7]=>{{1,2,5,6},{3},{4},{7,8}}
[5,1,3,6,2,4,8,7]=>{{1,2,5},{3},{4,6},{7,8}}
[1,5,7,6,8,2,4,3]=>{{1},{2,3,4,5,6,7,8}}
[5,7,1,3,8,4,2,6]=>{{1,3,4,5,6,8},{2,7}}
[2,6,1,4,3,7,8,5]=>{{1,2,3,5,6,7,8},{4}}
[1,6,2,4,3,5,8,7]=>{{1},{2,3,5,6},{4},{7,8}}
[5,3,7,6,1,8,4,2]=>{{1,5},{2,3,4,6,7,8}}
[1,5,6,3,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,5,6,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,3,6,1,5,8,4,2]=>{{1,4,7},{2,3,6,8},{5}}
[1,6,3,7,8,5,4,2]=>{{1},{2,5,6,8},{3},{4,7}}
[1,7,8,6,3,5,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,5,6,1,8,4,2]=>{{1,3,5},{2,4,6,7,8}}
[5,6,2,8,4,7,3,1]=>{{1,4,5,8},{2,3,6,7}}
[7,3,5,4,1,2,6,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,8,5,1,3,2,4,6]=>{{1,4,7},{2,6,8},{3,5}}
[7,5,1,3,8,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[7,1,3,8,2,5,4,6]=>{{1,2,4,5,6,7,8},{3}}
[3,1,5,4,7,2,6,8]=>{{1,2,3,5,6,7},{4},{8}}
[5,7,6,1,3,8,2,4]=>{{1,3,4,5,6,8},{2,7}}
[5,7,6,3,8,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[5,1,3,7,6,2,4,8]=>{{1,2,5,6},{3},{4,7},{8}}
[1,6,3,7,2,4,5,8]=>{{1},{2,4,5,6,7},{3},{8}}
[5,3,2,4,8,1,7,6]=>{{1,5,6,8},{2,3},{4},{7}}
[6,8,5,3,2,7,1,4]=>{{1,6,7},{2,3,4,5,8}}
[8,3,7,2,6,5,1,4]=>{{1,2,3,4,7,8},{5,6}}
[4,6,2,7,1,3,8,5]=>{{1,4,5,7,8},{2,3,6}}
[3,5,1,4,7,2,8,6]=>{{1,3},{2,5,6,7,8},{4}}
[5,1,4,8,7,3,2,6]=>{{1,2,5,7},{3,4,6,8}}
[6,1,3,4,2,7,8,5]=>{{1,2,5,6,7,8},{3},{4}}
[6,5,2,3,7,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[1,5,3,8,4,2,7,6]=>{{1},{2,4,5,6,8},{3},{7}}
[5,4,2,1,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[3,1,7,4,2,6,8,5]=>{{1,2,3,5,7,8},{4},{6}}
[7,4,8,2,3,5,1,6]=>{{1,7},{2,4},{3,5,6,8}}
[8,4,1,3,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[8,1,7,3,2,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,6,5,2,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[3,1,6,8,4,2,7,5]=>{{1,2,3,6},{4,5,8},{7}}
[5,6,2,3,7,4,1,8]=>{{1,5,7},{2,3,4,6},{8}}
[6,2,4,7,3,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[1,4,8,5,3,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[2,5,6,3,1,8,4,7]=>{{1,2,5},{3,4,6,7,8}}
[4,5,1,2,7,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,1,2,6,7,3]=>{{1,4},{2,3,5,8},{6},{7}}
[4,6,7,5,1,2,8,3]=>{{1,4,5},{2,6},{3,7,8}}
[7,2,8,1,4,5,3,6]=>{{1,3,4,5,6,7,8},{2}}
[6,1,4,7,3,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,3,4,8,2,5]=>{{1,2,7},{3,4,5,6,8}}
[2,8,4,6,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[8,2,6,3,5,1,4,7]=>{{1,3,4,6,7,8},{2},{5}}
[3,7,4,1,5,8,2,6]=>{{1,3,4},{2,7},{5},{6,8}}
[3,8,4,1,7,2,5,6]=>{{1,3,4},{2,6,8},{5,7}}
[6,7,5,1,3,8,2,4]=>{{1,4,6,8},{2,7},{3,5}}
[8,5,1,3,6,7,2,4]=>{{1,3,4,8},{2,5,6,7}}
[7,8,6,2,4,1,3,5]=>{{1,3,6,7},{2,4,5,8}}
[8,2,4,1,3,6,7,5]=>{{1,3,4,5,8},{2},{6},{7}}
[8,1,3,6,2,5,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[1,5,6,3,8,4,7,2]=>{{1},{2,5,8},{3,4,6},{7}}
[5,6,1,3,7,2,8,4]=>{{1,3,4,5,7,8},{2,6}}
[5,6,1,8,2,3,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[5,6,1,2,8,4,7,3]=>{{1,3,5,8},{2,4,6},{7}}
[3,7,8,1,6,4,2,5]=>{{1,3,4,5,6,8},{2,7}}
[1,7,8,6,3,4,2,5]=>{{1},{2,7},{3,5,8},{4,6}}
[1,7,3,8,6,4,2,5]=>{{1},{2,7},{3},{4,5,6,8}}
[5,7,1,8,6,4,2,3]=>{{1,3,4,5,6,8},{2,7}}
[7,8,1,5,6,4,2,3]=>{{1,2,3,7,8},{4,5,6}}
[7,1,8,5,6,4,2,3]=>{{1,2,7},{3,8},{4,5,6}}
[7,1,5,8,6,4,2,3]=>{{1,2,7},{3,4,5,6,8}}
[8,1,3,5,6,4,2,7]=>{{1,2,7,8},{3},{4,5,6}}
[1,3,8,5,6,4,2,7]=>{{1},{2,3,7,8},{4,5,6}}
[1,3,5,8,6,4,2,7]=>{{1},{2,3,4,5,6,7,8}}
[1,5,7,8,6,4,2,3]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,6,5,3,4,7]=>{{1},{2,3,4,6,7,8},{5}}
[8,6,1,5,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,5,1,6,2,3,4,7]=>{{1,3,4,6,7,8},{2,5}}
[7,6,1,2,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,4,1,3,5,6]=>{{1,2,5,7},{3,6,8},{4}}
[6,8,1,2,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,3,5,6,7,2,4]=>{{1,2,4,5,6,7,8},{3}}
[8,1,2,5,3,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,2,7,3,4,8,1,6]=>{{1,3,4,5,7},{2},{6,8}}
[2,7,5,4,1,3,6,8]=>{{1,2,3,5,6,7},{4},{8}}
[2,7,4,6,5,1,8,3]=>{{1,2,3,4,6,7,8},{5}}
[6,8,7,5,2,1,4,3]=>{{1,6},{2,3,4,5,7,8}}
[2,8,6,3,5,1,4,7]=>{{1,2,3,4,6,7,8},{5}}
[1,2,8,6,4,5,3,7]=>{{1},{2},{3,7,8},{4,5,6}}
[1,5,8,7,6,3,4,2]=>{{1},{2,3,5,6,8},{4,7}}
[1,4,7,8,5,6,3,2]=>{{1},{2,4,8},{3,7},{5},{6}}
[1,6,4,8,5,7,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,6,8,5,2,7,3,4]=>{{1},{2,3,4,5,6,7,8}}
[1,3,4,8,5,2,7,6]=>{{1},{2,3,4,6,8},{5},{7}}
[3,5,8,7,6,2,4,1]=>{{1,3,8},{2,5,6},{4,7}}
[6,5,3,7,4,1,8,2]=>{{1,6},{2,4,5,7,8},{3}}
[3,1,5,4,6,8,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[3,1,6,4,2,5,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[3,6,1,4,5,7,8,2]=>{{1,3},{2,6,7,8},{4},{5}}
[1,8,4,7,2,3,6,5]=>{{1},{2,5,8},{3,4,6,7}}
[5,7,8,2,4,6,1,3]=>{{1,2,4,5,7},{3,8},{6}}
[5,4,2,3,6,8,1,7]=>{{1,5,6,7,8},{2,3,4}}
[3,8,1,6,4,2,5,7]=>{{1,3},{2,4,5,6,7,8}}
[7,3,2,1,8,6,4,5]=>{{1,4,7},{2,3},{5,8},{6}}
[8,7,2,4,1,3,6,5]=>{{1,5,8},{2,3,6,7},{4}}
[8,2,6,3,5,7,1,4]=>{{1,3,4,6,7,8},{2},{5}}
[1,8,3,7,4,6,5,2]=>{{1},{2,8},{3},{4,5,7},{6}}
[8,2,3,1,7,4,5,6]=>{{1,4,6,8},{2},{3},{5,7}}
[3,1,7,8,6,2,5,4]=>{{1,2,3,5,6,7},{4,8}}
[4,8,1,2,6,5,7,3]=>{{1,2,3,4,8},{5,6},{7}}
[5,6,1,8,3,7,2,4]=>{{1,3,5},{2,6,7},{4,8}}
[2,8,1,6,5,3,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[2,1,5,7,6,3,8,4]=>{{1,2},{3,5,6},{4,7,8}}
[4,1,2,5,7,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[4,3,5,1,7,8,6,2]=>{{1,4},{2,3,5,6,7,8}}
[1,8,5,2,3,4,7,6]=>{{1},{2,4,6,8},{3,5},{7}}
[1,5,8,2,3,4,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,2,7,8,4,5,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,3,8,7,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,2,7,6,3,1]=>{{1,3,5,7,8},{2,4},{6}}
[2,3,6,1,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,2,1,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[4,6,1,7,5,8,3,2]=>{{1,3,4,7},{2,6,8},{5}}
[4,1,5,7,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,2,1,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[4,3,6,5,1,7,8,2]=>{{1,4,5},{2,3,6,7,8}}
[4,6,5,3,1,7,8,2]=>{{1,3,4,5},{2,6,7,8}}
[5,8,1,4,2,3,6,7]=>{{1,2,3,5,6,7,8},{4}}
[4,5,8,2,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,4,8,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[5,3,6,8,1,4,7,2]=>{{1,5},{2,3,4,6,8},{7}}
[3,5,1,8,6,4,7,2]=>{{1,3},{2,4,5,6,8},{7}}
[4,7,2,8,3,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[1,2,5,6,8,3,7,4]=>{{1},{2},{3,4,5,6,8},{7}}
[5,3,8,4,6,2,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[7,4,8,1,5,2,6,3]=>{{1,2,4,6,7},{3,8},{5}}
[8,3,2,1,6,5,7,4]=>{{1,4,8},{2,3},{5,6},{7}}
[4,1,5,6,8,7,2,3]=>{{1,2,4,6,7},{3,5,8}}
[1,2,5,6,8,4,7,3]=>{{1},{2},{3,5,8},{4,6},{7}}
[1,5,6,8,4,7,2,3]=>{{1},{2,3,4,5,6,7,8}}
[5,6,8,1,2,4,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[6,8,1,4,5,7,2,3]=>{{1,2,3,6,7,8},{4},{5}}
[4,3,5,1,8,6,7,2]=>{{1,4},{2,3,5,8},{6},{7}}
[1,3,5,6,8,4,7,2]=>{{1},{2,3,5,8},{4,6},{7}}
[5,6,8,2,3,4,7,1]=>{{1,3,5,8},{2,4,6},{7}}
[6,5,1,2,4,8,7,3]=>{{1,3,6,8},{2,4,5},{7}}
[5,8,7,2,1,3,6,4]=>{{1,5},{2,4,8},{3,6,7}}
[5,1,7,2,8,6,3,4]=>{{1,2,4,5,8},{3,7},{6}}
[6,1,5,3,4,8,7,2]=>{{1,2,6,8},{3,4,5},{7}}
[5,8,6,3,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,7,1,6,3,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[3,2,1,7,8,6,4,5]=>{{1,3},{2},{4,7},{5,8},{6}}
[8,6,7,1,2,5,3,4]=>{{1,4,8},{2,5,6},{3,7}}
[1,5,6,4,2,8,7,3]=>{{1},{2,5},{3,6,8},{4},{7}}
[7,5,1,4,8,2,3,6]=>{{1,3,7},{2,5,6,8},{4}}
[3,2,8,1,7,5,6,4]=>{{1,3,4,8},{2},{5,6,7}}
[8,4,3,1,7,5,6,2]=>{{1,2,4,8},{3},{5,6,7}}
[6,1,7,8,4,2,3,5]=>{{1,2,6},{3,7},{4,5,8}}
[7,4,3,1,8,5,2,6]=>{{1,2,4,7},{3},{5,6,8}}
[7,8,1,6,3,4,5,2]=>{{1,3,5,7},{2,8},{4,6}}
[6,8,1,7,3,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,3,8,2,7,1]=>{{1,3,4,5,8},{2,6},{7}}
[4,5,6,3,8,1,7,2]=>{{1,3,4,6},{2,5,8},{7}}
[7,8,3,5,2,1,6,4]=>{{1,6,7},{2,4,5,8},{3}}
[6,3,7,5,2,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[6,2,4,5,7,3,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[7,8,1,5,6,4,3,2]=>{{1,3,7},{2,8},{4,5,6}}
[6,3,7,5,1,4,2,8]=>{{1,4,5,6},{2,3,7},{8}}
[1,3,8,2,4,6,7,5]=>{{1},{2,3,4,5,8},{6},{7}}
[6,1,7,3,4,2,5,8]=>{{1,2,6},{3,4,5,7},{8}}
[3,1,7,2,5,8,6,4]=>{{1,2,3,4,6,7,8},{5}}
[2,8,7,6,3,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,7,1,5,6,4,3]=>{{1,2,3,4,7,8},{5},{6}}
[3,5,6,2,8,1,7,4]=>{{1,3,6},{2,4,5,8},{7}}
[4,1,5,7,3,8,2,6]=>{{1,2,4,7},{3,5},{6,8}}
[7,1,6,8,2,5,3,4]=>{{1,2,3,5,6,7},{4,8}}
[1,6,5,7,4,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[7,2,8,4,5,6,3,1]=>{{1,3,7,8},{2},{4},{5},{6}}
[6,8,7,3,2,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,1,4,5,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[7,5,8,6,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,3,8,5,1,4]=>{{1,2,7},{3,4,5,6,8}}
[2,3,1,8,4,6,5,7]=>{{1,2,3},{4,5,7,8},{6}}
[2,3,1,7,6,8,4,5]=>{{1,2,3},{4,7},{5,6,8}}
[2,3,1,8,4,6,7,5]=>{{1,2,3},{4,5,8},{6},{7}}
[4,2,3,5,1,8,6,7]=>{{1,4,5},{2},{3},{6,7,8}}
[5,8,7,2,6,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,1,7,4,3,2]=>{{1,4,6},{2,8},{3,5,7}}
[6,8,5,2,7,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,6,5,2,1,4]=>{{1,7},{2,3,4,6,8},{5}}
[7,5,8,1,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,2,6,4,1,3]=>{{1,7},{2,4,5,6},{3,8}}
[6,3,2,8,1,7,5,4]=>{{1,5,6,7},{2,3},{4,8}}
[2,6,8,7,1,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,7,6,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,1,4,5,2,8]=>{{1,3,4,5,6},{2,7},{8}}
[4,1,6,2,7,5,3,8]=>{{1,2,4},{3,5,6,7},{8}}
[7,6,2,5,3,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[4,3,1,7,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[4,5,3,1,2,8,6,7]=>{{1,4},{2,5},{3},{6,7,8}}
[2,4,5,3,1,8,6,7]=>{{1,2,3,4,5},{6,7,8}}
[5,7,6,2,3,1,4,8]=>{{1,3,5,6},{2,4,7},{8}}
[4,1,3,7,5,2,6,8]=>{{1,2,4,6,7},{3},{5},{8}}
[4,1,6,3,2,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,4,1,3,2,6,8]=>{{1,2,3,4,5,6,7},{8}}
[2,4,8,5,6,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,4,1,3,6,8]=>{{1,2,5},{3,6,7},{4},{8}}
[5,7,4,1,3,2,6,8]=>{{1,3,4,5},{2,6,7},{8}}
[2,6,8,4,5,3,1,7]=>{{1,2,3,6,7,8},{4},{5}}
[5,2,3,7,4,1,6,8]=>{{1,4,5,6,7},{2},{3},{8}}
[4,5,1,6,3,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,1,6,3,2,4,7,8]=>{{1,2,5},{3,4,6},{7},{8}}
[4,2,5,1,6,3,7,8]=>{{1,4},{2},{3,5,6},{7},{8}}
[5,1,6,2,4,3,7,8]=>{{1,2,4,5},{3,6},{7},{8}}
[5,3,4,8,7,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[8,3,1,6,7,5,4,2]=>{{1,2,3,8},{4,5,6,7}}
[8,4,6,5,7,2,3,1]=>{{1,8},{2,3,4,5,6,7}}
[1,8,2,6,7,4,5,3]=>{{1},{2,3,8},{4,6},{5,7}}
[8,5,7,2,4,3,6,1]=>{{1,8},{2,4,5},{3,6,7}}
[8,5,3,6,4,7,2,1]=>{{1,8},{2,4,5,6,7},{3}}
[8,2,5,3,6,7,4,1]=>{{1,8},{2},{3,4,5,6,7}}
[1,2,8,3,4,7,6,5]=>{{1},{2},{3,4,5,8},{6,7}}
[6,8,5,2,7,1,3,4]=>{{1,6},{2,4,8},{3,5,7}}
[7,6,4,5,2,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[8,2,4,7,6,3,1,5]=>{{1,3,4,5,6,7,8},{2}}
[8,7,5,1,4,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[7,3,8,5,4,2,1,6]=>{{1,7},{2,3,6,8},{4,5}}
[6,3,4,7,2,8,5,1]=>{{1,6,8},{2,3,4,5,7}}
[8,1,7,3,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,5,3,4,2,6]=>{{1,2,7},{3,4,5,6,8}}
[6,8,4,3,1,5,2,7]=>{{1,5,6},{2,7,8},{3,4}}
[1,4,5,8,3,2,6,7]=>{{1},{2,4,6,7,8},{3,5}}
[1,5,2,4,7,8,6,3]=>{{1},{2,3,5,6,7,8},{4}}
[5,2,7,4,3,8,6,1]=>{{1,3,5,6,7,8},{2},{4}}
[2,7,3,4,8,5,6,1]=>{{1,2,5,6,7,8},{3},{4}}
[2,7,6,8,3,5,4,1]=>{{1,2,4,7,8},{3,5,6}}
[2,7,4,5,3,8,6,1]=>{{1,2,6,7,8},{3,4,5}}
[6,2,3,7,4,5,8,1]=>{{1,4,5,6,7,8},{2},{3}}
[1,6,3,2,7,5,8,4]=>{{1},{2,4,5,6,7,8},{3}}
[7,3,5,2,6,8,1,4]=>{{1,7},{2,3,4,5,6,8}}
[6,4,2,7,1,5,8,3]=>{{1,5,6},{2,3,4,7,8}}
[2,5,3,6,4,7,8,1]=>{{1,2,4,5,6,7,8},{3}}
[4,2,5,3,6,7,8,1]=>{{1,3,4,5,6,7,8},{2}}
[1,6,5,2,4,7,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,7,2,4,6,3,5]=>{{1},{2,4,5,8},{3,7},{6}}
[1,8,7,2,5,4,3,6]=>{{1},{2,4,6,8},{3,7},{5}}
[1,5,4,2,7,3,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,5,4,2,8,7,3,6]=>{{1},{2,3,4,5,6,7,8}}
[1,6,8,3,5,2,4,7]=>{{1},{2,6},{3,4,7,8},{5}}
[1,7,6,2,3,5,8,4]=>{{1},{2,4,7,8},{3,5,6}}
[1,2,8,3,6,5,4,7]=>{{1},{2},{3,4,7,8},{5,6}}
[1,3,8,6,5,2,4,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,4,7,3,2,8,6,5]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,5,2,4,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,8,4,3,2,5,7]=>{{1},{2,6},{3,5,7,8},{4}}
[1,7,5,3,2,6,4,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,2,6,5,3,8,4,7]=>{{1},{2},{3,4,5,6,7,8}}
[1,7,3,2,8,4,6,5]=>{{1},{2,4,6,7},{3},{5,8}}
[1,6,5,2,8,4,7,3]=>{{1},{2,4,6},{3,5,8},{7}}
[1,8,3,7,2,4,6,5]=>{{1},{2,5,8},{3},{4,6,7}}
[5,4,2,8,7,6,1,3]=>{{1,5,7},{2,3,4,8},{6}}
[8,6,3,2,5,7,4,1]=>{{1,8},{2,4,6,7},{3},{5}}
[7,3,2,1,6,5,8,4]=>{{1,4,7,8},{2,3},{5,6}}
[7,3,2,6,1,5,8,4]=>{{1,4,5,6,7,8},{2,3}}
[6,8,5,2,7,1,4,3]=>{{1,6},{2,3,4,5,7,8}}
[6,8,2,5,1,7,4,3]=>{{1,4,5,6,7},{2,3,8}}
[6,8,5,7,2,1,4,3]=>{{1,6},{2,3,5,8},{4,7}}
[6,5,8,2,7,4,1,3]=>{{1,2,4,5,6,7},{3,8}}
[6,2,1,7,5,8,4,3]=>{{1,3,6,8},{2},{4,7},{5}}
[1,6,4,8,5,3,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[4,2,6,7,8,1,3,5]=>{{1,3,4,6,7},{2},{5,8}}
[4,6,5,1,3,7,8,2]=>{{1,4},{2,6,7,8},{3,5}}
[5,1,7,2,6,4,8,3]=>{{1,2,4,5,6},{3,7,8}}
[4,1,7,6,5,8,2,3]=>{{1,2,3,4,6,7,8},{5}}
[4,2,3,6,7,8,1,5]=>{{1,4,5,6,7,8},{2},{3}}
[4,7,2,1,6,5,8,3]=>{{1,4},{2,3,7,8},{5,6}}
[2,4,3,6,7,8,1,5]=>{{1,2,4,5,6,7,8},{3}}
[6,8,5,2,7,3,1,4]=>{{1,3,5,6,7},{2,4,8}}
[6,5,1,3,7,8,2,4]=>{{1,3,4,6,8},{2,5,7}}
[7,2,1,4,3,5,8,6]=>{{1,3,5,6,7,8},{2},{4}}
[6,1,2,4,3,7,8,5]=>{{1,2,3,5,6,7,8},{4}}
[8,1,5,4,2,3,6,7]=>{{1,2,3,5,6,7,8},{4}}
[7,1,2,4,6,3,8,5]=>{{1,2,3,5,6,7,8},{4}}
[7,1,2,6,5,3,8,4]=>{{1,2,3,4,6,7,8},{5}}
[7,5,6,1,2,4,8,3]=>{{1,3,4,6,7,8},{2,5}}
[7,1,4,5,2,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[6,1,4,8,7,2,3,5]=>{{1,2,6},{3,4,5,7,8}}
[6,1,8,5,7,2,3,4]=>{{1,2,6},{3,4,5,7,8}}
[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,7,5,8,2,3,4]=>{{1,2,6},{3,7},{4,5,8}}
[6,1,4,7,8,2,3,5]=>{{1,2,6},{3,4,7},{5,8}}
[8,1,2,3,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,1,2,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[1,6,8,7,5,3,4,2]=>{{1},{2,3,6,8},{4,7},{5}}
[6,1,8,7,5,2,3,4]=>{{1,2,6},{3,4,7,8},{5}}
[8,3,1,2,4,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[8,3,1,2,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[6,3,1,2,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[6,7,1,4,2,3,5,8]=>{{1,3,6},{2,5,7},{4},{8}}
[6,1,7,4,8,2,3,5]=>{{1,2,6},{3,7},{4},{5,8}}
[6,7,8,5,1,2,4,3]=>{{1,2,4,5,6,7},{3,8}}
[4,3,8,5,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,3,8,6,7,2,5,1]=>{{1,2,3,4,6,8},{5,7}}
[7,6,8,1,5,3,4,2]=>{{1,4,7},{2,3,6,8},{5}}
[7,4,6,1,5,3,8,2]=>{{1,2,4,7,8},{3,6},{5}}
[6,3,8,1,7,2,5,4]=>{{1,2,3,4,6,8},{5,7}}
[6,1,5,4,8,2,7,3]=>{{1,2,6},{3,5,8},{4},{7}}
[6,2,5,4,7,1,8,3]=>{{1,6},{2},{3,5,7,8},{4}}
[8,3,6,7,5,1,2,4]=>{{1,2,3,4,6,7,8},{5}}
[8,2,1,6,5,7,4,3]=>{{1,3,8},{2},{4,6,7},{5}}
[2,7,1,8,5,6,4,3]=>{{1,2,3,4,7,8},{5},{6}}
[4,6,8,2,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[6,8,2,1,3,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,6,4,8,2,7]=>{{1,3},{2,4,5,6,7,8}}
[3,5,8,6,2,1,4,7]=>{{1,3,4,6,7,8},{2,5}}
[2,4,8,5,6,1,3,7]=>{{1,2,4,5,6},{3,7,8}}
[4,8,2,5,6,1,3,7]=>{{1,4,5,6},{2,3,7,8}}
[5,3,8,4,2,7,6,1]=>{{1,2,3,5,8},{4},{6,7}}
[2,8,5,3,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[1,7,8,4,6,3,2,5]=>{{1},{2,7},{3,5,6,8},{4}}
[8,7,2,4,6,3,1,5]=>{{1,2,3,5,6,7,8},{4}}
[8,7,3,2,1,6,4,5]=>{{1,5,8},{2,4,7},{3},{6}}
[7,8,3,4,6,5,2,1]=>{{1,2,7,8},{3},{4},{5,6}}
[8,7,3,6,5,2,4,1]=>{{1,8},{2,4,6,7},{3},{5}}
[3,1,2,8,6,5,7,4]=>{{1,2,3},{4,8},{5,6},{7}}
[3,8,2,7,5,4,6,1]=>{{1,2,3,8},{4,6,7},{5}}
[8,7,1,4,5,3,6,2]=>{{1,2,3,6,7,8},{4},{5}}
[2,8,7,4,6,3,5,1]=>{{1,2,8},{3,5,6,7},{4}}
[2,8,7,4,6,3,1,5]=>{{1,2,3,5,6,7,8},{4}}
[8,3,4,1,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[8,4,1,3,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[7,3,8,6,2,1,4,5]=>{{1,4,6,7},{2,3,5,8}}
[7,2,8,4,6,5,1,3]=>{{1,7},{2},{3,8},{4},{5,6}}
[5,8,6,4,7,2,3,1]=>{{1,2,3,5,6,7,8},{4}}
[4,7,2,6,5,8,3,1]=>{{1,4,6,8},{2,3,7},{5}}
[3,6,8,5,7,4,2,1]=>{{1,3,8},{2,4,5,6,7}}
[6,7,5,2,4,8,3,1]=>{{1,6,8},{2,3,4,5,7}}
[8,1,2,7,5,6,3,4]=>{{1,2,3,4,7,8},{5},{6}}
[8,2,7,3,4,6,1,5]=>{{1,3,4,5,7,8},{2},{6}}
[6,7,5,4,8,1,3,2]=>{{1,6},{2,3,5,7,8},{4}}
[8,3,5,6,4,7,2,1]=>{{1,8},{2,3,4,5,6,7}}
[8,5,6,2,4,3,7,1]=>{{1,8},{2,4,5},{3,6},{7}}
[6,5,8,1,3,4,2,7]=>{{1,4,6},{2,3,5,7,8}}
[6,8,4,5,1,3,2,7]=>{{1,3,4,5,6},{2,7,8}}
[6,4,8,7,5,3,2,1]=>{{1,3,6,8},{2,4,7},{5}}
[6,7,1,4,3,2,8,5]=>{{1,2,3,5,6,7,8},{4}}
[7,2,5,1,4,8,3,6]=>{{1,3,4,5,7},{2},{6,8}}
[5,8,1,3,4,2,7,6]=>{{1,3,4,5},{2,6,8},{7}}
[1,5,6,3,2,8,7,4]=>{{1},{2,5},{3,4,6,8},{7}}
[1,3,7,6,8,4,2,5]=>{{1},{2,3,7},{4,6},{5,8}}
[1,6,7,3,2,8,5,4]=>{{1},{2,3,4,5,6,7,8}}
[3,2,7,6,8,4,5,1]=>{{1,3,5,7,8},{2},{4,6}}
[1,3,8,5,2,7,6,4]=>{{1},{2,3,4,5,8},{6,7}}
[6,4,1,5,2,8,7,3]=>{{1,3,6,8},{2,4,5},{7}}
[7,6,5,3,1,8,2,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,1,4,7,3,6,8]=>{{1,2,3,5,6,7},{4},{8}}
[3,1,6,5,7,2,4,8]=>{{1,2,3,6},{4,5,7},{8}}
[2,6,1,5,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,1,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,6,1,5,7,4,3,8]=>{{1,2,3,4,5,6,7},{8}}
[3,1,6,5,2,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[3,6,5,1,4,2,7,8]=>{{1,3,4,5},{2,6},{7},{8}}
[3,6,5,1,7,2,4,8]=>{{1,3,4,5,7},{2,6},{8}}
[3,6,5,2,1,4,7,8]=>{{1,3,5},{2,4,6},{7},{8}}
[5,4,3,6,1,7,2,8]=>{{1,5},{2,4,6,7},{3},{8}}
[4,5,2,7,6,1,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,5,3,1,2,7,8]=>{{1,3,4,5},{2,6},{7},{8}}
[5,4,1,6,3,7,2,8]=>{{1,3,5},{2,4,6,7},{8}}
[5,4,2,6,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[3,6,5,7,1,4,2,8]=>{{1,3,5},{2,4,6,7},{8}}
[3,6,5,1,4,7,2,8]=>{{1,3,4,5},{2,6,7},{8}}
[4,3,6,5,7,1,2,8]=>{{1,2,3,4,5,6,7},{8}}
[4,2,6,5,1,3,7,8]=>{{1,4,5},{2},{3,6},{7},{8}}
[4,1,6,5,3,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[4,2,5,7,6,1,3,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,4,7,6,1,2,5,8]=>{{1,3,5,7},{2,4,6},{8}}
[4,2,5,7,6,3,8,1]=>{{1,4,7,8},{2},{3,5,6}}
[4,1,6,5,2,7,3,8]=>{{1,2,4,5},{3,6,7},{8}}
[3,6,5,7,2,1,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[3,5,7,6,2,4,1,8]=>{{1,3,7},{2,5},{4,6},{8}}
[5,4,2,6,3,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,5,2,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,6,5,2,1,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,8,2,1,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,8,2,4,6,7,1]=>{{1,3,8},{2,4,5},{6},{7}}
[5,3,8,2,1,4,6,7]=>{{1,5},{2,3,4,6,7,8}}
[5,3,1,8,2,4,6,7]=>{{1,2,3,5},{4,6,7,8}}
[5,1,3,8,2,4,6,7]=>{{1,2,5},{3},{4,6,7,8}}
[1,5,8,4,2,3,6,7]=>{{1},{2,5},{3,6,7,8},{4}}
[5,8,2,1,4,3,6,7]=>{{1,4,5},{2,3,6,7,8}}
[5,8,2,4,1,6,7,3]=>{{1,5},{2,3,8},{4},{6},{7}}
[5,8,2,4,6,3,1,7]=>{{1,2,3,5,6,7,8},{4}}
[5,8,2,4,3,6,1,7]=>{{1,2,3,5,7,8},{4},{6}}
[5,8,1,4,6,2,3,7]=>{{1,2,3,5,6,7,8},{4}}
[1,5,8,4,6,7,2,3]=>{{1},{2,5,6,7},{3,8},{4}}
[5,1,8,4,6,7,2,3]=>{{1,2,5,6,7},{3,8},{4}}
[5,8,2,4,6,3,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[3,8,4,6,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,4,6,7,2,5,1]=>{{1,2,3,4,6,8},{5,7}}
[8,4,3,6,7,2,5,1]=>{{1,8},{2,4,6},{3},{5,7}}
[8,4,3,6,7,2,1,5]=>{{1,5,7,8},{2,4,6},{3}}
[8,6,2,4,5,3,7,1]=>{{1,8},{2,3,6},{4},{5},{7}}
[1,8,6,4,5,7,2,3]=>{{1},{2,3,6,7,8},{4},{5}}
[8,6,2,4,5,3,1,7]=>{{1,7,8},{2,3,6},{4},{5}}
[1,8,6,4,2,3,5,7]=>{{1},{2,5,7,8},{3,6},{4}}
[3,8,1,6,2,4,5,7]=>{{1,3},{2,5,7,8},{4,6}}
[3,8,6,2,1,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,2,4,1,5,7]=>{{1,3,6},{2,4,5,7,8}}
[3,8,6,2,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[8,3,6,2,4,5,1,7]=>{{1,7,8},{2,3,4,5,6}}
[8,1,3,6,2,4,5,7]=>{{1,2,5,7,8},{3},{4,6}}
[8,3,6,7,2,1,4,5]=>{{1,2,3,5,6,8},{4,7}}
[3,8,6,7,2,1,4,5]=>{{1,3,6},{2,5,8},{4,7}}
[8,2,6,4,5,1,7,3]=>{{1,3,6,8},{2},{4},{5},{7}}
[1,8,4,6,7,5,2,3]=>{{1},{2,3,4,5,6,7,8}}
[8,4,6,2,3,7,5,1]=>{{1,8},{2,4},{3,5,6,7}}
[8,4,7,2,1,3,6,5]=>{{1,5,8},{2,4},{3,6,7}}
[2,7,1,6,3,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,1,5,3,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[8,2,1,4,7,3,6,5]=>{{1,3,5,6,7,8},{2},{4}}
[1,6,2,5,8,4,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[2,1,5,8,7,3,6,4]=>{{1,2},{3,5,6,7},{4,8}}
[3,2,1,6,7,4,8,5]=>{{1,3},{2},{4,6},{5,7,8}}
[4,3,1,7,8,5,2,6]=>{{1,2,3,4,7},{5,6,8}}
[5,6,8,2,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,8,5,3,6,4,7,1]=>{{1,2,8},{3,4,5,6},{7}}
[1,2,8,6,4,7,3,5]=>{{1},{2},{3,4,5,6,7,8}}
[5,3,2,7,8,6,4,1]=>{{1,5,8},{2,3},{4,7},{6}}
[4,2,7,8,3,5,6,1]=>{{1,4,8},{2},{3,5,6,7}}
[2,8,3,7,1,4,6,5]=>{{1,2,5,8},{3},{4,6,7}}
[2,8,7,1,5,3,6,4]=>{{1,2,4,8},{3,6,7},{5}}
[7,3,5,6,4,2,8,1]=>{{1,7,8},{2,3,4,5,6}}
[3,8,4,2,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}
[4,8,3,2,7,5,6,1]=>{{1,2,4,8},{3},{5,6,7}}
[3,2,4,8,7,5,6,1]=>{{1,3,4,8},{2},{5,6,7}}
[2,6,8,1,5,3,4,7]=>{{1,2,3,4,6,7,8},{5}}
[3,2,5,6,8,1,4,7]=>{{1,3,4,5,6,7,8},{2}}
[3,8,1,6,4,5,2,7]=>{{1,3},{2,7,8},{4,5,6}}
[8,1,3,6,5,4,2,7]=>{{1,2,7,8},{3},{4,6},{5}}
[7,4,3,6,2,1,8,5]=>{{1,2,4,5,6,7,8},{3}}
[1,2,4,8,6,3,7,5]=>{{1},{2},{3,4,5,6,8},{7}}
[7,2,1,5,3,4,8,6]=>{{1,3,4,5,6,7,8},{2}}
[5,7,2,3,1,4,8,6]=>{{1,5},{2,3,4,6,7,8}}
[7,1,5,2,4,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[8,4,2,7,3,5,6,1]=>{{1,8},{2,3,4,5,6,7}}
[1,8,6,4,7,5,3,2]=>{{1},{2,8},{3,5,6,7},{4}}
[7,4,1,5,8,6,3,2]=>{{1,3,7},{2,4,5,8},{6}}
[4,5,8,7,3,1,2,6]=>{{1,2,3,4,5,6,7,8}}
[1,3,8,7,6,4,2,5]=>{{1},{2,3,4,5,6,7,8}}
[2,8,5,1,7,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[1,8,6,4,7,5,2,3]=>{{1},{2,3,5,6,7,8},{4}}
[2,7,4,6,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[1,2,8,6,4,7,5,3]=>{{1},{2},{3,8},{4,5,6,7}}
[4,1,8,6,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,4,3,1,6,2,5,7]=>{{1,2,4,5,6,7,8},{3}}
[7,5,4,3,8,1,6,2]=>{{1,6,7},{2,5,8},{3,4}}
[5,3,1,6,2,8,7,4]=>{{1,2,3,5},{4,6,8},{7}}
[3,5,4,1,7,8,2,6]=>{{1,3,4},{2,5,7},{6,8}}
[6,4,2,1,5,7,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[3,1,5,8,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,2,5,7,8,4,6,1]=>{{1,3,5,8},{2},{4,6,7}}
[5,3,7,4,2,6,8,1]=>{{1,2,3,5,7,8},{4},{6}}
[5,3,7,4,2,6,1,8]=>{{1,2,3,5,7},{4},{6},{8}}
[5,3,8,4,2,1,6,7]=>{{1,2,3,5,6,7,8},{4}}
[5,2,8,4,3,1,6,7]=>{{1,3,5,6,7,8},{2},{4}}
[5,1,8,4,3,2,6,7]=>{{1,2,3,5,6,7,8},{4}}
[5,2,7,4,3,6,1,8]=>{{1,3,5,7},{2},{4},{6},{8}}
[5,2,7,4,3,6,8,1]=>{{1,3,5,7,8},{2},{4},{6}}
[5,3,7,4,1,6,8,2]=>{{1,5},{2,3,7,8},{4},{6}}
[3,1,5,7,8,4,6,2]=>{{1,2,3,5,8},{4,6,7}}
[3,1,5,7,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[5,2,7,4,1,3,8,6]=>{{1,5},{2},{3,6,7,8},{4}}
[6,2,3,7,4,8,5,1]=>{{1,6,8},{2},{3},{4,5,7}}
[6,2,3,7,4,8,1,5]=>{{1,4,5,6,7,8},{2},{3}}
[6,2,3,7,4,5,1,8]=>{{1,4,5,6,7},{2},{3},{8}}
[6,1,3,7,4,5,8,2]=>{{1,2,4,5,6,7,8},{3}}
[1,2,8,6,4,3,5,7]=>{{1},{2},{3,4,5,6,7,8}}
[6,1,3,7,4,5,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[1,8,6,3,5,4,2,7]=>{{1},{2,7,8},{3,4,6},{5}}
[2,6,1,8,5,3,4,7]=>{{1,2,3,6},{4,7,8},{5}}
[4,5,7,8,1,6,3,2]=>{{1,2,4,5,8},{3,7},{6}}
[2,5,7,8,4,6,3,1]=>{{1,2,4,5,8},{3,7},{6}}
[1,8,2,7,5,3,4,6]=>{{1},{2,3,6,8},{4,7},{5}}
[2,5,4,1,8,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[5,6,8,3,4,2,7,1]=>{{1,3,4,5,8},{2,6},{7}}
[4,1,5,3,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[7,3,5,1,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[7,1,3,2,4,5,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[3,8,7,1,4,2,5,6]=>{{1,3,4,5,7},{2,6,8}}
[5,1,7,8,2,4,3,6]=>{{1,2,5},{3,7},{4,6,8}}
[8,5,4,6,1,7,3,2]=>{{1,2,5,8},{3,4,6,7}}
[5,3,2,1,4,6,8,7]=>{{1,4,5},{2,3},{6},{7,8}}
[5,3,2,4,8,1,6,7]=>{{1,5,6,7,8},{2,3},{4}}
[5,3,2,4,7,1,8,6]=>{{1,5,6,7,8},{2,3},{4}}
[8,4,5,3,7,1,2,6]=>{{1,6,8},{2,3,4,5,7}}
[4,8,1,7,3,5,6,2]=>{{1,3,4,5,6,7},{2,8}}
[5,3,2,4,6,8,1,7]=>{{1,5,6,7,8},{2,3},{4}}
[4,6,8,3,7,1,5,2]=>{{1,2,3,4,6,8},{5,7}}
[1,7,6,4,2,5,3,8]=>{{1},{2,3,5,6,7},{4},{8}}
[7,6,4,2,8,3,1,5]=>{{1,7},{2,3,4,6},{5,8}}
[8,5,2,4,3,7,1,6]=>{{1,6,7,8},{2,3,5},{4}}
[8,5,1,4,3,7,6,2]=>{{1,2,3,5,8},{4},{6,7}}
[7,5,4,1,3,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[3,6,7,2,5,1,8,4]=>{{1,2,3,4,6,7,8},{5}}
[2,6,5,7,1,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,7,8,4,6,2]=>{{1,3},{2,5,8},{4,6,7}}
[1,5,2,4,6,8,7,3]=>{{1},{2,3,5,6,8},{4},{7}}
[8,1,2,4,7,6,5,3]=>{{1,2,3,8},{4},{5,7},{6}}
[3,4,1,8,6,7,5,2]=>{{1,3},{2,4,8},{5,6,7}}
[4,3,8,5,1,7,6,2]=>{{1,4,5},{2,3,8},{6,7}}
[6,1,3,2,8,5,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[8,5,3,2,4,7,1,6]=>{{1,6,7,8},{2,4,5},{3}}
[6,7,4,2,5,8,3,1]=>{{1,6,8},{2,3,4,7},{5}}
[8,5,4,2,6,3,1,7]=>{{1,7,8},{2,3,4,5,6}}
[8,5,2,1,6,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,6,5,1,3,2,7]=>{{1,2,4,5,7,8},{3,6}}
[1,3,8,4,7,5,2,6]=>{{1},{2,3,5,6,7,8},{4}}
[5,3,7,1,4,6,8,2]=>{{1,4,5},{2,3,7,8},{6}}
[5,7,2,6,1,4,8,3]=>{{1,5},{2,3,7,8},{4,6}}
[3,8,5,7,6,1,2,4]=>{{1,3,5,6},{2,4,7,8}}
[8,4,7,5,2,1,3,6]=>{{1,6,8},{2,4,5},{3,7}}
[3,8,6,4,7,2,1,5]=>{{1,2,3,5,6,7,8},{4}}
[5,2,7,4,6,8,3,1]=>{{1,5,6,8},{2},{3,7},{4}}
[4,8,6,3,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,8,3,1,7,6,4,5]=>{{1,2,4,5,7,8},{3},{6}}
[2,5,6,4,8,1,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[5,7,2,1,6,8,3,4]=>{{1,4,5,6,8},{2,3,7}}
[4,7,8,5,1,6,2,3]=>{{1,4,5},{2,7},{3,8},{6}}
[4,5,2,1,6,7,8,3]=>{{1,4},{2,3,5,6,7,8}}
[4,5,6,3,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,7,4,1,8,2]=>{{1,3,6},{2,4,5,7,8}}
[3,5,1,4,2,8,7,6]=>{{1,3},{2,5},{4},{6,8},{7}}
[3,5,1,4,2,6,8,7]=>{{1,3},{2,5},{4},{6},{7,8}}
[3,5,1,4,2,6,7,8]=>{{1,3},{2,5},{4},{6},{7},{8}}
[1,3,8,4,6,2,5,7]=>{{1},{2,3,5,6,7,8},{4}}
[1,8,4,2,3,7,5,6]=>{{1},{2,3,4,5,6,7,8}}
[1,4,8,3,2,7,6,5]=>{{1},{2,3,4,5,8},{6,7}}
[1,3,7,6,5,2,4,8]=>{{1},{2,3,4,6,7},{5},{8}}
[1,2,8,6,7,5,4,3]=>{{1},{2},{3,8},{4,5,6,7}}
[1,7,5,4,3,2,6,8]=>{{1},{2,6,7},{3,5},{4},{8}}
[3,8,5,7,4,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[7,6,3,2,5,1,8,4]=>{{1,2,4,6,7,8},{3},{5}}
[4,2,5,7,8,6,3,1]=>{{1,3,4,5,7,8},{2},{6}}
[6,7,2,4,5,1,8,3]=>{{1,6},{2,3,7,8},{4},{5}}
[5,2,7,8,3,6,1,4]=>{{1,3,5,7},{2},{4,8},{6}}
[8,5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[5,2,8,3,1,4,7,6]=>{{1,5},{2},{3,4,6,8},{7}}
[8,7,2,5,1,4,3,6]=>{{1,4,5,6,8},{2,3,7}}
[8,4,1,3,2,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[8,3,5,1,2,4,7,6]=>{{1,4,6,8},{2,3,5},{7}}
[8,6,5,1,7,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,5,1,2,6,3]=>{{1,3,4,5,8},{2,6,7}}
[3,8,6,2,7,1,5,4]=>{{1,3,6},{2,4,8},{5,7}}
[3,8,4,2,1,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[8,3,1,7,5,6,2,4]=>{{1,2,3,4,7,8},{5},{6}}
[8,4,1,7,5,2,6,3]=>{{1,3,8},{2,4,6,7},{5}}
[8,4,2,7,5,3,1,6]=>{{1,2,3,4,6,7,8},{5}}
[8,4,3,7,5,1,2,6]=>{{1,6,8},{2,4,7},{3},{5}}
[8,5,7,6,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,6,5,2,1,3]=>{{1,3,7,8},{2,4,6},{5}}
[8,3,1,4,7,6,2,5]=>{{1,2,3,5,7,8},{4},{6}}
[8,3,5,7,6,2,4,1]=>{{1,8},{2,3,5,6},{4,7}}
[1,4,6,8,2,5,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[3,6,2,4,8,1,7,5]=>{{1,2,3,6},{4},{5,8},{7}}
[7,3,8,2,4,6,1,5]=>{{1,7},{2,3,4,5,8},{6}}
[1,5,2,6,8,3,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[4,5,3,1,8,2,6,7]=>{{1,4},{2,5,6,7,8},{3}}
[7,2,8,4,1,3,5,6]=>{{1,5,7},{2},{3,6,8},{4}}
[6,1,7,3,2,8,4,5]=>{{1,2,5,6,8},{3,4,7}}
[6,2,1,7,3,8,4,5]=>{{1,3,5,6,8},{2},{4,7}}
[5,8,2,1,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[4,2,5,1,8,3,6,7]=>{{1,4},{2},{3,5,6,7,8}}
[7,4,2,8,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,8,3,5,1,6]=>{{1,7},{2,3,4,5,6,8}}
[6,7,8,5,2,1,4,3]=>{{1,6},{2,4,5,7},{3,8}}
[1,6,2,7,8,4,3,5]=>{{1},{2,3,4,6,7},{5,8}}
[7,3,4,1,8,6,2,5]=>{{1,2,3,4,7},{5,8},{6}}
[4,7,6,3,5,8,2,1]=>{{1,3,4,6,8},{2,7},{5}}
[3,7,6,5,2,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[1,4,7,8,6,2,5,3]=>{{1},{2,3,4,5,6,7,8}}
[1,6,7,8,3,2,5,4]=>{{1},{2,6},{3,5,7},{4,8}}
[1,3,2,7,8,4,6,5]=>{{1},{2,3},{4,6,7},{5,8}}
[5,7,1,4,6,2,8,3]=>{{1,2,3,5,6,7,8},{4}}
[6,3,1,4,7,8,2,5]=>{{1,2,3,5,6,7,8},{4}}
[4,5,7,1,8,6,2,3]=>{{1,4},{2,3,5,7,8},{6}}
[4,3,8,6,5,2,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[2,3,8,6,5,1,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[5,4,7,3,1,2,6,8]=>{{1,5},{2,3,4,6,7},{8}}
[3,1,2,6,5,7,8,4]=>{{1,2,3},{4,6,7,8},{5}}
[7,3,2,6,1,4,8,5]=>{{1,5,7,8},{2,3},{4,6}}
[3,2,5,6,8,4,1,7]=>{{1,3,5,7,8},{2},{4,6}}
[7,2,6,8,5,4,3,1]=>{{1,3,4,6,7,8},{2},{5}}
[3,7,5,6,2,4,1,8]=>{{1,2,3,5,7},{4,6},{8}}
[4,2,5,1,3,6,8,7]=>{{1,4},{2},{3,5},{6},{7,8}}
[5,3,4,2,7,1,8,6]=>{{1,5,6,7,8},{2,3,4}}
[6,5,2,1,3,8,4,7]=>{{1,4,6,7,8},{2,3,5}}
[2,4,3,5,6,8,1,7]=>{{1,2,4,5,6,7,8},{3}}
[6,3,2,4,8,5,1,7]=>{{1,5,6,7,8},{2,3},{4}}
[6,3,1,2,7,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,1,2,5,3,6]=>{{1,2,4,5,6,8},{3,7}}
[7,4,6,1,8,5,2,3]=>{{1,2,4,7},{3,5,6,8}}
[8,5,6,7,2,1,4,3]=>{{1,3,6,8},{2,5},{4,7}}
[2,5,6,3,8,4,7,1]=>{{1,2,5,8},{3,4,6},{7}}
[1,7,6,2,8,3,5,4]=>{{1},{2,4,5,7,8},{3,6}}
[4,1,3,8,5,2,7,6]=>{{1,2,4,6,8},{3},{5},{7}}
[1,8,5,4,7,2,3,6]=>{{1},{2,6,8},{3,5,7},{4}}
[8,2,5,6,4,3,1,7]=>{{1,7,8},{2},{3,4,5,6}}
[2,4,3,8,6,5,1,7]=>{{1,2,4,7,8},{3},{5,6}}
[3,1,4,5,8,6,2,7]=>{{1,2,3,4,5,7,8},{6}}
[1,8,3,2,5,4,6,7]=>{{1},{2,4,6,7,8},{3},{5}}
[5,1,7,3,2,8,4,6]=>{{1,2,5},{3,4,7},{6,8}}
[5,7,8,1,3,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,2,4,1,6,7,3,5]=>{{1,3,4,5,6,7,8},{2}}
[8,7,3,6,2,4,1,5]=>{{1,2,5,7,8},{3},{4,6}}
[1,7,4,8,3,6,2,5]=>{{1},{2,7},{3,4,5,8},{6}}
[7,8,6,1,3,5,4,2]=>{{1,4,7},{2,8},{3,5,6}}
[1,7,5,8,4,3,2,6]=>{{1},{2,7},{3,4,5,6,8}}
[6,3,1,2,7,8,5,4]=>{{1,2,3,4,6,8},{5,7}}
[8,2,7,5,3,4,1,6]=>{{1,3,4,5,6,7,8},{2}}
[6,3,1,2,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,2,6,3,1,5]=>{{1,3,5,6,7,8},{2,4}}
[1,2,5,7,8,3,6,4]=>{{1},{2},{3,4,5,6,7,8}}
[7,6,3,4,2,1,8,5]=>{{1,2,5,6,7,8},{3},{4}}
[8,4,6,2,3,7,1,5]=>{{1,3,5,6,7,8},{2,4}}
[3,4,5,8,1,7,2,6]=>{{1,3,5},{2,4,6,7,8}}
[6,3,4,2,7,8,1,5]=>{{1,5,6,7,8},{2,3,4}}
[5,6,3,7,8,2,1,4]=>{{1,4,5,7,8},{2,6},{3}}
[8,6,3,4,7,2,1,5]=>{{1,5,7,8},{2,6},{3},{4}}
[4,3,8,6,7,5,1,2]=>{{1,4,5,6,7},{2,3,8}}
[4,5,6,2,7,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,2,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[4,5,6,2,1,7,8,3]=>{{1,2,4,5},{3,6,7,8}}
[4,5,6,2,1,7,3,8]=>{{1,2,4,5},{3,6,7},{8}}
[6,8,7,2,3,1,4,5]=>{{1,6},{2,3,4,5,7,8}}
[4,5,1,6,7,3,2,8]=>{{1,3,4,6},{2,5,7},{8}}
[2,5,1,8,3,7,4,6]=>{{1,2,3,5},{4,6,7,8}}
[5,7,2,1,3,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[7,1,5,4,2,6,3,8]=>{{1,2,3,5,7},{4},{6},{8}}
[2,7,4,5,6,8,1,3]=>{{1,2,7},{3,4,5,6,8}}
[2,3,4,6,8,1,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[2,3,5,8,1,6,7,4]=>{{1,2,3,5},{4,8},{6},{7}}
[2,4,7,5,6,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[7,3,4,6,2,8,1,5]=>{{1,7},{2,3,4,5,6,8}}
[4,7,6,5,2,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,8,6,7,3,1]=>{{1,2,3,4,5,6,7,8}}
[7,5,4,1,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,1,7,6,3,4]=>{{1,4,8},{2,3,5,7},{6}}
[2,7,3,6,4,1,8,5]=>{{1,2,4,5,6,7,8},{3}}
[7,2,1,8,5,6,4,3]=>{{1,3,4,7,8},{2},{5},{6}}
[3,6,5,1,4,8,2,7]=>{{1,3,4,5},{2,6,7,8}}
[6,3,5,4,8,1,2,7]=>{{1,6},{2,3,5,7,8},{4}}
[2,5,1,4,6,3,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[3,1,5,6,4,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[8,5,6,4,3,1,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[8,3,5,6,7,1,2,4]=>{{1,4,6,8},{2,3,5,7}}
[2,1,4,7,3,6,8,5]=>{{1,2},{3,4,5,7,8},{6}}
[5,3,7,6,4,8,2,1]=>{{1,4,5,6,8},{2,3,7}}
[3,7,6,4,2,8,1,5]=>{{1,2,3,5,6,7,8},{4}}
[8,6,1,4,3,7,2,5]=>{{1,3,5,8},{2,6,7},{4}}
[8,4,7,5,1,6,3,2]=>{{1,2,4,5,8},{3,7},{6}}
[2,1,5,3,7,8,6,4]=>{{1,2},{3,4,5,6,7,8}}
[5,1,4,7,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,3,7,6,5,2]=>{{1,2,3,4,8},{5,7},{6}}
[8,3,4,1,6,7,5,2]=>{{1,2,3,4,8},{5,6,7}}
[8,1,4,2,6,5,7,3]=>{{1,2,3,4,8},{5,6},{7}}
[5,8,1,4,3,2,6,7]=>{{1,3,5},{2,6,7,8},{4}}
[1,6,4,3,8,2,7,5]=>{{1},{2,6},{3,4},{5,8},{7}}
[7,8,1,4,3,2,5,6]=>{{1,3,5,7},{2,6,8},{4}}
[7,1,8,4,5,3,6,2]=>{{1,2,3,6,7,8},{4},{5}}
[4,3,1,8,6,5,7,2]=>{{1,2,3,4,8},{5,6},{7}}
[4,3,2,7,5,1,8,6]=>{{1,4,6,7,8},{2,3},{5}}
[5,2,3,7,4,1,8,6]=>{{1,4,5,6,7,8},{2},{3}}
[2,1,7,4,3,6,8,5]=>{{1,2},{3,5,7,8},{4},{6}}
[7,1,2,4,5,6,8,3]=>{{1,2,3,7,8},{4},{5},{6}}
[2,8,7,1,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,1,3,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,8,3,1,4,6,7,2]=>{{1,4,5},{2,8},{3},{6},{7}}
[1,7,2,5,4,6,8,3]=>{{1},{2,3,7,8},{4,5},{6}}
[2,5,3,8,1,6,7,4]=>{{1,2,5},{3},{4,8},{6},{7}}
[1,6,4,2,5,7,8,3]=>{{1},{2,3,4,6,7,8},{5}}
[6,5,3,4,1,7,8,2]=>{{1,2,5,6,7,8},{3},{4}}
[5,6,3,4,1,7,8,2]=>{{1,5},{2,6,7,8},{3},{4}}
[2,5,3,1,4,7,8,6]=>{{1,2,4,5},{3},{6,7,8}}
[6,8,2,3,1,5,7,4]=>{{1,5,6},{2,3,4,8},{7}}
[4,3,1,5,2,7,8,6]=>{{1,2,3,4,5},{6,7,8}}
[5,2,3,1,4,7,8,6]=>{{1,4,5},{2},{3},{6,7,8}}
[7,2,1,3,5,6,8,4]=>{{1,3,4,7,8},{2},{5},{6}}
[5,2,4,7,8,6,3,1]=>{{1,5,8},{2},{3,4,7},{6}}
[5,4,8,7,2,3,1,6]=>{{1,2,4,5,7},{3,6,8}}
[8,1,4,5,3,6,2,7]=>{{1,2,7,8},{3,4,5},{6}}
[8,3,5,1,4,6,2,7]=>{{1,2,3,4,5,7,8},{6}}
[5,8,2,1,7,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[6,5,7,2,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,1,3,8,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[3,6,8,4,1,7,2,5]=>{{1,3,5,8},{2,6,7},{4}}
[2,1,8,4,7,6,3,5]=>{{1,2},{3,5,7,8},{4},{6}}
[2,7,5,6,8,4,3,1]=>{{1,2,3,5,7,8},{4,6}}
[3,5,2,4,7,8,6,1]=>{{1,2,3,5,6,7,8},{4}}
[7,5,6,3,8,2,1,4]=>{{1,7},{2,3,4,5,6,8}}
[1,6,2,7,4,5,8,3]=>{{1},{2,3,4,5,6,7,8}}
[7,4,2,6,1,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,6,2,5,7,3]=>{{1,3,8},{2,4,5,6},{7}}
[7,3,4,5,1,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[8,4,2,7,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,1,2,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[8,4,7,6,1,2,5,3]=>{{1,3,5,7,8},{2,4,6}}
[8,7,6,2,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,1,6,2,4,3]=>{{1,2,4,5,6,7},{3,8}}
[6,8,7,4,2,5,1,3]=>{{1,2,3,5,6,7,8},{4}}
[6,8,4,5,7,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[3,1,6,5,4,7,2,8]=>{{1,2,3,6,7},{4,5},{8}}
[4,1,2,6,5,3,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[4,6,1,3,5,2,7,8]=>{{1,3,4},{2,6},{5},{7},{8}}
[4,2,6,3,5,1,7,8]=>{{1,3,4,6},{2},{5},{7},{8}}
[4,6,1,2,5,3,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[5,8,4,7,1,3,6,2]=>{{1,5},{2,8},{3,4,6,7}}
[6,4,7,1,3,5,2,8]=>{{1,2,3,4,5,6,7},{8}}
[6,8,3,1,5,4,7,2]=>{{1,4,6},{2,8},{3},{5},{7}}
[5,1,3,6,7,4,2,8]=>{{1,2,5,7},{3},{4,6},{8}}
[4,2,8,6,7,1,3,5]=>{{1,4,6},{2},{3,5,7,8}}
[6,1,2,4,7,3,5,8]=>{{1,2,3,6},{4},{5,7},{8}}
[5,3,1,6,4,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[4,2,8,1,6,5,7,3]=>{{1,4},{2},{3,8},{5,6},{7}}
[5,6,1,4,8,3,2,7]=>{{1,2,3,5,6,7,8},{4}}
[3,6,4,1,7,2,8,5]=>{{1,3,4},{2,6},{5,7,8}}
[5,2,6,3,7,8,4,1]=>{{1,3,4,5,6,7,8},{2}}
[2,4,1,3,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}
[2,6,1,5,7,8,4,3]=>{{1,2,3,6,8},{4,5,7}}
[5,1,6,4,7,8,2,3]=>{{1,2,5,7},{3,6,8},{4}}
[8,4,6,3,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[4,7,6,8,2,3,5,1]=>{{1,4,8},{2,5,7},{3,6}}
[5,7,4,8,1,2,6,3]=>{{1,5},{2,6,7},{3,4,8}}
[3,6,7,5,8,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[3,7,5,6,8,2,4,1]=>{{1,3,5,8},{2,4,6,7}}
[2,7,1,6,8,4,5,3]=>{{1,2,3,5,7,8},{4,6}}
[1,5,4,7,2,6,3,8]=>{{1},{2,5},{3,4,7},{6},{8}}
[2,4,5,8,3,1,7,6]=>{{1,2,4,6,8},{3,5},{7}}
[1,4,7,5,8,3,6,2]=>{{1},{2,4,5,8},{3,6,7}}
[2,6,8,7,3,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,6,2,5,1,3]=>{{1,2,4,5,6,7},{3,8}}
[4,8,7,3,5,6,2,1]=>{{1,2,3,4,7,8},{5},{6}}
[1,7,6,3,5,4,2,8]=>{{1},{2,7},{3,4,6},{5},{8}}
[4,3,8,1,6,5,7,2]=>{{1,4},{2,3,8},{5,6},{7}}
[1,3,6,2,5,8,7,4]=>{{1},{2,3,4,6,8},{5},{7}}
[5,8,7,1,4,6,3,2]=>{{1,4,5},{2,8},{3,7},{6}}
[6,2,5,1,3,4,8,7]=>{{1,4,6},{2},{3,5},{7,8}}
[2,6,5,1,3,4,8,7]=>{{1,2,4,6},{3,5},{7,8}}
[4,6,5,1,2,7,3,8]=>{{1,4},{2,3,5,6,7},{8}}
[5,6,4,1,2,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[8,1,5,6,2,4,3,7]=>{{1,2,3,5,7,8},{4,6}}
[6,4,5,1,2,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,4,6,1,3,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,7,1,4,3,2,6,8]=>{{1,3,5},{2,6,7},{4},{8}}
[2,6,4,1,3,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[7,8,5,3,2,1,6,4]=>{{1,6,7},{2,3,4,5,8}}
[1,2,6,7,8,4,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,1,4,8,2,7,5,3]=>{{1,2,5,6,7},{3,4,8}}
[5,2,3,7,1,8,4,6]=>{{1,5},{2},{3},{4,7},{6,8}}
[7,2,3,1,8,4,6,5]=>{{1,4,6,7},{2},{3},{5,8}}
[5,4,1,7,3,2,8,6]=>{{1,3,5},{2,4,6,7,8}}
[7,3,4,5,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[1,5,6,7,4,8,2,3]=>{{1},{2,4,5,7},{3,6,8}}
[6,3,2,5,7,4,8,1]=>{{1,4,5,6,7,8},{2,3}}
[4,5,2,7,6,3,1,8]=>{{1,4,7},{2,3,5,6},{8}}
[4,5,2,1,7,6,3,8]=>{{1,4},{2,3,5,7},{6},{8}}
[2,6,7,8,3,1,4,5]=>{{1,2,6},{3,4,5,7,8}}
[6,3,2,5,1,7,8,4]=>{{1,4,5,6,7,8},{2,3}}
[4,6,3,7,8,2,1,5]=>{{1,4,7},{2,6},{3},{5,8}}
[5,6,7,1,8,4,2,3]=>{{1,2,3,4,5,6,7,8}}
[1,7,8,4,6,5,2,3]=>{{1},{2,7},{3,8},{4},{5,6}}
[1,7,3,2,8,6,5,4]=>{{1},{2,4,5,7,8},{3},{6}}
[3,7,1,2,8,6,5,4]=>{{1,3},{2,4,5,7,8},{6}}
[2,7,8,1,6,5,3,4]=>{{1,2,3,4,7,8},{5,6}}
[8,1,5,7,3,4,6,2]=>{{1,2,8},{3,5},{4,6,7}}
[5,8,2,7,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,4,7,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[1,8,2,4,7,6,3,5]=>{{1},{2,3,5,7,8},{4},{6}}
[4,5,8,7,1,6,2,3]=>{{1,2,4,5,7},{3,8},{6}}
[1,8,2,4,6,7,5,3]=>{{1},{2,3,8},{4},{5,6,7}}
[2,5,1,8,4,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[3,4,2,8,1,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[2,4,5,8,1,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[3,1,8,2,6,7,5,4]=>{{1,2,3,4,8},{5,6,7}}
[2,6,8,1,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[1,6,5,2,8,7,3,4]=>{{1},{2,3,4,5,6,7,8}}
[2,6,1,5,8,7,3,4]=>{{1,2,3,6,7},{4,5,8}}
[8,1,7,3,5,2,4,6]=>{{1,2,6,8},{3,4,7},{5}}
[8,1,3,2,7,6,4,5]=>{{1,2,4,5,7,8},{3},{6}}
[7,3,4,8,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,1,6,2,3,4]=>{{1,3,4,7,8},{2,5,6}}
[6,8,4,5,3,1,7,2]=>{{1,6},{2,8},{3,4,5},{7}}
[6,7,5,3,2,8,4,1]=>{{1,6,8},{2,3,4,5,7}}
[6,2,5,3,8,1,4,7]=>{{1,6},{2},{3,4,5,7,8}}
[7,6,1,3,5,2,4,8]=>{{1,3,4,7},{2,6},{5},{8}}
[6,2,4,5,3,8,1,7]=>{{1,6,7,8},{2},{3,4,5}}
[6,1,5,4,7,2,3,8]=>{{1,2,6},{3,5,7},{4},{8}}
[6,8,5,4,7,1,3,2]=>{{1,6},{2,8},{3,5,7},{4}}
[1,6,8,4,2,5,7,3]=>{{1},{2,5,6},{3,8},{4},{7}}
[7,5,8,1,3,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[1,4,2,8,3,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,3,5,4,8,7,2,6]=>{{1},{2,3,5,6,7,8},{4}}
[1,6,2,4,8,3,7,5]=>{{1},{2,3,6},{4},{5,8},{7}}
[1,7,8,5,4,2,6,3]=>{{1},{2,6,7},{3,8},{4,5}}
[1,5,2,8,6,4,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,5,2,7,4,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[5,1,6,7,4,2,8,3]=>{{1,2,3,4,5,6,7,8}}
[1,5,4,2,8,6,7,3]=>{{1},{2,3,4,5,8},{6},{7}}
[1,8,5,4,6,2,7,3]=>{{1},{2,3,5,6,8},{4},{7}}
[1,7,5,4,6,2,8,3]=>{{1},{2,3,5,6,7,8},{4}}
[5,8,4,1,6,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,4,5,1,7,2,8,3]=>{{1,2,4,6},{3,5,7,8}}
[4,8,1,3,7,6,2,5]=>{{1,3,4},{2,5,7,8},{6}}
[4,5,3,1,2,8,7,6]=>{{1,4},{2,5},{3},{6,8},{7}}
[6,4,2,3,1,8,7,5]=>{{1,5,6,8},{2,3,4},{7}}
[6,5,2,1,3,8,7,4]=>{{1,4,6,8},{2,3,5},{7}}
[7,6,1,8,2,5,3,4]=>{{1,3,7},{2,5,6},{4,8}}
[8,4,2,3,7,6,1,5]=>{{1,5,7,8},{2,3,4},{6}}
[5,7,8,1,2,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[1,7,6,8,3,5,4,2]=>{{1},{2,4,7,8},{3,5,6}}
[5,7,6,4,2,1,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[6,5,7,4,1,3,2,8]=>{{1,2,3,5,6,7},{4},{8}}
[4,6,1,8,3,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,8,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,1,8,3,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,3,6,1,5,2,7]=>{{1,4,5,6},{2,7,8},{3}}
[1,7,8,6,4,5,3,2]=>{{1},{2,3,7,8},{4,5,6}}
[3,2,8,6,4,5,1,7]=>{{1,3,7,8},{2},{4,5,6}}
[8,4,3,6,2,5,1,7]=>{{1,7,8},{2,4,5,6},{3}}
[1,6,8,7,4,3,5,2]=>{{1},{2,3,6,8},{4,5,7}}
[3,1,2,6,8,7,5,4]=>{{1,2,3},{4,5,6,7,8}}
[5,7,4,2,1,8,6,3]=>{{1,5},{2,3,4,6,7,8}}
[8,6,5,7,2,4,3,1]=>{{1,8},{2,3,4,5,6,7}}
[7,4,6,1,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,4,6,3,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[7,4,8,1,6,3,2,5]=>{{1,2,4,7},{3,5,6,8}}
[7,4,8,3,6,2,1,5]=>{{1,7},{2,3,4,5,6,8}}
[6,4,8,2,3,5,7,1]=>{{1,3,5,6,8},{2,4},{7}}
[4,6,8,2,5,7,1,3]=>{{1,2,4,6,7},{3,8},{5}}
[6,4,8,2,5,7,1,3]=>{{1,6,7},{2,4},{3,8},{5}}
[6,2,4,5,8,3,7,1]=>{{1,3,4,5,6,8},{2},{7}}
[6,8,2,4,7,3,5,1]=>{{1,2,3,6,8},{4},{5,7}}
[8,4,6,2,7,1,3,5]=>{{1,3,5,6,7,8},{2,4}}
[6,8,4,2,7,1,3,5]=>{{1,6},{2,3,4,5,7,8}}
[6,8,2,4,1,7,3,5]=>{{1,2,3,5,6,7,8},{4}}
[7,5,1,6,2,4,8,3]=>{{1,3,7,8},{2,5},{4,6}}
[4,2,5,7,1,6,8,3]=>{{1,3,4,5,7,8},{2},{6}}
[4,5,2,3,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,7,6,1,3,8]=>{{1,2,5,6},{3,4,7},{8}}
[5,2,3,7,6,1,4,8]=>{{1,5,6},{2},{3},{4,7},{8}}
[4,2,3,7,6,1,5,8]=>{{1,4,5,6,7},{2},{3},{8}}
[4,2,7,3,5,1,6,8]=>{{1,3,4,6,7},{2},{5},{8}}
[5,6,2,3,8,4,7,1]=>{{1,5,8},{2,3,4,6},{7}}
[5,6,2,3,1,7,8,4]=>{{1,5},{2,3,4,6,7,8}}
[5,7,2,3,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[6,2,7,3,5,1,4,8]=>{{1,6},{2},{3,4,7},{5},{8}}
[7,2,6,3,5,1,4,8]=>{{1,3,4,6,7},{2},{5},{8}}
[6,5,2,3,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,3,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,5,2,1,4,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[8,5,2,3,1,6,4,7]=>{{1,2,3,4,5,7,8},{6}}
[8,6,2,3,1,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,2,6,3,1,7,4,5]=>{{1,5,8},{2},{3,4,6,7}}
[1,6,3,4,2,7,5,8]=>{{1},{2,5,6,7},{3},{4},{8}}
[8,5,2,7,3,4,6,1]=>{{1,8},{2,3,5},{4,6,7}}
[1,7,2,4,5,6,8,3]=>{{1},{2,3,7,8},{4},{5},{6}}
[1,8,3,2,5,6,4,7]=>{{1},{2,4,7,8},{3},{5},{6}}
[7,2,8,1,4,6,3,5]=>{{1,3,4,5,7,8},{2},{6}}
[2,7,8,1,5,6,3,4]=>{{1,2,3,4,7,8},{5},{6}}
[6,8,2,3,1,5,4,7]=>{{1,5,6},{2,3,4,7,8}}
[5,8,2,3,1,6,4,7]=>{{1,5},{2,3,4,7,8},{6}}
[5,7,2,1,4,6,8,3]=>{{1,4,5},{2,3,7,8},{6}}
[4,2,7,1,5,6,8,3]=>{{1,4},{2},{3,7,8},{5},{6}}
[4,2,3,8,1,7,5,6]=>{{1,4,5,6,7,8},{2},{3}}
[4,2,1,5,3,7,6,8]=>{{1,3,4,5},{2},{6,7},{8}}
[5,1,3,8,4,6,7,2]=>{{1,2,4,5,8},{3},{6},{7}}
[5,1,3,2,6,7,8,4]=>{{1,2,4,5,6,7,8},{3}}
[5,1,3,4,2,7,6,8]=>{{1,2,5},{3},{4},{6,7},{8}}
[6,1,3,4,2,7,5,8]=>{{1,2,5,6,7},{3},{4},{8}}
[7,2,1,3,5,8,4,6]=>{{1,3,4,7},{2},{5},{6,8}}
[6,8,7,2,3,4,5,1]=>{{1,2,4,6,8},{3,5,7}}
[3,7,2,8,1,4,5,6]=>{{1,2,3,5,7},{4,6,8}}
[5,2,3,7,4,6,1,8]=>{{1,4,5,7},{2},{3},{6},{8}}
[2,5,3,7,4,6,1,8]=>{{1,2,4,5,7},{3},{6},{8}}
[2,6,7,3,4,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[6,2,7,3,4,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,8,4,5,2,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,7,6,3,4,5,1,8]=>{{1,2,7},{3,4,5,6},{8}}
[2,8,7,5,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[4,5,7,2,8,3,6,1]=>{{1,2,4,5,8},{3,6,7}}
[5,2,1,3,6,7,8,4]=>{{1,3,4,5,6,7,8},{2}}
[7,5,2,6,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,1,5,2,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,6,8,4,1,3,2]=>{{1,3,6,7},{2,4,5,8}}
[8,3,7,5,1,4,2,6]=>{{1,4,5,6,8},{2,3,7}}
[8,1,5,7,3,6,2,4]=>{{1,2,4,7,8},{3,5},{6}}
[8,3,2,6,4,5,1,7]=>{{1,7,8},{2,3},{4,5,6}}
[8,5,3,7,4,1,2,6]=>{{1,6,8},{2,4,5,7},{3}}
[8,5,6,2,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,2,6,5,1,3]=>{{1,3,7,8},{2,4},{5,6}}
[8,5,7,3,2,6,1,4]=>{{1,3,4,7,8},{2,5},{6}}
[8,1,2,3,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}
[7,6,2,3,5,8,1,4]=>{{1,7},{2,3,4,6,8},{5}}
[4,5,3,7,8,1,6,2]=>{{1,4,6,7},{2,5,8},{3}}
[3,4,2,8,1,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[8,3,4,1,5,7,6,2]=>{{1,2,3,4,8},{5},{6,7}}
[4,3,7,5,1,6,2,8]=>{{1,4,5},{2,3,7},{6},{8}}
[5,2,6,1,4,3,7,8]=>{{1,4,5},{2},{3,6},{7},{8}}
[3,5,2,8,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[5,3,7,4,2,8,6,1]=>{{1,2,3,5,6,7,8},{4}}
[7,4,8,2,3,5,6,1]=>{{1,3,5,6,7,8},{2,4}}
[5,6,2,8,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[4,6,3,5,2,7,8,1]=>{{1,2,4,5,6,7,8},{3}}
[4,1,6,3,5,7,2,8]=>{{1,2,3,4,6,7},{5},{8}}
[3,1,5,7,4,6,8,2]=>{{1,2,3,4,5,7,8},{6}}
[7,2,5,8,6,1,4,3]=>{{1,3,4,5,6,7,8},{2}}
[4,3,6,1,5,7,8,2]=>{{1,4},{2,3,6,7,8},{5}}
[3,5,4,1,2,6,7,8]=>{{1,3,4},{2,5},{6},{7},{8}}
[5,3,1,4,6,7,8,2]=>{{1,2,3,5,6,7,8},{4}}
[4,6,7,1,3,5,8,2]=>{{1,4},{2,3,5,6,7,8}}
[5,6,1,3,4,7,2,8]=>{{1,3,4,5},{2,6,7},{8}}
[2,5,3,7,8,4,6,1]=>{{1,2,5,8},{3},{4,6,7}}
[4,6,2,1,3,7,8,5]=>{{1,4},{2,3,5,6,7,8}}
[3,6,2,4,1,7,5,8]=>{{1,2,3,5,6,7},{4},{8}}
[3,2,6,7,4,8,5,1]=>{{1,3,6,8},{2},{4,5,7}}
[7,1,3,8,4,5,2,6]=>{{1,2,7},{3},{4,5,6,8}}
[7,1,8,3,4,6,2,5]=>{{1,2,7},{3,4,5,8},{6}}
[6,3,2,7,5,8,4,1]=>{{1,6,8},{2,3},{4,7},{5}}
[6,2,7,1,4,5,3,8]=>{{1,4,5,6},{2},{3,7},{8}}
[4,2,6,1,5,7,3,8]=>{{1,4},{2},{3,6,7},{5},{8}}
[2,5,4,1,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[5,4,1,2,6,7,3,8]=>{{1,3,5,6,7},{2,4},{8}}
[6,5,2,7,4,1,3,8]=>{{1,6},{2,3,4,5,7},{8}}
[6,5,7,3,1,4,2,8]=>{{1,2,3,4,5,6,7},{8}}
[6,7,4,3,1,5,8,2]=>{{1,5,6},{2,7,8},{3,4}}
[3,1,6,7,8,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,6,2,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[6,4,5,2,7,1,8,3]=>{{1,6},{2,4},{3,5,7,8}}
[3,7,5,6,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,7,6,3,8,4,5,2]=>{{1},{2,5,7,8},{3,4,6}}
[6,4,1,2,7,8,3,5]=>{{1,3,5,6,7,8},{2,4}}
[6,4,1,3,5,2,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[5,1,8,3,4,6,2,7]=>{{1,2,3,4,5,7,8},{6}}
[4,5,8,2,3,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[7,3,4,8,2,5,1,6]=>{{1,7},{2,3,4,5,6,8}}
[4,7,2,5,1,6,8,3]=>{{1,4,5},{2,3,7,8},{6}}
[6,5,4,7,2,8,3,1]=>{{1,6,8},{2,5},{3,4,7}}
[3,2,4,6,5,8,1,7]=>{{1,3,4,6,7,8},{2},{5}}
[3,5,4,8,7,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,2,1,6,3,4,8]=>{{1,4,7},{2,3,5,6},{8}}
[6,3,1,7,4,2,5,8]=>{{1,2,3,6},{4,5,7},{8}}
[8,7,2,1,5,3,6,4]=>{{1,4,8},{2,3,6,7},{5}}
[6,8,5,3,7,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,2,8,1,5,6,4,3]=>{{1,4,7},{2},{3,8},{5},{6}}
[8,3,6,4,1,5,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[7,5,6,1,4,8,2,3]=>{{1,2,4,5,7},{3,6,8}}
[5,7,2,6,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,2,3,6,7,5]=>{{1,3,5,8},{2,4},{6},{7}}
[5,6,4,2,1,8,3,7]=>{{1,5},{2,3,4,6,7,8}}
[6,8,1,3,2,7,5,4]=>{{1,2,3,4,5,6,7,8}}
[5,7,3,6,4,1,2,8]=>{{1,4,5,6},{2,7},{3},{8}}
[7,2,4,3,8,1,5,6]=>{{1,5,6,7,8},{2},{3,4}}
[2,5,4,6,1,3,8,7]=>{{1,2,5},{3,4,6},{7,8}}
[2,4,3,5,8,1,6,7]=>{{1,2,4,5,6,7,8},{3}}
[2,6,5,3,8,1,4,7]=>{{1,2,6},{3,4,5,7,8}}
[6,1,2,4,3,5,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[6,5,8,2,7,3,4,1]=>{{1,3,6,8},{2,4,5,7}}
[1,7,6,8,4,3,2,5]=>{{1},{2,7},{3,6},{4,5,8}}
[1,7,6,5,3,8,2,4]=>{{1},{2,7},{3,4,5,6,8}}
[6,1,2,4,3,5,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[4,6,1,3,7,8,5,2]=>{{1,3,4},{2,6,8},{5,7}}
[8,4,1,5,2,6,7,3]=>{{1,3,8},{2,4,5},{6},{7}}
[1,5,6,3,8,7,2,4]=>{{1},{2,3,4,5,6,7,8}}
[5,3,2,6,8,7,1,4]=>{{1,4,5,6,7,8},{2,3}}
[6,3,5,2,7,1,4,8]=>{{1,6},{2,3,4,5,7},{8}}
[8,5,2,6,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,7,1,4,2,6]=>{{1,5},{2,3,4,6,7,8}}
[6,4,5,3,1,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[8,5,1,2,3,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[2,8,6,1,5,4,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[8,3,2,6,1,5,7,4]=>{{1,4,5,6,8},{2,3},{7}}
[3,8,6,4,7,1,2,5]=>{{1,3,6},{2,5,7,8},{4}}
[1,8,7,5,4,3,2,6]=>{{1},{2,3,6,7,8},{4,5}}
[8,6,4,7,1,3,2,5]=>{{1,5,8},{2,3,4,6,7}}
[3,1,4,7,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[5,3,4,1,6,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,7,1,4,6,3,5,8]=>{{1,2,3,5,6,7},{4},{8}}
[7,3,1,6,5,2,4,8]=>{{1,2,3,4,6,7},{5},{8}}
[7,1,5,2,4,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[6,1,4,5,2,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[6,1,5,8,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[7,1,2,3,6,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[2,8,4,6,5,1,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[7,4,1,3,6,5,2,8]=>{{1,2,3,4,7},{5,6},{8}}
[5,7,2,8,1,3,6,4]=>{{1,5},{2,3,6,7},{4,8}}
[5,4,1,2,6,3,8,7]=>{{1,3,5,6},{2,4},{7,8}}
[6,5,1,4,7,3,2,8]=>{{1,3,6},{2,5,7},{4},{8}}
[2,7,8,4,1,3,6,5]=>{{1,2,3,5,6,7,8},{4}}
[2,4,6,5,7,8,1,3]=>{{1,2,4,5,7},{3,6,8}}
[2,4,6,7,5,8,1,3]=>{{1,2,4,7},{3,6,8},{5}}
[2,4,6,3,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,4,5,6,8,7,1,3]=>{{1,2,4,6,7},{3,5,8}}
[2,4,5,6,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,4,5,6,3,8,1,7]=>{{1,2,4,6,7,8},{3,5}}
[2,3,4,6,8,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[5,2,8,3,4,1,6,7]=>{{1,3,4,5,6,7,8},{2}}
[3,6,4,1,2,7,8,5]=>{{1,3,4},{2,5,6,7,8}}
[4,1,7,3,8,6,2,5]=>{{1,2,3,4,7},{5,8},{6}}
[8,4,1,2,5,3,7,6]=>{{1,3,6,8},{2,4},{5},{7}}
[1,5,2,7,6,8,4,3]=>{{1},{2,3,5,6,8},{4,7}}
[4,7,6,8,3,1,2,5]=>{{1,3,4,5,6,8},{2,7}}
[4,8,2,7,6,5,1,3]=>{{1,4,7},{2,3,8},{5,6}}
[7,4,2,8,6,5,1,3]=>{{1,7},{2,3,4,8},{5,6}}
[8,6,5,2,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,2,7,1,4,3]=>{{1,6},{2,4,5,7},{3,8}}
[7,5,8,2,1,6,4,3]=>{{1,2,4,5,7},{3,8},{6}}
[3,2,1,6,5,8,4,7]=>{{1,3},{2},{4,6,7,8},{5}}
[2,6,4,8,5,7,3,1]=>{{1,2,3,4,6,7,8},{5}}
[6,3,1,4,5,8,2,7]=>{{1,2,3,6,7,8},{4},{5}}
[3,4,8,5,2,1,7,6]=>{{1,3,6,8},{2,4,5},{7}}
[4,8,7,1,3,2,6,5]=>{{1,4},{2,3,5,6,7,8}}
[5,8,7,4,6,1,3,2]=>{{1,5,6},{2,8},{3,7},{4}}
[3,4,1,8,7,6,2,5]=>{{1,3},{2,4,5,7,8},{6}}
[1,3,5,6,8,7,2,4]=>{{1},{2,3,4,5,6,7,8}}
[2,8,7,5,4,1,6,3]=>{{1,2,3,6,7,8},{4,5}}
[8,1,5,7,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,3,4,1,6,2]=>{{1,3,4,5,6,7},{2,8}}
[4,6,1,3,2,8,5,7]=>{{1,3,4},{2,5,6,7,8}}
[2,6,5,8,3,1,4,7]=>{{1,2,6},{3,5},{4,7,8}}
[6,7,8,2,4,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[3,2,8,4,5,7,1,6]=>{{1,3,6,7,8},{2},{4},{5}}
[6,1,8,2,4,5,3,7]=>{{1,2,4,5,6},{3,7,8}}
[8,3,6,4,2,7,1,5]=>{{1,2,3,5,6,7,8},{4}}
[1,3,8,4,7,6,2,5]=>{{1},{2,3,5,7,8},{4},{6}}
[8,3,7,5,4,1,2,6]=>{{1,6,8},{2,3,7},{4,5}}
[2,6,4,7,8,5,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,7,6,1,8,2]=>{{1,5,6},{2,4,7,8},{3}}
[8,6,3,7,1,4,2,5]=>{{1,5,8},{2,4,6,7},{3}}
[3,1,2,8,7,6,4,5]=>{{1,2,3},{4,5,7,8},{6}}
[8,5,4,1,2,3,7,6]=>{{1,3,4,6,8},{2,5},{7}}
[8,3,2,1,6,4,7,5]=>{{1,4,5,6,8},{2,3},{7}}
[2,3,8,4,1,7,5,6]=>{{1,2,3,5,6,7,8},{4}}
[4,6,1,3,2,7,8,5]=>{{1,3,4},{2,5,6,7,8}}
[6,7,2,5,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[4,1,7,8,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[3,4,6,7,1,5,8,2]=>{{1,3,5,6},{2,4,7,8}}
[3,4,5,7,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,4,3,5,2,6]=>{{1},{2,3,5,6,7,8},{4}}
[2,4,5,8,1,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,7,8,6,5,3,1,4]=>{{1,2,7},{3,4,6,8},{5}}
[6,3,1,5,8,4,2,7]=>{{1,2,3,4,5,6,7,8}}
[2,8,3,5,6,1,4,7]=>{{1,2,4,5,6,7,8},{3}}
[1,3,6,4,2,7,5,8]=>{{1},{2,3,5,6,7},{4},{8}}
[2,3,7,5,8,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,2,8,5,6,1,4,7]=>{{1,3,4,5,6,7,8},{2}}
[7,2,5,8,1,4,6,3]=>{{1,3,4,5,6,7,8},{2}}
[4,7,5,8,1,2,6,3]=>{{1,3,4,5,8},{2,6,7}}
[4,7,5,8,1,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,5,2,8,1,6]=>{{1,3,7},{2,4,5},{6,8}}
[4,3,2,5,7,8,1,6]=>{{1,4,5,7},{2,3},{6,8}}
[2,4,7,5,8,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[2,5,4,7,3,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[3,7,8,4,2,1,6,5]=>{{1,2,3,5,6,7,8},{4}}
[8,5,4,7,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,5,4,8,7,6,2,3]=>{{1},{2,5,7},{3,4,8},{6}}
[3,2,4,5,8,1,6,7]=>{{1,3,4,5,6,7,8},{2}}
[3,6,8,4,2,7,1,5]=>{{1,2,3,5,6,7,8},{4}}
[3,6,5,1,7,2,8,4]=>{{1,3,4,5,7,8},{2,6}}
[7,4,1,6,2,8,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,3,6,8,2,4,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,7,4,3,8,2,5]=>{{1},{2,3,5,6,7,8},{4}}
[7,3,1,6,5,2,8,4]=>{{1,2,3,4,6,7,8},{5}}
[8,5,4,1,6,2,7,3]=>{{1,3,4,8},{2,5,6},{7}}
[4,7,2,8,5,1,6,3]=>{{1,2,3,4,6,7,8},{5}}
[7,8,6,2,1,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[2,1,3,8,7,5,6,4]=>{{1,2},{3},{4,8},{5,6,7}}
[8,1,7,3,6,5,2,4]=>{{1,2,3,4,7,8},{5,6}}
[1,6,4,7,3,8,5,2]=>{{1},{2,6,8},{3,4,5,7}}
[4,8,1,6,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,1,6,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[1,7,6,2,4,8,5,3]=>{{1},{2,4,5,7},{3,6,8}}
[5,7,3,2,4,8,6,1]=>{{1,2,4,5,6,7,8},{3}}
[2,6,8,5,4,3,1,7]=>{{1,2,3,6,7,8},{4,5}}
[2,8,4,6,3,5,1,7]=>{{1,2,7,8},{3,4,5,6}}
[2,7,8,3,6,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,8,1,4,6,5,2,7]=>{{1,3},{2,7,8},{4},{5,6}}
[2,7,5,4,1,8,3,6]=>{{1,2,3,5,7},{4},{6,8}}
[4,6,1,8,5,3,2,7]=>{{1,2,3,4,6,7,8},{5}}
[3,8,5,2,1,6,4,7]=>{{1,3,5},{2,4,7,8},{6}}
[5,1,4,8,2,6,3,7]=>{{1,2,5},{3,4,7,8},{6}}
[4,5,8,1,3,7,6,2]=>{{1,4},{2,3,5,8},{6,7}}
[8,6,7,1,4,3,2,5]=>{{1,4,5,8},{2,3,6,7}}
[1,4,7,8,6,3,5,2]=>{{1},{2,4,8},{3,5,6,7}}
[8,5,2,6,3,4,7,1]=>{{1,8},{2,3,5},{4,6},{7}}
[8,3,6,1,2,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,1,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[3,7,6,2,1,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,6,1,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,6,3,2,7,1,5,4]=>{{1,2,4,6,8},{3},{5,7}}
[6,8,1,5,4,7,2,3]=>{{1,2,3,6,7,8},{4,5}}
[6,7,2,5,4,8,1,3]=>{{1,2,3,6,7,8},{4,5}}
[7,6,2,4,8,5,1,3]=>{{1,7},{2,3,5,6,8},{4}}
[4,6,8,7,3,1,2,5]=>{{1,2,4,6,7},{3,5,8}}
[4,7,5,2,6,3,8,1]=>{{1,2,4,7,8},{3,5,6}}
[3,5,6,2,8,1,4,7]=>{{1,3,6},{2,4,5,7,8}}
[6,1,8,2,4,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,8,2,5,3,4,7]=>{{1},{2,3,4,6,7,8},{5}}
[5,4,8,7,1,2,6,3]=>{{1,5},{2,4,6,7},{3,8}}
[2,5,6,4,3,8,1,7]=>{{1,2,3,5,6,7,8},{4}}
[8,7,3,5,1,4,6,2]=>{{1,2,4,5,6,7,8},{3}}
[8,6,3,5,2,1,4,7]=>{{1,2,4,5,6,7,8},{3}}
[8,7,3,5,2,4,6,1]=>{{1,8},{2,4,5,6,7},{3}}
[8,4,2,7,6,5,1,3]=>{{1,2,3,4,7,8},{5,6}}
[4,6,3,8,5,2,7,1]=>{{1,4,8},{2,6},{3},{5},{7}}
[4,1,3,8,5,6,2,7]=>{{1,2,4,7,8},{3},{5},{6}}
[5,2,8,3,1,6,7,4]=>{{1,5},{2},{3,4,8},{6},{7}}
[1,7,8,6,3,2,5,4]=>{{1},{2,3,4,5,6,7,8}}
[3,2,8,1,5,7,4,6]=>{{1,3,4,6,7,8},{2},{5}}
[3,4,6,7,2,1,5,8]=>{{1,3,6},{2,4,5,7},{8}}
[2,6,7,1,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[4,2,5,3,8,6,7,1]=>{{1,3,4,5,8},{2},{6},{7}}
[3,2,7,4,8,5,6,1]=>{{1,3,5,6,7,8},{2},{4}}
[7,2,5,1,6,3,8,4]=>{{1,4,7,8},{2},{3,5,6}}
[5,8,2,7,4,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[4,5,2,8,3,7,1,6]=>{{1,4,6,7,8},{2,3,5}}
[7,8,5,1,6,4,3,2]=>{{1,3,4,5,6,7},{2,8}}
[8,7,5,1,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[4,5,8,3,1,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,7,6,3,8,5,2,4]=>{{1},{2,7},{3,4,5,6,8}}
[1,3,8,7,4,5,6,2]=>{{1},{2,3,8},{4,5,6,7}}
[7,3,1,8,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[3,2,8,7,4,5,6,1]=>{{1,3,8},{2},{4,5,6,7}}
[6,2,4,3,7,5,8,1]=>{{1,5,6,7,8},{2},{3,4}}
[3,8,2,1,5,7,6,4]=>{{1,2,3,4,8},{5},{6,7}}
[1,3,2,8,7,4,6,5]=>{{1},{2,3},{4,5,6,7,8}}
[7,5,2,8,3,1,6,4]=>{{1,6,7},{2,3,5},{4,8}}
[4,6,3,7,8,1,2,5]=>{{1,2,4,6,7},{3},{5,8}}
[6,2,5,4,1,7,8,3]=>{{1,3,5,6,7,8},{2},{4}}
[4,1,5,6,3,8,7,2]=>{{1,2,4,6,8},{3,5},{7}}
[8,5,1,6,3,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,4,3,2,5,1]=>{{1,2,6,8},{3,5,7},{4}}
[8,1,5,4,6,7,3,2]=>{{1,2,8},{3,5,6,7},{4}}
[2,8,5,1,3,7,6,4]=>{{1,2,4,8},{3,5},{6,7}}
[2,4,5,8,3,7,6,1]=>{{1,2,4,8},{3,5},{6,7}}
[5,6,4,1,8,2,7,3]=>{{1,3,4,5,8},{2,6},{7}}
[6,4,5,1,3,8,7,2]=>{{1,2,4,6,8},{3,5},{7}}
[6,1,3,5,4,8,2,7]=>{{1,2,6,7,8},{3},{4,5}}
[1,3,8,7,2,5,6,4]=>{{1},{2,3,4,5,6,7,8}}
[2,5,4,1,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[5,1,4,8,3,7,6,2]=>{{1,2,3,4,5,8},{6,7}}
[8,4,1,2,7,6,5,3]=>{{1,3,8},{2,4},{5,7},{6}}
[4,8,3,2,7,6,5,1]=>{{1,2,4,8},{3},{5,7},{6}}
[1,8,7,3,4,6,5,2]=>{{1},{2,8},{3,4,5,7},{6}}
[5,3,1,2,4,6,8,7]=>{{1,2,3,4,5},{6},{7,8}}
[8,5,7,3,1,2,4,6]=>{{1,2,5,6,8},{3,4,7}}
[3,1,2,8,7,5,4,6]=>{{1,2,3},{4,5,6,7,8}}
[1,4,3,8,5,7,2,6]=>{{1},{2,4,6,7,8},{3},{5}}
[6,7,1,5,2,8,4,3]=>{{1,3,6,8},{2,4,5,7}}
[1,5,3,7,6,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,8,1,3,6,2,7,5]=>{{1,3,4},{2,5,6,8},{7}}
[2,7,3,4,8,6,5,1]=>{{1,2,5,7,8},{3},{4},{6}}
[1,8,2,4,7,3,6,5]=>{{1},{2,3,5,6,7,8},{4}}
[2,7,1,6,5,8,3,4]=>{{1,2,3,7},{4,6,8},{5}}
[6,2,3,8,1,5,7,4]=>{{1,5,6},{2},{3},{4,8},{7}}
[2,5,7,4,8,3,6,1]=>{{1,2,5,8},{3,6,7},{4}}
[8,5,6,2,4,7,1,3]=>{{1,3,6,7,8},{2,4,5}}
[8,1,5,7,3,6,4,2]=>{{1,2,8},{3,5},{4,7},{6}}
[4,3,7,1,2,8,5,6]=>{{1,4},{2,3,5,7},{6,8}}
[3,8,6,2,7,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[4,8,1,6,2,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,8,4,2,5,7,3,6]=>{{1},{2,3,4,6,7,8},{5}}
[5,8,3,1,2,4,6,7]=>{{1,2,4,5,6,7,8},{3}}
[1,4,8,5,2,3,6,7]=>{{1},{2,4,5},{3,6,7,8}}
[1,4,8,5,2,3,7,6]=>{{1},{2,4,5},{3,6,8},{7}}
[7,1,4,2,6,8,3,5]=>{{1,2,3,4,7},{5,6,8}}
[1,5,8,7,2,4,3,6]=>{{1},{2,5},{3,4,6,7,8}}
[1,5,4,2,8,3,7,6]=>{{1},{2,3,4,5,6,8},{7}}
[1,2,8,7,3,5,4,6]=>{{1},{2},{3,5,6,8},{4,7}}
[8,7,1,3,2,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,2,8,1,3,5]=>{{1,6},{2,3,4,7},{5,8}}
[4,1,6,8,7,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,6,2,8,3,1]=>{{1,4,6,8},{2,3,5,7}}
[8,4,3,6,7,5,2,1]=>{{1,8},{2,4,5,6,7},{3}}
[6,7,5,2,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,3,2,7,5,1]=>{{1,2,5,6,7,8},{3,4}}
[6,1,7,3,5,8,2,4]=>{{1,2,3,4,6,7,8},{5}}
[1,3,7,6,4,8,2,5]=>{{1},{2,3,7},{4,5,6,8}}
[2,6,4,8,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}
[2,1,8,7,3,5,4,6]=>{{1,2},{3,5,6,8},{4,7}}
[6,1,8,5,7,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,5,1,4,7,6,3,2]=>{{1,2,3,5,7,8},{4},{6}}
[8,1,3,7,2,4,6,5]=>{{1,2,5,8},{3},{4,6,7}}
[5,3,1,6,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,7,1,4,8,3]=>{{1,2,5},{3,4,6,7,8}}
[4,7,5,3,2,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[4,7,5,2,8,6,1,3]=>{{1,2,4,7},{3,5,8},{6}}
[3,8,6,7,2,5,4,1]=>{{1,2,3,5,6,8},{4,7}}
[5,8,1,2,7,4,3,6]=>{{1,3,5,7},{2,4,6,8}}
[6,3,1,8,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,6,3,7,8,1,5,2]=>{{1,2,4,5,6,7,8},{3}}
[6,3,1,8,4,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[7,6,2,4,8,3,1,5]=>{{1,7},{2,3,6},{4},{5,8}}
[6,5,8,1,4,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[8,1,4,2,7,5,6,3]=>{{1,2,3,4,8},{5,6,7}}
[8,6,3,5,2,1,7,4]=>{{1,2,4,5,6,8},{3},{7}}
[6,8,3,1,2,5,4,7]=>{{1,2,4,5,6,7,8},{3}}
[5,8,6,4,7,1,2,3]=>{{1,2,3,5,6,7,8},{4}}
[2,5,1,8,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[7,2,4,3,8,6,1,5]=>{{1,7},{2},{3,4},{5,8},{6}}
[6,8,4,3,5,1,7,2]=>{{1,6},{2,8},{3,4},{5},{7}}
[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,4,7,3,6,8,1,5]=>{{1,2,3,4,7},{5,6,8}}
[8,5,7,6,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[2,7,5,6,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[1,2,6,7,4,5,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,5,2,8,7,1,4,3]=>{{1,6},{2,3,4,5,7,8}}
[7,2,3,6,8,1,4,5]=>{{1,4,6,7},{2},{3},{5,8}}
[2,6,1,3,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[6,4,1,8,3,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[5,8,1,4,2,7,3,6]=>{{1,2,3,5,6,7,8},{4}}
[2,3,1,6,8,7,4,5]=>{{1,2,3},{4,6,7},{5,8}}
[6,4,8,2,1,7,3,5]=>{{1,3,5,6,7,8},{2,4}}
[2,3,1,8,7,5,6,4]=>{{1,2,3},{4,8},{5,6,7}}
[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[2,8,6,4,1,5,3,7]=>{{1,2,3,5,6,7,8},{4}}
[6,7,4,5,1,3,8,2]=>{{1,3,4,5,6},{2,7,8}}
[1,6,5,3,8,2,4,7]=>{{1},{2,6},{3,4,5,7,8}}
[5,6,1,2,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,5,1,3,2,6]=>{{1,3,4,5,6,8},{2,7}}
[8,5,1,2,7,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[4,1,8,7,2,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[3,2,4,6,1,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[3,6,7,4,1,2,5,8]=>{{1,3,5,7},{2,6},{4},{8}}
[1,4,7,5,8,2,3,6]=>{{1},{2,4,5,6,8},{3,7}}
[1,6,8,4,7,3,2,5]=>{{1},{2,3,5,6,7,8},{4}}
[3,6,7,5,4,8,1,2]=>{{1,3,7},{2,6,8},{4,5}}
[4,5,7,2,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,1,5,7,4,6,8,3]=>{{1,2},{3,4,5,7,8},{6}}
[2,3,5,7,8,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[1,5,7,4,2,3,6,8]=>{{1},{2,5},{3,6,7},{4},{8}}
[2,4,7,5,3,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[8,1,7,2,4,6,3,5]=>{{1,2,4,5,8},{3,7},{6}}
[1,2,4,7,8,6,3,5]=>{{1},{2},{3,4,7},{5,8},{6}}
[2,4,7,8,3,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[1,3,6,2,5,8,4,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,5,3,6,8,2,4,7]=>{{1},{2,4,5,6,7,8},{3}}
[4,8,1,2,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[5,8,1,2,6,3,7,4]=>{{1,3,5,6},{2,4,8},{7}}
[1,6,2,3,7,5,8,4]=>{{1},{2,3,4,5,6,7,8}}
[4,1,2,6,5,7,8,3]=>{{1,2,3,4,6,7,8},{5}}
[1,8,4,2,7,3,6,5]=>{{1},{2,3,4,5,6,7,8}}
[1,7,5,2,3,8,6,4]=>{{1},{2,4,6,7,8},{3,5}}
[8,1,4,7,3,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[8,4,3,6,1,7,2,5]=>{{1,5,8},{2,4,6,7},{3}}
[2,6,1,8,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,1,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}
[2,5,1,7,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,8,2,4,7,6]=>{{1,2,3,5},{4,6,8},{7}}
[1,2,6,3,7,5,8,4]=>{{1},{2},{3,4,5,6,7,8}}
[5,1,8,3,2,4,7,6]=>{{1,2,5},{3,4,6,8},{7}}
[3,1,5,4,6,7,8,2]=>{{1,2,3,5,6,7,8},{4}}
[2,8,5,7,3,1,4,6]=>{{1,2,6,8},{3,5},{4,7}}
[2,6,8,7,3,1,4,5]=>{{1,2,6},{3,5,8},{4,7}}
[7,4,2,1,3,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[7,2,1,3,8,5,4,6]=>{{1,3,4,7},{2},{5,6,8}}
[2,1,7,3,8,6,4,5]=>{{1,2},{3,4,7},{5,8},{6}}
[1,7,5,3,2,4,8,6]=>{{1},{2,3,4,5,6,7,8}}
[1,4,2,7,6,5,8,3]=>{{1},{2,3,4,7,8},{5,6}}
[3,4,1,6,5,7,8,2]=>{{1,3},{2,4,6,7,8},{5}}
[2,8,7,3,4,1,5,6]=>{{1,2,6,8},{3,4,5,7}}
[5,7,6,2,3,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[4,5,7,6,2,8,1,3]=>{{1,3,4,6,7,8},{2,5}}
[3,1,8,7,5,2,6,4]=>{{1,2,3,4,6,7,8},{5}}
[4,5,6,8,7,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[2,8,3,1,5,4,7,6]=>{{1,2,4,6,8},{3},{5},{7}}
[3,8,4,1,5,2,7,6]=>{{1,3,4},{2,6,8},{5},{7}}
[1,8,6,2,4,3,7,5]=>{{1},{2,4,5,8},{3,6},{7}}
[4,8,3,1,6,2,7,5]=>{{1,4},{2,5,6,8},{3},{7}}
[2,8,3,1,6,4,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[6,2,7,1,5,8,4,3]=>{{1,3,4,6,7,8},{2},{5}}
[4,8,5,1,3,2,6,7]=>{{1,4},{2,6,7,8},{3,5}}
[5,4,3,1,2,7,6,8]=>{{1,2,4,5},{3},{6,7},{8}}
[4,1,6,5,2,3,7,8]=>{{1,2,4,5},{3,6},{7},{8}}
[7,1,5,2,3,6,4,8]=>{{1,2,4,7},{3,5},{6},{8}}
[4,1,6,3,7,2,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[4,6,1,2,8,3,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[4,1,3,6,7,2,5,8]=>{{1,2,4,6},{3},{5,7},{8}}
[2,6,5,1,3,4,7,8]=>{{1,2,4,6},{3,5},{7},{8}}
[2,6,7,4,3,1,5,8]=>{{1,2,6},{3,5,7},{4},{8}}
[2,6,3,1,7,4,5,8]=>{{1,2,4,6},{3},{5,7},{8}}
[6,5,3,7,2,4,1,8]=>{{1,4,6,7},{2,5},{3},{8}}
[2,3,6,7,1,5,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[2,7,5,8,1,3,6,4]=>{{1,2,3,5,6,7},{4,8}}
[5,1,6,7,3,2,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[5,6,1,4,7,2,3,8]=>{{1,3,5,7},{2,6},{4},{8}}
[1,2,5,7,8,6,3,4]=>{{1},{2},{3,4,5,7,8},{6}}
[1,2,6,7,4,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,7,8,4,6,3,5]=>{{1},{2},{3,7},{4,5,8},{6}}
[8,6,5,2,1,7,4,3]=>{{1,3,5,8},{2,4,6,7}}
[4,3,8,6,7,1,5,2]=>{{1,4,6},{2,3,8},{5,7}}
[8,3,2,4,7,1,6,5]=>{{1,5,6,7,8},{2,3},{4}}
[7,3,2,8,6,1,5,4]=>{{1,5,6,7},{2,3},{4,8}}
[7,5,8,2,6,1,4,3]=>{{1,2,4,5,6,7},{3,8}}
[5,6,8,2,7,4,1,3]=>{{1,5,7},{2,4,6},{3,8}}
[7,4,1,2,6,5,8,3]=>{{1,3,7,8},{2,4},{5,6}}
[5,2,7,4,6,1,8,3]=>{{1,5,6},{2},{3,7,8},{4}}
[7,4,1,2,3,6,8,5]=>{{1,3,5,7,8},{2,4},{6}}
[5,4,8,6,3,2,1,7]=>{{1,3,5,7,8},{2,4,6}}
[8,4,6,7,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,1,3,6,8,5,2,7]=>{{1,2,4,5,6,7,8},{3}}
[6,3,5,7,1,2,8,4]=>{{1,2,3,5,6},{4,7,8}}
[1,8,5,3,2,4,6,7]=>{{1},{2,3,4,5,6,7,8}}
[1,6,7,3,4,2,5,8]=>{{1},{2,6},{3,4,5,7},{8}}
[1,6,8,3,4,2,5,7]=>{{1},{2,6},{3,4,5,7,8}}
[1,8,7,5,3,4,2,6]=>{{1},{2,3,4,5,6,7,8}}
[1,7,8,5,3,4,2,6]=>{{1},{2,7},{3,4,5,6,8}}
[1,7,6,8,4,2,3,5]=>{{1},{2,3,6,7},{4,5,8}}
[1,7,8,6,4,3,2,5]=>{{1},{2,7},{3,4,5,6,8}}
[5,1,7,8,4,2,3,6]=>{{1,2,4,5,6,8},{3,7}}
[3,8,2,1,6,7,5,4]=>{{1,2,3,4,8},{5,6,7}}
[2,8,3,1,7,5,6,4]=>{{1,2,4,8},{3},{5,6,7}}
[2,7,4,1,5,8,3,6]=>{{1,2,3,4,7},{5},{6,8}}
[2,1,6,4,7,8,3,5]=>{{1,2},{3,5,6,7,8},{4}}
[5,7,8,3,4,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,3,8,2,6,1]=>{{1,3,4,5,8},{2,6,7}}
[2,6,4,7,8,5,3,1]=>{{1,2,5,6,8},{3,4,7}}
[7,8,4,5,6,1,3,2]=>{{1,3,4,5,6,7},{2,8}}
[2,5,1,8,4,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[6,5,8,3,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[8,2,7,6,3,4,5,1]=>{{1,8},{2},{3,5,7},{4,6}}
[6,8,7,3,2,1,4,5]=>{{1,6},{2,5,8},{3,4,7}}
[3,4,8,2,7,1,5,6]=>{{1,3,6,8},{2,4},{5,7}}
[7,2,6,1,4,8,3,5]=>{{1,3,4,5,6,7,8},{2}}
[7,8,1,2,4,6,3,5]=>{{1,3,7},{2,4,5,8},{6}}
[7,2,8,3,4,5,1,6]=>{{1,7},{2},{3,4,5,6,8}}
[6,1,8,3,4,2,5,7]=>{{1,2,6},{3,4,5,7,8}}
[7,5,1,2,4,3,8,6]=>{{1,3,6,7,8},{2,4,5}}
[7,6,8,1,4,2,3,5]=>{{1,3,4,5,7,8},{2,6}}
[2,4,3,7,8,5,6,1]=>{{1,2,4,5,6,7,8},{3}}
[2,1,7,6,3,4,5,8]=>{{1,2},{3,5,7},{4,6},{8}}
[6,1,5,3,8,2,4,7]=>{{1,2,6},{3,4,5,7,8}}
[2,3,6,8,5,1,7,4]=>{{1,2,3,6},{4,8},{5},{7}}
[3,2,4,8,6,1,7,5]=>{{1,3,4,5,6,8},{2},{7}}
[2,1,3,8,4,5,7,6]=>{{1,2},{3},{4,5,6,8},{7}}
[3,1,2,8,5,4,7,6]=>{{1,2,3},{4,6,8},{5},{7}}
[2,1,3,7,8,4,6,5]=>{{1,2},{3},{4,6,7},{5,8}}
[2,1,3,8,4,7,6,5]=>{{1,2},{3},{4,5,8},{6,7}}
[3,1,2,8,4,5,7,6]=>{{1,2,3},{4,5,6,8},{7}}
[1,2,8,7,5,4,6,3]=>{{1},{2},{3,8},{4,6,7},{5}}
[4,6,7,2,3,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[3,2,6,5,7,8,1,4]=>{{1,3,4,5,6,7,8},{2}}
[2,1,8,7,4,6,5,3]=>{{1,2},{3,8},{4,5,7},{6}}
[6,1,5,8,4,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[1,4,6,8,5,7,2,3]=>{{1},{2,3,4,6,7,8},{5}}
[2,8,5,1,6,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[2,4,7,1,8,3,6,5]=>{{1,2,4},{3,6,7},{5,8}}
[6,1,5,4,2,3,8,7]=>{{1,2,3,5,6},{4},{7,8}}
[6,4,5,1,2,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,5,7,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[8,1,6,3,5,2,4,7]=>{{1,2,3,4,6,7,8},{5}}
[4,6,2,5,3,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[4,6,5,2,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,3,6,7,2,1]=>{{1,2,5,6,7,8},{3,4}}
[6,8,2,1,5,3,4,7]=>{{1,2,3,4,6,7,8},{5}}
[2,5,3,8,6,7,4,1]=>{{1,2,4,5,6,7,8},{3}}
[3,2,6,5,1,8,4,7]=>{{1,3,4,5,6,7,8},{2}}
[7,4,5,8,1,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[4,5,8,1,6,7,3,2]=>{{1,4},{2,3,5,6,7,8}}
[5,1,8,4,6,7,3,2]=>{{1,2,3,5,6,7,8},{4}}
[6,5,3,8,1,7,2,4]=>{{1,2,5,6,7},{3},{4,8}}
[8,3,7,1,6,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,4,6,5,7,2,3]=>{{1,2,3,4,6,7,8},{5}}
[8,1,7,5,6,4,2,3]=>{{1,2,3,7,8},{4,5,6}}
[8,6,1,5,3,7,2,4]=>{{1,3,4,5,8},{2,6,7}}
[7,2,3,6,8,1,5,4]=>{{1,4,5,6,7,8},{2},{3}}
[2,6,3,7,8,1,4,5]=>{{1,2,6},{3},{4,7},{5,8}}
[6,3,8,7,2,1,5,4]=>{{1,6},{2,3,4,5,7,8}}
[7,2,5,6,3,4,8,1]=>{{1,7,8},{2},{3,5},{4,6}}
[7,2,8,6,3,1,5,4]=>{{1,3,4,5,6,7,8},{2}}
[7,2,4,5,8,6,3,1]=>{{1,3,4,5,7,8},{2},{6}}
[6,3,8,4,7,2,5,1]=>{{1,2,3,6,8},{4},{5,7}}
[7,2,3,6,8,5,4,1]=>{{1,4,5,6,7,8},{2},{3}}
[7,2,8,5,4,1,3,6]=>{{1,3,6,7,8},{2},{4,5}}
[7,4,5,2,8,1,6,3]=>{{1,6,7},{2,4},{3,5,8}}
[7,5,4,2,8,1,6,3]=>{{1,6,7},{2,3,4,5,8}}
[7,6,3,2,8,4,5,1]=>{{1,5,7,8},{2,4,6},{3}}
[7,2,3,6,8,4,5,1]=>{{1,5,7,8},{2},{3},{4,6}}
[7,2,5,4,8,3,6,1]=>{{1,3,5,6,7,8},{2},{4}}
[7,2,8,3,6,1,4,5]=>{{1,3,4,5,6,7,8},{2}}
[7,4,5,2,8,3,6,1]=>{{1,3,5,6,7,8},{2,4}}
[5,1,3,2,4,6,8,7]=>{{1,2,4,5},{3},{6},{7,8}}
[6,5,3,4,1,8,2,7]=>{{1,2,5,6,7,8},{3},{4}}
[6,4,5,3,8,1,2,7]=>{{1,6},{2,3,4,5,7,8}}
[7,2,4,6,3,8,5,1]=>{{1,3,4,5,6,7,8},{2}}
[2,8,3,7,6,1,5,4]=>{{1,2,4,5,6,7,8},{3}}
[5,4,2,6,8,7,3,1]=>{{1,5,8},{2,3,4,6,7}}
[3,7,2,5,8,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[4,6,5,3,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[2,4,8,7,6,1,5,3]=>{{1,2,4,5,6,7},{3,8}}
[3,2,8,7,4,6,5,1]=>{{1,3,8},{2},{4,5,7},{6}}
[8,2,6,5,1,4,3,7]=>{{1,3,4,5,6,7,8},{2}}
[4,8,5,2,7,6,3,1]=>{{1,2,4,8},{3,5,7},{6}}
[2,8,6,5,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[3,8,4,7,2,1,6,5]=>{{1,3,4,6,7},{2,5,8}}
[5,8,1,7,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[3,4,6,2,5,7,1,8]=>{{1,3,6,7},{2,4},{5},{8}}
[1,7,5,2,6,8,3,4]=>{{1},{2,3,4,5,6,7,8}}
[7,4,8,3,6,5,1,2]=>{{1,7},{2,3,4,8},{5,6}}
[1,5,4,3,8,7,2,6]=>{{1},{2,5,6,7,8},{3,4}}
[1,5,8,2,6,4,3,7]=>{{1},{2,4,5,6},{3,7,8}}
[3,5,6,2,4,7,8,1]=>{{1,3,6,7,8},{2,4,5}}
[3,5,6,7,2,4,8,1]=>{{1,3,4,6,7,8},{2,5}}
[3,5,7,6,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,2,6,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,7,6,8,4,1]=>{{1,2,3,5,6,8},{4,7}}
[3,5,7,4,2,6,8,1]=>{{1,3,7,8},{2,5},{4},{6}}
[3,5,4,7,2,6,8,1]=>{{1,3,4,7,8},{2,5},{6}}
[3,4,5,7,2,6,8,1]=>{{1,2,3,4,5,7,8},{6}}
[3,4,5,7,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,4,7,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,4,7,2,8,6,1]=>{{1,3,4,6,7,8},{2,5}}
[3,2,5,7,4,8,6,1]=>{{1,3,4,5,6,7,8},{2}}
[3,5,7,4,2,8,6,1]=>{{1,3,6,7,8},{2,5},{4}}
[3,5,7,8,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[2,3,5,7,8,4,6,1]=>{{1,2,3,5,8},{4,6,7}}
[3,5,2,7,8,6,4,1]=>{{1,2,3,5,8},{4,7},{6}}
[3,5,7,8,2,6,4,1]=>{{1,3,4,7,8},{2,5},{6}}
[3,5,7,8,6,2,4,1]=>{{1,3,4,7,8},{2,5,6}}
[4,2,5,6,7,3,8,1]=>{{1,3,4,5,6,7,8},{2}}
[8,6,1,4,3,5,2,7]=>{{1,2,3,5,6,7,8},{4}}
[6,1,8,4,3,5,2,7]=>{{1,2,3,5,6,7,8},{4}}
[5,1,6,4,8,2,3,7]=>{{1,2,3,5,6,7,8},{4}}
[8,1,4,2,5,3,6,7]=>{{1,2,3,4,6,7,8},{5}}
[2,8,4,1,5,3,6,7]=>{{1,2,3,4,6,7,8},{5}}
[8,4,1,3,5,2,6,7]=>{{1,2,3,4,6,7,8},{5}}
[4,1,8,3,5,2,6,7]=>{{1,2,3,4,6,7,8},{5}}
[8,3,1,2,5,4,6,7]=>{{1,2,3,4,6,7,8},{5}}
[3,1,8,2,5,4,6,7]=>{{1,2,3,4,6,7,8},{5}}
[1,4,8,6,7,2,5,3]=>{{1},{2,4,6},{3,8},{5,7}}
[4,6,8,1,2,5,3,7]=>{{1,4},{2,5,6},{3,7,8}}
[3,5,6,8,2,1,4,7]=>{{1,3,6},{2,5},{4,7,8}}
[8,2,5,4,1,3,7,6]=>{{1,3,5,6,8},{2},{4},{7}}
[2,4,5,8,6,3,1,7]=>{{1,2,4,7,8},{3,5,6}}
[5,4,8,2,3,1,7,6]=>{{1,3,5,6,8},{2,4},{7}}
[4,7,5,8,2,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,5,1,8,3,2]=>{{1,4,5},{2,6,8},{3,7}}
[1,7,3,6,5,8,2,4]=>{{1},{2,7},{3},{4,6,8},{5}}
[8,3,4,2,6,7,1,5]=>{{1,5,6,7,8},{2,3,4}}
[7,5,3,8,6,2,1,4]=>{{1,7},{2,5,6},{3},{4,8}}
[7,3,1,8,2,6,5,4]=>{{1,2,3,5,7},{4,8},{6}}
[4,6,7,5,2,8,3,1]=>{{1,2,4,5,6,8},{3,7}}
[5,8,7,2,4,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,1,2,8,6,7,3,4]=>{{1,2,3,5,6,7},{4,8}}
[2,5,7,8,6,1,4,3]=>{{1,2,5,6},{3,4,7,8}}
[7,2,6,8,4,5,1,3]=>{{1,7},{2},{3,4,5,6,8}}
[5,1,7,6,8,2,3,4]=>{{1,2,4,5,6,8},{3,7}}
[1,7,6,2,4,3,8,5]=>{{1},{2,4,5,7,8},{3,6}}
[7,1,6,2,4,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[5,7,1,6,2,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,2,5,8,3,4,1,7]=>{{1,4,6,7,8},{2},{3,5}}
[5,6,8,7,1,3,2,4]=>{{1,5},{2,3,4,6,7,8}}
[1,5,3,4,8,2,6,7]=>{{1},{2,5,6,7,8},{3},{4}}
[2,1,3,6,5,8,4,7]=>{{1,2},{3},{4,6,7,8},{5}}
[5,1,2,8,6,3,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[6,1,5,7,8,4,2,3]=>{{1,2,4,6,7},{3,5,8}}
[4,6,1,5,7,2,8,3]=>{{1,3,4,5,7,8},{2,6}}
[2,5,8,4,6,3,7,1]=>{{1,2,3,5,6,8},{4},{7}}
[4,3,7,1,2,6,8,5]=>{{1,4},{2,3,5,7,8},{6}}
[8,1,6,5,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[6,8,1,5,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}
[4,5,8,2,3,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[1,7,3,2,4,8,6,5]=>{{1},{2,4,5,6,7,8},{3}}
[4,3,1,8,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[4,8,1,3,2,5,7,6]=>{{1,3,4},{2,5,6,8},{7}}
[1,7,5,3,8,6,2,4]=>{{1},{2,7},{3,4,5,8},{6}}
[2,5,3,8,1,4,7,6]=>{{1,2,5},{3},{4,6,8},{7}}
[4,2,5,8,1,3,7,6]=>{{1,3,4,5,6,8},{2},{7}}
[8,1,2,4,3,5,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[2,4,3,8,1,5,7,6]=>{{1,2,4,5,6,8},{3},{7}}
[3,1,7,4,8,6,5,2]=>{{1,2,3,5,7,8},{4},{6}}
[6,4,5,3,2,8,7,1]=>{{1,6,8},{2,3,4,5},{7}}
[2,7,3,8,5,1,6,4]=>{{1,2,6,7},{3},{4,8},{5}}
[8,7,3,2,5,6,4,1]=>{{1,8},{2,4,7},{3},{5},{6}}
[3,1,8,2,6,5,4,7]=>{{1,2,3,4,7,8},{5,6}}
[7,6,2,8,1,4,5,3]=>{{1,5,7},{2,3,4,6,8}}
[2,3,8,4,1,5,7,6]=>{{1,2,3,5,6,8},{4},{7}}
[8,4,2,3,1,5,7,6]=>{{1,5,6,8},{2,3,4},{7}}
[8,2,3,4,1,5,7,6]=>{{1,5,6,8},{2},{3},{4},{7}}
[7,1,6,2,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,1,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[6,5,8,1,3,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[2,1,8,5,3,4,6,7]=>{{1,2},{3,4,5,6,7,8}}
[8,4,1,3,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,1,2,3,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,5,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[2,8,6,3,1,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[5,7,2,8,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,3,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,6,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,8,1,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,1,8,4,6,3,2]=>{{1,3,7},{2,4,5,8},{6}}
[1,7,8,5,6,4,3,2]=>{{1},{2,3,7,8},{4,5,6}}
[2,8,1,7,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,3,6,2,5,4,8,1]=>{{1,7,8},{2,3,4,6},{5}}
[1,6,2,3,5,8,4,7]=>{{1},{2,3,4,6,7,8},{5}}
[1,8,5,6,4,3,7,2]=>{{1},{2,8},{3,4,5,6},{7}}
[2,6,8,4,5,1,7,3]=>{{1,2,6},{3,8},{4},{5},{7}}
[4,6,5,7,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[2,5,8,6,4,7,1,3]=>{{1,2,4,5,6,7},{3,8}}
[5,3,2,1,7,8,4,6]=>{{1,4,5,7},{2,3},{6,8}}
[8,4,1,3,6,7,2,5]=>{{1,2,3,4,5,6,7,8}}
[1,6,5,3,8,4,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[7,6,2,3,5,1,4,8]=>{{1,2,3,4,6,7},{5},{8}}
[6,2,5,3,4,8,1,7]=>{{1,6,7,8},{2},{3,4,5}}
[6,2,5,3,4,8,7,1]=>{{1,6,8},{2},{3,4,5},{7}}
[2,6,5,3,4,8,1,7]=>{{1,2,6,7,8},{3,4,5}}
[5,3,4,8,1,7,2,6]=>{{1,5},{2,3,4,6,7,8}}
[5,1,3,4,8,7,2,6]=>{{1,2,5,6,7,8},{3},{4}}
[1,5,3,4,8,7,2,6]=>{{1},{2,5,6,7,8},{3},{4}}
[5,1,3,8,4,7,6,2]=>{{1,2,4,5,8},{3},{6,7}}
[5,3,8,1,4,7,6,2]=>{{1,4,5},{2,3,8},{6,7}}
[4,3,5,8,1,7,6,2]=>{{1,2,3,4,5,8},{6,7}}
[3,6,5,4,8,1,2,7]=>{{1,2,3,5,6,7,8},{4}}
[3,6,5,4,8,2,7,1]=>{{1,3,5,8},{2,6},{4},{7}}
[3,5,2,4,8,7,6,1]=>{{1,2,3,5,8},{4},{6,7}}
[2,5,3,6,8,4,1,7]=>{{1,2,5,7,8},{3},{4,6}}
[4,6,2,5,1,7,8,3]=>{{1,4,5},{2,3,6,7,8}}
[2,3,6,5,8,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[2,3,1,7,4,8,6,5]=>{{1,2,3},{4,5,6,7,8}}
[1,8,3,6,4,2,7,5]=>{{1},{2,4,5,6,8},{3},{7}}
[2,1,7,4,8,5,3,6]=>{{1,2},{3,7},{4},{5,6,8}}
[8,1,7,3,2,5,4,6]=>{{1,2,5,6,8},{3,4,7}}
[7,8,5,2,6,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,5,7,4,6,3]=>{{1,2,3,8},{4,5,6,7}}
[8,2,5,3,6,1,4,7]=>{{1,3,4,5,6,7,8},{2}}
[6,8,7,4,1,5,2,3]=>{{1,5,6},{2,3,7,8},{4}}
[8,6,4,7,5,1,3,2]=>{{1,2,6,8},{3,4,7},{5}}
[6,1,2,4,7,8,3,5]=>{{1,2,3,5,6,7,8},{4}}
[2,4,6,5,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,5,2,1,7,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[4,2,7,8,6,5,1,3]=>{{1,3,4,7,8},{2},{5,6}}
[1,2,7,8,6,4,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,8,1,2,6,5,3,7]=>{{1,2,3,4,7,8},{5,6}}
[7,1,6,3,2,4,8,5]=>{{1,2,5,7,8},{3,4,6}}
[6,4,8,1,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[7,4,1,3,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,3,2,6,5,4]=>{{1,2,5,7},{3,4,8},{6}}
[7,2,5,1,6,4,3,8]=>{{1,3,4,5,6,7},{2},{8}}
[5,2,7,1,4,6,3,8]=>{{1,4,5},{2},{3,7},{6},{8}}
[6,3,8,5,7,1,4,2]=>{{1,6},{2,3,8},{4,5,7}}
[2,4,3,8,5,7,1,6]=>{{1,2,4,6,7,8},{3},{5}}
[2,8,3,1,4,6,5,7]=>{{1,2,4,5,7,8},{3},{6}}
[4,5,7,6,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,2,8,5,1,4,6,7]=>{{1,3,4,5,6,7,8},{2}}
[3,5,4,1,2,8,6,7]=>{{1,3,4},{2,5},{6,7,8}}
[5,3,8,1,4,2,6,7]=>{{1,4,5},{2,3,6,7,8}}
[5,3,8,1,4,2,7,6]=>{{1,4,5},{2,3,6,8},{7}}
[1,4,7,5,8,6,2,3]=>{{1},{2,3,4,5,7,8},{6}}
[8,5,7,6,3,4,1,2]=>{{1,2,3,5,7,8},{4,6}}
[7,5,2,6,1,4,8,3]=>{{1,2,3,5,7,8},{4,6}}
[2,4,5,1,8,3,7,6]=>{{1,2,4},{3,5,6,8},{7}}
[7,2,8,5,3,4,1,6]=>{{1,7},{2},{3,4,5,6,8}}
[6,4,5,3,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[7,3,5,6,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,3,4,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[4,6,2,1,5,8,3,7]=>{{1,4},{2,3,6,7,8},{5}}
[4,6,7,2,3,8,5,1]=>{{1,2,4,6,8},{3,5,7}}
[2,3,5,8,7,4,1,6]=>{{1,2,3,5,7},{4,6,8}}
[2,3,5,8,7,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,3,7,8,1,2,6]=>{{1,2,4,5,6,7,8},{3}}
[2,3,5,8,1,6,4,7]=>{{1,2,3,5},{4,7,8},{6}}
[1,7,4,5,8,3,6,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,1,5,4,2,7,3]=>{{1,3,8},{2,6},{4,5},{7}}
[2,8,5,6,3,1,4,7]=>{{1,2,4,6,7,8},{3,5}}
[4,8,2,6,1,5,7,3]=>{{1,4,5,6},{2,3,8},{7}}
[2,3,7,8,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}
[5,2,6,7,8,3,1,4]=>{{1,4,5,7,8},{2},{3,6}}
[5,6,2,7,8,3,1,4]=>{{1,4,5,7,8},{2,3,6}}
[2,3,7,5,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,5,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,7,1,8,4,3]=>{{1,2,5},{3,6,8},{4,7}}
[2,3,7,8,5,4,6,1]=>{{1,2,3,4,6,7,8},{5}}
[6,4,7,8,1,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,1,2,3,6,4]=>{{1,3,4,6,7,8},{2,5}}
[1,2,8,7,4,6,5,3]=>{{1},{2},{3,8},{4,5,7},{6}}
[5,1,4,8,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,3,1,8,7,5,6,2]=>{{1,2,3,4,8},{5,6,7}}
[4,3,2,7,6,1,5,8]=>{{1,4,5,6,7},{2,3},{8}}
[7,2,6,5,3,1,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[1,3,7,6,2,4,8,5]=>{{1},{2,3,5,7,8},{4,6}}
[1,3,8,2,7,4,6,5]=>{{1},{2,3,4,5,6,7,8}}
[8,2,7,1,6,4,3,5]=>{{1,4,5,6,8},{2},{3,7}}
[4,3,2,8,1,7,5,6]=>{{1,4,5,6,7,8},{2,3}}
[7,5,4,1,6,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[1,6,5,3,2,4,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[1,7,3,5,2,4,8,6]=>{{1},{2,4,5,6,7,8},{3}}
[4,3,7,2,5,1,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[5,1,4,3,2,6,8,7]=>{{1,2,5},{3,4},{6},{7,8}}
[7,2,1,3,5,4,6,8]=>{{1,3,4,6,7},{2},{5},{8}}
[8,3,7,5,4,2,6,1]=>{{1,8},{2,3,6,7},{4,5}}
[1,6,8,7,5,2,3,4]=>{{1},{2,6},{3,4,7,8},{5}}
[1,3,6,2,5,4,8,7]=>{{1},{2,3,4,6},{5},{7,8}}
[4,5,7,6,3,1,8,2]=>{{1,4,6},{2,3,5,7,8}}
[4,6,7,5,1,3,8,2]=>{{1,4,5},{2,3,6,7,8}}
[3,6,5,1,4,7,8,2]=>{{1,3,4,5},{2,6,7,8}}
[4,6,7,3,1,5,8,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,1,8,7,3,6,2]=>{{1,3,5,6,7},{2,4,8}}
[6,2,4,7,5,3,1,8]=>{{1,3,4,6,7},{2},{5},{8}}
[6,2,5,1,8,7,3,4]=>{{1,3,4,5,6,7,8},{2}}
[3,2,6,1,5,8,7,4]=>{{1,3,4,6,8},{2},{5},{7}}
[4,2,3,6,7,5,1,8]=>{{1,4,5,6,7},{2},{3},{8}}
[6,2,3,5,7,4,1,8]=>{{1,4,5,6,7},{2},{3},{8}}
[1,6,3,8,4,7,2,5]=>{{1},{2,6,7},{3},{4,5,8}}
[8,1,5,2,4,7,3,6]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,1,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}
[1,3,4,8,5,6,2,7]=>{{1},{2,3,4,7,8},{5},{6}}
[3,2,7,1,8,6,5,4]=>{{1,3,4,5,7,8},{2},{6}}
[6,2,4,1,5,7,8,3]=>{{1,3,4,6,7,8},{2},{5}}
[5,8,4,1,3,6,7,2]=>{{1,3,4,5},{2,8},{6},{7}}
[6,7,2,3,8,1,4,5]=>{{1,6},{2,3,4,7},{5,8}}
[5,2,8,1,7,4,6,3]=>{{1,4,5,6,7},{2},{3,8}}
[2,5,4,7,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[4,6,3,1,2,5,7,8]=>{{1,4},{2,5,6},{3},{7},{8}}
[7,4,6,8,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,7,3,1,2,6]=>{{1,6,8},{2,3,4,5,7}}
[7,3,2,1,5,4,8,6]=>{{1,4,6,7,8},{2,3},{5}}
[2,5,6,4,8,1,3,7]=>{{1,2,3,5,6,7,8},{4}}
[5,4,1,6,2,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[1,3,6,5,2,4,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,4,1,2,7,6,3,8]=>{{1,3,5,7},{2,4},{6},{8}}
[5,8,7,3,1,2,4,6]=>{{1,5},{2,6,8},{3,4,7}}
[2,7,8,1,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[4,1,2,8,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[6,1,2,4,3,8,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[3,7,8,1,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}
[7,3,4,1,2,6,8,5]=>{{1,2,3,4,5,7,8},{6}}
[8,4,3,1,2,6,5,7]=>{{1,2,4,5,7,8},{3},{6}}
[3,8,2,7,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,3,5,4,1,7]=>{{1,7,8},{2,3,4,6},{5}}
[8,2,6,1,3,5,4,7]=>{{1,4,7,8},{2},{3,5,6}}
[8,4,3,7,2,5,6,1]=>{{1,8},{2,4,5,6,7},{3}}
[8,3,1,7,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}
[8,2,4,5,1,7,3,6]=>{{1,3,4,5,6,7,8},{2}}
[6,8,2,4,5,1,7,3]=>{{1,6},{2,3,8},{4},{5},{7}}
[4,3,8,1,7,5,6,2]=>{{1,4},{2,3,8},{5,6,7}}
[8,4,3,7,1,5,6,2]=>{{1,2,4,5,6,7,8},{3}}
[8,3,4,7,2,6,5,1]=>{{1,8},{2,3,4,5,7},{6}}
[8,1,3,7,6,4,5,2]=>{{1,2,8},{3},{4,5,6,7}}
[8,3,7,1,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,6,1,2,5,4]=>{{1,2,4,5,6,7,8},{3}}
[8,3,7,6,2,4,5,1]=>{{1,8},{2,3,5,7},{4,6}}
[8,7,2,3,6,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,2,7,1,3,4,6,5]=>{{1,3,4,5,6,7,8},{2}}
[5,1,8,4,2,3,7,6]=>{{1,2,5},{3,6,8},{4},{7}}
[8,2,4,7,3,1,6,5]=>{{1,3,4,5,6,7,8},{2}}
[8,2,7,6,3,1,4,5]=>{{1,3,4,5,6,7,8},{2}}
[6,8,1,4,7,3,2,5]=>{{1,3,6},{2,5,7,8},{4}}
[8,5,7,2,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,2,7,3,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,6,7,5,4,3]=>{{1,2,3,8},{4,5,6,7}}
[8,4,1,7,5,6,2,3]=>{{1,3,8},{2,4,7},{5},{6}}
[8,2,4,7,6,5,1,3]=>{{1,3,4,7,8},{2},{5,6}}
[8,2,7,6,4,5,1,3]=>{{1,3,7,8},{2},{4,5,6}}
[8,4,7,2,3,6,5,1]=>{{1,8},{2,4},{3,5,7},{6}}
[8,2,4,7,3,6,5,1]=>{{1,8},{2},{3,4,5,7},{6}}
[8,1,7,6,4,5,2,3]=>{{1,2,3,7,8},{4,5,6}}
[8,1,2,7,6,4,5,3]=>{{1,2,3,8},{4,5,6,7}}
[8,1,4,7,3,6,5,2]=>{{1,2,8},{3,4,5,7},{6}}
[2,8,1,5,3,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[1,8,2,4,7,5,6,3]=>{{1},{2,3,8},{4},{5,6,7}}
[2,3,8,4,7,1,6,5]=>{{1,2,3,5,6,7,8},{4}}
[1,8,2,3,5,6,4,7]=>{{1},{2,3,4,7,8},{5},{6}}
[1,4,7,6,2,3,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,7,6,2,3,8,4,5]=>{{1},{2,4,7},{3,5,6,8}}
[1,8,2,3,7,6,4,5]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,3,8,6,2,5,4]=>{{1},{2,5,6,7},{3},{4,8}}
[5,8,2,3,7,4,1,6]=>{{1,5,7},{2,3,4,6,8}}
[4,2,8,3,7,6,1,5]=>{{1,3,4,5,7,8},{2},{6}}
[1,3,5,6,4,8,2,7]=>{{1},{2,3,4,5,6,7,8}}
[4,6,1,8,2,7,5,3]=>{{1,3,4,8},{2,5,6,7}}
[3,4,8,5,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,7,6,2,5,4,8,3]=>{{1},{2,3,4,6,7,8},{5}}
[5,6,1,7,4,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,7,2,1,5,6,8,4]=>{{1,2,3,4,7,8},{5},{6}}
[3,1,5,6,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[8,1,6,4,3,5,2,7]=>{{1,2,7,8},{3,5,6},{4}}
[2,1,6,5,3,8,7,4]=>{{1,2},{3,4,5,6,8},{7}}
[3,7,5,6,4,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[6,1,4,3,7,5,8,2]=>{{1,2,5,6,7,8},{3,4}}
[3,8,6,4,5,2,7,1]=>{{1,2,3,6,8},{4},{5},{7}}
[4,5,8,6,2,3,7,1]=>{{1,3,4,6,8},{2,5},{7}}
[4,6,8,5,3,7,2,1]=>{{1,3,4,5,8},{2,6,7}}
[4,5,7,2,8,6,3,1]=>{{1,2,4,5,8},{3,7},{6}}
[3,7,4,5,1,6,8,2]=>{{1,3,4,5},{2,7,8},{6}}
[4,6,8,1,2,5,7,3]=>{{1,4},{2,5,6},{3,8},{7}}
[4,6,8,5,1,3,7,2]=>{{1,4,5},{2,3,6,8},{7}}
[3,7,4,5,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,4,6,1,5,2]=>{{1,2,3,5,6,7,8},{4}}
[4,5,7,2,1,6,8,3]=>{{1,2,4,5},{3,7,8},{6}}
[4,5,1,6,8,3,7,2]=>{{1,3,4,6},{2,5,8},{7}}
[8,3,5,4,6,1,2,7]=>{{1,2,3,5,6,7,8},{4}}
[1,7,4,5,2,6,8,3]=>{{1},{2,3,4,5,7,8},{6}}
[1,4,2,6,5,3,8,7]=>{{1},{2,3,4,6},{5},{7,8}}
[3,1,5,8,4,6,2,7]=>{{1,2,3,4,5,7,8},{6}}
[8,2,6,3,4,1,5,7]=>{{1,3,4,5,6,7,8},{2}}
[4,6,5,8,2,1,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,4,8,3,5,6,2,7]=>{{1},{2,3,4,7,8},{5},{6}}
[1,8,7,4,2,3,6,5]=>{{1},{2,5,8},{3,6,7},{4}}
[4,3,1,8,5,7,2,6]=>{{1,2,3,4,6,7,8},{5}}
[7,3,2,4,8,1,6,5]=>{{1,6,7},{2,3},{4},{5,8}}
[3,7,2,4,5,8,1,6]=>{{1,2,3,7},{4},{5},{6,8}}
[3,2,7,4,6,1,8,5]=>{{1,3,5,6,7,8},{2},{4}}
[8,3,2,4,6,1,7,5]=>{{1,5,6,8},{2,3},{4},{7}}
[8,3,2,4,5,7,1,6]=>{{1,6,7,8},{2,3},{4},{5}}
[7,4,6,2,1,3,8,5]=>{{1,5,7,8},{2,4},{3,6}}
[3,6,7,2,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,2,3,5,6,1]=>{{1,8},{2,4},{3,5,6,7}}
[3,8,6,7,1,5,4,2]=>{{1,3,5,6},{2,8},{4,7}}
[4,3,2,8,6,1,5,7]=>{{1,4,5,6,7,8},{2,3}}
[4,1,6,3,2,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[5,7,1,8,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,7,6,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[8,4,6,3,1,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,5,2,4,7,8]=>{{1,3},{2,4,5,6},{7},{8}}
[3,7,6,2,5,4,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,7,1,5,3,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[8,4,5,1,2,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[5,2,3,8,7,1,6,4]=>{{1,5,6,7},{2},{3},{4,8}}
[7,5,2,4,1,3,8,6]=>{{1,2,3,5,6,7,8},{4}}
[7,2,6,8,5,1,3,4]=>{{1,3,6,7},{2},{4,8},{5}}
[8,6,5,4,1,3,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[8,2,3,4,1,6,7,5]=>{{1,5,8},{2},{3},{4},{6},{7}}
[7,4,3,8,1,6,5,2]=>{{1,5,7},{2,4,8},{3},{6}}
[6,5,1,4,3,8,7,2]=>{{1,2,3,5,6,8},{4},{7}}
[4,7,6,2,5,8,1,3]=>{{1,2,4,7},{3,6,8},{5}}
[6,3,2,4,5,8,1,7]=>{{1,6,7,8},{2,3},{4},{5}}
[2,6,4,5,8,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[3,7,4,8,6,2,5,1]=>{{1,3,4,8},{2,5,6,7}}
[7,3,5,2,8,1,4,6]=>{{1,2,3,4,5,6,7,8}}
[1,5,8,7,4,2,3,6]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,4,5,8,6,3]=>{{1},{2,3,6,7,8},{4},{5}}
[1,4,6,8,7,2,5,3]=>{{1},{2,3,4,6,8},{5,7}}
[1,6,2,7,5,3,4,8]=>{{1},{2,3,6},{4,7},{5},{8}}
[1,3,7,2,6,4,5,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,7,3,2,8,5,6,4]=>{{1},{2,4,5,6,7,8},{3}}
[1,6,5,2,4,8,3,7]=>{{1},{2,3,4,5,6,7,8}}
[1,7,3,8,4,2,5,6]=>{{1},{2,4,5,6,7,8},{3}}
[1,6,2,4,7,5,8,3]=>{{1},{2,3,5,6,7,8},{4}}
[1,6,2,7,4,3,8,5]=>{{1},{2,3,6},{4,5,7,8}}
[1,5,8,2,3,6,4,7]=>{{1},{2,3,4,5,7,8},{6}}
[2,5,3,6,7,1,4,8]=>{{1,2,4,5,6,7},{3},{8}}
[6,4,1,5,7,2,3,8]=>{{1,2,3,4,5,6,7},{8}}
[6,4,1,5,7,3,8,2]=>{{1,3,6},{2,4,5,7,8}}
[1,2,7,3,8,5,6,4]=>{{1},{2},{3,4,5,6,7,8}}
[7,4,1,6,3,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[1,5,7,4,3,8,6,2]=>{{1},{2,3,5,6,7,8},{4}}
[2,7,3,1,4,5,8,6]=>{{1,2,4,5,6,7,8},{3}}
[6,5,8,3,2,7,1,4]=>{{1,6,7},{2,5},{3,4,8}}
[8,4,3,1,7,6,5,2]=>{{1,2,4,8},{3},{5,7},{6}}
[1,2,6,7,5,3,4,8]=>{{1},{2},{3,6},{4,7},{5},{8}}
[3,4,5,6,8,2,7,1]=>{{1,3,5,8},{2,4,6},{7}}
[7,2,1,4,5,6,3,8]=>{{1,3,7},{2},{4},{5},{6},{8}}
[1,5,6,7,3,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,6,8,5,2,1,7,3]=>{{1,2,4,5,6},{3,8},{7}}
[1,6,7,8,2,4,5,3]=>{{1},{2,3,4,5,6,7,8}}
[5,7,8,3,2,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,2,3,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[4,5,2,7,8,6,1,3]=>{{1,4,7},{2,3,5,8},{6}}
[1,3,5,8,7,2,6,4]=>{{1},{2,3,5,6,7},{4,8}}
[6,4,1,8,5,7,3,2]=>{{1,3,6,7},{2,4,8},{5}}
[4,1,3,8,7,5,2,6]=>{{1,2,4,5,6,7,8},{3}}
[8,5,1,6,7,2,4,3]=>{{1,3,8},{2,4,5,6,7}}
[3,6,7,2,1,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,1,3,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[7,2,5,6,1,3,8,4]=>{{1,3,4,5,6,7,8},{2}}
[6,4,1,2,5,8,3,7]=>{{1,3,6,7,8},{2,4},{5}}
[4,7,3,5,2,6,8,1]=>{{1,2,4,5,7,8},{3},{6}}
[2,3,5,4,7,1,8,6]=>{{1,2,3,5,6,7,8},{4}}
[6,8,4,1,5,7,3,2]=>{{1,3,4,6,7},{2,8},{5}}
[8,1,6,2,3,7,5,4]=>{{1,2,4,8},{3,5,6,7}}
[2,8,3,6,4,1,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[6,5,3,4,8,2,1,7]=>{{1,2,5,6,7,8},{3},{4}}
[5,4,8,7,3,6,2,1]=>{{1,3,5,8},{2,4,7},{6}}
[5,2,7,6,8,3,4,1]=>{{1,5,8},{2},{3,4,6,7}}
[8,4,5,2,7,3,6,1]=>{{1,8},{2,4},{3,5,6,7}}
[6,3,7,4,5,2,8,1]=>{{1,2,3,6,7,8},{4},{5}}
[7,3,4,2,8,5,6,1]=>{{1,5,6,7,8},{2,3,4}}
[4,3,6,5,8,2,7,1]=>{{1,4,5,8},{2,3,6},{7}}
[8,2,7,4,5,3,6,1]=>{{1,8},{2},{3,6,7},{4},{5}}
[7,2,8,4,5,3,6,1]=>{{1,3,6,7,8},{2},{4},{5}}
[6,3,8,2,7,4,5,1]=>{{1,2,3,4,6,8},{5,7}}
[3,2,8,4,7,5,6,1]=>{{1,3,8},{2},{4},{5,6,7}}
[8,3,6,2,7,4,5,1]=>{{1,8},{2,3,4,6},{5,7}}
[1,7,8,4,3,6,5,2]=>{{1},{2,3,5,7,8},{4},{6}}
[1,7,8,3,6,5,4,2]=>{{1},{2,3,4,7,8},{5,6}}
[5,8,1,7,2,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[2,5,7,3,8,1,4,6]=>{{1,2,5,6,8},{3,4,7}}
[8,3,5,2,1,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[2,6,4,7,1,8,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,6,5,7,3,8,2,4]=>{{1},{2,4,6,7,8},{3,5}}
[1,8,5,3,7,6,2,4]=>{{1},{2,3,4,5,7,8},{6}}
[6,4,2,3,8,7,5,1]=>{{1,5,6,7,8},{2,3,4}}
[6,5,1,3,8,4,2,7]=>{{1,3,4,6},{2,5,7,8}}
[6,1,4,2,7,8,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,5,1,3,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,8,2,4,7,1,3]=>{{1,2,4,5,6,7},{3,8}}
[6,7,4,2,3,8,5,1]=>{{1,6,8},{2,3,4,5,7}}
[5,8,7,3,2,4,6,1]=>{{1,2,5,8},{3,4,6,7}}
[5,1,3,2,6,8,4,7]=>{{1,2,4,5,6,7,8},{3}}
[5,7,1,4,6,8,2,3]=>{{1,3,5,6,8},{2,7},{4}}
[2,4,1,7,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}
[1,4,3,7,6,2,8,5]=>{{1},{2,4,5,6,7,8},{3}}
[1,6,2,5,7,3,8,4]=>{{1},{2,3,6},{4,5,7,8}}
[1,4,3,8,2,5,7,6]=>{{1},{2,4,5,6,8},{3},{7}}
[1,5,7,3,6,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,7,2,4,8,3,5]=>{{1},{2,4,5,6,8},{3,7}}
[3,7,2,8,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[5,3,4,1,7,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,7,6,5,8,2,3,1]=>{{1,4,5,8},{2,3,6,7}}
[1,2,6,8,4,3,5,7]=>{{1},{2},{3,6},{4,5,7,8}}
[7,2,6,3,1,8,4,5]=>{{1,3,4,5,6,7,8},{2}}
[5,8,4,1,3,7,2,6]=>{{1,3,4,5},{2,6,7,8}}
[3,4,2,1,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}
[8,1,3,5,6,4,7,2]=>{{1,2,8},{3},{4,5,6},{7}}
[3,4,7,1,5,6,2,8]=>{{1,2,3,4,7},{5},{6},{8}}
[4,8,2,6,5,3,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[4,8,7,2,5,6,1,3]=>{{1,2,3,4,7,8},{5},{6}}
[5,8,6,4,7,3,2,1]=>{{1,2,5,7,8},{3,6},{4}}
[8,5,2,3,1,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[2,8,6,3,5,1,7,4]=>{{1,2,3,4,6,8},{5},{7}}
[8,3,2,6,4,1,7,5]=>{{1,4,5,6,8},{2,3},{7}}
[8,4,1,5,3,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[8,3,5,1,4,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[8,5,1,3,4,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[3,8,6,2,5,4,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[3,8,4,6,5,2,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[8,1,7,4,2,5,3,6]=>{{1,2,5,6,8},{3,7},{4}}
[8,3,2,5,1,4,7,6]=>{{1,4,5,6,8},{2,3},{7}}
[8,4,5,1,2,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[8,1,5,3,2,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[8,1,5,2,4,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[5,2,6,4,1,3,8,7]=>{{1,5},{2},{3,6},{4},{7,8}}
[8,6,4,7,1,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[2,1,8,5,4,3,7,6]=>{{1,2},{3,6,8},{4,5},{7}}
[6,4,8,5,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[8,5,4,6,2,7,1,3]=>{{1,3,4,6,7,8},{2,5}}
[6,8,5,4,7,2,3,1]=>{{1,2,6,8},{3,5,7},{4}}
[2,5,7,3,4,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[5,2,4,7,8,1,3,6]=>{{1,5,6,8},{2},{3,4,7}}
[4,8,5,6,1,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,5,6,8,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[1,7,8,5,4,6,2,3]=>{{1},{2,7},{3,8},{4,5},{6}}
[4,6,8,1,5,2,7,3]=>{{1,4},{2,6},{3,8},{5},{7}}
[8,2,3,6,4,1,7,5]=>{{1,4,5,6,8},{2},{3},{7}}
[2,3,7,5,8,6,1,4]=>{{1,2,3,7},{4,5,8},{6}}
[3,8,5,1,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[1,3,6,4,8,2,7,5]=>{{1},{2,3,6},{4},{5,8},{7}}
[1,7,6,2,8,5,3,4]=>{{1},{2,3,4,5,6,7,8}}
[1,5,8,6,4,7,2,3]=>{{1},{2,4,5,6,7},{3,8}}
[5,6,2,8,1,7,3,4]=>{{1,5},{2,3,6,7},{4,8}}
[6,8,4,5,1,3,7,2]=>{{1,3,4,5,6},{2,8},{7}}
[5,2,3,8,1,4,6,7]=>{{1,5},{2},{3},{4,6,7,8}}
[1,6,8,3,2,4,5,7]=>{{1},{2,3,4,5,6,7,8}}
[8,6,5,2,4,3,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[6,2,5,3,7,4,8,1]=>{{1,3,4,5,6,7,8},{2}}
[8,5,4,2,6,3,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[8,5,3,2,6,4,7,1]=>{{1,8},{2,4,5,6},{3},{7}}
[7,4,6,5,8,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[7,3,6,5,8,2,4,1]=>{{1,4,5,7,8},{2,3,6}}
[7,3,6,4,8,2,5,1]=>{{1,5,7,8},{2,3,6},{4}}
[7,3,5,4,8,2,6,1]=>{{1,2,3,5,6,7,8},{4}}
[7,3,6,8,4,5,1,2]=>{{1,7},{2,3,4,5,6,8}}
[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,2,7,4,8,5,6,3]=>{{1},{2},{3,5,6,7,8},{4}}
[2,6,7,4,8,5,1,3]=>{{1,2,3,5,6,7,8},{4}}
[2,5,8,6,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[6,4,2,5,7,1,8,3]=>{{1,6},{2,3,4,5,7,8}}
[8,1,4,7,3,5,6,2]=>{{1,2,8},{3,4,5,6,7}}
[8,3,7,2,4,5,6,1]=>{{1,8},{2,3,4,5,6,7}}
[8,1,4,5,7,3,6,2]=>{{1,2,8},{3,4,5,6,7}}
[5,6,3,4,2,8,7,1]=>{{1,2,5,6,8},{3},{4},{7}}
[2,5,7,4,6,8,1,3]=>{{1,2,3,5,6,7,8},{4}}
[2,5,6,4,1,3,8,7]=>{{1,2,5},{3,6},{4},{7,8}}
[4,6,1,3,5,7,2,8]=>{{1,3,4},{2,6,7},{5},{8}}
[3,2,7,5,8,1,6,4]=>{{1,3,6,7},{2},{4,5,8}}
[4,3,6,8,5,2,1,7]=>{{1,4,7,8},{2,3,6},{5}}
[4,5,3,2,1,8,6,7]=>{{1,2,4,5},{3},{6,7,8}}
[3,6,5,8,1,7,4,2]=>{{1,3,5},{2,4,6,7,8}}
[4,1,6,8,5,2,3,7]=>{{1,2,3,4,6,7,8},{5}}
[4,5,2,8,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[4,5,2,8,6,7,3,1]=>{{1,4,8},{2,3,5,6,7}}
[3,5,8,6,2,4,7,1]=>{{1,3,8},{2,5},{4,6},{7}}
[2,5,1,6,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[3,2,4,5,8,6,1,7]=>{{1,3,4,5,7,8},{2},{6}}
[4,5,2,1,3,8,6,7]=>{{1,4},{2,3,5},{6,7,8}}
[4,2,3,6,8,5,1,7]=>{{1,4,5,6,7,8},{2},{3}}
[4,5,1,3,2,8,6,7]=>{{1,3,4},{2,5},{6,7,8}}
[3,4,5,8,6,1,7,2]=>{{1,3,5,6},{2,4,8},{7}}
[3,4,5,8,6,1,2,7]=>{{1,3,5,6},{2,4,7,8}}
[6,4,1,3,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[6,3,1,2,5,4,8,7]=>{{1,2,3,4,6},{5},{7,8}}
[8,2,6,4,1,3,7,5]=>{{1,5,8},{2},{3,6},{4},{7}}
[1,5,8,2,4,3,7,6]=>{{1},{2,4,5},{3,6,8},{7}}
[4,3,7,8,2,6,5,1]=>{{1,4,8},{2,3,5,7},{6}}
[3,8,5,1,2,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[2,4,7,8,3,6,5,1]=>{{1,2,4,8},{3,5,7},{6}}
[5,4,7,8,3,6,1,2]=>{{1,3,5,7},{2,4,8},{6}}
[6,8,1,3,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[1,4,8,5,7,2,3,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,3,2,4,5,6]=>{{1},{2,3,4,5,6,7,8}}
[8,6,2,7,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,7,3,4,5,1]=>{{1,8},{2,3,4,5,6,7}}
[5,6,3,2,8,7,1,4]=>{{1,2,4,5,6,7,8},{3}}
[5,1,6,7,8,3,2,4]=>{{1,2,4,5,7,8},{3,6}}
[1,5,6,3,7,2,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,5,6,7,4,2,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,1,6,7,3,4,2,8]=>{{1,2,3,4,5,6,7},{8}}
[8,6,1,7,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,1,7,4,2,3]=>{{1,4,6},{2,3,5,7,8}}
[8,4,2,3,5,7,6,1]=>{{1,8},{2,3,4},{5},{6,7}}
[4,8,5,2,3,1,6,7]=>{{1,2,4,6,7,8},{3,5}}
[5,4,8,3,1,2,6,7]=>{{1,5},{2,3,4,6,7,8}}
[8,4,7,3,2,5,6,1]=>{{1,8},{2,3,4,5,6,7}}
[6,8,5,1,7,3,4,2]=>{{1,3,4,5,6,7},{2,8}}
[6,2,7,3,8,1,4,5]=>{{1,6},{2},{3,4,7},{5,8}}
[8,4,2,6,7,1,5,3]=>{{1,2,3,4,6,8},{5,7}}
[1,7,8,3,6,5,2,4]=>{{1},{2,7},{3,4,8},{5,6}}
[4,6,7,5,1,8,2,3]=>{{1,4,5},{2,3,6,7,8}}
[3,5,2,6,8,7,4,1]=>{{1,2,3,5,8},{4,6,7}}
[7,3,6,8,4,1,2,5]=>{{1,2,3,6,7},{4,5,8}}
[6,4,2,3,7,5,8,1]=>{{1,5,6,7,8},{2,3,4}}
[6,3,7,5,1,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[7,2,5,4,8,6,3,1]=>{{1,3,5,7,8},{2},{4},{6}}
[6,2,3,8,7,4,5,1]=>{{1,4,6,8},{2},{3},{5,7}}
[7,1,2,8,4,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[3,5,8,1,2,7,6,4]=>{{1,3,4,8},{2,5},{6,7}}
[1,4,3,6,8,5,2,7]=>{{1},{2,4,5,6,7,8},{3}}
[7,6,2,8,5,3,4,1]=>{{1,4,7,8},{2,3,6},{5}}
[6,8,3,5,4,7,2,1]=>{{1,2,6,7,8},{3},{4,5}}
[8,2,7,6,4,1,3,5]=>{{1,4,5,6,8},{2},{3,7}}
[8,3,7,5,1,6,2,4]=>{{1,4,5,8},{2,3,7},{6}}
[8,5,7,1,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,1,5,6,3,2,8]=>{{1,3,4,5,6},{2,7},{8}}
[4,5,7,1,6,3,8,2]=>{{1,4},{2,3,5,6,7,8}}
[4,6,5,7,2,3,8,1]=>{{1,4,7,8},{2,3,5,6}}
[3,6,7,2,5,8,4,1]=>{{1,2,3,4,6,7,8},{5}}
[5,3,6,7,4,8,1,2]=>{{1,4,5,7},{2,3,6,8}}
[4,2,7,8,3,6,5,1]=>{{1,4,8},{2},{3,5,7},{6}}
[4,2,7,8,5,6,1,3]=>{{1,3,4,7,8},{2},{5},{6}}
[5,4,3,7,8,1,6,2]=>{{1,2,4,5,6,7,8},{3}}
[3,5,7,8,4,2,1,6]=>{{1,3,7},{2,4,5,6,8}}
[4,6,7,3,2,8,1,5]=>{{1,3,4,7},{2,5,6,8}}
[4,6,5,3,7,8,1,2]=>{{1,3,4,5,7},{2,6,8}}
[5,6,2,4,7,8,3,1]=>{{1,2,3,5,6,7,8},{4}}
[5,6,3,2,8,4,7,1]=>{{1,5,8},{2,4,6},{3},{7}}
[5,6,2,8,3,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[3,7,4,8,1,6,5,2]=>{{1,2,3,4,5,7,8},{6}}
[5,2,4,8,6,7,3,1]=>{{1,3,4,5,6,7,8},{2}}
[5,2,6,4,8,7,3,1]=>{{1,5,8},{2},{3,6,7},{4}}
[2,4,7,8,6,5,1,3]=>{{1,2,3,4,7,8},{5,6}}
[5,2,6,7,8,1,4,3]=>{{1,3,5,6,8},{2},{4,7}}
[4,8,2,7,5,3,1,6]=>{{1,4,7},{2,3,6,8},{5}}
[1,2,4,6,5,8,3,7]=>{{1},{2},{3,4,6,7,8},{5}}
[5,4,2,3,1,7,8,6]=>{{1,5},{2,3,4},{6,7,8}}
[3,5,8,1,7,4,2,6]=>{{1,3,4,6,8},{2,5,7}}
[5,8,6,1,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,4,3,8,2,6,7]=>{{1,2,5,6,7,8},{3,4}}
[8,4,7,5,6,2,1,3]=>{{1,3,7,8},{2,4,5,6}}
[3,8,6,7,5,2,4,1]=>{{1,2,3,6,8},{4,7},{5}}
[8,2,5,4,7,3,6,1]=>{{1,8},{2},{3,5,6,7},{4}}
[4,2,8,7,3,6,5,1]=>{{1,3,4,5,7,8},{2},{6}}
[3,7,8,6,1,4,5,2]=>{{1,2,3,5,7,8},{4,6}}
[4,6,7,8,2,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[4,7,6,3,8,1,5,2]=>{{1,3,4,6},{2,5,7,8}}
[3,8,1,4,6,2,5,7]=>{{1,3},{2,5,6,7,8},{4}}
[2,4,5,3,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[4,7,5,6,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[8,7,5,1,6,3,2,4]=>{{1,4,8},{2,7},{3,5,6}}
[7,8,6,2,3,5,1,4]=>{{1,7},{2,4,8},{3,5,6}}
[2,8,4,6,7,3,5,1]=>{{1,2,8},{3,4,6},{5,7}}
[4,1,6,7,8,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[8,6,3,4,1,2,7,5]=>{{1,5,8},{2,6},{3},{4},{7}}
[2,5,8,4,6,1,3,7]=>{{1,2,5,6},{3,7,8},{4}}
[4,7,8,6,5,1,3,2]=>{{1,4,6},{2,3,7,8},{5}}
[6,8,4,7,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,8,3,6,2,1]=>{{1,2,4,7,8},{3,5},{6}}
[8,4,7,3,5,6,2,1]=>{{1,8},{2,3,4,7},{5},{6}}
[3,6,4,2,8,1,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[3,4,8,6,2,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[3,8,6,2,1,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,2,4,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[8,1,7,6,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,3,7,6,1,2]=>{{1,2,5,7,8},{3,4},{6}}
[4,8,1,3,6,7,5,2]=>{{1,3,4},{2,8},{5,6,7}}
[3,5,8,6,1,7,4,2]=>{{1,2,3,5,8},{4,6,7}}
[8,1,4,7,5,2,6,3]=>{{1,2,3,4,6,7,8},{5}}
[1,4,8,6,7,3,5,2]=>{{1},{2,3,4,6,8},{5,7}}
[4,1,6,7,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,6,4,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[4,6,1,5,7,2,3,8]=>{{1,3,4,5,7},{2,6},{8}}
[4,8,5,3,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,4,8,1,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[8,4,5,3,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,3,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,8,7,2,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,6,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,8,7,5,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[3,8,2,6,7,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[4,7,6,3,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,4,1,8,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,8,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,4,2,8,1,5,3]=>{{1,2,3,4,5,6,7,8}}
[6,3,4,8,7,1,2,5]=>{{1,6},{2,3,4,5,7,8}}
[2,7,4,8,1,6,3,5]=>{{1,2,3,4,5,7,8},{6}}
[5,3,1,6,7,8,2,4]=>{{1,2,3,5,7},{4,6,8}}
[3,4,7,8,6,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[2,1,4,7,8,6,3,5]=>{{1,2},{3,4,7},{5,8},{6}}
[2,4,5,8,1,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[3,4,6,8,2,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[1,8,5,6,4,2,3,7]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,6,2,4,5,3]=>{{1},{2,3,5,7,8},{4,6}}
[6,4,8,5,7,3,1,2]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,7,2,5,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[2,7,5,1,8,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[4,7,1,6,5,3,8,2]=>{{1,3,4,6},{2,7,8},{5}}
[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,4,8,5,7,3,1,6]=>{{1,2,4,5,7},{3,6,8}}
[8,3,1,4,6,2,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[7,2,6,4,5,8,1,3]=>{{1,7},{2},{3,6,8},{4},{5}}
[2,7,1,5,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[3,5,7,2,8,4,1,6]=>{{1,3,7},{2,4,5,6,8}}
[2,4,3,8,5,1,7,6]=>{{1,2,4,6,8},{3},{5},{7}}
[7,3,2,1,4,8,6,5]=>{{1,4,5,6,7,8},{2,3}}
[2,8,3,4,1,7,6,5]=>{{1,2,5,8},{3},{4},{6,7}}
[4,7,6,8,2,5,3,1]=>{{1,4,8},{2,3,5,6,7}}
[2,6,7,1,4,5,8,3]=>{{1,2,4,5,6},{3,7,8}}
[8,7,2,6,1,5,3,4]=>{{1,4,5,6,8},{2,3,7}}
[7,1,3,8,2,6,4,5]=>{{1,2,4,5,7,8},{3},{6}}
[6,2,5,3,4,7,1,8]=>{{1,6,7},{2},{3,4,5},{8}}
[2,7,3,4,1,5,8,6]=>{{1,2,5,6,7,8},{3},{4}}
[2,5,8,1,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,2,8,3,4,5,1,7]=>{{1,3,4,5,6,7,8},{2}}
[3,6,4,1,2,5,8,7]=>{{1,3,4},{2,5,6},{7,8}}
[3,5,4,1,6,2,8,7]=>{{1,3,4},{2,5,6},{7,8}}
[4,5,7,2,8,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[3,5,1,7,6,2,8,4]=>{{1,3},{2,5,6},{4,7,8}}
[8,3,6,2,7,5,4,1]=>{{1,8},{2,3,4,5,6,7}}
[8,4,2,6,5,3,7,1]=>{{1,8},{2,3,4,6},{5},{7}}
[5,4,2,7,1,8,6,3]=>{{1,5},{2,3,4,6,7,8}}
[4,1,7,6,5,3,2,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,3,6,7,1,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,2,7,8,5,4]=>{{1,3},{2,4,6,8},{5,7}}
[4,5,1,8,7,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[8,4,5,2,7,6,3,1]=>{{1,8},{2,4},{3,5,7},{6}}
[4,1,3,6,7,5,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[3,1,4,5,7,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,5,1,3,6,8,7,2]=>{{1,3,4},{2,5,6,8},{7}}
[3,8,5,1,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[8,5,1,2,4,3,6,7]=>{{1,3,6,7,8},{2,4,5}}
[5,8,4,1,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,5,8,1,4,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[2,8,5,7,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,5,1,2,3,6]=>{{1,4,5},{2,6,8},{3,7}}
[8,1,2,4,6,3,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[7,6,1,4,2,3,8,5]=>{{1,2,3,5,6,7,8},{4}}
[6,1,2,7,8,4,3,5]=>{{1,2,3,4,6,7},{5,8}}
[7,8,1,2,5,3,4,6]=>{{1,2,3,4,6,7,8},{5}}
[1,8,4,7,5,2,3,6]=>{{1},{2,6,8},{3,4,7},{5}}
[8,4,7,2,1,6,3,5]=>{{1,5,8},{2,4},{3,7},{6}}
[4,5,8,2,1,6,7,3]=>{{1,2,4,5},{3,8},{6},{7}}
[7,4,2,5,3,6,1,8]=>{{1,7},{2,3,4,5},{6},{8}}
[3,1,6,7,5,2,4,8]=>{{1,2,3,6},{4,7},{5},{8}}
[8,4,2,5,3,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}}
[4,8,1,5,3,6,7,2]=>{{1,3,4,5},{2,8},{6},{7}}
[4,1,7,5,2,6,3,8]=>{{1,2,4,5},{3,7},{6},{8}}
[7,1,5,3,6,8,2,4]=>{{1,2,7},{3,4,5,6,8}}
[4,5,2,6,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,6,7,3,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,4,1,7,8,3]=>{{1,2,3,5,6,7,8},{4}}
[5,4,8,2,1,3,6,7]=>{{1,5},{2,4},{3,6,7,8}}
[1,4,8,3,2,6,5,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,3,8,4,2,7,5,6]=>{{1},{2,3,5,6,7,8},{4}}
[7,2,8,3,1,4,5,6]=>{{1,5,7},{2},{3,4,6,8}}
[8,1,3,2,7,5,4,6]=>{{1,2,4,5,6,7,8},{3}}
[7,6,1,8,2,5,4,3]=>{{1,3,4,7,8},{2,5,6}}
[8,4,1,6,7,3,5,2]=>{{1,2,3,4,6,8},{5,7}}
[5,8,4,2,1,6,3,7]=>{{1,5},{2,3,4,7,8},{6}}
[7,6,4,1,2,5,3,8]=>{{1,3,4,7},{2,5,6},{8}}
[5,4,2,8,1,6,3,7]=>{{1,5},{2,3,4,7,8},{6}}
[8,7,2,6,4,5,3,1]=>{{1,8},{2,3,7},{4,5,6}}
[7,2,8,4,3,6,1,5]=>{{1,7},{2},{3,5,8},{4},{6}}
[1,7,5,4,8,6,2,3]=>{{1},{2,7},{3,5,8},{4},{6}}
[4,8,6,3,5,2,1,7]=>{{1,2,3,4,6,7,8},{5}}
[5,8,6,3,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,3,2,4,8,1]=>{{1,2,5,7,8},{3,4,6}}
[5,7,3,2,8,6,4,1]=>{{1,5,8},{2,4,7},{3},{6}}
[4,5,1,6,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}
[1,6,3,7,2,4,8,5]=>{{1},{2,4,5,6,7,8},{3}}
[4,3,1,6,7,2,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[6,3,1,5,7,2,4,8]=>{{1,2,3,6},{4,5,7},{8}}
[5,2,1,4,8,6,7,3]=>{{1,3,5,8},{2},{4},{6},{7}}
[4,5,2,1,3,7,6,8]=>{{1,4},{2,3,5},{6,7},{8}}
[8,2,7,4,1,6,5,3]=>{{1,3,5,7,8},{2},{4},{6}}
[3,2,8,4,1,6,5,7]=>{{1,3,5,7,8},{2},{4},{6}}
[7,1,6,5,4,2,8,3]=>{{1,2,3,6,7,8},{4,5}}
[7,1,8,4,2,3,6,5]=>{{1,2,3,5,6,7,8},{4}}
[2,7,6,4,5,1,8,3]=>{{1,2,3,6,7,8},{4},{5}}
[3,6,8,1,5,7,4,2]=>{{1,2,3,4,6,7,8},{5}}
[2,8,3,1,6,7,4,5]=>{{1,2,4,5,6,7,8},{3}}
[4,5,6,8,2,1,7,3]=>{{1,3,4,6,8},{2,5},{7}}
[4,5,6,8,1,3,7,2]=>{{1,2,4,5,8},{3,6},{7}}
[4,5,8,3,2,1,7,6]=>{{1,3,4,6,8},{2,5},{7}}
[4,5,1,3,2,6,7,8]=>{{1,3,4},{2,5},{6},{7},{8}}
[4,7,3,2,1,6,5,8]=>{{1,2,4,5,7},{3},{6},{8}}
[4,7,8,3,5,1,6,2]=>{{1,2,3,4,6,7,8},{5}}
[4,7,1,3,5,6,2,8]=>{{1,3,4},{2,7},{5},{6},{8}}
[4,8,3,2,1,6,7,5]=>{{1,2,4,5,8},{3},{6},{7}}
[5,2,8,1,4,6,7,3]=>{{1,4,5},{2},{3,8},{6},{7}}
[5,6,3,7,8,1,4,2]=>{{1,2,5,6,8},{3},{4,7}}
[5,7,1,4,3,6,2,8]=>{{1,3,5},{2,7},{4},{6},{8}}
[6,2,3,7,1,5,4,8]=>{{1,5,6},{2},{3},{4,7},{8}}
[6,2,8,1,5,4,7,3]=>{{1,4,6},{2},{3,8},{5},{7}}
[6,1,3,4,5,2,7,8]=>{{1,2,6},{3},{4},{5},{7},{8}}
[7,1,3,4,5,6,2,8]=>{{1,2,7},{3},{4},{5},{6},{8}}
[7,2,5,1,3,6,4,8]=>{{1,4,7},{2},{3,5},{6},{8}}
[6,5,2,7,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[7,5,3,6,4,2,1,8]=>{{1,7},{2,4,5,6},{3},{8}}
[2,3,6,5,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[1,3,6,7,5,2,4,8]=>{{1},{2,3,6},{4,7},{5},{8}}
[1,5,2,6,8,7,3,4]=>{{1},{2,3,4,5,6,7,8}}
[5,3,4,7,2,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[4,8,5,7,1,2,3,6]=>{{1,3,4,5,7},{2,6,8}}
[4,2,3,7,6,1,8,5]=>{{1,4,5,6,7,8},{2},{3}}
[4,2,6,3,1,5,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[4,6,3,2,5,8,7,1]=>{{1,2,4,6,8},{3},{5},{7}}
[5,8,4,3,2,6,1,7]=>{{1,2,5,7,8},{3,4},{6}}
[1,5,7,4,8,6,2,3]=>{{1},{2,3,5,7,8},{4},{6}}
[6,1,5,7,3,8,2,4]=>{{1,2,4,6,7,8},{3,5}}
[1,2,7,8,6,4,3,5]=>{{1},{2},{3,7},{4,5,6,8}}
[3,5,1,7,8,6,2,4]=>{{1,3},{2,4,5,7,8},{6}}
[5,2,4,1,7,6,8,3]=>{{1,3,4,5,7,8},{2},{6}}
[5,4,3,8,1,7,2,6]=>{{1,5},{2,4,6,7,8},{3}}
[7,3,1,5,6,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,2,3,1,6,8,4,5]=>{{1,4,7},{2},{3},{5,6,8}}
[5,7,8,1,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,2,7,3,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[1,4,2,5,8,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}
[4,8,2,1,5,7,3,6]=>{{1,4},{2,3,6,7,8},{5}}
[5,2,7,1,6,3,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[4,8,2,5,1,6,3,7]=>{{1,4,5},{2,3,7,8},{6}}
[5,8,1,2,4,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[5,1,7,3,6,4,2,8]=>{{1,2,3,4,5,6,7},{8}}
[3,2,7,5,6,1,4,8]=>{{1,3,4,5,6,7},{2},{8}}
[3,2,7,1,6,4,5,8]=>{{1,3,4,5,6,7},{2},{8}}
[6,3,1,7,5,4,2,8]=>{{1,2,3,4,6,7},{5},{8}}
[6,2,8,7,3,4,5,1]=>{{1,3,4,5,6,7,8},{2}}
[7,3,4,8,5,6,2,1]=>{{1,2,3,4,7,8},{5},{6}}
[7,3,6,8,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,6,2,8,3,1,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[1,4,7,5,6,2,8,3]=>{{1},{2,4,5,6},{3,7,8}}
[1,7,4,8,3,5,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,3,1,4,8,6,2,7]=>{{1,2,3,5,7,8},{4},{6}}
[5,2,4,8,3,1,6,7]=>{{1,3,4,5,6,7,8},{2}}
[7,4,5,1,8,6,2,3]=>{{1,2,4,7},{3,5,8},{6}}
[8,1,5,7,6,3,2,4]=>{{1,2,4,7,8},{3,5,6}}
[1,8,6,7,5,3,2,4]=>{{1},{2,4,7,8},{3,6},{5}}
[7,4,8,3,1,6,5,2]=>{{1,5,7},{2,3,4,8},{6}}
[8,1,5,3,7,6,2,4]=>{{1,2,3,4,5,7,8},{6}}
[6,4,8,7,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,1,4,2,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[6,5,1,8,3,7,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,1,4,3,8,6,5,2]=>{{1,2,5,7,8},{3,4},{6}}
[8,5,4,1,7,3,2,6]=>{{1,3,4,6,8},{2,5,7}}
[4,5,3,8,1,7,6,2]=>{{1,2,4,5,8},{3},{6,7}}
[4,7,6,3,2,8,5,1]=>{{1,3,4,6,8},{2,5,7}}
[5,7,6,3,8,2,4,1]=>{{1,5,8},{2,3,4,6,7}}
[6,8,4,7,1,2,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,3,7,6,8,4,5,2]=>{{1},{2,3,5,7,8},{4,6}}
[6,1,5,7,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,2,5,6,3,4]=>{{1},{2,4,8},{3,7},{5},{6}}
[1,8,2,6,7,4,3,5]=>{{1},{2,3,5,7,8},{4,6}}
[2,5,4,8,7,6,1,3]=>{{1,2,5,7},{3,4,8},{6}}
[1,8,7,6,3,5,4,2]=>{{1},{2,8},{3,4,5,6,7}}
[1,8,5,7,6,4,3,2]=>{{1},{2,8},{3,4,5,6,7}}
[7,2,4,1,8,5,3,6]=>{{1,3,4,7},{2},{5,6,8}}
[7,3,2,1,4,6,8,5]=>{{1,4,5,7,8},{2,3},{6}}
[4,7,2,6,1,8,3,5]=>{{1,4,5,6,8},{2,3,7}}
[7,5,3,2,1,6,8,4]=>{{1,2,4,5,7,8},{3},{6}}
[6,8,1,3,4,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[3,6,1,4,7,8,2,5]=>{{1,3},{2,5,6,7,8},{4}}
[2,5,7,1,3,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}
[1,4,7,2,5,3,6,8]=>{{1},{2,4},{3,6,7},{5},{8}}
[4,5,3,1,2,6,8,7]=>{{1,4},{2,5},{3},{6},{7,8}}
[4,5,1,3,8,2,6,7]=>{{1,3,4},{2,5,6,7,8}}
[4,1,5,3,2,7,6,8]=>{{1,2,3,4,5},{6,7},{8}}
[7,3,5,1,4,2,6,8]=>{{1,2,3,4,5,6,7},{8}}
[6,2,1,7,4,3,8,5]=>{{1,3,6},{2},{4,5,7,8}}
[2,4,3,6,7,1,5,8]=>{{1,2,4,6},{3},{5,7},{8}}
[7,3,5,2,1,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,6,5,2,1,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[2,5,6,1,4,3,7,8]=>{{1,2,4,5},{3,6},{7},{8}}
[6,1,5,3,7,2,4,8]=>{{1,2,6},{3,4,5,7},{8}}
[3,6,5,4,1,7,2,8]=>{{1,3,5},{2,6,7},{4},{8}}
[6,8,7,5,4,2,1,3]=>{{1,2,3,6,7,8},{4,5}}
[1,6,8,7,3,2,4,5]=>{{1},{2,6},{3,5,8},{4,7}}
[8,7,5,4,6,1,3,2]=>{{1,2,3,5,6,7,8},{4}}
[1,7,8,2,4,6,3,5]=>{{1},{2,3,4,5,7,8},{6}}
[7,5,4,8,1,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[5,6,1,8,4,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[1,8,2,6,7,5,4,3]=>{{1},{2,3,8},{4,5,6,7}}
[2,7,5,1,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,4,2,7,3,6,1]=>{{1,8},{2,3,4,5,6,7}}
[3,8,6,1,2,4,5,7]=>{{1,3,4,6},{2,5,7,8}}
[1,8,5,3,2,7,4,6]=>{{1},{2,3,4,5,6,7,8}}
[1,8,4,7,2,3,5,6]=>{{1},{2,3,4,5,6,7,8}}
[3,2,8,1,7,5,4,6]=>{{1,3,4,5,6,7,8},{2}}
[7,1,5,6,2,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[6,5,1,7,2,3,4,8]=>{{1,3,6},{2,5},{4,7},{8}}
[1,6,8,2,7,3,4,5]=>{{1},{2,3,4,5,6,7,8}}
[1,6,8,7,3,4,2,5]=>{{1},{2,4,6,7},{3,5,8}}
[4,1,3,6,7,8,5,2]=>{{1,2,4,6,8},{3},{5,7}}
[7,4,1,5,6,8,3,2]=>{{1,3,7},{2,4,5,6,8}}
[4,1,2,6,7,8,5,3]=>{{1,2,3,4,6,8},{5,7}}
[3,7,8,2,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,1,8,2,4,5]=>{{1,2,3,4,6,7},{5,8}}
[1,5,4,7,8,3,6,2]=>{{1},{2,5,8},{3,4,6,7}}
[5,1,4,7,8,3,6,2]=>{{1,2,5,8},{3,4,6,7}}
[4,8,1,5,6,2,3,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,4,1,7,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,8,2,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[3,7,8,5,4,2,1,6]=>{{1,2,3,6,7,8},{4,5}}
[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,2,4,5,6,8,3,1]=>{{1,3,4,5,6,7,8},{2}}
[2,7,4,5,6,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,4,7,8,3,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[5,4,3,6,8,1,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[3,7,4,5,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[1,4,3,5,6,8,2,7]=>{{1},{2,4,5,6,7,8},{3}}
[1,4,6,5,8,2,7,3]=>{{1},{2,3,4,5,6,8},{7}}
[4,6,1,7,3,2,8,5]=>{{1,3,4,5,7,8},{2,6}}
[1,7,3,6,4,2,8,5]=>{{1},{2,4,5,6,7,8},{3}}
[4,7,3,5,1,2,8,6]=>{{1,4,5},{2,6,7,8},{3}}
[1,6,4,2,3,5,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[4,8,3,5,2,1,6,7]=>{{1,2,4,5,6,7,8},{3}}
[1,6,8,4,7,5,3,2]=>{{1},{2,3,5,6,7,8},{4}}
[4,7,1,6,8,2,3,5]=>{{1,2,3,4,6,7},{5,8}}
[4,6,5,8,2,3,7,1]=>{{1,4,8},{2,3,5,6},{7}}
[7,1,8,2,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[5,7,8,2,3,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[5,2,3,8,7,1,4,6]=>{{1,4,5,6,7,8},{2},{3}}
[8,7,1,3,2,6,4,5]=>{{1,2,3,4,5,7,8},{6}}
[2,7,6,4,8,3,1,5]=>{{1,2,7},{3,6},{4},{5,8}}
[2,6,3,7,5,8,4,1]=>{{1,2,6,8},{3},{4,7},{5}}
[7,5,1,2,3,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[8,6,2,1,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[4,2,3,6,8,5,7,1]=>{{1,4,5,6,8},{2},{3},{7}}
[4,7,3,2,6,5,1,8]=>{{1,2,4,7},{3},{5,6},{8}}
[4,3,7,8,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}
[4,8,7,2,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[7,3,8,2,5,1,6,4]=>{{1,6,7},{2,3,4,8},{5}}
[4,5,3,8,6,1,2,7]=>{{1,2,4,5,6,7,8},{3}}
[6,3,5,8,4,1,2,7]=>{{1,6},{2,3,4,5,7,8}}
[7,3,8,4,5,1,2,6]=>{{1,2,3,6,7,8},{4},{5}}
[4,8,7,5,1,2,6,3]=>{{1,4,5},{2,3,6,7,8}}
[7,8,4,6,1,3,5,2]=>{{1,5,7},{2,8},{3,4,6}}
[4,8,7,5,1,3,6,2]=>{{1,4,5},{2,8},{3,6,7}}
[4,5,3,6,8,1,2,7]=>{{1,4,6},{2,5,7,8},{3}}
[7,8,6,2,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}
[7,8,6,3,1,2,5,4]=>{{1,5,7},{2,3,4,6,8}}
[5,2,8,4,7,1,3,6]=>{{1,3,5,6,7,8},{2},{4}}
[7,3,1,2,8,6,5,4]=>{{1,2,3,4,5,7,8},{6}}
[8,7,1,3,2,4,5,6]=>{{1,3,4,6,8},{2,5,7}}
[6,8,2,1,4,5,3,7]=>{{1,4,5,6},{2,3,7,8}}
[1,5,4,8,7,3,2,6]=>{{1},{2,5,7},{3,4,6,8}}
[4,3,1,2,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}}
[7,5,8,1,2,4,6,3]=>{{1,4,6,7},{2,5},{3,8}}
[6,1,5,2,8,7,4,3]=>{{1,2,4,6,7},{3,5,8}}
[4,6,3,5,7,1,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[1,4,7,2,6,5,8,3]=>{{1},{2,4},{3,7,8},{5,6}}
[1,5,7,2,6,4,8,3]=>{{1},{2,4,5,6},{3,7,8}}
[7,2,4,6,1,8,3,5]=>{{1,3,4,5,6,7,8},{2}}
[1,2,7,8,3,5,4,6]=>{{1},{2},{3,4,5,6,7,8}}
[1,7,6,2,8,5,4,3]=>{{1},{2,4,7},{3,5,6,8}}
[1,2,7,8,3,4,6,5]=>{{1},{2},{3,4,5,6,7,8}}
[1,7,6,8,3,4,2,5]=>{{1},{2,7},{3,4,5,6,8}}
[3,4,1,7,8,6,5,2]=>{{1,3},{2,4,5,7,8},{6}}
[2,4,8,6,5,7,1,3]=>{{1,2,4,6,7},{3,8},{5}}
[5,1,3,4,8,2,7,6]=>{{1,2,5,6,8},{3},{4},{7}}
[8,7,3,6,1,4,2,5]=>{{1,5,8},{2,7},{3},{4,6}}
[6,5,1,8,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[8,2,1,5,6,4,7,3]=>{{1,3,8},{2},{4,5,6},{7}}
[7,5,6,1,3,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[5,7,2,4,6,1,8,3]=>{{1,5,6},{2,3,7,8},{4}}
[2,1,5,6,3,8,7,4]=>{{1,2},{3,5},{4,6,8},{7}}
[3,2,7,5,8,6,4,1]=>{{1,3,4,5,7,8},{2},{6}}
[2,4,5,3,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[7,2,5,4,3,8,6,1]=>{{1,6,7,8},{2},{3,5},{4}}
[8,5,3,1,2,6,7,4]=>{{1,4,8},{2,5},{3},{6},{7}}
[7,2,5,1,3,6,8,4]=>{{1,4,7,8},{2},{3,5},{6}}
[8,4,7,3,1,2,6,5]=>{{1,5,8},{2,3,4,6,7}}
[1,8,7,3,5,2,6,4]=>{{1},{2,3,4,6,7,8},{5}}
[2,4,8,3,6,5,7,1]=>{{1,2,3,4,8},{5,6},{7}}
[3,1,8,2,6,5,7,4]=>{{1,2,3,4,8},{5,6},{7}}
[4,6,7,8,5,2,1,3]=>{{1,3,4,7,8},{2,6},{5}}
[4,7,2,1,8,6,5,3]=>{{1,4},{2,3,5,7,8},{6}}
[5,6,2,8,4,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[5,7,2,4,8,6,1,3]=>{{1,2,3,5,7,8},{4},{6}}
[6,7,2,4,8,5,1,3]=>{{1,2,3,5,6,7,8},{4}}
[6,7,3,2,8,5,1,4]=>{{1,2,4,5,6,7,8},{3}}
[7,2,3,1,8,6,5,4]=>{{1,4,5,7,8},{2},{3},{6}}
[7,2,8,3,5,6,1,4]=>{{1,7},{2},{3,4,8},{5},{6}}
[7,2,3,8,4,6,1,5]=>{{1,7},{2},{3},{4,5,8},{6}}
[1,7,3,4,8,5,2,6]=>{{1},{2,7},{3},{4},{5,6,8}}
[1,7,3,8,5,4,2,6]=>{{1},{2,7},{3},{4,6,8},{5}}
[7,2,8,4,5,3,1,6]=>{{1,7},{2},{3,6,8},{4},{5}}
[2,8,6,4,3,1,7,5]=>{{1,2,3,5,6,8},{4},{7}}
[1,7,3,4,8,2,5,6]=>{{1},{2,5,6,7,8},{3},{4}}
[1,5,8,3,4,6,2,7]=>{{1},{2,3,4,5,7,8},{6}}
[1,3,8,4,2,5,7,6]=>{{1},{2,3,5,6,8},{4},{7}}
[1,4,7,6,2,3,8,5]=>{{1},{2,3,4,5,6,7,8}}
[1,8,4,6,7,2,3,5]=>{{1},{2,3,4,5,6,7,8}}
[1,4,2,3,7,8,6,5]=>{{1},{2,3,4},{5,6,7,8}}
[5,7,1,6,4,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,8,1,3,6,2]=>{{1,3,5,6,7},{2,4,8}}
[1,4,3,6,2,5,8,7]=>{{1},{2,4,5,6},{3},{7,8}}
[1,3,6,5,8,2,4,7]=>{{1},{2,3,6},{4,5,7,8}}
[1,4,6,3,2,8,5,7]=>{{1},{2,3,4,5,6,7,8}}
[6,8,4,1,5,7,2,3]=>{{1,2,3,4,6,7,8},{5}}
[5,2,6,7,4,1,8,3]=>{{1,3,4,5,6,7,8},{2}}
[8,5,6,4,1,7,3,2]=>{{1,2,5,8},{3,6,7},{4}}
[7,8,3,1,6,4,5,2]=>{{1,4,5,6,7},{2,8},{3}}
[5,8,2,6,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[4,5,8,1,6,3,7,2]=>{{1,4},{2,3,5,6,8},{7}}
[8,1,4,6,2,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[4,5,8,1,6,2,7,3]=>{{1,4},{2,5,6},{3,8},{7}}
[5,2,6,8,1,4,3,7]=>{{1,5},{2},{3,4,6,7,8}}
[6,7,3,8,2,1,4,5]=>{{1,6},{2,4,5,7,8},{3}}
[2,7,3,5,4,1,8,6]=>{{1,2,6,7,8},{3},{4,5}}
[2,6,3,7,4,1,8,5]=>{{1,2,6},{3},{4,5,7,8}}
[2,1,4,8,5,3,7,6]=>{{1,2},{3,4,6,8},{5},{7}}
[2,7,3,8,4,1,6,5]=>{{1,2,6,7},{3},{4,5,8}}
[2,6,3,1,5,4,8,7]=>{{1,2,4,6},{3},{5},{7,8}}
[1,5,8,3,4,7,2,6]=>{{1},{2,3,4,5,6,7,8}}
[5,3,8,1,4,6,2,7]=>{{1,4,5},{2,3,7,8},{6}}
[4,5,8,1,3,6,2,7]=>{{1,4},{2,3,5,7,8},{6}}
[7,4,6,5,2,8,3,1]=>{{1,3,6,7,8},{2,4,5}}
[4,1,3,8,5,7,6,2]=>{{1,2,4,8},{3},{5},{6,7}}
[4,1,3,7,2,8,6,5]=>{{1,2,4,5,6,7,8},{3}}
[4,6,3,1,7,2,8,5]=>{{1,4},{2,6},{3},{5,7,8}}
[7,2,6,3,1,8,5,4]=>{{1,5,7},{2},{3,4,6,8}}
[4,8,7,2,5,3,1,6]=>{{1,2,3,4,6,7,8},{5}}
[1,6,3,2,8,7,4,5]=>{{1},{2,4,6,7},{3},{5,8}}
[2,8,1,7,5,4,6,3]=>{{1,2,3,8},{4,6,7},{5}}
[6,8,3,1,5,7,2,4]=>{{1,2,4,6,7,8},{3},{5}}
[8,7,3,1,2,5,6,4]=>{{1,4,8},{2,5,6,7},{3}}
[7,4,5,1,2,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[5,4,3,6,1,7,8,2]=>{{1,5},{2,4,6,7,8},{3}}
[3,2,7,8,5,6,1,4]=>{{1,3,7},{2},{4,8},{5},{6}}
[4,8,3,2,1,7,5,6]=>{{1,2,4,5,6,7,8},{3}}
[1,8,4,5,6,3,2,7]=>{{1},{2,7,8},{3,4,5,6}}
[8,5,1,7,4,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[1,3,7,8,4,6,2,5]=>{{1},{2,3,7},{4,5,8},{6}}
[4,8,7,3,6,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,3,7,1,2,6]=>{{1,2,5,6,7,8},{3,4}}
[5,6,4,8,7,2,1,3]=>{{1,5,7},{2,6},{3,4,8}}
[4,8,3,7,6,1,2,5]=>{{1,2,4,5,6,7,8},{3}}
[2,8,4,7,1,3,6,5]=>{{1,2,5,8},{3,4,6,7}}
[6,8,3,4,5,2,1,7]=>{{1,2,6,7,8},{3},{4},{5}}
[3,7,1,4,5,6,2,8]=>{{1,3},{2,7},{4},{5},{6},{8}}
[3,6,1,4,5,2,7,8]=>{{1,3},{2,6},{4},{5},{7},{8}}
[3,8,2,4,5,1,7,6]=>{{1,2,3,6,8},{4},{5},{7}}
[3,7,2,1,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}
[3,6,8,1,5,4,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[1,7,4,6,3,5,2,8]=>{{1},{2,7},{3,4,5,6},{8}}
[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[1,7,2,5,6,4,3,8]=>{{1},{2,3,7},{4,5,6},{8}}
[1,6,8,5,4,3,7,2]=>{{1},{2,3,6,8},{4,5},{7}}
[2,5,7,8,4,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[6,8,5,3,2,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[1,6,8,5,3,2,7,4]=>{{1},{2,6},{3,4,5,8},{7}}
[4,6,1,8,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,1,7,8,6,5,2,3]=>{{1,2,3,4,7,8},{5,6}}
[5,4,3,7,6,1,2,8]=>{{1,5,6},{2,4,7},{3},{8}}
[4,7,6,1,2,3,8,5]=>{{1,4},{2,5,7,8},{3,6}}
[4,5,2,6,7,8,1,3]=>{{1,2,3,4,5,6,7,8}}
[1,7,6,2,3,8,5,4]=>{{1},{2,3,4,5,6,7,8}}
[4,5,1,3,7,6,2,8]=>{{1,3,4},{2,5,7},{6},{8}}
[7,2,3,8,6,4,5,1]=>{{1,4,5,6,7,8},{2},{3}}
[1,5,4,3,8,6,2,7]=>{{1},{2,5,7,8},{3,4},{6}}
[1,3,7,5,8,4,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,1,2,7,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[1,6,7,4,5,3,2,8]=>{{1},{2,3,6,7},{4},{5},{8}}
[1,4,2,6,7,5,3,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,2,4,6,5,3,7]=>{{1},{2,3,7,8},{4},{5,6}}
[7,2,1,6,4,3,8,5]=>{{1,3,4,5,6,7,8},{2}}
[1,4,8,7,2,3,6,5]=>{{1},{2,3,4,5,6,7,8}}
[4,1,3,6,5,8,2,7]=>{{1,2,4,6,7,8},{3},{5}}
[4,3,7,1,5,8,2,6]=>{{1,4},{2,3,7},{5},{6,8}}
[1,8,6,5,2,7,4,3]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,2,7,4,3,5]=>{{1},{2,3,4,5,6,7,8}}
[6,4,1,8,3,7,5,2]=>{{1,3,5,6,7},{2,4,8}}
[4,5,8,7,3,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[3,5,4,1,7,8,6,2]=>{{1,3,4},{2,5,6,7,8}}
[6,8,7,2,1,5,4,3]=>{{1,5,6},{2,3,4,7,8}}
[8,1,6,3,7,5,4,2]=>{{1,2,8},{3,4,5,6,7}}
[8,5,1,3,7,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[8,3,6,5,4,2,1,7]=>{{1,7,8},{2,3,6},{4,5}}
[6,1,3,5,7,2,8,4]=>{{1,2,6},{3},{4,5,7,8}}
[2,8,1,5,6,4,3,7]=>{{1,2,3,7,8},{4,5,6}}
[1,6,7,5,8,4,2,3]=>{{1},{2,3,4,5,6,7,8}}
[7,4,1,6,5,2,8,3]=>{{1,3,7,8},{2,4,6},{5}}
[7,4,2,8,6,5,3,1]=>{{1,2,3,4,7,8},{5,6}}
[6,8,4,7,3,2,5,1]=>{{1,2,6,8},{3,4,5,7}}
[5,8,7,3,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,7,2,6,4,3,1]=>{{1,2,4,5,6,8},{3,7}}
[6,8,7,3,5,1,4,2]=>{{1,6},{2,8},{3,4,7},{5}}
[7,2,5,6,8,3,4,1]=>{{1,3,4,5,6,7,8},{2}}
[1,6,5,7,8,3,2,4]=>{{1},{2,3,4,5,6,7,8}}
[8,6,7,2,3,5,4,1]=>{{1,8},{2,3,4,5,6,7}}
[5,4,8,6,7,3,1,2]=>{{1,5,7},{2,3,4,6,8}}
[4,2,7,3,1,6,8,5]=>{{1,3,4,5,7,8},{2},{6}}
[7,3,6,4,2,1,8,5]=>{{1,2,3,5,6,7,8},{4}}
[4,8,5,2,7,3,1,6]=>{{1,2,3,4,5,6,7,8}}
[6,4,3,1,8,5,2,7]=>{{1,2,4,5,6,7,8},{3}}
[7,4,3,1,5,8,6,2]=>{{1,2,4,6,7,8},{3},{5}}
[7,4,8,6,5,3,1,2]=>{{1,7},{2,3,4,6,8},{5}}
[4,8,5,2,6,7,3,1]=>{{1,2,4,8},{3,5,6,7}}
[7,3,2,1,8,5,6,4]=>{{1,4,5,6,7,8},{2,3}}
[1,5,7,2,4,3,8,6]=>{{1},{2,4,5},{3,6,7,8}}
[1,2,7,5,8,4,3,6]=>{{1},{2},{3,7},{4,5,6,8}}
[5,1,3,8,2,7,4,6]=>{{1,2,5},{3},{4,6,7,8}}
[5,7,1,3,2,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[7,1,6,3,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,7,2,3,6,5,4]=>{{1,2,4,8},{3,5,7},{6}}
[7,1,2,6,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,4,7,8,3,2,5,6]=>{{1},{2,4,6,8},{3,5,7}}
[8,7,1,3,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,1,6,3,2,4,7,5]=>{{1,2,5,8},{3,4,6},{7}}
[1,8,2,7,6,3,5,4]=>{{1},{2,3,4,5,6,7,8}}
[8,1,6,3,2,7,4,5]=>{{1,2,5,8},{3,4,6,7}}
[8,2,1,7,6,3,4,5]=>{{1,3,5,6,8},{2},{4,7}}
[8,7,2,4,3,1,5,6]=>{{1,6,8},{2,3,5,7},{4}}
[4,7,6,2,3,1,5,8]=>{{1,2,3,4,5,6,7},{8}}
[4,7,6,1,3,2,8,5]=>{{1,4},{2,3,5,6,7,8}}
[2,8,1,3,5,6,4,7]=>{{1,2,3,4,7,8},{5},{6}}
[2,6,3,4,7,8,5,1]=>{{1,2,6,8},{3},{4},{5,7}}
[7,6,3,1,8,5,2,4]=>{{1,2,4,5,6,7,8},{3}}
[7,2,1,3,6,8,5,4]=>{{1,3,4,5,6,7,8},{2}}
[7,6,3,8,1,5,2,4]=>{{1,2,5,6,7},{3},{4,8}}
[1,6,4,7,8,5,3,2]=>{{1},{2,5,6,8},{3,4,7}}
[7,2,5,8,6,1,3,4]=>{{1,3,5,6,7},{2},{4,8}}
[4,1,3,6,2,5,8,7]=>{{1,2,4,5,6},{3},{7,8}}
[7,1,4,6,3,2,5,8]=>{{1,2,3,4,5,6,7},{8}}
[7,4,5,8,6,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,3,8,4,1,5]=>{{1,2,3,4,6,7},{5,8}}
[2,7,8,1,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}
[1,5,2,6,8,7,4,3]=>{{1},{2,3,5,8},{4,6,7}}
[1,8,3,7,5,2,6,4]=>{{1},{2,4,6,7,8},{3},{5}}
[8,1,3,6,5,2,7,4]=>{{1,2,4,6,8},{3},{5},{7}}
[7,1,3,8,5,2,6,4]=>{{1,2,6,7},{3},{4,8},{5}}
[4,7,1,5,2,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[7,4,1,5,2,6,8,3]=>{{1,3,7,8},{2,4,5},{6}}
[3,1,6,7,5,2,8,4]=>{{1,2,3,6},{4,7,8},{5}}
[8,6,2,4,5,1,7,3]=>{{1,2,3,6,8},{4},{5},{7}}
[8,6,7,5,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[7,1,4,5,2,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[4,1,6,2,3,8,7,5]=>{{1,2,4},{3,5,6,8},{7}}
[4,1,7,6,5,2,8,3]=>{{1,2,4,6},{3,7,8},{5}}
[8,4,1,5,6,2,7,3]=>{{1,3,8},{2,4,5,6},{7}}
[8,4,5,3,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[2,8,4,7,3,5,6,1]=>{{1,2,8},{3,4,5,6,7}}
[1,5,4,8,3,2,6,7]=>{{1},{2,3,4,5,6,7,8}}
[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[2,6,3,1,7,8,4,5]=>{{1,2,4,5,6,7,8},{3}}
[2,1,7,8,3,5,4,6]=>{{1,2},{3,4,5,6,7,8}}
[1,5,8,6,7,4,2,3]=>{{1},{2,5,7},{3,8},{4,6}}
[8,7,1,3,5,2,6,4]=>{{1,3,4,8},{2,6,7},{5}}
[3,7,8,2,5,4,1,6]=>{{1,2,3,4,6,7,8},{5}}
[4,7,6,5,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[4,7,8,6,2,1,5,3]=>{{1,4,6},{2,5,7},{3,8}}
[4,8,6,3,2,1,7,5]=>{{1,3,4,6},{2,5,8},{7}}
[5,1,4,7,6,8,3,2]=>{{1,2,5,6,8},{3,4,7}}
[5,6,4,7,1,8,3,2]=>{{1,5},{2,6,8},{3,4,7}}
[5,3,7,4,6,1,8,2]=>{{1,5,6},{2,3,7,8},{4}}
[4,1,5,7,8,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[3,6,7,1,5,4,8,2]=>{{1,2,3,4,6,7,8},{5}}
[3,6,4,7,5,8,2,1]=>{{1,2,3,4,6,7,8},{5}}
[8,1,7,3,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,1,5,2,8,3]=>{{1,2,4,6},{3,7,8},{5}}
[1,6,5,2,8,7,4,3]=>{{1},{2,4,6,7},{3,5,8}}
[4,1,7,2,5,8,3,6]=>{{1,2,4},{3,7},{5},{6,8}}
[3,2,5,8,6,1,7,4]=>{{1,3,5,6},{2},{4,8},{7}}
[4,5,1,7,2,8,6,3]=>{{1,3,4,6,7,8},{2,5}}
[4,7,1,8,5,3,6,2]=>{{1,2,3,4,6,7,8},{5}}
[6,4,7,2,5,3,1,8]=>{{1,3,6,7},{2,4},{5},{8}}
[7,1,4,3,6,8,2,5]=>{{1,2,7},{3,4},{5,6,8}}
[4,8,7,3,5,1,6,2]=>{{1,3,4,6,7},{2,8},{5}}
[5,3,8,7,1,6,2,4]=>{{1,5},{2,3,4,7,8},{6}}
[5,2,6,7,4,3,1,8]=>{{1,4,5,7},{2},{3,6},{8}}
[8,5,1,6,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[8,6,3,5,2,7,1,4]=>{{1,2,4,5,6,7,8},{3}}
[8,4,6,2,1,5,7,3]=>{{1,3,5,6,8},{2,4},{7}}
[8,5,2,1,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[1,7,2,8,5,4,6,3]=>{{1},{2,3,4,6,7,8},{5}}
[6,7,1,4,8,5,3,2]=>{{1,2,3,5,6,7,8},{4}}
[7,3,2,8,5,1,4,6]=>{{1,4,6,7,8},{2,3},{5}}
[4,1,7,3,2,8,5,6]=>{{1,2,3,4,5,7},{6,8}}
[8,3,5,2,4,7,1,6]=>{{1,6,7,8},{2,3,4,5}}
[4,3,7,8,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}
[1,2,6,3,7,8,5,4]=>{{1},{2},{3,4,6,8},{5,7}}
[6,1,3,7,8,5,4,2]=>{{1,2,5,6,8},{3},{4,7}}
[2,6,4,7,5,3,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[4,5,1,8,6,2,7,3]=>{{1,3,4,8},{2,5,6},{7}}
[5,6,1,8,7,2,3,4]=>{{1,3,5,7},{2,6},{4,8}}
[4,5,1,6,8,7,3,2]=>{{1,3,4,6,7},{2,5,8}}
[3,8,6,1,5,2,4,7]=>{{1,2,3,4,6,7,8},{5}}
[3,2,8,1,5,6,4,7]=>{{1,3,4,7,8},{2},{5},{6}}
[5,8,7,3,2,1,4,6]=>{{1,2,5,6,8},{3,4,7}}
[3,4,7,6,8,2,1,5]=>{{1,3,7},{2,4,6},{5,8}}
[2,8,1,3,7,5,6,4]=>{{1,2,3,4,8},{5,6,7}}
[1,8,7,2,5,6,4,3]=>{{1},{2,3,4,7,8},{5},{6}}
[3,4,7,1,5,8,2,6]=>{{1,2,3,4,7},{5},{6,8}}
[4,2,7,1,5,8,3,6]=>{{1,4},{2},{3,7},{5},{6,8}}
[1,4,7,5,2,3,6,8]=>{{1},{2,4,5},{3,6,7},{8}}
[2,5,7,6,8,3,4,1]=>{{1,2,5,8},{3,4,6,7}}
[3,1,6,7,2,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[1,5,3,6,8,4,7,2]=>{{1},{2,5,8},{3},{4,6},{7}}
[6,5,1,3,8,4,7,2]=>{{1,3,4,6},{2,5,8},{7}}
[1,7,4,8,5,3,2,6]=>{{1},{2,7},{3,4,6,8},{5}}
[7,3,1,6,8,4,5,2]=>{{1,2,3,5,7,8},{4,6}}
[8,5,1,4,6,7,3,2]=>{{1,2,3,5,6,7,8},{4}}
[3,4,7,5,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,8,5,2,6,1]=>{{1,2,3,4,6,7,8},{5}}
[4,8,1,7,5,6,3,2]=>{{1,3,4,7},{2,8},{5},{6}}
[1,8,7,5,2,6,3,4]=>{{1},{2,4,5,8},{3,7},{6}}
[1,7,6,3,4,5,8,2]=>{{1},{2,7,8},{3,4,5,6}}
[1,8,7,4,5,6,2,3]=>{{1},{2,3,7,8},{4},{5},{6}}
[1,8,7,3,6,4,2,5]=>{{1},{2,3,4,5,6,7,8}}
[1,4,7,5,8,2,6,3]=>{{1},{2,3,4,5,6,7,8}}
[1,4,7,2,3,6,5,8]=>{{1},{2,4},{3,5,7},{6},{8}}
[1,7,2,5,6,3,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,2,6,5,8,3,4,7]=>{{1},{2},{3,6},{4,5,7,8}}
[1,5,8,2,6,3,4,7]=>{{1},{2,3,4,5,6,7,8}}
[6,8,3,2,7,5,1,4]=>{{1,5,6,7},{2,4,8},{3}}
[7,3,6,8,1,2,5,4]=>{{1,5,7},{2,3,6},{4,8}}
[4,1,5,7,2,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[5,7,2,1,3,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}
[3,5,6,7,2,4,1,8]=>{{1,3,4,6,7},{2,5},{8}}
[6,4,7,5,2,3,1,8]=>{{1,3,6,7},{2,4,5},{8}}
[1,5,6,4,8,3,2,7]=>{{1},{2,5,7,8},{3,6},{4}}
[2,1,5,6,4,8,3,7]=>{{1,2},{3,4,5,6,7,8}}
[5,1,4,7,8,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[1,6,7,2,8,5,4,3]=>{{1},{2,3,4,5,6,7,8}}
[5,3,2,1,7,8,6,4]=>{{1,4,5,6,7,8},{2,3}}
[7,4,3,8,6,1,5,2]=>{{1,5,6,7},{2,4,8},{3}}
[4,3,7,1,5,8,6,2]=>{{1,4},{2,3,6,7,8},{5}}
[8,2,4,5,3,1,7,6]=>{{1,6,8},{2},{3,4,5},{7}}
[1,4,3,2,7,5,8,6]=>{{1},{2,4},{3},{5,6,7,8}}
[4,8,7,2,6,1,3,5]=>{{1,2,4,5,6,8},{3,7}}
[4,5,8,2,1,7,3,6]=>{{1,2,4,5},{3,6,7,8}}
[6,8,4,1,7,3,2,5]=>{{1,3,4,6},{2,5,7,8}}
[6,3,1,8,2,7,5,4]=>{{1,2,3,5,6,7},{4,8}}
[4,1,7,8,3,2,5,6]=>{{1,2,4,6,8},{3,5,7}}
[7,6,2,8,4,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[5,8,2,1,3,6,4,7]=>{{1,2,3,4,5,7,8},{6}}
[8,5,1,7,3,4,6,2]=>{{1,2,3,5,8},{4,6,7}}
[5,7,6,3,4,1,8,2]=>{{1,3,4,5,6},{2,7,8}}
[1,8,3,5,2,6,4,7]=>{{1},{2,4,5,7,8},{3},{6}}
[3,4,6,1,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[2,3,8,7,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[1,8,3,5,7,4,2,6]=>{{1},{2,4,5,6,7,8},{3}}
[2,5,8,4,6,7,1,3]=>{{1,2,5,6,7},{3,8},{4}}
[7,1,2,6,4,3,5,8]=>{{1,2,3,4,5,6,7},{8}}
[7,1,2,6,5,3,4,8]=>{{1,2,3,4,6,7},{5},{8}}
[4,7,8,6,2,3,5,1]=>{{1,3,4,6,8},{2,5,7}}
[7,1,2,4,8,6,5,3]=>{{1,2,3,5,7,8},{4},{6}}
[2,7,5,6,4,8,1,3]=>{{1,2,7},{3,4,5,6,8}}
[2,8,3,6,5,7,1,4]=>{{1,2,4,6,7,8},{3},{5}}
[7,4,3,1,6,5,2,8]=>{{1,2,4,7},{3},{5,6},{8}}
[3,5,1,2,6,8,7,4]=>{{1,3},{2,4,5,6,8},{7}}
[3,1,2,4,8,7,5,6]=>{{1,2,3},{4},{5,6,7,8}}
[5,4,1,2,3,7,8,6]=>{{1,3,5},{2,4},{6,7,8}}
[1,6,7,2,5,8,3,4]=>{{1},{2,4,6,8},{3,7},{5}}
[7,8,5,6,2,4,3,1]=>{{1,2,3,5,7,8},{4,6}}
[5,3,8,6,2,4,1,7]=>{{1,2,3,5,7,8},{4,6}}
[2,7,4,6,3,8,1,5]=>{{1,2,7},{3,4,5,6,8}}
[5,4,7,8,6,2,1,3]=>{{1,2,3,4,5,6,7,8}}
[2,7,4,8,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,2,1,3,7,4,6,5]=>{{1,3,4,5,6,7,8},{2}}
[6,5,8,2,3,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,8,2,3,6,4,5,1]=>{{1,2,3,4,5,6,7,8}}
[8,1,2,7,5,3,4,6]=>{{1,2,3,6,8},{4,7},{5}}
[4,2,8,1,3,7,5,6]=>{{1,4},{2},{3,5,6,7,8}}
[7,5,1,8,2,3,4,6]=>{{1,3,4,6,7,8},{2,5}}
[8,2,4,1,3,7,5,6]=>{{1,3,4,5,6,7,8},{2}}
[8,1,6,2,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[7,1,8,2,3,6,4,5]=>{{1,2,4,7},{3,5,8},{6}}
[4,2,6,7,5,1,8,3]=>{{1,3,4,6,7,8},{2},{5}}
[4,7,2,5,3,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[3,5,7,4,2,8,1,6]=>{{1,3,7},{2,5},{4},{6,8}}
[2,4,7,6,3,8,1,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,8,5,1,2,3,7]=>{{1,4,5},{2,6},{3,7,8}}
[4,6,5,7,1,2,3,8]=>{{1,3,4,5,7},{2,6},{8}}
[4,6,5,7,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,6,1,8,2,5]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,1,6,3,4,7]=>{{1,4,7,8},{2,3,5,6}}
[7,1,8,5,3,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,2,7,5,4,1,6,3]=>{{1,3,6,7,8},{2},{4,5}}
[4,2,8,5,7,1,6,3]=>{{1,4,5,6,7},{2},{3,8}}
[6,8,7,4,5,3,2,1]=>{{1,2,3,6,7,8},{4},{5}}
[5,2,6,7,4,8,3,1]=>{{1,3,4,5,6,7,8},{2}}
[6,5,8,1,7,3,2,4]=>{{1,3,4,6,8},{2,5,7}}
[6,4,8,1,5,2,3,7]=>{{1,2,4,6},{3,7,8},{5}}
[7,2,4,1,6,3,5,8]=>{{1,3,4,5,6,7},{2},{8}}
[2,6,1,5,3,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,8,7,5,4,2,6,1]=>{{1,2,3,6,7,8},{4,5}}
[5,7,8,2,3,6,4,1]=>{{1,3,5,8},{2,4,7},{6}}
[2,8,7,3,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[5,6,1,2,4,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,8,6,7,5,4,2,1]=>{{1,2,3,4,6,7,8},{5}}
[7,8,5,1,4,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[8,2,7,5,4,6,1,3]=>{{1,3,7,8},{2},{4,5},{6}}
[8,4,7,6,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,1,3,2,8,5]=>{{1,4},{2,6},{3,5,7,8}}
[6,4,7,5,3,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[8,4,6,3,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[7,3,1,4,5,6,8,2]=>{{1,2,3,7,8},{4},{5},{6}}
[6,7,3,4,2,1,8,5]=>{{1,6},{2,5,7,8},{3},{4}}
[6,4,8,3,1,5,7,2]=>{{1,5,6},{2,3,4,8},{7}}
[7,4,2,3,5,1,8,6]=>{{1,6,7,8},{2,3,4},{5}}
[3,1,6,5,2,4,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,5,3,8,6,4,1,7]=>{{1,2,4,5,6,7,8},{3}}
[5,8,4,1,3,2,7,6]=>{{1,3,4,5},{2,6,8},{7}}
[5,3,4,7,6,1,8,2]=>{{1,5,6},{2,3,4,7,8}}
[4,5,2,1,6,3,8,7]=>{{1,4},{2,3,5,6},{7,8}}
[4,5,2,1,6,7,3,8]=>{{1,4},{2,3,5,6,7},{8}}
[5,3,8,6,2,4,7,1]=>{{1,2,3,5,8},{4,6},{7}}
[2,5,1,6,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}
[3,6,2,8,5,7,1,4]=>{{1,2,3,6,7},{4,8},{5}}
[4,6,8,1,5,7,2,3]=>{{1,4},{2,6,7},{3,8},{5}}
[4,1,2,5,7,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[4,6,5,8,1,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[2,1,3,6,4,8,7,5]=>{{1,2},{3},{4,5,6,8},{7}}
[4,8,1,2,7,5,6,3]=>{{1,2,3,4,8},{5,6,7}}
[1,6,4,3,8,7,5,2]=>{{1},{2,5,6,7,8},{3,4}}
[4,5,1,6,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,4,7,2,5,8,6,1]=>{{1,3,6,7,8},{2,4},{5}}
[2,5,1,8,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,5,8,7,3,1,4,6]=>{{1,2,3,5,6,8},{4,7}}
[3,8,7,2,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,4,5,1,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,3,1,5,2,6]=>{{1,5,6,8},{2,3,4,7}}
[2,5,1,8,3,6,4,7]=>{{1,2,3,5},{4,7,8},{6}}
[5,8,4,7,3,2,1,6]=>{{1,3,4,5,7},{2,6,8}}
[4,3,8,6,1,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[4,8,6,5,7,1,3,2]=>{{1,3,4,5,6,7},{2,8}}
[7,2,3,5,6,8,4,1]=>{{1,4,5,6,7,8},{2},{3}}
[5,8,1,3,4,7,2,6]=>{{1,3,4,5},{2,6,7,8}}
[8,3,4,2,7,6,1,5]=>{{1,5,7,8},{2,3,4},{6}}
[8,7,5,6,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,7,4,2,3,6,5,1]=>{{1,8},{2,3,4,5,7},{6}}
[8,4,2,3,7,6,5,1]=>{{1,8},{2,3,4},{5,7},{6}}
[7,2,4,5,3,1,6,8]=>{{1,6,7},{2},{3,4,5},{8}}
[7,6,3,1,4,5,8,2]=>{{1,2,4,5,6,7,8},{3}}
[3,7,4,6,2,1,8,5]=>{{1,3,4,6},{2,5,7,8}}
[5,4,1,7,8,6,2,3]=>{{1,3,5,8},{2,4,7},{6}}
[5,3,4,7,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,3,7,6,5,1,8,2]=>{{1,4,6},{2,3,7,8},{5}}
[5,1,4,8,2,3,7,6]=>{{1,2,5},{3,4,6,8},{7}}
[3,2,8,5,4,1,6,7]=>{{1,3,6,7,8},{2},{4,5}}
[1,2,8,3,4,6,5,7]=>{{1},{2},{3,4,5,7,8},{6}}
[8,1,2,7,3,5,4,6]=>{{1,2,3,5,6,8},{4,7}}
[5,7,1,2,6,3,4,8]=>{{1,3,5,6},{2,4,7},{8}}
[1,2,7,5,6,3,4,8]=>{{1},{2},{3,4,5,6,7},{8}}
[5,1,4,7,2,3,6,8]=>{{1,2,5},{3,4,6,7},{8}}
[4,8,1,2,3,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[6,2,3,8,7,1,4,5]=>{{1,6},{2},{3},{4,5,7,8}}
[8,2,3,6,4,7,5,1]=>{{1,8},{2},{3},{4,5,6,7}}
[7,2,3,6,4,8,1,5]=>{{1,7},{2},{3},{4,5,6,8}}
[4,5,1,3,2,6,8,7]=>{{1,3,4},{2,5},{6},{7,8}}
[6,4,7,5,1,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[5,3,1,6,2,7,8,4]=>{{1,2,3,5},{4,6,7,8}}
[6,7,2,4,1,8,3,5]=>{{1,5,6,8},{2,3,7},{4}}
[5,1,6,3,2,7,8,4]=>{{1,2,5},{3,4,6,7,8}}
[5,2,1,6,4,7,3,8]=>{{1,3,4,5,6,7},{2},{8}}
[5,4,1,6,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,5,4,1,3,8]=>{{1,6},{2,3,7},{4,5},{8}}
[7,1,3,5,4,2,8,6]=>{{1,2,6,7,8},{3},{4,5}}
[7,6,8,2,4,5,3,1]=>{{1,3,7,8},{2,4,5,6}}
[4,2,8,6,5,1,3,7]=>{{1,4,6},{2},{3,7,8},{5}}
[3,8,5,4,7,1,2,6]=>{{1,2,3,5,6,7,8},{4}}
[1,4,8,3,6,2,7,5]=>{{1},{2,3,4,5,6,8},{7}}
[6,3,2,4,8,7,1,5]=>{{1,6,7},{2,3},{4},{5,8}}
[8,3,2,7,4,1,5,6]=>{{1,6,8},{2,3},{4,5,7}}
[7,3,2,6,5,8,1,4]=>{{1,7},{2,3},{4,6,8},{5}}
[3,6,2,5,7,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[2,7,1,5,8,6,4,3]=>{{1,2,3,4,5,7,8},{6}}
[7,2,4,1,6,8,5,3]=>{{1,3,4,5,6,7,8},{2}}
[6,4,7,2,3,8,5,1]=>{{1,6,8},{2,4},{3,5,7}}
[6,1,8,5,7,4,2,3]=>{{1,2,4,5,6,7},{3,8}}
[7,1,4,3,6,5,8,2]=>{{1,2,7,8},{3,4},{5,6}}
[7,1,5,6,3,4,8,2]=>{{1,2,7,8},{3,5},{4,6}}
[6,1,8,5,4,7,3,2]=>{{1,2,3,6,7,8},{4,5}}
[7,6,1,5,4,2,8,3]=>{{1,3,7,8},{2,6},{4,5}}
[5,1,6,8,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,5,3,1,8,2]=>{{1,2,3,4,5,6,7,8}}
[5,3,2,6,8,7,4,1]=>{{1,5,8},{2,3},{4,6,7}}
[5,4,6,2,8,7,3,1]=>{{1,5,8},{2,4},{3,6,7}}
[4,5,8,6,7,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,7,6,1,2,8,3]=>{{1,2,4,5,6},{3,7,8}}
[4,6,5,7,2,1,8,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,8,6,3,5,1,2]=>{{1,7},{2,3,4,5,6,8}}
[7,2,4,3,6,1,8,5]=>{{1,5,6,7,8},{2},{3,4}}
[2,3,4,7,8,6,1,5]=>{{1,2,3,4,7},{5,8},{6}}
[6,3,7,1,4,2,8,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,3,5,1,8,2,7]=>{{1,4,5},{2,6,7,8},{3}}
[8,5,7,6,2,3,4,1]=>{{1,8},{2,5},{3,4,6,7}}
[3,4,6,7,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[2,5,6,7,3,8,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,8,4,6,2,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[2,4,7,5,8,6,3,1]=>{{1,2,4,5,8},{3,7},{6}}
[1,6,8,3,4,2,7,5]=>{{1},{2,6},{3,4,5,8},{7}}
[4,1,7,6,2,8,3,5]=>{{1,2,4,5,6,8},{3,7}}
[4,1,8,2,7,5,3,6]=>{{1,2,4},{3,5,6,7,8}}
[4,1,7,2,8,5,3,6]=>{{1,2,4},{3,7},{5,6,8}}
[2,5,6,3,7,4,8,1]=>{{1,2,5,7,8},{3,4,6}}
[2,6,5,3,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[2,6,5,3,7,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[7,1,6,3,5,4,8,2]=>{{1,2,7,8},{3,4,6},{5}}
[5,7,3,2,8,4,1,6]=>{{1,2,4,5,6,7,8},{3}}
[2,8,6,1,7,5,3,4]=>{{1,2,4,8},{3,5,6,7}}
[8,1,5,2,7,4,3,6]=>{{1,2,4,6,8},{3,5,7}}
[7,1,4,2,8,5,3,6]=>{{1,2,3,4,7},{5,6,8}}
[2,6,8,1,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,4,6,5,3,8,2,7]=>{{1},{2,3,4,5,6,7,8}}
[2,4,5,8,7,1,3,6]=>{{1,2,4,6,8},{3,5,7}}
[3,1,6,8,7,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[3,1,8,7,5,6,4,2]=>{{1,2,3,8},{4,7},{5},{6}}
[5,1,8,7,6,3,4,2]=>{{1,2,3,5,6,8},{4,7}}
[8,2,7,5,3,6,4,1]=>{{1,8},{2},{3,4,5,7},{6}}
[8,7,2,3,1,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[2,8,5,7,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[1,8,7,2,6,4,5,3]=>{{1},{2,3,4,5,6,7,8}}
[8,7,2,1,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}
[1,8,4,7,6,2,5,3]=>{{1},{2,3,4,5,6,7,8}}
[8,7,1,6,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,4,1,7,3,6,5,2]=>{{1,2,3,4,5,7,8},{6}}
[4,5,1,8,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[3,8,5,2,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}
[4,3,8,5,2,6,1,7]=>{{1,2,3,4,5,7,8},{6}}
[3,6,4,7,5,2,1,8]=>{{1,3,4,7},{2,6},{5},{8}}
[5,7,4,1,2,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[2,8,6,7,5,3,1,4]=>{{1,2,4,7,8},{3,6},{5}}
[7,4,5,2,6,3,1,8]=>{{1,7},{2,4},{3,5,6},{8}}
[8,6,3,4,5,1,7,2]=>{{1,2,6,8},{3},{4},{5},{7}}
[8,6,3,5,4,1,7,2]=>{{1,2,6,8},{3},{4,5},{7}}
[8,7,4,5,1,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,5,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,3,1,2,5,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,3,5,1,6,4,2]=>{{1,2,4,5,7,8},{3},{6}}
[4,8,3,2,6,1,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[4,3,7,6,1,5,2,8]=>{{1,4,5,6},{2,3,7},{8}}
[7,5,4,3,6,1,8,2]=>{{1,2,5,6,7,8},{3,4}}
[4,6,8,5,3,1,2,7]=>{{1,2,3,4,5,6,7,8}}
[5,6,8,4,3,7,2,1]=>{{1,3,5,8},{2,6,7},{4}}
[7,5,8,4,2,1,6,3]=>{{1,6,7},{2,5},{3,8},{4}}
[1,4,8,7,6,2,5,3]=>{{1},{2,4,5,6,7},{3,8}}
[7,2,4,1,5,3,8,6]=>{{1,3,4,6,7,8},{2},{5}}
[8,5,3,4,1,7,2,6]=>{{1,2,5,6,7,8},{3},{4}}
[2,8,5,4,3,6,1,7]=>{{1,2,7,8},{3,5},{4},{6}}
[8,6,5,3,1,2,7,4]=>{{1,3,4,5,8},{2,6},{7}}
[7,4,6,5,3,2,8,1]=>{{1,7,8},{2,3,4,5,6}}
[5,6,7,2,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[8,4,2,6,5,7,3,1]=>{{1,8},{2,3,4,6,7},{5}}
[1,7,4,2,8,5,6,3]=>{{1},{2,3,4,5,6,7,8}}
[3,2,1,7,4,6,8,5]=>{{1,3},{2},{4,5,7,8},{6}}
[6,2,5,7,1,4,3,8]=>{{1,3,4,5,6,7},{2},{8}}
[4,8,5,3,1,2,6,7]=>{{1,3,4,5},{2,6,7,8}}
[8,5,2,4,6,1,3,7]=>{{1,2,3,5,6,7,8},{4}}
[1,5,3,4,7,2,6,8]=>{{1},{2,5,6,7},{3},{4},{8}}
[8,4,6,1,5,7,3,2]=>{{1,2,4,8},{3,6,7},{5}}
[6,4,7,2,1,3,8,5]=>{{1,3,5,6,7,8},{2,4}}
[6,7,3,1,2,4,8,5]=>{{1,4,6},{2,5,7,8},{3}}
[3,1,8,7,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}
[1,3,8,6,7,2,5,4]=>{{1},{2,3,4,6,8},{5,7}}
[5,2,3,6,1,8,4,7]=>{{1,5},{2},{3},{4,6,7,8}}
[3,2,6,4,7,1,5,8]=>{{1,3,6},{2},{4},{5,7},{8}}
[3,6,2,5,7,8,4,1]=>{{1,2,3,6,8},{4,5,7}}
[2,7,4,6,8,3,5,1]=>{{1,2,5,7,8},{3,4,6}}
[3,7,6,8,1,5,4,2]=>{{1,3,5,6},{2,4,7,8}}
[1,5,7,6,8,4,2,3]=>{{1},{2,3,5,7,8},{4,6}}
[2,7,4,6,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,8,5,1,4,2]=>{{1,3,6},{2,4,7,8},{5}}
[7,1,3,8,6,2,4,5]=>{{1,2,4,5,6,7,8},{3}}
[2,7,1,8,6,5,3,4]=>{{1,2,3,7},{4,8},{5,6}}
[8,1,5,2,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[5,3,4,7,6,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,1,8,5,7,2,6,3]=>{{1,2,4,5,6,7},{3,8}}
[4,1,8,2,7,5,6,3]=>{{1,2,4},{3,8},{5,6,7}}
[7,6,8,2,4,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[7,4,5,3,8,1,6,2]=>{{1,6,7},{2,3,4,5,8}}
[7,3,6,1,4,2,8,5]=>{{1,4,5,7,8},{2,3,6}}
[8,7,2,6,4,5,1,3]=>{{1,2,3,7,8},{4,5,6}}
[1,2,4,8,5,7,3,6]=>{{1},{2},{3,4,6,7,8},{5}}
[7,1,4,6,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,2,5,1,6,4,8,3]=>{{1,3,4,5,6,7,8},{2}}
[2,7,1,5,6,4,8,3]=>{{1,2,3,7,8},{4,5,6}}
[1,5,7,8,4,6,3,2]=>{{1},{2,4,5,8},{3,7},{6}}
[1,4,8,5,7,6,3,2]=>{{1},{2,3,4,5,7,8},{6}}
[2,8,1,5,6,4,7,3]=>{{1,2,3,8},{4,5,6},{7}}
[3,7,2,8,1,5,6,4]=>{{1,2,3,5,6,7},{4,8}}
[7,3,2,5,1,6,8,4]=>{{1,4,5,7,8},{2,3},{6}}
[8,7,2,1,3,6,5,4]=>{{1,4,8},{2,3,5,7},{6}}
[7,3,2,8,1,4,6,5]=>{{1,4,5,6,7,8},{2,3}}
[3,6,2,1,8,4,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[3,5,1,7,6,4,8,2]=>{{1,3},{2,4,5,6,7,8}}
[8,7,4,2,1,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[5,4,7,6,2,1,8,3]=>{{1,2,4,5,6},{3,7,8}}
[3,5,2,8,7,1,6,4]=>{{1,2,3,5,6,7},{4,8}}
[3,7,6,5,4,1,8,2]=>{{1,3,6},{2,7,8},{4,5}}
[4,6,5,3,1,8,7,2]=>{{1,3,4,5},{2,6,8},{7}}
[4,5,2,6,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,4,3,1,5,2]=>{{1,2,6,8},{3,5,7},{4}}
[4,7,1,8,5,3,2,6]=>{{1,3,4,6,8},{2,7},{5}}
[8,6,7,1,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,6,7,2,1,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,1,7,4,2,3]=>{{1,3,4,6,8},{2,5,7}}
[6,4,1,2,5,7,8,3]=>{{1,3,6,7,8},{2,4},{5}}
[6,1,5,4,2,7,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[6,4,2,3,1,7,5,8]=>{{1,5,6,7},{2,3,4},{8}}
[3,4,6,1,8,2,7,5]=>{{1,2,3,4,6},{5,8},{7}}
[5,3,1,4,7,6,2,8]=>{{1,2,3,5,7},{4},{6},{8}}
[6,4,5,2,7,1,3,8]=>{{1,6},{2,4},{3,5,7},{8}}
[7,4,3,5,1,6,2,8]=>{{1,2,4,5,7},{3},{6},{8}}
[7,5,3,6,2,1,4,8]=>{{1,4,6,7},{2,5},{3},{8}}
[6,4,3,7,1,8,2,5]=>{{1,5,6,8},{2,4,7},{3}}
[3,1,2,7,6,4,5,8]=>{{1,2,3},{4,5,6,7},{8}}
[5,1,2,7,6,3,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[5,6,1,7,2,4,3,8]=>{{1,2,3,4,5,6,7},{8}}
[3,5,6,8,1,2,7,4]=>{{1,2,3,5,6},{4,8},{7}}
[2,6,5,7,1,3,4,8]=>{{1,2,3,5,6},{4,7},{8}}
[2,3,7,1,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}
[2,6,5,3,4,1,7,8]=>{{1,2,6},{3,4,5},{7},{8}}
[2,6,1,3,5,4,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[4,6,1,5,2,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[6,1,5,4,2,7,8,3]=>{{1,2,3,5,6,7,8},{4}}
[4,6,1,5,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[2,8,6,5,1,3,7,4]=>{{1,2,4,5,8},{3,6},{7}}
[5,1,8,6,2,7,4,3]=>{{1,2,5},{3,8},{4,6,7}}
[3,6,8,2,7,5,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,6,4,1,7,2,8,3]=>{{1,3,4,5,7,8},{2,6}}
[3,8,6,1,5,7,4,2]=>{{1,3,4,6,7},{2,8},{5}}
[8,1,6,3,4,2,5,7]=>{{1,2,3,4,5,6,7,8}}
[7,4,2,3,1,6,8,5]=>{{1,5,7,8},{2,3,4},{6}}
[6,4,2,3,7,8,1,5]=>{{1,5,6,7,8},{2,3,4}}
[4,3,6,2,5,8,1,7]=>{{1,2,3,4,6,7,8},{5}}
[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,6,7,3,2,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[8,2,4,3,1,7,5,6]=>{{1,5,6,7,8},{2},{3,4}}
[8,2,1,4,3,7,5,6]=>{{1,3,5,6,7,8},{2},{4}}
[7,6,8,2,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,5,1,3,7,4]=>{{1,4,5,8},{2,3,6},{7}}
[7,1,6,8,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}
[5,7,2,6,4,1,8,3]=>{{1,4,5,6},{2,3,7,8}}
[4,5,6,1,3,8,2,7]=>{{1,4},{2,3,5,6,7,8}}
[6,3,5,7,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[7,6,4,8,5,3,1,2]=>{{1,7},{2,3,4,6,8},{5}}
[8,2,1,6,4,7,3,5]=>{{1,3,4,5,6,7,8},{2}}
[1,3,8,6,5,2,7,4]=>{{1},{2,3,4,6,8},{5},{7}}
[2,7,3,8,5,6,4,1]=>{{1,2,4,7,8},{3},{5},{6}}
[1,2,8,5,7,4,6,3]=>{{1},{2},{3,8},{4,5,6,7}}
[1,6,8,5,4,7,2,3]=>{{1},{2,6,7},{3,8},{4,5}}
[5,7,1,8,3,2,6,4]=>{{1,3,5},{2,6,7},{4,8}}
[8,2,5,4,3,7,1,6]=>{{1,6,7,8},{2},{3,5},{4}}
[5,8,4,3,7,6,2,1]=>{{1,2,5,7,8},{3,4},{6}}
[8,1,5,3,4,7,2,6]=>{{1,2,6,7,8},{3,4,5}}
[6,1,8,7,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[1,5,8,6,4,3,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[5,8,6,4,2,1,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[2,6,1,8,4,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[5,3,8,6,1,2,7,4]=>{{1,5},{2,3,4,6,8},{7}}
[5,8,1,4,6,2,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[3,7,6,2,1,4,8,5]=>{{1,2,3,4,5,6,7,8}}
[4,6,2,3,7,1,8,5]=>{{1,2,3,4,6},{5,7,8}}
[6,8,7,5,1,3,4,2]=>{{1,3,4,5,6,7},{2,8}}
[6,4,3,2,7,8,5,1]=>{{1,6,8},{2,4},{3},{5,7}}
[2,7,6,1,5,3,8,4]=>{{1,2,4,7,8},{3,6},{5}}
[7,8,6,4,2,5,3,1]=>{{1,2,3,5,6,7,8},{4}}
[6,4,5,8,7,1,3,2]=>{{1,6},{2,4,8},{3,5,7}}
[6,4,1,7,8,3,2,5]=>{{1,3,6},{2,4,7},{5,8}}
[6,4,3,8,7,2,5,1]=>{{1,2,4,6,8},{3},{5,7}}
[5,4,7,2,1,3,8,6]=>{{1,5},{2,4},{3,6,7,8}}
[2,6,4,5,7,1,8,3]=>{{1,2,6},{3,4,5,7,8}}
[3,7,4,6,1,5,8,2]=>{{1,3,4,5,6},{2,7,8}}
[3,4,6,5,2,8,1,7]=>{{1,3,6,7,8},{2,4,5}}
[4,6,7,5,8,2,1,3]=>{{1,3,4,5,7,8},{2,6}}
[2,5,7,6,4,1,8,3]=>{{1,2,4,5,6},{3,7,8}}
[5,1,4,6,2,7,8,3]=>{{1,2,5},{3,4,6,7,8}}
[1,2,5,3,7,8,6,4]=>{{1},{2},{3,4,5,6,7,8}}
[4,8,3,5,1,2,7,6]=>{{1,4,5},{2,6,8},{3},{7}}
[6,1,3,7,2,8,4,5]=>{{1,2,5,6,8},{3},{4,7}}
[3,8,5,4,1,7,2,6]=>{{1,3,5},{2,6,7,8},{4}}
[3,1,5,8,2,6,7,4]=>{{1,2,3,5},{4,8},{6},{7}}
[2,8,5,3,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[6,5,2,3,7,1,8,4]=>{{1,6},{2,3,4,5,7,8}}
[7,2,1,6,4,8,3,5]=>{{1,3,7},{2},{4,5,6,8}}
[2,1,3,7,5,8,4,6]=>{{1,2},{3},{4,7},{5},{6,8}}
[6,2,4,5,7,1,8,3]=>{{1,6},{2},{3,4,5,7,8}}
[2,3,8,7,1,4,6,5]=>{{1,2,3,5,8},{4,6,7}}
[4,2,7,5,6,8,1,3]=>{{1,3,4,5,6,7,8},{2}}
[6,8,2,5,4,7,3,1]=>{{1,2,3,6,7,8},{4,5}}
[5,3,2,7,6,1,8,4]=>{{1,5,6},{2,3},{4,7,8}}
[5,6,4,2,8,7,1,3]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,2,6,1,8,3]=>{{1,5,6},{2,3,4,7,8}}
[5,4,7,1,6,2,8,3]=>{{1,2,4,5,6},{3,7,8}}
[4,5,8,7,6,2,1,3]=>{{1,4,7},{2,5,6},{3,8}}
[6,4,7,1,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[6,1,7,3,8,4,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,2,3,1,6,4,7,5]=>{{1,4,5,6,8},{2},{3},{7}}
[1,8,7,2,3,4,6,5]=>{{1},{2,3,4,5,6,7,8}}
[1,8,3,7,6,2,5,4]=>{{1},{2,4,5,6,7,8},{3}}
[1,3,8,2,5,6,4,7]=>{{1},{2,3,4,7,8},{5},{6}}
[1,3,2,7,4,6,8,5]=>{{1},{2,3},{4,5,7,8},{6}}
[1,3,8,4,6,2,7,5]=>{{1},{2,3,5,6,8},{4},{7}}
[8,2,3,6,7,4,5,1]=>{{1,8},{2},{3},{4,6},{5,7}}
[5,6,4,2,1,7,3,8]=>{{1,5},{2,3,4,6,7},{8}}
[2,5,7,6,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,7,1,2,5,3,8]=>{{1,2,4,5,6},{3,7},{8}}
[1,2,7,5,8,6,3,4]=>{{1},{2},{3,7},{4,5,8},{6}}
[7,4,5,1,6,8,2,3]=>{{1,2,4,7},{3,5,6,8}}
[1,7,8,4,2,6,3,5]=>{{1},{2,3,5,7,8},{4},{6}}
[6,3,2,5,7,4,1,8]=>{{1,4,5,6,7},{2,3},{8}}
[6,2,1,5,3,7,8,4]=>{{1,3,4,5,6,7,8},{2}}
[6,2,5,1,3,8,7,4]=>{{1,4,6,8},{2},{3,5},{7}}
[6,2,8,5,1,3,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[4,1,7,8,3,6,5,2]=>{{1,2,4,8},{3,5,7},{6}}
[6,4,2,1,7,3,5,8]=>{{1,2,3,4,6},{5,7},{8}}
[5,8,4,2,1,3,6,7]=>{{1,5},{2,3,4,6,7,8}}
[1,7,5,8,4,3,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,1,6,4,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[2,4,7,5,1,8,6,3]=>{{1,2,4,5},{3,6,7,8}}
[2,3,7,1,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[6,5,1,2,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[3,6,5,7,8,2,4,1]=>{{1,3,5,8},{2,6},{4,7}}
[3,6,5,1,8,7,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,8,1,2,5,4,3,6]=>{{1,3,7},{2,4,6,8},{5}}
[2,8,4,3,5,1,7,6]=>{{1,2,6,8},{3,4},{5},{7}}
[5,2,4,7,6,8,1,3]=>{{1,3,4,5,6,7,8},{2}}
[3,1,5,7,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[4,1,7,6,8,2,5,3]=>{{1,2,4,6},{3,5,7,8}}
[7,2,6,4,1,5,3,8]=>{{1,3,5,6,7},{2},{4},{8}}
[1,2,6,5,8,3,7,4]=>{{1},{2},{3,6},{4,5,8},{7}}
[7,3,5,6,1,4,2,8]=>{{1,2,3,5,7},{4,6},{8}}
[5,8,3,1,6,7,4,2]=>{{1,4,5,6,7},{2,8},{3}}
[4,5,8,1,7,3,6,2]=>{{1,4},{2,3,5,6,7,8}}
[4,7,1,6,8,5,2,3]=>{{1,3,4,5,6,8},{2,7}}
[5,8,7,1,6,4,2,3]=>{{1,4,5,6},{2,3,7,8}}
[1,7,3,8,2,5,4,6]=>{{1},{2,4,5,6,7,8},{3}}
[8,4,1,3,6,7,5,2]=>{{1,2,3,4,8},{5,6,7}}
[5,3,1,8,6,7,4,2]=>{{1,2,3,4,5,6,7,8}}
[6,2,7,1,4,3,5,8]=>{{1,3,4,5,6,7},{2},{8}}
[8,3,2,6,5,1,7,4]=>{{1,4,6,8},{2,3},{5},{7}}
[2,6,8,4,7,1,3,5]=>{{1,2,6},{3,5,7,8},{4}}
[7,8,6,3,2,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[1,6,4,8,2,3,5,7]=>{{1},{2,3,4,5,6,7,8}}
[2,8,5,6,4,1,7,3]=>{{1,2,3,4,5,6,8},{7}}
[1,4,7,3,5,8,6,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,7,8,2,5,1,6,4]=>{{1,2,3,4,6,7,8},{5}}
[8,6,1,4,3,2,7,5]=>{{1,3,5,8},{2,6},{4},{7}}
[7,3,8,2,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}
[6,3,7,8,1,2,5,4]=>{{1,2,3,5,6,7},{4,8}}
[7,6,1,5,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,8,6,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[5,7,1,6,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}
[6,8,4,2,1,7,3,5]=>{{1,2,3,4,5,6,7,8}}
[6,3,2,8,1,7,4,5]=>{{1,4,5,6,7,8},{2,3}}
[6,4,1,3,7,8,5,2]=>{{1,2,3,4,6,8},{5,7}}
[6,8,5,4,3,7,1,2]=>{{1,6,7},{2,8},{3,5},{4}}
[5,7,4,8,3,1,2,6]=>{{1,3,4,5,6,8},{2,7}}
[6,1,2,4,8,3,7,5]=>{{1,2,3,6},{4},{5,8},{7}}
[2,5,6,8,1,4,7,3]=>{{1,2,5},{3,4,6,8},{7}}
[7,4,1,6,5,2,3,8]=>{{1,3,7},{2,4,6},{5},{8}}
[4,1,6,5,2,3,8,7]=>{{1,2,4,5},{3,6},{7,8}}
[4,5,1,7,8,6,2,3]=>{{1,2,3,4,5,7,8},{6}}
[8,5,7,3,4,6,2,1]=>{{1,8},{2,3,4,5,7},{6}}
[6,8,7,4,3,5,2,1]=>{{1,2,3,5,6,7,8},{4}}
[6,8,7,5,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}
[5,8,6,2,4,7,3,1]=>{{1,2,4,5,8},{3,6,7}}
[4,8,6,2,5,7,3,1]=>{{1,2,4,8},{3,6,7},{5}}
[1,6,4,7,5,3,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[1,6,5,3,2,7,4,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,8,7,4,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,4,7,5,3,2,6,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,7,5,4,3,2,8,6]=>{{1},{2,6,7,8},{3,5},{4}}
[1,4,7,5,3,2,8,6]=>{{1},{2,3,4,5,6,7,8}}
[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,8,7,2,3,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,6,1,8,2,4,3]=>{{1,2,3,4,5,6,7,8}}
[4,8,6,5,7,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[2,7,8,5,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[8,5,6,2,4,7,3,1]=>{{1,8},{2,4,5},{3,6,7}}
[8,1,3,6,4,5,2,7]=>{{1,2,7,8},{3},{4,5,6}}
[4,3,1,6,2,5,8,7]=>{{1,2,3,4,5,6},{7,8}}
[7,5,2,1,8,4,3,6]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,4,7,8,2,6]=>{{1,2,3,5,7},{4},{6,8}}
[7,1,2,4,8,3,5,6]=>{{1,2,3,5,6,7,8},{4}}
[8,6,1,3,5,7,4,2]=>{{1,2,3,4,6,7,8},{5}}
[7,1,5,8,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[3,6,8,5,1,4,2,7]=>{{1,2,3,4,5,6,7,8}}
[5,2,4,1,6,8,3,7]=>{{1,3,4,5,6,7,8},{2}}
[2,5,3,4,6,8,1,7]=>{{1,2,5,6,7,8},{3},{4}}
[4,7,1,2,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}
[6,7,3,1,8,2,4,5]=>{{1,2,4,6,7},{3},{5,8}}
[7,3,1,4,6,2,8,5]=>{{1,2,3,5,6,7,8},{4}}
[7,4,1,2,5,6,3,8]=>{{1,3,7},{2,4},{5},{6},{8}}
[5,4,1,3,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[5,7,4,8,1,6,3,2]=>{{1,5},{2,3,4,7,8},{6}}
[4,3,1,2,5,7,6,8]=>{{1,2,3,4},{5},{6,7},{8}}
[1,2,4,7,8,5,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,3,6,5,7,4,2,1]=>{{1,8},{2,3,4,5,6,7}}
[8,2,6,5,7,4,3,1]=>{{1,8},{2},{3,4,5,6,7}}
[8,4,7,1,5,2,6,3]=>{{1,2,3,4,6,7,8},{5}}
[8,2,6,3,7,5,4,1]=>{{1,8},{2},{3,4,5,6,7}}
[8,2,5,3,7,6,4,1]=>{{1,8},{2},{3,4,5,7},{6}}
[8,5,7,1,4,3,6,2]=>{{1,2,4,5,8},{3,6,7}}
[5,3,1,8,4,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[2,1,6,5,8,7,3,4]=>{{1,2},{3,6,7},{4,5,8}}
[6,1,5,4,7,3,8,2]=>{{1,2,3,5,6,7,8},{4}}
[3,1,8,4,2,7,6,5]=>{{1,2,3,5,8},{4},{6,7}}
[2,8,7,4,1,3,6,5]=>{{1,2,5,8},{3,6,7},{4}}
[8,2,3,1,7,6,4,5]=>{{1,4,5,7,8},{2},{3},{6}}
[8,7,2,3,1,6,4,5]=>{{1,5,8},{2,3,4,7},{6}}
[7,2,5,8,3,1,4,6]=>{{1,4,6,7,8},{2},{3,5}}
[6,8,2,3,1,7,4,5]=>{{1,2,3,4,5,6,7,8}}
[8,2,5,7,3,1,4,6]=>{{1,6,8},{2},{3,5},{4,7}}
[8,2,7,3,1,4,5,6]=>{{1,3,4,5,6,7,8},{2}}
[5,3,2,8,7,1,6,4]=>{{1,5,6,7},{2,3},{4,8}}
[8,6,7,4,1,3,5,2]=>{{1,2,3,5,6,7,8},{4}}
[4,1,3,6,5,2,8,7]=>{{1,2,4,6},{3},{5},{7,8}}
[4,6,3,2,5,1,8,7]=>{{1,2,4,6},{3},{5},{7,8}}
[4,8,3,2,6,5,7,1]=>{{1,2,4,8},{3},{5,6},{7}}
[4,8,3,6,5,2,7,1]=>{{1,2,4,6,8},{3},{5},{7}}
[8,1,6,2,5,4,7,3]=>{{1,2,3,4,6,8},{5},{7}}
[2,4,3,8,6,1,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[2,6,3,8,5,4,7,1]=>{{1,2,4,6,8},{3},{5},{7}}
[6,1,3,2,5,8,7,4]=>{{1,2,4,6,8},{3},{5},{7}}
[6,8,4,2,5,3,7,1]=>{{1,2,3,4,6,8},{5},{7}}
[6,8,4,3,5,2,7,1]=>{{1,2,6,8},{3,4},{5},{7}}
[8,1,4,6,5,3,7,2]=>{{1,2,8},{3,4,6},{5},{7}}
[3,5,4,6,1,2,8,7]=>{{1,2,3,4,5,6},{7,8}}
[7,3,5,6,1,8,2,4]=>{{1,2,3,5,7},{4,6,8}}
[5,7,6,3,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[4,6,7,2,3,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[6,5,4,8,7,2,3,1]=>{{1,2,3,4,5,6,7,8}}
[5,7,4,3,6,2,1,8]=>{{1,2,5,6,7},{3,4},{8}}
[1,8,5,6,2,3,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[8,5,6,1,3,2,7,4]=>{{1,4,8},{2,3,5,6},{7}}
[5,3,7,8,2,6,1,4]=>{{1,2,3,5,7},{4,8},{6}}
[4,5,8,3,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}
[4,5,8,7,2,3,1,6]=>{{1,4,7},{2,5},{3,6,8}}
[8,2,6,4,3,7,5,1]=>{{1,8},{2},{3,5,6,7},{4}}
[6,3,1,8,7,4,5,2]=>{{1,2,3,4,6,8},{5,7}}
[8,6,3,2,7,4,5,1]=>{{1,8},{2,4,6},{3},{5,7}}
[1,3,6,8,7,4,5,2]=>{{1},{2,3,4,6,8},{5,7}}
[5,7,1,3,6,2,4,8]=>{{1,2,3,4,5,6,7},{8}}
[4,7,5,2,3,6,8,1]=>{{1,2,4,7,8},{3,5},{6}}
[3,6,4,1,2,5,7,8]=>{{1,3,4},{2,5,6},{7},{8}}
[4,7,1,3,2,5,8,6]=>{{1,3,4},{2,5,6,7,8}}
[4,7,1,3,2,6,8,5]=>{{1,3,4},{2,5,7,8},{6}}
[5,7,1,3,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}
[6,8,2,5,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}
[4,8,5,2,3,6,1,7]=>{{1,2,4,7,8},{3,5},{6}}
[5,8,6,3,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}
[3,7,5,4,2,8,1,6]=>{{1,2,3,5,7},{4},{6,8}}
[4,6,5,1,7,8,2,3]=>{{1,4},{2,3,5,6,7,8}}
[4,7,1,3,2,8,5,6]=>{{1,3,4},{2,5,7},{6,8}}
[3,6,5,1,8,2,4,7]=>{{1,3,4,5,7,8},{2,6}}
[5,8,7,3,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,3,7,4,6,1]=>{{1,8},{2,3,4,5,6,7}}
[6,3,1,5,4,8,2,7]=>{{1,2,3,6,7,8},{4,5}}
[4,7,6,3,5,2,8,1]=>{{1,2,3,4,6,7,8},{5}}
[1,7,5,3,4,8,6,2]=>{{1},{2,6,7,8},{3,4,5}}
[5,8,2,3,4,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[8,7,3,2,6,4,5,1]=>{{1,8},{2,4,5,6,7},{3}}
[8,3,1,4,7,5,2,6]=>{{1,2,3,5,6,7,8},{4}}
[5,3,1,6,4,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[3,4,8,5,7,2,6,1]=>{{1,3,8},{2,4,5,6,7}}
[8,5,1,2,7,6,4,3]=>{{1,3,8},{2,4,5,7},{6}}
[3,7,8,5,6,2,4,1]=>{{1,3,8},{2,4,5,6,7}}
[7,4,3,6,2,5,8,1]=>{{1,7,8},{2,4,5,6},{3}}
[4,3,8,7,1,6,2,5]=>{{1,2,3,4,5,7,8},{6}}
[1,5,3,8,4,7,2,6]=>{{1},{2,4,5,6,7,8},{3}}
[8,2,3,1,6,5,7,4]=>{{1,4,8},{2},{3},{5,6},{7}}
[8,4,2,7,1,3,6,5]=>{{1,5,8},{2,3,4,6,7}}
[8,4,2,3,1,6,7,5]=>{{1,5,8},{2,3,4},{6},{7}}
[4,7,2,3,6,5,8,1]=>{{1,2,3,4,7,8},{5,6}}
[3,8,2,6,4,7,1,5]=>{{1,2,3,4,5,6,7,8}}
[1,7,5,8,6,2,4,3]=>{{1},{2,3,4,5,6,7,8}}
[6,5,1,7,4,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[7,6,3,5,1,4,8,2]=>{{1,2,4,5,6,7,8},{3}}
[6,5,4,1,7,2,3,8]=>{{1,2,3,4,5,6,7},{8}}
[8,3,6,1,7,4,5,2]=>{{1,2,3,4,6,8},{5,7}}
[7,1,2,6,4,8,3,5]=>{{1,2,3,7},{4,5,6,8}}
[3,5,1,8,6,2,4,7]=>{{1,3},{2,5,6},{4,7,8}}
[1,8,7,5,4,6,2,3]=>{{1},{2,3,7,8},{4,5},{6}}
[8,1,6,7,4,5,3,2]=>{{1,2,8},{3,4,5,6,7}}
[8,1,6,4,7,5,3,2]=>{{1,2,8},{3,5,6,7},{4}}
[6,4,8,1,5,3,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[1,6,4,3,5,8,2,7]=>{{1},{2,6,7,8},{3,4},{5}}
[5,1,4,3,7,8,6,2]=>{{1,2,5,6,7,8},{3,4}}
[5,7,1,8,6,3,2,4]=>{{1,3,5,6},{2,7},{4,8}}
[5,7,6,3,4,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[4,1,3,7,6,5,2,8]=>{{1,2,4,7},{3},{5,6},{8}}
[4,3,6,1,2,7,8,5]=>{{1,4},{2,3,5,6,7,8}}
[5,8,3,6,7,2,4,1]=>{{1,2,4,5,6,7,8},{3}}
[8,1,6,2,5,7,4,3]=>{{1,2,3,4,6,7,8},{5}}
[2,7,1,5,3,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[6,8,7,3,4,2,5,1]=>{{1,2,6,8},{3,4,5,7}}
[1,8,6,2,4,7,5,3]=>{{1},{2,3,4,5,6,7,8}}
[5,7,3,6,4,2,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[5,7,3,6,4,1,8,2]=>{{1,4,5,6},{2,7,8},{3}}
[3,7,5,6,4,1,8,2]=>{{1,3,4,5,6},{2,7,8}}
[2,8,5,7,3,4,6,1]=>{{1,2,8},{3,5},{4,6,7}}
[2,1,3,8,5,4,6,7]=>{{1,2},{3},{4,6,7,8},{5}}
[5,3,6,8,2,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[1,7,8,6,3,2,4,5]=>{{1},{2,4,6,7},{3,5,8}}
[7,1,2,5,3,8,4,6]=>{{1,2,3,4,5,7},{6,8}}
[3,7,4,2,5,1,8,6]=>{{1,2,3,4,6,7,8},{5}}
[1,8,3,4,5,7,2,6]=>{{1},{2,6,7,8},{3},{4},{5}}
[4,5,7,6,2,1,3,8]=>{{1,4,6},{2,5},{3,7},{8}}
[7,8,2,6,5,4,3,1]=>{{1,2,3,7,8},{4,6},{5}}
[5,3,7,8,4,2,1,6]=>{{1,2,3,4,5,6,7,8}}
[7,3,6,8,1,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[7,5,8,2,4,3,6,1]=>{{1,3,6,7,8},{2,4,5}}
[6,5,8,2,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[8,1,5,3,4,6,2,7]=>{{1,2,7,8},{3,4,5},{6}}
[5,8,7,2,4,3,6,1]=>{{1,2,4,5,8},{3,6,7}}
[1,7,2,4,8,5,6,3]=>{{1},{2,3,5,6,7,8},{4}}
[5,8,2,3,7,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[7,8,2,3,5,4,6,1]=>{{1,2,3,4,6,7,8},{5}}
[8,4,1,3,2,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[8,7,2,3,5,4,6,1]=>{{1,8},{2,3,4,6,7},{5}}
[1,7,6,8,4,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,3,1,8,5,6,4]=>{{1,2,4,5,6,7,8},{3}}
[3,8,5,2,1,6,7,4]=>{{1,3,5},{2,4,8},{6},{7}}
[4,8,7,1,2,5,3,6]=>{{1,4},{2,5,6,8},{3,7}}
[8,7,2,6,1,4,3,5]=>{{1,5,8},{2,3,7},{4,6}}
[6,1,7,3,8,2,4,5]=>{{1,2,6},{3,4,7},{5,8}}
[7,1,8,6,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}
[4,1,3,5,8,2,6,7]=>{{1,2,4,5,6,7,8},{3}}
[1,8,5,7,4,6,3,2]=>{{1},{2,8},{3,4,5,7},{6}}
[1,4,7,6,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,8,6,5,3,4]=>{{1},{2,3,7},{4,8},{5,6}}
[5,7,1,6,4,2,3,8]=>{{1,2,3,4,5,6,7},{8}}
[4,8,2,7,5,1,6,3]=>{{1,4,6,7},{2,3,8},{5}}
[2,8,4,6,7,1,5,3]=>{{1,2,3,4,6,8},{5,7}}
[3,8,5,1,4,2,6,7]=>{{1,3,4,5},{2,6,7,8}}
[1,7,6,2,5,3,8,4]=>{{1},{2,4,7,8},{3,6},{5}}
[1,7,5,2,4,3,8,6]=>{{1},{2,3,4,5,6,7,8}}
[2,8,5,1,4,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[3,1,2,5,7,6,8,4]=>{{1,2,3},{4,5,7,8},{6}}
[5,1,7,3,2,6,8,4]=>{{1,2,5},{3,4,7,8},{6}}
[4,7,2,3,5,1,6,8]=>{{1,2,3,4,6,7},{5},{8}}
[4,8,2,3,7,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[8,7,2,4,3,5,6,1]=>{{1,8},{2,3,5,6,7},{4}}
[8,6,2,4,3,5,1,7]=>{{1,7,8},{2,3,5,6},{4}}
[8,1,2,4,7,3,5,6]=>{{1,2,3,6,8},{4},{5,7}}
[7,6,2,8,4,5,1,3]=>{{1,7},{2,3,4,5,6,8}}
[6,8,1,5,7,3,2,4]=>{{1,3,6},{2,4,5,7,8}}
[4,1,7,5,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[3,7,6,2,1,4,5,8]=>{{1,2,3,4,5,6,7},{8}}
[1,6,8,7,2,5,4,3]=>{{1},{2,5,6},{3,8},{4,7}}
[1,4,8,7,6,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,7,5,2,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[6,2,5,3,1,8,7,4]=>{{1,3,4,5,6,8},{2},{7}}
[6,2,5,3,8,7,1,4]=>{{1,6,7},{2},{3,4,5,8}}
[6,4,5,3,8,7,1,2]=>{{1,6,7},{2,3,4,5,8}}
[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,7,5,2,3,1,6]=>{{1,3,6,7,8},{2,4,5}}
[8,2,7,4,5,3,1,6]=>{{1,3,6,7,8},{2},{4},{5}}
[8,2,4,7,5,3,1,6]=>{{1,3,4,6,7,8},{2},{5}}
[8,2,6,7,5,3,1,4]=>{{1,4,7,8},{2},{3,6},{5}}
[8,4,6,7,5,3,1,2]=>{{1,2,4,7,8},{3,6},{5}}
[6,4,5,8,7,3,1,2]=>{{1,3,5,6,7},{2,4,8}}
[6,2,8,7,5,3,1,4]=>{{1,3,4,6,7,8},{2},{5}}
[4,6,5,3,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}
[6,7,2,4,5,3,1,8]=>{{1,2,3,6,7},{4},{5},{8}}
[6,8,7,4,5,3,1,2]=>{{1,3,6,7},{2,8},{4},{5}}
[2,8,4,7,5,3,1,6]=>{{1,2,3,4,6,7,8},{5}}
[5,8,7,4,6,3,1,2]=>{{1,3,5,6,7},{2,8},{4}}
[6,5,8,4,7,2,1,3]=>{{1,2,5,6,7},{3,8},{4}}
[4,8,6,2,5,7,1,3]=>{{1,2,3,4,6,7,8},{5}}
[8,1,6,2,5,7,3,4]=>{{1,2,4,8},{3,6,7},{5}}
[6,8,1,2,4,7,3,5]=>{{1,3,6,7},{2,4,5,8}}
[8,1,5,3,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}
[8,3,7,6,2,5,4,1]=>{{1,8},{2,3,4,5,6,7}}
[4,6,1,3,5,8,2,7]=>{{1,3,4},{2,6,7,8},{5}}
[4,5,1,3,8,7,2,6]=>{{1,3,4},{2,5,6,7,8}}
[6,2,7,1,8,3,4,5]=>{{1,3,4,6,7},{2},{5,8}}
[6,4,5,8,1,7,2,3]=>{{1,2,3,4,5,6,7,8}}
[6,2,8,5,1,4,7,3]=>{{1,4,5,6},{2},{3,8},{7}}
[2,4,7,6,1,8,3,5]=>{{1,2,4,5,6,8},{3,7}}
[7,4,5,8,6,3,2,1]=>{{1,2,4,7,8},{3,5,6}}
[1,6,2,3,8,5,7,4]=>{{1},{2,3,4,5,6,8},{7}}
[3,4,2,6,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[7,4,1,3,6,8,2,5]=>{{1,2,3,4,7},{5,6,8}}
[6,8,1,2,7,3,4,5]=>{{1,3,6},{2,4,5,7,8}}
[1,6,2,8,7,3,4,5]=>{{1},{2,3,6},{4,5,7,8}}
[1,6,8,5,7,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,8,1,2,4,7,6,5]=>{{1,3},{2,4,5,8},{6,7}}
[1,4,5,7,3,6,8,2]=>{{1},{2,4,7,8},{3,5},{6}}
[2,3,8,1,4,6,5,7]=>{{1,2,3,4,5,7,8},{6}}
[3,6,2,4,7,5,8,1]=>{{1,2,3,5,6,7,8},{4}}
[3,1,8,4,6,2,5,7]=>{{1,2,3,5,6,7,8},{4}}
[4,2,7,3,5,8,1,6]=>{{1,3,4,7},{2},{5},{6,8}}
[3,1,8,4,5,6,2,7]=>{{1,2,3,7,8},{4},{5},{6}}
[4,2,7,8,6,3,1,5]=>{{1,3,4,5,6,7,8},{2}}
[7,1,4,2,8,6,3,5]=>{{1,2,3,4,7},{5,8},{6}}
[2,3,7,4,8,1,6,5]=>{{1,2,3,6,7},{4},{5,8}}
[1,6,3,5,8,7,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[8,4,6,3,5,1,7,2]=>{{1,2,3,4,6,8},{5},{7}}
[7,3,2,6,8,4,5,1]=>{{1,5,7,8},{2,3},{4,6}}
[2,4,5,7,1,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[8,4,2,6,7,3,5,1]=>{{1,8},{2,3,4,6},{5,7}}
[4,1,5,7,8,6,2,3]=>{{1,2,4,7},{3,5,8},{6}}
[6,1,4,8,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[7,6,2,3,5,8,4,1]=>{{1,2,3,4,6,7,8},{5}}
[2,8,5,7,6,3,4,1]=>{{1,2,8},{3,5,6},{4,7}}
[2,5,7,8,6,4,1,3]=>{{1,2,3,4,5,6,7,8}}
[7,4,1,6,2,5,8,3]=>{{1,3,7,8},{2,4,5,6}}
[5,6,2,4,8,7,3,1]=>{{1,5,8},{2,3,6,7},{4}}
[8,5,6,2,3,7,4,1]=>{{1,8},{2,3,4,5,6,7}}
[7,8,1,4,5,6,2,3]=>{{1,2,3,7,8},{4},{5},{6}}
[8,3,1,2,5,4,7,6]=>{{1,2,3,4,6,8},{5},{7}}
[8,1,5,3,7,4,2,6]=>{{1,2,3,4,5,6,7,8}}
[1,2,6,7,8,3,5,4]=>{{1},{2},{3,6},{4,5,7,8}}
[1,2,4,8,6,7,3,5]=>{{1},{2},{3,4,5,6,7,8}}
[8,1,2,6,5,7,3,4]=>{{1,2,3,4,6,7,8},{5}}
[7,1,2,6,5,8,3,4]=>{{1,2,3,7},{4,6,8},{5}}
[2,6,1,4,7,5,8,3]=>{{1,2,3,5,6,7,8},{4}}
[3,1,5,7,2,6,8,4]=>{{1,2,3,5},{4,7,8},{6}}
[3,1,7,5,2,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[3,2,7,5,1,6,8,4]=>{{1,3,4,5,7,8},{2},{6}}
[5,2,7,3,1,6,8,4]=>{{1,5},{2},{3,4,7,8},{6}}
[6,7,2,1,3,4,8,5]=>{{1,4,6},{2,3,5,7,8}}
[4,6,3,1,2,7,8,5]=>{{1,4},{2,5,6,7,8},{3}}
[2,3,5,6,8,4,7,1]=>{{1,2,3,5,8},{4,6},{7}}
[2,4,5,8,3,6,7,1]=>{{1,2,4,8},{3,5},{6},{7}}
[4,5,8,7,6,3,1,2]=>{{1,4,7},{2,3,5,6,8}}
[8,7,4,6,5,3,1,2]=>{{1,2,7,8},{3,4,6},{5}}
[8,1,4,3,6,2,5,7]=>{{1,2,5,6,7,8},{3,4}}
[1,6,3,7,8,4,2,5]=>{{1},{2,4,6,7},{3},{5,8}}
[7,4,2,8,5,6,3,1]=>{{1,2,3,4,7,8},{5},{6}}
[5,2,1,3,8,4,6,7]=>{{1,3,4,5,6,7,8},{2}}
[1,4,3,5,8,2,6,7]=>{{1},{2,4,5,6,7,8},{3}}
[2,1,3,8,6,4,5,7]=>{{1,2},{3},{4,5,6,7,8}}
[1,3,6,4,5,8,2,7]=>{{1},{2,3,6,7,8},{4},{5}}
[6,1,4,3,5,8,2,7]=>{{1,2,6,7,8},{3,4},{5}}
[6,5,1,3,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,4,3,8,6,2,5,7]=>{{1},{2,4,5,6,7,8},{3}}
[4,1,3,8,6,2,5,7]=>{{1,2,4,5,6,7,8},{3}}
[7,1,5,4,6,3,8,2]=>{{1,2,7,8},{3,5,6},{4}}
[6,4,7,8,3,5,1,2]=>{{1,3,5,6,7},{2,4,8}}
[3,5,6,7,1,8,4,2]=>{{1,2,3,5,6,8},{4,7}}
[3,5,2,4,8,6,7,1]=>{{1,2,3,5,8},{4},{6},{7}}
[3,7,6,1,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,4,7,1,5,6,2,3]=>{{1,2,3,4,7,8},{5},{6}}
[1,7,5,4,3,8,2,6]=>{{1},{2,7},{3,5},{4},{6,8}}
[4,5,8,1,7,3,2,6]=>{{1,4},{2,5,7},{3,6,8}}
[4,6,7,1,3,8,2,5]=>{{1,4},{2,3,5,6,7,8}}
[2,6,3,1,4,7,8,5]=>{{1,2,4,5,6,7,8},{3}}
[2,7,3,4,1,8,5,6]=>{{1,2,5,7},{3},{4},{6,8}}
[8,6,4,5,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[7,4,8,5,3,6,1,2]=>{{1,7},{2,3,4,5,8},{6}}
[8,4,6,5,1,3,7,2]=>{{1,2,4,5,8},{3,6},{7}}
[4,5,3,8,7,1,2,6]=>{{1,4,6,8},{2,5,7},{3}}
[8,5,4,7,6,1,2,3]=>{{1,2,3,4,5,6,7,8}}
[2,3,7,8,1,4,6,5]=>{{1,2,3,4,5,6,7,8}}
[8,2,3,5,4,1,7,6]=>{{1,6,8},{2},{3},{4,5},{7}}
[7,1,3,8,2,4,6,5]=>{{1,2,4,5,6,7,8},{3}}
[7,2,3,6,4,1,8,5]=>{{1,4,5,6,7,8},{2},{3}}
[6,5,2,4,1,8,3,7]=>{{1,2,3,5,6,7,8},{4}}
[5,7,2,4,1,3,8,6]=>{{1,5},{2,3,6,7,8},{4}}
[6,2,5,4,1,8,3,7]=>{{1,3,5,6,7,8},{2},{4}}
[4,2,6,3,5,8,1,7]=>{{1,3,4,6,7,8},{2},{5}}
[7,4,2,6,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[8,5,2,4,6,3,1,7]=>{{1,7,8},{2,3,5,6},{4}}
[7,4,1,2,8,5,6,3]=>{{1,3,5,6,7,8},{2,4}}
[6,4,1,8,5,2,3,7]=>{{1,2,3,4,6,7,8},{5}}
[8,4,1,6,3,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[7,3,4,1,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,3,5,7,4,1]=>{{1,8},{2,3,4,6,7},{5}}
[8,6,2,5,7,3,4,1]=>{{1,8},{2,3,6},{4,5,7}}
[6,3,4,8,5,1,2,7]=>{{1,6},{2,3,4,7,8},{5}}
[8,5,1,2,7,4,6,3]=>{{1,3,8},{2,4,5,6,7}}
[7,2,6,8,3,4,5,1]=>{{1,3,4,5,6,7,8},{2}}
[1,6,7,5,4,8,2,3]=>{{1},{2,3,6,7,8},{4,5}}
[1,8,5,4,2,6,3,7]=>{{1},{2,3,5,7,8},{4},{6}}
[5,8,6,1,2,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[4,1,5,7,3,6,8,2]=>{{1,2,4,7,8},{3,5},{6}}
[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[5,7,2,1,6,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[2,6,3,1,7,8,5,4]=>{{1,2,4,6,8},{3},{5,7}}
[6,2,5,7,4,1,8,3]=>{{1,6},{2},{3,4,5,7,8}}
[3,6,1,8,7,4,5,2]=>{{1,3},{2,4,6,8},{5,7}}
[4,7,1,3,5,6,8,2]=>{{1,3,4},{2,7,8},{5},{6}}
[4,3,5,7,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[5,3,2,7,6,4,1,8]=>{{1,4,5,6,7},{2,3},{8}}
[5,3,7,4,6,2,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[5,7,3,2,1,8,6,4]=>{{1,5},{2,4,6,7,8},{3}}
[5,7,6,3,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[3,2,7,5,4,1,8,6]=>{{1,3,6,7,8},{2},{4,5}}
[1,7,3,5,4,2,6,8]=>{{1},{2,6,7},{3},{4,5},{8}}
[5,3,7,4,1,8,6,2]=>{{1,5},{2,3,6,7,8},{4}}
[7,3,5,4,1,6,8,2]=>{{1,2,3,5,7,8},{4},{6}}
[7,5,1,6,8,3,2,4]=>{{1,2,3,4,5,6,7,8}}
[5,3,1,7,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}
[7,1,5,3,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[7,1,5,2,4,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[1,8,3,6,2,4,7,5]=>{{1},{2,5,8},{3},{4,6},{7}}
[1,8,7,5,6,4,2,3]=>{{1},{2,3,7,8},{4,5,6}}
[6,8,2,1,5,4,3,7]=>{{1,4,6},{2,3,7,8},{5}}
[6,3,2,1,5,8,4,7]=>{{1,4,6,7,8},{2,3},{5}}
[4,3,5,6,2,8,1,7]=>{{1,4,6,7,8},{2,3,5}}
[6,3,5,2,7,8,4,1]=>{{1,6,8},{2,3,4,5,7}}
[4,5,3,1,6,8,2,7]=>{{1,4},{2,5,6,7,8},{3}}
[3,4,6,7,5,1,8,2]=>{{1,3,6},{2,4,7,8},{5}}
[7,4,1,2,5,6,8,3]=>{{1,3,7,8},{2,4},{5},{6}}
[4,8,2,6,7,1,5,3]=>{{1,4,6},{2,3,8},{5,7}}
[6,5,8,3,7,1,4,2]=>{{1,6},{2,3,4,5,7,8}}
[1,5,2,4,7,6,8,3]=>{{1},{2,3,5,7,8},{4},{6}}
[2,5,4,7,1,8,3,6]=>{{1,2,5},{3,4,7},{6,8}}
[8,1,2,4,6,3,5,7]=>{{1,2,3,5,6,7,8},{4}}
[3,7,8,4,5,6,1,2]=>{{1,2,3,7,8},{4},{5},{6}}
[1,3,8,6,7,4,5,2]=>{{1},{2,3,8},{4,6},{5,7}}
[2,6,5,3,7,1,8,4]=>{{1,2,6},{3,4,5,7,8}}
[5,7,1,3,6,4,8,2]=>{{1,3,4,5,6},{2,7,8}}
[8,2,5,4,1,7,3,6]=>{{1,3,5,6,7,8},{2},{4}}
[8,1,7,6,4,2,3,5]=>{{1,2,4,5,6,8},{3,7}}
[1,8,6,3,7,4,5,2]=>{{1},{2,8},{3,4,6},{5,7}}
[5,7,3,4,2,8,6,1]=>{{1,2,5,6,7,8},{3},{4}}
[5,8,3,4,2,7,6,1]=>{{1,2,5,8},{3},{4},{6,7}}
[7,6,4,2,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[3,5,6,8,2,4,7,1]=>{{1,3,4,6,8},{2,5},{7}}
[4,8,7,3,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[3,7,4,2,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[6,4,8,7,3,2,5,1]=>{{1,2,3,4,5,6,7,8}}
[5,6,2,8,7,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[6,2,8,3,7,4,5,1]=>{{1,3,4,6,8},{2},{5,7}}
[3,7,5,6,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[5,2,3,8,6,1,4,7]=>{{1,5,6},{2},{3},{4,7,8}}
[1,4,3,8,5,6,2,7]=>{{1},{2,4,7,8},{3},{5},{6}}
[7,8,2,6,4,3,5,1]=>{{1,2,3,4,5,6,7,8}}
[4,5,8,7,2,3,6,1]=>{{1,3,4,6,7,8},{2,5}}
[7,8,6,1,4,2,5,3]=>{{1,4,5,7},{2,3,6,8}}
[8,3,6,5,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}
[5,1,3,6,4,2,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[6,1,2,4,7,5,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[8,3,1,4,6,7,2,5]=>{{1,2,3,5,6,7,8},{4}}
[7,8,5,1,2,6,3,4]=>{{1,2,3,4,5,7,8},{6}}
[6,4,5,1,8,7,3,2]=>{{1,2,3,4,5,6,7,8}}
[8,6,2,1,7,3,5,4]=>{{1,4,8},{2,3,6},{5,7}}
[7,8,6,1,4,3,5,2]=>{{1,4,5,7},{2,8},{3,6}}
[4,3,6,2,5,7,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[1,6,5,7,3,4,8,2]=>{{1},{2,4,6,7,8},{3,5}}
[8,2,6,5,1,7,4,3]=>{{1,3,4,5,6,7,8},{2}}
[7,6,4,1,2,5,8,3]=>{{1,3,4,7,8},{2,5,6}}
[2,6,5,4,8,7,1,3]=>{{1,2,6,7},{3,5,8},{4}}
[5,6,7,1,3,2,4,8]=>{{1,3,4,5,7},{2,6},{8}}
[7,1,8,4,3,2,6,5]=>{{1,2,6,7},{3,5,8},{4}}
[1,8,5,2,7,6,4,3]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,6,8,2,5,4,3]=>{{1},{2,3,4,5,6,7,8}}
[1,7,8,6,2,5,4,3]=>{{1},{2,4,5,6,7},{3,8}}
[4,6,5,7,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}
[7,5,3,6,8,4,2,1]=>{{1,2,5,7,8},{3},{4,6}}
[7,2,5,6,4,8,3,1]=>{{1,3,4,5,6,7,8},{2}}
[7,4,6,2,8,5,3,1]=>{{1,3,5,6,7,8},{2,4}}
[1,6,3,4,2,5,8,7]=>{{1},{2,5,6},{3},{4},{7,8}}
[1,5,7,6,2,3,8,4]=>{{1},{2,5},{3,4,6,7,8}}
[1,4,3,7,6,2,5,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[3,7,4,6,8,1,5,2]=>{{1,3,4,6},{2,5,7,8}}
[4,8,3,1,7,6,2,5]=>{{1,4},{2,5,7,8},{3},{6}}
[5,6,1,4,3,8,7,2]=>{{1,3,5},{2,6,8},{4},{7}}
[5,8,6,4,3,1,7,2]=>{{1,3,5,6},{2,8},{4},{7}}
[4,1,3,7,8,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}
[9,1,2,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,2,3,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[7,1,2,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,2,3,4,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[7,1,2,3,4,5,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[6,1,2,3,4,9,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[6,1,2,3,4,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,2,3,4,7,5,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,2,3,4,8,5,6,7]=>{{1,2,3,4,5,7,9},{6,8}}
[8,1,2,3,4,7,5,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[6,1,2,3,4,7,9,5,8]=>{{1,2,3,4,5,6,7,8,9}}
[6,1,2,3,4,9,8,5,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,2,3,4,7,8,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[6,1,2,3,4,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[5,1,2,3,9,4,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[5,1,2,3,8,4,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,2,3,6,4,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,2,3,9,4,5,6,7]=>{{1,2,3,4,6,8},{5,7,9}}
[5,1,2,3,9,8,4,6,7]=>{{1,2,3,4,5,7,9},{6,8}}
[9,1,2,3,6,8,4,5,7]=>{{1,2,3,4,7,9},{5,6,8}}
[5,1,2,3,6,9,8,4,7]=>{{1,2,3,4,5,6,7,8,9}}
[5,1,2,3,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[4,1,2,8,3,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[4,1,2,9,3,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[4,1,2,9,3,8,5,6,7]=>{{1,2,3,4,5,7,9},{6,8}}
[9,1,2,5,3,4,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,2,8,3,4,5,6,7]=>{{1,2,3,5,7,9},{4,6,8}}
[7,1,2,8,3,4,5,9,6]=>{{1,2,3,5,7},{4,6,8,9}}
[4,1,2,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[4,1,2,8,9,3,5,6,7]=>{{1,2,3,4,6,8},{5,7,9}}
[8,1,2,5,9,3,4,6,7]=>{{1,2,3,6,8},{4,5,7,9}}
[8,1,2,9,6,3,4,5,7]=>{{1,2,3,5,6,8},{4,7,9}}
[4,1,2,5,9,8,3,6,7]=>{{1,2,3,4,5,7,9},{6,8}}
[9,1,2,8,6,7,3,4,5]=>{{1,2,3,5,6,7,9},{4,8}}
[4,1,2,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[4,1,2,9,6,7,8,3,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,2,5,6,7,8,3,4]=>{{1,2,3,4,5,6,7,8,9}}
[4,1,2,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,9,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,8,2,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,9,2,4,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,4,2,3,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,4,2,3,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[6,1,4,2,3,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,8,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,7,2,3,4,5,9,6]=>{{1,2,4,6,8,9},{3,5,7}}
[3,1,4,9,2,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,4,9,2,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,9,8,2,4,5,6,7]=>{{1,2,3,5,7,9},{4,6,8}}
[9,1,4,5,2,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[7,1,4,5,2,3,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[7,1,4,9,2,3,5,6,8]=>{{1,2,5,7},{3,4,6,8,9}}
[9,1,4,8,2,3,5,6,7]=>{{1,2,5,7,9},{3,4,6,8}}
[9,1,6,5,2,3,4,7,8]=>{{1,2,4,5,7,8,9},{3,6}}
[7,1,9,6,2,3,4,5,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,8,6,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8,9}}
[7,1,8,9,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,4,8,9,2,5,6,7]=>{{1,2,3,4,6,8},{5,7,9}}
[3,1,8,9,7,2,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,4,5,6,2,3,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,4,9,7,2,3,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,9,5,6,2,3,4,7]=>{{1,2,4,5,6,8},{3,7,9}}
[8,1,9,7,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[7,1,4,5,6,2,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,4,5,6,9,2,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,4,9,8,7,2,5,6]=>{{1,2,3,4,6,7,9},{5,8}}
[3,1,9,8,6,7,2,4,5]=>{{1,2,3,5,6,7,9},{4,8}}
[9,1,4,5,6,7,2,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,4,8,6,7,2,3,5]=>{{1,2,5,6,7,9},{3,4,8}}
[9,1,8,5,6,7,2,3,4]=>{{1,2,4,5,6,7,9},{3,8}}
[8,1,4,5,6,7,2,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,4,5,6,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,4,9,6,7,8,2,5]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,9,5,6,7,8,2,4]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,4,5,6,7,8,2,3]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,4,5,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,1,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,8,1,3,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,7,1,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,1,3,4,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,7,1,3,4,5,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[2,6,1,3,4,9,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,1,3,4,8,5,6,7]=>{{1,2,3,4,5,7,9},{6,8}}
[2,8,1,3,9,4,5,6,7]=>{{1,2,3,4,6,8},{5,7,9}}
[2,9,1,3,8,7,4,5,6]=>{{1,2,3,4,6,7,9},{5,8}}
[2,9,1,3,6,7,8,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[2,5,1,3,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,1,8,3,4,5,6,7]=>{{1,2,3,5,7,9},{4,6,8}}
[2,7,1,6,3,4,8,9,5]=>{{1,2,3,5,7,8,9},{4,6}}
[2,6,1,5,3,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,4,1,8,9,3,5,6,7]=>{{1,2,3,4,6,8},{5,7,9}}
[2,8,1,9,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,1,8,6,7,3,4,5]=>{{1,2,3,5,6,7,9},{4,8}}
[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,4,1,5,6,9,8,3,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,1,5,6,7,8,3,4]=>{{1,2,3,4,5,6,7,8,9}}
[2,4,1,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,1,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[8,3,1,2,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,1,2,4,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[6,3,1,2,4,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,1,2,6,7,8,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[5,3,1,2,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[9,4,1,2,3,5,6,7,8]=>{{1,3,5,6,7,8,9},{2,4}}
[7,4,1,2,3,5,8,9,6]=>{{1,3,5,6,7,8,9},{2,4}}
[6,4,1,2,3,7,8,9,5]=>{{1,3,5,6,7,8,9},{2,4}}
[5,9,1,2,3,4,6,7,8]=>{{1,3,5},{2,4,6,7,8,9}}
[5,8,1,2,3,4,6,9,7]=>{{1,3,5},{2,4,6,7,8,9}}
[5,7,1,2,3,4,8,9,6]=>{{1,3,5},{2,4,6,7,8,9}}
[9,6,1,2,3,4,5,7,8]=>{{1,3,5,7,8,9},{2,4,6}}
[8,6,1,2,3,4,5,9,7]=>{{1,3,5,7,8,9},{2,4,6}}
[9,7,1,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[8,9,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[8,7,1,2,3,4,5,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[7,6,1,2,3,4,9,5,8]=>{{1,3,5,7,8,9},{2,4,6}}
[9,6,1,2,3,4,8,5,7]=>{{1,3,5,7,8,9},{2,4,6}}
[9,7,1,2,3,4,8,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[7,6,1,2,3,4,8,9,5]=>{{1,3,5,7,8,9},{2,4,6}}
[5,6,1,2,3,9,4,7,8]=>{{1,3,5},{2,4,6,7,8,9}}
[5,9,1,2,3,8,4,6,7]=>{{1,3,5},{2,4,7,9},{6,8}}
[9,6,1,2,3,7,4,5,8]=>{{1,3,5,8,9},{2,4,6,7}}
[9,8,1,2,3,7,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[8,6,1,2,3,7,4,9,5]=>{{1,3,5,8,9},{2,4,6,7}}
[5,6,1,2,3,7,9,4,8]=>{{1,3,5},{2,4,6,7,8,9}}
[9,6,1,2,3,7,8,4,5]=>{{1,3,5,9},{2,4,6,7,8}}
[5,6,1,2,3,7,8,9,4]=>{{1,3,5},{2,4,6,7,8,9}}
[5,4,1,2,9,3,6,7,8]=>{{1,3,5,6,7,8,9},{2,4}}
[8,4,1,2,9,3,5,6,7]=>{{1,3,6,8},{2,4},{5,7,9}}
[5,9,1,2,6,3,4,7,8]=>{{1,3,5,6},{2,4,7,8,9}}
[5,8,1,2,9,3,4,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,7,1,2,6,3,8,4,5]=>{{1,3,5,6,9},{2,4,7,8}}
[5,4,1,2,6,9,3,7,8]=>{{1,3,5,6,7,8,9},{2,4}}
[9,8,1,2,6,7,3,4,5]=>{{1,3,5,6,7,9},{2,4,8}}
[5,4,1,2,6,7,9,3,8]=>{{1,3,5,6,7,8,9},{2,4}}
[5,4,1,2,6,7,8,9,3]=>{{1,3,5,6,7,8,9},{2,4}}
[4,3,1,9,2,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,1,8,2,4,5,6,7]=>{{1,2,3,5,7,9},{4,6,8}}
[9,4,1,5,2,3,6,7,8]=>{{1,3,6,7,8,9},{2,4,5}}
[9,4,1,8,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[6,9,1,5,2,3,4,7,8]=>{{1,3,6},{2,4,5,7,8,9}}
[9,7,1,6,2,3,4,5,8]=>{{1,2,3,4,5,6,7,8,9}}
[8,7,1,9,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[8,7,1,6,2,3,4,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,4,1,6,2,8,3,5,7]=>{{1,3,7,9},{2,4,5,6,8}}
[9,8,1,6,2,7,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[4,3,1,5,9,2,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,1,7,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[4,3,1,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[4,3,1,5,9,8,2,6,7]=>{{1,2,3,4,5,7,9},{6,8}}
[4,3,1,5,8,7,2,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[8,9,1,5,6,7,2,3,4]=>{{1,3,8},{2,4,5,6,7,9}}
[4,3,1,5,6,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[4,3,1,5,6,9,8,2,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,1,5,6,7,8,2,4]=>{{1,2,3,4,5,6,7,8,9}}
[9,4,1,5,6,7,8,2,3]=>{{1,3,9},{2,4,5,6,7,8}}
[4,3,1,5,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,1,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,8,1,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,1,4,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,1,4,7,8,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,1,8,7,4,5,6]=>{{1,2,3,4,6,7,9},{5,8}}
[2,3,8,1,6,7,4,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,1,6,7,8,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,4,1,3,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,6,4,1,3,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,5,1,3,4,6,7,8]=>{{1,2,4,6,7,8,9},{3,5}}
[2,6,9,1,3,4,5,7,8]=>{{1,2,4,6},{3,5,7,8,9}}
[2,9,7,1,3,4,5,6,8]=>{{1,2,4,6,8,9},{3,5,7}}
[2,9,8,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,6,7,1,3,4,8,9,5]=>{{1,2,4,6},{3,5,7,8,9}}
[2,9,4,1,6,3,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,8,4,1,9,3,5,6,7]=>{{1,2,3,4,6,8},{5,7,9}}
[2,9,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,8,1,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,5,1,6,7,8,3,4]=>{{1,2,4,9},{3,5,6,7,8}}
[9,3,4,1,2,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[6,3,4,1,2,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,7,1,2,4,5,6,8]=>{{1,4,6,8,9},{2,3,5,7}}
[9,3,8,1,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,5,4,1,2,3,6,7,8]=>{{1,3,4,6,7,8,9},{2,5}}
[8,5,4,1,2,3,6,9,7]=>{{1,3,4,6,7,8,9},{2,5}}
[6,9,4,1,2,3,5,7,8]=>{{1,3,4,6},{2,5,7,8,9}}
[6,8,4,1,2,3,5,9,7]=>{{1,3,4,6},{2,5,7,8,9}}
[9,7,4,1,2,3,5,6,8]=>{{1,3,4,6,8,9},{2,5,7}}
[9,8,4,1,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[6,9,5,1,2,3,4,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[6,8,5,1,2,3,4,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[8,7,5,1,2,3,4,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[6,7,9,1,2,3,4,5,8]=>{{1,2,3,4,5,6,7,8,9}}
[6,9,8,1,2,3,4,5,7]=>{{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}}
[6,7,8,1,2,3,4,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[6,5,4,1,2,8,3,9,7]=>{{1,3,4,6,7,8,9},{2,5}}
[9,8,5,1,7,2,3,4,6]=>{{1,2,4,6,8,9},{3,5,7}}
[7,8,9,1,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[7,8,5,1,6,2,3,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[5,3,4,1,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,4,1,8,7,2,5,6]=>{{1,2,3,4,6,7,9},{5,8}}
[8,3,4,1,6,7,2,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,5,4,1,8,7,2,3,6]=>{{1,2,3,4,5,6,7,8,9}}
[8,5,4,1,6,7,2,9,3]=>{{1,3,4,8,9},{2,5,6,7}}
[5,3,4,1,9,7,8,2,6]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,5,1,6,7,8,2,4]=>{{1,4,9},{2,3,5,6,7,8}}
[9,5,4,1,6,7,8,2,3]=>{{1,3,4,9},{2,5,6,7,8}}
[5,3,4,1,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,9,1,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,9,1,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,9,1,7,8,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,5,1,4,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,6,1,4,5,7,8]=>{{1,2,3,5,7,8,9},{4,6}}
[2,3,7,9,1,4,5,6,8]=>{{1,2,3,5,7},{4,6,8,9}}
[2,3,9,8,1,4,5,6,7]=>{{1,2,3,5,7,9},{4,6,8}}
[2,3,9,5,1,7,4,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,6,1,7,8,4,5]=>{{1,2,3,5,9},{4,6,7,8}}
[2,9,4,5,1,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,7,4,5,1,3,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,8,6,1,3,4,5,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,7,8,9,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[2,8,9,6,1,7,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,6,5,1,7,8,3,4]=>{{1,2,4,5,9},{3,6,7,8}}
[7,3,4,5,1,2,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,4,8,1,2,5,6,7]=>{{1,5,7,9},{2,3,4,6,8}}
[7,3,4,8,1,2,5,9,6]=>{{1,5,7},{2,3,4,6,8,9}}
[7,3,8,9,1,2,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,4,5,1,2,3,6,7]=>{{1,3,4,5,7,9},{2,6,8}}
[7,8,4,6,1,2,3,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,6,5,1,2,3,4,7]=>{{1,2,3,4,5,6,7,8,9}}
[7,8,9,6,1,2,3,4,5]=>{{1,3,5,7,9},{2,4,6,8}}
[7,8,6,5,1,2,3,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[8,3,9,6,1,7,2,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[8,3,6,5,1,7,2,9,4]=>{{1,4,5,8,9},{2,3,6,7}}
[8,6,4,5,1,7,2,9,3]=>{{1,3,4,5,8,9},{2,6,7}}
[6,3,4,5,1,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[6,3,4,5,1,9,8,2,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,4,6,1,7,8,2,5]=>{{1,5,9},{2,3,4,6,7,8}}
[6,3,4,5,1,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,9,1,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,8,1,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,9,1,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,9,6,1,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,9,7,1,5,6,8]=>{{1,2,3,4,6,8,9},{5,7}}
[2,3,4,9,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,9,7,1,8,5,6]=>{{1,2,3,4,6,9},{5,7,8}}
[2,3,9,5,6,1,4,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,8,5,6,1,4,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,5,6,1,8,4,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,8,4,5,6,1,3,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,8,9,5,7,1,3,4,6]=>{{1,2,3,4,5,6,7,8,9}}
[2,8,9,7,6,1,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,7,5,6,1,8,3,4]=>{{1,2,4,5,6,9},{3,7,8}}
[8,3,4,5,6,1,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[8,3,4,7,6,1,2,9,5]=>{{1,5,6,8,9},{2,3,4,7}}
[8,3,9,7,6,1,2,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[8,3,7,5,6,1,2,9,4]=>{{1,4,5,6,8,9},{2,3,7}}
[9,7,4,5,6,1,2,3,8]=>{{1,3,4,5,6,8,9},{2,7}}
[8,9,4,5,6,1,2,3,7]=>{{1,3,4,5,6,8},{2,7,9}}
[8,9,7,5,6,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9}}
[8,7,4,5,6,1,2,9,3]=>{{1,3,4,5,6,8,9},{2,7}}
[7,3,4,5,6,1,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,4,5,6,1,8,2,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,7,5,6,1,8,2,4]=>{{1,4,5,6,9},{2,3,7,8}}
[7,3,4,5,6,1,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,6,9,1,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,9,7,1,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,9,8,1,6,7]=>{{1,2,3,4,5,7,9},{6,8}}
[2,3,4,9,6,7,1,5,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,5,6,7,1,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,5,6,8,1,4,7]=>{{1,2,3,7,9},{4,5,6,8}}
[2,9,4,5,6,7,1,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,4,5,6,8,1,3,7]=>{{1,2,7,9},{3,4,5,6,8}}
[2,9,4,5,8,7,1,3,6]=>{{1,2,6,7,9},{3,4,5,8}}
[2,9,4,8,6,7,1,3,5]=>{{1,2,5,6,7,9},{3,4,8}}
[2,9,8,5,6,7,1,3,4]=>{{1,2,4,5,6,7,9},{3,8}}
[2,8,4,5,6,7,1,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,4,5,6,7,1,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,4,5,6,8,1,2,7]=>{{1,7,9},{2,3,4,5,6,8}}
[9,8,4,5,6,7,1,2,3]=>{{1,3,4,5,6,7,9},{2,8}}
[8,3,4,5,6,7,1,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,6,9,8,1,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,9,7,8,1,6]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,9,6,7,8,1,5]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,9,5,6,7,8,1,4]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,4,5,6,7,8,1,3]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,4,5,6,7,8,1,2]=>{{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}}
[2,3,4,5,6,7,8,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[2,3,4,5,6,8,9,1,7]=>{{1,2,3,4,5,6,8},{7,9}}
[2,3,4,5,7,8,9,1,6]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,6,7,8,9,1,5]=>{{1,2,3,4,6,8},{5,7,9}}
[2,3,5,6,7,8,9,1,4]=>{{1,2,3,4,5,6,7,8,9}}
[2,4,5,6,7,8,9,1,3]=>{{1,2,4,6,8},{3,5,7,9}}
[3,4,5,6,7,8,9,1,2]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,6,7,1,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[2,3,4,5,6,1,9,7,8]=>{{1,2,3,4,5,6},{7,8,9}}
[2,3,4,5,1,8,9,6,7]=>{{1,2,3,4,5},{6,8},{7,9}}
[2,3,4,1,7,8,9,5,6]=>{{1,2,3,4},{5,6,7,8,9}}
[2,3,1,6,7,8,9,4,5]=>{{1,2,3},{4,6,8},{5,7,9}}
[2,1,5,6,7,8,9,3,4]=>{{1,2},{3,4,5,6,7,8,9}}
[1,4,5,6,7,8,9,2,3]=>{{1},{2,4,6,8},{3,5,7,9}}
[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]=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}
[1,8,2,3,4,5,6,9,7]=>{{1},{2,3,4,5,6,7,8,9}}
[7,1,2,3,4,5,6,9,8]=>{{1,2,3,4,5,6,7},{8,9}}
[2,1,9,3,4,5,6,7,8]=>{{1,2},{3,4,5,6,7,8,9}}
[2,8,1,3,4,5,6,7,9]=>{{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},{7,8,9}}
[1,2,3,4,5,7,8,9,6]=>{{1},{2},{3},{4},{5},{6,7,8,9}}
[1,2,3,4,6,7,8,9,5]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[1,2,3,5,6,7,8,9,4]=>{{1},{2},{3},{4,5,6,7,8,9}}
[1,2,4,5,6,7,8,9,3]=>{{1},{2},{3,4,5,6,7,8,9}}
[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[1,2,3,4,5,6,9,8,7]=>{{1},{2},{3},{4},{5},{6},{7,9},{8}}
[1,2,3,4,5,8,7,9,6]=>{{1},{2},{3},{4},{5},{6,8,9},{7}}
[1,2,3,4,7,6,8,9,5]=>{{1},{2},{3},{4},{5,7,8,9},{6}}
[1,2,3,6,5,7,8,9,4]=>{{1},{2},{3},{4,6,7,8,9},{5}}
[1,2,5,4,6,7,8,9,3]=>{{1},{2},{3,5,6,7,8,9},{4}}
[1,4,3,5,6,7,8,9,2]=>{{1},{2,4,5,6,7,8,9},{3}}
[3,2,4,5,6,7,8,9,1]=>{{1,3,4,5,6,7,8,9},{2}}
[9,8,7,6,5,4,3,2,1]=>{{1,9},{2,8},{3,7},{4,6},{5}}
[8,9,7,6,5,4,3,2,1]=>{{1,2,8,9},{3,7},{4,6},{5}}
[8,7,9,6,5,4,3,2,1]=>{{1,2,3,7,8,9},{4,6},{5}}
[8,7,6,9,5,4,3,2,1]=>{{1,2,3,4,6,7,8,9},{5}}
[8,7,6,5,9,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[8,7,6,5,4,9,3,2,1]=>{{1,2,3,6,7,8,9},{4,5}}
[8,7,6,5,4,3,9,2,1]=>{{1,2,7,8,9},{3,6},{4,5}}
[8,7,6,5,4,3,2,9,1]=>{{1,8,9},{2,7},{3,6},{4,5}}
[8,7,6,5,4,3,2,1,9]=>{{1,8},{2,7},{3,6},{4,5},{9}}
[7,8,9,6,5,4,3,2,1]=>{{1,3,7,9},{2,8},{4,6},{5}}
[8,6,7,9,5,4,3,2,1]=>{{1,2,4,6,8,9},{3,7},{5}}
[8,7,5,6,9,4,3,2,1]=>{{1,2,3,5,7,8,9},{4,6}}
[8,7,6,4,5,9,3,2,1]=>{{1,2,3,6,7,8,9},{4},{5}}
[8,7,6,5,3,4,9,2,1]=>{{1,2,7,8,9},{3,4,5,6}}
[8,7,6,5,4,2,3,9,1]=>{{1,8,9},{2,3,6,7},{4,5}}
[8,7,6,5,4,3,1,2,9]=>{{1,2,7,8},{3,6},{4,5},{9}}
[1,9,8,7,6,5,4,3,2]=>{{1},{2,9},{3,8},{4,7},{5,6}}
[8,7,6,4,5,3,2,1,9]=>{{1,8},{2,7},{3,6},{4},{5},{9}}
[1,9,8,7,5,6,4,3,2]=>{{1},{2,9},{3,8},{4,7},{5},{6}}
[8,7,5,4,6,3,2,1,9]=>{{1,8},{2,7},{3,5,6},{4},{9}}
[8,7,4,6,5,3,2,1,9]=>{{1,8},{2,7},{3,4,6},{5},{9}}
[1,9,8,6,5,7,4,3,2]=>{{1},{2,9},{3,8},{4,6,7},{5}}
[1,9,8,5,7,6,4,3,2]=>{{1},{2,9},{3,8},{4,5,7},{6}}
[9,2,1,3,4,5,6,7,8]=>{{1,3,4,5,6,7,8,9},{2}}
[9,2,3,1,4,5,6,7,8]=>{{1,4,5,6,7,8,9},{2},{3}}
[4,2,3,5,6,7,8,9,1]=>{{1,4,5,6,7,8,9},{2},{3}}
[3,4,2,5,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[1,2,3,4,5,6,9,7,8]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,2,3,4,5,8,6,9,7]=>{{1},{2},{3},{4},{5},{6,7,8,9}}
[1,2,3,4,7,5,8,9,6]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[1,2,3,6,4,7,8,9,5]=>{{1},{2},{3},{4,5,6,7,8,9}}
[1,2,5,3,6,7,8,9,4]=>{{1},{2},{3,4,5,6,7,8,9}}
[1,4,2,5,6,7,8,9,3]=>{{1},{2,3,4,5,6,7,8,9}}
[9,8,1,2,3,4,5,6,7]=>{{1,3,5,7,9},{2,4,6,8}}
[7,8,9,1,2,3,4,5,6]=>{{1,4,7},{2,5,8},{3,6,9}}
[9,8,7,1,2,3,4,5,6]=>{{1,3,4,6,7,9},{2,5,8}}
[6,7,8,9,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,6,7,8,1,2,3,4,5]=>{{1,5,9},{2,6},{3,7},{4,8}}
[8,9,6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,6,7,1,2,3,4,5]=>{{1,5,9},{2,3,4,6,7,8}}
[9,8,7,6,1,2,3,4,5]=>{{1,5,9},{2,4,6,8},{3,7}}
[9,5,6,7,8,1,2,3,4]=>{{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}}
[9,8,5,6,7,1,2,3,4]=>{{1,4,6,9},{2,3,5,7,8}}
[9,7,8,5,6,1,2,3,4]=>{{1,4,5,6,9},{2,7},{3,8}}
[9,8,7,5,6,1,2,3,4]=>{{1,4,5,6,9},{2,3,7,8}}
[9,8,7,6,5,1,2,3,4]=>{{1,4,6,9},{2,3,7,8},{5}}
[7,8,9,4,5,6,1,2,3]=>{{1,7},{2,8},{3,9},{4},{5},{6}}
[9,7,8,4,5,6,1,2,3]=>{{1,2,3,7,8,9},{4},{5},{6}}
[9,8,7,4,5,6,1,2,3]=>{{1,3,7,9},{2,8},{4},{5},{6}}
[8,9,6,7,4,5,1,2,3]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,6,7,4,5,1,2,3]=>{{1,3,4,5,6,7,9},{2,8}}
[9,8,7,6,4,5,1,2,3]=>{{1,3,7,9},{2,8},{4,5,6}}
[9,8,7,6,5,4,1,2,3]=>{{1,3,7,9},{2,8},{4,6},{5}}
[9,7,8,5,6,3,4,1,2]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,7,5,6,3,4,1,2]=>{{1,2,8,9},{3,4,5,6,7}}
[9,8,7,6,5,3,4,1,2]=>{{1,2,8,9},{3,4,6,7},{5}}
[9,8,7,6,5,4,3,1,2]=>{{1,2,8,9},{3,7},{4,6},{5}}
[7,8,6,5,4,3,2,1,9]=>{{1,2,7,8},{3,6},{4,5},{9}}
[1,8,9,7,6,5,4,3,2]=>{{1},{2,3,8,9},{4,7},{5,6}}
[7,6,8,5,4,3,2,1,9]=>{{1,2,3,6,7,8},{4,5},{9}}
[6,8,7,5,4,3,2,1,9]=>{{1,2,3,6,7,8},{4,5},{9}}
[1,8,7,9,6,5,4,3,2]=>{{1},{2,3,4,7,8,9},{5,6}}
[1,7,9,8,6,5,4,3,2]=>{{1},{2,3,4,7,8,9},{5,6}}
[8,1,2,3,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[1,9,2,3,4,5,6,7,8]=>{{1},{2,3,4,5,6,7,8,9}}
[7,8,1,2,3,4,5,6,9]=>{{1,3,5,7},{2,4,6,8},{9}}
[1,8,9,2,3,4,5,6,7]=>{{1},{2,4,6,8},{3,5,7,9}}
[7,1,8,2,3,4,5,6,9]=>{{1,2,3,4,5,6,7,8},{9}}
[6,8,1,2,3,4,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[1,8,2,9,3,4,5,6,7]=>{{1},{2,3,4,5,6,7,8,9}}
[1,7,9,2,3,4,5,6,8]=>{{1},{2,3,4,5,6,7,8,9}}
[2,1,4,3,6,5,8,7,9]=>{{1,2},{3,4},{5,6},{7,8},{9}}
[2,4,1,3,6,5,8,7,9]=>{{1,2,3,4},{5,6},{7,8},{9}}
[2,4,1,6,3,5,8,7,9]=>{{1,2,3,4,5,6},{7,8},{9}}
[2,4,1,6,3,8,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[2,4,1,6,3,7,5,9,8]=>{{1,2,3,4,5,6,7},{8,9}}
[2,4,1,5,3,7,6,9,8]=>{{1,2,3,4,5},{6,7},{8,9}}
[2,3,1,5,4,7,6,9,8]=>{{1,2,3},{4,5},{6,7},{8,9}}
[1,3,2,5,4,7,6,9,8]=>{{1},{2,3},{4,5},{6,7},{8,9}}
[2,4,6,1,3,5,8,7,9]=>{{1,2,4},{3,5,6},{7,8},{9}}
[2,4,1,6,8,3,5,7,9]=>{{1,2,3,4,6},{5,7,8},{9}}
[2,4,1,6,3,8,9,5,7]=>{{1,2,3,4,5,6,8},{7,9}}
[2,4,1,6,3,7,5,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[2,4,1,5,3,8,6,9,7]=>{{1,2,3,4,5},{6,7,8,9}}
[2,3,1,6,4,7,5,9,8]=>{{1,2,3},{4,5,6,7},{8,9}}
[1,4,2,5,3,7,6,9,8]=>{{1},{2,3,4,5},{6,7},{8,9}}
[7,1,2,3,4,5,6,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[3,4,1,2,5,6,7,8,9]=>{{1,3},{2,4},{5},{6},{7},{8},{9}}
[3,2,1,4,5,6,7,8,9]=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}
[4,5,6,1,2,3,7,8,9]=>{{1,4},{2,5},{3,6},{7},{8},{9}}
[4,2,5,1,3,6,7,8,9]=>{{1,4},{2},{3,5},{6},{7},{8},{9}}
[4,3,2,1,5,6,7,8,9]=>{{1,4},{2,3},{5},{6},{7},{8},{9}}
[5,6,7,8,1,2,3,4,9]=>{{1,5},{2,6},{3,7},{4,8},{9}}
[5,2,6,7,1,3,4,8,9]=>{{1,5},{2},{3,6},{4,7},{8},{9}}
[5,6,3,4,1,2,7,8,9]=>{{1,5},{2,6},{3},{4},{7},{8},{9}}
[5,3,2,6,1,4,7,8,9]=>{{1,5},{2,3},{4,6},{7},{8},{9}}
[5,4,3,2,1,6,7,8,9]=>{{1,5},{2,4},{3},{6},{7},{8},{9}}
[6,2,7,8,9,1,3,4,5]=>{{1,6},{2},{3,7},{4,8},{5,9}}
[6,7,3,4,8,1,2,5,9]=>{{1,6},{2,7},{3},{4},{5,8},{9}}
[6,3,2,7,8,1,4,5,9]=>{{1,6},{2,3},{4,7},{5,8},{9}}
[6,4,7,2,5,1,3,8,9]=>{{1,6},{2,4},{3,7},{5},{8},{9}}
[6,4,3,2,7,1,5,8,9]=>{{1,6},{2,4},{3},{5,7},{8},{9}}
[6,5,4,3,2,1,7,8,9]=>{{1,6},{2,5},{3,4},{7},{8},{9}}
[7,4,8,2,5,9,1,3,6]=>{{1,7},{2,4},{3,8},{5},{6,9}}
[7,4,3,2,8,9,1,5,6]=>{{1,7},{2,4},{3},{5,8},{6,9}}
[7,8,5,6,3,4,1,2,9]=>{{1,7},{2,8},{3,5},{4,6},{9}}
[7,5,3,8,2,6,1,4,9]=>{{1,7},{2,5},{3},{4,8},{6},{9}}
[7,5,4,3,2,8,1,6,9]=>{{1,7},{2,5},{3,4},{6,8},{9}}
[7,6,5,4,3,2,1,8,9]=>{{1,7},{2,6},{3,5},{4},{8},{9}}
[8,6,9,4,7,2,5,1,3]=>{{1,8},{2,6},{3,9},{4},{5,7}}
[8,6,4,3,9,2,7,1,5]=>{{1,8},{2,6},{3,4},{5,9},{7}}
[8,6,5,4,3,2,9,1,7]=>{{1,8},{2,6},{3,5},{4},{7,9}}
[2,3,1,4,5,6,7,8,9]=>{{1,2,3},{4},{5},{6},{7},{8},{9}}
[2,3,4,1,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[2,3,4,5,1,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[2,3,4,5,6,1,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[2,4,3,1,5,6,7,8,9]=>{{1,2,4},{3},{5},{6},{7},{8},{9}}
[2,3,5,4,1,6,7,8,9]=>{{1,2,3,5},{4},{6},{7},{8},{9}}
[2,3,4,6,5,1,7,8,9]=>{{1,2,3,4,6},{5},{7},{8},{9}}
[2,3,4,5,7,6,1,8,9]=>{{1,2,3,4,5,7},{6},{8},{9}}
[2,3,4,5,6,8,7,1,9]=>{{1,2,3,4,5,6,8},{7},{9}}
[2,3,4,5,6,7,9,8,1]=>{{1,2,3,4,5,6,7,9},{8}}
[3,4,1,5,6,7,8,9,2]=>{{1,3},{2,4,5,6,7,8,9}}
[3,4,5,1,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[3,4,5,6,1,7,8,9,2]=>{{1,3,5},{2,4,6,7,8,9}}
[3,4,5,6,7,1,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[3,4,5,6,7,8,1,9,2]=>{{1,3,5,7},{2,4,6,8,9}}
[3,1,2,5,6,7,8,9,4]=>{{1,2,3},{4,5,6,7,8,9}}
[3,4,1,2,6,7,8,9,5]=>{{1,3},{2,4},{5,6,7,8,9}}
[3,4,5,1,2,7,8,9,6]=>{{1,2,3,4,5},{6,7,8,9}}
[3,4,5,6,1,2,8,9,7]=>{{1,3,5},{2,4,6},{7,8,9}}
[3,4,5,6,7,1,2,9,8]=>{{1,2,3,4,5,6,7},{8,9}}
[3,4,5,6,7,8,1,2,9]=>{{1,3,5,7},{2,4,6,8},{9}}
[8,7,6,5,4,3,1,9,2]=>{{1,2,7,8,9},{3,6},{4,5}}
[7,9,6,5,4,3,2,1,8]=>{{1,2,7,8,9},{3,6},{4,5}}
[1,7,6,5,4,3,9,8,2]=>{{1},{2,7,9},{3,6},{4,5},{8}}
[1,9,6,5,4,3,2,8,7]=>{{1},{2,7,9},{3,6},{4,5},{8}}
[8,1,6,5,4,3,9,7,2]=>{{1,2,7,8,9},{3,6},{4,5}}
[3,7,6,5,4,9,1,8,2]=>{{1,2,3,6,7,9},{4,5},{8}}
[7,9,1,5,4,3,2,8,6]=>{{1,2,3,6,7,9},{4,5},{8}}
[2,9,6,5,4,3,8,1,7]=>{{1,2,7,8,9},{3,6},{4,5}}
[8,7,1,5,4,3,9,6,2]=>{{1,3,6,8},{2,7,9},{4,5}}
[1,3,6,5,4,9,8,7,2]=>{{1},{2,3,6,9},{4,5},{7,8}}
[4,7,6,5,9,3,1,8,2]=>{{1,2,4,5,7,9},{3,6},{8}}
[7,9,6,1,4,3,2,8,5]=>{{1,2,4,5,7,9},{3,6},{8}}
[1,9,2,5,4,3,8,7,6]=>{{1},{2,3,6,9},{4,5},{7,8}}
[3,9,6,5,4,8,2,1,7]=>{{1,3,6,8},{2,7,9},{4,5}}
[7,9,6,5,4,3,2,8,1]=>{{1,2,7,9},{3,6},{4,5},{8}}
[8,9,6,5,4,3,2,1,7]=>{{1,8},{2,7,9},{3,6},{4,5}}
[8,7,6,5,4,3,9,1,2]=>{{1,8},{2,7,9},{3,6},{4,5}}
[9,7,6,5,4,3,1,8,2]=>{{1,2,7,9},{3,6},{4,5},{8}}
[7,9,8,6,5,4,3,2,1]=>{{1,2,3,7,8,9},{4,6},{5}}
[6,9,8,7,5,4,3,2,1]=>{{1,2,3,4,6,7,8,9},{5}}
[5,9,8,7,6,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[4,9,8,7,6,5,3,2,1]=>{{1,2,3,4,7,8,9},{5,6}}
[3,9,8,7,6,5,4,2,1]=>{{1,2,3,8,9},{4,7},{5,6}}
[2,9,8,7,6,5,4,3,1]=>{{1,2,9},{3,8},{4,7},{5,6}}
[6,9,7,8,5,4,3,2,1]=>{{1,2,4,6,8,9},{3,7},{5}}
[5,9,8,6,7,4,3,2,1]=>{{1,2,3,5,7,8,9},{4,6}}
[4,9,8,7,5,6,3,2,1]=>{{1,2,3,4,7,8,9},{5},{6}}
[3,9,8,7,6,4,5,2,1]=>{{1,2,3,8,9},{4,5,6,7}}
[2,9,8,7,6,5,3,4,1]=>{{1,2,9},{3,4,7,8},{5,6}}
[1,9,8,7,6,5,4,2,3]=>{{1},{2,3,8,9},{4,7},{5,6}}
[1,2,3,4,5,9,6,7,8]=>{{1},{2},{3},{4},{5},{6,7,8,9}}
[1,2,3,4,9,5,6,7,8]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[1,2,3,9,4,5,6,7,8]=>{{1},{2},{3},{4,5,6,7,8,9}}
[1,2,9,3,4,5,6,7,8]=>{{1},{2},{3,4,5,6,7,8,9}}
[1,2,3,4,5,9,7,6,8]=>{{1},{2},{3},{4},{5},{6,8,9},{7}}
[1,2,3,4,9,6,5,7,8]=>{{1},{2},{3},{4},{5,7,8,9},{6}}
[1,2,3,9,5,4,6,7,8]=>{{1},{2},{3},{4,6,7,8,9},{5}}
[1,2,9,4,3,5,6,7,8]=>{{1},{2},{3,5,6,7,8,9},{4}}
[1,9,3,2,4,5,6,7,8]=>{{1},{2,4,5,6,7,8,9},{3}}
[7,6,9,8,5,4,3,2,1]=>{{1,3,7,9},{2,4,6,8},{5}}
[6,5,4,9,8,7,3,2,1]=>{{1,3,4,6,7,9},{2,5,8}}
[6,8,5,9,7,4,3,2,1]=>{{1,4,6,9},{2,8},{3,5,7}}
[6,7,8,9,5,4,3,2,1]=>{{1,4,6,9},{2,3,7,8},{5}}
[5,4,3,2,9,8,7,6,1]=>{{1,5,9},{2,4},{3},{6,8},{7}}
[5,8,4,3,9,7,6,2,1]=>{{1,5,9},{2,8},{3,4},{6,7}}
[5,4,7,6,9,8,3,2,1]=>{{1,5,9},{2,4,6,8},{3,7}}
[5,7,8,4,9,6,3,2,1]=>{{1,5,9},{2,3,7,8},{4},{6}}
[5,6,7,8,9,4,3,2,1]=>{{1,5,9},{2,4,6,8},{3,7}}
[4,8,3,2,1,9,7,6,5]=>{{1,2,4,5,6,8,9},{3},{7}}
[4,3,7,6,2,9,8,5,1]=>{{1,4,6,9},{2,3,5,7,8}}
[4,7,8,3,2,9,6,5,1]=>{{1,2,3,4,5,6,7,8,9}}
[4,6,3,8,5,9,7,2,1]=>{{1,2,4,6,8,9},{3},{5},{7}}
[4,6,7,8,3,9,5,2,1]=>{{1,2,4,6,8,9},{3,5,7}}
[4,5,6,7,8,9,3,2,1]=>{{1,3,4,6,7,9},{2,5,8}}
[3,2,1,6,5,4,9,8,7]=>{{1,3},{2},{4,6},{5},{7,9},{8}}
[3,6,2,8,5,1,9,7,4]=>{{1,2,3,6},{4,7,8,9},{5}}
[3,6,7,8,2,1,9,5,4]=>{{1,2,3,4,5,6,7,8,9}}
[3,2,5,4,7,6,9,8,1]=>{{1,3,5,7,9},{2},{4},{6},{8}}
[3,5,7,2,8,4,9,6,1]=>{{1,3,7,9},{2,4,5,6,8}}
[3,5,6,7,8,2,9,4,1]=>{{1,2,3,4,5,6,7,8,9}}
[3,4,5,6,7,8,9,2,1]=>{{1,3,5,7,9},{2,4,6,8}}
[2,4,6,7,1,8,3,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[2,4,5,6,7,8,1,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[3,1,2,4,5,6,7,8,9]=>{{1,2,3},{4},{5},{6},{7},{8},{9}}
[2,4,1,3,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[2,3,5,1,4,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[2,3,4,6,1,5,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[2,3,4,5,7,1,6,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[2,3,4,5,6,8,1,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[7,6,5,4,3,2,9,1,8]=>{{1,7,8,9},{2,6},{3,5},{4}}
[6,5,4,3,9,2,8,1,7]=>{{1,2,5,6,7,8,9},{3,4}}
[6,5,4,3,2,8,1,7,9]=>{{1,6,7,8},{2,5},{3,4},{9}}
[5,4,9,3,8,2,7,1,6]=>{{1,5,8},{2,3,4,6,9},{7}}
[5,4,3,8,2,7,1,6,9]=>{{1,2,4,5,6,7,8},{3},{9}}
[5,4,3,2,7,9,1,6,8]=>{{1,5,7},{2,4},{3},{6,8,9}}
[5,4,3,2,7,1,6,8,9]=>{{1,5,6,7},{2,4},{3},{8},{9}}
[4,8,3,7,2,6,1,5,9]=>{{1,4,7},{2,5,8},{3},{6},{9}}
[4,3,7,2,6,9,1,5,8]=>{{1,2,3,4,7},{5,6,8,9}}
[4,3,7,2,6,1,5,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[4,3,2,6,8,1,5,7,9]=>{{1,4,6},{2,3},{5,7,8},{9}}
[4,3,2,6,1,5,7,8,9]=>{{1,4,5,6},{2,3},{7},{8},{9}}
[3,6,9,2,5,8,1,4,7]=>{{1,3,7,9},{2,4,6,8},{5}}
[3,6,2,5,8,1,4,7,9]=>{{1,2,3,6},{4,5,7,8},{9}}
[3,6,2,5,1,4,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[3,2,5,7,9,1,4,6,8]=>{{1,3,5,6,8,9},{2},{4,7}}
[3,2,5,7,1,4,6,8,9]=>{{1,3,5},{2},{4,6,7},{8},{9}}
[3,2,5,1,4,6,7,8,9]=>{{1,3,4,5},{2},{6},{7},{8},{9}}
[2,4,6,8,1,3,5,7,9]=>{{1,2,4,5,7,8},{3,6},{9}}
[2,4,6,1,3,5,7,8,9]=>{{1,2,4},{3,5,6},{7},{8},{9}}
[8,7,6,5,4,2,1,9,3]=>{{1,2,3,6,7,8,9},{4,5}}
[8,7,6,5,3,2,1,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[8,7,6,4,3,2,1,9,5]=>{{1,2,3,5,6,7,8,9},{4}}
[8,7,5,4,3,2,1,9,6]=>{{1,2,6,7,8,9},{3,5},{4}}
[8,6,5,4,3,2,1,9,7]=>{{1,7,8,9},{2,6},{3,5},{4}}
[7,6,5,4,3,2,1,9,8]=>{{1,7},{2,6},{3,5},{4},{8,9}}
[8,7,6,5,4,9,1,3,2]=>{{1,2,3,6,7,8,9},{4,5}}
[8,7,6,5,9,2,1,4,3]=>{{1,2,3,4,5,6,7,8,9}}
[8,7,6,9,3,2,1,5,4]=>{{1,2,3,5,6,7,8},{4,9}}
[8,7,9,4,3,2,1,6,5]=>{{1,2,6,7,8},{3,5,9},{4}}
[8,9,5,4,3,2,1,7,6]=>{{1,7,8},{2,6,9},{3,5},{4}}
[9,6,5,4,3,2,1,8,7]=>{{1,7,9},{2,6},{3,5},{4},{8}}
[2,9,8,7,6,5,4,1,3]=>{{1,2,3,8,9},{4,7},{5,6}}
[2,4,5,6,7,8,1,3,9]=>{{1,2,3,4,5,6,7,8},{9}}
[1,4,5,6,7,8,2,9,3]=>{{1},{2,3,4,5,6,7,8,9}}
[9,7,8,5,6,3,1,4,2]=>{{1,2,7,9},{3,4,5,6,8}}
[9,7,8,5,3,6,1,4,2]=>{{1,2,7,9},{3,4,5,8},{6}}
[9,7,5,8,3,6,1,4,2]=>{{1,2,7,9},{3,5},{4,8},{6}}
[7,9,5,8,3,6,1,4,2]=>{{1,7},{2,9},{3,5},{4,8},{6}}
[8,9,5,7,3,6,1,4,2]=>{{1,4,7,8},{2,9},{3,5},{6}}
[8,9,6,7,3,5,1,4,2]=>{{1,4,7,8},{2,9},{3,5,6}}
[8,9,6,7,4,5,1,3,2]=>{{1,3,4,5,6,7,8},{2,9}}
[8,9,6,7,4,5,2,3,1]=>{{1,2,3,4,5,6,7,8,9}}
[9,7,8,5,3,1,6,4,2]=>{{1,2,6,7,9},{3,4,5,8}}
[9,7,5,3,8,6,1,4,2]=>{{1,2,7,9},{3,4,5,8},{6}}
[7,5,9,8,3,6,1,4,2]=>{{1,7},{2,3,5,9},{4,8},{6}}
[9,8,5,7,3,6,1,4,2]=>{{1,2,4,7,8,9},{3,5},{6}}
[7,9,6,8,3,5,1,4,2]=>{{1,7},{2,9},{3,5,6},{4,8}}
[8,9,5,7,4,6,1,3,2]=>{{1,3,4,5,7,8},{2,9},{6}}
[8,9,6,7,3,5,2,4,1]=>{{1,2,4,7,8,9},{3,5,6}}
[6,5,4,3,2,1,9,8,7]=>{{1,6},{2,5},{3,4},{7,9},{8}}
[6,5,4,3,2,1,8,7,9]=>{{1,6},{2,5},{3,4},{7,8},{9}}
[5,4,3,2,1,9,8,7,6]=>{{1,5},{2,4},{3},{6,9},{7,8}}
[5,4,3,2,1,8,7,6,9]=>{{1,5},{2,4},{3},{6,8},{7},{9}}
[5,4,3,2,1,7,6,9,8]=>{{1,5},{2,4},{3},{6,7},{8,9}}
[5,4,3,2,1,7,6,8,9]=>{{1,5},{2,4},{3},{6,7},{8},{9}}
[4,3,2,1,8,7,6,5,9]=>{{1,4},{2,3},{5,8},{6,7},{9}}
[4,3,2,1,7,6,5,9,8]=>{{1,4},{2,3},{5,7},{6},{8,9}}
[4,3,2,1,7,6,5,8,9]=>{{1,4},{2,3},{5,7},{6},{8},{9}}
[4,3,2,1,6,5,8,7,9]=>{{1,4},{2,3},{5,6},{7,8},{9}}
[4,3,2,1,6,5,7,8,9]=>{{1,4},{2,3},{5,6},{7},{8},{9}}
[3,2,1,6,5,4,8,7,9]=>{{1,3},{2},{4,6},{5},{7,8},{9}}
[3,2,1,6,5,4,7,8,9]=>{{1,3},{2},{4,6},{5},{7},{8},{9}}
[3,2,1,5,4,7,6,9,8]=>{{1,3},{2},{4,5},{6,7},{8,9}}
[3,2,1,5,4,7,6,8,9]=>{{1,3},{2},{4,5},{6,7},{8},{9}}
[3,2,1,5,4,6,7,8,9]=>{{1,3},{2},{4,5},{6},{7},{8},{9}}
[2,1,4,3,6,5,7,8,9]=>{{1,2},{3,4},{5,6},{7},{8},{9}}
[2,1,4,3,5,6,7,8,9]=>{{1,2},{3,4},{5},{6},{7},{8},{9}}
[3,1,4,2,6,5,8,7,9]=>{{1,2,3,4},{5,6},{7,8},{9}}
[3,1,5,2,6,4,8,7,9]=>{{1,2,3,4,5,6},{7,8},{9}}
[3,1,5,2,4,7,6,9,8]=>{{1,2,3,4,5},{6,7},{8,9}}
[3,1,2,5,4,7,6,9,8]=>{{1,2,3},{4,5},{6,7},{8,9}}
[4,1,5,2,6,3,8,7,9]=>{{1,2,4},{3,5,6},{7,8},{9}}
[3,1,6,2,7,4,8,5,9]=>{{1,2,3,4,6},{5,7,8},{9}}
[1,3,5,2,4,7,6,9,8]=>{{1},{2,3,4,5},{6,7},{8,9}}
[4,5,6,7,8,9,1,2,3]=>{{1,4,7},{2,5,8},{3,6,9}}
[4,5,6,7,8,9,2,3,1]=>{{1,2,3,4,5,6,7,8,9}}
[5,6,7,8,9,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9}}
[6,7,8,9,2,3,4,5,1]=>{{1,2,3,4,5,6,7,8,9}}
[8,9,6,7,5,4,3,2,1]=>{{1,2,8,9},{3,4,6,7},{5}}
[9,8,7,6,5,4,2,1,3]=>{{1,2,3,7,8,9},{4,6},{5}}
[9,8,7,6,5,3,2,1,4]=>{{1,2,3,4,6,7,8,9},{5}}
[9,8,7,6,4,3,2,1,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,7,5,4,3,2,1,6]=>{{1,2,3,6,7,8,9},{4,5}}
[9,8,6,5,4,3,2,1,7]=>{{1,2,7,8,9},{3,6},{4,5}}
[9,7,6,5,4,3,2,1,8]=>{{1,8,9},{2,7},{3,6},{4,5}}
[9,8,7,6,5,4,1,3,2]=>{{1,2,3,7,8,9},{4,6},{5}}
[9,8,7,6,5,2,4,1,3]=>{{1,2,3,4,6,7,8,9},{5}}
[9,8,7,6,3,5,2,1,4]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,7,4,6,3,2,1,5]=>{{1,2,3,5,6,7,8,9},{4}}
[9,8,5,7,4,3,2,1,6]=>{{1,2,3,4,5,6,7,8,9}}
[9,6,8,5,4,3,2,1,7]=>{{1,2,3,6,7,8,9},{4,5}}
[9,8,7,3,6,2,5,1,4]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,7,6,3,5,1,2,4]=>{{1,3,4,5,6,7,9},{2,8}}
[9,4,8,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,4,7,3,6,1,2,5]=>{{1,3,4,5,7,9},{2,8},{6}}
[9,8,7,2,4,6,1,3,5]=>{{1,2,3,4,5,7,8,9},{6}}
[9,8,7,4,6,1,2,3,5]=>{{1,5,6,9},{2,3,7,8},{4}}
[5,9,4,8,3,7,1,2,6]=>{{1,2,3,4,5,6,7,8,9}}
[9,5,8,2,4,7,1,3,6]=>{{1,6,7,9},{2,4,5},{3,8}}
[9,5,8,4,7,1,2,3,6]=>{{1,6,9},{2,5,7},{3,8},{4}}
[9,8,3,5,7,1,2,4,6]=>{{1,6,9},{2,4,5,7,8},{3}}
[9,8,5,7,1,2,3,4,6]=>{{1,2,3,4,5,6,7,8,9}}
[6,9,3,5,8,1,2,4,7]=>{{1,6},{2,7,9},{3},{4,5,8}}
[6,9,5,8,1,2,3,4,7]=>{{1,2,3,5,6,7,9},{4,8}}
[9,2,4,6,8,1,3,5,7]=>{{1,3,4,6,7,9},{2},{5,8}}
[9,4,6,8,1,2,3,5,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,6,8,1,2,3,4,5,7]=>{{1,4,7,9},{2,3,5,6,8}}
[3,5,7,9,1,2,4,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[5,7,9,1,2,3,4,6,8]=>{{1,2,4,5,7},{3,6,8,9}}
[7,9,1,2,3,4,5,6,8]=>{{1,3,5,7},{2,4,6,8,9}}
[7,6,5,4,3,2,9,8,1]=>{{1,7,9},{2,6},{3,5},{4},{8}}
[9,6,5,4,3,2,8,1,7]=>{{1,7,8,9},{2,6},{3,5},{4}}
[9,7,5,4,3,2,1,8,6]=>{{1,2,6,7,9},{3,5},{4},{8}}
[7,6,5,4,3,9,2,8,1]=>{{1,2,6,7,9},{3,5},{4},{8}}
[8,6,5,4,3,2,9,7,1]=>{{1,7,8,9},{2,6},{3,5},{4}}
[9,1,2,3,5,4,6,7,8]=>{{1,2,3,4,6,7,8,9},{5}}
[2,3,4,6,5,7,8,9,1]=>{{1,2,3,4,6,7,8,9},{5}}
[9,1,2,3,5,6,4,7,8]=>{{1,2,3,4,7,8,9},{5},{6}}
[2,3,4,7,5,6,8,9,1]=>{{1,2,3,4,7,8,9},{5},{6}}
[2,3,4,6,7,5,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[7,6,5,8,4,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[7,6,5,4,9,3,2,1,8]=>{{1,2,3,5,6,7,8,9},{4}}
[7,6,5,4,3,8,2,1,9]=>{{1,2,6,7,8},{3,5},{4},{9}}
[7,6,5,4,3,2,8,1,9]=>{{1,7,8},{2,6},{3,5},{4},{9}}
[6,9,8,5,4,3,2,1,7]=>{{1,3,6,8},{2,7,9},{4,5}}
[7,5,8,9,4,3,2,1,6]=>{{1,2,3,4,5,6,7,8,9}}
[7,6,4,8,9,3,2,1,5]=>{{1,2,3,4,6,7,8},{5,9}}
[7,6,5,3,9,8,2,1,4]=>{{1,2,6,7,8},{3,4,5,9}}
[7,6,5,4,2,8,9,1,3]=>{{1,2,3,5,6,7,8,9},{4}}
[7,6,5,4,3,1,8,9,2]=>{{1,2,6,7,8,9},{3,5},{4}}
[6,5,8,7,4,3,2,1,9]=>{{1,3,6,8},{2,4,5,7},{9}}
[7,5,4,8,6,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[5,9,8,7,4,3,2,1,6]=>{{1,2,3,4,5,6,7,8,9}}
[7,6,4,3,9,5,2,1,8]=>{{1,2,5,6,7,8,9},{3,4}}
[7,4,8,9,6,3,2,1,5]=>{{1,2,3,4,5,6,7,8,9}}
[7,6,5,3,2,8,4,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[7,6,3,8,9,5,2,1,4]=>{{1,2,4,5,6,7,8,9},{3}}
[7,6,5,4,2,1,8,3,9]=>{{1,2,3,5,6,7,8},{4},{9}}
[7,6,5,2,9,8,4,1,3]=>{{1,2,4,6,7,8},{3,5,9}}
[7,6,5,4,1,8,9,3,2]=>{{1,2,3,5,6,7,8,9},{4}}
[2,3,4,5,6,8,9,7,1]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,7,8,9,6,1]=>{{1,2,3,4,5,7,9},{6,8}}
[2,4,5,6,7,8,9,3,1]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,9,7,6,5,4,3,2]=>{{1,2,3,8,9},{4,7},{5,6}}
[9,2,8,7,6,5,4,1,3]=>{{1,3,8,9},{2},{4,7},{5,6}}
[3,9,8,7,6,5,4,1,2]=>{{1,3,8},{2,9},{4,7},{5,6}}
[8,9,1,7,6,5,4,3,2]=>{{1,3,8},{2,9},{4,7},{5,6}}
[8,2,9,7,6,5,4,3,1]=>{{1,3,8,9},{2},{4,7},{5,6}}
[8,1,2,3,4,5,9,6,7]=>{{1,2,3,4,5,6,8},{7,9}}
[8,1,2,3,4,9,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,2,9,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,9,2,3,4,5,6,7]=>{{1,2,4,6,8},{3,5,7,9}}
[4,1,2,3,8,9,5,6,7]=>{{1,2,3,4},{5,6,7,8,9}}
[2,1,8,9,3,4,5,6,7]=>{{1,2},{3,4,5,6,7,8,9}}
[9,8,7,6,5,2,3,1,4]=>{{1,2,4,6,8,9},{3,7},{5}}
[9,8,7,6,3,4,2,1,5]=>{{1,2,3,5,7,8,9},{4,6}}
[9,8,7,4,5,3,2,1,6]=>{{1,2,3,6,7,8,9},{4},{5}}
[9,8,5,6,4,3,2,1,7]=>{{1,2,7,8,9},{3,4,5,6}}
[9,6,7,5,4,3,2,1,8]=>{{1,8,9},{2,3,6,7},{4,5}}
[8,2,1,7,6,5,4,3,9]=>{{1,3,8},{2},{4,7},{5,6},{9}}
[3,2,8,7,6,5,4,1,9]=>{{1,3,8},{2},{4,7},{5,6},{9}}
[8,3,1,7,6,5,4,9,2]=>{{1,2,3,8,9},{4,7},{5,6}}
[8,2,9,1,6,5,4,3,7]=>{{1,3,4,7,8,9},{2},{5,6}}
[4,2,8,7,6,5,9,1,3]=>{{1,3,4,7,8,9},{2},{5,6}}
[3,9,2,7,6,5,4,1,8]=>{{1,2,3,8,9},{4,7},{5,6}}
[8,4,1,7,6,5,9,3,2]=>{{1,3,8},{2,4,7,9},{5,6}}
[8,3,2,1,6,5,4,7,9]=>{{1,4,7,8},{2,3},{5,6},{9}}
[8,2,9,7,1,5,4,3,6]=>{{1,3,5,6,8,9},{2},{4,7}}
[5,2,8,7,6,9,4,1,3]=>{{1,3,5,6,8,9},{2},{4,7}}
[4,3,2,7,6,5,8,1,9]=>{{1,4,7,8},{2,3},{5,6},{9}}
[3,9,8,2,6,5,4,1,7]=>{{1,3,8},{2,4,7,9},{5,6}}
[8,7,6,5,4,2,1,3,9]=>{{1,2,3,6,7,8},{4,5},{9}}
[1,9,8,7,6,5,3,2,4]=>{{1},{2,3,4,7,8,9},{5,6}}
[1,9,8,7,6,5,2,4,3]=>{{1},{2,3,4,7,8,9},{5,6}}
[2,1,9,8,7,6,5,4,3]=>{{1,2},{3,9},{4,8},{5,7},{6}}
[1,2,9,8,7,6,5,4,3]=>{{1},{2},{3,9},{4,8},{5,7},{6}}
[3,2,1,9,8,7,6,5,4]=>{{1,3},{2},{4,9},{5,8},{6,7}}
[1,3,2,9,8,7,6,5,4]=>{{1},{2,3},{4,9},{5,8},{6,7}}
[1,2,3,9,8,7,6,5,4]=>{{1},{2},{3},{4,9},{5,8},{6,7}}
[4,3,2,1,9,8,7,6,5]=>{{1,4},{2,3},{5,9},{6,8},{7}}
[1,4,3,2,9,8,7,6,5]=>{{1},{2,4},{3},{5,9},{6,8},{7}}
[2,1,4,3,9,8,7,6,5]=>{{1,2},{3,4},{5,9},{6,8},{7}}
[1,2,4,3,9,8,7,6,5]=>{{1},{2},{3,4},{5,9},{6,8},{7}}
[1,2,3,4,9,8,7,6,5]=>{{1},{2},{3},{4},{5,9},{6,8},{7}}
[1,5,4,3,2,9,8,7,6]=>{{1},{2,5},{3,4},{6,9},{7,8}}
[2,1,5,4,3,9,8,7,6]=>{{1,2},{3,5},{4},{6,9},{7,8}}
[1,2,5,4,3,9,8,7,6]=>{{1},{2},{3,5},{4},{6,9},{7,8}}
[1,3,2,5,4,9,8,7,6]=>{{1},{2,3},{4,5},{6,9},{7,8}}
[1,2,3,5,4,9,8,7,6]=>{{1},{2},{3},{4,5},{6,9},{7,8}}
[1,2,3,4,5,9,8,7,6]=>{{1},{2},{3},{4},{5},{6,9},{7,8}}
[1,3,2,6,5,4,9,8,7]=>{{1},{2,3},{4,6},{5},{7,9},{8}}
[1,2,3,6,5,4,9,8,7]=>{{1},{2},{3},{4,6},{5},{7,9},{8}}
[2,1,4,3,6,5,9,8,7]=>{{1,2},{3,4},{5,6},{7,9},{8}}
[1,2,4,3,6,5,9,8,7]=>{{1},{2},{3,4},{5,6},{7,9},{8}}
[1,2,3,4,6,5,9,8,7]=>{{1},{2},{3},{4},{5,6},{7,9},{8}}
[1,2,3,5,4,7,6,9,8]=>{{1},{2},{3},{4,5},{6,7},{8,9}}
[1,2,3,4,5,7,6,9,8]=>{{1},{2},{3},{4},{5},{6,7},{8,9}}
[9,8,7,6,5,2,1,4,3]=>{{1,3,7,9},{2,4,6,8},{5}}
[9,8,7,3,2,1,6,5,4]=>{{1,3,4,6,7,9},{2,5,8}}
[9,8,7,6,3,1,5,2,4]=>{{1,4,6,9},{2,8},{3,5,7}}
[9,4,3,2,1,8,7,6,5]=>{{1,5,9},{2,4},{3},{6,8},{7}}
[9,8,4,3,1,7,6,2,5]=>{{1,5,9},{2,8},{3,4},{6,7}}
[9,8,7,2,1,4,3,6,5]=>{{1,5,9},{2,4,6,8},{3,7}}
[9,8,7,4,1,6,2,3,5]=>{{1,5,9},{2,3,7,8},{4},{6}}
[5,4,3,1,9,8,7,2,6]=>{{1,2,4,5,6,8,9},{3},{7}}
[9,5,2,1,8,4,3,7,6]=>{{1,4,6,9},{2,3,5,7,8}}
[9,8,3,1,5,2,7,4,6]=>{{1,2,4,6,8,9},{3},{5},{7}}
[6,3,1,9,5,2,8,4,7]=>{{1,2,3,6},{4,7,8,9},{5}}
[6,5,1,9,8,2,3,4,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,2,1,4,3,6,5,8,7]=>{{1,3,5,7,9},{2},{4},{6},{8}}
[9,6,1,8,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8,9}}
[5,1,7,2,9,3,4,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[7,1,9,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,8,7,6,5,4,3,2]=>{{1,2,9},{3,8},{4,7},{5,6}}
[7,1,9,8,6,5,4,3,2]=>{{1,2,3,4,7,8,9},{5,6}}
[6,1,9,8,7,5,4,3,2]=>{{1,2,3,4,5,6,7,8,9}}
[5,1,9,8,7,6,4,3,2]=>{{1,2,3,4,5,7,8,9},{6}}
[4,1,9,8,7,6,5,3,2]=>{{1,2,3,4,8,9},{5,7},{6}}
[3,1,9,8,7,6,5,4,2]=>{{1,2,3,9},{4,8},{5,7},{6}}
[9,8,1,7,6,5,4,3,2]=>{{1,2,3,8,9},{4,7},{5,6}}
[8,7,9,1,6,5,4,3,2]=>{{1,2,3,4,7,8,9},{5,6}}
[7,6,9,8,1,5,4,3,2]=>{{1,2,3,4,5,6,7,8,9}}
[6,5,9,8,7,1,4,3,2]=>{{1,6},{2,3,4,5,7,8,9}}
[5,4,9,8,7,6,1,3,2]=>{{1,5,7},{2,3,4,8,9},{6}}
[4,3,9,8,7,6,5,1,2]=>{{1,4,8},{2,3,9},{5,7},{6}}
[3,2,9,8,7,6,5,4,1]=>{{1,3,9},{2},{4,8},{5,7},{6}}
[9,1,2,3,4,5,6,8,7]=>{{1,2,3,4,5,6,7,9},{8}}
[9,1,2,3,4,5,7,8,6]=>{{1,2,3,4,5,6,9},{7},{8}}
[2,3,4,5,6,9,7,8,1]=>{{1,2,3,4,5,6,9},{7},{8}}
[9,2,1,8,7,6,5,4,3]=>{{1,3,9},{2},{4,8},{5,7},{6}}
[3,9,2,8,7,6,5,4,1]=>{{1,2,3,9},{4,8},{5,7},{6}}
[4,2,9,8,7,6,5,3,1]=>{{1,3,4,8,9},{2},{5,7},{6}}
[9,2,8,1,7,6,5,4,3]=>{{1,3,4,8,9},{2},{5,7},{6}}
[9,3,1,8,7,6,5,4,2]=>{{1,2,3,9},{4,8},{5,7},{6}}
[2,3,5,6,4,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,6,4,5,7,8,9,1]=>{{1,2,3,6,7,8,9},{4},{5}}
[9,1,2,4,5,3,6,7,8]=>{{1,2,3,6,7,8,9},{4},{5}}
[7,9,6,8,5,4,3,2,1]=>{{1,2,3,4,6,7,8,9},{5}}
[6,9,8,5,7,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[5,9,8,7,4,6,3,2,1]=>{{1,2,3,4,5,7,8,9},{6}}
[4,9,8,7,6,3,5,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[3,9,8,7,6,5,2,4,1]=>{{1,2,3,4,7,8,9},{5,6}}
[8,6,9,7,4,5,2,3,1]=>{{1,3,8,9},{2,4,5,6,7}}
[8,6,9,4,7,5,2,3,1]=>{{1,3,8,9},{2,5,6,7},{4}}
[8,6,9,4,7,2,5,3,1]=>{{1,3,8,9},{2,6},{4},{5,7}}
[8,6,9,4,7,3,5,1,2]=>{{1,8},{2,3,6,9},{4},{5,7}}
[8,6,9,5,7,3,4,1,2]=>{{1,8},{2,3,6,9},{4,5,7}}
[8,7,9,5,6,3,4,1,2]=>{{1,8},{2,3,4,5,6,7,9}}
[8,6,4,9,7,5,2,3,1]=>{{1,3,4,8,9},{2,5,6,7}}
[8,6,9,4,2,7,5,3,1]=>{{1,3,8,9},{2,5,6,7},{4}}
[8,6,9,4,7,2,1,5,3]=>{{1,5,7,8},{2,6},{3,9},{4}}
[8,6,9,4,7,3,5,2,1]=>{{1,2,3,6,8,9},{4},{5,7}}
[8,6,9,5,7,2,4,1,3]=>{{1,8},{2,6},{3,9},{4,5,7}}
[8,7,9,4,6,3,5,1,2]=>{{1,8},{2,3,5,6,7,9},{4}}
[9,6,8,5,7,3,4,1,2]=>{{1,2,3,6,8,9},{4,5,7}}
[1,3,4,5,6,7,9,2,8]=>{{1},{2,3,4,5,6,7,8,9}}
[2,3,4,5,6,7,1,9,8]=>{{1,2,3,4,5,6,7},{8,9}}
[2,1,4,5,6,7,8,9,3]=>{{1,2},{3,4,5,6,7,8,9}}
[3,1,4,5,6,7,8,2,9]=>{{1,2,3,4,5,6,7,8},{9}}
[1,2,3,4,5,7,9,6,8]=>{{1},{2},{3},{4},{5},{6,7,8,9}}
[1,2,3,4,6,9,5,7,8]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[1,2,3,5,9,4,6,7,8]=>{{1},{2},{3},{4,5,6,7,8,9}}
[1,2,4,9,3,5,6,7,8]=>{{1},{2},{3,4,5,6,7,8,9}}
[1,3,9,2,4,5,6,7,8]=>{{1},{2,3,4,5,6,7,8,9}}
[1,9,8,7,6,2,5,4,3]=>{{1},{2,3,4,5,6,7,8,9}}
[2,9,8,7,1,6,5,4,3]=>{{1,2,3,4,5,7,8,9},{6}}
[1,9,8,2,7,6,5,4,3]=>{{1},{2,3,4,8,9},{5,7},{6}}
[1,9,2,8,7,6,5,4,3]=>{{1},{2,3,9},{4,8},{5,7},{6}}
[3,9,8,7,6,5,2,1,4]=>{{1,3,8},{2,4,7,9},{5,6}}
[4,9,8,7,6,1,2,5,3]=>{{1,2,3,4,5,6,7,8,9}}
[5,9,8,7,1,2,6,4,3]=>{{1,5},{2,3,4,6,7,8,9}}
[6,9,8,2,1,7,5,4,3]=>{{1,5,6,7},{2,3,4,8,9}}
[7,9,1,2,8,6,5,4,3]=>{{1,2,3,4,5,7,8,9},{6}}
[8,1,2,9,7,6,5,4,3]=>{{1,2,3,4,8,9},{5,7},{6}}
[1,9,8,7,6,3,2,5,4]=>{{1},{2,4,7,9},{3,5,6,8}}
[1,9,8,7,4,2,6,5,3]=>{{1},{2,3,4,5,6,7,8,9}}
[4,9,8,7,6,3,2,1,5]=>{{1,2,3,4,5,6,7,8,9}}
[2,9,8,5,1,7,6,4,3]=>{{1,2,3,4,5,8,9},{6,7}}
[5,9,8,7,4,1,2,6,3]=>{{1,2,3,4,5,6,7,8,9}}
[1,9,6,2,8,7,5,4,3]=>{{1},{2,3,4,5,6,7,8,9}}
[6,9,8,5,1,2,7,4,3]=>{{1,2,3,4,5,6,8,9},{7}}
[1,7,2,9,8,6,5,4,3]=>{{1},{2,3,4,5,7,8,9},{6}}
[7,9,6,2,1,8,5,4,3]=>{{1,5,7},{2,3,4,6,8,9}}
[8,7,1,2,9,6,5,4,3]=>{{1,2,3,4,5,7,8,9},{6}}
[1,6,7,8,9,2,3,4,5]=>{{1},{2,6},{3,7},{4,8},{5,9}}
[6,7,8,1,2,3,4,5,9]=>{{1,2,3,4,5,6,7,8},{9}}
[1,7,8,9,2,3,4,5,6]=>{{1},{2,3,4,5,6,7,8,9}}
[5,6,7,1,8,2,3,4,9]=>{{1,4,5,8},{2,6},{3,7},{9}}
[4,6,7,8,1,2,3,5,9]=>{{1,4,5,8},{2,6},{3,7},{9}}
[1,6,7,8,2,9,3,4,5]=>{{1},{2,5,6,9},{3,7},{4,8}}
[1,5,7,8,9,2,3,4,6]=>{{1},{2,5,6,9},{3,7},{4,8}}
[9,2,3,4,5,6,7,8,1]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}
[8,2,3,4,5,6,7,1,9]=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}
[7,2,3,4,5,6,1,8,9]=>{{1,7},{2},{3},{4},{5},{6},{8},{9}}
[6,2,3,4,5,1,7,8,9]=>{{1,6},{2},{3},{4},{5},{7},{8},{9}}
[5,2,3,4,1,6,7,8,9]=>{{1,5},{2},{3},{4},{6},{7},{8},{9}}
[4,2,3,1,5,6,7,8,9]=>{{1,4},{2},{3},{5},{6},{7},{8},{9}}
[1,2,4,3,5,6,7,8,9]=>{{1},{2},{3,4},{5},{6},{7},{8},{9}}
[1,2,4,6,8,9,7,5,3]=>{{1},{2},{3,4,6,9},{5,8},{7}}
[1,2,4,5,3,6,7,8,9]=>{{1},{2},{3,4,5},{6},{7},{8},{9}}
[2,4,1,3,6,8,5,7,9]=>{{1,2,3,4},{5,6,7,8},{9}}
[8,2,1,3,4,5,6,7,9]=>{{1,3,4,5,6,7,8},{2},{9}}
[3,2,4,5,6,7,8,1,9]=>{{1,3,4,5,6,7,8},{2},{9}}
[8,3,1,2,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[8,2,3,1,4,5,6,7,9]=>{{1,4,5,6,7,8},{2},{3},{9}}
[4,2,3,5,6,7,8,1,9]=>{{1,4,5,6,7,8},{2},{3},{9}}
[1,9,3,4,5,6,7,8,2]=>{{1},{2,9},{3},{4},{5},{6},{7},{8}}
[1,9,8,4,5,6,7,3,2]=>{{1},{2,9},{3,8},{4},{5},{6},{7}}
[1,7,2,3,4,5,6,9,8]=>{{1},{2,3,4,5,6,7},{8,9}}
[6,9,1,2,3,4,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,3,4,5,6,7,9,8,2]=>{{1},{2,3,4,5,6,7,9},{8}}
[7,3,4,5,6,8,1,2,9]=>{{1,7},{2,3,4,5,6,8},{9}}
[2,3,4,5,7,6,8,1,9]=>{{1,2,3,4,5,7,8},{6},{9}}
[1,8,4,5,6,7,9,2,3]=>{{1},{2,8},{3,4,5,6,7,9}}
[1,3,4,5,6,8,7,9,2]=>{{1},{2,3,4,5,6,8,9},{7}}
[1,2,3,4,5,9,7,8,6]=>{{1},{2},{3},{4},{5},{6,9},{7},{8}}
[1,2,3,4,9,6,7,8,5]=>{{1},{2},{3},{4},{5,9},{6},{7},{8}}
[1,2,3,9,5,6,7,8,4]=>{{1},{2},{3},{4,9},{5},{6},{7},{8}}
[1,2,9,4,5,6,7,8,3]=>{{1},{2},{3,9},{4},{5},{6},{7},{8}}
[1,2,3,4,9,7,6,8,5]=>{{1},{2},{3},{4},{5,9},{6,7},{8}}
[1,2,3,9,6,5,7,8,4]=>{{1},{2},{3},{4,9},{5,6},{7},{8}}
[1,2,9,5,4,6,7,8,3]=>{{1},{2},{3,9},{4,5},{6},{7},{8}}
[1,9,4,3,5,6,7,8,2]=>{{1},{2,9},{3,4},{5},{6},{7},{8}}
[9,3,2,4,5,6,7,8,1]=>{{1,9},{2,3},{4},{5},{6},{7},{8}}
[3,5,6,7,8,9,4,2,1]=>{{1,3,6,9},{2,5,8},{4,7}}
[1,2,3,5,7,4,6,9,8]=>{{1},{2},{3},{4,5,6,7},{8,9}}
[1,2,3,6,4,7,5,9,8]=>{{1},{2},{3},{4,5,6,7},{8,9}}
[1,2,3,4,6,8,5,7,9]=>{{1},{2},{3},{4},{5,6,7,8},{9}}
[1,2,3,4,7,5,8,6,9]=>{{1},{2},{3},{4},{5,6,7,8},{9}}
[1,2,5,7,3,4,6,9,8]=>{{1},{2},{3,5},{4,6,7},{8,9}}
[1,2,4,5,7,3,6,9,8]=>{{1},{2},{3,4,5,6,7},{8,9}}
[1,2,6,3,4,7,5,9,8]=>{{1},{2},{3,4,5,6,7},{8,9}}
[1,2,5,6,3,7,4,9,8]=>{{1},{2},{3,5},{4,6,7},{8,9}}
[2,3,1,9,4,5,6,7,8]=>{{1,2,3},{4,5,6,7,8,9}}
[4,9,1,2,3,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[3,9,1,2,4,5,6,7,8]=>{{1,3},{2,4,5,6,7,8,9}}
[6,8,1,9,2,3,4,5,7]=>{{1,3,6},{2,5,8},{4,7,9}}
[4,8,1,2,3,9,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[3,8,1,2,4,5,9,6,7]=>{{1,3},{2,4,5,6,8},{7,9}}
[1,8,2,3,4,5,6,7,9]=>{{1},{2,3,4,5,6,7,8},{9}}
[9,8,7,5,6,4,3,2,1]=>{{1,9},{2,8},{3,7},{4,5,6}}
[2,1,9,8,6,7,5,4,3]=>{{1,2},{3,9},{4,8},{5,6,7}}
[9,8,7,5,4,6,3,2,1]=>{{1,9},{2,8},{3,7},{4,5},{6}}
[9,8,7,4,6,5,3,2,1]=>{{1,9},{2,8},{3,7},{4},{5,6}}
[2,1,9,8,6,5,7,4,3]=>{{1,2},{3,9},{4,8},{5,6},{7}}
[2,1,9,8,5,7,6,4,3]=>{{1,2},{3,9},{4,8},{5},{6,7}}
[1,8,7,6,5,4,3,2,9]=>{{1},{2,8},{3,7},{4,6},{5},{9}}
[2,1,8,7,6,5,4,3,9]=>{{1,2},{3,8},{4,7},{5,6},{9}}
[2,8,9,7,6,5,4,3,1]=>{{1,2,3,8,9},{4,7},{5,6}}
[4,5,6,7,8,1,2,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[4,5,6,7,1,2,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[4,5,6,1,2,7,8,9,3]=>{{1,4},{2,5},{3,6,7,8,9}}
[4,5,1,2,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[7,8,1,2,3,4,5,9,6]=>{{1,3,5,7},{2,4,6,8,9}}
[2,8,9,1,3,4,5,6,7]=>{{1,2,4,6,8},{3,5,7,9}}
[7,1,8,2,9,3,4,5,6]=>{{1,2,4,7},{3,5,6,8,9}}
[6,1,7,2,8,3,9,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[5,1,6,2,7,3,8,4,9]=>{{1,2,4,5,7,8},{3,6},{9}}
[7,1,8,2,3,9,4,5,6]=>{{1,2,4,7},{3,5,8},{6,9}}
[6,1,7,2,8,3,4,9,5]=>{{1,2,3,4,6,7},{5,8,9}}
[5,1,6,2,7,3,9,4,8]=>{{1,2,4,5,7,8,9},{3,6}}
[4,1,5,2,7,3,8,6,9]=>{{1,2,4},{3,5,6,7,8},{9}}
[2,1,3,4,5,6,8,9,7]=>{{1,2},{3},{4},{5},{6},{7,8,9}}
[2,1,3,4,5,6,7,9,8]=>{{1,2},{3},{4},{5},{6},{7},{8,9}}
[2,3,1,4,5,6,8,9,7]=>{{1,2,3},{4},{5},{6},{7,8,9}}
[1,3,2,4,5,6,8,9,7]=>{{1},{2,3},{4},{5},{6},{7,8,9}}
[2,3,1,4,5,6,7,9,8]=>{{1,2,3},{4},{5},{6},{7},{8,9}}
[1,3,2,4,5,6,7,9,8]=>{{1},{2,3},{4},{5},{6},{7},{8,9}}
[6,7,1,2,3,4,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[7,8,6,5,4,3,2,9,1]=>{{1,2,7,8,9},{3,6},{4,5}}
[9,7,6,5,4,3,1,2,8]=>{{1,2,7,8,9},{3,6},{4,5}}
[2,4,3,5,6,7,8,9,1]=>{{1,2,4,5,6,7,8,9},{3}}
[4,5,6,7,8,9,2,1,3]=>{{1,2,4,5,7,8},{3,6,9}}
[5,6,7,8,9,2,1,3,4]=>{{1,3,4,5,7,8,9},{2,6}}
[6,7,8,9,2,1,3,4,5]=>{{1,6},{2,3,4,5,7,8,9}}
[7,8,9,2,1,3,4,5,6]=>{{1,2,4,5,7,8},{3,6,9}}
[8,9,2,1,3,4,5,6,7]=>{{1,4,6,8},{2,3,5,7,9}}
[8,6,4,3,2,1,9,7,5]=>{{1,2,5,6,7,8,9},{3,4}}
[7,5,4,3,2,1,8,6,9]=>{{1,6,7,8},{2,5},{3,4},{9}}
[8,6,4,2,1,9,7,5,3]=>{{1,5,8},{2,3,4,6,9},{7}}
[7,5,3,2,1,8,6,4,9]=>{{1,2,4,5,6,7,8},{3},{9}}
[7,4,3,2,1,8,5,9,6]=>{{1,5,7},{2,4},{3},{6,8,9}}
[6,4,3,2,1,7,5,8,9]=>{{1,5,6,7},{2,4},{3},{8},{9}}
[7,5,3,1,8,6,4,2,9]=>{{1,4,7},{2,5,8},{3},{6},{9}}
[7,4,2,1,8,5,3,9,6]=>{{1,2,3,4,7},{5,6,8,9}}
[6,4,2,1,7,5,3,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[6,3,2,1,7,4,8,5,9]=>{{1,4,6},{2,3},{5,7,8},{9}}
[5,3,2,1,6,4,7,8,9]=>{{1,4,5,6},{2,3},{7},{8},{9}}
[7,4,1,8,5,2,9,6,3]=>{{1,3,7,9},{2,4,6,8},{5}}
[6,3,1,7,4,2,8,5,9]=>{{1,2,3,6},{4,5,7,8},{9}}
[5,3,1,6,4,2,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[6,2,1,7,3,8,4,9,5]=>{{1,3,5,6,8,9},{2},{4,7}}
[5,2,1,6,3,7,4,8,9]=>{{1,3,5},{2},{4,6,7},{8},{9}}
[4,2,1,5,3,6,7,8,9]=>{{1,3,4,5},{2},{6},{7},{8},{9}}
[4,1,5,2,6,3,7,8,9]=>{{1,2,4},{3,5,6},{7},{8},{9}}
[3,1,4,2,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[1,7,2,3,4,5,6,8,9]=>{{1},{2,3,4,5,6,7},{8},{9}}
[1,2,3,4,5,6,8,7,9]=>{{1},{2},{3},{4},{5},{6},{7,8},{9}}
[1,2,3,4,5,7,6,8,9]=>{{1},{2},{3},{4},{5},{6,7},{8},{9}}
[9,2,3,4,5,6,7,1,8]=>{{1,8,9},{2},{3},{4},{5},{6},{7}}
[8,2,3,4,5,6,9,1,7]=>{{1,8},{2},{3},{4},{5},{6},{7,9}}
[8,2,3,9,5,6,7,1,4]=>{{1,8},{2},{3},{4,9},{5},{6},{7}}
[8,2,9,4,5,6,7,1,3]=>{{1,8},{2},{3,9},{4},{5},{6},{7}}
[8,9,3,4,5,6,7,1,2]=>{{1,8},{2,9},{3},{4},{5},{6},{7}}
[4,2,3,1,9,8,7,6,5]=>{{1,4},{2},{3},{5,9},{6,8},{7}}
[3,2,1,9,8,6,7,5,4]=>{{1,3},{2},{4,9},{5,8},{6},{7}}
[1,3,2,4,5,6,7,8,9]=>{{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,4,2,3,5,6,7,8,9]=>{{1},{2,3,4},{5},{6},{7},{8},{9}}
[8,2,3,4,5,6,7,9,1]=>{{1,8,9},{2},{3},{4},{5},{6},{7}}
[7,2,3,4,5,6,9,8,1]=>{{1,7,9},{2},{3},{4},{5},{6},{8}}
[6,2,3,4,5,9,7,8,1]=>{{1,6,9},{2},{3},{4},{5},{7},{8}}
[5,2,3,4,9,6,7,8,1]=>{{1,5,9},{2},{3},{4},{6},{7},{8}}
[4,2,3,9,5,6,7,8,1]=>{{1,4,9},{2},{3},{5},{6},{7},{8}}
[3,2,9,4,5,6,7,8,1]=>{{1,3,9},{2},{4},{5},{6},{7},{8}}
[2,9,3,4,5,6,7,8,1]=>{{1,2,9},{3},{4},{5},{6},{7},{8}}
[6,2,3,4,5,1,8,9,7]=>{{1,6},{2},{3},{4},{5},{7,8,9}}
[5,2,3,4,1,7,9,8,6]=>{{1,5},{2},{3},{4},{6,7,9},{8}}
[4,2,3,1,6,9,7,8,5]=>{{1,4},{2},{3},{5,6,9},{7},{8}}
[3,2,1,5,9,6,7,8,4]=>{{1,3},{2},{4,5,9},{6},{7},{8}}
[2,1,4,9,5,6,7,8,3]=>{{1,2},{3,4,9},{5},{6},{7},{8}}
[1,3,9,4,5,6,7,8,2]=>{{1},{2,3,9},{4},{5},{6},{7},{8}}
[2,3,4,5,6,1,8,7,9]=>{{1,2,3,4,5,6},{7,8},{9}}
[2,3,4,5,1,7,6,8,9]=>{{1,2,3,4,5},{6,7},{8},{9}}
[2,3,4,1,6,5,7,8,9]=>{{1,2,3,4},{5,6},{7},{8},{9}}
[2,3,1,5,4,6,7,8,9]=>{{1,2,3},{4,5},{6},{7},{8},{9}}
[1,8,6,4,2,9,7,5,3]=>{{1},{2,5,8},{3,6,9},{4},{7}}
[8,6,4,2,1,7,5,3,9]=>{{1,2,3,4,5,6,7,8},{9}}
[8,7,5,3,1,6,4,2,9]=>{{1,2,3,4,5,7,8},{6},{9}}
[1,9,7,5,3,2,8,6,4]=>{{1},{2,3,4,5,6,7,8,9}}
[1,9,8,6,4,2,7,5,3]=>{{1},{2,3,4,5,6,8,9},{7}}
[8,6,5,4,3,2,1,7,9]=>{{1,7,8},{2,6},{3,5},{4},{9}}
[9,4,3,2,5,6,7,8,1]=>{{1,9},{2,4},{3},{5},{6},{7},{8}}
[1,9,2,3,4,5,6,8,7]=>{{1},{2,3,4,5,6,7,9},{8}}
[1,3,4,5,6,7,8,2,9]=>{{1},{2,3,4,5,6,7,8},{9}}
[2,1,4,5,6,7,9,3,8]=>{{1,2},{3,4,5,6,7,8,9}}
[2,1,4,5,6,7,8,3,9]=>{{1,2},{3,4,5,6,7,8},{9}}
[1,3,9,8,7,6,5,4,2]=>{{1},{2,3,9},{4,8},{5,7},{6}}
[9,3,4,2,5,6,7,8,1]=>{{1,9},{2,3,4},{5},{6},{7},{8}}
[1,2,3,4,5,7,9,8,6]=>{{1},{2},{3},{4},{5},{6,7,9},{8}}
[1,2,3,4,6,7,9,8,5]=>{{1},{2},{3},{4},{5,6,7,9},{8}}
[1,2,3,4,6,8,9,7,5]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[1,2,3,4,6,9,8,7,5]=>{{1},{2},{3},{4},{5,6,9},{7,8}}
[1,2,3,5,6,7,9,8,4]=>{{1},{2},{3},{4,5,6,7,9},{8}}
[1,2,3,5,6,8,9,7,4]=>{{1},{2},{3},{4,5,6,7,8,9}}
[1,2,3,5,6,9,8,7,4]=>{{1},{2},{3},{4,5,6,9},{7,8}}
[1,2,3,5,7,9,8,6,4]=>{{1},{2},{3},{4,5,6,7,8,9}}
[1,2,3,5,9,8,7,6,4]=>{{1},{2},{3},{4,5,9},{6,8},{7}}
[1,2,4,5,7,8,9,6,3]=>{{1},{2},{3,4,5,7,9},{6,8}}
[1,2,4,5,7,9,8,6,3]=>{{1},{2},{3,4,5,6,7,8,9}}
[1,2,4,5,9,8,7,6,3]=>{{1},{2},{3,4,5,9},{6,8},{7}}
[1,2,4,6,9,8,7,5,3]=>{{1},{2},{3,4,5,6,8,9},{7}}
[1,2,4,9,8,7,6,5,3]=>{{1},{2},{3,4,9},{5,8},{6,7}}
[1,3,5,7,9,8,6,4,2]=>{{1},{2,3,5,9},{4,6,7,8}}
[1,3,5,9,8,7,6,4,2]=>{{1},{2,3,4,5,8,9},{6,7}}
[6,5,1,2,3,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[3,4,1,6,2,5,8,7,9]=>{{1,3},{2,4,5,6},{7,8},{9}}
[3,4,1,2,6,5,8,7,9]=>{{1,3},{2,4},{5,6},{7,8},{9}}
[3,5,1,6,2,4,8,7,9]=>{{1,3},{2,5},{4,6},{7,8},{9}}
[2,5,1,6,3,4,8,7,9]=>{{1,2,3,5},{4,6},{7,8},{9}}
[3,5,1,2,6,4,8,7,9]=>{{1,3},{2,4,5,6},{7,8},{9}}
[2,5,1,3,6,4,8,7,9]=>{{1,2,3,4,5,6},{7,8},{9}}
[8,6,4,2,1,3,5,7,9]=>{{1,5,7,8},{2,3,4,6},{9}}
[8,6,2,1,4,3,5,7,9]=>{{1,4,5,7,8},{2,3,6},{9}}
[8,4,2,1,6,3,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[6,4,2,1,8,3,5,7,9]=>{{1,2,3,4,6},{5,7,8},{9}}
[8,6,4,2,9,1,3,5,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,6,4,2,7,1,3,5,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,7,4,2,5,1,3,6,8]=>{{1,6,8,9},{2,3,4,7},{5}}
[9,7,5,2,3,1,4,6,8]=>{{1,6,8,9},{2,4,7},{3,5}}
[9,7,5,3,1,2,4,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[8,2,1,4,3,6,5,7,9]=>{{1,3,5,7,8},{2},{4},{6},{9}}
[4,2,1,6,3,5,8,7,9]=>{{1,3,4,5,6},{2},{7,8},{9}}
[6,4,2,1,8,3,5,9,7]=>{{1,2,3,4,6},{5,7,8,9}}
[6,4,2,7,1,3,5,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[8,9,4,2,5,1,3,6,7]=>{{1,6,8},{2,3,4,7,9},{5}}
[9,6,7,2,3,1,4,5,8]=>{{1,2,3,4,5,6,7,8,9}}
[9,7,4,5,1,2,3,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,2,9,3,4,5,6,8,7]=>{{1},{2},{3,4,5,6,7,9},{8}}
[1,2,3,8,4,5,9,6,7]=>{{1},{2},{3},{4,5,6,8},{7,9}}
[1,2,3,4,9,5,6,8,7]=>{{1},{2},{3},{4},{5,6,7,9},{8}}
[1,2,3,4,5,9,6,8,7]=>{{1},{2},{3},{4},{5},{6,7,9},{8}}
[7,1,2,3,4,8,5,9,6]=>{{1,2,3,4,5,7},{6,8,9}}
[6,9,1,2,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8,9}}
[5,1,9,2,3,4,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[4,1,2,3,5,8,6,9,7]=>{{1,2,3,4},{5},{6,7,8,9}}
[3,1,2,4,9,5,8,6,7]=>{{1,2,3},{4},{5,6,7,8,9}}
[2,1,3,4,5,9,6,8,7]=>{{1,2},{3},{4},{5},{6,7,9},{8}}
[1,7,2,3,4,5,9,8,6]=>{{1},{2,3,4,5,6,7,9},{8}}
[1,6,2,3,4,5,9,8,7]=>{{1},{2,3,4,5,6},{7,9},{8}}
[6,1,2,3,7,4,8,9,5]=>{{1,2,3,4,6},{5,7,8,9}}
[1,2,3,8,5,4,6,9,7]=>{{1},{2},{3},{4,6,7,8,9},{5}}
[5,9,1,2,6,3,4,8,7]=>{{1,3,5,6},{2,4,7,9},{8}}
[1,4,2,3,5,6,9,8,7]=>{{1},{2,3,4},{5},{6},{7,9},{8}}
[4,1,9,5,2,3,6,8,7]=>{{1,2,4,5},{3,6,7,9},{8}}
[1,3,2,4,5,6,9,8,7]=>{{1},{2,3},{4},{5},{6},{7,9},{8}}
[3,4,1,2,5,6,8,9,7]=>{{1,3},{2,4},{5},{6},{7,8,9}}
[2,3,1,4,9,5,6,8,7]=>{{1,2,3},{4},{5,6,7,9},{8}}
[8,1,2,3,4,6,9,5,7]=>{{1,2,3,4,5,8},{6},{7,9}}
[8,1,2,4,6,9,3,5,7]=>{{1,2,3,5,6,7,8,9},{4}}
[6,1,2,3,4,5,9,8,7]=>{{1,2,3,4,5,6},{7,9},{8}}
[5,1,2,3,4,8,6,9,7]=>{{1,2,3,4,5},{6,7,8,9}}
[4,1,2,3,9,6,8,5,7]=>{{1,2,3,4},{5,7,8,9},{6}}
[3,1,2,8,4,6,9,5,7]=>{{1,2,3},{4,5,8},{6},{7,9}}
[2,1,9,4,6,8,3,5,7]=>{{1,2},{3,7,9},{4},{5,6,8}}
[1,8,2,4,6,9,3,5,7]=>{{1},{2,3,5,6,7,8,9},{4}}
[4,3,5,6,7,8,9,1,2]=>{{1,4,6,8},{2,3,5,7,9}}
[6,7,8,5,4,3,2,1,9]=>{{1,3,6,8},{2,7},{4,5},{9}}
[6,5,7,8,4,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[6,5,4,7,8,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[6,5,4,3,7,8,2,1,9]=>{{1,6,8},{2,5,7},{3,4},{9}}
[6,5,4,3,2,7,8,1,9]=>{{1,6,7,8},{2,5},{3,4},{9}}
[7,8,9,5,4,3,2,1,6]=>{{1,2,7,8},{3,6,9},{4,5}}
[6,7,8,9,4,3,2,1,5]=>{{1,3,6,8},{2,7},{4,5,9}}
[6,5,7,8,9,3,2,1,4]=>{{1,2,3,4,5,6,7,8,9}}
[6,5,4,7,8,9,2,1,3]=>{{1,2,3,4,5,6,7,8,9}}
[6,5,4,3,7,8,9,1,2]=>{{1,6,8},{2,5,7,9},{3,4}}
[6,5,4,3,2,7,8,9,1]=>{{1,6,7,8,9},{2,5},{3,4}}
[8,7,6,5,3,2,1,4,9]=>{{1,2,3,4,5,6,7,8},{9}}
[8,7,6,4,3,2,1,5,9]=>{{1,2,3,5,6,7,8},{4},{9}}
[8,7,5,4,3,2,1,6,9]=>{{1,2,6,7,8},{3,5},{4},{9}}
[8,7,6,5,4,1,2,3,9]=>{{1,3,6,8},{2,7},{4,5},{9}}
[8,7,6,5,2,3,1,4,9]=>{{1,2,4,5,7,8},{3,6},{9}}
[8,7,6,3,4,2,1,5,9]=>{{1,2,3,4,5,6,7,8},{9}}
[8,7,4,5,3,2,1,6,9]=>{{1,2,6,7,8},{3,4,5},{9}}
[8,5,6,4,3,2,1,7,9]=>{{1,7,8},{2,3,5,6},{4},{9}}
[6,7,5,4,3,2,1,8,9]=>{{1,2,6,7},{3,5},{4},{8},{9}}
[6,8,7,9,5,4,3,2,1]=>{{1,4,6,9},{2,8},{3,7},{5}}
[5,8,7,6,9,4,3,2,1]=>{{1,5,9},{2,8},{3,7},{4,6}}
[4,8,7,6,5,9,3,2,1]=>{{1,4,6,9},{2,8},{3,7},{5}}
[3,8,7,6,5,4,9,2,1]=>{{1,3,7,9},{2,8},{4,6},{5}}
[2,8,7,6,5,4,3,9,1]=>{{1,2,8,9},{3,7},{4,6},{5}}
[9,1,3,4,5,6,7,8,2]=>{{1,2,9},{3},{4},{5},{6},{7},{8}}
[1,8,3,4,5,6,9,2,7]=>{{1},{2,8},{3},{4},{5},{6},{7,9}}
[8,2,3,4,5,1,9,7,6]=>{{1,6,7,8,9},{2},{3},{4},{5}}
[8,1,9,4,5,6,7,3,2]=>{{1,2,3,8,9},{4},{5},{6},{7}}
[7,9,3,4,5,6,1,8,2]=>{{1,7},{2,9},{3},{4},{5},{6},{8}}
[1,2,8,4,5,6,9,3,7]=>{{1},{2},{3,8},{4},{5},{6},{7,9}}
[7,8,3,4,5,2,9,1,6]=>{{1,2,6,7,8,9},{3},{4},{5}}
[8,2,3,4,1,6,9,7,5]=>{{1,5,7,8,9},{2},{3},{4},{6}}
[8,1,3,9,5,6,7,4,2]=>{{1,2,4,8,9},{3},{5},{6},{7}}
[7,8,9,4,5,6,3,1,2]=>{{1,2,3,7,8,9},{4},{5},{6}}
[6,9,3,4,5,1,7,8,2]=>{{1,6},{2,9},{3},{4},{5},{7},{8}}
[4,1,5,6,7,8,9,2,3]=>{{1,2,4,6,8},{3,5,7,9}}
[2,3,4,5,8,9,1,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,6,7,1,8,9,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,7,6,5,4,2,3,1]=>{{1,9},{2,3,7,8},{4,6},{5}}
[2,3,9,8,7,6,5,4,1]=>{{1,2,3,9},{4,8},{5,7},{6}}
[9,1,3,2,4,5,6,7,8]=>{{1,2,4,5,6,7,8,9},{3}}
[3,5,2,4,7,6,9,8,1]=>{{1,2,3,5,7,9},{4},{6},{8}}
[2,4,3,6,5,8,7,1,9]=>{{1,2,4,6,8},{3},{5},{7},{9}}
[3,5,1,2,4,7,6,9,8]=>{{1,3},{2,4,5},{6,7},{8,9}}
[3,4,5,6,7,8,2,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[1,4,5,6,7,8,3,9,2]=>{{1},{2,4,6,8,9},{3,5,7}}
[3,4,5,6,7,2,1,9,8]=>{{1,3,5,7},{2,4,6},{8,9}}
[2,1,5,6,7,8,9,4,3]=>{{1,2},{3,5,7,9},{4,6,8}}
[2,4,5,6,7,8,3,1,9]=>{{1,2,4,6,8},{3,5,7},{9}}
[8,7,6,4,5,3,2,9,1]=>{{1,8,9},{2,7},{3,6},{4},{5}}
[2,9,8,7,5,6,4,3,1]=>{{1,2,9},{3,8},{4,7},{5},{6}}
[8,6,9,7,5,4,3,2,1]=>{{1,2,3,4,6,7,8,9},{5}}
[5,6,4,7,3,8,2,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[5,6,4,7,3,9,2,8,1]=>{{1,2,3,4,5,6,7,9},{8}}
[5,4,6,3,7,2,8,1,9]=>{{1,5,7,8},{2,3,4,6},{9}}
[1,8,3,4,5,6,7,9,2]=>{{1},{2,8,9},{3},{4},{5},{6},{7}}
[7,2,3,4,5,6,1,9,8]=>{{1,7},{2},{3},{4},{5},{6},{8,9}}
[2,1,9,4,5,6,7,8,3]=>{{1,2},{3,9},{4},{5},{6},{7},{8}}
[2,8,3,4,5,6,7,1,9]=>{{1,2,8},{3},{4},{5},{6},{7},{9}}
[6,1,2,3,4,5,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[5,1,2,3,4,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[4,1,2,3,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[9,8,2,3,4,5,6,7,1]=>{{1,9},{2,3,4,5,6,7,8}}
[8,9,2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,7,6,4,5,3,2,1]=>{{1,9},{2,8},{3,7},{4,5,6}}
[5,6,7,9,8,4,3,2,1]=>{{1,2,4,5,6,8,9},{3,7}}
[5,6,7,8,9,1,4,3,2]=>{{1,2,5,6,9},{3,4,7,8}}
[1,8,9,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7,8,9}}
[3,4,5,6,1,8,9,2,7]=>{{1,3,5},{2,4,6,8},{7,9}}
[3,4,5,6,8,1,9,2,7]=>{{1,2,3,4,5,6,8},{7,9}}
[3,4,5,6,8,9,1,2,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,4,5,1,6,7,8,9,3]=>{{1,2,4},{3,5,6,7,8,9}}
[2,3,4,1,6,7,8,9,5]=>{{1,2,3,4},{5,6,7,8,9}}
[3,4,5,6,1,2,9,7,8]=>{{1,3,5},{2,4,6},{7,8,9}}
[3,4,5,6,8,1,2,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[3,4,5,1,6,7,8,2,9]=>{{1,2,3,4,5,6,7,8},{9}}
[5,6,1,7,8,9,2,3,4]=>{{1,3,5,8},{2,4,6,7,9}}
[1,3,5,2,6,7,8,9,4]=>{{1},{2,3,4,5,6,7,8,9}}
[2,1,4,3,6,7,8,9,5]=>{{1,2},{3,4},{5,6,7,8,9}}
[2,3,1,5,6,7,8,9,4]=>{{1,2,3},{4,5,6,7,8,9}}
[9,7,8,5,4,3,2,1,6]=>{{1,3,6,8,9},{2,7},{4,5}}
[1,2,3,4,6,5,7,8,9]=>{{1},{2},{3},{4},{5,6},{7},{8},{9}}
[1,2,3,5,4,6,7,8,9]=>{{1},{2},{3},{4,5},{6},{7},{8},{9}}
[1,8,2,3,4,5,9,6,7]=>{{1},{2,3,4,5,6,8},{7,9}}
[1,3,4,5,6,8,9,2,7]=>{{1},{2,3,4,5,6,8},{7,9}}
[4,5,2,3,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[4,3,2,5,6,7,8,9,1]=>{{1,4,5,6,7,8,9},{2,3}}
[5,6,7,2,3,4,8,9,1]=>{{1,3,5,7,8,9},{2,4,6}}
[5,3,6,2,4,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[5,4,3,2,6,7,8,9,1]=>{{1,5,6,7,8,9},{2,4},{3}}
[6,3,7,8,2,4,5,9,1]=>{{1,4,6,8,9},{2,3,5,7}}
[6,7,4,5,2,3,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[6,4,3,7,2,5,8,9,1]=>{{1,2,4,5,6,7,8,9},{3}}
[7,8,4,5,9,2,3,6,1]=>{{1,3,4,5,7,9},{2,6,8}}
[7,4,3,8,9,2,5,6,1]=>{{1,5,7,9},{2,4,6,8},{3}}
[7,5,8,3,6,2,4,9,1]=>{{1,3,4,7,8,9},{2,5,6}}
[7,5,4,3,8,2,6,9,1]=>{{1,2,5,6,7,8,9},{3,4}}
[7,6,5,4,3,2,8,9,1]=>{{1,7,8,9},{2,6},{3,5},{4}}
[8,6,4,9,3,7,2,5,1]=>{{1,3,4,5,8,9},{2,6,7}}
[8,6,5,4,3,9,2,7,1]=>{{1,2,6,7,8,9},{3,5},{4}}
[2,4,1,5,3,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[4,5,6,7,8,3,9,1,2]=>{{1,2,4,5,7,8,9},{3,6}}
[8,9,2,3,4,5,1,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[5,6,7,4,8,9,1,2,3]=>{{1,2,3,5,6,7,8,9},{4}}
[7,8,9,2,3,1,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[6,5,7,8,9,1,2,3,4]=>{{1,6},{2,3,4,5,7,8,9}}
[7,1,2,3,4,5,8,6,9]=>{{1,2,3,4,5,6,7,8},{9}}
[6,1,2,3,4,7,5,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[5,1,2,3,6,4,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[4,1,2,5,3,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[9,1,2,3,8,5,6,7,4]=>{{1,2,3,4,9},{5,6,7,8}}
[1,2,3,4,5,8,9,6,7]=>{{1},{2},{3},{4},{5},{6,8},{7,9}}
[1,2,3,4,7,9,5,8,6]=>{{1},{2},{3},{4},{5,7},{6,9},{8}}
[1,2,3,6,9,4,7,8,5]=>{{1},{2},{3},{4,6},{5,9},{7},{8}}
[1,2,5,9,3,6,7,8,4]=>{{1},{2},{3,5},{4,9},{6},{7},{8}}
[1,4,9,2,5,6,7,8,3]=>{{1},{2,4},{3,9},{5},{6},{7},{8}}
[3,9,1,4,5,6,7,8,2]=>{{1,3},{2,9},{4},{5},{6},{7},{8}}
[2,8,1,9,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,4,2,3,6,5,8,7,9]=>{{1},{2,3,4},{5,6},{7,8},{9}}
[1,3,4,2,6,5,8,7,9]=>{{1},{2,3,4},{5,6},{7,8},{9}}
[2,3,1,4,6,5,8,7,9]=>{{1,2,3},{4},{5,6},{7,8},{9}}
[4,6,1,2,3,5,8,7,9]=>{{1,2,3,4,5,6},{7,8},{9}}
[3,4,5,1,6,2,8,7,9]=>{{1,2,3,4,5,6},{7,8},{9}}
[3,1,2,4,6,5,8,7,9]=>{{1,2,3},{4},{5,6},{7,8},{9}}
[2,1,3,4,5,6,9,7,8]=>{{1,2},{3},{4},{5},{6},{7,8,9}}
[1,2,3,4,5,7,8,6,9]=>{{1},{2},{3},{4},{5},{6,7,8},{9}}
[7,1,9,3,4,5,6,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[7,2,1,9,4,5,6,3,8]=>{{1,3,4,5,6,7,8,9},{2}}
[6,9,7,3,4,5,1,2,8]=>{{1,3,4,5,6,7},{2,8,9}}
[3,8,1,2,9,5,6,7,4]=>{{1,3},{2,4,5,6,7,8,9}}
[8,7,9,1,2,3,4,5,6]=>{{1,2,4,5,7,8},{3,6,9}}
[7,2,3,1,9,5,6,4,8]=>{{1,4,5,6,7,8,9},{2},{3}}
[6,1,2,7,4,5,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[5,9,6,3,4,1,7,2,8]=>{{1,3,4,5,6},{2,8,9},{7}}
[3,8,1,4,2,9,6,7,5]=>{{1,3},{2,5,6,7,8,9},{4}}
[9,7,2,3,8,5,6,1,4]=>{{1,2,3,4,5,6,7,8,9}}
[7,6,8,9,1,2,3,4,5]=>{{1,3,4,5,7,8,9},{2,6}}
[5,4,6,7,8,9,1,2,3]=>{{1,2,4,5,7,8},{3,6,9}}
[1,4,3,2,5,6,7,8,9]=>{{1},{2,4},{3},{5},{6},{7},{8},{9}}
[2,3,4,5,6,9,8,7,1]=>{{1,2,3,4,5,6,9},{7,8}}
[2,3,4,5,8,7,9,6,1]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,6,5,7,8,9,4,1]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,8,9,7,6,1]=>{{1,2,3,4,5,6,8,9},{7}}
[3,4,5,6,7,1,2,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[2,3,5,1,4,7,6,9,8]=>{{1,2,3,4,5},{6,7},{8,9}}
[3,4,1,5,2,7,6,9,8]=>{{1,3},{2,4,5},{6,7},{8,9}}
[4,1,2,5,3,7,6,9,8]=>{{1,2,3,4,5},{6,7},{8,9}}
[4,2,6,8,1,3,5,7,9]=>{{1,4,5,7,8},{2},{3,6},{9}}
[4,6,2,8,1,3,5,7,9]=>{{1,4,5,7,8},{2,3,6},{9}}
[4,6,8,2,1,3,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[4,6,8,2,9,1,3,5,7]=>{{1,2,4,6},{3,5,7,8,9}}
[4,6,2,7,9,1,3,5,8]=>{{1,2,3,4,6,7},{5,8,9}}
[4,2,5,7,9,1,3,6,8]=>{{1,3,4,5,6,7,8,9},{2}}
[2,3,5,7,9,1,4,6,8]=>{{1,2,3,5,6,8,9},{4,7}}
[6,4,2,8,1,3,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[8,4,6,2,1,3,5,7,9]=>{{1,5,7,8},{2,4},{3,6},{9}}
[4,6,8,9,2,1,3,5,7]=>{{1,2,3,4,5,6,7,8,9}}
[4,6,2,7,1,3,5,8,9]=>{{1,4,5,7},{2,3,6},{8},{9}}
[4,8,2,5,9,1,3,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[6,2,3,7,9,1,4,5,8]=>{{1,6},{2},{3},{4,7},{5,8,9}}
[1,4,5,7,9,2,3,6,8]=>{{1},{2,3,4,5,6,7,8,9}}
[8,6,4,9,7,5,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[7,8,5,9,6,4,3,2,1]=>{{1,3,4,5,6,7,9},{2,8}}
[8,6,4,2,9,7,5,3,1]=>{{1,2,3,4,5,6,7,8,9}}
[7,8,5,3,9,6,4,2,1]=>{{1,3,4,5,7,9},{2,8},{6}}
[7,4,8,5,9,6,3,2,1]=>{{1,2,3,4,5,7,8,9},{6}}
[6,7,8,4,9,5,3,2,1]=>{{1,5,6,9},{2,3,7,8},{4}}
[7,8,5,3,1,9,6,4,2]=>{{1,2,3,4,5,6,7,8,9}}
[7,4,8,5,2,9,6,3,1]=>{{1,6,7,9},{2,4,5},{3,8}}
[6,7,8,4,2,9,5,3,1]=>{{1,6,9},{2,5,7},{3,8},{4}}
[6,7,3,8,4,9,5,2,1]=>{{1,6,9},{2,4,5,7,8},{3}}
[5,6,7,8,3,9,4,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[6,7,3,8,4,1,9,5,2]=>{{1,6},{2,7,9},{3},{4,5,8}}
[5,6,7,8,3,1,9,4,2]=>{{1,2,3,5,6,7,9},{4,8}}
[6,2,7,3,8,4,9,5,1]=>{{1,3,4,6,7,9},{2},{5,8}}
[5,6,7,2,8,3,9,4,1]=>{{1,2,3,4,5,6,7,8,9}}
[4,5,6,7,8,2,9,3,1]=>{{1,4,7,9},{2,3,5,6,8}}
[5,6,1,7,2,8,3,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[4,5,6,7,1,8,2,9,3]=>{{1,2,4,5,7},{3,6,8,9}}
[2,3,4,5,9,6,7,8,1]=>{{1,2,3,4,5,9},{6},{7},{8}}
[2,3,4,9,5,6,7,8,1]=>{{1,2,3,4,9},{5},{6},{7},{8}}
[2,3,9,4,5,6,7,8,1]=>{{1,2,3,9},{4},{5},{6},{7},{8}}
[2,3,4,5,9,7,6,8,1]=>{{1,2,3,4,5,9},{6,7},{8}}
[2,3,4,9,6,5,7,8,1]=>{{1,2,3,4,9},{5,6},{7},{8}}
[2,3,9,5,4,6,7,8,1]=>{{1,2,3,9},{4,5},{6},{7},{8}}
[2,9,4,3,5,6,7,8,1]=>{{1,2,9},{3,4},{5},{6},{7},{8}}
[2,3,4,5,9,7,8,6,1]=>{{1,2,3,4,5,9},{6,7,8}}
[2,1,8,3,4,5,6,7,9]=>{{1,2},{3,4,5,6,7,8},{9}}
[1,9,6,2,3,4,5,8,7]=>{{1},{2,3,4,5,6,7,9},{8}}
[9,8,7,4,5,6,3,2,1]=>{{1,9},{2,8},{3,7},{4},{5},{6}}
[1,5,6,7,8,9,2,3,4]=>{{1},{2,3,4,5,6,7,8,9}}
[1,7,2,8,9,3,4,5,6]=>{{1},{2,3,4,5,6,7,8,9}}
[1,6,2,7,8,9,3,4,5]=>{{1},{2,3,4,5,6,7,8,9}}
[1,5,2,6,7,8,9,3,4]=>{{1},{2,3,4,5,6,7,8,9}}
[3,4,2,1,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[4,3,1,2,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[4,5,2,1,3,6,7,8,9]=>{{1,4},{2,3,5},{6},{7},{8},{9}}
[3,4,2,5,1,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[5,3,1,2,4,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[4,3,5,1,2,6,7,8,9]=>{{1,4},{2,3,5},{6},{7},{8},{9}}
[5,4,3,1,2,6,7,8,9]=>{{1,2,4,5},{3},{6},{7},{8},{9}}
[6,5,4,3,1,2,7,8,9]=>{{1,2,5,6},{3,4},{7},{8},{9}}
[8,5,4,3,9,1,2,6,7]=>{{1,6,8},{2,5,7,9},{3,4}}
[2,3,4,5,9,7,1,8,6]=>{{1,2,3,4,5,6,7,9},{8}}
[2,3,4,9,6,7,1,8,5]=>{{1,2,3,4,5,6,7,9},{8}}
[2,3,9,5,6,1,7,8,4]=>{{1,2,3,4,5,6,9},{7},{8}}
[2,3,9,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,9},{8}}
[2,1,3,4,5,6,8,7,9]=>{{1,2},{3},{4},{5},{6},{7,8},{9}}
[2,3,4,5,6,8,7,9,1]=>{{1,2,3,4,5,6,8,9},{7}}
[8,6,5,4,3,2,7,9,1]=>{{1,8,9},{2,6},{3,5},{4},{7}}
[8,9,5,4,3,2,1,6,7]=>{{1,2,6,7,8,9},{3,5},{4}}
[7,6,5,4,3,8,9,1,2]=>{{1,2,6,7,8,9},{3,5},{4}}
[9,6,5,4,3,2,7,1,8]=>{{1,8,9},{2,6},{3,5},{4},{7}}
[9,2,3,4,5,6,1,7,8]=>{{1,7,8,9},{2},{3},{4},{5},{6}}
[3,1,5,6,7,8,9,2,4]=>{{1,2,3,4,5,6,7,8,9}}
[2,1,3,5,6,7,8,9,4]=>{{1,2},{3},{4,5,6,7,8,9}}
[3,4,5,6,7,9,1,2,8]=>{{1,3,5,7},{2,4,6,8,9}}
[3,4,5,7,8,9,1,2,6]=>{{1,2,3,4,5,7,8},{6,9}}
[3,5,6,7,8,9,1,2,4]=>{{1,3,4,6,7,9},{2,5,8}}
[3,4,5,6,9,1,2,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[3,4,5,6,1,2,7,8,9]=>{{1,3,5},{2,4,6},{7},{8},{9}}
[5,1,6,7,8,9,2,3,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,2,5,6,7,3,8,9,4]=>{{1},{2},{3,4,5,6,7,8,9}}
[1,2,4,3,5,7,8,9,6]=>{{1},{2},{3,4},{5},{6,7,8,9}}
[3,1,2,4,5,6,7,9,8]=>{{1,2,3},{4},{5},{6},{7},{8,9}}
[9,8,7,1,5,6,4,3,2]=>{{1,2,3,4,7,8,9},{5},{6}}
[9,1,7,8,6,5,4,3,2]=>{{1,2,9},{3,4,7,8},{5,6}}
[1,3,4,5,6,7,2,9,8]=>{{1},{2,3,4,5,6,7},{8,9}}
[3,4,5,6,7,1,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[3,2,4,1,6,5,8,7,9]=>{{1,3,4},{2},{5,6},{7,8},{9}}
[4,2,5,1,6,3,8,7,9]=>{{1,4},{2},{3,5,6},{7,8},{9}}
[4,2,6,1,7,3,8,5,9]=>{{1,4},{2},{3,6},{5,7,8},{9}}
[4,2,6,1,8,3,9,5,7]=>{{1,4},{2},{3,6},{5,8},{7,9}}
[4,2,6,1,7,3,5,9,8]=>{{1,4},{2},{3,6},{5,7},{8,9}}
[4,2,5,1,3,7,6,9,8]=>{{1,4},{2},{3,5},{6,7},{8,9}}
[3,2,5,4,6,1,8,7,9]=>{{1,3,5,6},{2},{4},{7,8},{9}}
[4,2,5,1,7,6,8,3,9]=>{{1,4},{2},{3,5,7,8},{6},{9}}
[4,2,6,1,7,3,9,8,5]=>{{1,4},{2},{3,6},{5,7,9},{8}}
[4,2,6,1,7,3,5,8,9]=>{{1,4},{2},{3,6},{5,7},{8},{9}}
[4,2,5,1,3,8,9,6,7]=>{{1,4},{2},{3,5},{6,8},{7,9}}
[3,2,1,6,7,4,5,9,8]=>{{1,3},{2},{4,6},{5,7},{8,9}}
[1,4,5,2,3,7,6,9,8]=>{{1},{2,4},{3,5},{6,7},{8,9}}
[7,6,5,4,3,1,2,9,8]=>{{1,2,6,7},{3,5},{4},{8,9}}
[7,6,5,4,2,1,3,9,8]=>{{1,2,3,5,6,7},{4},{8,9}}
[7,6,5,4,1,3,2,9,8]=>{{1,2,3,5,6,7},{4},{8,9}}
[9,8,7,6,5,3,2,4,1]=>{{1,9},{2,3,4,6,7,8},{5}}
[9,8,7,6,5,2,4,3,1]=>{{1,9},{2,3,4,6,7,8},{5}}
[2,3,4,8,6,7,9,5,1]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,8,5,6,7,9,1,4]=>{{1,2,3,8},{4,5,6,7,9}}
[2,8,4,5,6,7,9,3,1]=>{{1,2,3,4,5,6,7,8,9}}
[8,3,4,5,6,7,9,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,7,9,1,8,6]=>{{1,2,3,4,5,7},{6,9},{8}}
[2,3,4,6,7,1,9,5,8]=>{{1,2,3,4,6},{5,7,8,9}}
[2,3,5,6,1,7,9,4,8]=>{{1,2,3,5},{4,6,7,8,9}}
[2,4,5,1,6,7,9,8,3]=>{{1,2,4},{3,5,6,7,9},{8}}
[3,4,1,5,6,7,9,2,8]=>{{1,3},{2,4,5,6,7,8,9}}
[3,2,4,5,6,7,9,1,8]=>{{1,3,4,5,6,7,8,9},{2}}
[2,3,4,7,6,9,8,5,1]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,6,9,1,7,8,5]=>{{1,2,3,4,6},{5,9},{7},{8}}
[2,5,4,6,8,7,9,1,3]=>{{1,2,5,8},{3,4,6,7,9}}
[2,3,5,7,1,6,9,4,8]=>{{1,2,3,5},{4,7,8,9},{6}}
[4,3,5,8,6,7,9,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[2,4,6,1,5,7,9,3,8]=>{{1,2,4},{3,6,7,8,9},{5}}
[2,4,8,5,6,7,9,1,3]=>{{1,2,3,4,5,6,7,8,9}}
[3,5,1,4,6,7,9,8,2]=>{{1,3},{2,5,6,7,9},{4},{8}}
[4,2,3,5,6,7,9,1,8]=>{{1,4,5,6,7,8,9},{2},{3}}
[1,4,2,6,3,7,5,9,8]=>{{1},{2,3,4,5,6,7},{8,9}}
[1,3,2,6,4,7,5,9,8]=>{{1},{2,3},{4,5,6,7},{8,9}}
[2,1,6,3,7,4,8,5,9]=>{{1,2},{3,4,6},{5,7,8},{9}}
[6,5,4,3,2,7,1,8,9]=>{{1,6,7},{2,5},{3,4},{8},{9}}
[5,4,3,2,6,1,7,8,9]=>{{1,5,6},{2,4},{3},{7},{8},{9}}
[4,3,2,5,1,6,7,8,9]=>{{1,4,5},{2,3},{6},{7},{8},{9}}
[3,2,4,1,5,6,7,8,9]=>{{1,3,4},{2},{5},{6},{7},{8},{9}}
[1,3,5,2,7,4,6,9,8]=>{{1},{2,3,4,5,6,7},{8,9}}
[1,2,4,3,6,5,8,7,9]=>{{1},{2},{3,4},{5,6},{7,8},{9}}
[1,3,5,7,2,4,6,9,8]=>{{1},{2,3,5},{4,6,7},{8,9}}
[1,3,5,7,2,9,4,6,8]=>{{1},{2,3,5},{4,7},{6,8,9}}
[5,6,2,1,3,7,4,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[3,2,5,1,6,4,7,8,9]=>{{1,3,4,5,6},{2},{7},{8},{9}}
[6,7,2,1,8,3,4,9,5]=>{{1,2,3,4,6,7},{5,8,9}}
[3,6,4,1,7,2,8,5,9]=>{{1,3,4},{2,6},{5,7,8},{9}}
[3,6,7,2,1,4,8,5,9]=>{{1,3,5,7,8},{2,4,6},{9}}
[4,2,6,1,7,5,3,8,9]=>{{1,4},{2},{3,5,6,7},{8},{9}}
[4,3,2,6,1,7,5,8,9]=>{{1,4,5,6,7},{2,3},{8},{9}}
[4,7,2,5,1,8,3,9,6]=>{{1,4,5},{2,3,7},{6,8,9}}
[4,3,7,8,2,1,5,9,6]=>{{1,4,6,8,9},{2,3,5,7}}
[3,5,2,7,1,8,6,4,9]=>{{1,2,3,5},{4,6,7,8},{9}}
[5,4,3,2,7,1,8,6,9]=>{{1,5,6,7,8},{2,4},{3},{9}}
[6,4,2,8,1,9,7,5,3]=>{{1,2,3,4,5,6,8,9},{7}}
[4,3,6,2,8,1,9,7,5]=>{{1,2,3,4,6},{5,7,8,9}}
[6,5,4,3,2,8,1,9,7]=>{{1,6,7,8,9},{2,5},{3,4}}
[2,8,7,9,6,5,4,3,1]=>{{1,2,3,4,7,8,9},{5,6}}
[3,1,2,9,4,5,6,7,8]=>{{1,2,3},{4,5,6,7,8,9}}
[4,1,2,3,9,5,6,7,8]=>{{1,2,3,4},{5,6,7,8,9}}
[5,1,2,3,4,9,6,7,8]=>{{1,2,3,4,5},{6,7,8,9}}
[6,1,2,3,4,5,9,7,8]=>{{1,2,3,4,5,6},{7,8,9}}
[3,4,1,2,9,5,6,7,8]=>{{1,3},{2,4},{5,6,7,8,9}}
[4,5,1,2,3,9,6,7,8]=>{{1,2,3,4,5},{6,7,8,9}}
[5,6,1,2,3,4,9,7,8]=>{{1,3,5},{2,4,6},{7,8,9}}
[6,7,1,2,3,4,5,9,8]=>{{1,2,3,4,5,6,7},{8,9}}
[9,7,5,3,1,8,6,4,2]=>{{1,2,3,4,5,6,7,8,9}}
[9,6,3,8,5,2,7,4,1]=>{{1,9},{2,6},{3},{4,8},{5},{7}}
[8,5,2,9,6,3,7,4,1]=>{{1,4,8,9},{2,3,5,6},{7}}
[9,5,1,6,2,7,3,8,4]=>{{1,3,4,6,7,9},{2,5},{8}}
[9,5,1,8,4,7,3,6,2]=>{{1,2,3,4,5,6,7,8,9}}
[8,4,7,3,6,2,9,5,1]=>{{1,2,3,4,5,6,7,8,9}}
[7,3,8,4,6,2,9,5,1]=>{{1,7,9},{2,3,5,6,8},{4}}
[9,4,7,2,5,8,3,6,1]=>{{1,9},{2,4},{3,7},{5},{6,8}}
[9,4,6,1,8,3,5,7,2]=>{{1,2,4,9},{3,6},{5,7,8}}
[8,3,5,7,2,9,4,6,1]=>{{1,6,8,9},{2,3,5},{4,7}}
[7,2,8,3,9,4,5,6,1]=>{{1,5,7,9},{2},{3,4,6,8}}
[8,3,7,2,9,4,5,6,1]=>{{1,2,3,4,5,6,7,8,9}}
[5,8,3,7,2,9,4,6,1]=>{{1,2,5,6,8,9},{3},{4,7}}
[4,5,6,9,3,8,2,7,1]=>{{1,4,9},{2,3,5,6,7,8}}
[4,5,6,8,2,9,3,7,1]=>{{1,3,4,6,7,8,9},{2,5}}
[9,3,6,5,4,7,1,8,2]=>{{1,2,3,6,7,9},{4,5},{8}}
[8,2,9,3,6,5,4,7,1]=>{{1,3,4,7,8,9},{2},{5,6}}
[6,5,4,8,2,9,3,7,1]=>{{1,6,9},{2,5},{3,4,7,8}}
[5,6,4,8,2,9,3,7,1]=>{{1,2,5,6,9},{3,4,7,8}}
[9,2,7,4,5,6,3,8,1]=>{{1,9},{2},{3,7},{4},{5},{6},{8}}
[7,4,5,6,3,9,2,8,1]=>{{1,2,4,6,7,9},{3,5},{8}}
[5,7,4,6,3,9,2,8,1]=>{{1,3,4,5,6,9},{2,7},{8}}
[4,2,5,6,7,8,9,1,3]=>{{1,4,6,8},{2},{3,5,7,9}}
[5,6,7,9,1,2,3,4,8]=>{{1,5},{2,6},{3,7},{4,8,9}}
[4,5,6,7,9,1,2,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,6,5,7,4,8,3,9,2]=>{{1},{2,6,8,9},{3,4,5,7}}
[5,4,6,3,8,2,7,1,9]=>{{1,5,8},{2,3,4,6},{7},{9}}
[3,4,5,6,7,8,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[3,4,5,6,7,2,1,8,9]=>{{1,3,5,7},{2,4,6},{8},{9}}
[4,5,6,7,8,1,2,3,9]=>{{1,2,3,4,5,6,7,8},{9}}
[4,3,1,2,6,5,8,7,9]=>{{1,2,3,4},{5,6},{7,8},{9}}
[6,5,3,1,2,4,8,7,9]=>{{1,4,6},{2,5},{3},{7,8},{9}}
[8,7,5,3,1,2,4,6,9]=>{{1,2,3,4,5,6,7,8},{9}}
[7,5,3,1,2,4,6,9,8]=>{{1,4,6,7},{2,5},{3},{8,9}}
[5,3,1,2,4,7,6,9,8]=>{{1,2,3,4,5},{6,7},{8,9}}
[4,1,2,6,5,3,8,7,9]=>{{1,2,3,4,6},{5},{7,8},{9}}
[6,3,1,2,4,8,7,5,9]=>{{1,2,3,4,5,6,8},{7},{9}}
[8,5,3,1,2,4,6,9,7]=>{{1,4,6,7,8,9},{2,5},{3}}
[7,5,3,1,2,4,6,8,9]=>{{1,4,6,7},{2,5},{3},{8},{9}}
[5,3,1,2,4,9,7,6,8]=>{{1,2,3,4,5},{6,8,9},{7}}
[3,1,2,7,5,4,6,9,8]=>{{1,2,3},{4,6,7},{5},{8,9}}
[1,5,3,2,4,7,6,9,8]=>{{1},{2,4,5},{3},{6,7},{8,9}}
[1,7,6,5,4,3,2,9,8]=>{{1},{2,7},{3,6},{4,5},{8,9}}
[1,7,8,9,6,5,4,3,2]=>{{1},{2,4,7,9},{3,8},{5,6}}
[1,6,7,8,9,5,4,3,2]=>{{1},{2,5,6,9},{3,4,7,8}}
[1,5,6,7,8,9,4,3,2]=>{{1},{2,3,5,6,8,9},{4,7}}
[1,4,5,6,7,8,9,3,2]=>{{1},{2,3,4,5,6,7,8,9}}
[1,7,6,8,9,5,4,3,2]=>{{1},{2,3,4,5,6,7,8,9}}
[1,6,5,7,8,9,4,3,2]=>{{1},{2,6,9},{3,5,8},{4,7}}
[1,5,4,6,7,8,9,3,2]=>{{1},{2,5,7,9},{3,4,6,8}}
[9,8,7,6,5,2,1,3,4]=>{{1,2,3,4,6,7,8,9},{5}}
[9,7,8,6,5,4,3,2,1]=>{{1,9},{2,3,7,8},{4,6},{5}}
[3,2,5,6,7,8,9,1,4]=>{{1,3,4,5,6,7,8,9},{2}}
[4,2,5,6,7,8,9,3,1]=>{{1,3,4,5,6,7,8,9},{2}}
[1,2,5,6,7,4,8,9,3]=>{{1},{2},{3,5,7,8,9},{4,6}}
[1,3,4,5,6,7,2,8,9]=>{{1},{2,3,4,5,6,7},{8},{9}}
[2,3,4,7,8,9,1,5,6]=>{{1,2,3,4,7},{5,8},{6,9}}
[2,3,6,7,8,9,1,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[2,5,6,7,8,9,1,3,4]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,1,9,6,7,8]=>{{1,2,3,4,5},{6,7,8,9}}
[2,3,4,1,8,9,5,6,7]=>{{1,2,3,4},{5,6,7,8,9}}
[2,3,1,7,8,9,4,5,6]=>{{1,2,3},{4,7},{5,8},{6,9}}
[2,1,6,7,8,9,3,4,5]=>{{1,2},{3,4,5,6,7,8,9}}
[4,1,2,3,6,5,8,7,9]=>{{1,2,3,4},{5,6},{7,8},{9}}
[4,1,6,2,3,5,8,7,9]=>{{1,2,4},{3,5,6},{7,8},{9}}
[2,3,1,9,8,7,6,5,4]=>{{1,2,3},{4,9},{5,8},{6,7}}
[3,4,2,1,9,8,7,6,5]=>{{1,2,3,4},{5,9},{6,8},{7}}
[4,5,3,2,1,9,8,7,6]=>{{1,2,4,5},{3},{6,9},{7,8}}
[5,6,4,3,2,1,9,8,7]=>{{1,2,5,6},{3,4},{7,9},{8}}
[6,7,5,4,3,2,1,9,8]=>{{1,2,6,7},{3,5},{4},{8,9}}
[3,4,5,6,1,7,2,9,8]=>{{1,3,5},{2,4,6,7},{8,9}}
[1,4,5,9,6,7,2,8,3]=>{{1},{2,3,4,5,6,7,9},{8}}
[2,4,5,9,6,1,7,3,8]=>{{1,2,3,4,5,6,8,9},{7}}
[3,4,5,7,6,1,9,2,8]=>{{1,3,5,6},{2,4,7,8,9}}
[3,5,6,9,7,1,8,2,4]=>{{1,3,6},{2,5,7,8},{4,9}}
[1,4,8,5,6,2,7,9,3]=>{{1},{2,4,5,6},{3,8,9},{7}}
[2,5,9,6,7,3,1,4,8]=>{{1,2,5,7},{3,4,6,8,9}}
[4,1,5,2,7,6,3,9,8]=>{{1,2,4},{3,5,7},{6},{8,9}}
[3,4,1,6,9,5,7,2,8]=>{{1,3},{2,4,5,6,8,9},{7}}
[6,7,9,8,1,3,4,2,5]=>{{1,3,5,6,9},{2,4,7,8}}
[9,1,5,2,8,6,3,7,4]=>{{1,2,4,9},{3,5,7,8},{6}}
[1,7,4,5,2,6,8,9,3]=>{{1},{2,3,4,5,7,8,9},{6}}
[6,8,9,1,2,3,4,5,7]=>{{1,3,4,6,7,9},{2,5,8}}
[5,8,9,1,2,3,4,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,1,7,6,9,8]=>{{1,2,3,4,5},{6,7},{8,9}}
[2,3,4,1,6,5,8,7,9]=>{{1,2,3,4},{5,6},{7,8},{9}}
[2,3,4,5,1,8,6,9,7]=>{{1,2,3,4,5},{6,7,8,9}}
[2,3,4,1,7,5,8,6,9]=>{{1,2,3,4},{5,6,7,8},{9}}
[3,4,5,6,7,9,1,8,2]=>{{1,3,5,7},{2,4,6,9},{8}}
[3,4,5,6,7,9,2,8,1]=>{{1,2,3,4,5,6,7,9},{8}}
[3,4,5,6,7,1,9,8,2]=>{{1,2,3,4,5,6,7,9},{8}}
[5,3,4,2,1,9,8,7,6]=>{{1,5},{2,3,4},{6,9},{7,8}}
[6,5,3,4,2,1,9,8,7]=>{{1,6},{2,5},{3},{4},{7,9},{8}}
[7,6,4,5,3,2,1,9,8]=>{{1,7},{2,6},{3,4,5},{8,9}}
[3,4,5,1,2,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[2,4,1,5,3,6,8,7,9]=>{{1,2,3,4,5},{6},{7,8},{9}}
[2,4,1,7,3,8,5,6,9]=>{{1,2,3,4,5,7},{6,8},{9}}
[8,5,9,3,6,1,2,4,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,7,1,5,8,3,6,2,4]=>{{1,2,3,4,5,6,7,8,9}}
[9,7,5,4,1,3,8,2,6]=>{{1,3,5,6,9},{2,7,8},{4}}
[9,6,5,4,3,2,1,7,8]=>{{1,7,8,9},{2,6},{3,5},{4}}
[9,8,5,4,3,2,1,6,7]=>{{1,7,9},{2,6,8},{3,5},{4}}
[9,1,2,3,4,5,8,7,6]=>{{1,2,3,4,5,6,9},{7,8}}
[9,1,2,3,4,8,6,7,5]=>{{1,2,3,4,5,9},{6,7,8}}
[9,1,2,8,4,5,6,7,3]=>{{1,2,3,9},{4,5,6,7,8}}
[9,1,8,3,4,5,6,7,2]=>{{1,2,9},{3,4,5,6,7,8}}
[9,1,2,3,4,7,8,6,5]=>{{1,2,3,4,5,9},{6,7,8}}
[9,1,2,3,6,8,5,7,4]=>{{1,2,3,4,9},{5,6,7,8}}
[9,1,2,5,8,4,6,7,3]=>{{1,2,3,9},{4,5,6,7,8}}
[9,1,4,8,3,5,6,7,2]=>{{1,2,9},{3,4,5,6,7,8}}
[9,3,8,2,4,5,6,7,1]=>{{1,9},{2,3,4,5,6,7,8}}
[3,4,5,6,8,9,1,7,2]=>{{1,3,5,7,8},{2,4,6,9}}
[3,4,6,7,8,9,1,5,2]=>{{1,2,3,4,6,7,9},{5,8}}
[3,5,6,7,8,9,1,4,2]=>{{1,2,3,4,5,6,7,8,9}}
[4,5,6,7,8,9,1,3,2]=>{{1,4,7},{2,3,5,6,8,9}}
[5,4,2,3,6,7,8,9,1]=>{{1,5,6,7,8,9},{2,3,4}}
[6,5,4,2,3,7,8,9,1]=>{{1,6,7,8,9},{2,3,4,5}}
[7,6,5,4,2,3,8,9,1]=>{{1,7,8,9},{2,3,5,6},{4}}
[4,6,7,8,9,1,2,3,5]=>{{1,2,3,4,6,7,8},{5,9}}
[5,7,8,9,1,2,3,4,6]=>{{1,5},{2,3,4,6,7,8,9}}
[8,7,5,4,6,3,2,9,1]=>{{1,8,9},{2,7},{3,5,6},{4}}
[8,7,4,6,5,3,2,9,1]=>{{1,8,9},{2,7},{3,4,6},{5}}
[2,3,4,7,8,9,6,5,1]=>{{1,2,3,4,6,7,9},{5,8}}
[2,3,6,7,8,9,5,4,1]=>{{1,2,3,6,9},{4,5,7,8}}
[2,5,6,7,8,9,4,3,1]=>{{1,2,3,5,6,8,9},{4,7}}
[2,3,4,5,6,1,9,8,7]=>{{1,2,3,4,5,6},{7,9},{8}}
[2,3,4,5,1,9,8,7,6]=>{{1,2,3,4,5},{6,9},{7,8}}
[2,3,4,1,8,9,7,6,5]=>{{1,2,3,4},{5,6,8,9},{7}}
[2,3,1,7,8,9,6,5,4]=>{{1,2,3},{4,6,7,9},{5,8}}
[2,1,6,7,8,9,5,4,3]=>{{1,2},{3,6,9},{4,5,7,8}}
[8,9,7,6,5,4,3,1,2]=>{{1,8},{2,9},{3,7},{4,6},{5}}
[8,6,7,5,4,3,2,1,9]=>{{1,8},{2,3,6,7},{4,5},{9}}
[8,7,9,6,5,4,3,1,2]=>{{1,8},{2,3,7,9},{4,6},{5}}
[9,7,8,6,5,4,3,1,2]=>{{1,2,3,7,8,9},{4,6},{5}}
[8,7,5,4,3,6,9,2,1]=>{{1,2,7,8,9},{3,5},{4},{6}}
[8,7,6,9,5,3,4,2,1]=>{{1,2,4,7,8,9},{3,6},{5}}
[8,7,9,6,5,4,2,3,1]=>{{1,3,8,9},{2,7},{4,6},{5}}
[3,2,1,5,6,7,8,9,4]=>{{1,3},{2},{4,5,6,7,8,9}}
[3,2,6,1,4,7,8,9,5]=>{{1,3,4,5,6,7,8,9},{2}}
[4,3,2,1,6,7,8,9,5]=>{{1,4},{2,3},{5,6,7,8,9}}
[3,2,7,8,1,4,5,9,6]=>{{1,3,5,7},{2},{4,6,8,9}}
[4,7,2,5,1,3,8,9,6]=>{{1,4,5},{2,3,6,7,8,9}}
[4,3,2,7,1,5,8,9,6]=>{{1,4,5,6,7,8,9},{2,3}}
[5,4,3,2,1,7,8,9,6]=>{{1,5},{2,4},{3},{6,7,8,9}}
[4,3,2,8,9,1,5,6,7]=>{{1,4,6,8},{2,3},{5,7,9}}
[8,5,6,3,4,1,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[5,3,8,2,6,1,4,9,7]=>{{1,5,6},{2,3,4,7,8,9}}
[5,4,3,2,8,1,6,9,7]=>{{1,5,6,7,8,9},{2,4},{3}}
[6,5,4,3,2,1,8,9,7]=>{{1,6},{2,5},{3,4},{7,8,9}}
[6,9,4,7,2,5,1,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[6,4,3,9,2,7,1,5,8]=>{{1,6,7},{2,4,5,8,9},{3}}
[6,5,4,3,2,9,1,7,8]=>{{1,6,7,8,9},{2,5},{3,4}}
[2,3,4,9,6,7,8,5,1]=>{{1,2,3,4,9},{5,6,7,8}}
[2,3,9,5,6,7,8,4,1]=>{{1,2,3,9},{4,5,6,7,8}}
[2,9,4,5,6,7,8,3,1]=>{{1,2,9},{3,4,5,6,7,8}}
[9,3,4,5,6,7,8,2,1]=>{{1,9},{2,3,4,5,6,7,8}}
[2,3,4,1,9,7,8,6,5]=>{{1,2,3,4},{5,9},{6,7,8}}
[2,3,1,9,6,7,8,5,4]=>{{1,2,3},{4,9},{5,6,7,8}}
[2,1,9,5,6,7,8,4,3]=>{{1,2},{3,9},{4,5,6,7,8}}
[1,9,4,5,6,7,8,3,2]=>{{1},{2,9},{3,4,5,6,7,8}}
[5,6,4,7,3,9,1,8,2]=>{{1,3,4,5,7},{2,6,9},{8}}
[5,6,4,9,1,8,2,7,3]=>{{1,5},{2,6,7,8},{3,4,9}}
[5,9,1,8,2,7,3,6,4]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,8,2,7,3,6,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[5,4,9,1,8,2,7,3,6]=>{{1,2,3,4,5,6,8,9},{7}}
[5,4,6,3,9,1,8,2,7]=>{{1,2,3,4,5,6,7,8,9}}
[5,4,6,3,7,2,9,1,8]=>{{1,5,7,8,9},{2,3,4,6}}
[5,6,4,8,2,9,1,7,3]=>{{1,2,3,4,5,6,7,8,9}}
[5,7,3,9,1,8,2,6,4]=>{{1,5},{2,7},{3},{4,9},{6,8}}
[6,4,9,1,8,2,7,3,5]=>{{1,2,4,6},{3,5,8,9},{7}}
[4,5,9,1,8,2,7,3,6]=>{{1,4},{2,3,5,6,8,9},{7}}
[6,4,5,3,9,1,8,2,7]=>{{1,6},{2,3,4,5,7,8,9}}
[5,4,7,3,6,2,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}
[5,4,3,2,1,8,9,7,6]=>{{1,5},{2,4},{3},{6,7,8,9}}
[4,3,2,1,8,9,7,6,5]=>{{1,4},{2,3},{5,6,8,9},{7}}
[3,2,1,8,9,7,6,5,4]=>{{1,3},{2},{4,5,8,9},{6,7}}
[2,1,8,9,7,6,5,4,3]=>{{1,2},{3,4,8,9},{5,7},{6}}
[9,8,3,4,5,6,7,1,2]=>{{1,2,8,9},{3},{4},{5},{6},{7}}
[9,8,2,3,4,5,6,1,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,4,5,6,7,8,2,1,3]=>{{1,2,3,4,5,6,7,8,9}}
[9,3,4,5,6,7,2,1,8]=>{{1,8,9},{2,3,4,5,6,7}}
[7,2,9,8,3,4,5,6,1]=>{{1,3,5,7,9},{2},{4,6,8}}
[9,8,2,3,4,5,1,6,7]=>{{1,7,9},{2,3,4,5,6,8}}
[9,5,6,7,8,2,1,3,4]=>{{1,4,7,9},{2,3,5,6,8}}
[8,3,9,4,5,6,7,2,1]=>{{1,2,3,8,9},{4},{5},{6},{7}}
[9,3,4,5,6,2,1,7,8]=>{{1,7,8,9},{2,3,4,5,6}}
[1,6,2,7,3,8,4,9,5]=>{{1},{2,3,5,6,8,9},{4,7}}
[6,7,1,9,2,3,4,5,8]=>{{1,3,6},{2,4,5,7,8,9}}
[6,1,8,9,2,3,4,5,7]=>{{1,2,3,5,6,8},{4,7,9}}
[3,4,5,6,2,1,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[3,4,5,2,1,6,7,8,9]=>{{1,3,5},{2,4},{6},{7},{8},{9}}
[3,4,5,8,9,1,2,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[3,4,7,8,9,1,2,5,6]=>{{1,2,3,4,5,6,7,8,9}}
[3,6,7,8,9,1,2,4,5]=>{{1,2,3,6,7},{4,8},{5,9}}
[3,4,5,6,1,7,2,8,9]=>{{1,3,5},{2,4,6,7},{8},{9}}
[3,4,5,1,6,2,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[3,4,1,5,9,2,6,7,8]=>{{1,3},{2,4,5,6,7,8,9}}
[1,3,7,8,9,2,4,5,6]=>{{1},{2,3,4,5,6,7,8,9}}
[2,6,7,8,9,1,3,4,5]=>{{1,2,6},{3,7},{4,8},{5,9}}
[4,3,5,2,6,1,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[4,5,3,6,2,7,1,8,9]=>{{1,4,6,7},{2,5},{3},{8},{9}}
[1,3,5,7,2,8,4,9,6]=>{{1},{2,3,5},{4,7},{6,8,9}}
[1,3,5,6,2,7,4,9,8]=>{{1},{2,3,5},{4,6,7},{8,9}}
[1,3,4,5,2,7,6,9,8]=>{{1},{2,3,4,5},{6,7},{8,9}}
[3,5,7,1,2,4,6,9,8]=>{{1,3,4,6,7},{2,5},{8,9}}
[3,5,7,8,1,9,2,4,6]=>{{1,2,3,5,7},{4,8},{6,9}}
[3,5,6,7,1,8,2,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,9,8,7,6,4,3,2,5]=>{{1},{2,3,4,5,6,7,8,9}}
[1,9,8,7,5,4,3,2,6]=>{{1},{2,3,4,6,7,8,9},{5}}
[1,9,8,6,5,4,3,2,7]=>{{1},{2,3,7,8,9},{4,6},{5}}
[1,9,7,6,5,4,3,2,8]=>{{1},{2,8,9},{3,7},{4,6},{5}}
[1,9,8,7,6,5,2,3,4]=>{{1},{2,4,7,9},{3,8},{5,6}}
[1,9,8,7,6,3,4,2,5]=>{{1},{2,3,5,6,8,9},{4,7}}
[1,9,8,7,4,5,3,2,6]=>{{1},{2,3,4,5,6,7,8,9}}
[1,9,8,5,6,4,3,2,7]=>{{1},{2,3,7,8,9},{4,5,6}}
[1,9,6,7,5,4,3,2,8]=>{{1},{2,8,9},{3,4,6,7},{5}}
[1,7,8,6,5,4,3,2,9]=>{{1},{2,3,7,8},{4,6},{5},{9}}
[8,9,2,3,4,5,6,1,7]=>{{1,8},{2,3,4,5,6,7,9}}
[7,8,9,2,3,4,5,1,6]=>{{1,2,3,4,5,6,7,8,9}}
[6,7,8,9,2,3,4,1,5]=>{{1,3,6,8},{2,4,5,7,9}}
[5,6,7,8,9,2,3,1,4]=>{{1,4,5,8,9},{2,6},{3,7}}
[7,8,9,2,3,4,1,5,6]=>{{1,7},{2,3,4,5,6,8,9}}
[6,7,8,9,2,3,1,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[4,5,6,7,8,1,9,2,3]=>{{1,3,4,6,7,9},{2,5,8}}
[7,9,3,4,5,6,2,1,8]=>{{1,2,7,8,9},{3},{4},{5},{6}}
[3,9,2,1,5,6,7,8,4]=>{{1,2,3,4,9},{5},{6},{7},{8}}
[3,8,1,4,5,6,7,2,9]=>{{1,3},{2,8},{4},{5},{6},{7},{9}}
[6,9,3,4,5,2,7,1,8]=>{{1,2,6,8,9},{3},{4},{5},{7}}
[3,9,2,4,1,6,7,8,5]=>{{1,2,3,5,9},{4},{6},{7},{8}}
[3,8,9,1,5,6,7,4,2]=>{{1,2,3,4,8,9},{5},{6},{7}}
[3,7,1,4,5,6,2,8,9]=>{{1,3},{2,7},{4},{5},{6},{8},{9}}
[2,8,7,6,5,4,3,1,9]=>{{1,2,8},{3,7},{4,6},{5},{9}}
[2,1,4,9,8,7,6,5,3]=>{{1,2},{3,4,9},{5,8},{6,7}}
[3,7,6,5,4,2,1,9,8]=>{{1,2,3,6,7},{4,5},{8,9}}
[3,2,1,6,9,8,7,5,4]=>{{1,3},{2},{4,5,6,8,9},{7}}
[4,6,5,3,2,1,9,8,7]=>{{1,2,3,4,5,6},{7,9},{8}}
[7,8,1,9,2,3,4,5,6]=>{{1,3,4,6,7,9},{2,5,8}}
[6,7,8,1,9,2,3,4,5]=>{{1,2,3,4,6,7,8},{5,9}}
[5,6,7,8,1,9,2,3,4]=>{{1,5},{2,3,4,6,7,8,9}}
[9,1,2,3,4,5,7,6,8]=>{{1,2,3,4,5,6,8,9},{7}}
[2,1,3,4,5,9,6,7,8]=>{{1,2},{3},{4},{5},{6,7,8,9}}
[7,2,6,5,4,3,1,9,8]=>{{1,7},{2},{3,6},{4,5},{8,9}}
[3,2,1,9,5,8,7,6,4]=>{{1,3},{2},{4,9},{5},{6,8},{7}}
[6,3,5,4,2,1,9,8,7]=>{{1,6},{2,3,5},{4},{7,9},{8}}
[4,3,2,1,9,7,8,6,5]=>{{1,4},{2,3},{5,9},{6,7,8}}
[9,1,2,3,4,8,6,5,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,2,3,8,5,6,4,7]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,2,9,4,5,6,3,7]=>{{1,2,3,8},{4,5,6,7,9}}
[9,1,8,3,4,5,6,2,7]=>{{1,2,3,4,5,6,7,8,9}}
[7,1,2,3,4,9,5,8,6]=>{{1,2,3,4,5,7},{6,9},{8}}
[6,1,2,3,8,4,5,9,7]=>{{1,2,3,4,6},{5,7,8,9}}
[5,1,2,8,3,4,6,9,7]=>{{1,2,3,5},{4,6,7,8,9}}
[4,1,9,2,3,5,6,8,7]=>{{1,2,4},{3,5,6,7,9},{8}}
[3,8,1,2,4,5,6,9,7]=>{{1,3},{2,4,5,6,7,8,9}}
[8,2,1,3,4,5,6,9,7]=>{{1,3,4,5,6,7,8,9},{2}}
[9,1,2,3,8,5,4,7,6]=>{{1,2,3,4,5,6,7,8,9}}
[6,1,2,3,9,4,7,8,5]=>{{1,2,3,4,6},{5,9},{7},{8}}
[5,1,2,8,3,6,4,9,7]=>{{1,2,3,5},{4,7,8,9},{6}}
[9,8,2,1,4,5,6,7,3]=>{{1,2,3,4,5,6,7,8,9}}
[4,1,8,2,5,3,6,9,7]=>{{1,2,4},{3,6,7,8,9},{5}}
[3,9,1,4,2,5,6,8,7]=>{{1,3},{2,5,6,7,9},{4},{8}}
[8,2,3,1,4,5,6,9,7]=>{{1,4,5,6,7,8,9},{2},{3}}
[2,3,4,5,7,8,1,9,6]=>{{1,2,3,4,5,7},{6,8,9}}
[1,3,4,5,2,6,7,8,9]=>{{1},{2,3,4,5},{6},{7},{8},{9}}
[2,3,4,5,7,9,1,6,8]=>{{1,2,3,4,5,7},{6,8,9}}
[2,3,4,5,1,6,7,9,8]=>{{1,2,3,4,5},{6},{7},{8,9}}
[4,5,6,1,7,8,9,2,3]=>{{1,4},{2,3,5,6,7,8,9}}
[2,1,4,5,3,6,7,8,9]=>{{1,2},{3,4,5},{6},{7},{8},{9}}
[1,3,2,5,4,6,7,8,9]=>{{1},{2,3},{4,5},{6},{7},{8},{9}}
[4,1,6,2,8,3,5,7,9]=>{{1,2,4},{3,6},{5,7,8},{9}}
[4,1,6,2,8,3,9,5,7]=>{{1,2,4},{3,6},{5,8},{7,9}}
[4,1,6,2,7,3,8,5,9]=>{{1,2,4},{3,6},{5,7,8},{9}}
[8,7,9,1,4,5,6,2,3]=>{{1,2,4,5,6,7,8},{3,9}}
[7,6,9,1,4,5,2,8,3]=>{{1,2,4,5,6,7},{3,9},{8}}
[3,9,2,4,5,6,7,8,1]=>{{1,2,3,9},{4},{5},{6},{7},{8}}
[1,3,5,2,4,6,7,8,9]=>{{1},{2,3,4,5},{6},{7},{8},{9}}
[4,1,2,3,5,6,8,7,9]=>{{1,2,3,4},{5},{6},{7,8},{9}}
[1,2,4,7,3,5,6,8,9]=>{{1},{2},{3,4,5,6,7},{8},{9}}
[5,1,2,3,4,7,6,8,9]=>{{1,2,3,4,5},{6,7},{8},{9}}
[5,6,4,3,2,1,7,8,9]=>{{1,2,5,6},{3,4},{7},{8},{9}}
[4,5,3,2,1,6,7,8,9]=>{{1,2,4,5},{3},{6},{7},{8},{9}}
[6,7,4,3,2,1,5,8,9]=>{{1,6},{2,5,7},{3,4},{8},{9}}
[5,6,4,3,2,7,1,8,9]=>{{1,2,5,6,7},{3,4},{8},{9}}
[7,5,4,3,1,2,6,8,9]=>{{1,2,5,6,7},{3,4},{8},{9}}
[6,5,4,3,7,1,2,8,9]=>{{1,6},{2,5,7},{3,4},{8},{9}}
[6,7,9,8,5,4,3,2,1]=>{{1,2,3,4,6,7,8,9},{5}}
[7,6,8,9,5,4,3,2,1]=>{{1,2,3,4,6,7,8,9},{5}}
[6,7,5,9,8,4,3,2,1]=>{{1,4,6,9},{2,3,5,7,8}}
[5,7,9,8,6,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[7,6,8,5,9,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[6,5,8,9,7,4,3,2,1]=>{{1,4,6,9},{2,3,5,7,8}}
[7,6,4,3,5,2,1,9,8]=>{{1,7},{2,6},{3,4},{5},{8,9}}
[7,6,3,5,4,2,1,9,8]=>{{1,7},{2,6},{3},{4,5},{8,9}}
[9,8,6,1,2,3,4,5,7]=>{{1,4,7,9},{2,5,8},{3,6}}
[9,8,7,5,1,2,3,4,6]=>{{1,2,4,5,6,8,9},{3,7}}
[9,8,7,6,4,1,2,3,5]=>{{1,4,5,6,9},{2,3,7,8}}
[9,8,7,6,5,3,1,2,4]=>{{1,3,4,6,7,9},{2,8},{5}}
[9,8,4,7,6,5,3,2,1]=>{{1,9},{2,8},{3,4,7},{5,6}}
[9,8,3,7,6,5,4,2,1]=>{{1,9},{2,8},{3},{4,7},{5,6}}
[9,3,8,7,6,5,4,2,1]=>{{1,9},{2,3,8},{4,7},{5,6}}
[9,2,8,7,6,5,4,3,1]=>{{1,9},{2},{3,8},{4,7},{5,6}}
[9,8,4,6,5,7,3,2,1]=>{{1,9},{2,8},{3,4,6,7},{5}}
[9,8,3,6,5,4,7,2,1]=>{{1,9},{2,8},{3},{4,6},{5},{7}}
[9,3,7,6,5,4,8,2,1]=>{{1,9},{2,3,7,8},{4,6},{5}}
[9,2,7,6,5,4,3,8,1]=>{{1,9},{2},{3,7},{4,6},{5},{8}}
[9,2,3,4,1,5,6,7,8]=>{{1,5,6,7,8,9},{2},{3},{4}}
[9,8,4,5,7,6,3,2,1]=>{{1,9},{2,8},{3,4,5,7},{6}}
[9,8,5,4,6,7,3,2,1]=>{{1,9},{2,8},{3,5,6,7},{4}}
[9,8,4,5,3,7,6,2,1]=>{{1,9},{2,8},{3,4,5},{6,7}}
[9,8,3,5,7,6,4,2,1]=>{{1,9},{2,8},{3},{4,5,7},{6}}
[9,8,5,4,6,3,7,2,1]=>{{1,9},{2,8},{3,5,6},{4},{7}}
[9,8,4,3,6,7,5,2,1]=>{{1,9},{2,8},{3,4},{5,6,7}}
[9,8,7,4,3,2,1,5,6]=>{{1,2,3,5,6,7,8,9},{4}}
[9,8,7,6,3,2,1,4,5]=>{{1,3,5,7,9},{2,4,6,8}}
[7,8,9,1,3,4,5,6,2]=>{{1,2,3,4,5,6,7,8,9}}
[6,1,2,9,3,4,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[4,1,2,3,5,9,6,7,8]=>{{1,2,3,4},{5},{6,7,8,9}}
[3,1,2,4,5,6,9,7,8]=>{{1,2,3},{4},{5},{6},{7,8,9}}
[1,3,4,2,5,6,7,8,9]=>{{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,2,4,5,6,3,7,8,9]=>{{1},{2},{3,4,5,6},{7},{8},{9}}
[1,2,3,5,6,7,8,4,9]=>{{1},{2},{3},{4,5,6,7,8},{9}}
[2,1,5,3,6,7,4,8,9]=>{{1,2},{3,4,5,6,7},{8},{9}}
[1,3,5,6,4,2,7,8,9]=>{{1},{2,3,4,5,6},{7},{8},{9}}
[3,5,2,1,6,4,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[2,1,3,6,4,7,8,9,5]=>{{1,2},{3},{4,5,6,7,8,9}}
[1,3,4,6,7,2,8,5,9]=>{{1},{2,3,4,6},{5,7,8},{9}}
[3,2,6,1,4,7,8,5,9]=>{{1,3,4,5,6,7,8},{2},{9}}
[2,4,6,1,7,5,3,8,9]=>{{1,2,4},{3,5,6,7},{8},{9}}
[4,6,3,2,1,7,5,8,9]=>{{1,2,4,5,6,7},{3},{8},{9}}
[2,4,1,7,5,8,3,9,6]=>{{1,2,3,4,7},{5},{6,8,9}}
[4,3,7,2,1,5,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,3,5,7,8,6,4,2,9]=>{{1},{2,3,5,8},{4,7},{6},{9}}
[3,5,7,2,1,8,6,4,9]=>{{1,2,3,4,5,6,7,8},{9}}
[5,7,4,3,2,1,8,6,9]=>{{1,2,5,6,7,8},{3,4},{9}}
[2,4,6,8,1,9,7,5,3]=>{{1,2,4,5,8},{3,6,9},{7}}
[4,6,8,3,2,1,9,7,5]=>{{1,2,3,4,5,6,7,8,9}}
[6,8,5,4,3,2,1,9,7]=>{{1,2,6,7,8,9},{3,5},{4}}
[4,5,6,3,7,2,8,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[1,5,6,7,4,8,3,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[3,5,6,7,8,9,2,4,1]=>{{1,3,6,9},{2,4,5,7,8}}
[2,4,6,7,8,9,1,3,5]=>{{1,2,4,7},{3,5,6,8,9}}
[2,5,6,7,8,9,3,1,4]=>{{1,2,5,8},{3,4,6,7,9}}
[5,4,6,3,8,1,7,2,9]=>{{1,2,3,4,5,6,8},{7},{9}}
[1,6,5,7,4,9,2,8,3]=>{{1},{2,3,4,5,6,7,9},{8}}
[5,4,8,1,7,2,6,3,9]=>{{1,2,4,5,6,7},{3,8},{9}}
[5,4,8,1,6,3,7,2,9]=>{{1,2,3,4,5,6,8},{7},{9}}
[1,6,5,9,2,8,3,7,4]=>{{1},{2,3,5,6,7,8},{4,9}}
[1,6,5,9,2,7,4,8,3]=>{{1},{2,3,4,5,6,7,9},{8}}
[2,5,6,7,8,1,9,3,4]=>{{1,2,3,5,6,8},{4,7,9}}
[4,5,6,7,1,2,8,3,9]=>{{1,2,3,4,5,6,7,8},{9}}
[1,3,6,7,8,9,2,4,5]=>{{1},{2,3,4,5,6,7,8,9}}
[3,5,6,7,8,1,2,9,4]=>{{1,3,6},{2,4,5,7,8,9}}
[2,3,4,5,7,6,8,9,1]=>{{1,2,3,4,5,7,8,9},{6}}
[2,3,4,5,7,8,6,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[2,3,4,5,8,7,6,9,1]=>{{1,2,3,4,5,8,9},{6,7}}
[2,3,4,5,7,9,8,6,1]=>{{1,2,3,4,5,6,7,8,9}}
[4,5,6,3,7,8,9,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[1,2,3,4,7,9,5,6,8]=>{{1},{2},{3},{4},{5,7},{6,8,9}}
[1,2,3,4,6,7,9,5,8]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[1,2,3,4,8,5,6,9,7]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[1,2,3,4,7,8,5,9,6]=>{{1},{2},{3},{4},{5,7},{6,8,9}}
[8,7,9,6,5,4,2,1,3]=>{{1,8},{2,7},{3,9},{4,6},{5}}
[8,9,7,6,5,4,2,1,3]=>{{1,8},{2,3,7,9},{4,6},{5}}
[8,9,7,6,5,4,2,3,1]=>{{1,2,3,7,8,9},{4,6},{5}}
[2,3,4,5,8,6,7,9,1]=>{{1,2,3,4,5,8,9},{6},{7}}
[2,3,4,5,9,6,8,7,1]=>{{1,2,3,4,5,9},{6},{7,8}}
[9,3,4,5,2,6,7,8,1]=>{{1,9},{2,3,4,5},{6},{7},{8}}
[2,1,3,4,5,8,6,7,9]=>{{1,2},{3},{4},{5},{6,7,8},{9}}
[9,2,3,4,5,1,6,7,8]=>{{1,6,7,8,9},{2},{3},{4},{5}}
[7,2,3,4,5,6,9,1,8]=>{{1,7,8,9},{2},{3},{4},{5},{6}}
[6,2,3,4,5,9,1,7,8]=>{{1,6,7,8,9},{2},{3},{4},{5}}
[5,2,3,4,9,1,6,7,8]=>{{1,5,6,7,8,9},{2},{3},{4}}
[4,2,3,9,1,5,6,7,8]=>{{1,4,5,6,7,8,9},{2},{3}}
[3,2,9,1,4,5,6,7,8]=>{{1,3,4,5,6,7,8,9},{2}}
[4,5,6,7,8,1,3,9,2]=>{{1,3,4,6,7},{2,5,8,9}}
[2,1,9,8,7,6,5,3,4]=>{{1,2},{3,4,8,9},{5,7},{6}}
[2,1,9,8,7,6,4,3,5]=>{{1,2},{3,4,5,7,8,9},{6}}
[2,1,9,8,7,6,3,5,4]=>{{1,2},{3,4,5,7,8,9},{6}}
[4,5,3,6,7,8,9,1,2]=>{{1,4,6,8},{2,5,7,9},{3}}
[5,3,4,6,7,8,9,1,2]=>{{1,2,3,4,5,6,7,8,9}}
[9,5,4,3,2,1,6,7,8]=>{{1,6,7,8,9},{2,5},{3,4}}
[1,2,3,7,4,8,5,9,6]=>{{1},{2},{3},{4,5,7},{6,8,9}}
[1,2,3,4,7,5,9,8,6]=>{{1},{2},{3},{4},{5,6,7,9},{8}}
[1,2,6,3,7,4,9,8,5]=>{{1},{2},{3,4,6},{5,7,9},{8}}
[1,2,3,8,6,4,9,7,5]=>{{1},{2},{3},{4,5,6,7,8,9}}
[1,2,3,6,4,9,8,7,5]=>{{1},{2},{3},{4,5,6,9},{7,8}}
[5,1,6,2,7,3,9,8,4]=>{{1,2,4,5,7,9},{3,6},{8}}
[1,5,2,8,6,3,9,7,4]=>{{1},{2,3,5,6},{4,7,8,9}}
[1,5,2,6,3,9,8,7,4]=>{{1},{2,3,5},{4,6,9},{7,8}}
[1,2,7,5,3,9,8,6,4]=>{{1},{2},{3,4,5,6,7,8,9}}
[1,2,5,3,9,8,7,6,4]=>{{1},{2},{3,4,5,9},{6,8},{7}}
[4,1,7,5,2,9,8,6,3]=>{{1,2,4,5},{3,6,7,8,9}}
[4,1,5,2,9,8,7,6,3]=>{{1,2,4},{3,5,9},{6,8},{7}}
[1,6,4,2,9,8,7,5,3]=>{{1},{2,3,4,5,6,8,9},{7}}
[1,4,2,9,8,7,6,5,3]=>{{1},{2,3,4,9},{5,8},{6,7}}
[7,5,3,1,9,8,6,4,2]=>{{1,4,6,7,8},{2,5,9},{3}}
[5,3,1,9,8,7,6,4,2]=>{{1,2,3,4,5,8,9},{6,7}}
[1,2,3,4,5,8,9,7,6]=>{{1},{2},{3},{4},{5},{6,7,8,9}}
[1,2,3,4,8,9,6,7,5]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[1,2,3,8,9,5,6,7,4]=>{{1},{2},{3},{4,5,6,7,8,9}}
[1,2,8,9,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7,8,9}}
[1,4,2,5,6,7,9,8,3]=>{{1},{2,3,4,5,6,7,9},{8}}
[2,1,4,5,6,9,7,3,8]=>{{1,2},{3,4,5,6,8,9},{7}}
[3,1,5,2,9,6,7,8,4]=>{{1,2,3,4,5,9},{6},{7},{8}}
[4,5,1,6,8,7,9,2,3]=>{{1,3,4,6,7,9},{2,5,8}}
[2,3,1,5,9,6,7,4,8]=>{{1,2,3},{4,5,8,9},{6},{7}}
[1,2,4,5,7,9,6,3,8]=>{{1},{2},{3,4,5,6,7,8,9}}
[3,4,6,5,7,1,2,9,8]=>{{1,3,6},{2,4,5,7},{8,9}}
[3,1,9,4,2,6,7,8,5]=>{{1,2,3,5,9},{4},{6},{7},{8}}
[1,2,5,3,9,6,8,7,4]=>{{1},{2},{3,4,5,9},{6},{7,8}}
[4,5,1,7,6,8,2,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[4,8,7,6,5,3,2,1,9]=>{{1,2,3,4,6,7,8},{5},{9}}
[5,8,7,4,6,3,2,1,9]=>{{1,2,3,5,6,7,8},{4},{9}}
[8,4,7,6,5,3,2,1,9]=>{{1,8},{2,3,4,6,7},{5},{9}}
[6,9,8,5,7,4,1,3,2]=>{{1,4,5,6,7},{2,9},{3,8}}
[9,8,7,5,1,6,4,3,2]=>{{1,2,3,4,5,7,8,9},{6}}
[1,2,8,3,4,5,6,9,7]=>{{1},{2},{3,4,5,6,7,8,9}}
[1,9,5,2,3,8,4,6,7]=>{{1},{2,4,7,9},{3,5},{6,8}}
[1,8,2,9,4,3,5,6,7]=>{{1},{2,3,6,8},{4,5,7,9}}
[1,3,2,4,9,8,5,6,7]=>{{1},{2,3},{4},{5,7,9},{6,8}}
[2,1,3,4,5,9,8,6,7]=>{{1,2},{3},{4},{5},{6,7,8,9}}
[9,1,7,2,3,4,5,8,6]=>{{1,2,4,6,9},{3,5,7},{8}}
[1,8,5,2,3,4,6,9,7]=>{{1},{2,4,6,7,8,9},{3,5}}
[9,8,1,2,3,5,6,4,7]=>{{1,3,5,6,7,9},{2,4,8}}
[1,4,2,3,9,5,6,8,7]=>{{1},{2,3,4},{5,6,7,9},{8}}
[4,9,8,1,2,5,3,6,7]=>{{1,4},{2,3,5,6,7,8,9}}
[1,3,2,4,5,9,6,8,7]=>{{1},{2,3},{4},{5},{6,7,9},{8}}
[1,8,3,9,4,2,5,6,7]=>{{1},{2,6,8},{3},{4,5,7,9}}
[2,3,1,4,9,8,5,6,7]=>{{1,2,3},{4},{5,7,9},{6,8}}
[8,7,5,6,4,3,2,1,9]=>{{1,8},{2,7},{3,4,5,6},{9}}
[8,6,5,7,4,3,2,1,9]=>{{1,8},{2,3,4,5,6,7},{9}}
[9,8,7,6,4,3,2,5,1]=>{{1,9},{2,3,4,5,6,7,8}}
[9,8,7,6,4,3,5,2,1]=>{{1,9},{2,8},{3,4,5,6,7}}
[8,5,6,7,4,3,2,1,9]=>{{1,8},{2,4,5,7},{3,6},{9}}
[6,7,5,8,4,3,2,1,9]=>{{1,3,4,5,6,8},{2,7},{9}}
[8,9,7,6,4,3,2,1,5]=>{{1,8},{2,3,4,5,6,7,9}}
[7,6,5,3,2,1,4,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[9,8,7,6,4,3,5,1,2]=>{{1,2,8,9},{3,4,5,6,7}}
[9,8,7,6,4,5,2,3,1]=>{{1,9},{2,3,7,8},{4,5,6}}
[9,8,7,6,5,3,4,2,1]=>{{1,9},{2,8},{3,4,6,7},{5}}
[8,7,6,5,4,2,3,1,9]=>{{1,8},{2,3,6,7},{4,5},{9}}
[2,9,8,6,5,7,4,3,1]=>{{1,2,9},{3,8},{4,6,7},{5}}
[7,1,8,2,3,4,5,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[6,8,1,2,3,4,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[9,6,7,4,5,2,3,1,8]=>{{1,8,9},{2,6},{3,7},{4},{5}}
[9,8,6,5,4,3,7,2,1]=>{{1,9},{2,8},{3,6},{4,5},{7}}
[2,3,6,4,5,1,7,8,9]=>{{1,2,3,6},{4},{5},{7},{8},{9}}
[2,3,4,8,5,6,7,1,9]=>{{1,2,3,4,8},{5},{6},{7},{9}}
[3,5,4,7,2,6,1,8,9]=>{{1,3,4,7},{2,5},{6},{8},{9}}
[2,6,4,1,5,3,7,8,9]=>{{1,2,3,4,6},{5},{7},{8},{9}}
[4,5,2,6,3,1,7,8,9]=>{{1,4,6},{2,3,5},{7},{8},{9}}
[3,6,4,5,9,2,7,8,1]=>{{1,3,4,5,9},{2,6},{7},{8}}
[2,5,4,7,8,6,3,1,9]=>{{1,2,5,8},{3,4,7},{6},{9}}
[4,6,2,5,8,3,7,1,9]=>{{1,4,5,8},{2,3,6},{7},{9}}
[3,5,7,6,1,4,2,8,9]=>{{1,2,3,5,7},{4,6},{8},{9}}
[5,6,2,3,7,4,1,8,9]=>{{1,5,7},{2,3,4,6},{8},{9}}
[5,7,2,3,6,9,4,8,1]=>{{1,5,6,9},{2,3,4,7},{8}}
[2,8,4,1,6,3,7,5,9]=>{{1,2,3,4,5,6,8},{7},{9}}
[4,6,7,8,3,1,5,2,9]=>{{1,2,4,6,8},{3,5,7},{9}}
[6,7,2,3,4,8,5,1,9]=>{{1,6,8},{2,3,4,5,7},{9}}
[3,5,9,7,1,8,2,6,4]=>{{1,2,3,4,5,7,9},{6,8}}
[5,7,8,3,9,4,1,6,2]=>{{1,2,5,7,9},{3,4,6,8}}
[7,8,2,3,4,5,9,6,1]=>{{1,7,9},{2,3,4,5,6,8}}
[9,7,6,5,4,3,2,8,1]=>{{1,9},{2,7},{3,6},{4,5},{8}}
[3,1,4,6,2,5,8,7,9]=>{{1,2,3,4,5,6},{7,8},{9}}
[1,3,2,5,7,4,6,9,8]=>{{1},{2,3},{4,5,6,7},{8,9}}
[1,9,8,5,6,7,4,3,2]=>{{1},{2,9},{3,8},{4,5,6,7}}
[1,9,8,5,4,6,7,3,2]=>{{1},{2,9},{3,8},{4,5},{6},{7}}
[1,9,5,4,6,7,8,3,2]=>{{1},{2,9},{3,5,6,7,8},{4}}
[1,2,3,4,7,5,6,9,8]=>{{1},{2},{3},{4},{5,6,7},{8,9}}
[9,8,7,6,5,3,1,4,2]=>{{1,2,3,4,6,7,8,9},{5}}
[1,2,7,4,5,6,8,9,3]=>{{1},{2},{3,7,8,9},{4},{5},{6}}
[1,2,3,4,7,8,5,6,9]=>{{1},{2},{3},{4},{5,7},{6,8},{9}}
[1,2,3,4,6,5,8,7,9]=>{{1},{2},{3},{4},{5,6},{7,8},{9}}
[1,2,3,4,8,9,5,6,7]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[2,1,7,8,9,3,4,5,6]=>{{1,2},{3,4,5,6,7,8,9}}
[9,7,5,3,8,6,4,2,1]=>{{1,9},{2,3,4,5,7,8},{6}}
[8,6,9,7,4,3,2,1,5]=>{{1,8},{2,3,4,5,6,7,9}}
[8,6,3,2,1,4,9,7,5]=>{{1,5,7,8,9},{2,4,6},{3}}
[8,6,4,9,7,5,2,1,3]=>{{1,8},{2,5,6,7},{3,4,9}}
[9,7,5,3,8,6,4,1,2]=>{{1,2,3,4,5,7,8,9},{6}}
[9,6,7,8,5,4,3,2,1]=>{{1,9},{2,4,6,8},{3,7},{5}}
[8,5,6,9,7,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[8,6,3,2,1,9,7,4,5]=>{{1,2,4,5,6,8,9},{3},{7}}
[9,7,8,4,3,2,1,5,6]=>{{1,2,6,7,9},{3,5,8},{4}}
[8,6,3,4,9,7,5,2,1]=>{{1,2,5,6,7,8,9},{3},{4}}
[8,6,9,7,3,2,1,4,5]=>{{1,4,7,8},{2,6},{3,5,9}}
[9,7,5,2,3,8,6,4,1]=>{{1,9},{2,4,6,7,8},{3,5}}
[8,6,2,1,3,4,9,7,5]=>{{1,2,3,4,5,6,7,8,9}}
[8,6,4,9,7,5,1,2,3]=>{{1,2,5,6,7,8},{3,4,9}}
[2,5,1,6,3,7,4,8,9]=>{{1,2,3,5},{4,6,7},{8},{9}}
[2,6,1,7,3,8,4,9,5]=>{{1,2,3,5,6,8,9},{4,7}}
[3,4,6,1,7,2,8,5,9]=>{{1,2,3,4,6},{5,7,8},{9}}
[3,2,6,1,7,4,8,5,9]=>{{1,3,4,6},{2},{5,7,8},{9}}
[4,2,5,6,1,7,3,8,9]=>{{1,3,4,5,6,7},{2},{8},{9}}
[3,4,2,6,1,7,5,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[4,2,5,7,1,8,3,9,6]=>{{1,3,4,5,7},{2},{6,8,9}}
[3,4,2,7,1,8,5,9,6]=>{{1,2,3,4,5,7},{6,8,9}}
[5,3,6,4,7,1,8,2,9]=>{{1,2,3,5,6,7,8},{4},{9}}
[3,5,2,6,7,1,8,4,9]=>{{1,2,3,4,5,6,7,8},{9}}
[4,3,5,2,7,1,8,6,9]=>{{1,2,3,4,5,6,7,8},{9}}
[4,6,2,7,5,8,1,9,3]=>{{1,4,7},{2,3,6,8,9},{5}}
[4,3,6,2,7,8,1,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[4,5,3,6,2,8,1,9,7]=>{{1,4,6,7,8,9},{2,5},{3}}
[9,8,7,6,5,2,3,4,1]=>{{1,9},{2,4,6,8},{3,7},{5}}
[6,1,7,8,9,2,3,4,5]=>{{1,2,6},{3,7},{4,8},{5,9}}
[4,5,6,7,1,9,2,3,8]=>{{1,2,4,5,7},{3,6,8,9}}
[3,5,6,7,9,1,2,4,8]=>{{1,3,6},{2,4,5,7,8,9}}
[5,1,6,7,8,2,9,3,4]=>{{1,2,3,5,6,8},{4,7,9}}
[4,1,6,7,8,9,2,3,5]=>{{1,2,4,7},{3,5,6,8,9}}
[2,3,1,5,6,8,9,4,7]=>{{1,2,3},{4,5,6,8},{7,9}}
[5,6,7,8,9,1,3,4,2]=>{{1,2,5,6,9},{3,7},{4,8}}
[6,7,8,9,1,3,4,5,2]=>{{1,3,5,6,8},{2,4,7,9}}
[6,7,8,9,1,4,5,2,3]=>{{1,2,3,4,5,6,7,8,9}}
[6,7,8,9,1,4,5,3,2]=>{{1,2,4,5,6,7,9},{3,8}}
[6,7,8,9,1,5,4,3,2]=>{{1,5,6},{2,4,7,9},{3,8}}
[7,8,9,1,4,5,6,2,3]=>{{1,4,5,6,7},{2,8},{3,9}}
[7,8,9,1,4,5,6,3,2]=>{{1,4,5,6,7},{2,3,8,9}}
[7,8,9,1,5,6,3,4,2]=>{{1,2,3,4,7,8,9},{5},{6}}
[7,8,9,1,5,6,4,3,2]=>{{1,4,7},{2,3,8,9},{5},{6}}
[7,8,9,1,6,5,4,3,2]=>{{1,4,7},{2,3,8,9},{5,6}}
[8,9,1,5,6,7,3,4,2]=>{{1,3,4,5,6,7,8},{2,9}}
[8,9,1,5,6,7,4,3,2]=>{{1,3,8},{2,9},{4,5,6,7}}
[8,9,1,6,7,4,5,2,3]=>{{1,2,3,8,9},{4,6},{5,7}}
[8,9,1,6,7,4,5,3,2]=>{{1,3,8},{2,9},{4,6},{5,7}}
[8,9,1,6,7,5,4,3,2]=>{{1,3,8},{2,9},{4,5,6,7}}
[9,1,7,8,5,6,3,4,2]=>{{1,2,9},{3,7},{4,8},{5},{6}}
[9,1,7,8,5,6,4,3,2]=>{{1,2,9},{3,4,7,8},{5},{6}}
[2,3,4,5,7,9,6,8,1]=>{{1,2,3,4,5,6,7,9},{8}}
[2,3,4,6,9,5,7,8,1]=>{{1,2,3,4,5,6,9},{7},{8}}
[2,3,5,9,4,6,7,8,1]=>{{1,2,3,4,5,9},{6},{7},{8}}
[2,4,9,3,5,6,7,8,1]=>{{1,2,3,4,9},{5},{6},{7},{8}}
[5,9,8,7,6,4,3,1,2]=>{{1,3,4,5,6,7,8},{2,9}}
[5,4,8,7,6,3,2,1,9]=>{{1,3,5,6,8},{2,4,7},{9}}
[6,5,9,8,7,4,3,1,2]=>{{1,4,6,8},{2,3,5,7,9}}
[9,5,8,7,6,4,3,1,2]=>{{1,2,3,4,5,6,7,8,9}}
[7,6,8,5,4,3,2,9,1]=>{{1,2,3,6,7,8,9},{4,5}}
[6,8,7,5,4,3,2,9,1]=>{{1,2,3,6,7,8,9},{4,5}}
[2,3,4,5,6,1,8,9,7]=>{{1,2,3,4,5,6},{7,8,9}}
[2,3,4,5,1,7,8,9,6]=>{{1,2,3,4,5},{6,7,8,9}}
[2,9,3,4,5,6,1,7,8]=>{{1,2,7,8,9},{3},{4},{5},{6}}
[2,8,3,4,5,1,6,9,7]=>{{1,2,6,7,8,9},{3},{4},{5}}
[2,7,3,4,1,5,8,9,6]=>{{1,2,5,6,7,8,9},{3},{4}}
[2,6,3,1,4,7,8,9,5]=>{{1,2,4,5,6,7,8,9},{3}}
[4,2,5,3,7,6,9,8,1]=>{{1,3,4,5,7,9},{2},{6},{8}}
[4,2,6,3,7,5,9,8,1]=>{{1,3,4,5,6,7,9},{2},{8}}
[4,2,6,3,8,5,9,7,1]=>{{1,3,4,5,6,7,8,9},{2}}
[4,2,6,3,8,5,1,7,9]=>{{1,3,4,5,6,7,8},{2},{9}}
[4,2,6,3,8,5,7,1,9]=>{{1,3,4,5,6,8},{2},{7},{9}}
[4,2,6,3,5,8,7,1,9]=>{{1,3,4,6,8},{2},{5},{7},{9}}
[4,2,3,6,5,8,7,1,9]=>{{1,4,6,8},{2},{3},{5},{7},{9}}
[5,2,6,3,7,4,9,8,1]=>{{1,5,7,9},{2},{3,4,6},{8}}
[4,2,7,3,8,5,9,6,1]=>{{1,3,4,7,9},{2},{5,6,8}}
[4,2,6,3,9,5,1,7,8]=>{{1,3,4,5,6,7,8,9},{2}}
[4,2,6,3,8,5,7,9,1]=>{{1,3,4,5,6,8,9},{2},{7}}
[4,2,6,3,5,8,1,7,9]=>{{1,3,4,6,7,8},{2},{5},{9}}
[4,2,3,6,8,5,7,1,9]=>{{1,4,5,6,8},{2},{3},{7},{9}}
[2,4,6,3,5,8,7,1,9]=>{{1,2,3,4,6,8},{5},{7},{9}}
[3,4,5,6,9,2,1,8,7]=>{{1,3,5,7,9},{2,4,6},{8}}
[3,4,5,8,2,9,1,7,6]=>{{1,2,3,4,5,7,8},{6,9}}
[3,4,7,2,8,9,1,5,6]=>{{1,3,7},{2,4},{5,8},{6,9}}
[3,6,2,7,8,9,1,5,4]=>{{1,2,3,4,6,7,9},{5,8}}
[5,2,6,7,8,9,1,4,3]=>{{1,4,5,7,8},{2},{3,6,9}}
[3,4,5,6,9,1,7,8,2]=>{{1,2,3,4,5,6,9},{7},{8}}
[3,4,5,8,9,6,1,7,2]=>{{1,2,3,4,5,7,8,9},{6}}
[3,4,7,8,5,9,1,2,6]=>{{1,3,7},{2,4,8},{5},{6,9}}
[3,4,5,9,2,6,1,8,7]=>{{1,2,3,4,5,7,9},{6},{8}}
[3,6,7,4,8,9,1,5,2]=>{{1,3,7},{2,6,9},{4},{5,8}}
[3,4,8,2,5,9,1,7,6]=>{{1,3,7,8},{2,4},{5},{6,9}}
[5,6,3,7,8,9,1,4,2]=>{{1,4,5,7,8},{2,6,9},{3}}
[3,7,2,4,8,9,1,5,6]=>{{1,2,3,7},{4},{5,8},{6,9}}
[6,2,3,7,8,9,1,5,4]=>{{1,4,6,7,9},{2},{3},{5,8}}
[8,9,7,6,5,4,1,3,2]=>{{1,3,7,8},{2,9},{4,6},{5}}
[8,7,9,6,5,4,1,3,2]=>{{1,2,3,7,8,9},{4,6},{5}}
[9,7,8,6,5,4,1,3,2]=>{{1,2,7,9},{3,8},{4,6},{5}}
[1,3,2,4,5,6,9,7,8]=>{{1},{2,3},{4},{5},{6},{7,8,9}}
[2,3,1,4,5,6,9,7,8]=>{{1,2,3},{4},{5},{6},{7,8,9}}
[4,3,9,5,6,7,8,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[3,2,8,5,6,7,1,9,4]=>{{1,3,4,5,6,7,8,9},{2}}
[7,8,4,5,6,1,3,9,2]=>{{1,3,4,5,6,7},{2,8,9}}
[3,4,1,9,6,7,8,2,5]=>{{1,3},{2,4,5,6,7,8,9}}
[4,8,9,5,6,7,2,1,3]=>{{1,2,4,5,6,7,8},{3,9}}
[4,2,3,8,6,7,1,9,5]=>{{1,4,5,6,7,8,9},{2},{3}}
[6,8,4,5,1,3,7,9,2]=>{{1,3,4,5,6},{2,8,9},{7}}
[3,5,1,4,9,7,8,2,6]=>{{1,3},{2,5,6,7,8,9},{4}}
[8,3,4,9,6,7,2,5,1]=>{{1,2,3,4,5,6,7,8,9}}
[4,7,9,5,6,2,1,8,3]=>{{1,2,4,5,6,7},{3,9},{8}}
[8,1,2,5,3,4,6,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[1,9,2,3,6,4,5,7,8]=>{{1},{2,3,4,5,6,7,8,9}}
[8,1,2,6,4,3,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[8,1,2,6,3,5,4,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[1,9,2,3,7,5,4,6,8]=>{{1},{2,3,4,5,6,7,8,9}}
[1,9,2,3,7,4,6,5,8]=>{{1},{2,3,4,5,6,7,8,9}}
[5,6,7,8,9,3,2,1,4]=>{{1,4,5,8,9},{2,3,6,7}}
[6,7,8,9,3,4,1,2,5]=>{{1,2,3,4,5,6,7,8,9}}
[6,7,8,9,3,4,2,1,5]=>{{1,3,4,5,6,8,9},{2,7}}
[7,8,9,3,4,5,1,2,6]=>{{1,7},{2,8},{3,4,5,6,9}}
[7,8,9,3,4,5,2,1,6]=>{{1,2,7,8},{3,4,5,6,9}}
[7,8,9,4,5,2,3,1,6]=>{{1,2,3,6,7,8,9},{4},{5}}
[7,8,9,4,5,3,2,1,6]=>{{1,2,7,8},{3,6,9},{4},{5}}
[8,9,4,5,6,2,3,1,7]=>{{1,8},{2,3,4,5,6,7,9}}
[8,9,4,5,6,3,2,1,7]=>{{1,8},{2,7,9},{3,4,5,6}}
[8,9,5,6,3,4,1,2,7]=>{{1,2,7,8,9},{3,5},{4,6}}
[8,9,5,6,3,4,2,1,7]=>{{1,8},{2,7,9},{3,5},{4,6}}
[8,9,5,6,4,3,2,1,7]=>{{1,8},{2,7,9},{3,4,5,6}}
[9,6,7,4,5,3,2,1,8]=>{{1,8,9},{2,3,6,7},{4},{5}}
[9,7,1,8,2,3,4,5,6]=>{{1,3,6,9},{2,4,5,7,8}}
[9,6,1,7,2,8,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[8,6,1,9,7,2,3,4,5]=>{{1,3,4,5,7,8,9},{2,6}}
[9,8,6,1,7,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}
[8,5,1,9,6,2,7,3,4]=>{{1,3,8},{2,5,6},{4,9},{7}}
[9,8,5,1,6,2,7,3,4]=>{{1,4,9},{2,3,5,6,8},{7}}
[9,7,5,1,8,6,2,3,4]=>{{1,4,9},{2,7},{3,5,8},{6}}
[9,8,7,5,1,6,2,3,4]=>{{1,4,5,9},{2,3,7,8},{6}}
[9,7,4,1,8,5,2,6,3]=>{{1,3,4,9},{2,7},{5,6,8}}
[9,8,7,4,1,5,2,6,3]=>{{1,2,3,5,6,7,8,9},{4}}
[8,6,4,1,9,7,5,2,3]=>{{1,2,3,4,5,6,7,8,9}}
[9,8,6,4,1,7,5,2,3]=>{{1,3,5,6,7,9},{2,8},{4}}
[9,8,7,6,4,1,5,2,3]=>{{1,3,4,5,6,7,9},{2,8}}
[9,8,7,5,3,1,6,4,2]=>{{1,2,3,4,5,6,7,8,9}}
[9,1,2,8,4,3,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,9,3,2,4,6,5,7]=>{{1,2,5,8},{3,4,6,7,9}}
[9,8,2,1,3,5,6,4,7]=>{{1,2,3,4,5,6,7,8,9}}
[8,1,9,2,4,5,6,3,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,4,3,6,5,8,7,9,2]=>{{1},{2,4,6,8,9},{3},{5},{7}}
[1,4,2,6,5,8,7,9,3]=>{{1},{2,3,4,6,8,9},{5},{7}}
[1,5,2,6,4,8,7,9,3]=>{{1},{2,3,4,5,6,8,9},{7}}
[1,5,2,7,4,8,6,9,3]=>{{1},{2,3,4,5,6,7,8,9}}
[1,5,2,7,4,9,6,8,3]=>{{1},{2,3,4,5,6,7,9},{8}}
[1,5,2,7,4,6,9,8,3]=>{{1},{2,3,4,5,7,9},{6},{8}}
[1,5,2,4,7,6,9,8,3]=>{{1},{2,3,5,7,9},{4},{6},{8}}
[1,2,5,4,7,6,9,8,3]=>{{1},{2},{3,5,7,9},{4},{6},{8}}
[1,5,2,6,3,8,7,9,4]=>{{1},{2,3,5},{4,6,8,9},{7}}
[1,6,2,7,4,8,5,9,3]=>{{1},{2,3,6,8,9},{4,5,7}}
[1,5,2,8,4,9,6,7,3]=>{{1},{2,3,4,5,6,7,8,9}}
[1,5,2,7,4,6,8,9,3]=>{{1},{2,3,4,5,7,8,9},{6}}
[1,5,2,4,7,9,6,8,3]=>{{1},{2,3,5,6,7,9},{4},{8}}
[1,2,5,7,4,6,9,8,3]=>{{1},{2},{3,4,5,7,9},{6},{8}}
[4,5,6,7,9,8,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[5,4,6,7,8,9,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[6,5,7,8,9,4,3,2,1]=>{{1,2,4,5,6,8,9},{3,7}}
[4,5,6,7,3,9,8,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[3,5,6,7,9,8,4,2,1]=>{{1,2,3,5,6,8,9},{4,7}}
[5,4,6,7,8,3,9,2,1]=>{{1,2,4,5,7,8,9},{3,6}}
[4,3,6,7,8,9,5,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[3,4,5,6,8,9,7,1,2]=>{{1,3,5,8},{2,4,6,9},{7}}
[3,4,5,7,8,9,6,1,2]=>{{1,3,5,8},{2,4,6,7,9}}
[3,5,6,7,8,9,4,1,2]=>{{1,2,3,5,6,8,9},{4,7}}
[4,5,6,7,8,9,3,1,2]=>{{1,2,3,4,5,6,7,8,9}}
[3,4,5,8,1,9,7,6,2]=>{{1,3,5},{2,4,6,8,9},{7}}
[3,4,7,1,8,9,6,5,2]=>{{1,2,3,4,6,7,9},{5,8}}
[3,6,1,7,8,9,4,5,2]=>{{1,3},{2,6,9},{4,7},{5,8}}
[5,1,6,7,8,9,4,3,2]=>{{1,2,3,5,6,8,9},{4,7}}
[1,5,6,7,8,9,3,2,4]=>{{1},{2,5,8},{3,4,6,7,9}}
[3,4,5,8,9,6,7,1,2]=>{{1,2,3,4,5,8,9},{6},{7}}
[3,4,7,8,5,9,6,1,2]=>{{1,2,3,4,6,7,8,9},{5}}
[3,4,5,9,1,6,7,8,2]=>{{1,3,5},{2,4,9},{6},{7},{8}}
[3,4,8,1,5,9,7,6,2]=>{{1,2,3,4,6,8,9},{5},{7}}
[5,6,3,7,8,9,4,1,2]=>{{1,5,8},{2,6,9},{3},{4,7}}
[3,7,1,4,8,9,6,5,2]=>{{1,3},{2,6,7,9},{4},{5,8}}
[5,2,6,7,8,9,3,1,4]=>{{1,5,8},{2},{3,4,6,7,9}}
[6,1,3,7,8,9,4,5,2]=>{{1,2,6,9},{3},{4,7},{5,8}}
[1,2,6,7,8,9,4,3,5]=>{{1},{2},{3,5,6,8,9},{4,7}}
[9,3,4,5,6,8,7,2,1]=>{{1,9},{2,3,4,5,6,8},{7}}
[9,4,3,5,6,7,8,2,1]=>{{1,9},{2,4,5,6,7,8},{3}}
[9,8,3,4,5,7,6,2,1]=>{{1,9},{2,8},{3},{4},{5},{6,7}}
[9,8,4,3,5,6,7,2,1]=>{{1,9},{2,8},{3,4},{5},{6},{7}}
[9,3,4,5,6,2,8,7,1]=>{{1,9},{2,3,4,5,6},{7,8}}
[9,2,4,5,6,8,7,3,1]=>{{1,9},{2},{3,4,5,6,8},{7}}
[9,4,3,5,6,7,2,8,1]=>{{1,9},{2,4,5,6,7},{3},{8}}
[9,3,2,5,6,7,8,4,1]=>{{1,9},{2,3},{4,5,6,7,8}}
[4,6,3,5,7,2,8,1,9]=>{{1,4,5,7,8},{2,6},{3},{9}}
[5,6,3,4,7,2,8,1,9]=>{{1,5,7,8},{2,6},{3},{4},{9}}
[1,5,7,4,6,8,3,9,2]=>{{1},{2,5,6,8,9},{3,7},{4}}
[1,6,7,4,5,8,3,9,2]=>{{1},{2,6,8,9},{3,7},{4},{5}}
[1,2,3,4,8,5,9,6,7]=>{{1},{2},{3},{4},{5,6,8},{7,9}}
[1,2,3,7,4,5,8,6,9]=>{{1},{2},{3},{4,5,6,7,8},{9}}
[1,2,3,4,8,6,5,7,9]=>{{1},{2},{3},{4},{5,7,8},{6},{9}}
[1,2,3,4,9,7,5,6,8]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[2,1,4,9,3,5,6,7,8]=>{{1,2},{3,4,5,6,7,8,9}}
[3,7,1,2,4,5,6,9,8]=>{{1,3},{2,4,5,6,7},{8,9}}
[3,1,2,6,9,4,5,7,8]=>{{1,2,3},{4,6},{5,7,8,9}}
[4,6,1,2,3,5,9,7,8]=>{{1,2,3,4,5,6},{7,8,9}}
[9,7,6,5,4,3,8,2,1]=>{{1,9},{2,7,8},{3,6},{4,5}}
[9,8,6,5,4,7,3,2,1]=>{{1,9},{2,8},{3,6,7},{4,5}}
[5,4,3,2,1,9,7,8,6]=>{{1,5},{2,4},{3},{6,9},{7},{8}}
[2,1,4,3,6,5,8,7,10,9]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[3,4,1,2,6,5,8,7,10,9]=>{{1,3},{2,4},{5,6},{7,8},{9,10}}
[4,3,2,1,6,5,8,7,10,9]=>{{1,4},{2,3},{5,6},{7,8},{9,10}}
[6,5,4,3,2,1,8,7,10,9]=>{{1,6},{2,5},{3,4},{7,8},{9,10}}
[8,9,5,6,3,4,10,1,2,7]=>{{1,8},{2,9},{3,5},{4,6},{7,10}}
[4,3,2,1,8,7,6,5,10,9]=>{{1,4},{2,3},{5,8},{6,7},{9,10}}
[8,7,6,5,4,3,2,1,10,9]=>{{1,8},{2,7},{3,6},{4,5},{9,10}}
[9,7,6,5,4,3,2,10,1,8]=>{{1,9},{2,7},{3,6},{4,5},{8,10}}
[10,8,9,6,7,4,5,2,3,1]=>{{1,10},{2,8},{3,9},{4,6},{5,7}}
[6,7,8,9,10,1,2,3,4,5]=>{{1,6},{2,7},{3,8},{4,9},{5,10}}
[7,3,2,8,9,10,1,4,5,6]=>{{1,7},{2,3},{4,8},{5,9},{6,10}}
[8,5,4,3,2,9,10,1,6,7]=>{{1,8},{2,5},{3,4},{6,9},{7,10}}
[2,1,4,3,6,5,10,9,8,7]=>{{1,2},{3,4},{5,6},{7,10},{8,9}}
[2,1,6,5,4,3,10,9,8,7]=>{{1,2},{3,6},{4,5},{7,10},{8,9}}
[6,5,4,3,2,1,10,9,8,7]=>{{1,6},{2,5},{3,4},{7,10},{8,9}}
[9,7,5,10,3,8,2,6,1,4]=>{{1,9},{2,7},{3,5},{4,10},{6,8}}
[2,1,4,3,10,9,8,7,6,5]=>{{1,2},{3,4},{5,10},{6,9},{7,8}}
[4,3,2,1,10,9,8,7,6,5]=>{{1,4},{2,3},{5,10},{6,9},{7,8}}
[2,1,10,9,8,7,6,5,4,3]=>{{1,2},{3,10},{4,9},{5,8},{6,7}}
[9,10,8,7,6,5,4,3,1,2]=>{{1,9},{2,10},{3,8},{4,7},{5,6}}
[10,9,8,7,6,5,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,7},{5,6}}
[3,4,2,1,6,5,8,7,10,9]=>{{1,2,3,4},{5,6},{7,8},{9,10}}
[3,5,2,6,4,1,8,7,10,9]=>{{1,2,3,4,5,6},{7,8},{9,10}}
[3,5,2,7,4,8,6,1,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[3,5,2,7,4,9,6,10,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,1,5,6,4,3,8,7,10,9]=>{{1,2},{3,4,5,6},{7,8},{9,10}}
[4,5,6,3,2,1,8,7,10,9]=>{{1,3,4,6},{2,5},{7,8},{9,10}}
[4,5,7,3,2,8,6,1,10,9]=>{{1,3,4,6,7,8},{2,5},{9,10}}
[4,5,7,3,2,9,6,10,8,1]=>{{1,3,4,6,7,8,9,10},{2,5}}
[2,1,5,7,4,8,6,3,10,9]=>{{1,2},{3,4,5,6,7,8},{9,10}}
[4,6,7,3,8,5,2,1,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[4,6,7,3,9,5,2,10,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,1,5,7,4,9,6,10,8,3]=>{{1,2},{3,4,5,6,7,8,9,10}}
[4,6,8,3,9,5,10,7,2,1]=>{{1,3,4,7,8,10},{2,5,6,9}}
[2,1,4,3,7,8,6,5,10,9]=>{{1,2},{3,4},{5,6,7,8},{9,10}}
[3,4,2,1,7,8,6,5,10,9]=>{{1,2,3,4},{5,6,7,8},{9,10}}
[3,6,2,7,8,5,4,1,10,9]=>{{1,2,3,5,6,8},{4,7},{9,10}}
[3,6,2,7,9,5,4,10,8,1]=>{{1,2,3,5,6,8,9,10},{4,7}}
[2,1,6,7,8,5,4,3,10,9]=>{{1,2},{3,5,6,8},{4,7},{9,10}}
[5,6,7,8,4,3,2,1,10,9]=>{{1,4,5,8},{2,3,6,7},{9,10}}
[5,6,7,9,4,3,2,10,8,1]=>{{1,4,5,8,9,10},{2,3,6,7}}
[2,1,6,7,9,5,4,10,8,3]=>{{1,2},{3,5,6,8,9,10},{4,7}}
[5,6,8,9,4,3,10,7,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,1,4,3,7,9,6,10,8,5]=>{{1,2},{3,4},{5,6,7,8,9,10}}
[3,4,2,1,7,9,6,10,8,5]=>{{1,2,3,4},{5,6,7,8,9,10}}
[3,6,2,8,9,5,10,7,4,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,1,6,8,9,5,10,7,4,3]=>{{1,2},{3,4,5,6,7,8,9,10}}
[5,7,8,9,4,10,6,3,2,1]=>{{1,2,4,5,6,7,9,10},{3,8}}
[6,7,8,9,10,1,4,5,3,2]=>{{1,6},{2,3,4,5,7,8,9,10}}
[6,7,8,9,10,1,4,5,2,3]=>{{1,6},{2,4,7,9},{3,5,8,10}}
[6,7,8,9,10,4,3,2,1,5]=>{{1,4,6,9},{2,3,7,8},{5,10}}
[6,7,8,9,10,1,3,4,5,2]=>{{1,6},{2,3,4,5,7,8,9,10}}
[6,7,8,9,10,3,4,1,2,5]=>{{1,3,6,8},{2,4,7,9},{5,10}}
[6,7,8,9,10,3,4,2,1,5]=>{{1,2,3,4,6,7,8,9},{5,10}}
[6,7,8,9,10,2,3,4,1,5]=>{{1,2,3,4,6,7,8,9},{5,10}}
[2,1,4,3,6,5,9,10,8,7]=>{{1,2},{3,4},{5,6},{7,8,9,10}}
[3,4,2,1,6,5,9,10,8,7]=>{{1,2,3,4},{5,6},{7,8,9,10}}
[3,5,2,6,4,1,9,10,8,7]=>{{1,2,3,4,5,6},{7,8,9,10}}
[3,5,2,8,4,9,10,7,6,1]=>{{1,2,3,4,5,7,8,10},{6,9}}
[2,1,5,6,4,3,9,10,8,7]=>{{1,2},{3,4,5,6},{7,8,9,10}}
[4,5,6,3,2,1,9,10,8,7]=>{{1,3,4,6},{2,5},{7,8,9,10}}
[4,5,8,3,2,9,10,7,6,1]=>{{1,3,4,7,8,10},{2,5},{6,9}}
[2,1,5,8,4,9,10,7,6,3]=>{{1,2},{3,4,5,7,8,10},{6,9}}
[4,7,8,3,9,10,6,5,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,1,4,3,8,9,10,7,6,5]=>{{1,2},{3,4},{5,7,8,10},{6,9}}
[3,4,2,1,8,9,10,7,6,5]=>{{1,2,3,4},{5,7,8,10},{6,9}}
[3,7,2,8,9,10,6,5,4,1]=>{{1,2,3,6,7,10},{4,5,8,9}}
[2,1,7,8,9,10,6,5,4,3]=>{{1,2},{3,6,7,10},{4,5,8,9}}
[6,7,8,9,10,1,5,4,3,2]=>{{1,6},{2,5,7,10},{3,4,8,9}}
[6,7,8,9,10,5,4,3,2,1]=>{{1,5,6,10},{2,4,7,9},{3,8}}
[2,3,4,5,6,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,7,8,9,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,7,9,10,1,8]=>{{1,2,3,4,5,6,7,9},{8,10}}
[2,3,4,5,6,8,9,10,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,7,8,9,10,1,6]=>{{1,2,3,4,5,7,9},{6,8,10}}
[2,3,4,6,7,8,9,10,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,5,6,7,8,9,10,1,4]=>{{1,2,3,5,7,9},{4,6,8,10}}
[2,4,5,6,7,8,9,10,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,5,6,7,8,9,10,1,2]=>{{1,3,5,7,9},{2,4,6,8,10}}
[10,8,9,5,6,7,1,2,3,4]=>{{1,4,5,6,7,10},{2,8},{3,9}}
[10,8,9,4,5,6,1,2,3,7]=>{{1,7,10},{2,8},{3,9},{4},{5},{6}}
[10,7,8,5,6,9,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,7,8,4,5,9,1,2,3,6]=>{{1,2,3,6,7,8,9,10},{4},{5}}
[10,6,7,4,5,8,1,2,3,9]=>{{1,3,7,9,10},{2,6,8},{4},{5}}
[10,7,8,3,4,9,1,2,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,6,7,3,4,8,1,2,5,9]=>{{1,3,4,5,7,9,10},{2,6,8}}
[9,8,10,5,6,7,1,2,3,4]=>{{1,3,4,5,6,7,9,10},{2,8}}
[9,8,10,4,5,6,1,2,3,7]=>{{1,3,7,9,10},{2,8},{4},{5},{6}}
[9,7,10,5,6,8,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,7,10,4,5,8,1,2,3,6]=>{{1,2,3,6,7,8,9,10},{4},{5}}
[9,6,10,4,5,7,1,2,3,8]=>{{1,2,3,6,7,8,9,10},{4},{5}}
[9,7,10,3,4,8,1,2,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,6,10,3,4,7,1,2,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,7,9,5,6,10,1,2,3,4]=>{{1,2,7,8},{3,9},{4,5,6,10}}
[8,7,9,4,5,10,1,2,3,6]=>{{1,2,7,8},{3,9},{4},{5},{6,10}}
[8,6,9,4,5,10,1,2,3,7]=>{{1,2,6,7,8,10},{3,9},{4},{5}}
[7,6,8,4,5,9,1,2,3,10]=>{{1,7},{2,3,6,8,9},{4},{5},{10}}
[8,7,9,3,4,10,1,2,5,6]=>{{1,2,7,8},{3,4,5,9},{6,10}}
[8,6,9,3,4,10,1,2,5,7]=>{{1,2,6,7,8,10},{3,4,5,9}}
[7,6,8,3,4,9,1,2,5,10]=>{{1,7},{2,3,4,5,6,8,9},{10}}
[9,6,10,5,7,8,1,2,3,4]=>{{1,3,4,5,7,9,10},{2,6,8}}
[9,6,10,4,7,8,1,2,3,5]=>{{1,3,5,7,9,10},{2,6,8},{4}}
[9,5,10,4,6,7,1,2,3,8]=>{{1,2,3,5,6,7,8,9,10},{4}}
[9,6,10,3,7,8,1,2,4,5]=>{{1,3,4,5,7,9,10},{2,6,8}}
[9,5,10,3,6,7,1,2,4,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,6,9,5,7,10,1,2,3,4]=>{{1,2,4,5,6,7,8,10},{3,9}}
[8,6,9,4,7,10,1,2,3,5]=>{{1,2,5,6,7,8,10},{3,9},{4}}
[8,5,9,4,6,10,1,2,3,7]=>{{1,2,5,6,7,8,10},{3,9},{4}}
[7,5,8,4,6,9,1,2,3,10]=>{{1,7},{2,3,5,6,8,9},{4},{10}}
[8,6,9,3,7,10,1,2,4,5]=>{{1,2,5,6,7,8,10},{3,4,9}}
[8,5,9,3,6,10,1,2,4,7]=>{{1,2,5,6,7,8,10},{3,4,9}}
[7,5,8,3,6,9,1,2,4,10]=>{{1,7},{2,3,4,5,6,8,9},{10}}
[8,4,9,3,5,10,1,2,6,7]=>{{1,2,3,4,6,7,8,9,10},{5}}
[7,4,8,3,5,9,1,2,6,10]=>{{1,7},{2,3,4,8},{5},{6,9},{10}}
[9,6,10,2,7,8,1,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,5,10,2,6,7,1,3,4,8]=>{{1,2,4,5,6,7,9},{3,8,10}}
[8,6,9,2,7,10,1,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,5,9,2,6,10,1,3,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,5,8,2,6,9,1,3,4,10]=>{{1,7},{2,4,5,6,9},{3,8},{10}}
[8,4,9,2,5,10,1,3,6,7]=>{{1,3,6,7,8,9,10},{2,4},{5}}
[7,4,8,2,5,9,1,3,6,10]=>{{1,7},{2,4},{3,8},{5},{6,9},{10}}
[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]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
[9,1,2,3,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,10,1,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,2,3,4,5,6,7,9,10,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,2,3,4,5,6,8,9,10,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,2,3,4,5,7,8,9,10,6]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,2,3,4,6,7,8,9,10,5]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,2,3,5,6,7,8,9,10,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[1,2,4,5,6,7,8,9,10,3]=>{{1},{2},{3,4,5,6,7,8,9,10}}
[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[9,10,8,7,6,5,4,3,2,1]=>{{1,2,9,10},{3,8},{4,7},{5,6}}
[9,8,10,7,6,5,4,3,2,1]=>{{1,2,3,8,9,10},{4,7},{5,6}}
[9,8,7,10,6,5,4,3,2,1]=>{{1,2,3,4,7,8,9,10},{5,6}}
[9,8,7,6,10,5,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,8,7,6,5,10,4,3,2,1]=>{{1,2,3,4,6,7,8,9,10},{5}}
[9,8,7,6,5,4,10,3,2,1]=>{{1,2,3,7,8,9,10},{4,6},{5}}
[9,8,7,6,5,4,3,10,2,1]=>{{1,2,8,9,10},{3,7},{4,6},{5}}
[9,8,7,6,5,4,3,2,10,1]=>{{1,9,10},{2,8},{3,7},{4,6},{5}}
[9,8,7,6,5,4,3,2,1,10]=>{{1,9},{2,8},{3,7},{4,6},{5},{10}}
[10,1,2,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,1,2,3,4,5,6,9,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,1,2,3,4,5,9,6,7,8]=>{{1,2,3,4,5,6,8,10},{7,9}}
[9,1,2,3,4,10,5,6,7,8]=>{{1,2,3,4,5,7,9},{6,8,10}}
[10,1,2,3,9,4,5,6,7,8]=>{{1,2,3,4,6,8,10},{5,7,9}}
[10,1,2,9,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,1,10,2,3,4,5,6,7,8]=>{{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}}
[8,1,2,3,4,5,6,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,1,2,3,4,5,10,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,1,2,3,4,10,9,5,7,8]=>{{1,2,3,4,5,6,8,10},{7,9}}
[5,1,2,3,9,10,4,6,7,8]=>{{1,2,3,4,5,7,9},{6,8,10}}
[4,1,2,10,9,3,5,6,7,8]=>{{1,2,3,4,6,8,10},{5,7,9}}
[3,1,10,9,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,9,10,1,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,10,9,8,7,6,5,4,3,2]=>{{1},{2,10},{3,9},{4,8},{5,7},{6}}
[9,8,7,5,6,4,3,2,1,10]=>{{1,9},{2,8},{3,7},{4,5,6},{10}}
[1,10,9,8,6,7,5,4,3,2]=>{{1},{2,10},{3,9},{4,8},{5,6,7}}
[10,2,1,3,4,5,6,7,8,9]=>{{1,3,4,5,6,7,8,9,10},{2}}
[3,2,4,5,6,7,8,9,10,1]=>{{1,3,4,5,6,7,8,9,10},{2}}
[2,4,6,8,10,1,3,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,4,6,9,10,1,3,5,7,8]=>{{1,2,3,4,6,7,9},{5,8,10}}
[2,4,7,8,10,1,3,5,6,9]=>{{1,2,4,5,6,8,9,10},{3,7}}
[2,4,7,9,10,1,3,5,6,8]=>{{1,2,4,6,9},{3,7},{5,8,10}}
[2,4,8,9,10,1,3,5,6,7]=>{{1,2,4,6,9},{3,5,7,8,10}}
[2,5,6,8,10,1,3,4,7,9]=>{{1,2,3,5,6,7,9,10},{4,8}}
[2,5,6,9,10,1,3,4,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,5,7,8,10,1,3,4,6,9]=>{{1,2,5,6,9,10},{3,7},{4,8}}
[2,5,7,9,10,1,3,4,6,8]=>{{1,2,4,5,6,8,9,10},{3,7}}
[2,5,8,9,10,1,3,4,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,6,7,8,10,1,3,4,5,9]=>{{1,2,6},{3,7},{4,8},{5,9,10}}
[2,6,7,9,10,1,3,4,5,8]=>{{1,2,6},{3,7},{4,5,8,9,10}}
[2,6,8,9,10,1,3,4,5,7]=>{{1,2,6},{3,4,5,7,8,9,10}}
[2,7,8,9,10,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,6,8,10,1,2,5,7,9]=>{{1,3,6},{2,4,5,7,8,9,10}}
[3,4,6,9,10,1,2,5,7,8]=>{{1,3,6},{2,4,7,9},{5,8,10}}
[3,4,7,8,10,1,2,5,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,7,9,10,1,2,5,6,8]=>{{1,2,3,4,6,7,9},{5,8,10}}
[3,4,8,9,10,1,2,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,5,6,8,10,1,2,4,7,9]=>{{1,3,6},{2,5,7,9,10},{4,8}}
[3,5,6,9,10,1,2,4,7,8]=>{{1,3,6},{2,4,5,7,8,9,10}}
[3,5,7,8,10,1,2,4,6,9]=>{{1,2,3,5,6,7,9,10},{4,8}}
[3,5,7,9,10,1,2,4,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,5,8,9,10,1,2,4,6,7]=>{{1,3,4,6,8,9},{2,5,7,10}}
[3,6,7,8,10,1,2,4,5,9]=>{{1,2,3,6,7},{4,8},{5,9,10}}
[3,6,7,9,10,1,2,4,5,8]=>{{1,2,3,6,7},{4,5,8,9,10}}
[3,6,8,9,10,1,2,4,5,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,7,8,9,10,1,2,4,5,6]=>{{1,3,4,5,6,8,9,10},{2,7}}
[4,5,6,8,10,1,2,3,7,9]=>{{1,3,4,6,8},{2,5,7,9,10}}
[4,5,6,9,10,1,2,3,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,5,7,8,10,1,2,3,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,5,7,9,10,1,2,3,6,8]=>{{1,4,6,9},{2,3,5,7,8,10}}
[4,5,8,9,10,1,2,3,6,7]=>{{1,4,6,9},{2,5,7,10},{3,8}}
[4,6,7,8,10,1,2,3,5,9]=>{{1,2,3,4,6,7,8},{5,9,10}}
[4,6,7,9,10,1,2,3,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,6,8,9,10,1,2,3,5,7]=>{{1,2,4,5,6,7,9,10},{3,8}}
[4,7,8,9,10,1,2,3,5,6]=>{{1,4,5,6,9,10},{2,7},{3,8}}
[5,6,7,8,10,1,2,3,4,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,6,7,9,10,1,2,3,4,8]=>{{1,2,3,5,6,7,8,10},{4,9}}
[5,6,8,9,10,1,2,3,4,7]=>{{1,2,5,6,7,10},{3,8},{4,9}}
[5,7,8,9,10,1,2,3,4,6]=>{{1,5,6,10},{2,7},{3,8},{4,9}}
[3,1,4,5,6,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,3,4,5,6,7,8,1,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,1,4,5,6,7,8,9,2,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,10,4,5,6,7,8,1,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,3,4,5,6,7,1,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,1,10,5,6,7,8,9,2,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,1,4,5,6,7,8,2,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,10,1,2,3,4,5,6,7,8]=>{{1,3,5,7,9},{2,4,6,8,10}}
[8,9,10,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,9,1,2,3,4,5,6,7]=>{{1,4,7,10},{2,5,8},{3,6,9}}
[10,9,8,1,2,3,4,5,6,7]=>{{1,4,7,10},{2,3,5,6,8,9}}
[7,8,9,10,1,2,3,4,5,6]=>{{1,3,5,7,9},{2,4,6,8,10}}
[10,7,8,9,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,10,7,8,1,2,3,4,5,6]=>{{1,5,9},{2,6,10},{3,7},{4,8}}
[10,9,7,8,1,2,3,4,5,6]=>{{1,2,5,6,9,10},{3,7},{4,8}}
[10,9,8,7,1,2,3,4,5,6]=>{{1,2,5,6,9,10},{3,4,7,8}}
[10,6,7,8,9,1,2,3,4,5]=>{{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}}
[10,9,6,7,8,1,2,3,4,5]=>{{1,3,5,6,8,10},{2,4,7,9}}
[10,8,9,6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,8,6,7,1,2,3,4,5]=>{{1,2,4,5,6,7,9,10},{3,8}}
[10,9,8,7,6,1,2,3,4,5]=>{{1,5,6,10},{2,4,7,9},{3,8}}
[9,10,5,6,7,8,1,2,3,4]=>{{1,3,5,7,9},{2,4,6,8,10}}
[10,9,5,6,7,8,1,2,3,4]=>{{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}}
[10,9,8,5,6,7,1,2,3,4]=>{{1,4,5,6,7,10},{2,3,8,9}}
[9,10,7,8,5,6,1,2,3,4]=>{{1,3,7,9},{2,4,8,10},{5},{6}}
[10,9,7,8,5,6,1,2,3,4]=>{{1,2,3,4,7,8,9,10},{5},{6}}
[10,9,8,7,5,6,1,2,3,4]=>{{1,4,7,10},{2,3,8,9},{5},{6}}
[10,9,8,7,6,5,1,2,3,4]=>{{1,4,7,10},{2,3,8,9},{5,6}}
[10,7,8,9,4,5,6,1,2,3]=>{{1,3,8,10},{2,4,5,6,7,9}}
[9,10,7,8,4,5,6,1,2,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,7,8,4,5,6,1,2,3]=>{{1,3,4,5,6,7,8,10},{2,9}}
[10,9,8,7,4,5,6,1,2,3]=>{{1,3,8,10},{2,9},{4,5,6,7}}
[10,8,9,6,7,4,5,1,2,3]=>{{1,2,3,8,9,10},{4,6},{5,7}}
[10,9,8,6,7,4,5,1,2,3]=>{{1,3,8,10},{2,9},{4,6},{5,7}}
[10,9,8,7,6,4,5,1,2,3]=>{{1,3,8,10},{2,9},{4,5,6,7}}
[10,9,8,7,6,5,4,1,2,3]=>{{1,3,8,10},{2,9},{4,7},{5,6}}
[9,10,7,8,5,6,3,4,1,2]=>{{1,9},{2,10},{3,7},{4,8},{5},{6}}
[10,9,7,8,5,6,3,4,1,2]=>{{1,2,9,10},{3,7},{4,8},{5},{6}}
[10,9,8,7,5,6,3,4,1,2]=>{{1,2,9,10},{3,4,7,8},{5},{6}}
[10,9,8,7,6,5,3,4,1,2]=>{{1,2,9,10},{3,4,7,8},{5,6}}
[10,9,8,7,6,5,4,3,1,2]=>{{1,2,9,10},{3,8},{4,7},{5,6}}
[8,9,7,6,5,4,3,2,1,10]=>{{1,2,8,9},{3,7},{4,6},{5},{10}}
[1,9,10,8,7,6,5,4,3,2]=>{{1},{2,3,9,10},{4,8},{5,7},{6}}
[9,1,2,3,4,5,6,7,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[1,10,2,3,4,5,6,7,8,9]=>{{1},{2,3,4,5,6,7,8,9,10}}
[8,9,1,2,3,4,5,6,7,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[1,9,10,2,3,4,5,6,7,8]=>{{1},{2,3,4,5,6,7,8,9,10}}
[2,4,1,3,6,5,8,7,10,9]=>{{1,2,3,4},{5,6},{7,8},{9,10}}
[2,4,1,6,3,5,8,7,10,9]=>{{1,2,3,4,5,6},{7,8},{9,10}}
[2,4,1,6,3,8,5,7,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,4,1,6,3,8,5,9,7,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[2,4,1,6,3,7,5,9,8,10]=>{{1,2,3,4,5,6,7},{8,9},{10}}
[2,4,1,5,3,7,6,9,8,10]=>{{1,2,3,4,5},{6,7},{8,9},{10}}
[2,3,1,5,4,7,6,9,8,10]=>{{1,2,3},{4,5},{6,7},{8,9},{10}}
[1,3,2,5,4,7,6,9,8,10]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[3,4,1,2,5,6,7,8,9,10]=>{{1,3},{2,4},{5},{6},{7},{8},{9},{10}}
[3,2,1,4,5,6,7,8,9,10]=>{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}
[4,5,6,1,2,3,7,8,9,10]=>{{1,4},{2,5},{3,6},{7},{8},{9},{10}}
[4,2,5,1,3,6,7,8,9,10]=>{{1,4},{2},{3,5},{6},{7},{8},{9},{10}}
[4,3,2,1,5,6,7,8,9,10]=>{{1,4},{2,3},{5},{6},{7},{8},{9},{10}}
[5,6,7,8,1,2,3,4,9,10]=>{{1,5},{2,6},{3,7},{4,8},{9},{10}}
[5,2,6,7,1,3,4,8,9,10]=>{{1,5},{2},{3,6},{4,7},{8},{9},{10}}
[5,6,3,4,1,2,7,8,9,10]=>{{1,5},{2,6},{3},{4},{7},{8},{9},{10}}
[5,3,2,6,1,4,7,8,9,10]=>{{1,5},{2,3},{4,6},{7},{8},{9},{10}}
[5,4,3,2,1,6,7,8,9,10]=>{{1,5},{2,4},{3},{6},{7},{8},{9},{10}}
[6,2,7,8,9,1,3,4,5,10]=>{{1,6},{2},{3,7},{4,8},{5,9},{10}}
[6,7,3,4,8,1,2,5,9,10]=>{{1,6},{2,7},{3},{4},{5,8},{9},{10}}
[6,3,2,7,8,1,4,5,9,10]=>{{1,6},{2,3},{4,7},{5,8},{9},{10}}
[6,4,7,2,5,1,3,8,9,10]=>{{1,6},{2,4},{3,7},{5},{8},{9},{10}}
[6,4,3,2,7,1,5,8,9,10]=>{{1,6},{2,4},{3},{5,7},{8},{9},{10}}
[6,5,4,3,2,1,7,8,9,10]=>{{1,6},{2,5},{3,4},{7},{8},{9},{10}}
[7,8,3,4,9,10,1,2,5,6]=>{{1,7},{2,8},{3},{4},{5,9},{6,10}}
[7,8,9,4,5,6,1,2,3,10]=>{{1,7},{2,8},{3,9},{4},{5},{6},{10}}
[7,4,3,2,8,9,1,5,6,10]=>{{1,7},{2,4},{3},{5,8},{6,9},{10}}
[7,8,5,6,3,4,1,2,9,10]=>{{1,7},{2,8},{3,5},{4,6},{9},{10}}
[7,5,3,8,2,6,1,4,9,10]=>{{1,7},{2,5},{3},{4,8},{6},{9},{10}}
[7,5,4,3,2,8,1,6,9,10]=>{{1,7},{2,5},{3,4},{6,8},{9},{10}}
[7,6,5,4,3,2,1,8,9,10]=>{{1,7},{2,6},{3,5},{4},{8},{9},{10}}
[8,5,9,10,2,6,7,1,3,4]=>{{1,8},{2,5},{3,9},{4,10},{6},{7}}
[8,5,3,9,2,6,10,1,4,7]=>{{1,8},{2,5},{3},{4,9},{6},{7,10}}
[8,6,9,4,7,2,5,1,3,10]=>{{1,8},{2,6},{3,9},{4},{5,7},{10}}
[8,6,4,3,9,2,7,1,5,10]=>{{1,8},{2,6},{3,4},{5,9},{7},{10}}
[8,6,5,4,3,2,9,1,7,10]=>{{1,8},{2,6},{3,5},{4},{7,9},{10}}
[8,7,6,5,4,3,2,1,9,10]=>{{1,8},{2,7},{3,6},{4,5},{9},{10}}
[9,7,5,4,3,10,2,8,1,6]=>{{1,9},{2,7},{3,5},{4},{6,10},{8}}
[2,3,1,4,5,6,7,8,9,10]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[2,3,4,1,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[2,3,4,5,1,6,7,8,9,10]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}
[2,3,4,5,6,1,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}
[2,3,4,5,6,7,1,8,9,10]=>{{1,2,3,4,5,6,7},{8},{9},{10}}
[2,3,4,5,6,7,8,1,9,10]=>{{1,2,3,4,5,6,7,8},{9},{10}}
[3,4,1,5,6,7,8,9,10,2]=>{{1,3},{2,4,5,6,7,8,9,10}}
[3,4,5,1,6,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,5,6,1,7,8,9,10,2]=>{{1,3,5},{2,4,6,7,8,9,10}}
[3,4,5,6,7,1,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,5,6,7,8,1,9,10,2]=>{{1,3,5,7},{2,4,6,8,9,10}}
[3,4,5,6,7,8,9,1,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,8,7,6,5,4,3,1,10,2]=>{{1,2,8,9,10},{3,7},{4,6},{5}}
[8,10,7,6,5,4,3,2,1,9]=>{{1,2,8,9,10},{3,7},{4,6},{5}}
[1,8,7,6,5,4,3,10,9,2]=>{{1},{2,8,10},{3,7},{4,6},{5},{9}}
[1,10,7,6,5,4,3,2,9,8]=>{{1},{2,8,10},{3,7},{4,6},{5},{9}}
[9,1,7,6,5,4,3,10,8,2]=>{{1,2,8,9,10},{3,7},{4,6},{5}}
[3,8,7,6,5,4,10,1,9,2]=>{{1,2,3,7,8,10},{4,6},{5},{9}}
[8,10,1,6,5,4,3,2,9,7]=>{{1,2,3,7,8,10},{4,6},{5},{9}}
[2,10,7,6,5,4,3,9,1,8]=>{{1,2,8,9,10},{3,7},{4,6},{5}}
[8,10,9,7,6,5,4,3,2,1]=>{{1,2,3,8,9,10},{4,7},{5,6}}
[7,10,9,8,6,5,4,3,2,1]=>{{1,2,3,4,7,8,9,10},{5,6}}
[6,10,9,8,7,5,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,10,9,8,7,6,4,3,2,1]=>{{1,2,3,4,5,7,8,9,10},{6}}
[4,10,9,8,7,6,5,3,2,1]=>{{1,2,3,4,8,9,10},{5,7},{6}}
[3,10,9,8,7,6,5,4,2,1]=>{{1,2,3,9,10},{4,8},{5,7},{6}}
[2,10,9,8,7,6,5,4,3,1]=>{{1,2,10},{3,9},{4,8},{5,7},{6}}
[1,2,3,4,5,6,7,10,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,2,3,4,5,6,10,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,2,3,4,5,10,6,7,8,9]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,2,3,4,10,5,6,7,8,9]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,2,3,10,4,5,6,7,8,9]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[1,2,10,3,4,5,6,7,8,9]=>{{1},{2},{3,4,5,6,7,8,9,10}}
[8,7,10,9,6,5,4,3,2,1]=>{{1,3,8,10},{2,4,7,9},{5,6}}
[8,9,10,7,6,5,4,3,2,1]=>{{1,3,8,10},{2,9},{4,7},{5,6}}
[7,6,5,10,9,8,4,3,2,1]=>{{1,4,7,10},{2,3,5,6,8,9}}
[7,9,6,10,8,5,4,3,2,1]=>{{1,4,7,10},{2,9},{3,5,6,8}}
[7,8,9,10,6,5,4,3,2,1]=>{{1,4,7,10},{2,3,8,9},{5,6}}
[6,5,4,3,10,9,8,7,2,1]=>{{1,2,5,6,9,10},{3,4},{7,8}}
[6,9,5,4,10,8,7,3,2,1]=>{{1,3,5,6,8,10},{2,9},{4},{7}}
[6,5,8,7,10,9,4,3,2,1]=>{{1,2,5,6,9,10},{3,8},{4,7}}
[6,8,9,5,10,7,4,3,2,1]=>{{1,4,5,6,7,10},{2,3,8,9}}
[5,4,3,2,1,10,9,8,7,6]=>{{1,5},{2,4},{3},{6,10},{7,9},{8}}
[5,9,4,3,2,10,8,7,6,1]=>{{1,2,5,6,9,10},{3,4},{7,8}}
[5,4,8,7,3,10,9,6,2,1]=>{{1,3,5,6,8,10},{2,4,7,9}}
[5,8,9,4,3,10,7,6,2,1]=>{{1,2,3,5,6,8,9,10},{4},{7}}
[5,7,4,9,6,10,8,3,2,1]=>{{1,5,6,10},{2,3,4,7,8,9}}
[5,6,7,8,9,10,4,3,2,1]=>{{1,2,5,6,9,10},{3,4,7,8}}
[4,3,8,7,2,1,10,9,6,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,8,9,3,2,1,10,7,6,5]=>{{1,3,4,6,9},{2,5,7,8,10}}
[4,3,2,7,6,5,10,9,8,1]=>{{1,4,7,10},{2,3},{5,6},{8,9}}
[4,7,3,9,6,2,10,8,5,1]=>{{1,2,4,5,6,7,9,10},{3},{8}}
[4,7,8,9,3,2,10,6,5,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,6,5,8,7,10,9,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,6,7,8,9,3,10,5,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,5,6,7,8,9,10,3,2,1]=>{{1,4,7,10},{2,3,5,6,8,9}}
[3,6,2,1,9,5,4,10,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,2,6,5,8,7,1,10,9,4]=>{{1,3,6,7},{2},{4,5,8,10},{9}}
[3,6,8,2,9,5,1,10,7,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,6,7,8,9,2,1,10,5,4]=>{{1,3,7},{2,6},{4,8,10},{5,9}}
[3,5,7,8,2,9,4,10,6,1]=>{{1,3,4,7,8,10},{2,5},{6,9}}
[3,5,6,7,8,9,2,10,4,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,5,6,7,8,9,10,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,4,6,1,8,3,9,5,10,7]=>{{1,2,4},{3,6},{5,8},{7,9,10}}
[2,4,6,7,8,1,9,3,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,4,5,6,7,8,9,1,10,3]=>{{1,2,4,6,8},{3,5,7,9,10}}
[7,8,10,9,5,6,3,4,1,2]=>{{1,2,3,4,7,8,9,10},{5},{6}}
[9,10,5,6,8,7,3,4,1,2]=>{{1,9},{2,10},{3,4,5,6,7,8}}
[5,8,10,6,9,7,3,4,1,2]=>{{1,5,9},{2,3,4,6,7,8,10}}
[5,6,7,10,9,8,3,4,1,2]=>{{1,5,9},{2,4,6,8,10},{3,7}}
[9,10,7,8,3,4,6,5,1,2]=>{{1,9},{2,10},{3,4,5,6,7,8}}
[7,8,10,9,3,4,6,5,1,2]=>{{1,4,6,7,9},{2,3,5,8,10}}
[9,10,3,6,8,4,7,5,1,2]=>{{1,9},{2,10},{3},{4,6},{5,8},{7}}
[3,8,10,6,9,4,7,5,1,2]=>{{1,2,3,5,8,9,10},{4,6},{7}}
[3,6,7,10,9,4,8,5,1,2]=>{{1,3,5,7,8,9},{2,4,6,10}}
[9,10,3,4,5,8,7,6,1,2]=>{{1,9},{2,10},{3},{4},{5},{6,8},{7}}
[3,8,10,4,5,9,7,6,1,2]=>{{1,2,3,6,8,9,10},{4},{5},{7}}
[3,4,7,10,5,9,8,6,1,2]=>{{1,3,6,7,8,9},{2,4,10},{5}}
[3,4,5,6,10,9,8,7,1,2]=>{{1,2,3,4,5,6,9,10},{7,8}}
[9,10,7,8,5,6,1,2,4,3]=>{{1,2,3,4,7,8,9,10},{5},{6}}
[7,8,10,9,5,6,1,2,4,3]=>{{1,7},{2,8},{3,10},{4,9},{5},{6}}
[9,10,5,6,8,7,1,2,4,3]=>{{1,4,6,7,9},{2,3,5,8,10}}
[5,8,10,6,9,7,1,2,4,3]=>{{1,4,5,6,7,9},{2,8},{3,10}}
[5,6,7,10,9,8,1,2,4,3]=>{{1,3,4,5,7,9,10},{2,6,8}}
[9,10,7,8,1,4,6,2,5,3]=>{{1,5,9},{2,3,4,6,7,8,10}}
[7,8,10,9,1,4,6,2,5,3]=>{{1,4,5,6,7,9},{2,8},{3,10}}
[9,10,1,6,8,4,7,2,5,3]=>{{1,2,3,5,8,9,10},{4,6},{7}}
[1,8,10,6,9,4,7,2,5,3]=>{{1},{2,8},{3,10},{4,6},{5,9},{7}}
[1,6,7,10,9,4,8,2,5,3]=>{{1},{2,3,4,6,7,8,10},{5,9}}
[9,10,1,4,5,8,7,2,6,3]=>{{1,2,3,6,8,9,10},{4},{5},{7}}
[1,8,10,4,5,9,7,2,6,3]=>{{1},{2,8},{3,10},{4},{5},{6,9},{7}}
[1,4,7,10,5,9,8,2,6,3]=>{{1},{2,3,4,7,8,10},{5},{6,9}}
[1,4,5,6,10,9,8,2,7,3]=>{{1},{2,4,6,7,8,9},{3,5,10}}
[9,10,7,8,1,2,3,6,5,4]=>{{1,5,9},{2,4,6,8,10},{3,7}}
[7,8,10,9,1,2,3,6,5,4]=>{{1,3,4,5,7,9,10},{2,6,8}}
[9,10,1,6,8,2,3,7,5,4]=>{{1,3,5,7,8,9},{2,4,6,10}}
[1,8,10,6,9,2,3,7,5,4]=>{{1},{2,3,4,6,7,8,10},{5,9}}
[1,6,7,10,9,2,3,8,5,4]=>{{1},{2,6},{3,7},{4,10},{5,9},{8}}
[9,10,1,2,5,8,3,7,6,4]=>{{1,3,6,7,8,9},{2,4,10},{5}}
[1,8,10,2,5,9,3,7,6,4]=>{{1},{2,3,4,7,8,10},{5},{6,9}}
[1,2,7,10,5,9,3,8,6,4]=>{{1},{2},{3,7},{4,10},{5},{6,9},{8}}
[1,2,5,6,10,9,3,8,7,4]=>{{1},{2},{3,4,5,6,7,9,10},{8}}
[9,10,1,2,3,4,8,7,6,5]=>{{1,2,3,4,5,6,9,10},{7,8}}
[1,8,10,2,3,4,9,7,6,5]=>{{1},{2,4,6,7,8,9},{3,5,10}}
[1,2,7,10,3,4,9,8,6,5]=>{{1},{2},{3,4,5,6,7,9,10},{8}}
[1,2,3,6,10,4,9,8,7,5]=>{{1},{2},{3},{4,6},{5,10},{7,9},{8}}
[1,2,3,4,5,10,9,8,7,6]=>{{1},{2},{3},{4},{5},{6,10},{7,9},{8}}
[4,3,2,1,7,6,5,9,8,10]=>{{1,4},{2,3},{5,7},{6},{8,9},{10}}
[7,3,2,1,6,5,4,9,8,10]=>{{1,4,7},{2,3},{5,6},{8,9},{10}}
[4,3,2,1,9,6,5,8,7,10]=>{{1,4},{2,3},{5,7,9},{6},{8},{10}}
[6,3,2,1,9,5,4,8,7,10]=>{{1,4,5,6,7,9},{2,3},{8},{10}}
[9,3,2,1,8,5,4,7,6,10]=>{{1,4,5,6,7,8,9},{2,3},{10}}
[6,5,2,1,9,4,3,8,7,10]=>{{1,4,6},{2,3,5,7,9},{8},{10}}
[9,5,2,1,8,4,3,7,6,10]=>{{1,4,6,9},{2,3,5,7,8},{10}}
[4,3,2,1,7,6,5,10,8,9]=>{{1,4},{2,3},{5,7},{6},{8,9,10}}
[7,3,2,1,6,5,4,10,8,9]=>{{1,4,7},{2,3},{5,6},{8,9,10}}
[4,3,2,1,8,6,5,10,7,9]=>{{1,4},{2,3},{5,7,8,9,10},{6}}
[6,3,2,1,8,5,4,10,7,9]=>{{1,4,5,6,7,8,9,10},{2,3}}
[8,3,2,1,7,5,4,10,6,9]=>{{1,4,5,6,7,8,9,10},{2,3}}
[6,5,2,1,8,4,3,10,7,9]=>{{1,4,6},{2,3,5,7,8,9,10}}
[8,5,2,1,7,4,3,10,6,9]=>{{1,4,6,8,9,10},{2,3,5,7}}
[4,3,2,1,10,6,5,9,7,8]=>{{1,4},{2,3},{5,7,8,9,10},{6}}
[6,3,2,1,10,5,4,9,7,8]=>{{1,4,5,6,7,8,9,10},{2,3}}
[7,3,2,1,10,5,4,9,6,8]=>{{1,4,7},{2,3},{5,6,8,9,10}}
[10,3,2,1,9,5,4,8,6,7]=>{{1,4,7,10},{2,3},{5,6,9},{8}}
[6,5,2,1,10,4,3,9,7,8]=>{{1,4,6},{2,3,5,7,8,9,10}}
[7,5,2,1,10,4,3,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,5,2,1,9,4,3,8,6,7]=>{{1,2,3,4,5,6,7,9,10},{8}}
[4,3,2,1,8,7,5,10,6,9]=>{{1,4},{2,3},{5,6,7,8,9,10}}
[5,3,2,1,8,7,4,10,6,9]=>{{1,4,5,6,7,8,9,10},{2,3}}
[8,3,2,1,7,6,4,10,5,9]=>{{1,4,5,7,8,9,10},{2,3},{6}}
[5,4,2,1,8,7,3,10,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,4,2,1,7,6,3,10,5,9]=>{{1,2,3,4,5,7,8,9,10},{6}}
[4,3,2,1,10,7,5,9,6,8]=>{{1,4},{2,3},{5,6,7,8,9,10}}
[5,3,2,1,10,7,4,9,6,8]=>{{1,4,5,6,7,8,9,10},{2,3}}
[7,3,2,1,10,6,4,9,5,8]=>{{1,4,7},{2,3},{5,8,9,10},{6}}
[10,3,2,1,9,6,4,8,5,7]=>{{1,4,7,10},{2,3},{5,9},{6},{8}}
[5,4,2,1,10,7,3,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,4,2,1,10,6,3,9,5,8]=>{{1,2,3,4,7},{5,8,9,10},{6}}
[10,4,2,1,9,6,3,8,5,7]=>{{1,2,3,4,7,10},{5,9},{6},{8}}
[7,6,2,1,10,5,3,9,4,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,6,2,1,9,5,3,8,4,7]=>{{1,2,3,4,5,6,7,9,10},{8}}
[5,4,3,1,8,7,2,10,6,9]=>{{1,2,4,5,6,7,8,9,10},{3}}
[8,4,3,1,7,6,2,10,5,9]=>{{1,2,4,5,7,8,9,10},{3},{6}}
[5,4,3,1,10,7,2,9,6,8]=>{{1,2,4,5,6,7,8,9,10},{3}}
[7,4,3,1,10,6,2,9,5,8]=>{{1,2,4,7},{3},{5,8,9,10},{6}}
[10,4,3,1,9,6,2,8,5,7]=>{{1,2,4,7,10},{3},{5,9},{6},{8}}
[7,6,3,1,10,5,2,9,4,8]=>{{1,2,4,5,6,7,8,9,10},{3}}
[10,6,3,1,9,5,2,8,4,7]=>{{1,2,4,5,6,7,9,10},{3},{8}}
[4,3,1,2,6,5,8,7,10,9]=>{{1,2,3,4},{5,6},{7,8},{9,10}}
[10,3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,4,1,6,2,8,3,5,7]=>{{1,3,4,7,8,10},{2,5,6,9}}
[10,9,8,5,1,7,2,3,4,6]=>{{1,2,4,5,6,7,9,10},{3,8}}
[8,7,6,5,4,3,2,10,1,9]=>{{1,8,9,10},{2,7},{3,6},{4,5}}
[7,6,5,4,3,10,2,9,1,8]=>{{1,2,6,7,8,9,10},{3,5},{4}}
[7,6,5,4,3,2,9,1,8,10]=>{{1,7,8,9},{2,6},{3,5},{4},{10}}
[6,5,4,10,3,9,2,8,1,7]=>{{1,6,9},{2,3,4,5,7,10},{8}}
[6,5,4,3,9,2,8,1,7,10]=>{{1,2,5,6,7,8,9},{3,4},{10}}
[6,5,4,3,2,8,10,1,7,9]=>{{1,6,8},{2,5},{3,4},{7,9,10}}
[6,5,4,3,2,8,1,7,9,10]=>{{1,6,7,8},{2,5},{3,4},{9},{10}}
[5,10,4,9,3,8,2,7,1,6]=>{{1,3,4,5,9},{2,6,7,8,10}}
[5,4,9,3,8,2,7,1,6,10]=>{{1,5,8},{2,3,4,6,9},{7},{10}}
[5,4,3,8,2,7,10,1,6,9]=>{{1,2,4,5,8},{3},{6,7,9,10}}
[5,4,3,8,2,7,1,6,9,10]=>{{1,2,4,5,6,7,8},{3},{9},{10}}
[5,4,3,2,7,9,1,6,8,10]=>{{1,5,7},{2,4},{3},{6,8,9},{10}}
[5,4,3,2,7,1,6,8,9,10]=>{{1,5,6,7},{2,4},{3},{8},{9},{10}}
[4,8,3,7,2,6,10,1,5,9]=>{{1,2,4,5,7,8,9,10},{3},{6}}
[4,8,3,7,2,6,1,5,9,10]=>{{1,4,7},{2,5,8},{3},{6},{9},{10}}
[4,3,7,10,2,6,9,1,5,8]=>{{1,4,8,10},{2,3,5,7,9},{6}}
[4,3,7,2,6,9,1,5,8,10]=>{{1,2,3,4,7},{5,6,8,9},{10}}
[4,3,7,2,6,1,5,8,9,10]=>{{1,2,3,4,5,6,7},{8},{9},{10}}
[4,3,2,6,8,10,1,5,7,9]=>{{1,4,6,7,9,10},{2,3},{5,8}}
[4,3,2,6,8,1,5,7,9,10]=>{{1,4,6},{2,3},{5,7,8},{9},{10}}
[4,3,2,6,1,5,7,8,9,10]=>{{1,4,5,6},{2,3},{7},{8},{9},{10}}
[3,6,9,2,5,8,1,4,7,10]=>{{1,3,7,9},{2,4,6,8},{5},{10}}
[3,6,2,5,8,10,1,4,7,9]=>{{1,2,3,6,7,9,10},{4,5,8}}
[3,6,2,5,8,1,4,7,9,10]=>{{1,2,3,6},{4,5,7,8},{9},{10}}
[3,6,2,5,1,4,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}
[3,2,5,7,9,1,4,6,8,10]=>{{1,3,5,6,8,9},{2},{4,7},{10}}
[3,2,5,7,1,4,6,8,9,10]=>{{1,3,5},{2},{4,6,7},{8},{9},{10}}
[3,2,5,1,4,6,7,8,9,10]=>{{1,3,4,5},{2},{6},{7},{8},{9},{10}}
[2,4,6,8,1,3,5,7,9,10]=>{{1,2,4,5,7,8},{3,6},{9},{10}}
[2,4,6,1,3,5,7,8,9,10]=>{{1,2,4},{3,5,6},{7},{8},{9},{10}}
[2,4,1,3,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[9,8,7,6,5,4,2,1,10,3]=>{{1,2,3,7,8,9,10},{4,6},{5}}
[9,8,7,6,5,3,2,1,10,4]=>{{1,2,3,4,6,7,8,9,10},{5}}
[9,8,7,6,4,3,2,1,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,8,7,5,4,3,2,1,10,6]=>{{1,2,3,6,7,8,9,10},{4,5}}
[9,8,6,5,4,3,2,1,10,7]=>{{1,2,7,8,9,10},{3,6},{4,5}}
[9,7,6,5,4,3,2,1,10,8]=>{{1,8,9,10},{2,7},{3,6},{4,5}}
[7,8,4,5,9,2,3,6,10,1]=>{{1,3,4,5,7,9,10},{2,6,8}}
[8,10,7,9,5,6,3,4,1,2]=>{{1,4,8,9},{2,10},{3,7},{5},{6}}
[9,10,6,8,5,7,3,4,1,2]=>{{1,9},{2,10},{3,6,7},{4,8},{5}}
[8,10,6,9,5,7,3,4,1,2]=>{{1,4,8,9},{2,10},{3,6,7},{5}}
[7,10,6,9,5,8,3,4,1,2]=>{{1,3,4,6,7,8,9},{2,10},{5}}
[9,10,7,8,4,6,3,5,1,2]=>{{1,9},{2,10},{3,7},{4,5,8},{6}}
[8,10,7,9,4,6,3,5,1,2]=>{{1,4,5,8,9},{2,10},{3,7},{6}}
[9,10,6,8,4,7,3,5,1,2]=>{{1,9},{2,10},{3,6,7},{4,5,8}}
[8,10,6,9,4,7,3,5,1,2]=>{{1,4,5,8,9},{2,10},{3,6,7}}
[7,10,6,9,4,8,3,5,1,2]=>{{1,3,4,5,6,7,8,9},{2,10}}
[9,10,5,8,4,7,3,6,1,2]=>{{1,9},{2,10},{3,4,5,6,7,8}}
[8,10,5,9,4,7,3,6,1,2]=>{{1,3,4,5,6,7,8,9},{2,10}}
[7,10,5,9,4,8,3,6,1,2]=>{{1,3,4,5,7,9},{2,10},{6,8}}
[6,10,5,9,4,8,3,7,1,2]=>{{1,3,4,5,6,7,8,9},{2,10}}
[9,10,7,8,5,6,2,4,1,3]=>{{1,9},{2,3,7,10},{4,8},{5},{6}}
[8,10,7,9,5,6,2,4,1,3]=>{{1,4,8,9},{2,3,7,10},{5},{6}}
[9,10,6,8,5,7,2,4,1,3]=>{{1,9},{2,3,6,7,10},{4,8},{5}}
[8,10,6,9,5,7,2,4,1,3]=>{{1,4,8,9},{2,3,6,7,10},{5}}
[7,10,6,9,5,8,2,4,1,3]=>{{1,2,3,4,6,7,8,9,10},{5}}
[9,10,7,8,4,6,2,5,1,3]=>{{1,9},{2,3,7,10},{4,5,8},{6}}
[8,10,7,9,4,6,2,5,1,3]=>{{1,4,5,8,9},{2,3,7,10},{6}}
[9,10,6,8,4,7,2,5,1,3]=>{{1,9},{2,3,6,7,10},{4,5,8}}
[8,10,6,9,4,7,2,5,1,3]=>{{1,4,5,8,9},{2,3,6,7,10}}
[7,10,6,9,4,8,2,5,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,10,5,8,4,7,2,6,1,3]=>{{1,9},{2,3,4,5,6,7,8,10}}
[8,10,5,9,4,7,2,6,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,10,5,9,4,8,2,6,1,3]=>{{1,2,3,4,5,7,9,10},{6,8}}
[6,10,5,9,4,8,2,7,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,10,7,8,3,6,2,5,1,4]=>{{1,9},{2,3,4,5,7,8,10},{6}}
[8,10,7,9,3,6,2,5,1,4]=>{{1,2,3,4,5,7,8,9,10},{6}}
[9,10,6,8,3,7,2,5,1,4]=>{{1,9},{2,3,4,5,6,7,8,10}}
[8,10,6,9,3,7,2,5,1,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,10,6,9,3,8,2,5,1,4]=>{{1,2,4,7,9,10},{3,5,6,8}}
[9,10,5,8,3,7,2,6,1,4]=>{{1,9},{2,4,6,7,8,10},{3,5}}
[8,10,5,9,3,7,2,6,1,4]=>{{1,2,4,6,7,8,9,10},{3,5}}
[7,10,5,9,3,8,2,6,1,4]=>{{1,2,4,7,9,10},{3,5},{6,8}}
[6,10,5,9,3,8,2,7,1,4]=>{{1,2,4,6,7,8,9,10},{3,5}}
[9,10,4,8,3,7,2,6,1,5]=>{{1,9},{2,3,4,5,6,7,8,10}}
[8,10,4,9,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,10,4,9,3,8,2,6,1,5]=>{{1,2,3,4,5,7,9,10},{6,8}}
[6,10,4,9,3,8,2,7,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,5,6,7,8,9,1,2,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[1,4,5,6,7,8,9,10,2,3]=>{{1},{2,3,4,5,6,7,8,9,10}}
[9,10,7,8,5,6,3,1,4,2]=>{{1,4,8,9},{2,10},{3,7},{5},{6}}
[9,10,7,8,5,3,6,1,4,2]=>{{1,4,8,9},{2,10},{3,6,7},{5}}
[9,10,7,5,8,3,6,1,4,2]=>{{1,4,5,8,9},{2,10},{3,6,7}}
[9,7,10,5,8,3,6,1,4,2]=>{{1,4,5,8,9},{2,3,6,7,10}}
[10,7,9,5,8,3,6,1,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,9,5,7,3,6,1,4,2]=>{{1,2,8,10},{3,4,5,6,7,9}}
[10,8,9,6,7,3,5,1,4,2]=>{{1,2,8,10},{3,4,6,9},{5,7}}
[10,8,9,6,7,4,5,1,3,2]=>{{1,2,8,10},{3,9},{4,6},{5,7}}
[7,6,5,4,3,2,1,10,9,8]=>{{1,7},{2,6},{3,5},{4},{8,10},{9}}
[7,6,5,4,3,2,1,9,8,10]=>{{1,7},{2,6},{3,5},{4},{8,9},{10}}
[6,5,4,3,2,1,9,8,7,10]=>{{1,6},{2,5},{3,4},{7,9},{8},{10}}
[6,5,4,3,2,1,8,7,9,10]=>{{1,6},{2,5},{3,4},{7,8},{9},{10}}
[5,4,3,2,1,9,8,7,6,10]=>{{1,5},{2,4},{3},{6,9},{7,8},{10}}
[5,4,3,2,1,8,7,6,10,9]=>{{1,5},{2,4},{3},{6,8},{7},{9,10}}
[5,4,3,2,1,8,7,6,9,10]=>{{1,5},{2,4},{3},{6,8},{7},{9},{10}}
[5,4,3,2,1,7,6,9,8,10]=>{{1,5},{2,4},{3},{6,7},{8,9},{10}}
[5,4,3,2,1,7,6,8,9,10]=>{{1,5},{2,4},{3},{6,7},{8},{9},{10}}
[4,3,2,1,8,7,6,5,9,10]=>{{1,4},{2,3},{5,8},{6,7},{9},{10}}
[4,3,2,1,7,6,5,10,9,8]=>{{1,4},{2,3},{5,7},{6},{8,10},{9}}
[4,3,2,1,7,6,5,8,9,10]=>{{1,4},{2,3},{5,7},{6},{8},{9},{10}}
[4,3,2,1,6,5,8,7,9,10]=>{{1,4},{2,3},{5,6},{7,8},{9},{10}}
[4,3,2,1,6,5,7,8,9,10]=>{{1,4},{2,3},{5,6},{7},{8},{9},{10}}
[3,2,1,6,5,4,9,8,7,10]=>{{1,3},{2},{4,6},{5},{7,9},{8},{10}}
[3,2,1,6,5,4,8,7,10,9]=>{{1,3},{2},{4,6},{5},{7,8},{9,10}}
[3,2,1,6,5,4,8,7,9,10]=>{{1,3},{2},{4,6},{5},{7,8},{9},{10}}
[3,2,1,6,5,4,7,8,9,10]=>{{1,3},{2},{4,6},{5},{7},{8},{9},{10}}
[3,2,1,5,4,7,6,9,8,10]=>{{1,3},{2},{4,5},{6,7},{8,9},{10}}
[3,2,1,5,4,7,6,8,9,10]=>{{1,3},{2},{4,5},{6,7},{8},{9},{10}}
[3,2,1,5,4,6,7,8,9,10]=>{{1,3},{2},{4,5},{6},{7},{8},{9},{10}}
[2,1,4,3,6,5,8,7,9,10]=>{{1,2},{3,4},{5,6},{7,8},{9},{10}}
[2,1,4,3,6,5,7,8,9,10]=>{{1,2},{3,4},{5,6},{7},{8},{9},{10}}
[2,1,4,3,5,6,7,8,9,10]=>{{1,2},{3,4},{5},{6},{7},{8},{9},{10}}
[3,1,4,2,6,5,8,7,10,9]=>{{1,2,3,4},{5,6},{7,8},{9,10}}
[3,1,5,2,6,4,8,7,10,9]=>{{1,2,3,4,5,6},{7,8},{9,10}}
[3,1,5,2,7,4,8,6,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,1,5,2,7,4,9,6,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[3,1,2,5,4,7,6,9,8,10]=>{{1,2,3},{4,5},{6,7},{8,9},{10}}
[4,5,6,7,8,9,10,1,2,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,5,6,7,8,9,10,2,3,1]=>{{1,4,7,10},{2,5,8},{3,6,9}}
[5,6,7,8,9,10,1,2,3,4]=>{{1,3,5,7,9},{2,4,6,8,10}}
[5,6,7,8,9,10,3,4,1,2]=>{{1,5,9},{2,6,10},{3,7},{4,8}}
[7,8,9,10,3,4,5,6,1,2]=>{{1,3,5,7,9},{2,4,6,8,10}}
[7,8,9,10,5,6,3,4,1,2]=>{{1,3,7,9},{2,4,8,10},{5},{6}}
[8,9,10,5,6,7,2,3,4,1]=>{{1,3,8,10},{2,4,5,6,7,9}}
[9,7,5,3,1,10,8,6,4,2]=>{{1,3,4,5,9},{2,6,7,8,10}}
[8,7,5,3,1,10,9,6,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,6,5,3,1,10,8,7,4,2]=>{{1,3,4,5,9},{2,6,10},{7,8}}
[8,6,5,3,1,10,9,7,4,2]=>{{1,3,4,5,7,8,9},{2,6,10}}
[7,6,5,3,1,10,9,8,4,2]=>{{1,3,4,5,7,9},{2,6,10},{8}}
[9,7,4,3,1,10,8,6,5,2]=>{{1,5,9},{2,6,7,8,10},{3,4}}
[8,7,4,3,1,10,9,6,5,2]=>{{1,2,5,6,7,8,9,10},{3,4}}
[9,6,4,3,1,10,8,7,5,2]=>{{1,5,9},{2,6,10},{3,4},{7,8}}
[8,6,4,3,1,10,9,7,5,2]=>{{1,5,7,8,9},{2,6,10},{3,4}}
[7,6,4,3,1,10,9,8,5,2]=>{{1,5,7,9},{2,6,10},{3,4},{8}}
[9,5,4,3,1,10,8,7,6,2]=>{{1,2,5,6,9,10},{3,4},{7,8}}
[8,5,4,3,1,10,9,7,6,2]=>{{1,2,5,6,7,8,9,10},{3,4}}
[7,5,4,3,1,10,9,8,6,2]=>{{1,2,5,6,7,9,10},{3,4},{8}}
[6,5,4,3,1,10,9,8,7,2]=>{{1,2,5,6,10},{3,4},{7,9},{8}}
[9,7,5,2,1,10,8,6,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,7,5,2,1,10,9,6,4,3]=>{{1,3,5,6,8,10},{2,4,7,9}}
[9,6,5,2,1,10,8,7,4,3]=>{{1,2,3,4,5,6,9,10},{7,8}}
[8,6,5,2,1,10,9,7,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,6,5,2,1,10,9,8,4,3]=>{{1,2,3,4,5,6,7,9,10},{8}}
[9,7,4,2,1,10,8,6,5,3]=>{{1,5,9},{2,3,4,6,7,8,10}}
[8,7,4,2,1,10,9,6,5,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,6,4,2,1,10,8,7,5,3]=>{{1,5,9},{2,3,4,6,10},{7,8}}
[8,6,4,2,1,10,9,7,5,3]=>{{1,5,7,8,9},{2,3,4,6,10}}
[7,6,4,2,1,10,9,8,5,3]=>{{1,5,7,9},{2,3,4,6,10},{8}}
[9,5,4,2,1,10,8,7,6,3]=>{{1,2,3,4,5,6,9,10},{7,8}}
[8,5,4,2,1,10,9,7,6,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,5,4,2,1,10,9,8,6,3]=>{{1,2,3,4,5,6,7,9,10},{8}}
[6,5,4,2,1,10,9,8,7,3]=>{{1,2,3,4,5,6,10},{7,9},{8}}
[9,7,3,2,1,10,8,6,5,4]=>{{1,5,9},{2,4,6,7,8,10},{3}}
[8,7,3,2,1,10,9,6,5,4]=>{{1,2,4,5,6,7,8,9,10},{3}}
[9,6,3,2,1,10,8,7,5,4]=>{{1,5,9},{2,4,6,10},{3},{7,8}}
[8,6,3,2,1,10,9,7,5,4]=>{{1,5,7,8,9},{2,4,6,10},{3}}
[7,6,3,2,1,10,9,8,5,4]=>{{1,5,7,9},{2,4,6,10},{3},{8}}
[9,5,3,2,1,10,8,7,6,4]=>{{1,2,4,5,6,9,10},{3},{7,8}}
[8,5,3,2,1,10,9,7,6,4]=>{{1,2,4,5,6,7,8,9,10},{3}}
[7,5,3,2,1,10,9,8,6,4]=>{{1,2,4,5,6,7,9,10},{3},{8}}
[6,5,3,2,1,10,9,8,7,4]=>{{1,2,4,5,6,10},{3},{7,9},{8}}
[9,4,3,2,1,10,8,7,6,5]=>{{1,5,6,9,10},{2,4},{3},{7,8}}
[8,4,3,2,1,10,9,7,6,5]=>{{1,5,6,7,8,9,10},{2,4},{3}}
[7,4,3,2,1,10,9,8,6,5]=>{{1,5,6,7,9,10},{2,4},{3},{8}}
[6,4,3,2,1,10,9,8,7,5]=>{{1,5,6,10},{2,4},{3},{7,9},{8}}
[6,1,7,2,8,3,9,4,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,1,7,8,9,10,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,8,7,6,5,4,2,1,3]=>{{1,2,3,8,9,10},{4,7},{5,6}}
[10,9,8,7,6,5,3,2,1,4]=>{{1,2,3,4,7,8,9,10},{5,6}}
[10,9,8,7,6,4,3,2,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,8,7,5,4,3,2,1,6]=>{{1,2,3,4,6,7,8,9,10},{5}}
[10,9,8,6,5,4,3,2,1,7]=>{{1,2,3,7,8,9,10},{4,6},{5}}
[10,9,7,6,5,4,3,2,1,8]=>{{1,2,8,9,10},{3,7},{4,6},{5}}
[10,8,7,6,5,4,3,2,1,9]=>{{1,9,10},{2,8},{3,7},{4,6},{5}}
[10,3,1,2,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,4,1,2,3,5,6,7,8,9]=>{{1,3,5,6,7,8,9,10},{2,4}}
[5,10,1,2,3,4,6,7,8,9]=>{{1,3,5},{2,4,6,7,8,9,10}}
[10,6,1,2,3,4,5,7,8,9]=>{{1,3,5,7,8,9,10},{2,4,6}}
[10,7,1,2,3,4,5,6,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,10,1,2,3,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,10,1,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,1,10,2,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,4,1,2,10,3,6,7,8,9]=>{{1,3,5,6,7,8,9,10},{2,4}}
[5,6,1,2,3,10,4,7,8,9]=>{{1,3,5},{2,4,6,7,8,9,10}}
[7,6,1,2,3,4,10,5,8,9]=>{{1,3,5,7,8,9,10},{2,4,6}}
[8,7,1,2,3,4,5,10,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,1,2,3,4,5,6,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,8,7,6,5,2,4,1,3]=>{{1,2,3,4,7,8,9,10},{5,6}}
[10,9,8,7,3,6,2,5,1,4]=>{{1,2,4,7,9,10},{3,5,8},{6}}
[10,9,8,7,6,3,5,1,2,4]=>{{1,3,4,5,6,7,8,10},{2,9}}
[10,9,4,8,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,8,4,7,3,6,1,2,5]=>{{1,3,5,6,7,8,10},{2,9},{4}}
[10,9,8,7,2,4,6,1,3,5]=>{{1,2,3,5,8,9,10},{4,6,7}}
[10,9,8,7,4,6,1,2,3,5]=>{{1,4,5,7,10},{2,3,8,9},{6}}
[10,5,9,4,8,3,7,1,2,6]=>{{1,2,3,5,6,8,9,10},{4},{7}}
[10,9,5,8,2,4,7,1,3,6]=>{{1,4,6,8,10},{2,3,5,9},{7}}
[10,9,5,8,4,7,1,2,3,6]=>{{1,6,7,10},{2,3,4,5,8,9}}
[10,9,8,3,5,7,1,2,4,6]=>{{1,6,7,10},{2,3,4,8,9},{5}}
[10,9,8,5,7,1,2,3,4,6]=>{{1,6,10},{2,4,5,7,9},{3,8}}
[6,10,5,9,2,4,8,1,3,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,10,5,9,4,8,1,2,3,7]=>{{1,2,6,7,8,10},{3,4,5,9}}
[10,3,6,9,2,5,8,1,4,7]=>{{1,7,8,10},{2,3,5,6},{4,9}}
[10,6,9,3,5,8,1,2,4,7]=>{{1,7,10},{2,6,8},{3,4,9},{5}}
[10,6,9,5,8,1,2,3,4,7]=>{{1,2,6,7,10},{3,4,5,8,9}}
[10,9,2,4,6,8,1,3,5,7]=>{{1,7,10},{2,3,5,6,8,9},{4}}
[10,9,4,6,8,1,2,3,5,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,6,8,1,2,3,4,5,7]=>{{1,2,3,5,6,7,9,10},{4,8}}
[4,7,10,3,6,9,1,2,5,8]=>{{1,2,3,4,7,8,10},{5,6,9}}
[7,10,2,4,6,9,1,3,5,8]=>{{1,7},{2,3,8,10},{4},{5,6,9}}
[7,10,4,6,9,1,2,3,5,8]=>{{1,2,3,4,6,7,8,10},{5,9}}
[7,10,6,9,1,2,3,4,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,3,5,7,9,1,2,4,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,5,7,9,1,2,3,4,6,8]=>{{1,2,4,5,6,8,9,10},{3,7}}
[10,7,9,1,2,3,4,5,6,8]=>{{1,2,4,5,7,8,10},{3,6,9}}
[4,6,8,10,1,2,3,5,7,9]=>{{1,3,4,5,7,8,9,10},{2,6}}
[6,8,10,1,2,3,4,5,7,9]=>{{1,3,4,6,7,9,10},{2,5,8}}
[10,7,6,5,4,3,2,1,9,8]=>{{1,8,10},{2,7},{3,6},{4,5},{9}}
[8,7,6,5,4,3,2,10,9,1]=>{{1,8,10},{2,7},{3,6},{4,5},{9}}
[10,1,2,3,4,6,5,7,8,9]=>{{1,2,3,4,5,7,8,9,10},{6}}
[2,3,4,5,7,6,8,9,10,1]=>{{1,2,3,4,5,7,8,9,10},{6}}
[9,10,5,6,7,8,3,4,1,2]=>{{1,9},{2,10},{3,5,7},{4,6,8}}
[5,8,9,6,7,10,3,4,1,2]=>{{1,3,5,7,9},{2,4,6,8,10}}
[9,10,7,8,3,4,5,6,1,2]=>{{1,9},{2,10},{3,5,7},{4,6,8}}
[9,10,3,6,7,4,5,8,1,2]=>{{1,9},{2,10},{3},{4,6},{5,7},{8}}
[3,8,9,6,7,4,5,10,1,2]=>{{1,3,9},{2,8,10},{4,6},{5,7}}
[3,6,7,8,9,4,5,10,1,2]=>{{1,3,5,7,9},{2,4,6,8,10}}
[9,10,3,4,5,6,7,8,1,2]=>{{1,9},{2,10},{3},{4},{5},{6},{7},{8}}
[3,8,9,4,5,6,7,10,1,2]=>{{1,3,9},{2,8,10},{4},{5},{6},{7}}
[3,4,7,8,5,6,9,10,1,2]=>{{1,3,7,9},{2,4,8,10},{5},{6}}
[7,8,9,10,5,6,1,2,3,4]=>{{1,7},{2,8},{3,9},{4,10},{5},{6}}
[5,8,9,6,7,10,1,2,3,4]=>{{1,5,7},{2,8},{3,9},{4,6,10}}
[9,10,7,8,1,4,5,2,3,6]=>{{1,3,5,7,9},{2,4,6,8,10}}
[7,8,9,10,1,4,5,2,3,6]=>{{1,5,7},{2,8},{3,9},{4,6,10}}
[9,10,1,6,7,4,5,2,3,8]=>{{1,3,9},{2,8,10},{4,6},{5,7}}
[1,8,9,6,7,4,5,2,3,10]=>{{1},{2,8},{3,9},{4,6},{5,7},{10}}
[1,6,7,8,9,4,5,2,3,10]=>{{1},{2,4,6,8},{3,5,7,9},{10}}
[9,10,1,4,5,6,7,2,3,8]=>{{1,3,9},{2,8,10},{4},{5},{6},{7}}
[1,8,9,4,5,6,7,2,3,10]=>{{1},{2,8},{3,9},{4},{5},{6},{7},{10}}
[1,4,7,8,5,6,9,2,3,10]=>{{1},{2,4,8},{3,7,9},{5},{6},{10}}
[1,4,5,6,7,8,9,2,3,10]=>{{1},{2,4,6,8},{3,5,7,9},{10}}
[9,10,1,6,7,2,3,4,5,8]=>{{1,3,5,7,9},{2,4,6,8,10}}
[1,8,9,6,7,2,3,4,5,10]=>{{1},{2,4,6,8},{3,5,7,9},{10}}
[1,6,7,8,9,2,3,4,5,10]=>{{1},{2,6},{3,7},{4,8},{5,9},{10}}
[9,10,1,2,5,6,3,4,7,8]=>{{1,3,7,9},{2,4,8,10},{5},{6}}
[1,8,9,2,5,6,3,4,7,10]=>{{1},{2,4,8},{3,7,9},{5},{6},{10}}
[1,2,7,8,5,6,3,4,9,10]=>{{1},{2},{3,7},{4,8},{5},{6},{9},{10}}
[1,2,5,6,7,8,3,4,9,10]=>{{1},{2},{3,5,7},{4,6,8},{9},{10}}
[1,8,9,2,3,4,5,6,7,10]=>{{1},{2,4,6,8},{3,5,7,9},{10}}
[1,2,7,8,3,4,5,6,9,10]=>{{1},{2},{3,5,7},{4,6,8},{9},{10}}
[1,2,3,6,7,4,5,8,9,10]=>{{1},{2},{3},{4,6},{5,7},{8},{9},{10}}
[9,8,7,6,4,5,3,2,1,10]=>{{1,9},{2,8},{3,7},{4,5,6},{10}}
[8,7,9,6,5,4,3,2,1,10]=>{{1,2,3,7,8,9},{4,6},{5},{10}}
[8,7,6,9,5,4,3,2,1,10]=>{{1,2,3,4,6,7,8,9},{5},{10}}
[8,7,6,5,10,4,3,2,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,7,6,5,4,9,3,2,1,10]=>{{1,2,3,6,7,8,9},{4,5},{10}}
[8,7,6,5,4,3,9,2,1,10]=>{{1,2,7,8,9},{3,6},{4,5},{10}}
[7,10,9,6,5,4,3,2,1,8]=>{{1,3,7,9},{2,8,10},{4,6},{5}}
[8,6,9,10,5,4,3,2,1,7]=>{{1,2,3,4,6,7,8,9,10},{5}}
[8,7,5,9,10,4,3,2,1,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,7,6,4,10,9,3,2,1,5]=>{{1,2,3,6,7,8,9},{4},{5,10}}
[8,7,6,5,3,9,10,2,1,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,7,6,5,4,2,9,10,1,3]=>{{1,2,3,6,7,8,9,10},{4,5}}
[8,7,6,5,4,3,1,10,9,2]=>{{1,2,7,8,10},{3,6},{4,5},{9}}
[2,3,4,5,6,7,10,1,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,10,9,8,7,6,5,4,1,3]=>{{1,2,3,9,10},{4,8},{5,7},{6}}
[9,1,10,8,7,6,5,4,3,2]=>{{1,2,3,9,10},{4,8},{5,7},{6}}
[9,1,2,3,4,5,6,10,7,8]=>{{1,2,3,4,5,6,7,9},{8,10}}
[9,2,1,8,7,6,5,4,3,10]=>{{1,3,9},{2},{4,8},{5,7},{6},{10}}
[3,2,9,8,7,6,5,4,1,10]=>{{1,3,9},{2},{4,8},{5,7},{6},{10}}
[9,3,1,8,7,6,5,4,10,2]=>{{1,2,3,9,10},{4,8},{5,7},{6}}
[9,2,10,1,7,6,5,4,3,8]=>{{1,3,4,8,9,10},{2},{5,7},{6}}
[4,2,9,8,7,6,5,10,1,3]=>{{1,3,4,8,9,10},{2},{5,7},{6}}
[3,10,2,8,7,6,5,4,1,9]=>{{1,2,3,9,10},{4,8},{5,7},{6}}
[9,8,7,6,5,4,3,1,2,10]=>{{1,2,8,9},{3,7},{4,6},{5},{10}}
[1,10,9,8,7,6,5,4,2,3]=>{{1},{2,3,9,10},{4,8},{5,7},{6}}
[1,2,10,9,8,7,6,5,4,3]=>{{1},{2},{3,10},{4,9},{5,8},{6,7}}
[3,2,1,10,9,8,7,6,5,4]=>{{1,3},{2},{4,10},{5,9},{6,8},{7}}
[1,3,2,10,9,8,7,6,5,4]=>{{1},{2,3},{4,10},{5,9},{6,8},{7}}
[1,2,3,10,9,8,7,6,5,4]=>{{1},{2},{3},{4,10},{5,9},{6,8},{7}}
[1,4,3,2,10,9,8,7,6,5]=>{{1},{2,4},{3},{5,10},{6,9},{7,8}}
[1,2,4,3,10,9,8,7,6,5]=>{{1},{2},{3,4},{5,10},{6,9},{7,8}}
[1,2,3,4,10,9,8,7,6,5]=>{{1},{2},{3},{4},{5,10},{6,9},{7,8}}
[1,5,4,3,2,10,9,8,7,6]=>{{1},{2,5},{3,4},{6,10},{7,9},{8}}
[2,1,5,4,3,10,9,8,7,6]=>{{1,2},{3,5},{4},{6,10},{7,9},{8}}
[1,2,5,4,3,10,9,8,7,6]=>{{1},{2},{3,5},{4},{6,10},{7,9},{8}}
[1,3,2,5,4,10,9,8,7,6]=>{{1},{2,3},{4,5},{6,10},{7,9},{8}}
[1,2,3,5,4,10,9,8,7,6]=>{{1},{2},{3},{4,5},{6,10},{7,9},{8}}
[1,2,6,5,4,3,10,9,8,7]=>{{1},{2},{3,6},{4,5},{7,10},{8,9}}
[3,2,1,6,5,4,10,9,8,7]=>{{1,3},{2},{4,6},{5},{7,10},{8,9}}
[1,3,2,6,5,4,10,9,8,7]=>{{1},{2,3},{4,6},{5},{7,10},{8,9}}
[1,2,3,6,5,4,10,9,8,7]=>{{1},{2},{3},{4,6},{5},{7,10},{8,9}}
[1,2,4,3,6,5,10,9,8,7]=>{{1},{2},{3,4},{5,6},{7,10},{8,9}}
[1,2,3,4,6,5,10,9,8,7]=>{{1},{2},{3},{4},{5,6},{7,10},{8,9}}
[1,2,3,4,5,6,10,9,8,7]=>{{1},{2},{3},{4},{5},{6},{7,10},{8,9}}
[1,4,3,2,7,6,5,10,9,8]=>{{1},{2,4},{3},{5,7},{6},{8,10},{9}}
[2,1,4,3,7,6,5,10,9,8]=>{{1,2},{3,4},{5,7},{6},{8,10},{9}}
[1,2,4,3,7,6,5,10,9,8]=>{{1},{2},{3,4},{5,7},{6},{8,10},{9}}
[1,2,3,4,7,6,5,10,9,8]=>{{1},{2},{3},{4},{5,7},{6},{8,10},{9}}
[1,3,2,5,4,7,6,10,9,8]=>{{1},{2,3},{4,5},{6,7},{8,10},{9}}
[1,2,3,5,4,7,6,10,9,8]=>{{1},{2},{3},{4,5},{6,7},{8,10},{9}}
[1,2,3,4,5,7,6,10,9,8]=>{{1},{2},{3},{4},{5},{6,7},{8,10},{9}}
[1,2,3,4,5,6,7,10,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}
[1,2,4,3,6,5,8,7,10,9]=>{{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,2,3,4,6,5,8,7,10,9]=>{{1},{2},{3},{4},{5,6},{7,8},{9,10}}
[1,2,3,4,5,6,8,7,10,9]=>{{1},{2},{3},{4},{5},{6},{7,8},{9,10}}
[10,9,8,7,6,5,2,1,4,3]=>{{1,3,8,10},{2,4,7,9},{5,6}}
[10,9,8,7,3,2,1,6,5,4]=>{{1,4,7,10},{2,3,5,6,8,9}}
[10,9,8,7,6,3,1,5,2,4]=>{{1,4,7,10},{2,9},{3,5,6,8}}
[10,9,4,3,2,1,8,7,6,5]=>{{1,2,5,6,9,10},{3,4},{7,8}}
[10,9,8,4,3,1,7,6,2,5]=>{{1,3,5,6,8,10},{2,9},{4},{7}}
[10,9,8,7,2,1,4,3,6,5]=>{{1,2,5,6,9,10},{3,8},{4,7}}
[10,9,8,7,4,1,6,2,3,5]=>{{1,4,5,6,7,10},{2,3,8,9}}
[10,5,4,3,1,9,8,7,2,6]=>{{1,2,5,6,9,10},{3,4},{7,8}}
[10,9,5,2,1,8,4,3,7,6]=>{{1,3,5,6,8,10},{2,4,7,9}}
[10,9,5,4,1,8,7,2,3,6]=>{{1,2,3,5,6,8,9,10},{4},{7}}
[10,9,8,3,1,5,2,7,4,6]=>{{1,5,6,10},{2,3,4,7,8,9}}
[6,5,2,1,10,9,4,3,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,5,4,1,10,9,8,2,3,7]=>{{1,3,4,6,9},{2,5,7,8,10}}
[10,3,2,1,6,5,4,9,8,7]=>{{1,4,7,10},{2,3},{5,6},{8,9}}
[10,6,5,1,9,8,2,3,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,2,1,4,3,6,5,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,6,1,8,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,1,7,6,2,10,9,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,2,1,10,4,3,6,5,9,8]=>{{1,3,6,7},{2},{4,5,8,10},{9}}
[7,4,1,10,6,2,9,3,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,6,1,10,9,2,3,4,5,8]=>{{1,3,7},{2,6},{4,8,10},{5,9}}
[10,5,1,7,2,9,3,4,6,8]=>{{1,3,4,7,8,10},{2,5},{6,9}}
[10,7,1,9,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,1,6,2,8,3,10,5,7,9]=>{{1,2,4},{3,6},{5,8},{7,9,10}}
[6,1,8,2,10,3,4,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,1,10,2,3,4,5,6,7,9]=>{{1,2,4,6,8},{3,5,7,9,10}}
[10,1,9,8,7,6,5,4,3,2]=>{{1,2,10},{3,9},{4,8},{5,7},{6}}
[8,1,10,9,7,6,5,4,3,2]=>{{1,2,3,4,8,9,10},{5,7},{6}}
[7,1,10,9,8,6,5,4,3,2]=>{{1,2,3,4,5,7,8,9,10},{6}}
[6,1,10,9,8,7,5,4,3,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,1,10,9,8,7,6,4,3,2]=>{{1,2,3,4,5,8,9,10},{6,7}}
[4,1,10,9,8,7,6,5,3,2]=>{{1,2,3,4,9,10},{5,8},{6,7}}
[3,1,10,9,8,7,6,5,4,2]=>{{1,2,3,10},{4,9},{5,8},{6,7}}
[9,10,7,8,5,6,2,1,3,4]=>{{1,2,3,4,7,8,9,10},{5},{6}}
[9,10,7,8,4,3,5,6,1,2]=>{{1,9},{2,10},{3,4,5,6,7,8}}
[9,10,7,8,4,2,5,1,3,6]=>{{1,3,4,5,7,8,9},{2,6,10}}
[9,10,7,8,3,2,1,4,5,6]=>{{1,3,5,7,9},{2,6,10},{4,8}}
[9,10,6,5,7,8,3,4,1,2]=>{{1,9},{2,10},{3,4,5,6,7,8}}
[9,10,6,5,7,8,2,1,3,4]=>{{1,3,6,8,9},{2,4,5,7,10}}
[9,10,6,4,7,3,5,8,1,2]=>{{1,9},{2,10},{3,6},{4},{5,7},{8}}
[9,10,6,4,7,2,5,1,3,8]=>{{1,2,3,6,8,9,10},{4},{5,7}}
[9,10,6,3,7,2,1,4,5,8]=>{{1,5,7,9},{2,3,4,6,8,10}}
[9,10,5,4,3,6,7,8,1,2]=>{{1,9},{2,10},{3,5},{4},{6},{7},{8}}
[9,10,5,4,2,6,7,1,3,8]=>{{1,2,3,5,8,9,10},{4},{6},{7}}
[9,10,5,3,2,6,1,4,7,8]=>{{1,7,9},{2,3,4,5,8,10},{6}}
[9,10,4,3,2,1,5,6,7,8]=>{{1,2,5,6,7,8,9,10},{3,4}}
[8,7,9,10,5,6,3,4,1,2]=>{{1,2,3,4,7,8,9,10},{5},{6}}
[8,7,9,10,5,6,2,1,3,4]=>{{1,8},{2,7},{3,9},{4,10},{5},{6}}
[8,7,9,10,4,3,5,6,1,2]=>{{1,3,6,8,9},{2,4,5,7,10}}
[8,7,9,10,4,2,5,1,3,6]=>{{1,8},{2,4,5,6,7,10},{3,9}}
[8,7,9,10,3,2,1,4,5,6]=>{{1,2,4,6,7,8,10},{3,5,9}}
[8,6,9,5,7,10,3,4,1,2]=>{{1,3,4,5,7,8,9},{2,6,10}}
[8,6,9,5,7,10,2,1,3,4]=>{{1,8},{2,4,5,6,7,10},{3,9}}
[8,6,9,4,7,3,5,10,1,2]=>{{1,2,3,6,8,9,10},{4},{5,7}}
[8,6,9,3,7,2,1,4,5,10]=>{{1,3,4,5,7,8,9},{2,6},{10}}
[8,5,9,4,3,6,7,10,1,2]=>{{1,2,3,5,8,9,10},{4},{6},{7}}
[8,5,9,4,2,6,7,1,3,10]=>{{1,8},{2,5},{3,9},{4},{6},{7},{10}}
[8,5,9,3,2,6,1,4,7,10]=>{{1,3,4,7,8,9},{2,5},{6},{10}}
[8,4,9,3,2,1,5,6,7,10]=>{{1,6,8},{2,3,4,5,7,9},{10}}
[7,6,5,8,9,10,3,4,1,2]=>{{1,3,5,7,9},{2,6,10},{4,8}}
[7,6,5,8,9,10,2,1,3,4]=>{{1,2,4,6,7,8,10},{3,5,9}}
[7,6,4,8,9,3,5,10,1,2]=>{{1,5,7,9},{2,3,4,6,8,10}}
[7,6,4,8,9,2,5,1,3,10]=>{{1,3,4,5,7,8,9},{2,6},{10}}
[7,6,3,8,9,2,1,4,5,10]=>{{1,7},{2,6},{3},{4,8},{5,9},{10}}
[7,5,4,8,3,6,9,10,1,2]=>{{1,7,9},{2,3,4,5,8,10},{6}}
[7,5,4,8,2,6,9,1,3,10]=>{{1,3,4,7,8,9},{2,5},{6},{10}}
[7,4,3,8,2,1,5,6,9,10]=>{{1,2,4,5,6,7,8},{3},{9},{10}}
[6,5,4,3,7,8,9,10,1,2]=>{{1,2,5,6,7,8,9,10},{3,4}}
[6,5,4,2,7,8,9,1,3,10]=>{{1,6,8},{2,3,4,5,7,9},{10}}
[6,5,3,2,7,8,1,4,9,10]=>{{1,2,4,5,6,7,8},{3},{9},{10}}
[1,3,2,7,6,5,10,9,8,4]=>{{1},{2,3},{4,7,10},{5,6},{8,9}}
[1,4,3,6,5,2,10,9,8,7]=>{{1},{2,4,6},{3},{5},{7,10},{8,9}}
[1,4,3,7,6,2,10,9,8,5]=>{{1},{2,4,5,6,7,10},{3},{8,9}}
[1,5,4,7,6,3,10,9,8,2]=>{{1},{2,3,4,5,6,7,10},{8,9}}
[1,4,3,8,7,2,10,9,6,5]=>{{1},{2,4,6,8,9},{3},{5,7,10}}
[1,5,4,8,7,3,10,9,6,2]=>{{1},{2,5,7,10},{3,4,6,8,9}}
[2,3,1,6,5,4,10,9,8,7]=>{{1,2,3},{4,6},{5},{7,10},{8,9}}
[2,3,1,7,6,5,10,9,8,4]=>{{1,2,3},{4,7,10},{5,6},{8,9}}
[2,4,1,6,5,3,10,9,8,7]=>{{1,2,3,4,6},{5},{7,10},{8,9}}
[2,4,1,7,6,3,10,9,8,5]=>{{1,2,3,4,5,6,7,10},{8,9}}
[2,5,1,7,6,4,10,9,8,3]=>{{1,2,3,4,5,6,7,10},{8,9}}
[2,4,1,8,7,3,10,9,6,5]=>{{1,2,3,4,6,8,9},{5,7,10}}
[2,5,1,8,7,4,10,9,6,3]=>{{1,2,3,5,7,10},{4,6,8,9}}
[3,4,2,6,5,1,10,9,8,7]=>{{1,2,3,4,6},{5},{7,10},{8,9}}
[3,4,2,7,6,1,10,9,8,5]=>{{1,2,3,4,5,6,7,10},{8,9}}
[3,5,2,7,6,1,10,9,8,4]=>{{1,2,3,5,6},{4,7,10},{8,9}}
[4,5,3,7,6,2,10,9,8,1]=>{{1,4,7,10},{2,5,6},{3},{8,9}}
[3,4,2,8,7,1,10,9,6,5]=>{{1,2,3,4,6,8,9},{5,7,10}}
[3,5,2,8,7,1,10,9,6,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,5,3,8,7,2,10,9,6,1]=>{{1,2,4,5,6,7,8,9,10},{3}}
[2,5,1,6,4,3,10,9,8,7]=>{{1,2,3,4,5,6},{7,10},{8,9}}
[2,5,1,7,4,3,10,9,8,6]=>{{1,2,3,4,5,6,7,10},{8,9}}
[2,6,1,7,5,4,10,9,8,3]=>{{1,2,3,4,6,7,10},{5},{8,9}}
[2,5,1,8,4,3,10,9,7,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,6,1,8,5,4,10,9,7,3]=>{{1,2,3,4,6,7,8,9,10},{5}}
[3,5,2,6,4,1,10,9,8,7]=>{{1,2,3,4,5,6},{7,10},{8,9}}
[3,5,2,7,4,1,10,9,8,6]=>{{1,2,3,4,5,6,7,10},{8,9}}
[3,6,2,7,5,1,10,9,8,4]=>{{1,2,3,6},{4,7,10},{5},{8,9}}
[4,6,3,7,5,2,10,9,8,1]=>{{1,4,7,10},{2,6},{3},{5},{8,9}}
[3,5,2,8,4,1,10,9,7,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,6,2,8,5,1,10,9,7,4]=>{{1,2,3,6},{4,7,8,9,10},{5}}
[4,6,3,8,5,2,10,9,7,1]=>{{1,4,7,8,9,10},{2,6},{3},{5}}
[3,7,2,8,6,1,10,9,5,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,7,3,8,6,2,10,9,5,1]=>{{1,2,4,5,6,7,8,9,10},{3}}
[2,5,1,9,4,3,10,8,7,6]=>{{1,2,3,4,5,6,7,9,10},{8}}
[2,6,1,9,5,4,10,8,7,3]=>{{1,2,3,4,6,7,9,10},{5},{8}}
[3,5,2,9,4,1,10,8,7,6]=>{{1,2,3,4,5,6,7,9,10},{8}}
[3,6,2,9,5,1,10,8,7,4]=>{{1,2,3,6},{4,7,9,10},{5},{8}}
[4,6,3,9,5,2,10,8,7,1]=>{{1,4,7,9,10},{2,6},{3},{5},{8}}
[3,7,2,9,6,1,10,8,5,4]=>{{1,2,3,4,5,6,7,9,10},{8}}
[10,1,2,3,4,5,6,7,9,8]=>{{1,2,3,4,5,6,7,8,10},{9}}
[2,3,4,5,6,7,8,10,9,1]=>{{1,2,3,4,5,6,7,8,10},{9}}
[3,2,10,9,8,7,6,5,4,1]=>{{1,3,10},{2},{4,9},{5,8},{6,7}}
[10,2,1,9,8,7,6,5,4,3]=>{{1,3,10},{2},{4,9},{5,8},{6,7}}
[2,3,4,6,5,7,8,9,10,1]=>{{1,2,3,4,6,7,8,9,10},{5}}
[10,1,2,3,5,4,6,7,8,9]=>{{1,2,3,4,6,7,8,9,10},{5}}
[9,7,10,8,5,6,3,4,1,2]=>{{1,9},{2,3,7,10},{4,8},{5},{6}}
[9,7,10,5,8,6,3,4,1,2]=>{{1,9},{2,3,7,10},{4,5,8},{6}}
[9,7,10,5,8,3,6,4,1,2]=>{{1,9},{2,3,6,7,10},{4,5,8}}
[9,7,10,5,8,3,6,2,4,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,7,10,5,8,4,6,2,3,1]=>{{1,3,9,10},{2,4,5,6,7,8}}
[9,7,10,6,8,4,5,2,3,1]=>{{1,3,9,10},{2,5,7,8},{4,6}}
[9,8,10,6,7,4,5,2,3,1]=>{{1,3,9,10},{2,8},{4,6},{5,7}}
[1,10,9,8,7,6,5,2,4,3]=>{{1},{2,3,4,8,9,10},{5,7},{6}}
[1,10,9,8,7,6,2,5,4,3]=>{{1},{2,3,4,5,7,8,9,10},{6}}
[2,10,9,8,7,1,6,5,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,10,9,8,2,7,6,5,4,3]=>{{1},{2,3,4,5,8,9,10},{6,7}}
[1,10,9,2,8,7,6,5,4,3]=>{{1},{2,3,4,9,10},{5,8},{6,7}}
[2,10,1,9,8,7,6,5,4,3]=>{{1,2,3,10},{4,9},{5,8},{6,7}}
[3,10,9,8,7,6,5,2,1,4]=>{{1,3,9},{2,4,8,10},{5,7},{6}}
[4,10,9,8,7,6,1,2,5,3]=>{{1,2,3,4,5,7,8,9,10},{6}}
[5,10,9,8,7,1,2,6,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,10,9,8,2,1,7,5,4,3]=>{{1,6},{2,3,4,5,8,9,10},{7}}
[7,10,9,1,2,8,6,5,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,10,1,2,9,7,6,5,4,3]=>{{1,2,3,4,5,8,9,10},{6,7}}
[9,2,1,10,8,7,6,5,4,3]=>{{1,3,4,9,10},{2},{5,8},{6,7}}
[10,1,3,2,5,4,7,6,9,8]=>{{1,2,4,6,8,10},{3},{5},{7},{9}}
[10,1,2,3,4,6,7,8,9,5]=>{{1,2,3,4,5,10},{6},{7},{8},{9}}
[6,7,8,9,1,2,3,4,5,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[1,7,8,9,10,2,3,4,5,6]=>{{1},{2,3,4,5,6,7,8,9,10}}
[5,6,7,8,9,1,2,3,4,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[1,6,7,8,9,10,2,3,4,5]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,2,4,3,5,6,7,8,9,10]=>{{1},{2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,2,4,6,8,10,9,7,5,3]=>{{1},{2},{3,4,6,10},{5,7,8,9}}
[2,4,1,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,1,2,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,1,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,6,1,5,3,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,3,4,1,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,8,1,6,7,4,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,3,4,5,1,8,2,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,10,1,7,8,9,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,2,1,3,4,5,6,7,8,10]=>{{1,3,4,5,6,7,8,9},{2},{10}}
[8,7,2,4,6,10,1,3,5,9]=>{{1,2,3,7,8},{4},{5,6,9,10}}
[2,10,7,9,4,6,8,1,3,5]=>{{1,2,3,4,5,7,8,9,10},{6}}
[6,5,2,4,8,10,1,3,7,9]=>{{1,6,7,9,10},{2,3,5,8},{4}}
[2,8,5,7,4,6,10,1,3,9]=>{{1,2,8},{3,4,5,7,9,10},{6}}
[10,5,2,4,7,9,6,8,1,3]=>{{1,2,3,5,6,7,9,10},{4},{8}}
[10,9,2,8,5,7,4,6,1,3]=>{{1,2,3,9,10},{4,6,7,8},{5}}
[8,7,6,5,2,4,10,1,3,9]=>{{1,8},{2,3,4,5,6,7,9,10}}
[10,7,2,6,5,9,4,8,1,3]=>{{1,2,3,4,6,7,9,10},{5},{8}}
[6,10,5,9,8,7,2,4,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,10,3,9,2,6,8,1,5,7]=>{{1,2,4,5,7,8,9,10},{3},{6}}
[4,3,10,7,9,2,6,8,1,5]=>{{1,2,3,4,5,6,7,9,10},{8}}
[3,6,2,5,4,8,10,1,7,9]=>{{1,2,3,6,8},{4,5},{7,9,10}}
[3,6,10,2,5,9,4,8,1,7]=>{{1,2,3,4,6,7,9,10},{5},{8}}
[3,5,8,2,4,7,6,10,1,9]=>{{1,3,8,9,10},{2,4,5},{6,7}}
[3,5,7,10,2,4,6,9,8,1]=>{{1,3,4,6,7,10},{2,5},{8,9}}
[10,9,3,5,8,2,4,7,6,1]=>{{1,10},{2,6,9},{3},{4,5,7,8}}
[8,7,3,6,2,5,4,10,1,9]=>{{1,8,9,10},{2,4,5,6,7},{3}}
[7,6,3,5,10,2,4,9,8,1]=>{{1,4,5,7,10},{2,6},{3},{8,9}}
[3,6,10,9,8,2,5,7,4,1]=>{{1,3,10},{2,6},{4,9},{5,7,8}}
[10,9,8,7,3,6,2,5,4,1]=>{{1,10},{2,4,7,9},{3,5,8},{6}}
[5,4,3,8,2,7,6,10,1,9]=>{{1,2,4,5,8,9,10},{3},{6,7}}
[5,4,3,7,10,2,6,9,8,1]=>{{1,5,10},{2,4,6,7},{3},{8,9}}
[5,10,4,9,3,8,2,7,6,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,8,3,7,6,5,2,10,1,9]=>{{1,2,4,7,8,9,10},{3},{5,6}}
[4,7,3,6,5,10,2,9,8,1]=>{{1,4,6,10},{2,7},{3},{5},{8,9}}
[4,6,10,3,5,9,8,7,2,1]=>{{1,3,4,10},{2,6,9},{5},{7,8}}
[10,9,4,8,3,7,6,5,2,1]=>{{1,10},{2,9},{3,4,5,8},{6,7}}
[7,6,5,4,3,10,2,9,8,1]=>{{1,2,6,7,10},{3,5},{4},{8,9}}
[6,5,4,10,3,9,8,7,2,1]=>{{1,2,3,4,5,6,9,10},{7,8}}
[5,10,4,9,8,7,6,3,2,1]=>{{1,2,3,4,5,8,9,10},{6,7}}
[9,2,3,4,5,6,7,8,1,10]=>{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}
[1,10,3,4,5,6,7,8,9,2]=>{{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,10,9,4,5,6,7,8,3,2]=>{{1},{2,10},{3,9},{4},{5},{6},{7},{8}}
[8,1,2,3,4,5,6,7,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[2,3,4,5,6,7,9,8,1,10]=>{{1,2,3,4,5,6,7,9},{8},{10}}
[1,3,4,5,6,7,8,10,9,2]=>{{1},{2,3,4,5,6,7,8,10},{9}}
[1,2,3,4,5,6,10,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,10},{8},{9}}
[1,2,3,4,5,10,7,8,9,6]=>{{1},{2},{3},{4},{5},{6,10},{7},{8},{9}}
[1,2,3,4,10,6,7,8,9,5]=>{{1},{2},{3},{4},{5,10},{6},{7},{8},{9}}
[1,2,3,10,5,6,7,8,9,4]=>{{1},{2},{3},{4,10},{5},{6},{7},{8},{9}}
[1,2,10,4,5,6,7,8,9,3]=>{{1},{2},{3,10},{4},{5},{6},{7},{8},{9}}
[10,2,3,4,5,6,7,8,9,1]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,2,3,4,6,8,5,7,10,9]=>{{1},{2},{3},{4},{5,6,7,8},{9,10}}
[1,2,3,4,7,5,8,6,10,9]=>{{1},{2},{3},{4},{5,6,7,8},{9,10}}
[1,2,3,5,7,4,6,9,8,10]=>{{1},{2},{3},{4,5,6,7},{8,9},{10}}
[1,2,3,6,4,7,5,9,8,10]=>{{1},{2},{3},{4,5,6,7},{8,9},{10}}
[7,10,1,2,3,4,5,6,8,9]=>{{1,3,5,7},{2,4,6,8,9,10}}
[6,10,1,2,3,4,5,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,10,1,2,3,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,10,1,2,4,5,6,7,8,9]=>{{1,3},{2,4,5,6,7,8,9,10}}
[10,9,8,7,5,6,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,7},{5},{6}}
[2,1,10,9,8,6,7,5,4,3]=>{{1,2},{3,10},{4,9},{5,8},{6},{7}}
[1,9,8,7,6,5,4,3,2,10]=>{{1},{2,9},{3,8},{4,7},{5,6},{10}}
[2,8,9,10,1,3,4,5,6,7]=>{{1,2,5,8},{3,6,9},{4,7,10}}
[8,1,9,2,10,3,4,5,6,7]=>{{1,2,4,5,7,8,10},{3,6,9}}
[7,1,8,2,9,3,10,4,5,6]=>{{1,2,3,4,6,7,8,10},{5,9}}
[5,1,6,2,7,3,8,4,10,9]=>{{1,2,4,5,7,8},{3,6},{9,10}}
[4,1,5,2,6,3,8,7,10,9]=>{{1,2,4},{3,5,6},{7,8},{9,10}}
[2,1,3,4,5,6,7,9,10,8]=>{{1,2},{3},{4},{5},{6},{7},{8,9,10}}
[2,1,3,4,5,6,7,8,10,9]=>{{1,2},{3},{4},{5},{6},{7},{8},{9,10}}
[7,1,2,3,4,5,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,1,2,3,4,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,1,2,3,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,7,5,4,3,2,1,10,8,6]=>{{1,2,6,7,8,9,10},{3,5},{4}}
[8,6,5,4,3,2,1,9,7,10]=>{{1,7,8,9},{2,6},{3,5},{4},{10}}
[9,7,5,3,2,1,10,8,6,4]=>{{1,6,9},{2,3,4,5,7,10},{8}}
[8,6,4,3,2,1,9,7,5,10]=>{{1,2,5,6,7,8,9},{3,4},{10}}
[8,5,4,3,2,1,9,6,10,7]=>{{1,6,8},{2,5},{3,4},{7,9,10}}
[7,5,4,3,2,1,8,6,9,10]=>{{1,6,7,8},{2,5},{3,4},{9},{10}}
[8,6,4,2,1,9,7,5,3,10]=>{{1,5,8},{2,3,4,6,9},{7},{10}}
[8,5,3,2,1,9,6,4,10,7]=>{{1,2,4,5,8},{3},{6,7,9,10}}
[7,5,3,2,1,8,6,4,9,10]=>{{1,2,4,5,6,7,8},{3},{9},{10}}
[7,4,3,2,1,8,5,9,6,10]=>{{1,5,7},{2,4},{3},{6,8,9},{10}}
[6,4,3,2,1,7,5,8,9,10]=>{{1,5,6,7},{2,4},{3},{8},{9},{10}}
[8,5,3,1,9,6,4,2,10,7]=>{{1,2,4,5,7,8,9,10},{3},{6}}
[7,5,3,1,8,6,4,2,9,10]=>{{1,4,7},{2,5,8},{3},{6},{9},{10}}
[8,5,2,1,9,6,3,10,7,4]=>{{1,4,8,10},{2,3,5,7,9},{6}}
[7,4,2,1,8,5,3,9,6,10]=>{{1,2,3,4,7},{5,6,8,9},{10}}
[6,4,2,1,7,5,3,8,9,10]=>{{1,2,3,4,5,6,7},{8},{9},{10}}
[7,3,2,1,8,4,9,5,10,6]=>{{1,4,6,7,9,10},{2,3},{5,8}}
[6,3,2,1,7,4,8,5,9,10]=>{{1,4,6},{2,3},{5,7,8},{9},{10}}
[5,3,2,1,6,4,7,8,9,10]=>{{1,4,5,6},{2,3},{7},{8},{9},{10}}
[7,4,1,8,5,2,9,6,3,10]=>{{1,3,7,9},{2,4,6,8},{5},{10}}
[7,3,1,8,4,2,9,5,10,6]=>{{1,2,3,6,7,9,10},{4,5,8}}
[6,3,1,7,4,2,8,5,9,10]=>{{1,2,3,6},{4,5,7,8},{9},{10}}
[5,3,1,6,4,2,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}
[6,2,1,7,3,8,4,9,5,10]=>{{1,3,5,6,8,9},{2},{4,7},{10}}
[5,2,1,6,3,7,4,8,9,10]=>{{1,3,5},{2},{4,6,7},{8},{9},{10}}
[4,2,1,5,3,6,7,8,9,10]=>{{1,3,4,5},{2},{6},{7},{8},{9},{10}}
[5,1,6,2,7,3,8,4,9,10]=>{{1,2,4,5,7,8},{3,6},{9},{10}}
[4,1,5,2,6,3,7,8,9,10]=>{{1,2,4},{3,5,6},{7},{8},{9},{10}}
[3,1,4,2,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[1,9,2,3,4,5,6,7,8,10]=>{{1},{2,3,4,5,6,7,8,9},{10}}
[1,2,3,4,5,6,7,9,8,10]=>{{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}
[10,3,4,5,6,7,8,9,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,3,4,5,6,7,8,1,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,3,4,5,6,7,1,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,3,4,5,6,1,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,3,4,5,1,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,3,4,1,6,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,1,5,6,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,4,5,6,7,8,1,2,3]=>{{1,3,4,5,6,7,8,10},{2,9}}
[10,3,8,5,6,7,1,9,2,4]=>{{1,4,5,6,7,10},{2,3,8,9}}
[10,3,4,7,6,1,8,9,2,5]=>{{1,5,6,10},{2,3,4,7,8,9}}
[10,3,4,5,1,7,8,9,2,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,3,4,1,6,10,8,9,2,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,1,5,6,7,10,9,2,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,1,4,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,2,3,4,5,6,7,10,1,8]=>{{1,9},{2},{3},{4},{5},{6},{7},{8,10}}
[9,2,10,4,5,6,7,8,1,3]=>{{1,9},{2},{3,10},{4},{5},{6},{7},{8}}
[2,10,4,5,6,7,8,9,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,8,4,5,6,7,1,2,10,3]=>{{1,3,4,5,6,7,9,10},{2,8}}
[2,10,9,5,6,7,8,1,3,4]=>{{1,2,4,5,6,7,8,10},{3,9}}
[9,3,8,5,6,7,1,2,10,4]=>{{1,4,5,6,7,9,10},{2,3,8}}
[9,7,4,5,6,1,8,2,10,3]=>{{1,3,4,5,6,9,10},{2,7,8}}
[2,10,4,9,6,7,8,1,3,5]=>{{1,2,5,6,7,8,10},{3,4,9}}
[2,10,8,5,6,7,1,9,3,4]=>{{1,2,4,5,6,7,10},{3,8,9}}
[1,3,2,4,5,6,7,8,9,10]=>{{1},{2,3},{4},{5},{6},{7},{8},{9},{10}}
[9,2,3,4,5,6,7,8,10,1]=>{{1,9,10},{2},{3},{4},{5},{6},{7},{8}}
[8,2,3,4,5,6,7,10,9,1]=>{{1,8,10},{2},{3},{4},{5},{6},{7},{9}}
[7,2,3,4,5,6,10,8,9,1]=>{{1,7,10},{2},{3},{4},{5},{6},{8},{9}}
[6,2,3,4,5,10,7,8,9,1]=>{{1,6,10},{2},{3},{4},{5},{7},{8},{9}}
[5,2,3,4,10,6,7,8,9,1]=>{{1,5,10},{2},{3},{4},{6},{7},{8},{9}}
[4,2,3,10,5,6,7,8,9,1]=>{{1,4,10},{2},{3},{5},{6},{7},{8},{9}}
[3,2,10,4,5,6,7,8,9,1]=>{{1,3,10},{2},{4},{5},{6},{7},{8},{9}}
[2,10,3,4,5,6,7,8,9,1]=>{{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[9,7,5,3,1,8,6,4,2,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[1,10,8,6,4,2,9,7,5,3]=>{{1},{2,3,4,5,6,7,8,9,10}}
[3,1,2,4,5,6,7,8,9,10]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[9,7,6,5,4,3,2,1,8,10]=>{{1,8,9},{2,7},{3,6},{4,5},{10}}
[10,3,2,4,5,6,7,8,9,1]=>{{1,10},{2,3},{4},{5},{6},{7},{8},{9}}
[1,10,2,3,4,5,6,7,9,8]=>{{1},{2,3,4,5,6,7,8,10},{9}}
[1,3,4,5,6,7,8,10,2,9]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,3,4,5,6,7,8,9,2,10]=>{{1},{2,3,4,5,6,7,8,9},{10}}
[1,2,3,4,5,6,8,10,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,10},{9}}
[1,2,3,4,5,7,8,10,9,6]=>{{1},{2},{3},{4},{5},{6,7,8,10},{9}}
[1,2,3,4,5,7,9,10,8,6]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,2,3,4,5,7,10,9,8,6]=>{{1},{2},{3},{4},{5},{6,7,10},{8,9}}
[1,2,3,4,6,7,8,10,9,5]=>{{1},{2},{3},{4},{5,6,7,8,10},{9}}
[1,2,3,4,6,7,9,10,8,5]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,2,3,4,6,7,10,9,8,5]=>{{1},{2},{3},{4},{5,6,7,10},{8,9}}
[1,2,3,4,6,8,10,9,7,5]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,2,3,4,6,10,9,8,7,5]=>{{1},{2},{3},{4},{5,6,10},{7,9},{8}}
[1,2,3,5,6,7,9,10,8,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[1,2,3,5,6,7,10,9,8,4]=>{{1},{2},{3},{4,5,6,7,10},{8,9}}
[1,2,3,5,6,8,9,10,7,4]=>{{1},{2},{3},{4,5,6,8,10},{7,9}}
[1,2,3,5,6,8,10,9,7,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[1,2,3,5,6,10,9,8,7,4]=>{{1},{2},{3},{4,5,6,10},{7,9},{8}}
[1,2,3,5,7,9,10,8,6,4]=>{{1},{2},{3},{4,5,7,10},{6,9},{8}}
[1,2,3,5,7,10,9,8,6,4]=>{{1},{2},{3},{4,5,6,7,9,10},{8}}
[1,2,3,5,10,9,8,7,6,4]=>{{1},{2},{3},{4,5,10},{6,9},{7,8}}
[1,2,4,5,7,8,10,9,6,3]=>{{1},{2},{3,4,5,7,10},{6,8,9}}
[1,2,4,5,7,9,10,8,6,3]=>{{1},{2},{3,4,5,7,10},{6,9},{8}}
[1,2,4,5,7,10,9,8,6,3]=>{{1},{2},{3,4,5,6,7,9,10},{8}}
[1,2,4,5,10,9,8,7,6,3]=>{{1},{2},{3,4,5,10},{6,9},{7,8}}
[1,2,4,6,10,9,8,7,5,3]=>{{1},{2},{3,4,5,6,9,10},{7,8}}
[1,2,4,10,9,8,7,6,5,3]=>{{1},{2},{3,4,10},{5,9},{6,8},{7}}
[1,3,5,7,9,10,8,6,4,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,3,5,7,10,9,8,6,4,2]=>{{1},{2,3,5,10},{4,6,7,8,9}}
[1,3,5,10,9,8,7,6,4,2]=>{{1},{2,3,4,5,9,10},{6,8},{7}}
[1,3,10,9,8,7,6,5,4,2]=>{{1},{2,3,10},{4,9},{5,8},{6,7}}
[9,1,8,2,3,4,5,6,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,7,1,2,3,4,5,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,10,1,9,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,10,8,1,3,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,3,4,5,6,7,9,1,2,8]=>{{1,8,10},{2,3,4,5,6,7,9}}
[3,5,7,9,1,2,4,6,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[4,1,2,3,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[5,1,2,3,4,6,7,8,9,10]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}
[8,1,2,3,4,5,6,7,9,10]=>{{1,2,3,4,5,6,7,8},{9},{10}}
[7,1,2,3,4,5,6,8,9,10]=>{{1,2,3,4,5,6,7},{8},{9},{10}}
[6,1,2,3,4,5,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}
[3,4,1,6,2,5,8,7,10,9]=>{{1,3},{2,4,5,6},{7,8},{9,10}}
[10,8,6,4,2,1,3,5,7,9]=>{{1,3,6,7,9,10},{2,5,8},{4}}
[10,8,6,2,1,4,3,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,4,2,1,6,3,5,7,9]=>{{1,2,3,4,5,7,8,9,10},{6}}
[10,6,4,2,1,8,3,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,6,4,2,1,10,3,5,7,9]=>{{1,5,8},{2,3,4,6,7,9,10}}
[8,6,4,2,9,1,3,5,7,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[9,6,4,2,7,1,3,5,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[9,7,4,2,5,1,3,6,8,10]=>{{1,6,8,9},{2,3,4,7},{5},{10}}
[9,7,5,2,3,1,4,6,8,10]=>{{1,6,8,9},{2,4,7},{3,5},{10}}
[9,7,5,3,1,2,4,6,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[1,2,10,3,4,5,6,7,9,8]=>{{1},{2},{3,4,5,6,7,8,10},{9}}
[1,2,3,9,4,5,6,10,7,8]=>{{1},{2},{3},{4,5,6,7,9},{8,10}}
[1,2,3,4,10,5,6,7,9,8]=>{{1},{2},{3},{4},{5,6,7,8,10},{9}}
[1,2,3,4,5,10,6,7,9,8]=>{{1},{2},{3},{4},{5},{6,7,8,10},{9}}
[1,2,3,4,5,6,9,10,7,8]=>{{1},{2},{3},{4},{5},{6},{7,9},{8,10}}
[8,1,2,3,4,5,9,6,10,7]=>{{1,2,3,4,5,6,8},{7,9,10}}
[7,10,1,2,3,4,5,9,6,8]=>{{1,3,5,7},{2,4,6,8,9,10}}
[6,1,10,2,3,4,5,9,7,8]=>{{1,2,4,6},{3,5,7,8,9,10}}
[5,1,2,3,4,6,9,7,10,8]=>{{1,2,3,4,5},{6},{7,8,9,10}}
[4,1,2,3,10,5,6,9,7,8]=>{{1,2,3,4},{5,6,7,8,9,10}}
[3,1,2,4,5,10,6,9,7,8]=>{{1,2,3},{4},{5},{6,7,8,9,10}}
[9,1,2,3,4,5,7,10,6,8]=>{{1,2,3,4,5,6,9},{7},{8,10}}
[9,1,2,3,5,7,10,4,6,8]=>{{1,2,3,4,6,7,8,9,10},{5}}
[9,1,3,5,7,10,2,4,6,8]=>{{1,2,4,5,6,7,8,9,10},{3}}
[7,8,9,6,5,4,3,2,1,10]=>{{1,3,7,9},{2,8},{4,6},{5},{10}}
[7,6,8,9,5,4,3,2,1,10]=>{{1,2,3,4,6,7,8,9},{5},{10}}
[7,6,5,8,9,4,3,2,1,10]=>{{1,3,5,7,9},{2,4,6,8},{10}}
[7,6,5,4,8,9,3,2,1,10]=>{{1,2,3,5,6,7,8,9},{4},{10}}
[7,6,5,4,3,8,9,2,1,10]=>{{1,7,9},{2,6,8},{3,5},{4},{10}}
[7,6,5,4,3,2,8,9,1,10]=>{{1,7,8,9},{2,6},{3,5},{4},{10}}
[9,8,7,6,5,4,2,1,3,10]=>{{1,2,3,7,8,9},{4,6},{5},{10}}
[9,8,7,6,5,3,2,1,4,10]=>{{1,2,3,4,6,7,8,9},{5},{10}}
[9,8,7,6,4,3,2,1,5,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[9,8,7,5,4,3,2,1,6,10]=>{{1,2,3,6,7,8,9},{4,5},{10}}
[9,8,6,5,4,3,2,1,7,10]=>{{1,2,7,8,9},{3,6},{4,5},{10}}
[10,1,3,4,5,6,7,8,9,2]=>{{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,9,3,4,5,6,7,10,2,8]=>{{1},{2,9},{3},{4},{5},{6},{7},{8,10}}
[9,2,3,4,5,6,1,10,8,7]=>{{1,7,8,9,10},{2},{3},{4},{5},{6}}
[9,1,10,4,5,6,7,8,3,2]=>{{1,2,3,9,10},{4},{5},{6},{7},{8}}
[8,10,3,4,5,6,7,1,9,2]=>{{1,8},{2,10},{3},{4},{5},{6},{7},{9}}
[10,6,1,2,3,4,9,5,7,8]=>{{1,3,5,8,10},{2,4,6},{7,9}}
[10,7,1,2,3,4,9,5,6,8]=>{{1,3,5,8,10},{2,4,6,7,9}}
[9,10,1,2,3,4,8,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,1,5,2,3,4,6,7,8,9]=>{{1,2,4,6,7,8,9,10},{3,5}}
[10,1,2,5,3,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,1,2,3,10,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,6,1,2,3,4,10,9,5,8]=>{{1,3,5,7,8,9,10},{2,4,6}}
[9,7,1,2,3,4,8,5,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,9,1,2,3,4,6,7,10,8]=>{{1,3,5},{2,4,6,7,8,9,10}}
[10,8,4,9,1,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,10,1,5,3,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,1,5,2,10,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,1,2,10,3,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,10,1,8,7,6,5,4,3,2]=>{{1,3,9},{2,10},{4,8},{5,7},{6}}
[3,2,5,4,7,6,9,8,1,10]=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}
[2,4,3,6,5,8,7,10,9,1]=>{{1,2,4,6,8,10},{3},{5},{7},{9}}
[3,4,5,6,7,8,9,2,10,1]=>{{1,3,5,7,9,10},{2,4,6,8}}
[2,4,5,6,7,8,9,10,3,1]=>{{1,2,4,6,8,10},{3,5,7,9}}
[3,2,5,4,7,6,1,10,8,9]=>{{1,3,5,7},{2},{4},{6},{8,9,10}}
[3,2,5,4,9,8,6,7,1,10]=>{{1,3,5,9},{2},{4},{6,7,8},{10}}
[3,2,5,4,1,8,6,10,7,9]=>{{1,3,5},{2},{4},{6,7,8,9,10}}
[3,2,5,4,1,10,9,6,7,8]=>{{1,3,5},{2},{4},{6,8,10},{7,9}}
[3,2,7,6,4,5,9,8,1,10]=>{{1,3,7,9},{2},{4,5,6},{8},{10}}
[3,2,7,6,4,5,1,10,8,9]=>{{1,3,7},{2},{4,5,6},{8,9,10}}
[3,2,9,6,4,8,5,7,1,10]=>{{1,3,9},{2},{4,5,6,7,8},{10}}
[3,2,1,6,4,8,5,10,7,9]=>{{1,3},{2},{4,5,6,7,8,9,10}}
[3,2,1,6,4,10,9,5,7,8]=>{{1,3},{2},{4,5,6,8,10},{7,9}}
[3,2,9,8,7,4,5,6,1,10]=>{{1,3,9},{2},{4,6,8},{5,7},{10}}
[3,2,1,8,7,4,5,10,6,9]=>{{1,3},{2},{4,6,8,9,10},{5,7}}
[3,2,1,10,7,4,9,5,6,8]=>{{1,3},{2},{4,5,6,7,8,9,10}}
[3,2,1,10,9,8,4,5,6,7]=>{{1,3},{2},{4,7,10},{5,6,8,9}}
[5,4,2,3,7,6,9,8,1,10]=>{{1,5,7,9},{2,3,4},{6},{8},{10}}
[5,4,2,3,7,6,1,10,8,9]=>{{1,5,7},{2,3,4},{6},{8,9,10}}
[5,4,2,3,9,8,6,7,1,10]=>{{1,5,9},{2,3,4},{6,7,8},{10}}
[5,4,2,3,1,8,6,10,7,9]=>{{1,5},{2,3,4},{6,7,8,9,10}}
[5,4,2,3,1,10,9,6,7,8]=>{{1,5},{2,3,4},{6,8,10},{7,9}}
[7,4,2,6,3,5,9,8,1,10]=>{{1,7,9},{2,3,4,5,6},{8},{10}}
[7,4,2,6,3,5,1,10,8,9]=>{{1,7},{2,3,4,5,6},{8,9,10}}
[9,4,2,6,3,8,5,7,1,10]=>{{1,9},{2,3,4,5,6,7,8},{10}}
[1,4,2,6,3,8,5,10,7,9]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,4,2,6,3,10,9,5,7,8]=>{{1},{2,3,4,5,6,8,10},{7,9}}
[9,4,2,8,7,3,5,6,1,10]=>{{1,9},{2,3,4,6,8},{5,7},{10}}
[1,4,2,8,7,3,5,10,6,9]=>{{1},{2,3,4,6,8,9,10},{5,7}}
[1,4,2,10,7,3,9,5,6,8]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,4,2,10,9,8,3,5,6,7]=>{{1},{2,3,4,7,10},{5,6,8,9}}
[7,6,5,2,3,4,9,8,1,10]=>{{1,7,9},{2,4,6},{3,5},{8},{10}}
[7,6,5,2,3,4,1,10,8,9]=>{{1,7},{2,4,6},{3,5},{8,9,10}}
[9,6,5,2,3,8,4,7,1,10]=>{{1,9},{2,4,6,7,8},{3,5},{10}}
[1,6,5,2,3,8,4,10,7,9]=>{{1},{2,4,6,7,8,9,10},{3,5}}
[1,6,5,2,3,10,9,4,7,8]=>{{1},{2,4,6,8,10},{3,5},{7,9}}
[9,8,5,2,7,3,4,6,1,10]=>{{1,9},{2,3,4,5,6,7,8},{10}}
[1,8,5,2,7,3,4,10,6,9]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,10,5,2,7,3,9,4,6,8]=>{{1},{2,4,8,10},{3,5,6,7,9}}
[1,10,5,2,9,8,3,4,6,7]=>{{1},{2,3,4,5,6,7,8,9,10}}
[9,8,7,6,2,3,4,5,1,10]=>{{1,9},{2,5,8},{3,4,6,7},{10}}
[1,8,7,6,2,3,4,10,5,9]=>{{1},{2,5,8,9,10},{3,4,6,7}}
[1,10,7,6,2,3,9,4,5,8]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,10,9,6,2,8,3,4,5,7]=>{{1},{2,3,5,7,9,10},{4,6,8}}
[1,10,9,8,7,2,3,4,5,6]=>{{1},{2,6,10},{3,5,7,9},{4,8}}
[3,2,5,4,7,6,1,10,9,8]=>{{1,3,5,7},{2},{4},{6},{8,10},{9}}
[3,2,5,4,9,8,7,6,1,10]=>{{1,3,5,9},{2},{4},{6,8},{7},{10}}
[3,2,5,4,1,8,7,10,9,6]=>{{1,3,5},{2},{4},{6,8,10},{7},{9}}
[3,2,5,4,1,10,9,8,7,6]=>{{1,3,5},{2},{4},{6,10},{7,9},{8}}
[3,2,7,6,5,4,9,8,1,10]=>{{1,3,7,9},{2},{4,6},{5},{8},{10}}
[3,2,7,6,5,4,1,10,9,8]=>{{1,3,7},{2},{4,6},{5},{8,10},{9}}
[3,2,9,6,5,8,7,4,1,10]=>{{1,3,9},{2},{4,6,8},{5},{7},{10}}
[3,2,1,6,5,8,7,10,9,4]=>{{1,3},{2},{4,6,8,10},{5},{7},{9}}
[3,2,1,6,5,10,9,8,7,4]=>{{1,3},{2},{4,6,10},{5},{7,9},{8}}
[3,2,1,8,7,6,5,10,9,4]=>{{1,3},{2},{4,8,10},{5,7},{6},{9}}
[3,2,1,10,7,6,9,8,5,4]=>{{1,3},{2},{4,10},{5,7,9},{6},{8}}
[5,4,3,2,7,6,9,8,1,10]=>{{1,5,7,9},{2,4},{3},{6},{8},{10}}
[5,4,3,2,7,6,1,10,9,8]=>{{1,5,7},{2,4},{3},{6},{8,10},{9}}
[5,4,3,2,9,8,7,6,1,10]=>{{1,5,9},{2,4},{3},{6,8},{7},{10}}
[5,4,3,2,1,8,7,10,9,6]=>{{1,5},{2,4},{3},{6,8,10},{7},{9}}
[7,4,3,6,5,2,9,8,1,10]=>{{1,7,9},{2,4,6},{3},{5},{8},{10}}
[7,4,3,6,5,2,1,10,9,8]=>{{1,7},{2,4,6},{3},{5},{8,10},{9}}
[9,4,3,6,5,8,7,2,1,10]=>{{1,9},{2,4,6,8},{3},{5},{7},{10}}
[1,4,3,6,5,8,7,10,9,2]=>{{1},{2,4,6,8,10},{3},{5},{7},{9}}
[1,4,3,6,5,10,9,8,7,2]=>{{1},{2,4,6,10},{3},{5},{7,9},{8}}
[9,4,3,8,7,6,5,2,1,10]=>{{1,9},{2,4,8},{3},{5,7},{6},{10}}
[1,4,3,8,7,6,5,10,9,2]=>{{1},{2,4,8,10},{3},{5,7},{6},{9}}
[1,4,3,10,7,6,9,8,5,2]=>{{1},{2,4,10},{3},{5,7,9},{6},{8}}
[1,4,3,10,9,8,7,6,5,2]=>{{1},{2,4,10},{3},{5,9},{6,8},{7}}
[7,6,5,4,3,2,9,8,1,10]=>{{1,7,9},{2,6},{3,5},{4},{8},{10}}
[9,6,5,4,3,8,7,2,1,10]=>{{1,9},{2,6,8},{3,5},{4},{7},{10}}
[1,6,5,4,3,8,7,10,9,2]=>{{1},{2,6,8,10},{3,5},{4},{7},{9}}
[1,6,5,4,3,10,9,8,7,2]=>{{1},{2,6,10},{3,5},{4},{7,9},{8}}
[9,8,5,4,7,6,3,2,1,10]=>{{1,9},{2,8},{3,5,7},{4},{6},{10}}
[1,8,5,4,7,6,3,10,9,2]=>{{1},{2,8,10},{3,5,7},{4},{6},{9}}
[1,10,5,4,7,6,9,8,3,2]=>{{1},{2,10},{3,5,7,9},{4},{6},{8}}
[1,10,5,4,9,8,7,6,3,2]=>{{1},{2,10},{3,5,9},{4},{6,8},{7}}
[1,10,7,6,5,4,9,8,3,2]=>{{1},{2,10},{3,7,9},{4,6},{5},{8}}
[1,10,9,6,5,8,7,4,3,2]=>{{1},{2,10},{3,9},{4,6,8},{5},{7}}
[6,5,7,4,8,3,9,2,10,1]=>{{1,3,6,7,9,10},{2,5,8},{4}}
[6,5,7,4,8,3,10,2,9,1]=>{{1,3,6,7,10},{2,5,8},{4},{9}}
[5,6,4,7,3,8,2,9,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[9,8,7,6,1,2,3,4,5,10]=>{{1,5,9},{2,4,6,8},{3,7},{10}}
[8,10,1,2,3,4,5,9,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,1,9,2,3,4,5,6,7]=>{{1,3,4,6,7,9,10},{2,5,8}}
[8,7,1,2,3,4,5,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,10,1,5,6,7,8,9,3,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,2,3,4,5,6,7,8,1]=>{{1,10},{2,3,4,5,6,7,8,9}}
[2,4,3,1,6,5,8,7,10,9]=>{{1,2,4},{3},{5,6},{7,8},{9,10}}
[7,8,4,9,5,2,10,6,3,1]=>{{1,7,10},{2,6,8},{3,4,9},{5}}
[2,1,4,3,6,5,8,10,9,7]=>{{1,2},{3,4},{5,6},{7,8,10},{9}}
[2,1,4,3,6,8,7,5,10,9]=>{{1,2},{3,4},{5,6,8},{7},{9,10}}
[2,1,4,3,8,10,7,9,5,6]=>{{1,2},{3,4},{5,8,9},{6,10},{7}}
[2,1,4,3,6,7,10,8,9,5]=>{{1,2},{3,4},{5,6,7,10},{8},{9}}
[2,1,4,6,5,3,8,7,10,9]=>{{1,2},{3,4,6},{5},{7,8},{9,10}}
[2,1,4,6,5,3,8,10,9,7]=>{{1,2},{3,4,6},{5},{7,8,10},{9}}
[2,1,6,8,5,7,3,4,10,9]=>{{1,2},{3,6,7},{4,8},{5},{9,10}}
[2,1,8,7,5,10,4,9,3,6]=>{{1,2},{3,8,9},{4,7},{5},{6,10}}
[2,1,6,7,5,10,8,4,9,3]=>{{1,2},{3,6,10},{4,7,8},{5},{9}}
[2,1,4,5,8,6,7,3,10,9]=>{{1,2},{3,4,5,8},{6},{7},{9,10}}
[2,1,8,5,10,6,7,9,3,4]=>{{1,2},{3,8,9},{4,5,10},{6},{7}}
[2,1,4,7,10,6,9,8,3,5]=>{{1,2},{3,4,7,9},{5,10},{6},{8}}
[2,1,4,5,6,10,7,8,9,3]=>{{1,2},{3,4,5,6,10},{7},{8},{9}}
[2,4,3,1,6,5,8,10,9,7]=>{{1,2,4},{3},{5,6},{7,8,10},{9}}
[2,4,3,1,6,8,7,5,10,9]=>{{1,2,4},{3},{5,6,8},{7},{9,10}}
[2,4,3,1,8,10,7,9,5,6]=>{{1,2,4},{3},{5,8,9},{6,10},{7}}
[2,4,3,1,6,7,10,8,9,5]=>{{1,2,4},{3},{5,6,7,10},{8},{9}}
[4,6,3,5,1,2,8,7,10,9]=>{{1,4,5},{2,6},{3},{7,8},{9,10}}
[4,6,3,5,1,2,8,10,9,7]=>{{1,4,5},{2,6},{3},{7,8,10},{9}}
[6,5,3,8,2,7,1,4,10,9]=>{{1,6,7},{2,5},{3},{4,8},{9,10}}
[8,5,3,7,2,10,4,9,1,6]=>{{1,8,9},{2,5},{3},{4,7},{6,10}}
[6,5,3,7,2,10,8,4,9,1]=>{{1,6,10},{2,5},{3},{4,7,8},{9}}
[4,5,3,8,6,2,7,1,10,9]=>{{1,4,8},{2,5,6},{3},{7},{9,10}}
[8,6,3,5,10,2,7,9,1,4]=>{{1,8,9},{2,6},{3},{4,5,10},{7}}
[4,7,3,6,10,1,9,8,2,5]=>{{1,4,6},{2,7,9},{3},{5,10},{8}}
[4,5,3,6,10,7,1,8,9,2]=>{{1,4,6,7},{2,5,10},{3},{8},{9}}
[2,3,6,4,5,1,8,7,10,9]=>{{1,2,3,6},{4},{5},{7,8},{9,10}}
[2,3,6,4,5,1,8,10,9,7]=>{{1,2,3,6},{4},{5},{7,8,10},{9}}
[6,3,8,4,5,7,1,2,10,9]=>{{1,6,7},{2,3,8},{4},{5},{9,10}}
[8,3,7,4,5,10,2,9,1,6]=>{{1,8,9},{2,3,7},{4},{5},{6,10}}
[6,3,7,4,5,10,8,2,9,1]=>{{1,6,10},{2,3,7,8},{4},{5},{9}}
[2,5,8,4,7,6,1,3,10,9]=>{{1,2,5,7},{3,8},{4},{6},{9,10}}
[8,5,10,4,7,6,2,9,1,3]=>{{1,8,9},{2,5,7},{3,10},{4},{6}}
[2,7,10,4,8,6,9,5,1,3]=>{{1,2,7,9},{3,10},{4},{5,8},{6}}
[2,5,6,4,10,8,7,3,9,1]=>{{1,2,5,10},{3,6,8},{4},{7},{9}}
[2,3,4,8,5,6,7,1,10,9]=>{{1,2,3,4,8},{5},{6},{7},{9,10}}
[8,3,4,10,5,6,7,9,1,2]=>{{1,8,9},{2,3,4,10},{5},{6},{7}}
[2,7,4,10,5,6,9,8,1,3]=>{{1,2,7,9},{3,4,10},{5},{6},{8}}
[2,3,6,10,5,9,7,8,1,4]=>{{1,2,3,6,9},{4,10},{5},{7},{8}}
[2,3,4,5,10,6,7,8,9,1]=>{{1,2,3,4,5,10},{6},{7},{8},{9}}
[2,3,4,5,6,1,8,9,10,7]=>{{1,2,3,4,5,6},{7,8,9,10}}
[2,3,4,5,6,8,9,1,10,7]=>{{1,2,3,4,5,6,8},{7,9,10}}
[4,5,6,1,7,8,9,10,2,3]=>{{1,4},{2,5,7,9},{3,6,8,10}}
[3,5,6,1,7,8,9,10,2,4]=>{{1,3,4,6,8,10},{2,5,7,9}}
[3,4,6,1,7,8,9,10,2,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,5,1,7,8,9,10,2,6]=>{{1,2,3,4,5,7,9},{6,8,10}}
[2,1,4,3,6,5,8,9,10,7]=>{{1,2},{3,4},{5,6},{7,8,9,10}}
[2,1,4,3,6,7,8,5,10,9]=>{{1,2},{3,4},{5,6,7,8},{9,10}}
[2,1,4,3,8,7,9,10,5,6]=>{{1,2},{3,4},{5,6,7,8,9,10}}
[2,1,4,3,6,7,8,9,10,5]=>{{1,2},{3,4},{5,6,7,8,9,10}}
[2,1,4,5,6,3,8,7,10,9]=>{{1,2},{3,4,5,6},{7,8},{9,10}}
[2,1,4,5,6,3,8,9,10,7]=>{{1,2},{3,4,5,6},{7,8,9,10}}
[2,1,6,5,7,8,3,4,10,9]=>{{1,2},{3,4,5,6,7,8},{9,10}}
[2,1,8,5,9,7,3,10,6,4]=>{{1,2},{3,4,5,6,7,8,9,10}}
[2,1,6,5,7,8,9,10,3,4]=>{{1,2},{3,4,5,6,7,8,9,10}}
[2,1,4,5,6,7,8,3,10,9]=>{{1,2},{3,4,5,6,7,8},{9,10}}
[2,1,8,5,6,7,9,10,3,4]=>{{1,2},{3,4,5,6,7,8,9,10}}
[2,1,4,7,6,8,9,3,10,5]=>{{1,2},{3,4,5,6,7,8,9,10}}
[2,1,4,5,6,7,8,9,10,3]=>{{1,2},{3,4,5,6,7,8,9,10}}
[2,3,4,1,6,5,8,7,10,9]=>{{1,2,3,4},{5,6},{7,8},{9,10}}
[2,3,4,1,6,5,8,9,10,7]=>{{1,2,3,4},{5,6},{7,8,9,10}}
[2,3,4,1,6,7,8,5,10,9]=>{{1,2,3,4},{5,6,7,8},{9,10}}
[2,3,4,1,8,7,9,10,5,6]=>{{1,2,3,4},{5,6,7,8,9,10}}
[2,3,4,1,6,7,8,9,10,5]=>{{1,2,3,4},{5,6,7,8,9,10}}
[4,3,5,6,1,2,8,7,10,9]=>{{1,2,3,4,5,6},{7,8},{9,10}}
[4,3,5,6,1,2,8,9,10,7]=>{{1,2,3,4,5,6},{7,8,9,10}}
[6,3,7,5,1,8,4,2,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[8,3,9,5,1,7,4,10,6,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,3,7,5,1,8,9,10,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,5,6,7,8,1,2,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[8,3,9,5,6,7,1,10,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,7,8,6,10,9,2,5,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,5,6,7,8,9,10,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,1,8,7,10,9]=>{{1,2,3,4,5,6},{7,8},{9,10}}
[6,3,4,5,7,8,1,2,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[8,3,4,5,9,7,1,10,6,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,3,4,5,7,8,9,10,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,5,4,6,7,1,8,3,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[8,5,4,6,7,1,9,10,3,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,7,4,8,6,1,9,5,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,5,4,6,7,8,9,1,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,7,8,1,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[8,3,4,5,6,7,9,10,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,7,4,5,6,8,9,1,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,6,5,7,8,1,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,5,2,3,6,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,2,5,6,7,8,9,10,1]=>{{1,4,5,6,7,8,9,10},{2,3}}
[5,6,7,2,3,4,8,9,10,1]=>{{1,3,5,7,8,9,10},{2,4,6}}
[5,3,6,2,4,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,4,3,2,6,7,8,9,10,1]=>{{1,5,6,7,8,9,10},{2,4},{3}}
[6,7,8,9,2,3,4,5,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,3,7,8,2,4,5,9,10,1]=>{{1,4,6,8,9,10},{2,3,5,7}}
[6,7,4,5,2,3,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,4,3,7,2,5,8,9,10,1]=>{{1,2,4,5,6,7,8,9,10},{3}}
[6,5,4,3,2,7,8,9,10,1]=>{{1,6,7,8,9,10},{2,5},{3,4}}
[7,8,9,10,1,3,4,5,6,2]=>{{1,2,4,5,7,8,10},{3,6,9}}
[7,3,8,9,10,2,4,5,6,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,4,3,8,9,2,5,6,10,1]=>{{1,5,7,9,10},{2,4,6,8},{3}}
[7,5,8,3,6,2,4,9,10,1]=>{{1,3,4,7,8,9,10},{2,5,6}}
[7,5,4,3,8,2,6,9,10,1]=>{{1,2,5,6,7,8,9,10},{3,4}}
[7,6,5,4,3,2,8,9,10,1]=>{{1,7,8,9,10},{2,6},{3,5},{4}}
[8,5,9,3,6,10,2,4,7,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,5,4,3,9,10,2,6,7,1]=>{{1,6,8,10},{2,5,7,9},{3,4}}
[8,9,6,7,4,5,2,3,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,6,4,9,3,7,2,5,10,1]=>{{1,3,4,5,8,9,10},{2,6,7}}
[8,6,5,4,3,9,2,7,10,1]=>{{1,2,6,7,8,9,10},{3,5},{4}}
[8,7,6,5,4,3,2,9,10,1]=>{{1,8,9,10},{2,7},{3,6},{4,5}}
[9,7,5,4,10,3,8,2,6,1]=>{{1,3,5,6,9,10},{2,7,8},{4}}
[9,7,6,5,4,3,10,2,8,1]=>{{1,2,7,8,9,10},{3,6},{4,5}}
[10,1,9,2,8,3,7,4,6,5]=>{{1,2,4,5,8,10},{3,6,9},{7}}
[1,4,3,6,5,10,9,7,8,2]=>{{1},{2,4,6,10},{3},{5},{7,8,9}}
[1,4,3,8,7,5,6,10,9,2]=>{{1},{2,4,8,10},{3},{5,6,7},{9}}
[1,4,3,10,7,5,9,6,8,2]=>{{1},{2,4,10},{3},{5,6,7,8,9}}
[1,4,3,10,9,8,5,6,7,2]=>{{1},{2,4,10},{3},{5,7,9},{6,8}}
[1,6,5,3,4,8,7,10,9,2]=>{{1},{2,6,8,10},{3,4,5},{7},{9}}
[1,6,5,3,4,10,9,7,8,2]=>{{1},{2,6,10},{3,4,5},{7,8,9}}
[1,8,5,3,7,4,6,10,9,2]=>{{1},{2,8,10},{3,4,5,6,7},{9}}
[1,10,5,3,7,4,9,6,8,2]=>{{1},{2,10},{3,4,5,6,7,8,9}}
[1,10,5,3,9,8,4,6,7,2]=>{{1},{2,10},{3,4,5,7,9},{6,8}}
[1,8,7,6,3,4,5,10,9,2]=>{{1},{2,8,10},{3,5,7},{4,6},{9}}
[1,10,7,6,3,4,9,5,8,2]=>{{1},{2,10},{3,5,7,8,9},{4,6}}
[1,10,9,6,3,8,4,5,7,2]=>{{1},{2,10},{3,4,5,6,7,8,9}}
[1,10,9,8,7,3,4,5,6,2]=>{{1},{2,10},{3,6,9},{4,5,7,8}}
[3,1,2,6,5,8,7,10,9,4]=>{{1,2,3},{4,6,8,10},{5},{7},{9}}
[3,1,2,6,5,10,9,7,8,4]=>{{1,2,3},{4,6,10},{5},{7,8,9}}
[3,1,2,8,7,5,6,10,9,4]=>{{1,2,3},{4,8,10},{5,6,7},{9}}
[3,1,2,10,7,5,9,6,8,4]=>{{1,2,3},{4,10},{5,6,7,8,9}}
[3,1,2,10,9,8,5,6,7,4]=>{{1,2,3},{4,10},{5,7,9},{6,8}}
[3,1,5,2,4,8,7,10,9,6]=>{{1,2,3,4,5},{6,8,10},{7},{9}}
[3,1,5,2,4,10,9,7,8,6]=>{{1,2,3,4,5},{6,10},{7,8,9}}
[3,1,5,2,7,4,6,10,9,8]=>{{1,2,3,4,5,6,7},{8,10},{9}}
[3,1,5,2,9,8,4,6,7,10]=>{{1,2,3,4,5,7,9},{6,8},{10}}
[3,1,7,6,2,4,5,10,9,8]=>{{1,2,3,5,7},{4,6},{8,10},{9}}
[3,1,7,6,2,4,9,5,8,10]=>{{1,2,3,5,7,8,9},{4,6},{10}}
[3,1,9,6,2,8,4,5,7,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[3,1,9,8,7,2,4,5,6,10]=>{{1,2,3,6,9},{4,5,7,8},{10}}
[5,4,1,2,3,8,7,10,9,6]=>{{1,3,5},{2,4},{6,8,10},{7},{9}}
[5,4,1,2,3,10,9,7,8,6]=>{{1,3,5},{2,4},{6,10},{7,8,9}}
[5,4,1,2,7,3,6,10,9,8]=>{{1,3,5,6,7},{2,4},{8,10},{9}}
[5,4,1,2,7,3,9,6,8,10]=>{{1,3,5,6,7,8,9},{2,4},{10}}
[5,4,1,2,9,8,3,6,7,10]=>{{1,3,5,7,9},{2,4},{6,8},{10}}
[7,4,1,6,2,3,5,10,9,8]=>{{1,2,3,4,5,6,7},{8,10},{9}}
[7,4,1,6,2,3,9,5,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[9,4,1,6,2,8,3,5,7,10]=>{{1,3,7,9},{2,4,5,6,8},{10}}
[9,4,1,8,7,2,3,5,6,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[7,6,5,1,2,3,4,10,9,8]=>{{1,4,7},{2,3,5,6},{8,10},{9}}
[7,6,5,1,2,3,9,4,8,10]=>{{1,4,7,8,9},{2,3,5,6},{10}}
[9,6,5,1,2,8,3,4,7,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[9,8,5,1,7,2,3,4,6,10]=>{{1,2,4,6,8,9},{3,5,7},{10}}
[10,1,2,3,4,9,6,7,8,5]=>{{1,2,3,4,5,10},{6,7,8,9}}
[10,1,9,3,4,5,6,7,8,2]=>{{1,2,10},{3,4,5,6,7,8,9}}
[1,9,2,10,3,4,5,6,7,8]=>{{1},{2,3,5,7,9},{4,6,8,10}}
[1,4,2,3,6,5,8,7,10,9]=>{{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,3,4,2,6,5,8,7,10,9]=>{{1},{2,3,4},{5,6},{7,8},{9,10}}
[2,1,3,4,5,6,7,10,8,9]=>{{1,2},{3},{4},{5},{6},{7},{8,9,10}}
[10,2,3,4,5,6,7,8,1,9]=>{{1,9,10},{2},{3},{4},{5},{6},{7},{8}}
[3,10,1,4,5,6,7,8,9,2]=>{{1,3},{2,10},{4},{5},{6},{7},{8},{9}}
[8,1,10,3,4,5,6,7,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,2,1,10,4,5,6,7,3,9]=>{{1,3,4,5,6,7,8,9,10},{2}}
[7,10,8,3,4,5,6,1,2,9]=>{{1,3,4,5,6,7,8},{2,9,10}}
[3,9,1,2,10,5,6,7,8,4]=>{{1,3},{2,4,5,6,7,8,9,10}}
[2,3,4,5,6,7,10,9,8,1]=>{{1,2,3,4,5,6,7,10},{8,9}}
[2,3,4,5,6,9,8,10,7,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,5,9,4,8,3,7,2,6,1]=>{{1,10},{2,5,8},{3,6,9},{4},{7}}
[1,3,5,2,4,7,6,9,8,10]=>{{1},{2,3,4,5},{6,7},{8,9},{10}}
[1,4,2,5,3,7,6,9,8,10]=>{{1},{2,3,4,5},{6,7},{8,9},{10}}
[10,3,1,5,6,7,8,9,2,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,4,1,5,6,7,8,9,2,3]=>{{1,3,10},{2,4,5,6,7,8,9}}
[4,2,6,8,10,1,3,5,7,9]=>{{1,3,4,5,6,7,8,9,10},{2}}
[4,6,2,8,10,1,3,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,6,8,2,10,1,3,5,7,9]=>{{1,2,4,6},{3,5,7,8,9,10}}
[4,6,8,10,2,1,3,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,6,8,2,9,1,3,5,7,10]=>{{1,2,4,6},{3,5,7,8,9},{10}}
[4,6,2,7,9,1,3,5,8,10]=>{{1,2,3,4,6,7},{5,8,9},{10}}
[4,2,5,7,9,1,3,6,8,10]=>{{1,3,4,5,6,7,8,9},{2},{10}}
[2,3,5,7,9,1,4,6,8,10]=>{{1,2,3,5,6,8,9},{4,7},{10}}
[9,7,10,8,6,5,4,3,2,1]=>{{1,2,3,4,7,8,9,10},{5,6}}
[9,7,5,10,8,6,4,3,2,1]=>{{1,2,4,7,9,10},{3,5,8},{6}}
[8,9,6,10,7,5,4,3,2,1]=>{{1,3,4,5,6,7,8,10},{2,9}}
[9,7,5,3,10,8,6,4,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,6,4,10,7,5,3,2,1]=>{{1,3,5,6,7,8,10},{2,9},{4}}
[8,5,9,6,10,7,4,3,2,1]=>{{1,2,3,5,8,9,10},{4,6,7}}
[7,8,9,5,10,6,4,3,2,1]=>{{1,4,5,7,10},{2,3,8,9},{6}}
[8,9,6,4,2,10,7,5,3,1]=>{{1,2,3,5,6,8,9,10},{4},{7}}
[8,5,9,6,3,10,7,4,2,1]=>{{1,4,6,8,10},{2,3,5,9},{7}}
[7,8,9,5,3,10,6,4,2,1]=>{{1,6,7,10},{2,3,4,5,8,9}}
[7,8,4,9,5,10,6,3,2,1]=>{{1,6,7,10},{2,3,4,8,9},{5}}
[6,7,8,9,4,10,5,3,2,1]=>{{1,6,10},{2,4,5,7,9},{3,8}}
[8,5,9,6,3,1,10,7,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,9,5,3,1,10,6,4,2]=>{{1,2,6,7,8,10},{3,4,5,9}}
[8,5,2,9,6,3,10,7,4,1]=>{{1,7,8,10},{2,3,5,6},{4,9}}
[6,7,8,9,4,2,10,5,3,1]=>{{1,2,6,7,10},{3,4,5,8,9}}
[7,3,8,4,9,5,10,6,2,1]=>{{1,7,10},{2,3,5,6,8,9},{4}}
[6,7,8,3,9,4,10,5,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,6,7,8,9,3,10,4,2,1]=>{{1,2,3,5,6,7,9,10},{4,8}}
[7,8,4,1,9,5,2,10,6,3]=>{{1,2,3,4,7,8,10},{5,6,9}}
[7,3,8,4,9,5,1,10,6,2]=>{{1,7},{2,3,8,10},{4},{5,6,9}}
[6,7,8,3,9,4,1,10,5,2]=>{{1,2,3,4,6,7,8,10},{5,9}}
[5,6,7,8,9,3,1,10,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,7,2,8,3,9,4,10,5,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,6,7,8,2,9,3,10,4,1]=>{{1,2,4,5,6,8,9,10},{3,7}}
[4,5,6,7,8,9,2,10,3,1]=>{{1,2,4,5,7,8,10},{3,6,9}}
[5,6,7,1,8,2,9,3,10,4]=>{{1,3,4,5,7,8,9,10},{2,6}}
[4,5,6,7,8,1,9,2,10,3]=>{{1,3,4,6,7,9,10},{2,5,8}}
[2,3,4,5,6,7,10,8,9,1]=>{{1,2,3,4,5,6,7,10},{8},{9}}
[2,3,4,5,6,10,7,8,9,1]=>{{1,2,3,4,5,6,10},{7},{8},{9}}
[2,3,4,10,5,6,7,8,9,1]=>{{1,2,3,4,10},{5},{6},{7},{8},{9}}
[2,3,10,4,5,6,7,8,9,1]=>{{1,2,3,10},{4},{5},{6},{7},{8},{9}}
[2,1,4,3,6,5,9,8,10,7]=>{{1,2},{3,4},{5,6},{7,9,10},{8}}
[2,1,4,3,7,6,8,5,10,9]=>{{1,2},{3,4},{5,7,8},{6},{9,10}}
[2,1,4,3,7,6,9,8,10,5]=>{{1,2},{3,4},{5,7,9,10},{6},{8}}
[2,1,4,3,8,7,9,6,10,5]=>{{1,2},{3,4},{5,6,7,8,9,10}}
[2,1,5,4,6,3,8,7,10,9]=>{{1,2},{3,5,6},{4},{7,8},{9,10}}
[2,1,5,4,6,3,9,8,10,7]=>{{1,2},{3,5,6},{4},{7,9,10},{8}}
[2,1,5,4,7,6,8,3,10,9]=>{{1,2},{3,5,7,8},{4},{6},{9,10}}
[2,1,5,4,7,6,9,8,10,3]=>{{1,2},{3,5,7,9,10},{4},{6},{8}}
[2,1,5,4,8,7,9,6,10,3]=>{{1,2},{3,5,6,7,8,9,10},{4}}
[2,1,6,5,7,4,8,3,10,9]=>{{1,2},{3,4,5,6,7,8},{9,10}}
[2,1,6,5,7,4,9,8,10,3]=>{{1,2},{3,4,5,6,7,9,10},{8}}
[2,1,6,5,8,7,9,4,10,3]=>{{1,2},{3,6,7,9,10},{4,5,8}}
[2,1,7,6,8,5,9,4,10,3]=>{{1,2},{3,7,9,10},{4,5,6,8}}
[3,2,4,1,6,5,8,7,10,9]=>{{1,3,4},{2},{5,6},{7,8},{9,10}}
[3,2,4,1,6,5,9,8,10,7]=>{{1,3,4},{2},{5,6},{7,9,10},{8}}
[3,2,4,1,7,6,8,5,10,9]=>{{1,3,4},{2},{5,7,8},{6},{9,10}}
[3,2,4,1,7,6,9,8,10,5]=>{{1,3,4},{2},{5,7,9,10},{6},{8}}
[3,2,4,1,8,7,9,6,10,5]=>{{1,3,4},{2},{5,6,7,8,9,10}}
[3,2,5,4,6,1,8,7,10,9]=>{{1,3,5,6},{2},{4},{7,8},{9,10}}
[3,2,5,4,6,1,9,8,10,7]=>{{1,3,5,6},{2},{4},{7,9,10},{8}}
[3,2,5,4,7,6,8,1,10,9]=>{{1,3,5,7,8},{2},{4},{6},{9,10}}
[3,2,5,4,7,6,9,8,10,1]=>{{1,3,5,7,9,10},{2},{4},{6},{8}}
[3,2,5,4,8,7,9,6,10,1]=>{{1,3,5,6,7,8,9,10},{2},{4}}
[3,2,6,5,7,4,8,1,10,9]=>{{1,3,4,5,6,7,8},{2},{9,10}}
[3,2,6,5,7,4,9,8,10,1]=>{{1,3,4,5,6,7,9,10},{2},{8}}
[3,2,6,5,8,7,9,4,10,1]=>{{1,3,6,7,9,10},{2},{4,5,8}}
[3,2,7,6,8,5,9,4,10,1]=>{{1,3,7,9,10},{2},{4,5,6,8}}
[4,3,5,2,6,1,8,7,10,9]=>{{1,2,3,4,5,6},{7,8},{9,10}}
[4,3,5,2,6,1,9,8,10,7]=>{{1,2,3,4,5,6},{7,9,10},{8}}
[4,3,5,2,7,6,8,1,10,9]=>{{1,2,3,4,5,7,8},{6},{9,10}}
[4,3,5,2,7,6,9,8,10,1]=>{{1,2,3,4,5,7,9,10},{6},{8}}
[4,3,5,2,8,7,9,6,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,6,5,7,2,8,1,10,9]=>{{1,4,5,7,8},{2,3,6},{9,10}}
[4,3,6,5,7,2,9,8,10,1]=>{{1,4,5,7,9,10},{2,3,6},{8}}
[4,3,6,5,8,7,9,2,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,7,6,8,5,9,2,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,4,6,3,7,2,8,1,10,9]=>{{1,5,7,8},{2,3,4,6},{9,10}}
[5,4,6,3,7,2,9,8,10,1]=>{{1,5,7,9,10},{2,3,4,6},{8}}
[5,4,6,3,8,7,9,2,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,4,7,6,8,3,9,2,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,2,3,4,5,6,9,7,10,8]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[2,3,4,5,6,9,10,1,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,2,3,4,5,7,6,8,9,10]=>{{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,2,3,5,4,6,7,8,9,10]=>{{1},{2},{3},{4,5},{6},{7},{8},{9},{10}}
[1,2,3,5,4,7,6,9,8,10]=>{{1},{2},{3},{4,5},{6,7},{8,9},{10}}
[1,8,9,10,2,3,4,5,6,7]=>{{1},{2,5,8},{3,6,9},{4,7,10}}
[1,5,6,7,8,9,10,2,3,4]=>{{1},{2,5,8},{3,6,9},{4,7,10}}
[3,4,2,1,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[4,3,1,2,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[6,5,4,3,1,2,7,8,9,10]=>{{1,2,5,6},{3,4},{7},{8},{9},{10}}
[7,6,5,4,3,1,2,8,9,10]=>{{1,2,6,7},{3,5},{4},{8},{9},{10}}
[9,6,5,4,3,10,1,2,7,8]=>{{1,7,9},{2,6,8,10},{3,5},{4}}
[2,3,4,5,6,7,10,9,1,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,10,8,9,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,10,8,1,9,7]=>{{1,2,3,4,5,6,7,8,10},{9}}
[2,3,4,5,6,10,8,1,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,10,1,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,10,7,8,9,1,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,10,7,8,1,9,6]=>{{1,2,3,4,5,6,7,8,10},{9}}
[2,3,4,5,10,7,8,1,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,10,7,1,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,10,7,1,6,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,10,1,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,10,6,7,8,1,9,5]=>{{1,2,3,4,5,6,7,8,10},{9}}
[2,3,4,10,6,7,8,1,5,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,10,6,7,1,8,9,5]=>{{1,2,3,4,5,6,7,10},{8},{9}}
[2,3,4,10,6,7,1,9,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,10,6,7,1,5,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,10,6,1,8,5,9,7]=>{{1,2,3,4,5,6,7,8,10},{9}}
[2,3,4,10,6,1,8,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,10,6,1,5,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,10,1,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,10,5,6,1,8,9,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,10,5,6,1,8,4,9,7]=>{{1,2,3,4,5,6,7,8,10},{9}}
[2,3,10,5,6,1,8,4,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,10,5,6,1,4,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,10,5,1,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,10,5,1,7,4,6,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,10,5,1,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,10,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,10},{9}}
[2,10,4,1,6,3,8,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,10,4,1,6,3,5,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,10,4,1,3,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,7,6,5,4,3,2,9,1,10]=>{{1,8,9},{2,7},{3,6},{4,5},{10}}
[3,4,5,6,8,9,10,1,2,7]=>{{1,3,5,8},{2,4,6,9},{7,10}}
[3,5,6,7,8,9,10,1,2,4]=>{{1,2,3,5,6,8,9},{4,7,10}}
[3,4,5,6,7,8,1,2,9,10]=>{{1,3,5,7},{2,4,6,8},{9},{10}}
[8,9,10,1,5,6,7,3,4,2]=>{{1,2,3,4,8,9,10},{5},{6},{7}}
[8,9,10,5,6,7,1,3,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,10,1,5,6,3,4,7,2]=>{{1,4,8},{2,3,7,9,10},{5},{6}}
[8,9,10,5,6,1,3,4,7,2]=>{{1,4,5,6,8},{2,3,7,9,10}}
[8,9,10,5,6,3,4,7,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,5,6,10,1,3,4,7,2]=>{{1,4,6,8},{2,3,5,7,9,10}}
[8,9,5,6,10,3,4,7,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,10,1,5,6,7,3,2,4]=>{{1,3,4,8,10},{2,9},{5},{6},{7}}
[8,9,10,5,6,7,1,3,2,4]=>{{1,3,4,5,6,7,8,10},{2,9}}
[8,9,10,1,5,6,3,7,2,4]=>{{1,3,4,7,8,10},{2,9},{5},{6}}
[8,9,10,5,6,1,3,7,2,4]=>{{1,3,4,5,6,7,8,10},{2,9}}
[8,9,10,5,6,3,7,1,2,4]=>{{1,8},{2,9},{3,4,5,6,10},{7}}
[8,9,5,6,10,1,3,7,2,4]=>{{1,3,4,5,6,7,8,10},{2,9}}
[8,9,5,6,10,3,7,1,2,4]=>{{1,8},{2,9},{3,4,5,6,10},{7}}
[8,9,10,1,5,6,3,2,4,7]=>{{1,2,4,8,9},{3,7,10},{5},{6}}
[8,9,10,5,6,1,3,2,4,7]=>{{1,2,4,5,6,8,9},{3,7,10}}
[8,9,10,5,6,3,1,2,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,10,5,6,3,2,4,7,1]=>{{1,3,4,5,6,8,10},{2,7,9}}
[8,9,5,6,10,1,3,2,4,7]=>{{1,2,4,6,8,9},{3,5,7,10}}
[8,9,5,6,10,3,1,2,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,5,6,10,3,2,4,7,1]=>{{1,3,4,5,6,8,10},{2,7,9}}
[8,9,10,1,5,3,6,7,2,4]=>{{1,3,4,6,7,8,10},{2,9},{5}}
[8,9,10,5,1,3,6,7,2,4]=>{{1,3,4,5,6,7,8,10},{2,9}}
[8,9,10,5,3,6,7,1,2,4]=>{{1,8},{2,9},{3,4,5,10},{6},{7}}
[8,9,5,10,1,3,6,7,2,4]=>{{1,3,5,6,7,8},{2,9},{4,10}}
[8,9,5,10,3,6,7,1,2,4]=>{{1,8},{2,9},{3,5},{4,10},{6},{7}}
[8,9,10,1,5,3,6,2,4,7]=>{{1,2,4,8,9},{3,6,7,10},{5}}
[8,9,10,5,1,3,6,2,4,7]=>{{1,2,4,5,8,9},{3,6,7,10}}
[8,9,10,5,3,6,1,2,4,7]=>{{1,2,3,4,5,7,8,9,10},{6}}
[8,9,10,5,3,6,2,4,7,1]=>{{1,3,4,5,8,10},{2,7,9},{6}}
[8,9,5,10,1,3,6,2,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,5,10,3,6,1,2,4,7]=>{{1,2,4,7,8,9,10},{3,5},{6}}
[8,9,5,10,3,6,2,4,7,1]=>{{1,4,8,10},{2,7,9},{3,5},{6}}
[8,9,5,3,6,10,1,2,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,5,3,6,10,2,4,7,1]=>{{1,3,4,5,6,8,10},{2,7,9}}
[8,5,9,10,1,3,6,7,2,4]=>{{1,2,3,5,6,7,8,9},{4,10}}
[8,5,9,10,3,6,7,1,2,4]=>{{1,8},{2,3,5,9},{4,10},{6},{7}}
[8,5,9,10,1,3,6,2,4,7]=>{{1,2,5,8},{3,4,6,7,9,10}}
[8,5,9,10,3,6,1,2,4,7]=>{{1,2,3,4,5,7,8,9,10},{6}}
[8,5,9,10,3,6,2,4,7,1]=>{{1,4,8,10},{2,3,5,7,9},{6}}
[10,1,9,5,6,7,8,2,3,4]=>{{1,2,4,5,6,7,8,10},{3,9}}
[9,1,10,8,6,7,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,1,9,10,7,2,3,4,5,6]=>{{1,2,4,6,8,10},{3,5,7,9}}
[10,1,8,9,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,1,10,9,6,7,8,2,4,5]=>{{1,2,3,5,6,7,8,10},{4,9}}
[3,1,9,10,8,7,2,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,1,8,9,10,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,2,5,1,6,3,8,7,10,9]=>{{1,4},{2},{3,5,6},{7,8},{9,10}}
[4,2,6,1,7,3,8,5,10,9]=>{{1,4},{2},{3,6},{5,7,8},{9,10}}
[4,2,6,1,8,3,9,5,10,7]=>{{1,4},{2},{3,6},{5,8},{7,9,10}}
[4,2,6,1,8,3,9,5,7,10]=>{{1,4},{2},{3,6},{5,8},{7,9},{10}}
[4,2,6,1,7,3,5,9,8,10]=>{{1,4},{2},{3,6},{5,7},{8,9},{10}}
[4,2,5,1,3,7,6,9,8,10]=>{{1,4},{2},{3,5},{6,7},{8,9},{10}}
[8,7,6,5,4,3,1,2,10,9]=>{{1,2,7,8},{3,6},{4,5},{9,10}}
[10,9,8,7,6,5,4,2,3,1]=>{{1,10},{2,3,8,9},{4,7},{5,6}}
[2,3,4,5,9,7,8,10,6,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,9,6,7,8,10,1,5]=>{{1,2,3,4,9},{5,6,7,8,10}}
[2,3,9,5,6,7,8,10,4,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,9,4,5,6,7,8,10,3,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,3,4,5,6,7,8,10,1,2]=>{{1,9},{2,3,4,5,6,7,8,10}}
[2,3,4,5,6,8,10,1,9,7]=>{{1,2,3,4,5,6,8},{7,10},{9}}
[2,3,4,5,7,8,1,10,6,9]=>{{1,2,3,4,5,7},{6,8,9,10}}
[2,3,4,6,7,1,8,10,5,9]=>{{1,2,3,4,6},{5,7,8,9,10}}
[2,3,5,6,1,7,8,10,9,4]=>{{1,2,3,5},{4,6,7,8,10},{9}}
[2,4,5,1,6,7,8,10,3,9]=>{{1,2,4},{3,5,6,7,8,9,10}}
[3,4,1,5,6,7,8,10,2,9]=>{{1,3},{2,4,5,6,7,8,9,10}}
[3,2,4,5,6,7,8,10,9,1]=>{{1,3,4,5,6,7,8,10},{2},{9}}
[1,3,5,7,2,4,6,9,8,10]=>{{1},{2,3,5},{4,6,7},{8,9},{10}}
[2,4,1,5,3,6,7,8,9,10]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}
[5,6,2,1,3,7,4,8,9,10]=>{{1,2,3,4,5,6,7},{8},{9},{10}}
[3,2,5,1,6,4,7,8,9,10]=>{{1,3,4,5,6},{2},{7},{8},{9},{10}}
[6,7,2,1,8,3,4,9,5,10]=>{{1,2,3,4,6,7},{5,8,9},{10}}
[3,6,4,1,7,2,8,5,9,10]=>{{1,3,4},{2,6},{5,7,8},{9},{10}}
[3,6,7,2,1,4,8,5,9,10]=>{{1,3,5,7,8},{2,4,6},{9},{10}}
[4,2,6,1,7,5,3,8,9,10]=>{{1,4},{2},{3,5,6,7},{8},{9},{10}}
[4,3,2,6,1,7,5,8,9,10]=>{{1,4,5,6,7},{2,3},{8},{9},{10}}
[3,4,7,1,8,2,9,5,10,6]=>{{1,2,3,4,6,7,9,10},{5,8}}
[7,8,9,3,2,1,4,5,10,6]=>{{1,3,4,6,7,9,10},{2,5,8}}
[4,7,2,5,1,8,3,9,6,10]=>{{1,4,5},{2,3,7},{6,8,9},{10}}
[4,3,7,8,2,1,5,9,6,10]=>{{1,4,6,8,9},{2,3,5,7},{10}}
[3,5,2,7,1,8,6,4,9,10]=>{{1,2,3,5},{4,6,7,8},{9},{10}}
[5,4,3,2,7,1,8,6,9,10]=>{{1,5,6,7,8},{2,4},{3},{9},{10}}
[5,8,9,2,1,6,3,10,7,4]=>{{1,5},{2,4,8,10},{3,7,9},{6}}
[5,3,8,6,4,1,9,2,10,7]=>{{1,4,5,6},{2,3,8},{7,9,10}}
[3,5,8,2,6,1,9,4,10,7]=>{{1,2,3,4,5,6,8},{7,9,10}}
[5,4,3,8,9,2,1,6,10,7]=>{{1,5,7,9,10},{2,4,6,8},{3}}
[6,4,2,8,1,9,7,5,3,10]=>{{1,2,3,4,5,6,8,9},{7},{10}}
[4,3,6,2,8,1,9,7,5,10]=>{{1,2,3,4,6},{5,7,8,9},{10}}
[6,5,4,3,2,8,1,9,7,10]=>{{1,6,7,8,9},{2,5},{3,4},{10}}
[5,3,7,2,9,1,10,8,6,4]=>{{1,5,6,9},{2,3,4,7,10},{8}}
[5,4,3,7,2,9,1,10,8,6]=>{{1,2,4,5,7},{3},{6,8,9,10}}
[7,6,5,4,3,2,9,1,10,8]=>{{1,7,8,9,10},{2,6},{3,5},{4}}
[1,9,8,10,7,6,5,4,3,2]=>{{1},{2,3,4,8,9,10},{5,7},{6}}
[2,1,10,3,4,5,6,7,8,9]=>{{1,2},{3,4,5,6,7,8,9,10}}
[3,1,2,10,4,5,6,7,8,9]=>{{1,2,3},{4,5,6,7,8,9,10}}
[4,1,2,3,10,5,6,7,8,9]=>{{1,2,3,4},{5,6,7,8,9,10}}
[5,1,2,3,4,10,6,7,8,9]=>{{1,2,3,4,5},{6,7,8,9,10}}
[6,1,2,3,4,5,10,7,8,9]=>{{1,2,3,4,5,6},{7,8,9,10}}
[7,1,2,3,4,5,6,10,8,9]=>{{1,2,3,4,5,6,7},{8,9,10}}
[10,8,6,4,2,9,7,5,3,1]=>{{1,10},{2,5,8},{3,6,9},{4},{7}}
[10,7,4,1,8,5,2,9,6,3]=>{{1,3,4,10},{2,7},{5,6,8,9}}
[9,6,3,8,5,2,10,7,4,1]=>{{1,4,7,8,9,10},{2,6},{3},{5}}
[9,5,1,7,3,10,6,2,8,4]=>{{1,2,3,5,8,9},{4,6,7,10}}
[10,6,2,7,3,8,4,9,5,1]=>{{1,10},{2,3,5,6,8,9},{4,7}}
[7,3,8,4,10,6,2,9,5,1]=>{{1,2,3,5,7,8,9,10},{4},{6}}
[8,4,7,3,10,6,2,9,5,1]=>{{1,5,8,9,10},{2,3,4,7},{6}}
[10,5,8,3,6,1,9,4,7,2]=>{{1,2,5,6,10},{3,4,8},{7,9}}
[9,4,7,2,10,5,8,3,6,1]=>{{1,5,6,9,10},{2,4},{3,7,8}}
[10,5,7,2,8,3,9,4,6,1]=>{{1,10},{2,4,5,8},{3,6,7,9}}
[8,3,10,5,7,2,9,4,6,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,3,9,4,7,2,10,5,6,1]=>{{1,5,7,8,10},{2,3,6,9},{4}}
[9,3,5,7,1,10,4,6,8,2]=>{{1,2,3,5,6,8,9,10},{4,7}}
[10,4,6,8,2,9,3,5,7,1]=>{{1,10},{2,4,5,8},{3,6,7,9}}
[10,4,5,6,7,1,8,2,9,3]=>{{1,2,3,4,5,6,7,8,10},{9}}
[8,2,9,3,10,4,5,6,7,1]=>{{1,3,4,5,6,7,8,9,10},{2}}
[9,3,8,2,10,4,5,6,7,1]=>{{1,5,7,9,10},{2,3,4,6,8}}
[5,6,9,3,7,1,10,4,8,2]=>{{1,2,5,6,7,10},{3,4,8,9}}
[5,6,10,4,8,2,9,3,7,1]=>{{1,3,5,8,10},{2,6},{4},{7,9}}
[5,6,9,3,8,2,10,4,7,1]=>{{1,3,4,5,7,8,9,10},{2,6}}
[6,5,9,3,8,2,10,4,7,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,2,7,6,5,4,10,3,8,1]=>{{1,3,7,8,9,10},{2},{4,6},{5}}
[10,3,7,6,5,4,8,1,9,2]=>{{1,2,3,7,8,10},{4,6},{5},{9}}
[9,2,10,3,7,6,5,4,8,1]=>{{1,3,4,8,9,10},{2},{5,7},{6}}
[7,6,5,4,9,2,10,3,8,1]=>{{1,7,10},{2,6},{3,5,8,9},{4}}
[6,4,7,5,10,3,9,2,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,4,7,5,9,2,10,3,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,5,6,4,9,2,10,3,8,1]=>{{1,7,10},{2,3,5,6,8,9},{4}}
[6,5,7,4,9,2,10,3,8,1]=>{{1,2,3,5,6,7,8,9,10},{4}}
[5,6,7,3,8,4,9,1,10,2]=>{{1,5,8},{2,3,4,6,7,9,10}}
[5,6,7,3,8,4,10,2,9,1]=>{{1,2,3,4,5,6,7,8,10},{9}}
[5,6,8,4,7,3,10,2,9,1]=>{{1,5,7,10},{2,3,6,8},{4},{9}}
[6,5,8,4,7,3,10,2,9,1]=>{{1,2,3,5,6,7,8,10},{4},{9}}
[4,2,5,6,7,8,9,10,1,3]=>{{1,3,4,5,6,7,8,9,10},{2}}
[7,8,10,1,2,3,4,5,6,9]=>{{1,4,7},{2,5,8},{3,6,9,10}}
[4,5,6,7,8,10,1,2,3,9]=>{{1,4,7},{2,5,8},{3,6,9,10}}
[1,6,7,5,8,4,9,3,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,2,3,4,5,6,8,10,7,9]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[8,9,10,4,5,6,2,3,1,7]=>{{1,2,3,7,8,9,10},{4},{5},{6}}
[8,9,4,5,6,10,2,3,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,10,4,5,2,3,6,1,7]=>{{1,2,6,8,9},{3,7,10},{4},{5}}
[8,9,4,5,10,2,3,6,1,7]=>{{1,2,6,8,9},{3,4,5,7,10}}
[8,9,4,5,2,3,6,10,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,4,5,9,10,2,3,6,1,7]=>{{1,2,4,6,8,9},{3,5,7,10}}
[8,4,5,9,2,3,6,10,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,10,4,5,6,2,1,3,7]=>{{1,8},{2,3,7,9,10},{4},{5},{6}}
[8,9,4,5,6,10,2,1,3,7]=>{{1,8},{2,3,4,5,6,7,9,10}}
[8,9,10,4,5,2,6,1,3,7]=>{{1,8},{2,3,6,7,9,10},{4},{5}}
[8,9,4,5,10,2,6,1,3,7]=>{{1,8},{2,3,4,5,6,7,9,10}}
[8,9,4,5,2,6,10,1,3,7]=>{{1,8},{2,3,4,5,9},{6},{7,10}}
[8,4,5,9,10,2,6,1,3,7]=>{{1,8},{2,3,4,5,6,7,9,10}}
[8,4,5,9,2,6,10,1,3,7]=>{{1,8},{2,3,4,5,9},{6},{7,10}}
[8,9,10,4,5,2,1,3,6,7]=>{{1,3,7,8,10},{2,6,9},{4},{5}}
[8,9,4,5,10,2,1,3,6,7]=>{{1,3,4,5,7,8,10},{2,6,9}}
[8,9,4,5,2,10,1,3,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,4,5,2,1,3,6,10,7]=>{{1,6,8},{2,3,4,5,7,9,10}}
[8,4,5,9,10,2,1,3,6,7]=>{{1,3,5,7,8,10},{2,4,6,9}}
[8,4,5,9,2,10,1,3,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,4,5,9,2,1,3,6,10,7]=>{{1,6,8},{2,3,4,5,7,9,10}}
[8,9,10,4,2,5,6,1,3,7]=>{{1,8},{2,3,5,6,7,9,10},{4}}
[8,9,4,10,2,5,6,1,3,7]=>{{1,8},{2,3,4,5,6,7,9,10}}
[8,9,4,2,5,6,10,1,3,7]=>{{1,8},{2,3,4,9},{5},{6},{7,10}}
[8,4,9,10,2,5,6,1,3,7]=>{{1,8},{2,4,5,6,7,10},{3,9}}
[8,4,9,2,5,6,10,1,3,7]=>{{1,8},{2,4},{3,9},{5},{6},{7,10}}
[8,9,10,4,2,5,1,3,6,7]=>{{1,3,7,8,10},{2,5,6,9},{4}}
[8,9,4,10,2,5,1,3,6,7]=>{{1,3,4,7,8,10},{2,5,6,9}}
[8,9,4,2,5,10,1,3,6,7]=>{{1,2,3,4,6,7,8,9,10},{5}}
[8,9,4,2,5,1,3,6,10,7]=>{{1,6,8},{2,3,4,7,9,10},{5}}
[8,4,9,10,2,5,1,3,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,4,9,2,5,1,3,6,10,7]=>{{1,6,8},{2,4},{3,7,9,10},{5}}
[8,4,2,5,9,10,1,3,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,4,2,5,9,1,3,6,10,7]=>{{1,6,8},{2,3,4,5,7,9,10}}
[4,8,9,10,2,5,6,1,3,7]=>{{1,2,4,5,6,7,8,10},{3,9}}
[4,8,9,2,5,6,10,1,3,7]=>{{1,2,4,8},{3,9},{5},{6},{7,10}}
[4,8,9,10,2,5,1,3,6,7]=>{{1,4,7,10},{2,3,5,6,8,9}}
[4,8,9,2,5,10,1,3,6,7]=>{{1,2,3,4,6,7,8,9,10},{5}}
[4,8,9,2,5,1,3,6,10,7]=>{{1,2,4,6,8},{3,7,9,10},{5}}
[4,8,2,5,9,10,1,3,6,7]=>{{1,4,5,6,7,9,10},{2,3,8}}
[4,8,2,5,9,1,3,6,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,5,3,1,2,4,8,7,10,9]=>{{1,4,6},{2,5},{3},{7,8},{9,10}}
[8,7,5,3,1,2,4,6,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[10,9,7,5,3,1,2,4,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,5,3,1,2,4,6,9,8,10]=>{{1,4,6,7},{2,5},{3},{8,9},{10}}
[5,3,1,2,4,7,6,9,8,10]=>{{1,2,3,4,5},{6,7},{8,9},{10}}
[2,1,4,3,6,5,9,7,10,8]=>{{1,2},{3,4},{5,6},{7,8,9,10}}
[2,1,4,3,7,5,8,6,10,9]=>{{1,2},{3,4},{5,6,7,8},{9,10}}
[2,1,4,3,7,5,9,6,10,8]=>{{1,2},{3,4},{5,6,7,8,9,10}}
[2,1,4,3,8,5,9,6,10,7]=>{{1,2},{3,4},{5,6,8},{7,9,10}}
[2,1,5,3,6,4,8,7,10,9]=>{{1,2},{3,4,5,6},{7,8},{9,10}}
[2,1,5,3,6,4,9,7,10,8]=>{{1,2},{3,4,5,6},{7,8,9,10}}
[2,1,5,3,7,4,8,6,10,9]=>{{1,2},{3,4,5,6,7,8},{9,10}}
[2,1,5,3,7,4,9,6,10,8]=>{{1,2},{3,4,5,6,7,8,9,10}}
[2,1,5,3,8,4,9,6,10,7]=>{{1,2},{3,4,5,6,8},{7,9,10}}
[2,1,6,3,7,4,8,5,10,9]=>{{1,2},{3,4,6},{5,7,8},{9,10}}
[2,1,6,3,7,4,9,5,10,8]=>{{1,2},{3,4,6},{5,7,8,9,10}}
[2,1,6,3,8,4,9,5,10,7]=>{{1,2},{3,4,6},{5,8},{7,9,10}}
[2,1,7,3,8,4,9,5,10,6]=>{{1,2},{3,4,6,7,9,10},{5,8}}
[3,1,4,2,6,5,9,7,10,8]=>{{1,2,3,4},{5,6},{7,8,9,10}}
[3,1,4,2,7,5,8,6,10,9]=>{{1,2,3,4},{5,6,7,8},{9,10}}
[3,1,4,2,7,5,9,6,10,8]=>{{1,2,3,4},{5,6,7,8,9,10}}
[3,1,4,2,8,5,9,6,10,7]=>{{1,2,3,4},{5,6,8},{7,9,10}}
[3,1,5,2,6,4,9,7,10,8]=>{{1,2,3,4,5,6},{7,8,9,10}}
[3,1,5,2,8,4,9,6,10,7]=>{{1,2,3,4,5,6,8},{7,9,10}}
[3,1,6,2,7,4,8,5,10,9]=>{{1,2,3,4,6},{5,7,8},{9,10}}
[3,1,6,2,7,4,9,5,10,8]=>{{1,2,3,4,6},{5,7,8,9,10}}
[3,1,6,2,8,4,9,5,10,7]=>{{1,2,3,4,6},{5,8},{7,9,10}}
[3,1,7,2,8,4,9,5,10,6]=>{{1,2,3,4,6,7,9,10},{5,8}}
[4,1,5,2,6,3,9,7,10,8]=>{{1,2,4},{3,5,6},{7,8,9,10}}
[4,1,5,2,7,3,8,6,10,9]=>{{1,2,4},{3,5,6,7,8},{9,10}}
[4,1,5,2,7,3,9,6,10,8]=>{{1,2,4},{3,5,6,7,8,9,10}}
[4,1,5,2,8,3,9,6,10,7]=>{{1,2,4},{3,5,6,8},{7,9,10}}
[4,1,6,2,7,3,8,5,10,9]=>{{1,2,4},{3,6},{5,7,8},{9,10}}
[4,1,6,2,7,3,9,5,10,8]=>{{1,2,4},{3,6},{5,7,8,9,10}}
[4,1,6,2,8,3,9,5,10,7]=>{{1,2,4},{3,6},{5,8},{7,9,10}}
[4,1,7,2,8,3,9,5,10,6]=>{{1,2,4},{3,6,7,9,10},{5,8}}
[5,1,6,2,7,3,9,4,10,8]=>{{1,2,4,5,7,8,9,10},{3,6}}
[5,1,6,2,8,3,9,4,10,7]=>{{1,2,4,5,8},{3,6},{7,9,10}}
[5,1,7,2,8,3,9,4,10,6]=>{{1,2,4,5,8},{3,6,7,9,10}}
[9,3,4,5,6,7,1,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,7,2,8,3,9,4,10,5,6]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,7,2,8,3,9,10,4,5,6]=>{{1},{2,3,5,6,7,9,10},{4,8}}
[1,7,2,8,9,3,4,10,5,6]=>{{1},{2,3,4,6,7,8,10},{5,9}}
[1,7,2,8,9,3,10,4,5,6]=>{{1},{2,3,6,7,10},{4,8},{5,9}}
[1,7,2,8,9,10,3,4,5,6]=>{{1},{2,3,7},{4,8},{5,9},{6,10}}
[1,7,8,2,3,9,4,10,5,6]=>{{1},{2,4,7},{3,5,6,8,9,10}}
[1,7,8,2,3,9,10,4,5,6]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,7,8,2,9,3,4,10,5,6]=>{{1},{2,4,7},{3,6,8,10},{5,9}}
[1,7,8,2,9,3,10,4,5,6]=>{{1},{2,3,4,6,7,8,10},{5,9}}
[1,7,8,2,9,10,3,4,5,6]=>{{1},{2,3,4,7,8},{5,9},{6,10}}
[1,7,8,9,2,3,4,10,5,6]=>{{1},{2,4,5,7,9},{3,6,8,10}}
[1,7,8,9,2,3,10,4,5,6]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,7,8,9,2,10,3,4,5,6]=>{{1},{2,3,4,5,7,8,9},{6,10}}
[7,1,2,8,3,9,4,10,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,1,2,8,3,9,10,4,5,6]=>{{1,2,3,5,6,7,9,10},{4,8}}
[7,1,2,8,9,3,4,10,5,6]=>{{1,2,3,4,6,7,8,10},{5,9}}
[7,1,2,8,9,3,10,4,5,6]=>{{1,2,3,6,7,10},{4,8},{5,9}}
[7,1,2,8,9,10,3,4,5,6]=>{{1,2,3,7},{4,8},{5,9},{6,10}}
[7,1,8,2,3,9,4,10,5,6]=>{{1,2,4,7},{3,5,6,8,9,10}}
[7,1,8,2,3,9,10,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,1,8,2,9,3,4,10,5,6]=>{{1,2,4,7},{3,6,8,10},{5,9}}
[7,1,8,2,9,10,3,4,5,6]=>{{1,2,3,4,7,8},{5,9},{6,10}}
[7,1,8,9,2,3,4,10,5,6]=>{{1,2,4,5,7,9},{3,6,8,10}}
[7,1,8,9,2,3,10,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,1,8,9,2,10,3,4,5,6]=>{{1,2,3,4,5,7,8,9},{6,10}}
[7,1,8,9,10,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,1,2,3,9,4,10,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,1,2,3,9,10,4,5,6]=>{{1,3,5,6,7,9,10},{2,4,8}}
[7,8,1,2,9,3,4,10,5,6]=>{{1,2,3,4,6,7,8,10},{5,9}}
[7,8,1,2,9,3,10,4,5,6]=>{{1,3,6,7,10},{2,4,8},{5,9}}
[7,8,1,2,9,10,3,4,5,6]=>{{1,3,7},{2,4,8},{5,9},{6,10}}
[7,8,1,9,2,3,4,10,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,1,9,2,3,10,4,5,6]=>{{1,3,6,7,10},{2,4,5,8,9}}
[7,8,1,9,2,10,3,4,5,6]=>{{1,3,7},{2,4,5,8,9},{6,10}}
[7,8,1,9,10,2,3,4,5,6]=>{{1,3,7},{2,4,5,6,8,9,10}}
[7,8,9,1,2,3,4,10,5,6]=>{{1,4,7},{2,3,5,6,8,9,10}}
[7,8,9,1,2,3,10,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,9,1,2,10,3,4,5,6]=>{{1,2,3,4,5,7,8,9},{6,10}}
[7,8,9,1,10,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,8,9,10,7,6,5,4,3,2]=>{{1},{2,4,8,10},{3,9},{5,7},{6}}
[1,7,8,9,10,6,5,4,3,2]=>{{1},{2,5,7,10},{3,4,8,9},{6}}
[1,6,7,8,9,10,5,4,3,2]=>{{1},{2,6,10},{3,5,7,9},{4,8}}
[1,5,6,7,8,9,10,4,3,2]=>{{1},{2,4,5,7,8,10},{3,6,9}}
[1,4,5,6,7,8,9,10,3,2]=>{{1},{2,4,6,8,10},{3,5,7,9}}
[7,2,8,9,10,1,3,4,5,6]=>{{1,3,4,5,6,7,8,9,10},{2}}
[9,10,6,4,2,1,3,5,8,7]=>{{1,2,3,5,6,7,8,9,10},{4}}
[10,7,8,4,2,1,3,6,5,9]=>{{1,2,3,5,6,7,8,9,10},{4}}
[9,7,10,4,2,1,3,6,8,5]=>{{1,6,8,9},{2,3,5,7,10},{4}}
[8,9,10,4,2,1,3,7,6,5]=>{{1,2,3,5,6,7,8,9,10},{4}}
[10,8,5,6,2,1,4,3,7,9]=>{{1,4,6,7,9,10},{2,3,5,8}}
[9,10,5,6,2,1,4,3,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,7,5,8,2,1,4,6,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,7,5,10,2,1,4,6,8,3]=>{{1,6,8,9},{2,3,4,5,7,10}}
[8,9,5,10,2,1,4,7,6,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,6,7,8,2,1,5,4,3,9]=>{{1,2,3,5,6,7,9,10},{4,8}}
[9,6,7,10,2,1,5,4,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,6,9,10,2,1,5,7,4,3]=>{{1,2,5,6,7,8},{3,4,9,10}}
[7,8,9,10,2,1,6,5,4,3]=>{{1,6,7},{2,5,8},{3,4,9,10}}
[10,8,6,3,4,2,1,5,7,9]=>{{1,7,9,10},{2,3,4,5,6,8}}
[9,10,6,3,4,2,1,5,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,7,8,3,4,2,1,6,5,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,7,10,3,4,2,1,6,8,5]=>{{1,2,6,7,8,9},{3,4,5,10}}
[8,9,10,3,4,2,1,7,6,5]=>{{1,7,8},{2,6,9},{3,4,5,10}}
[10,8,5,3,6,2,4,1,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,10,5,3,6,2,4,1,8,7]=>{{1,8,9},{2,3,4,5,6,7,10}}
[10,7,5,3,8,2,4,6,1,9]=>{{1,9,10},{2,3,4,5,6,7,8}}
[9,7,5,3,10,2,4,6,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,5,3,10,2,4,7,6,1]=>{{1,3,4,5,7,8,10},{2,6,9}}
[10,6,7,3,8,2,5,4,1,9]=>{{1,9,10},{2,6},{3,4,5,7,8}}
[9,6,7,3,10,2,5,4,8,1]=>{{1,3,4,5,7,8,9,10},{2,6}}
[8,6,9,3,10,2,5,7,4,1]=>{{1,5,7,8,10},{2,6},{3,4,9}}
[7,8,9,3,10,2,6,5,4,1]=>{{1,2,5,6,7,8,10},{3,4,9}}
[10,8,4,5,6,3,2,1,7,9]=>{{1,2,7,8,9,10},{3,4,5,6}}
[9,10,4,5,6,3,2,1,8,7]=>{{1,8,9},{2,7,10},{3,4,5,6}}
[10,7,4,5,8,3,2,6,1,9]=>{{1,9,10},{2,7},{3,4,5,6,8}}
[9,7,4,5,10,3,2,6,8,1]=>{{1,3,4,5,6,8,9,10},{2,7}}
[8,9,4,5,10,3,2,7,6,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,6,4,7,8,3,5,2,1,9]=>{{1,9,10},{2,3,4,5,6,7,8}}
[9,6,4,7,10,3,5,2,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,6,4,9,10,3,5,7,2,1]=>{{1,5,7,8,10},{2,3,4,6,9}}
[7,8,4,9,10,3,6,5,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,5,6,7,8,4,3,2,1,9]=>{{1,9,10},{2,5,8},{3,4,6,7}}
[9,5,6,7,10,4,3,2,8,1]=>{{1,2,5,8,9,10},{3,4,6,7}}
[8,5,6,9,10,4,3,7,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,5,8,9,10,4,6,3,2,1]=>{{1,2,4,5,6,7,9,10},{3,8}}
[2,10,4,5,6,7,9,1,3,8]=>{{1,2,8,10},{3,4,5,6,7,9}}
[10,3,4,5,6,7,1,9,2,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,8,6,4,2,1,3,5,7]=>{{1,7,10},{2,4,5,6,9},{3,8}}
[10,8,7,6,4,2,1,3,5,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,7,9,6,4,2,1,3,8,5]=>{{1,2,4,5,6,7,10},{3,8,9}}
[10,9,8,7,6,4,2,1,3,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,6,5,4,2,1,3,7,9]=>{{1,7,9,10},{2,3,6,8},{4,5}}
[10,9,8,6,5,4,2,1,3,7]=>{{1,2,3,7,8,9,10},{4,6},{5}}
[10,8,5,7,4,2,1,6,3,9]=>{{1,3,4,5,7,9,10},{2,6,8}}
[10,5,9,7,4,2,1,6,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,8,5,7,4,2,1,6,3]=>{{1,3,8,10},{2,4,5,6,7,9}}
[10,8,7,6,5,4,2,1,3,9]=>{{1,2,3,7,8,9,10},{4,6},{5}}
[10,7,9,6,5,4,2,1,8,3]=>{{1,3,8,9,10},{2,7},{4,6},{5}}
[10,6,9,8,5,7,2,1,4,3]=>{{1,3,4,8,9,10},{2,6,7},{5}}
[10,8,6,4,3,2,1,5,7,9]=>{{1,7,9,10},{2,3,5,6,8},{4}}
[10,9,8,6,4,3,2,1,5,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,7,6,4,3,2,1,5,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,7,9,6,4,3,2,1,8,5]=>{{1,3,4,5,6,8,9,10},{2,7}}
[10,8,6,3,5,2,4,1,7,9]=>{{1,2,3,4,6,7,8,9,10},{5}}
[10,9,8,6,3,5,2,4,1,7]=>{{1,2,7,9,10},{3,4,5,6,8}}
[10,8,3,7,5,2,4,6,1,9]=>{{1,9,10},{2,6,8},{3},{4,7},{5}}
[10,3,9,7,5,2,4,6,8,1]=>{{1,10},{2,3,6,8,9},{4,7},{5}}
[10,9,8,3,7,5,2,4,6,1]=>{{1,10},{2,5,6,7,9},{3,4,8}}
[10,8,7,6,3,5,2,4,1,9]=>{{1,9,10},{2,3,4,5,6,7,8}}
[10,7,9,6,3,5,2,4,8,1]=>{{1,10},{2,7},{3,4,5,6,8,9}}
[10,9,3,8,6,5,2,7,4,1]=>{{1,10},{2,4,7,8,9},{3},{5,6}}
[10,9,8,7,6,3,5,2,4,1]=>{{1,10},{2,3,4,5,6,7,8,9}}
[10,8,6,5,4,3,2,1,7,9]=>{{1,2,7,8,9,10},{3,6},{4,5}}
[10,8,5,7,4,3,2,6,1,9]=>{{1,9,10},{2,3,4,5,6,7,8}}
[10,5,9,7,4,3,2,6,8,1]=>{{1,10},{2,4,5,7},{3,6,8,9}}
[10,9,8,5,7,4,3,2,6,1]=>{{1,10},{2,3,4,5,6,7,8,9}}
[10,8,4,7,6,3,5,2,1,9]=>{{1,9,10},{2,8},{3,4,5,6,7}}
[10,4,9,7,6,3,5,2,8,1]=>{{1,10},{2,3,4,5,6,7,8,9}}
[10,4,9,6,8,3,5,7,2,1]=>{{1,10},{2,3,4,6,9},{5,7,8}}
[10,9,8,4,7,6,3,5,2,1]=>{{1,10},{2,9},{3,5,7,8},{4},{6}}
[10,7,9,6,5,4,3,2,8,1]=>{{1,10},{2,3,7,8,9},{4,6},{5}}
[10,6,9,8,5,4,3,7,2,1]=>{{1,10},{2,3,4,6,7,8,9},{5}}
[10,5,9,8,7,4,6,3,2,1]=>{{1,10},{2,3,4,5,6,7,8,9}}
[3,2,8,9,10,1,4,5,6,7]=>{{1,3,4,5,6,7,8,9,10},{2}}
[2,3,4,5,8,9,10,1,6,7]=>{{1,2,3,4,5,8},{6,9},{7,10}}
[2,3,4,7,8,9,10,1,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,6,7,8,9,10,1,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,5,6,7,8,9,10,1,3,4]=>{{1,2,5,8},{3,6,9},{4,7,10}}
[1,2,7,3,8,4,9,5,10,6]=>{{1},{2},{3,4,6,7,9,10},{5,8}}
[4,1,2,3,6,5,8,7,10,9]=>{{1,2,3,4},{5,6},{7,8},{9,10}}
[7,1,2,3,4,5,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,5,6,7,1,8,2,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[1,4,5,6,10,7,8,2,9,3]=>{{1},{2,4,6,7,8},{3,5,10},{9}}
[2,4,5,6,10,7,1,8,3,9]=>{{1,2,4,6,7},{3,5,9,10},{8}}
[3,4,5,6,8,7,1,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,5,6,7,10,8,1,9,2,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,4,5,9,6,7,2,8,10,3]=>{{1},{2,3,4,5,6,7,9,10},{8}}
[2,3,4,5,6,7,1,9,8,10]=>{{1,2,3,4,5,6,7},{8,9},{10}}
[2,3,4,5,1,7,6,9,8,10]=>{{1,2,3,4,5},{6,7},{8,9},{10}}
[3,4,5,6,7,8,10,1,9,2]=>{{1,2,3,4,5,6,7,8,10},{9}}
[7,8,9,6,1,2,3,4,10,5]=>{{1,3,5,7,9,10},{2,4,6,8}}
[2,8,9,10,7,1,3,4,5,6]=>{{1,2,4,6,8,10},{3,5,7,9}}
[8,9,7,5,6,1,2,3,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,9,10,8,6,7,1,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,9,5,1,2,3,4,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,9,1,6,2,3,4,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,8,9,10,6,1,3,4,5,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,8,9,10,1,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,2,3,5,6,7,8,9,10,1]=>{{1,4,5,6,7,8,9,10},{2},{3}}
[9,10,6,7,4,5,2,3,1,8]=>{{1,9},{2,3,4,5,6,7,8,10}}
[8,9,4,5,10,1,2,3,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,4,3,9,10,1,2,5,6,7]=>{{1,2,4,5,6,7,8,9,10},{3}}
[9,6,10,1,3,7,8,2,4,5]=>{{1,4,9},{2,6,7,8},{3,5,10}}
[9,10,6,7,4,5,1,2,3,8]=>{{1,3,4,5,6,7,9},{2,8,10}}
[9,6,4,10,3,7,1,2,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,1,8,9,6,7,4,5,2,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,6,1,4,9,3,7,2,5]=>{{1,4,5,10},{2,3,6,7,8,9}}
[10,8,6,5,4,1,3,9,2,7]=>{{1,3,6,7,10},{2,8,9},{4,5}}
[10,8,7,6,5,4,3,1,2,9]=>{{1,2,8,9,10},{3,7},{4,6},{5}}
[1,2,3,4,6,5,7,8,9,10]=>{{1},{2},{3},{4},{5,6},{7},{8},{9},{10}}
[1,2,3,4,5,6,8,7,9,10]=>{{1},{2},{3},{4},{5},{6},{7,8},{9},{10}}
[10,7,6,5,4,3,2,1,8,9]=>{{1,8,9,10},{2,7},{3,6},{4,5}}
[10,1,2,3,4,5,6,9,8,7]=>{{1,2,3,4,5,6,7,10},{8,9}}
[10,1,2,3,4,5,9,7,8,6]=>{{1,2,3,4,5,6,10},{7,8,9}}
[10,1,2,3,9,5,6,7,8,4]=>{{1,2,3,4,10},{5,6,7,8,9}}
[10,1,2,9,4,5,6,7,8,3]=>{{1,2,3,10},{4,5,6,7,8,9}}
[3,4,5,6,7,9,10,1,8,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,5,7,8,9,10,1,6,2]=>{{1,3,5,8},{2,4,7,10},{6,9}}
[3,4,6,7,8,9,10,1,5,2]=>{{1,3,5,6,8,9},{2,4,7,10}}
[4,5,6,7,8,9,10,1,3,2]=>{{1,2,4,5,7,8,10},{3,6,9}}
[6,4,5,7,3,8,2,9,1,10]=>{{1,6,8,9},{2,4,7},{3,5},{10}}
[9,8,7,5,6,4,3,2,10,1]=>{{1,9,10},{2,8},{3,7},{4,5,6}}
[2,3,4,5,6,9,10,8,7,1]=>{{1,2,3,4,5,6,7,9,10},{8}}
[2,3,4,5,8,9,10,7,6,1]=>{{1,2,3,4,5,7,8,10},{6,9}}
[2,3,4,7,8,9,10,6,5,1]=>{{1,2,3,4,7,10},{5,6,8,9}}
[2,3,6,7,8,9,10,5,4,1]=>{{1,2,3,4,6,7,9,10},{5,8}}
[2,5,6,7,8,9,10,4,3,1]=>{{1,2,4,5,7,8,10},{3,6,9}}
[9,10,2,4,6,8,1,3,5,7]=>{{1,2,3,5,6,7,8,9,10},{4}}
[7,8,2,4,6,10,1,3,5,9]=>{{1,7},{2,3,8},{4},{5,6,9,10}}
[9,7,10,2,4,6,8,1,3,5]=>{{1,2,3,4,5,7,8,9,10},{6}}
[8,9,10,7,2,4,6,1,3,5]=>{{1,8},{2,3,5,9,10},{4,6,7}}
[5,6,2,4,8,10,1,3,7,9]=>{{1,2,3,5,6,7,8,9,10},{4}}
[5,6,9,10,2,4,8,1,3,7]=>{{1,2,4,5,6,7,8,10},{3,9}}
[7,5,8,2,4,6,10,1,3,9]=>{{1,3,7,8,9,10},{2,4,5},{6}}
[7,9,5,10,2,4,6,8,1,3]=>{{1,2,3,4,5,6,7,9,10},{8}}
[5,8,9,10,7,2,4,6,1,3]=>{{1,3,4,5,7,9,10},{2,6,8}}
[6,7,8,5,2,4,10,1,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,6,7,5,10,2,4,8,1,3]=>{{1,9},{2,6},{3,4,5,7,10},{8}}
[8,9,6,10,5,7,2,4,1,3]=>{{1,2,3,4,6,7,8,9,10},{5}}
[7,8,9,10,6,5,2,4,1,3]=>{{1,2,3,4,7,8,9,10},{5,6}}
[3,4,2,6,8,10,1,5,7,9]=>{{1,2,3,4,6,7,9,10},{5,8}}
[3,4,9,10,2,6,8,1,5,7]=>{{1,2,3,4,5,7,8,9,10},{6}}
[3,4,7,8,2,6,10,1,5,9]=>{{1,2,3,4,5,7,8,9,10},{6}}
[9,3,4,7,10,2,6,8,1,5]=>{{1,9},{2,3,4,6,7},{5,10},{8}}
[8,9,10,3,4,7,2,6,1,5]=>{{1,2,6,7,8,9},{3,4,5,10}}
[5,3,6,2,4,8,10,1,7,9]=>{{1,2,3,4,5,6,8},{7,9,10}}
[5,3,6,9,10,2,4,8,1,7]=>{{1,4,5,7,9,10},{2,3,6},{8}}
[5,7,3,8,2,4,6,10,1,9]=>{{1,2,4,5,6,7,8,9,10},{3}}
[5,7,9,3,10,2,4,6,8,1]=>{{1,5,10},{2,3,4,6,7,8,9}}
[8,5,9,10,3,7,2,4,6,1]=>{{1,4,8,10},{2,3,5,6,7,9}}
[3,6,7,8,5,2,4,10,1,9]=>{{1,3,4,7,8,9,10},{2,6},{5}}
[9,3,6,7,5,10,2,4,8,1]=>{{1,2,3,4,6,7,8,9,10},{5}}
[6,8,3,9,10,5,7,2,4,1]=>{{1,5,6,10},{2,8},{3},{4,9},{7}}
[7,8,9,10,3,6,5,2,4,1]=>{{1,3,4,5,7,9,10},{2,8},{6}}
[4,5,6,3,2,8,10,1,7,9]=>{{1,3,4,6,8},{2,5},{7,9,10}}
[4,5,6,3,9,10,2,8,1,7]=>{{1,2,3,4,5,6,7,9,10},{8}}
[7,4,5,3,8,2,6,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,4,5,9,3,10,2,6,8,1]=>{{1,2,4,6,7,8,9,10},{3,5}}
[4,8,5,9,10,3,7,2,6,1]=>{{1,3,4,5,6,9,10},{2,8},{7}}
[6,7,4,8,3,5,2,10,1,9]=>{{1,3,4,5,6,8,9,10},{2,7}}
[6,7,9,4,3,5,10,2,8,1]=>{{1,2,3,5,6,7,8,9,10},{4}}
[8,6,9,4,10,3,5,7,2,1]=>{{1,5,7,8,10},{2,3,6,9},{4}}
[7,4,8,9,10,6,3,5,2,1]=>{{1,3,5,7,8,10},{2,4,9},{6}}
[5,6,7,8,4,3,2,10,1,9]=>{{1,4,5,8,9,10},{2,3,6,7}}
[9,5,6,7,4,3,10,2,8,1]=>{{1,2,4,5,7,8,9,10},{3,6}}
[8,9,5,6,4,10,3,7,2,1]=>{{1,3,4,5,6,7,8,10},{2,9}}
[7,8,9,5,10,4,6,3,2,1]=>{{1,4,5,6,7,10},{2,3,8,9}}
[1,2,4,5,6,8,10,9,3,7]=>{{1},{2},{3,4,5,6,8,9},{7,10}}
[1,2,3,5,7,8,10,6,9,4]=>{{1},{2},{3},{4,5,7,10},{6,8},{9}}
[1,2,4,5,7,8,10,3,9,6]=>{{1},{2},{3,4,5,6,7,8,10},{9}}
[1,2,4,6,7,5,10,8,3,9]=>{{1},{2},{3,4,5,6,7,9,10},{8}}
[1,3,4,2,7,8,10,5,9,6]=>{{1},{2,3,4},{5,6,7,8,10},{9}}
[1,3,4,6,7,2,10,8,5,9]=>{{1},{2,3,4,6},{5,7,9,10},{8}}
[1,2,3,5,6,9,8,10,7,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[1,2,4,5,6,9,8,10,3,7]=>{{1},{2},{3,4,5,6,9},{7,8,10}}
[1,2,3,5,7,9,6,10,8,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[1,2,4,5,7,9,3,10,8,6]=>{{1},{2},{3,4,5,7},{6,8,9,10}}
[1,2,4,6,5,9,7,10,3,8]=>{{1},{2},{3,4,6,9},{5},{7},{8,10}}
[1,3,4,2,7,9,5,10,8,6]=>{{1},{2,3,4},{5,7},{6,8,9,10}}
[1,3,4,6,2,9,7,10,5,8]=>{{1},{2,3,4,5,6,9},{7},{8,10}}
[1,2,3,5,8,7,9,6,10,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[1,2,4,5,8,7,9,3,10,6]=>{{1},{2},{3,4,5,8},{6,7,9,10}}
[1,2,4,6,8,5,9,3,10,7]=>{{1},{2},{3,4,5,6,8},{7,9,10}}
[1,2,4,7,6,8,5,9,3,10]=>{{1},{2},{3,4,5,6,7,8,9},{10}}
[1,3,4,2,8,7,9,5,10,6]=>{{1},{2,3,4},{5,8},{6,7,9,10}}
[1,3,4,6,8,2,9,5,10,7]=>{{1},{2,3,4,6},{5,8},{7,9,10}}
[1,3,4,7,6,8,2,9,5,10]=>{{1},{2,3,4,7},{5,6,8,9},{10}}
[1,2,3,6,5,9,7,10,8,4]=>{{1},{2},{3},{4,6,8,9,10},{5},{7}}
[1,2,4,6,3,9,7,10,8,5]=>{{1},{2},{3,4,5,6,8,9,10},{7}}
[1,2,5,4,6,9,7,10,3,8]=>{{1},{2},{3,5,6,9},{4},{7},{8,10}}
[1,3,2,6,4,9,7,10,8,5]=>{{1},{2,3},{4,5,6,8,9,10},{7}}
[1,3,5,2,6,9,7,10,4,8]=>{{1},{2,3,4,5,6,9},{7},{8,10}}
[1,2,3,6,8,5,9,7,10,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[1,2,4,6,8,3,9,7,10,5]=>{{1},{2},{3,4,6},{5,7,8,9,10}}
[1,2,5,4,8,6,9,3,10,7]=>{{1},{2},{3,5,8},{4},{6},{7,9,10}}
[1,2,5,7,4,8,6,9,3,10]=>{{1},{2},{3,4,5,6,7,8,9},{10}}
[1,3,2,6,8,4,9,7,10,5]=>{{1},{2,3},{4,6},{5,7,8,9,10}}
[1,3,5,2,8,6,9,4,10,7]=>{{1},{2,3,4,5,8},{6},{7,9,10}}
[1,3,5,7,2,8,6,9,4,10]=>{{1},{2,3,5},{4,6,7,8,9},{10}}
[1,4,3,5,8,2,9,6,10,7]=>{{1},{2,4,5,6,8},{3},{7,9,10}}
[1,4,3,7,5,8,2,9,6,10]=>{{1},{2,4,7},{3},{5},{6,8,9},{10}}
[2,1,3,6,4,9,7,10,8,5]=>{{1,2},{3},{4,5,6,8,9,10},{7}}
[2,1,5,3,6,9,7,10,4,8]=>{{1,2},{3,4,5,6,9},{7},{8,10}}
[2,1,3,6,8,4,9,7,10,5]=>{{1,2},{3},{4,6},{5,7,8,9,10}}
[2,1,5,3,8,6,9,4,10,7]=>{{1,2},{3,4,5,8},{6},{7,9,10}}
[2,1,5,7,3,8,6,9,4,10]=>{{1,2},{3,5},{4,6,7,8,9},{10}}
[2,4,1,5,8,3,9,6,10,7]=>{{1,2,3,4,5,6,8},{7,9,10}}
[2,4,1,7,5,8,3,9,6,10]=>{{1,2,3,4,7},{5},{6,8,9},{10}}
[5,6,1,2,3,7,8,9,10,4]=>{{1,3,5},{2,4,6,7,8,9,10}}
[2,5,1,3,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,2,1,5,6,7,8,9,10,4]=>{{1,3},{2},{4,5,6,7,8,9,10}}
[6,7,8,1,2,3,4,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,6,7,1,3,4,8,9,10,5]=>{{1,2,4,6},{3,5,7,8,9,10}}
[6,3,4,1,2,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,2,6,1,4,7,8,9,10,5]=>{{1,3,4,5,6,7,8,9,10},{2}}
[4,3,2,1,6,7,8,9,10,5]=>{{1,4},{2,3},{5,6,7,8,9,10}}
[2,7,8,9,1,3,4,5,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,3,4,8,1,2,5,9,10,6]=>{{1,5,7},{2,3,4,6,8,9,10}}
[3,2,7,8,1,4,5,9,10,6]=>{{1,3,5,7},{2},{4,6,8,9,10}}
[4,7,2,5,1,3,8,9,10,6]=>{{1,4,5},{2,3,6,7,8,9,10}}
[4,3,2,7,1,5,8,9,10,6]=>{{1,4,5,6,7,8,9,10},{2,3}}
[5,4,3,2,1,7,8,9,10,6]=>{{1,5},{2,4},{3},{6,7,8,9,10}}
[8,3,4,9,10,1,2,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,9,4,5,6,1,2,3,10,7]=>{{1,3,4,5,6,8},{2,7,9,10}}
[4,3,2,8,9,1,5,6,10,7]=>{{1,4,6,8},{2,3},{5,7,9,10}}
[8,5,6,3,4,1,2,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,3,8,2,6,1,4,9,10,7]=>{{1,5,6},{2,3,4,7,8,9,10}}
[5,4,3,2,8,1,6,9,10,7]=>{{1,5,6,7,8,9,10},{2,4},{3}}
[6,5,4,3,2,1,8,9,10,7]=>{{1,6},{2,5},{3,4},{7,8,9,10}}
[5,9,10,2,6,7,1,3,4,8]=>{{1,5,6,7},{2,4,9},{3,8,10}}
[9,5,6,3,4,10,1,2,7,8]=>{{1,7,9},{2,3,4,5,6,8,10}}
[5,3,9,2,6,10,1,4,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,4,3,2,9,10,1,6,7,8]=>{{1,5,7,9},{2,4},{3},{6,8,10}}
[6,9,4,7,2,5,1,3,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,4,3,9,2,7,1,5,10,8]=>{{1,6,7},{2,4,5,8,9,10},{3}}
[6,5,4,3,2,9,1,7,10,8]=>{{1,6,7,8,9,10},{2,5},{3,4}}
[7,6,5,4,3,2,1,9,10,8]=>{{1,7},{2,6},{3,5},{4},{8,9,10}}
[10,7,8,5,6,3,4,1,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,5,10,3,8,2,6,1,4,9]=>{{1,2,5,6,7,8},{3,4,9,10}}
[7,5,4,3,10,2,8,1,6,9]=>{{1,7,8},{2,5,6,9,10},{3,4}}
[7,6,5,4,3,2,10,1,8,9]=>{{1,7,8,9,10},{2,6},{3,5},{4}}
[2,1,8,7,4,3,6,5,10,9]=>{{1,2},{3,4,5,6,7,8},{9,10}}
[2,1,4,3,6,5,7,9,10,8]=>{{1,2},{3,4},{5,6},{7},{8,9,10}}
[2,1,4,3,5,7,8,6,10,9]=>{{1,2},{3,4},{5},{6,7,8},{9,10}}
[2,1,4,3,5,7,6,9,10,8]=>{{1,2},{3,4},{5},{6,7},{8,9,10}}
[2,1,4,3,5,6,8,9,10,7]=>{{1,2},{3,4},{5},{6},{7,8,9,10}}
[2,1,3,5,6,4,8,7,10,9]=>{{1,2},{3},{4,5,6},{7,8},{9,10}}
[2,1,3,5,6,4,7,9,10,8]=>{{1,2},{3},{4,5,6},{7},{8,9,10}}
[2,1,3,5,4,7,8,6,10,9]=>{{1,2},{3},{4,5},{6,7,8},{9,10}}
[2,1,3,5,4,7,6,9,10,8]=>{{1,2},{3},{4,5},{6,7},{8,9,10}}
[2,1,3,5,4,6,8,9,10,7]=>{{1,2},{3},{4,5},{6},{7,8,9,10}}
[2,1,3,4,6,7,8,5,10,9]=>{{1,2},{3},{4},{5,6,7,8},{9,10}}
[2,1,3,4,6,7,5,9,10,8]=>{{1,2},{3},{4},{5,6,7},{8,9,10}}
[2,1,3,4,6,5,8,9,10,7]=>{{1,2},{3},{4},{5,6},{7,8,9,10}}
[2,1,3,4,5,7,8,9,10,6]=>{{1,2},{3},{4},{5},{6,7,8,9,10}}
[1,3,4,2,6,5,7,9,10,8]=>{{1},{2,3,4},{5,6},{7},{8,9,10}}
[1,3,4,2,5,7,8,6,10,9]=>{{1},{2,3,4},{5},{6,7,8},{9,10}}
[1,3,4,2,5,7,6,9,10,8]=>{{1},{2,3,4},{5},{6,7},{8,9,10}}
[1,3,4,2,5,6,8,9,10,7]=>{{1},{2,3,4},{5},{6},{7,8,9,10}}
[1,3,2,5,6,4,8,7,10,9]=>{{1},{2,3},{4,5,6},{7,8},{9,10}}
[1,3,2,5,6,4,7,9,10,8]=>{{1},{2,3},{4,5,6},{7},{8,9,10}}
[1,3,2,5,4,7,8,6,10,9]=>{{1},{2,3},{4,5},{6,7,8},{9,10}}
[1,3,2,5,4,7,6,9,10,8]=>{{1},{2,3},{4,5},{6,7},{8,9,10}}
[1,3,2,5,4,6,8,9,10,7]=>{{1},{2,3},{4,5},{6},{7,8,9,10}}
[1,3,2,4,6,7,8,5,10,9]=>{{1},{2,3},{4},{5,6,7,8},{9,10}}
[1,3,2,4,6,7,5,9,10,8]=>{{1},{2,3},{4},{5,6,7},{8,9,10}}
[1,3,2,4,6,5,8,9,10,7]=>{{1},{2,3},{4},{5,6},{7,8,9,10}}
[1,3,2,4,5,7,8,9,10,6]=>{{1},{2,3},{4},{5},{6,7,8,9,10}}
[1,2,4,5,6,3,8,7,10,9]=>{{1},{2},{3,4,5,6},{7,8},{9,10}}
[1,2,4,5,6,3,7,9,10,8]=>{{1},{2},{3,4,5,6},{7},{8,9,10}}
[1,2,4,5,3,7,8,6,10,9]=>{{1},{2},{3,4,5},{6,7,8},{9,10}}
[1,2,4,5,3,7,6,9,10,8]=>{{1},{2},{3,4,5},{6,7},{8,9,10}}
[1,2,4,5,3,6,8,9,10,7]=>{{1},{2},{3,4,5},{6},{7,8,9,10}}
[1,2,4,3,6,7,8,5,10,9]=>{{1},{2},{3,4},{5,6,7,8},{9,10}}
[1,2,4,3,6,7,5,9,10,8]=>{{1},{2},{3,4},{5,6,7},{8,9,10}}
[1,2,4,3,6,5,8,9,10,7]=>{{1},{2},{3,4},{5,6},{7,8,9,10}}
[1,2,4,3,5,7,8,9,10,6]=>{{1},{2},{3,4},{5},{6,7,8,9,10}}
[1,2,3,5,6,7,8,4,10,9]=>{{1},{2},{3},{4,5,6,7,8},{9,10}}
[1,2,3,5,6,7,4,9,10,8]=>{{1},{2},{3},{4,5,6,7},{8,9,10}}
[1,2,3,5,6,4,8,9,10,7]=>{{1},{2},{3},{4,5,6},{7,8,9,10}}
[1,2,3,5,4,7,8,9,10,6]=>{{1},{2},{3},{4,5},{6,7,8,9,10}}
[2,3,4,5,6,10,8,9,7,1]=>{{1,2,3,4,5,6,10},{7,8,9}}
[2,3,4,5,10,7,8,9,6,1]=>{{1,2,3,4,5,10},{6,7,8,9}}
[2,3,4,10,6,7,8,9,5,1]=>{{1,2,3,4,10},{5,6,7,8,9}}
[2,3,10,5,6,7,8,9,4,1]=>{{1,2,3,10},{4,5,6,7,8,9}}
[2,10,4,5,6,7,8,9,3,1]=>{{1,2,10},{3,4,5,6,7,8,9}}
[10,3,4,5,6,7,8,9,2,1]=>{{1,10},{2,3,4,5,6,7,8,9}}
[6,5,7,4,8,3,10,1,9,2]=>{{1,2,3,5,6,7,8,10},{4},{9}}
[6,5,7,4,10,1,9,2,8,3]=>{{1,6},{2,3,5,7,8,9,10},{4}}
[6,5,10,1,9,2,8,3,7,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,10,1,9,2,8,3,7,4,6]=>{{1,2,3,5,6,7,8,10},{4,9}}
[5,6,4,10,1,9,2,8,3,7]=>{{1,5},{2,3,4,6,7,9,10},{8}}
[5,6,4,7,3,10,1,9,2,8]=>{{1,3,4,5,7},{2,6,8,9,10}}
[5,6,4,7,3,8,2,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,10,1,3,4,5,6,9,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,9,1,3,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,3,1,2,4,5,6,9,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,1,10,2,4,5,6,9,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,3,1,2,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,1,9,2,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,3,4,5,6,7,8,1,2]=>{{1,2,9,10},{3},{4},{5},{6},{7},{8}}
[10,9,2,3,4,5,6,7,1,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,4,5,6,7,8,9,2,1,3]=>{{1,3,5,7,9,10},{2,4,6,8}}
[10,3,4,5,6,7,8,2,1,9]=>{{1,9,10},{2,3,4,5,6,7,8}}
[1,8,5,2,9,6,3,10,7,4]=>{{1},{2,4,8,10},{3,5,7,9},{6}}
[10,9,3,8,7,6,5,4,2,1]=>{{1,10},{2,9},{3},{4,8},{5,7},{6}}
[8,7,6,4,5,3,2,1,10,9]=>{{1,8},{2,7},{3,6},{4},{5},{9,10}}
[10,9,8,6,5,4,7,3,2,1]=>{{1,10},{2,9},{3,8},{4,6},{5},{7}}
[8,1,9,10,2,3,4,5,6,7]=>{{1,2,5,8},{3,6,9},{4,7,10}}
[3,4,5,6,7,10,1,2,8,9]=>{{1,3,5,7},{2,4,6,8,9,10}}
[3,4,5,6,9,10,1,2,7,8]=>{{1,3,5,7,9},{2,4,6,8,10}}
[3,4,5,8,9,10,1,2,6,7]=>{{1,3,5,6,7,9,10},{2,4,8}}
[3,4,7,8,9,10,1,2,5,6]=>{{1,3,7},{2,4,8},{5,9},{6,10}}
[3,6,7,8,9,10,1,2,4,5]=>{{1,3,7},{2,4,5,6,8,9,10}}
[2,1,4,3,6,5,10,7,9,8]=>{{1,2},{3,4},{5,6},{7,8,10},{9}}
[2,1,4,3,8,5,7,6,10,9]=>{{1,2},{3,4},{5,6,8},{7},{9,10}}
[2,1,4,3,10,9,7,5,6,8]=>{{1,2},{3,4},{5,8,10},{6,9},{7}}
[2,1,4,3,10,5,6,8,9,7]=>{{1,2},{3,4},{5,6,7,10},{8},{9}}
[2,1,6,3,5,4,8,7,10,9]=>{{1,2},{3,4,6},{5},{7,8},{9,10}}
[2,1,6,3,5,4,10,7,9,8]=>{{1,2},{3,4,6},{5},{7,8,10},{9}}
[2,1,8,7,5,3,4,6,10,9]=>{{1,2},{3,6,8},{4,7},{5},{9,10}}
[2,1,10,7,5,9,4,3,6,8]=>{{1,2},{3,8,10},{4,7},{5},{6,9}}
[2,1,10,8,5,3,6,4,9,7]=>{{1,2},{3,6,7,10},{4,8},{5},{9}}
[2,1,8,3,4,6,7,5,10,9]=>{{1,2},{3,4,5,8},{6},{7},{9,10}}
[2,1,10,9,4,6,7,3,5,8]=>{{1,2},{3,8,10},{4,5,9},{6},{7}}
[2,1,10,3,9,6,4,8,5,7]=>{{1,2},{3,4,7,10},{5,9},{6},{8}}
[2,1,10,3,4,5,7,8,9,6]=>{{1,2},{3,4,5,6,10},{7},{8},{9}}
[4,1,3,2,6,5,8,7,10,9]=>{{1,2,4},{3},{5,6},{7,8},{9,10}}
[4,1,3,2,6,5,10,7,9,8]=>{{1,2,4},{3},{5,6},{7,8,10},{9}}
[4,1,3,2,8,5,7,6,10,9]=>{{1,2,4},{3},{5,6,8},{7},{9,10}}
[4,1,3,2,10,9,7,5,6,8]=>{{1,2,4},{3},{5,8,10},{6,9},{7}}
[4,1,3,2,10,5,6,8,9,7]=>{{1,2,4},{3},{5,6,7,10},{8},{9}}
[6,5,3,1,2,4,10,7,9,8]=>{{1,4,6},{2,5},{3},{7,8,10},{9}}
[8,5,3,7,2,1,4,6,10,9]=>{{1,6,8},{2,5},{3},{4,7},{9,10}}
[10,5,3,7,2,9,4,1,6,8]=>{{1,8,10},{2,5},{3},{4,7},{6,9}}
[10,5,3,8,2,1,6,4,9,7]=>{{1,6,7,10},{2,5},{3},{4,8},{9}}
[8,6,3,1,4,2,7,5,10,9]=>{{1,4,5,8},{2,6},{3},{7},{9,10}}
[10,6,3,9,4,2,7,1,5,8]=>{{1,8,10},{2,6},{3},{4,5,9},{7}}
[10,6,3,1,9,2,4,8,5,7]=>{{1,4,7,10},{2,6},{3},{5,9},{8}}
[10,7,3,1,4,5,2,8,9,6]=>{{1,4,5,6,10},{2,7},{3},{8},{9}}
[6,1,2,4,5,3,8,7,10,9]=>{{1,2,3,6},{4},{5},{7,8},{9,10}}
[6,1,2,4,5,3,10,7,9,8]=>{{1,2,3,6},{4},{5},{7,8,10},{9}}
[8,7,2,4,5,1,3,6,10,9]=>{{1,6,8},{2,3,7},{4},{5},{9,10}}
[10,7,2,4,5,9,3,1,6,8]=>{{1,8,10},{2,3,7},{4},{5},{6,9}}
[10,8,2,4,5,1,6,3,9,7]=>{{1,6,7,10},{2,3,8},{4},{5},{9}}
[8,1,7,4,2,6,3,5,10,9]=>{{1,2,5,8},{3,7},{4},{6},{9,10}}
[10,9,7,4,2,6,3,1,5,8]=>{{1,8,10},{2,5,9},{3,7},{4},{6}}
[10,1,8,4,9,6,2,3,5,7]=>{{1,2,7,10},{3,8},{4},{5,9},{6}}
[10,1,8,4,2,5,7,3,9,6]=>{{1,2,5,6,10},{3,8},{4},{7},{9}}
[8,1,2,3,5,6,7,4,10,9]=>{{1,2,3,4,8},{5},{6},{7},{9,10}}
[10,9,2,3,5,6,7,1,4,8]=>{{1,8,10},{2,3,4,9},{5},{6},{7}}
[10,1,9,3,5,6,2,8,4,7]=>{{1,2,7,10},{3,4,9},{5},{6},{8}}
[10,1,2,9,5,3,7,8,4,6]=>{{1,2,3,6,10},{4,9},{5},{7},{8}}
[10,9,7,6,5,4,3,8,2,1]=>{{1,10},{2,9},{3,7},{4,6},{5},{8}}
[3,2,4,1,5,6,7,8,9,10]=>{{1,3,4},{2},{5},{6},{7},{8},{9},{10}}
[3,4,2,5,1,6,7,8,9,10]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}
[4,3,5,2,6,1,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}
[4,5,3,6,2,7,1,8,9,10]=>{{1,4,6,7},{2,5},{3},{8},{9},{10}}
[5,4,6,3,7,2,8,1,9,10]=>{{1,5,7,8},{2,3,4,6},{9},{10}}
[2,1,4,3,6,5,10,7,8,9]=>{{1,2},{3,4},{5,6},{7,8,9,10}}
[2,1,4,3,8,5,6,7,10,9]=>{{1,2},{3,4},{5,6,7,8},{9,10}}
[2,1,4,3,10,9,6,5,8,7]=>{{1,2},{3,4},{5,6,7,8,9,10}}
[2,1,4,3,10,5,6,7,8,9]=>{{1,2},{3,4},{5,6,7,8,9,10}}
[2,1,6,3,4,5,8,7,10,9]=>{{1,2},{3,4,5,6},{7,8},{9,10}}
[2,1,6,3,4,5,10,7,8,9]=>{{1,2},{3,4,5,6},{7,8,9,10}}
[2,1,10,7,4,9,6,3,8,5]=>{{1,2},{3,4,5,6,7,8,9,10}}
[2,1,10,9,4,3,6,7,8,5]=>{{1,2},{3,4,5,6,7,8,9,10}}
[2,1,8,3,4,5,6,7,10,9]=>{{1,2},{3,4,5,6,7,8},{9,10}}
[2,1,10,9,4,5,6,3,8,7]=>{{1,2},{3,4,5,6,7,8,9,10}}
[2,1,10,3,8,5,4,7,6,9]=>{{1,2},{3,4,5,6,7,8,9,10}}
[4,1,2,3,6,5,10,7,8,9]=>{{1,2,3,4},{5,6},{7,8,9,10}}
[4,1,2,3,8,5,6,7,10,9]=>{{1,2,3,4},{5,6,7,8},{9,10}}
[4,1,2,3,10,9,6,5,8,7]=>{{1,2,3,4},{5,6,7,8,9,10}}
[6,5,2,1,4,3,8,7,10,9]=>{{1,2,3,4,5,6},{7,8},{9,10}}
[6,5,2,1,4,3,10,7,8,9]=>{{1,2,3,4,5,6},{7,8,9,10}}
[8,5,2,7,4,1,6,3,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[10,5,2,7,4,9,6,1,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,5,2,9,4,1,6,7,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,7,2,1,4,5,6,3,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[10,7,2,9,4,5,6,1,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,2,1,8,5,4,7,6,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,2,1,4,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,1,2,3,4,5,8,7,10,9]=>{{1,2,3,4,5,6},{7,8},{9,10}}
[8,7,2,3,4,1,6,5,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[10,7,2,3,4,9,6,1,8,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,2,3,4,1,6,7,8,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,1,6,3,2,5,4,7,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}}
[10,9,6,3,2,5,4,1,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,1,6,3,8,5,2,7,4,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,1,8,3,2,5,6,7,4,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,2,3,4,5,6,1,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,1,8,3,4,5,2,7,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,1,2,7,4,3,6,5,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,2,9,7,5,3,10,8,6,4]=>{{1},{2},{3,6,9},{4,7,10},{5},{8}}
[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,3,5,7,2,9,4,6,8,10]=>{{1},{2,3,5},{4,7},{6,8,9},{10}}
[1,3,5,7,2,9,4,10,6,8]=>{{1},{2,3,5},{4,7},{6,9},{8,10}}
[1,3,5,7,2,8,4,9,6,10]=>{{1},{2,3,5},{4,7},{6,8,9},{10}}
[1,3,5,6,2,7,4,9,8,10]=>{{1},{2,3,5},{4,6,7},{8,9},{10}}
[1,3,4,5,2,7,6,9,8,10]=>{{1},{2,3,4,5},{6,7},{8,9},{10}}
[1,10,9,8,7,6,5,3,2,4]=>{{1},{2,3,4,8,9,10},{5,7},{6}}
[1,10,9,8,7,6,4,3,2,5]=>{{1},{2,3,4,5,7,8,9,10},{6}}
[1,10,9,8,7,5,4,3,2,6]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,10,9,8,6,5,4,3,2,7]=>{{1},{2,3,4,7,8,9,10},{5,6}}
[1,10,9,7,6,5,4,3,2,8]=>{{1},{2,3,8,9,10},{4,7},{5,6}}
[1,10,8,7,6,5,4,3,2,9]=>{{1},{2,9,10},{3,8},{4,7},{5,6}}
[9,10,2,3,4,5,6,7,1,8]=>{{1,9},{2,3,4,5,6,7,8,10}}
[8,9,10,2,3,4,5,6,1,7]=>{{1,2,4,6,8,9},{3,5,7,10}}
[7,8,9,10,2,3,4,5,1,6]=>{{1,3,4,6,7,9,10},{2,5,8}}
[5,6,7,8,9,10,2,3,1,4]=>{{1,5,9},{2,3,4,6,7,8,10}}
[4,5,6,7,8,9,10,2,1,3]=>{{1,3,4,6,7,9,10},{2,5,8}}
[8,10,3,4,5,6,7,2,1,9]=>{{1,2,8,9,10},{3},{4},{5},{6},{7}}
[3,10,2,1,5,6,7,8,9,4]=>{{1,2,3,4,10},{5},{6},{7},{8},{9}}
[3,9,1,4,5,6,7,8,2,10]=>{{1,3},{2,9},{4},{5},{6},{7},{8},{10}}
[2,1,4,3,10,5,7,6,9,8]=>{{1,2},{3,4},{5,6,8,10},{7},{9}}
[2,1,4,3,9,6,10,5,8,7]=>{{1,2},{3,4},{5,8,9},{6},{7,10}}
[2,1,8,3,5,4,7,6,10,9]=>{{1,2},{3,4,6,8},{5},{7},{9,10}}
[2,1,10,3,5,4,7,6,9,8]=>{{1,2},{3,4,6,8,10},{5},{7},{9}}
[2,1,9,6,10,3,5,4,8,7]=>{{1,2},{3,4,6,8,9},{5,7,10}}
[2,1,7,4,8,3,6,5,10,9]=>{{1,2},{3,6,7},{4},{5,8},{9,10}}
[2,1,7,4,10,3,6,5,9,8]=>{{1,2},{3,6,7},{4},{5,8,10},{9}}
[2,1,10,3,6,5,9,4,8,7]=>{{1,2},{3,4,7,8,9,10},{5,6}}
[2,1,9,4,8,5,10,3,7,6]=>{{1,2},{3,5,6,7,8,9,10},{4}}
[4,1,3,2,10,5,7,6,9,8]=>{{1,2,4},{3},{5,6,8,10},{7},{9}}
[4,1,3,2,9,6,10,5,8,7]=>{{1,2,4},{3},{5,8,9},{6},{7,10}}
[6,1,3,2,5,4,8,7,10,9]=>{{1,2,4,6},{3},{5},{7,8},{9,10}}
[6,1,3,2,5,4,10,7,9,8]=>{{1,2,4,6},{3},{5},{7,8,10},{9}}
[8,1,3,2,5,4,7,6,10,9]=>{{1,2,4,6,8},{3},{5},{7},{9,10}}
[9,6,10,1,3,2,5,4,8,7]=>{{1,4,8,9},{2,6},{3,5,7,10}}
[7,4,8,1,3,2,6,5,10,9]=>{{1,2,4,6,7},{3,5,8},{9,10}}
[7,4,10,1,3,2,6,5,9,8]=>{{1,2,4,6,7},{3,5,8,10},{9}}
[10,1,3,2,6,5,9,4,8,7]=>{{1,2,4,7,8,9,10},{3},{5,6}}
[9,4,8,5,10,1,3,2,7,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,2,6,1,4,3,8,7,10,9]=>{{1,4,5},{2},{3,6},{7,8},{9,10}}
[5,2,6,1,4,3,10,7,9,8]=>{{1,4,5},{2},{3,6},{7,8,10},{9}}
[5,2,8,1,4,3,7,6,10,9]=>{{1,4,5},{2},{3,6,8},{7},{9,10}}
[5,2,10,1,4,3,7,6,9,8]=>{{1,4,5},{2},{3,6,8,10},{7},{9}}
[5,2,9,6,10,1,4,3,8,7]=>{{1,4,5,6,7,10},{2},{3,8,9}}
[8,1,4,3,7,2,6,5,10,9]=>{{1,2,5,6,7,8},{3,4},{9,10}}
[10,1,4,3,7,2,6,5,9,8]=>{{1,2,5,6,7,8,10},{3,4},{9}}
[9,2,6,5,10,1,4,3,8,7]=>{{1,3,6,8,9},{2},{4,5,7,10}}
[10,1,4,3,8,5,9,2,7,6]=>{{1,2,5,6,8,10},{3,4},{7,9}}
[7,2,6,3,8,1,5,4,10,9]=>{{1,3,4,5,6,7,8},{2},{9,10}}
[7,2,6,3,10,1,5,4,9,8]=>{{1,3,4,5,6,7,8,10},{2},{9}}
[10,1,5,4,9,2,6,3,8,7]=>{{1,2,6,7,10},{3,5,8,9},{4}}
[8,3,10,1,5,4,9,2,7,6]=>{{1,2,3,4,6,8,10},{5},{7,9}}
[8,3,9,2,7,4,10,1,6,5]=>{{1,8},{2,3,4,6,9},{5,7,10}}
[1,2,3,4,5,6,8,9,7,10]=>{{1},{2},{3},{4},{5},{6},{7,8,9},{10}}
[10,1,2,3,4,5,9,7,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,1,2,3,4,9,6,7,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,1,2,3,10,5,6,7,4,8]=>{{1,2,3,4,9},{5,6,7,8,10}}
[10,1,2,9,4,5,6,7,3,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,1,9,3,4,5,6,7,2,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,1,2,3,4,5,10,6,9,7]=>{{1,2,3,4,5,6,8},{7,10},{9}}
[7,1,2,3,4,9,5,6,10,8]=>{{1,2,3,4,5,7},{6,8,9,10}}
[6,1,2,3,9,4,5,7,10,8]=>{{1,2,3,4,6},{5,7,8,9,10}}
[5,1,2,10,3,4,6,7,9,8]=>{{1,2,3,5},{4,6,7,8,10},{9}}
[4,1,9,2,3,5,6,7,10,8]=>{{1,2,4},{3,5,6,7,8,9,10}}
[3,9,1,2,4,5,6,7,10,8]=>{{1,3},{2,4,5,6,7,8,9,10}}
[10,2,1,3,4,5,6,7,9,8]=>{{1,3,4,5,6,7,8,10},{2},{9}}
[1,2,3,4,5,7,8,6,9,10]=>{{1},{2},{3},{4},{5},{6,7,8},{9},{10}}
[1,2,3,4,5,7,8,9,6,10]=>{{1},{2},{3},{4},{5},{6,7,8,9},{10}}
[2,4,5,6,1,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,5,6,1,7,8,9,10,4]=>{{1,2,3,5},{4,6,7,8,9,10}}
[9,8,10,1,4,5,6,7,2,3]=>{{1,2,4,5,6,7,8,9},{3,10}}
[7,1,10,9,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,7,9,1,2,3,4,5,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,8,1,9,10,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,7,1,10,2,3,4,5,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,5,2,8,6,3,10,9,7,4]=>{{1},{2,3,5,6},{4,7,8,9,10}}
[4,1,5,2,8,6,3,10,9,7]=>{{1,2,4},{3,5,7,8,10},{6},{9}}
[1,7,5,2,8,6,3,10,9,4]=>{{1},{2,3,4,5,7,8,10},{6},{9}}
[4,1,7,5,2,8,3,10,9,6]=>{{1,2,4,5},{3,7},{6,8,10},{9}}
[6,4,1,7,5,2,8,3,10,9]=>{{1,2,3,4,6,7,8},{5},{9,10}}
[3,4,1,7,2,8,5,10,9,6]=>{{1,3},{2,4,5,7},{6,8,10},{9}}
[3,6,4,1,7,2,8,5,10,9]=>{{1,3,4},{2,6},{5,7,8},{9,10}}
[1,5,2,9,8,6,3,10,7,4]=>{{1},{2,3,4,5,7,8,9,10},{6}}
[4,1,5,2,9,8,6,3,10,7]=>{{1,2,4},{3,5,6,7,8,9,10}}
[1,7,5,2,9,6,3,10,8,4]=>{{1},{2,3,4,5,7,8,9,10},{6}}
[4,1,7,5,2,9,3,10,8,6]=>{{1,2,4,5},{3,7},{6,8,9,10}}
[4,1,9,6,5,2,7,3,10,8]=>{{1,2,4,6},{3,8,9,10},{5},{7}}
[3,4,1,7,2,9,5,10,8,6]=>{{1,3},{2,4,5,7},{6,8,9,10}}
[3,6,1,9,4,2,7,5,10,8]=>{{1,3},{2,6},{4,5,8,9,10},{7}}
[1,8,7,5,2,9,6,3,10,4]=>{{1},{2,3,4,5,6,7,8,9,10}}
[4,1,8,7,5,2,9,3,10,6]=>{{1,2,4,6,7,9,10},{3,8},{5}}
[6,4,1,8,5,2,9,3,10,7]=>{{1,2,3,4,6,8},{5},{7,9,10}}
[7,6,4,1,8,5,2,9,3,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[3,4,1,8,7,2,9,5,10,6]=>{{1,3},{2,4,5,6,7,8,9,10}}
[3,6,4,1,8,2,9,5,10,7]=>{{1,3,4},{2,6},{5,8},{7,9,10}}
[3,7,6,4,1,8,2,9,5,10]=>{{1,3,5,6,8,9},{2,7},{4},{10}}
[1,9,6,5,2,7,3,10,8,4]=>{{1},{2,4,5,8,9,10},{3,6,7}}
[6,1,9,4,2,7,3,10,8,5]=>{{1,2,3,5,6,7,8,9,10},{4}}
[5,4,1,9,6,2,7,3,10,8]=>{{1,2,3,4,5,6,8,9,10},{7}}
[9,3,1,6,2,7,4,10,8,5]=>{{1,2,3,5,8,9,10},{4,6,7}}
[9,5,3,1,6,2,7,4,10,8]=>{{1,4,8,9,10},{2,5,6},{3},{7}}
[6,1,8,5,2,9,7,3,10,4]=>{{1,2,4,5,6,9,10},{3,8},{7}}
[6,4,1,8,2,9,7,3,10,5]=>{{1,2,3,4,5,6,8,9,10},{7}}
[8,5,4,1,6,2,9,3,10,7]=>{{1,3,4,8},{2,5,6},{7,9,10}}
[5,7,4,1,8,6,2,9,3,10]=>{{1,3,4,5,8,9},{2,7},{6},{10}}
[3,6,1,8,2,9,7,4,10,5]=>{{1,3},{2,5,6,9,10},{4,8},{7}}
[5,8,3,1,6,2,9,4,10,7]=>{{1,2,4,5,6,8},{3},{7,9,10}}
[5,3,7,1,8,6,2,9,4,10]=>{{1,4,5,8,9},{2,3,7},{6},{10}}
[4,3,8,1,9,5,2,6,10,7]=>{{1,4},{2,3,5,6,7,8,9,10}}
[7,4,3,5,1,8,2,9,6,10]=>{{1,2,4,5,7},{3},{6,8,9},{10}}
[9,6,2,1,3,7,4,10,8,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,9,2,1,6,3,7,4,10,8]=>{{1,2,3,4,5,6,8,9,10},{7}}
[6,8,2,1,3,9,7,4,10,5]=>{{1,2,3,4,5,6,8,9,10},{7}}
[8,2,5,1,6,3,9,4,10,7]=>{{1,4,8},{2},{3,5,6},{7,9,10}}
[2,5,7,1,8,6,3,9,4,10]=>{{1,2,4,5,8,9},{3,7},{6},{10}}
[2,4,8,1,9,5,3,6,10,7]=>{{1,2,4},{3,5,6,7,8,9,10}}
[5,6,4,3,2,1,7,8,9,10]=>{{1,2,5,6},{3,4},{7},{8},{9},{10}}
[6,7,5,4,3,2,1,8,9,10]=>{{1,2,6,7},{3,5},{4},{8},{9},{10}}
[7,8,10,9,6,5,4,3,2,1]=>{{1,2,3,4,7,8,9,10},{5,6}}
[8,7,9,10,6,5,4,3,2,1]=>{{1,2,3,4,7,8,9,10},{5,6}}
[7,8,9,10,1,5,6,3,4,2]=>{{1,5,6,7},{2,3,4,8,9,10}}
[10,9,8,5,7,6,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,5,7},{6}}
[10,9,8,4,7,6,5,3,2,1]=>{{1,10},{2,9},{3,8},{4},{5,7},{6}}
[10,9,4,8,7,6,5,3,2,1]=>{{1,10},{2,9},{3,4,8},{5,7},{6}}
[10,3,9,8,7,6,5,4,2,1]=>{{1,10},{2,3,9},{4,8},{5,7},{6}}
[10,2,9,8,7,6,5,4,3,1]=>{{1,10},{2},{3,9},{4,8},{5,7},{6}}
[9,10,2,1,6,4,3,5,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,10,2,1,8,4,3,5,6,9]=>{{1,2,3,4,6,7,9,10},{5,8}}
[2,9,1,10,7,4,3,5,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,8,1,9,4,3,10,5,6,7]=>{{1,2,3,4,5,6,8,9},{7,10}}
[10,8,5,2,1,6,3,4,7,9]=>{{1,3,5,7,9,10},{2,4,8},{6}}
[9,5,2,1,10,6,3,4,7,8]=>{{1,2,3,4,5,7,8,9,10},{6}}
[10,7,2,1,8,5,3,4,6,9]=>{{1,4,5,6,8,9,10},{2,3,7}}
[9,2,1,10,7,5,3,4,6,8]=>{{1,3,5,6,7,9},{2},{4,8,10}}
[2,8,1,9,3,10,5,4,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,6,2,1,7,3,8,4,5,9]=>{{1,4,5,7,8,9,10},{2,3,6}}
[9,2,1,10,6,3,7,4,5,8]=>{{1,3,5,6,9},{2},{4,8,10},{7}}
[8,2,1,9,3,10,6,4,5,7]=>{{1,3,4,5,8,9},{2},{6,7,10}}
[7,2,1,8,3,9,4,10,5,6]=>{{1,3,4,5,6,7,8,9,10},{2}}
[10,8,6,3,1,4,2,5,7,9]=>{{1,2,5,7,8,9,10},{3,4,6}}
[3,9,1,10,6,4,2,5,7,8]=>{{1,3},{2,7,9},{4,5,6,8,10}}
[10,7,3,1,8,4,2,5,6,9]=>{{1,4,6,9,10},{2,7},{3},{5,8}}
[9,3,1,10,7,4,2,5,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,3,1,9,4,2,10,5,6,7]=>{{1,2,3,4,5,6,8,9},{7,10}}
[10,8,5,1,6,3,2,4,7,9]=>{{1,2,4,7,8,9,10},{3,5,6}}
[9,5,1,10,6,3,2,4,7,8]=>{{1,2,3,5,6,7,9},{4,8,10}}
[10,7,1,8,5,3,2,4,6,9]=>{{1,3,6,9,10},{2,7},{4,8},{5}}
[9,1,10,7,5,3,2,4,6,8]=>{{1,2,3,4,6,7,8,9,10},{5}}
[8,3,1,9,2,10,5,4,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,6,1,7,3,2,8,4,5,9]=>{{1,3,5,9,10},{2,6},{4,7,8}}
[9,1,10,6,3,2,7,4,5,8]=>{{1,2,3,4,5,6,8,9,10},{7}}
[8,1,9,3,2,10,6,4,5,7]=>{{1,2,3,4,5,8,9},{6,7,10}}
[7,1,8,3,2,9,4,10,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,4,1,5,2,6,3,7,9]=>{{1,2,3,4,6,7,8,9,10},{5}}
[9,4,1,10,5,2,6,3,7,8]=>{{1,2,3,4,6,7,8,9,10},{5}}
[10,7,1,8,4,2,5,3,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,1,10,7,4,2,5,3,6,8]=>{{1,2,6,9},{3,8,10},{4,5,7}}
[8,1,9,4,2,10,5,3,6,7]=>{{1,2,3,5,6,7,8,9,10},{4}}
[10,6,1,7,2,8,4,3,5,9]=>{{1,2,3,5,6,8,9,10},{4,7}}
[9,1,10,6,2,7,4,3,5,8]=>{{1,2,5,9},{3,8,10},{4,6,7}}
[8,1,9,2,10,6,4,3,5,7]=>{{1,2,3,4,5,7,8,9,10},{6}}
[7,1,8,2,9,4,3,10,5,6]=>{{1,2,3,4,6,7,8,10},{5,9}}
[10,5,1,6,2,7,3,8,4,9]=>{{1,3,4,6,7,9,10},{2,5},{8}}
[9,1,10,5,2,6,3,7,4,8]=>{{1,2,4,5,9},{3,7,8,10},{6}}
[8,1,9,2,10,5,3,6,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,1,8,2,9,3,10,5,4,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,2,3,1,4,5,6,7,8,9]=>{{1,4,5,6,7,8,9,10},{2},{3}}
[10,9,8,6,5,7,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,6,7},{5}}
[10,9,8,4,5,7,6,3,2,1]=>{{1,10},{2,9},{3,8},{4},{5},{6,7}}
[10,9,8,5,4,6,7,3,2,1]=>{{1,10},{2,9},{3,8},{4,5},{6},{7}}
[1,3,4,2,5,6,7,8,9,10]=>{{1},{2,3,4},{5},{6},{7},{8},{9},{10}}
[1,2,4,5,6,3,7,8,9,10]=>{{1},{2},{3,4,5,6},{7},{8},{9},{10}}
[1,2,3,5,6,7,8,4,9,10]=>{{1},{2},{3},{4,5,6,7,8},{9},{10}}
[2,1,5,3,6,7,4,8,9,10]=>{{1,2},{3,4,5,6,7},{8},{9},{10}}
[1,3,5,6,4,2,7,8,9,10]=>{{1},{2,3,4,5,6},{7},{8},{9},{10}}
[3,5,2,1,6,4,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}
[2,1,3,6,4,7,8,9,5,10]=>{{1,2},{3},{4,5,6,7,8,9},{10}}
[1,3,4,6,7,2,8,5,9,10]=>{{1},{2,3,4,6},{5,7,8},{9},{10}}
[3,2,6,1,4,7,8,5,9,10]=>{{1,3,4,5,6,7,8},{2},{9},{10}}
[2,4,6,1,7,5,3,8,9,10]=>{{1,2,4},{3,5,6,7},{8},{9},{10}}
[4,6,3,2,1,7,5,8,9,10]=>{{1,2,4,5,6,7},{3},{8},{9},{10}}
[1,3,4,2,7,8,5,9,10,6]=>{{1},{2,3,4},{5,7},{6,8,9,10}}
[3,2,1,7,4,5,8,9,10,6]=>{{1,3},{2},{4,5,6,7,8,9,10}}
[1,2,4,5,7,8,9,6,3,10]=>{{1},{2},{3,4,5,7,9},{6,8},{10}}
[4,3,7,2,1,5,8,9,6,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[1,3,5,7,8,6,4,2,9,10]=>{{1},{2,3,5,8},{4,7},{6},{9},{10}}
[3,5,7,2,1,8,6,4,9,10]=>{{1,2,3,4,5,6,7,8},{9},{10}}
[5,7,4,3,2,1,8,6,9,10]=>{{1,2,5,6,7,8},{3,4},{9},{10}}
[2,1,5,3,8,6,9,10,7,4]=>{{1,2},{3,4,5,8,10},{6},{7,9}}
[1,3,5,6,8,9,4,2,10,7]=>{{1},{2,3,5,8},{4,6,7,9,10}}
[3,5,2,8,1,6,9,4,10,7]=>{{1,2,3,5},{4,8},{6},{7,9,10}}
[5,4,8,3,2,1,6,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,4,6,8,1,9,7,5,3,10]=>{{1,2,4,5,8},{3,6,9},{7},{10}}
[4,6,8,3,2,1,9,7,5,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[6,8,5,4,3,2,1,9,7,10]=>{{1,2,6,7,8,9},{3,5},{4},{10}}
[3,5,7,9,2,1,10,8,6,4]=>{{1,3,4,6,7,9,10},{2,5},{8}}
[5,7,9,4,3,2,1,10,8,6]=>{{1,2,3,5,6,7,8,9,10},{4}}
[7,9,6,5,4,3,2,1,10,8]=>{{1,2,7,8,9,10},{3,6},{4,5}}
[2,3,7,5,6,1,10,9,4,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,10,6,9,8,5,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,6,5,9,10,8,4,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,9,5,8,7,4,1,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,5,4,9,6,10,8,3,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,5,4,8,9,7,3,1,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,10,6,7,1,9,8,5]=>{{1,2,3,4,5,6,7,10},{8,9}}
[2,3,7,5,6,1,10,9,8,4]=>{{1,2,3,4,5,6,7,10},{8,9}}
[2,3,4,10,6,8,9,1,7,5]=>{{1,2,3,4,5,6,8,10},{7,9}}
[2,3,6,5,8,10,9,1,7,4]=>{{1,2,3,4,5,6,8,10},{7,9}}
[2,3,8,5,7,9,1,10,6,4]=>{{1,2,3,4,5,7,8,10},{6,9}}
[2,5,4,8,6,10,9,1,7,3]=>{{1,2,3,4,5,6,8,10},{7,9}}
[2,5,4,7,8,9,1,10,6,3]=>{{1,2,3,4,5,7,8,10},{6,9}}
[2,3,4,10,6,9,8,7,5,1]=>{{1,2,3,4,10},{5,6,9},{7,8}}
[2,3,6,5,9,10,8,7,4,1]=>{{1,2,3,6,10},{4,5,9},{7,8}}
[2,3,7,5,9,8,10,6,4,1]=>{{1,2,3,7,10},{4,5,9},{6,8}}
[2,3,9,5,8,7,6,4,1,10]=>{{1,2,3,9},{4,5,8},{6,7},{10}}
[2,5,4,9,6,10,8,7,3,1]=>{{1,2,5,6,10},{3,4,9},{7,8}}
[2,5,4,9,7,8,10,6,3,1]=>{{1,2,5,7,10},{3,4,9},{6,8}}
[2,5,4,8,9,7,6,3,1,10]=>{{1,2,5,9},{3,4,8},{6,7},{10}}
[2,3,4,10,7,9,8,1,6,5]=>{{1,2,3,4,5,7,8,10},{6,9}}
[2,3,5,7,10,9,8,1,6,4]=>{{1,2,3,4,5,7,8,10},{6,9}}
[2,3,8,6,9,7,1,10,5,4]=>{{1,2,3,4,6,7,8,10},{5,9}}
[2,4,7,5,10,9,8,1,6,3]=>{{1,2,3,4,5,7,8,10},{6,9}}
[2,4,6,8,9,7,1,10,5,3]=>{{1,2,3,4,6,7,8,10},{5,9}}
[2,3,4,10,7,8,9,6,5,1]=>{{1,2,3,4,10},{5,7,9},{6,8}}
[2,3,5,7,10,8,9,6,4,1]=>{{1,2,3,5,10},{4,7,9},{6,8}}
[2,3,7,6,8,9,10,5,4,1]=>{{1,2,3,7,10},{4,6,9},{5,8}}
[2,3,9,6,7,8,5,4,1,10]=>{{1,2,3,9},{4,6,8},{5,7},{10}}
[2,4,7,5,10,8,9,6,3,1]=>{{1,2,4,5,10},{3,7,9},{6,8}}
[2,4,6,7,8,9,10,5,3,1]=>{{1,2,4,7,10},{3,6,9},{5,8}}
[2,4,6,9,7,8,5,3,1,10]=>{{1,2,4,9},{3,6,8},{5,7},{10}}
[2,6,5,8,9,7,10,4,3,1]=>{{1,2,6,7,10},{3,5,9},{4,8}}
[2,6,5,7,8,9,4,3,1,10]=>{{1,2,6,9},{3,5,8},{4,7},{10}}
[3,7,4,5,10,9,8,1,6,2]=>{{1,2,3,4,5,7,8,10},{6,9}}
[3,6,4,8,9,7,1,10,5,2]=>{{1,2,3,4,6,7,8,10},{5,9}}
[3,7,4,5,10,8,9,6,2,1]=>{{1,3,4,5,10},{2,7,9},{6,8}}
[3,6,4,7,8,9,10,5,2,1]=>{{1,3,4,7,10},{2,6,9},{5,8}}
[3,6,4,9,7,8,5,2,1,10]=>{{1,3,4,9},{2,6,8},{5,7},{10}}
[3,5,6,8,9,7,10,4,2,1]=>{{1,3,6,7,10},{2,5,9},{4,8}}
[3,5,6,7,8,9,4,2,1,10]=>{{1,3,6,9},{2,5,8},{4,7},{10}}
[5,6,4,7,3,9,1,8,2,10]=>{{1,3,4,5,7},{2,6,9},{8},{10}}
[1,6,7,5,8,4,10,2,9,3]=>{{1},{2,4,5,6,8},{3,7,10},{9}}
[4,5,6,7,8,9,1,10,2,3]=>{{1,4,7},{2,3,5,6,8,9,10}}
[3,2,5,4,7,6,8,10,9,1]=>{{1,3,5,7,8,10},{2},{4},{6},{9}}
[3,2,5,4,6,9,7,8,10,1]=>{{1,3,5,6,9,10},{2},{4},{7},{8}}
[3,2,5,4,6,8,7,10,9,1]=>{{1,3,5,6,8,10},{2},{4},{7},{9}}
[3,2,5,4,6,7,10,8,9,1]=>{{1,3,5,6,7,10},{2},{4},{8},{9}}
[3,2,4,7,5,6,9,8,10,1]=>{{1,3,4,7,9,10},{2},{5},{6},{8}}
[3,2,4,7,5,6,8,10,9,1]=>{{1,3,4,7,8,10},{2},{5},{6},{9}}
[3,2,4,6,5,9,7,8,10,1]=>{{1,3,4,6,9,10},{2},{5},{7},{8}}
[3,2,4,6,5,8,7,10,9,1]=>{{1,3,4,6,8,10},{2},{5},{7},{9}}
[3,2,4,6,5,7,10,8,9,1]=>{{1,3,4,6,7,10},{2},{5},{8},{9}}
[3,2,4,5,9,6,7,8,10,1]=>{{1,3,4,5,9,10},{2},{6},{7},{8}}
[3,2,4,5,8,6,7,10,9,1]=>{{1,3,4,5,8,10},{2},{6},{7},{9}}
[3,2,4,5,7,6,10,8,9,1]=>{{1,3,4,5,7,10},{2},{6},{8},{9}}
[3,2,4,5,6,10,7,8,9,1]=>{{1,3,4,5,6,10},{2},{7},{8},{9}}
[2,5,3,4,7,6,9,8,10,1]=>{{1,2,5,7,9,10},{3},{4},{6},{8}}
[2,5,3,4,7,6,8,10,9,1]=>{{1,2,5,7,8,10},{3},{4},{6},{9}}
[2,5,3,4,6,9,7,8,10,1]=>{{1,2,5,6,9,10},{3},{4},{7},{8}}
[2,5,3,4,6,8,7,10,9,1]=>{{1,2,5,6,8,10},{3},{4},{7},{9}}
[2,5,3,4,6,7,10,8,9,1]=>{{1,2,5,6,7,10},{3},{4},{8},{9}}
[2,4,3,7,5,6,9,8,10,1]=>{{1,2,4,7,9,10},{3},{5},{6},{8}}
[2,4,3,7,5,6,8,10,9,1]=>{{1,2,4,7,8,10},{3},{5},{6},{9}}
[2,4,3,6,5,9,7,8,10,1]=>{{1,2,4,6,9,10},{3},{5},{7},{8}}
[2,4,3,6,5,7,10,8,9,1]=>{{1,2,4,6,7,10},{3},{5},{8},{9}}
[2,4,3,5,9,6,7,8,10,1]=>{{1,2,4,5,9,10},{3},{6},{7},{8}}
[2,4,3,5,8,6,7,10,9,1]=>{{1,2,4,5,8,10},{3},{6},{7},{9}}
[2,4,3,5,7,6,10,8,9,1]=>{{1,2,4,5,7,10},{3},{6},{8},{9}}
[2,4,3,5,6,10,7,8,9,1]=>{{1,2,4,5,6,10},{3},{7},{8},{9}}
[2,3,7,4,5,6,9,8,10,1]=>{{1,2,3,7,9,10},{4},{5},{6},{8}}
[2,3,7,4,5,6,8,10,9,1]=>{{1,2,3,7,8,10},{4},{5},{6},{9}}
[2,3,6,4,5,9,7,8,10,1]=>{{1,2,3,6,9,10},{4},{5},{7},{8}}
[2,3,6,4,5,8,7,10,9,1]=>{{1,2,3,6,8,10},{4},{5},{7},{9}}
[2,3,6,4,5,7,10,8,9,1]=>{{1,2,3,6,7,10},{4},{5},{8},{9}}
[2,3,5,4,9,6,7,8,10,1]=>{{1,2,3,5,9,10},{4},{6},{7},{8}}
[2,3,5,4,8,6,7,10,9,1]=>{{1,2,3,5,8,10},{4},{6},{7},{9}}
[2,3,5,4,7,6,10,8,9,1]=>{{1,2,3,5,7,10},{4},{6},{8},{9}}
[2,3,5,4,6,10,7,8,9,1]=>{{1,2,3,5,6,10},{4},{7},{8},{9}}
[2,3,4,9,5,6,7,8,10,1]=>{{1,2,3,4,9,10},{5},{6},{7},{8}}
[2,3,4,8,5,6,7,10,9,1]=>{{1,2,3,4,8,10},{5},{6},{7},{9}}
[2,3,4,7,5,6,10,8,9,1]=>{{1,2,3,4,7,10},{5},{6},{8},{9}}
[2,3,4,6,5,10,7,8,9,1]=>{{1,2,3,4,6,10},{5},{7},{8},{9}}
[3,4,5,6,2,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,4,5,6,3,7,8,9,10,1]=>{{1,2,4,6,7,8,9,10},{3,5}}
[2,3,5,6,4,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,3,10,1,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,3,1,9,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,1,4,10,2,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,8,10,7,6,5,4,3,1,2]=>{{1,9},{2,3,8,10},{4,7},{5,6}}
[10,7,1,2,3,4,8,9,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,2,3,4,5,7,8,9,10,1]=>{{1,6,7,8,9,10},{2},{3},{4},{5}}
[2,6,3,4,5,7,8,9,10,1]=>{{1,2,6,7,8,9,10},{3},{4},{5}}
[2,3,6,4,5,7,8,9,10,1]=>{{1,2,3,6,7,8,9,10},{4},{5}}
[10,2,3,4,5,6,7,1,8,9]=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}
[10,2,3,4,5,6,1,7,8,9]=>{{1,7,8,9,10},{2},{3},{4},{5},{6}}
[10,2,3,4,5,1,6,7,8,9]=>{{1,6,7,8,9,10},{2},{3},{4},{5}}
[10,2,3,4,1,5,6,7,8,9]=>{{1,5,6,7,8,9,10},{2},{3},{4}}
[2,8,1,3,4,5,6,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,7,1,2,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,5,6,8,2,9,3,10,7,1]=>{{1,4,8,10},{2,5},{3,6,7,9}}
[10,4,5,6,9,3,8,2,7,1]=>{{1,10},{2,3,4,5,6,7,8,9}}
[4,5,10,6,9,3,8,2,7,1]=>{{1,3,4,6,10},{2,5,7,8,9}}
[4,5,8,2,6,10,9,3,7,1]=>{{1,2,4,5,6,10},{3,8},{7,9}}
[10,6,9,5,4,3,8,2,7,1]=>{{1,10},{2,3,6,7,8,9},{4,5}}
[8,2,6,10,9,5,4,3,7,1]=>{{1,3,4,5,6,7,8,9,10},{2}}
[8,2,10,4,5,6,7,1,9,3]=>{{1,8},{2},{3,10},{4},{5},{6},{7},{9}}
[4,5,6,8,2,10,7,1,9,3]=>{{1,4,8},{2,5},{3,6,10},{7},{9}}
[10,4,5,6,8,2,7,1,9,3]=>{{1,3,5,8,10},{2,4,6},{7},{9}}
[4,5,10,6,8,2,7,1,9,3]=>{{1,2,4,5,6,8},{3,10},{7},{9}}
[4,5,10,8,2,6,7,1,9,3]=>{{1,4,8},{2,5},{3,10},{6},{7},{9}}
[10,6,8,2,7,1,9,5,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,2,6,7,1,9,5,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,2,7,1,9,3,10,4,5,6]=>{{1,4,8},{2},{3,6,7,10},{5,9}}
[4,5,8,2,7,1,9,3,10,6]=>{{1,2,4,5,6,7,9,10},{3,8}}
[4,5,9,3,10,7,1,8,2,6]=>{{1,2,3,4,5,6,7,9,10},{8}}
[4,5,7,1,9,3,8,2,6,10]=>{{1,4},{2,3,5,6,7,8,9},{10}}
[8,2,7,1,9,5,4,3,10,6]=>{{1,3,4,7,8},{2},{5,6,9,10}}
[9,5,4,3,10,7,1,8,2,6]=>{{1,2,5,6,7,9,10},{3,4},{8}}
[7,1,9,5,4,3,8,2,6,10]=>{{1,2,7,8},{3,6,9},{4,5},{10}}
[8,2,6,10,4,5,7,1,9,3]=>{{1,8},{2},{3,4,5,6,10},{7},{9}}
[4,8,2,6,10,5,7,1,9,3]=>{{1,2,3,4,5,6,8,10},{7},{9}}
[4,10,8,2,5,6,7,1,9,3]=>{{1,2,3,4,8,10},{5},{6},{7},{9}}
[8,2,6,10,5,7,1,9,4,3]=>{{1,3,4,6,7,8,9,10},{2},{5}}
[10,8,2,5,6,7,1,9,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,3,10,4,5,7,1,8,2,6]=>{{1,2,3,6,7,9,10},{4},{5},{8}}
[4,9,3,10,5,7,1,8,2,6]=>{{1,4,6,7,10},{2,9},{3},{5},{8}}
[4,9,3,10,7,1,8,2,5,6]=>{{1,4,6,10},{2,5,7,8,9},{3}}
[4,7,1,9,3,8,2,5,6,10]=>{{1,3,4,5,6,8,9},{2,7},{10}}
[9,4,3,10,5,7,1,8,2,6]=>{{1,2,4,6,7,9,10},{3},{5},{8}}
[9,4,3,10,7,1,8,2,5,6]=>{{1,2,4,5,6,7,8,9,10},{3}}
[7,1,9,4,3,8,2,5,6,10]=>{{1,2,7},{3,5,6,8,9},{4},{10}}
[5,10,7,1,8,2,4,3,9,6]=>{{1,3,4,5,7,8},{2,6,10},{9}}
[5,7,1,8,2,4,3,9,6,10]=>{{1,2,3,5,7},{4,6,8,9},{10}}
[10,5,7,1,9,4,2,6,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,4,2,5,6,7,1,10,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,5,7,1,8,3,9,4,2,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,7,1,8,3,9,4,2,5,6]=>{{1,3,5,6,9,10},{2,4,7,8}}
[7,1,8,3,9,4,2,5,6,10]=>{{1,2,7},{3,4,5,6,8,9},{10}}
[4,2,5,10,7,1,8,3,9,6]=>{{1,4,6,10},{2},{3,5,7,8},{9}}
[4,2,5,7,1,8,3,9,6,10]=>{{1,3,4,5,7},{2},{6,8,9},{10}}
[4,5,6,7,8,9,1,2,10,3]=>{{1,4,7},{2,5,8},{3,6,9,10}}
[2,1,10,9,8,7,6,5,3,4]=>{{1,2},{3,4,9,10},{5,8},{6,7}}
[10,9,7,3,6,1,2,4,8,5]=>{{1,5,6,10},{2,3,4,7,8,9}}
[9,7,3,6,1,2,4,10,8,5]=>{{1,5,8,9,10},{2,4,6,7},{3}}
[7,3,10,9,6,1,2,4,8,5]=>{{1,2,3,5,6,7,10},{4,8,9}}
[7,3,9,6,1,2,4,10,8,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,6,1,2,4,10,7,3,8,5]=>{{1,3,8,9},{2,4,5,6,10},{7}}
[8,4,10,9,7,3,6,1,2,5]=>{{1,8},{2,4,9},{3,5,6,7,10}}
[10,8,4,9,7,3,6,1,2,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,3,8,4,10,9,6,1,2,5]=>{{1,2,3,6,7,8,9},{4},{5,10}}
[7,3,10,8,4,9,6,1,2,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,7,3,8,4,9,6,1,2,5]=>{{1,4,5,8,10},{2,6,7,9},{3}}
[6,1,2,7,3,8,4,10,9,5]=>{{1,2,3,5,6,8,10},{4,7},{9}}
[6,1,2,7,3,10,8,4,9,5]=>{{1,2,3,5,6,10},{4,7,8},{9}}
[6,1,2,10,7,3,8,4,9,5]=>{{1,2,3,6},{4,5,7,8,10},{9}}
[10,6,1,2,7,3,8,4,9,5]=>{{1,2,3,4,5,6,7,8,10},{9}}
[6,1,3,10,9,7,2,4,8,5]=>{{1,2,6,7},{3},{4,5,8,9,10}}
[6,1,3,9,7,2,4,10,8,5]=>{{1,2,6},{3},{4,5,7,8,9,10}}
[10,9,6,1,3,7,2,4,8,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,6,1,3,7,2,4,10,8,5]=>{{1,3,4,5,7,8,9,10},{2,6}}
[10,7,2,4,9,6,1,3,8,5]=>{{1,2,3,5,7,8,9,10},{4},{6}}
[6,1,3,8,4,10,9,7,2,5]=>{{1,2,4,5,6,7,8,9,10},{3}}
[6,1,3,10,8,4,9,7,2,5]=>{{1,2,4,5,6,7,8,9,10},{3}}
[8,4,10,9,6,1,3,7,2,5]=>{{1,3,5,6,7,8,10},{2,4,9}}
[10,8,4,9,6,1,3,7,2,5]=>{{1,5,6,10},{2,3,4,7,8,9}}
[9,6,1,3,8,4,10,7,2,5]=>{{1,2,3,4,6,9},{5,7,8,10}}
[7,2,6,1,3,8,4,10,9,5]=>{{1,4,7},{2},{3,5,6,8,10},{9}}
[7,2,6,1,3,10,8,4,9,5]=>{{1,4,7,8},{2},{3,5,6,10},{9}}
[10,7,2,6,1,3,8,4,9,5]=>{{1,5,10},{2,3,4,6,7,8},{9}}
[7,2,10,6,1,3,8,4,9,5]=>{{1,3,4,5,6,7,8,10},{2},{9}}
[8,3,6,1,4,10,9,7,2,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,3,6,1,4,9,7,2,5]=>{{1,5,10},{2,7,8,9},{3},{4,6}}
[10,9,6,1,4,8,3,7,2,5]=>{{1,4,5,10},{2,9},{3,6,7,8}}
[9,6,1,4,10,8,3,7,2,5]=>{{1,2,3,6,7,8,9},{4},{5,10}}
[8,3,9,6,1,4,10,7,2,5]=>{{1,5,7,8,10},{2,3,9},{4,6}}
[8,3,7,2,6,1,4,10,9,5]=>{{1,5,6,8,10},{2,3,4,7},{9}}
[10,8,3,7,2,6,1,4,9,5]=>{{1,2,4,5,7,8,10},{3},{6},{9}}
[8,3,10,7,2,6,1,4,9,5]=>{{1,4,7,8},{2,3,5,10},{6},{9}}
[7,2,8,3,10,6,1,4,9,5]=>{{1,7},{2},{3,4,8},{5,10},{6},{9}}
[9,4,10,8,3,7,2,6,1,5]=>{{1,9},{2,4,6,7,8},{3,5,10}}
[8,3,9,4,10,7,2,6,1,5]=>{{1,2,3,6,7,8,9},{4},{5,10}}
[7,2,8,3,9,4,10,6,1,5]=>{{1,5,7,9,10},{2},{3,4,6,8}}
[10,3,4,1,2,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,2,3,4,8,5,9,6,10,7]=>{{1},{2},{3},{4},{5,6,8},{7,9,10}}
[1,2,3,4,5,8,6,10,9,7]=>{{1},{2},{3},{4},{5},{6,7,8,10},{9}}
[1,2,3,7,4,8,5,10,9,6]=>{{1},{2},{3},{4,5,7},{6,8,10},{9}}
[1,2,3,4,9,7,5,10,8,6]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,2,3,4,7,5,10,9,8,6]=>{{1},{2},{3},{4},{5,6,7,10},{8,9}}
[1,6,2,7,3,8,4,10,9,5]=>{{1},{2,3,5,6,8,10},{4,7},{9}}
[1,2,6,3,9,7,4,10,8,5]=>{{1},{2},{3,4,6,7},{5,8,9,10}}
[1,2,6,3,7,4,10,9,8,5]=>{{1},{2},{3,4,6},{5,7,10},{8,9}}
[1,2,3,8,6,4,10,9,7,5]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[1,2,3,6,4,10,9,8,7,5]=>{{1},{2},{3},{4,5,6,10},{7,9},{8}}
[5,1,6,2,9,7,3,10,8,4]=>{{1,2,4,5,8,9,10},{3,6,7}}
[5,1,6,2,7,3,10,9,8,4]=>{{1,2,4,5,7,10},{3,6},{8,9}}
[1,5,2,6,3,10,9,8,7,4]=>{{1},{2,3,5},{4,6,10},{7,9},{8}}
[1,2,7,5,3,10,9,8,6,4]=>{{1},{2},{3,4,5,6,7,9,10},{8}}
[1,2,5,3,10,9,8,7,6,4]=>{{1},{2},{3,4,5,10},{6,9},{7,8}}
[7,4,1,8,5,2,10,9,6,3]=>{{1,3,7,10},{2,4,6,8,9},{5}}
[4,1,9,7,5,2,10,8,6,3]=>{{1,2,3,4,6,7,9,10},{5},{8}}
[4,1,7,5,2,10,9,8,6,3]=>{{1,2,4,5},{3,6,7,9,10},{8}}
[4,1,5,2,10,9,8,7,6,3]=>{{1,2,4},{3,5,10},{6,9},{7,8}}
[1,8,6,4,2,10,9,7,5,3]=>{{1},{2,5,7,8,9},{3,6,10},{4}}
[1,6,4,2,10,9,8,7,5,3]=>{{1},{2,3,4,5,6,9,10},{7,8}}
[1,4,2,10,9,8,7,6,5,3]=>{{1},{2,3,4,10},{5,9},{6,8},{7}}
[7,5,3,1,10,9,8,6,4,2]=>{{1,4,6,7,8,9},{2,5,10},{3}}
[5,3,1,10,9,8,7,6,4,2]=>{{1,2,3,4,5,9,10},{6,8},{7}}
[1,4,2,5,6,7,8,10,9,3]=>{{1},{2,3,4,5,6,7,8,10},{9}}
[2,1,4,5,6,7,10,8,3,9]=>{{1,2},{3,4,5,6,7,9,10},{8}}
[3,1,5,2,6,10,7,8,9,4]=>{{1,2,3,4,5,6,10},{7},{8},{9}}
[4,5,1,6,7,9,8,10,2,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,2,8,3,9,4,10,5,1,6]=>{{1,3,4,5,6,7,8,9,10},{2}}
[7,2,8,3,9,4,10,1,5,6]=>{{1,3,4,6,7,8,10},{2},{5,9}}
[7,2,8,3,9,10,4,5,1,6]=>{{1,3,4,5,7,8,9},{2},{6,10}}
[7,2,8,3,9,10,4,1,5,6]=>{{1,3,4,7,8},{2},{5,9},{6,10}}
[7,2,8,3,9,10,1,4,5,6]=>{{1,7},{2},{3,4,8},{5,9},{6,10}}
[7,2,8,9,3,4,10,5,1,6]=>{{1,4,6,7,9,10},{2},{3,5,8}}
[7,2,8,9,3,4,10,1,5,6]=>{{1,3,4,5,6,7,8,9,10},{2}}
[7,2,8,9,3,10,4,5,1,6]=>{{1,4,7,9},{2},{3,5,8},{6,10}}
[7,2,8,9,3,10,4,1,5,6]=>{{1,3,4,5,7,8,9},{2},{6,10}}
[7,2,8,9,3,10,1,4,5,6]=>{{1,7},{2},{3,4,5,8,9},{6,10}}
[7,2,8,9,10,3,4,5,1,6]=>{{1,4,7,9},{2},{3,5,6,8,10}}
[7,2,8,9,10,3,4,1,5,6]=>{{1,3,4,5,6,7,8,9,10},{2}}
[7,2,8,9,10,3,1,4,5,6]=>{{1,7},{2},{3,4,5,6,8,9,10}}
[7,8,2,3,9,4,10,5,1,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,2,3,9,4,10,1,5,6]=>{{1,2,3,4,6,7,8,10},{5,9}}
[7,8,2,3,9,10,4,5,1,6]=>{{1,2,3,4,5,7,8,9},{6,10}}
[7,8,2,3,9,10,4,1,5,6]=>{{1,2,3,4,7,8},{5,9},{6,10}}
[7,8,2,3,9,10,1,4,5,6]=>{{1,7},{2,3,4,8},{5,9},{6,10}}
[7,8,2,9,3,4,10,5,1,6]=>{{1,4,6,7,9,10},{2,3,5,8}}
[7,8,2,9,3,4,10,1,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,2,9,3,10,4,5,1,6]=>{{1,4,7,9},{2,3,5,8},{6,10}}
[7,8,2,9,3,10,4,1,5,6]=>{{1,2,3,4,5,7,8,9},{6,10}}
[7,8,2,9,3,10,1,4,5,6]=>{{1,7},{2,3,4,5,8,9},{6,10}}
[7,8,2,9,10,3,4,5,1,6]=>{{1,4,7,9},{2,3,5,6,8,10}}
[7,8,2,9,10,3,4,1,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,2,9,10,3,1,4,5,6]=>{{1,7},{2,3,4,5,6,8,9,10}}
[7,8,2,9,10,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,9,2,3,4,10,5,1,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,9,2,3,4,10,1,5,6]=>{{1,2,4,6,7,8,10},{3,5,9}}
[7,8,9,2,3,10,4,5,1,6]=>{{1,2,3,4,5,7,8,9},{6,10}}
[7,8,9,2,3,10,4,1,5,6]=>{{1,2,4,7,8},{3,5,9},{6,10}}
[7,8,9,2,3,10,1,4,5,6]=>{{1,7},{2,4,8},{3,5,9},{6,10}}
[7,8,9,2,10,3,4,5,1,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,9,2,10,3,4,1,5,6]=>{{1,2,4,7,8},{3,5,6,9,10}}
[7,8,9,2,10,3,1,4,5,6]=>{{1,7},{2,4,8},{3,5,6,9,10}}
[7,8,9,2,10,1,3,4,5,6]=>{{1,3,5,6,7,9,10},{2,4,8}}
[7,8,9,10,2,3,4,1,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,8,9,10,2,3,1,4,5,6]=>{{1,7},{2,3,4,5,6,8,9,10}}
[7,8,9,10,2,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,9,8,7,6,4,3,2,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[10,9,8,6,1,7,5,4,3,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,2,9,3,4,5,6,7,10,8]=>{{1},{2},{3,4,5,6,7,8,9,10}}
[1,2,3,4,5,9,6,7,10,8]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,10,6,2,3,4,9,5,7,8]=>{{1},{2,3,4,5,6,8,10},{7,9}}
[1,5,2,9,3,10,4,6,7,8]=>{{1},{2,3,5},{4,7,9},{6,8,10}}
[1,2,4,3,10,9,5,6,7,8]=>{{1},{2},{3,4},{5,6,7,8,9,10}}
[1,3,2,4,5,10,9,6,7,8]=>{{1},{2,3},{4},{5},{6,8,10},{7,9}}
[2,1,3,4,5,9,6,10,7,8]=>{{1,2},{3},{4},{5},{6,7,9},{8,10}}
[10,7,8,1,2,3,4,5,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[6,7,10,1,2,3,4,5,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,10,2,3,4,7,5,6,8,9]=>{{1},{2,3,4,5,6,7,8,9,10}}
[10,9,8,6,7,5,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,5,6,7}}
[10,9,7,6,8,5,4,3,2,1]=>{{1,10},{2,9},{3,4,5,6,7,8}}
[10,8,7,6,9,5,4,3,2,1]=>{{1,10},{2,3,4,5,6,7,8,9}}
[9,8,7,6,4,3,2,5,1,10]=>{{1,9},{2,3,4,5,6,7,8},{10}}
[9,8,7,6,4,3,5,2,1,10]=>{{1,9},{2,8},{3,4,5,6,7},{10}}
[1,10,9,8,6,5,7,4,3,2]=>{{1},{2,10},{3,9},{4,8},{5,6},{7}}
[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,4,3,1,5,6,7,8,9,10]=>{{1,2,4},{3},{5},{6},{7},{8},{9},{10}}
[2,3,6,4,5,1,7,8,9,10]=>{{1,2,3,6},{4},{5},{7},{8},{9},{10}}
[3,4,5,2,1,6,7,8,9,10]=>{{1,3,5},{2,4},{6},{7},{8},{9},{10}}
[2,3,4,8,5,6,7,1,9,10]=>{{1,2,3,4,8},{5},{6},{7},{9},{10}}
[3,5,4,7,2,6,1,8,9,10]=>{{1,3,4,7},{2,5},{6},{8},{9},{10}}
[2,6,4,1,5,3,7,8,9,10]=>{{1,2,3,4,6},{5},{7},{8},{9},{10}}
[4,5,2,6,3,1,7,8,9,10]=>{{1,4,6},{2,3,5},{7},{8},{9},{10}}
[3,6,4,5,9,2,7,8,1,10]=>{{1,3,4,5,9},{2,6},{7},{8},{10}}
[2,5,4,7,8,6,3,1,9,10]=>{{1,2,5,8},{3,4,7},{6},{9},{10}}
[4,6,2,5,8,3,7,1,9,10]=>{{1,4,5,8},{2,3,6},{7},{9},{10}}
[3,5,7,6,1,4,2,8,9,10]=>{{1,2,3,5,7},{4,6},{8},{9},{10}}
[5,6,2,3,7,4,1,8,9,10]=>{{1,5,7},{2,3,4,6},{8},{9},{10}}
[2,5,4,8,6,10,7,3,9,1]=>{{1,2,5,6,10},{3,4,8},{7},{9}}
[4,7,2,5,6,10,3,8,9,1]=>{{1,4,5,6,10},{2,3,7},{8},{9}}
[2,3,9,5,6,1,7,8,4,10]=>{{1,2,3,4,5,6,9},{7},{8},{10}}
[5,7,2,3,6,9,4,8,1,10]=>{{1,5,6,9},{2,3,4,7},{8},{10}}
[2,8,4,1,6,3,7,5,9,10]=>{{1,2,3,4,5,6,8},{7},{9},{10}}
[4,6,7,8,3,1,5,2,9,10]=>{{1,2,4,6,8},{3,5,7},{9},{10}}
[6,7,2,3,4,8,5,1,9,10]=>{{1,6,8},{2,3,4,5,7},{9},{10}}
[3,6,4,10,8,7,1,5,9,2]=>{{1,2,3,4,6,7,10},{5,8},{9}}
[2,7,4,9,6,3,10,8,5,1]=>{{1,2,7,10},{3,4,5,6,9},{8}}
[4,6,8,7,3,9,10,5,2,1]=>{{1,4,7,10},{2,6,9},{3,5,8}}
[6,8,2,3,4,7,10,5,9,1]=>{{1,6,7,10},{2,3,4,5,8},{9}}
[3,5,9,7,1,8,2,6,4,10]=>{{1,2,3,4,5,7,9},{6,8},{10}}
[5,7,8,3,9,4,1,6,2,10]=>{{1,2,5,7,9},{3,4,6,8},{10}}
[7,8,2,3,4,5,9,6,1,10]=>{{1,7,9},{2,3,4,5,6,8},{10}}
[4,6,8,10,9,1,5,2,7,3]=>{{1,2,3,4,6,8,10},{5,7,9}}
[6,8,9,3,4,10,5,1,7,2]=>{{1,2,6,8,10},{3,4,5,7,9}}
[8,9,2,3,4,5,6,10,7,1]=>{{1,8,10},{2,3,4,5,6,7,9}}
[10,1,2,9,6,3,4,5,7,8]=>{{1,2,3,5,6,8,10},{4,7,9}}
[4,1,2,10,3,5,9,6,7,8]=>{{1,2,3,4,5,6,8,10},{7,9}}
[1,10,9,8,5,6,7,4,3,2]=>{{1},{2,10},{3,9},{4,8},{5},{6},{7}}
[1,10,9,5,6,7,8,4,3,2]=>{{1},{2,10},{3,9},{4,5,6,7,8}}
[1,10,4,5,6,7,8,9,3,2]=>{{1},{2,10},{3,4,5,6,7,8,9}}
[5,3,1,2,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[7,3,4,5,1,2,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[8,3,4,5,6,1,2,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,6,7,8,9,10,1,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,9,7,6,5,4,3,2,1]=>{{1,10},{2,3,8,9},{4,7},{5,6}}
[10,8,6,4,9,7,5,3,2,1]=>{{1,10},{2,3,5,6,7,8,9},{4}}
[10,8,6,4,2,1,9,7,5,3]=>{{1,3,6,10},{2,5,7,8,9},{4}}
[10,8,9,6,5,4,3,2,1,7]=>{{1,3,7,9,10},{2,8},{4,6},{5}}
[9,7,10,8,5,4,3,2,1,6]=>{{1,9},{2,3,4,6,7,8,10},{5}}
[9,7,4,3,2,1,5,10,8,6]=>{{1,6,8,9,10},{2,5,7},{3,4}}
[9,7,5,10,8,6,3,2,1,4]=>{{1,9},{2,3,5,7,8},{4,10},{6}}
[10,8,6,4,9,7,5,2,1,3]=>{{1,3,5,6,7,9,10},{2,8},{4}}
[10,8,6,4,1,2,9,7,5,3]=>{{1,2,3,5,6,7,8,9,10},{4}}
[2,5,1,6,3,7,4,8,9,10]=>{{1,2,3,5},{4,6,7},{8},{9},{10}}
[3,4,5,1,6,2,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}
[2,6,1,7,3,8,4,9,5,10]=>{{1,2,3,5,6,8,9},{4,7},{10}}
[3,4,6,1,7,2,8,5,9,10]=>{{1,2,3,4,6},{5,7,8},{9},{10}}
[3,2,6,1,7,4,8,5,9,10]=>{{1,3,4,6},{2},{5,7,8},{9},{10}}
[4,2,5,6,1,7,3,8,9,10]=>{{1,3,4,5,6,7},{2},{8},{9},{10}}
[3,4,2,6,1,7,5,8,9,10]=>{{1,2,3,4,5,6,7},{8},{9},{10}}
[3,2,7,1,8,4,9,5,10,6]=>{{1,3,4,6,7,9,10},{2},{5,8}}
[4,5,6,7,1,8,2,9,3,10]=>{{1,2,4,5,7},{3,6,8,9},{10}}
[3,4,2,7,1,8,5,9,6,10]=>{{1,2,3,4,5,7},{6,8,9},{10}}
[5,3,6,4,7,1,8,2,9,10]=>{{1,2,3,5,6,7,8},{4},{9},{10}}
[3,5,2,6,7,1,8,4,9,10]=>{{1,2,3,4,5,6,7,8},{9},{10}}
[4,3,5,2,7,1,8,6,9,10]=>{{1,2,3,4,5,6,7,8},{9},{10}}
[5,2,6,7,8,1,9,3,10,4]=>{{1,3,5,6,8},{2},{4,7,9,10}}
[5,3,6,4,8,1,9,2,10,7]=>{{1,2,3,5,6,8},{4},{7,9,10}}
[3,5,2,6,8,1,9,4,10,7]=>{{1,2,3,4,5,6,8},{7,9,10}}
[4,3,5,2,8,1,9,6,10,7]=>{{1,2,3,4,5,6,8},{7,9,10}}
[4,6,2,7,5,8,1,9,3,10]=>{{1,4,7},{2,3,6,8,9},{5},{10}}
[4,3,6,2,7,8,1,9,5,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[4,5,3,6,2,8,1,9,7,10]=>{{1,4,6,7,8,9},{2,5},{3},{10}}
[5,3,7,2,8,6,9,1,10,4]=>{{1,5,8},{2,3,4,7,9,10},{6}}
[4,5,3,7,2,8,9,1,10,6]=>{{1,4,6,7,8,9,10},{2,5},{3}}
[5,4,6,3,7,2,9,1,10,8]=>{{1,5,7,8,9,10},{2,3,4,6}}
[5,1,6,7,8,9,10,2,3,4]=>{{1,2,5,8},{3,6,9},{4,7,10}}
[5,6,7,8,9,10,1,3,4,2]=>{{1,3,4,5,7,8,9},{2,6,10}}
[5,6,7,8,9,10,1,4,3,2]=>{{1,3,5,7,9},{2,6,10},{4,8}}
[7,8,9,10,1,4,5,6,2,3]=>{{1,5,7},{2,3,4,6,8,9,10}}
[7,8,9,10,1,4,5,6,3,2]=>{{1,5,7},{2,4,6,8,10},{3,9}}
[7,8,9,10,1,5,6,4,3,2]=>{{1,5,6,7},{2,4,8,10},{3,9}}
[7,8,9,10,1,6,5,4,3,2]=>{{1,5,7},{2,4,8,10},{3,9},{6}}
[8,9,10,1,4,5,6,7,2,3]=>{{1,4,5,6,7,8},{2,9},{3,10}}
[8,9,10,1,4,5,6,7,3,2]=>{{1,4,5,6,7,8},{2,3,9,10}}
[8,9,10,1,5,6,7,2,3,4]=>{{1,2,3,4,8,9,10},{5},{6},{7}}
[8,9,10,1,5,6,7,4,3,2]=>{{1,4,8},{2,3,9,10},{5},{6},{7}}
[8,9,10,1,6,7,4,5,2,3]=>{{1,4,5,6,7,8},{2,9},{3,10}}
[8,9,10,1,6,7,4,5,3,2]=>{{1,4,5,6,7,8},{2,3,9,10}}
[8,9,10,1,6,7,5,4,3,2]=>{{1,4,8},{2,3,9,10},{5,6,7}}
[8,9,10,1,7,6,5,4,3,2]=>{{1,4,8},{2,3,9,10},{5,7},{6}}
[9,10,1,6,7,8,3,4,5,2]=>{{1,3,5,7,9},{2,10},{4,6,8}}
[9,10,1,6,7,8,4,5,2,3]=>{{1,2,3,9,10},{4,5,6,7,8}}
[9,10,1,6,7,8,4,5,3,2]=>{{1,3,9},{2,10},{4,5,6,7,8}}
[9,10,1,6,7,8,5,4,3,2]=>{{1,3,9},{2,10},{4,6,8},{5,7}}
[9,10,1,7,8,5,6,3,4,2]=>{{1,3,4,5,6,7,8,9},{2,10}}
[9,10,1,7,8,5,6,4,3,2]=>{{1,3,9},{2,10},{4,5,6,7,8}}
[9,10,1,7,8,6,5,4,3,2]=>{{1,3,9},{2,10},{4,5,7,8},{6}}
[10,1,8,9,6,7,4,5,3,2]=>{{1,2,10},{3,4,5,6,7,8,9}}
[10,1,8,9,6,7,5,4,3,2]=>{{1,2,10},{3,4,8,9},{5,6,7}}
[10,1,8,9,7,6,5,4,3,2]=>{{1,2,10},{3,4,8,9},{5,7},{6}}
[6,10,9,8,7,5,4,3,1,2]=>{{1,3,4,5,6,7,8,9},{2,10}}
[8,9,7,6,5,4,3,2,10,1]=>{{1,2,8,9,10},{3,7},{4,6},{5}}
[2,3,4,5,6,7,1,9,10,8]=>{{1,2,3,4,5,6,7},{8,9,10}}
[2,3,4,5,1,7,8,9,10,6]=>{{1,2,3,4,5},{6,7,8,9,10}}
[2,3,1,5,6,7,8,9,10,4]=>{{1,2,3},{4,5,6,7,8,9,10}}
[4,2,5,3,7,6,9,8,1,10]=>{{1,3,4,5,7,9},{2},{6},{8},{10}}
[4,2,6,3,7,5,9,8,1,10]=>{{1,3,4,5,6,7,9},{2},{8},{10}}
[4,2,6,3,8,5,9,7,1,10]=>{{1,3,4,5,6,7,8,9},{2},{10}}
[4,2,6,3,8,5,10,7,1,9]=>{{1,3,4,5,6,7,8,9,10},{2}}
[4,2,6,3,8,5,10,7,9,1]=>{{1,3,4,5,6,7,8,10},{2},{9}}
[4,2,6,3,8,5,7,10,9,1]=>{{1,3,4,5,6,8,10},{2},{7},{9}}
[4,2,6,3,5,8,7,10,9,1]=>{{1,3,4,6,8,10},{2},{5},{7},{9}}
[4,2,3,6,5,8,7,10,9,1]=>{{1,4,6,8,10},{2},{3},{5},{7},{9}}
[3,4,5,6,7,10,2,1,9,8]=>{{1,2,3,4,5,6,7,8,10},{9}}
[3,4,5,6,9,2,10,1,8,7]=>{{1,3,5,8,9},{2,4,6},{7,10}}
[3,4,5,8,2,9,10,1,6,7]=>{{1,2,3,4,5,8},{6,9},{7,10}}
[3,4,7,2,8,9,10,1,6,5]=>{{1,3,5,7,8,10},{2,4},{6,9}}
[3,6,2,7,8,9,10,1,5,4]=>{{1,2,3,5,6,8,9},{4,7,10}}
[5,2,6,7,8,9,10,1,3,4]=>{{1,5,8},{2},{3,6,9},{4,7,10}}
[9,10,8,7,6,5,4,1,3,2]=>{{1,3,8,9},{2,10},{4,7},{5,6}}
[10,8,7,6,5,4,3,2,9,1]=>{{1,10},{2,8},{3,7},{4,6},{5},{9}}
[2,9,4,5,6,7,8,1,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[4,3,10,5,6,7,8,9,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,2,9,5,6,7,8,1,10,4]=>{{1,3,4,5,6,7,8,9,10},{2}}
[8,9,4,5,6,7,1,3,10,2]=>{{1,3,4,5,6,7,8},{2,9,10}}
[3,4,1,10,6,7,8,9,2,5]=>{{1,3},{2,4,5,6,7,8,9,10}}
[4,9,10,5,6,7,8,2,1,3]=>{{1,2,4,5,6,7,8,9},{3,10}}
[9,1,2,3,6,4,5,7,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[5,6,7,8,9,10,3,2,1,4]=>{{1,5,9},{2,4,6,8,10},{3,7}}
[7,8,9,10,3,4,5,1,2,6]=>{{1,2,3,5,7,8,9},{4,6,10}}
[7,8,9,10,3,4,5,2,1,6]=>{{1,3,5,7,9},{2,8},{4,6,10}}
[7,8,9,10,4,5,2,3,1,6]=>{{1,2,3,7,8,9},{4,5,6,10}}
[7,8,9,10,4,5,3,2,1,6]=>{{1,3,7,9},{2,8},{4,5,6,10}}
[7,8,9,10,5,4,3,2,1,6]=>{{1,3,7,9},{2,8},{4,6,10},{5}}
[8,9,10,3,4,5,6,1,2,7]=>{{1,8},{2,9},{3,4,5,6,7,10}}
[8,9,10,3,4,5,6,2,1,7]=>{{1,2,8,9},{3,4,5,6,7,10}}
[8,9,10,4,5,6,1,2,3,7]=>{{1,2,3,7,8,9,10},{4},{5},{6}}
[8,9,10,4,5,6,3,2,1,7]=>{{1,2,8,9},{3,7,10},{4},{5},{6}}
[8,9,10,5,6,3,4,1,2,7]=>{{1,8},{2,9},{3,4,5,6,7,10}}
[8,9,10,5,6,3,4,2,1,7]=>{{1,2,8,9},{3,4,5,6,7,10}}
[8,9,10,5,6,4,3,2,1,7]=>{{1,2,8,9},{3,7,10},{4,5,6}}
[8,9,10,6,5,4,3,2,1,7]=>{{1,2,8,9},{3,7,10},{4,6},{5}}
[9,10,5,6,7,2,3,4,1,8]=>{{1,9},{2,4,6,8,10},{3,5,7}}
[9,10,5,6,7,3,4,1,2,8]=>{{1,2,8,9,10},{3,4,5,6,7}}
[9,10,5,6,7,3,4,2,1,8]=>{{1,9},{2,8,10},{3,4,5,6,7}}
[9,10,5,6,7,4,3,2,1,8]=>{{1,9},{2,8,10},{3,5,7},{4,6}}
[9,10,6,7,4,5,3,2,1,8]=>{{1,9},{2,8,10},{3,4,5,6,7}}
[9,10,6,7,5,4,3,2,1,8]=>{{1,9},{2,8,10},{3,4,6,7},{5}}
[9,10,7,6,5,4,3,2,1,8]=>{{1,9},{2,8,10},{3,7},{4,6},{5}}
[10,7,8,5,6,3,4,2,1,9]=>{{1,9,10},{2,3,4,5,6,7,8}}
[10,7,8,5,6,4,3,2,1,9]=>{{1,9,10},{2,3,7,8},{4,5,6}}
[10,7,8,6,5,4,3,2,1,9]=>{{1,9,10},{2,3,7,8},{4,6},{5}}
[10,9,1,2,3,7,8,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,1,2,8,7,3,4,5,6]=>{{1,3,6,7,10},{2,4,5,8,9}}
[9,8,1,10,7,2,3,4,5,6]=>{{1,3,5,7,9},{2,4,6,8,10}}
[8,6,1,2,3,4,5,9,10,7]=>{{1,3,5,7,8,9,10},{2,4,6}}
[5,7,1,2,3,4,8,9,10,6]=>{{1,3,5},{2,4,6,7,8,9,10}}
[10,4,1,2,3,7,8,9,5,6]=>{{1,3,5,6,7,8,9,10},{2,4}}
[10,3,1,2,9,7,8,4,5,6]=>{{1,2,3,4,6,7,8,10},{5,9}}
[2,9,1,10,8,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,7,1,8,2,9,3,4,5,6]=>{{1,2,3,5,6,7,9,10},{4,8}}
[9,7,1,10,8,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,7,1,8,2,3,4,5,6]=>{{1,2,4,5,6,8,9,10},{3,7}}
[10,6,1,7,2,8,3,9,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[9,6,1,10,7,2,8,3,4,5]=>{{1,3,4,5,7,8,9,10},{2,6}}
[10,9,6,1,7,2,8,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,8,6,1,9,7,2,3,4,5]=>{{1,4,5,9,10},{2,3,6,7,8}}
[10,9,8,6,1,7,2,3,4,5]=>{{1,5,10},{2,4,6,7,9},{3,8}}
[9,5,1,10,6,2,7,3,8,4]=>{{1,3,8,9},{2,5,6},{4,10},{7}}
[10,9,5,1,6,2,7,3,8,4]=>{{1,4,10},{2,3,5,6,8,9},{7}}
[8,5,1,9,6,2,10,7,3,4]=>{{1,3,4,7,8,9,10},{2,5,6}}
[10,8,5,1,9,6,2,7,3,4]=>{{1,4,10},{2,7,8},{3,5,9},{6}}
[10,9,8,5,1,6,2,7,3,4]=>{{1,4,5,10},{2,3,7,8,9},{6}}
[9,7,5,1,10,8,6,2,3,4]=>{{1,3,4,5,9,10},{2,6,7,8}}
[10,9,7,5,1,8,6,2,3,4]=>{{1,4,5,10},{2,3,6,7,8,9}}
[10,9,8,7,5,1,6,2,3,4]=>{{1,4,6,7,10},{2,3,8,9},{5}}
[9,7,4,1,10,8,5,2,6,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,7,4,1,8,5,2,6,3]=>{{1,3,5,7,10},{2,6,8,9},{4}}
[10,9,8,7,4,1,5,2,6,3]=>{{1,2,3,6,8,9,10},{4,5,7}}
[10,8,6,4,1,9,7,5,2,3]=>{{1,2,3,5,6,8,9,10},{4},{7}}
[10,9,8,6,4,1,7,5,2,3]=>{{1,3,4,5,6,8,10},{2,9},{7}}
[10,9,8,7,6,4,1,5,2,3]=>{{1,3,4,5,6,7,8,10},{2,9}}
[10,9,7,5,3,1,8,6,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,9,8,7,5,3,1,6,4,2]=>{{1,2,4,7,9,10},{3,6,8},{5}}
[10,9,8,7,6,5,3,1,4,2]=>{{1,2,3,4,7,8,9,10},{5,6}}
[2,3,4,10,6,7,8,9,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,10,5,6,7,8,9,1,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,10,1,9,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,10,1,8,9,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,10,1,6,7,8,9,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,4,2,6,5,8,7,10,9,3]=>{{1},{2,3,4,6,8,10},{5},{7},{9}}
[1,5,2,6,4,8,7,10,9,3]=>{{1},{2,3,4,5,6,8,10},{7},{9}}
[1,5,2,7,4,8,6,10,9,3]=>{{1},{2,3,4,5,6,7,8,10},{9}}
[1,5,2,7,4,9,6,10,8,3]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,5,2,7,4,9,6,8,10,3]=>{{1},{2,3,4,5,6,7,9,10},{8}}
[1,5,2,7,4,6,9,8,10,3]=>{{1},{2,3,4,5,7,9,10},{6},{8}}
[1,5,2,4,7,6,9,8,10,3]=>{{1},{2,3,5,7,9,10},{4},{6},{8}}
[1,2,5,4,7,6,9,8,10,3]=>{{1},{2},{3,5,7,9,10},{4},{6},{8}}
[5,6,7,8,10,9,4,3,2,1]=>{{1,5,10},{2,6,9},{3,4,7,8}}
[6,5,7,8,9,10,4,3,2,1]=>{{1,6,10},{2,5,9},{3,4,7,8}}
[4,5,6,7,8,10,9,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[5,4,6,7,8,9,10,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,5,6,7,9,10,8,1,2]=>{{1,2,3,4,5,6,7,9,10},{8}}
[3,4,5,6,8,9,10,7,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[3,4,6,7,8,9,10,5,1,2]=>{{1,3,6,9},{2,4,7,10},{5,8}}
[3,5,6,7,8,9,10,4,1,2]=>{{1,3,6,9},{2,4,5,7,8,10}}
[3,4,5,6,7,10,1,8,9,2]=>{{1,3,5,7},{2,4,6,10},{8},{9}}
[3,4,5,6,9,1,10,8,7,2]=>{{1,2,3,4,5,6,7,9,10},{8}}
[3,4,5,8,1,9,10,7,6,2]=>{{1,3,5},{2,4,7,8,10},{6,9}}
[3,4,7,1,8,9,10,5,6,2]=>{{1,2,3,4,7,10},{5,8},{6,9}}
[3,6,1,7,8,9,10,5,4,2]=>{{1,3},{2,4,6,7,9,10},{5,8}}
[5,1,6,7,8,9,10,4,3,2]=>{{1,2,4,5,7,8,10},{3,6,9}}
[6,10,5,1,2,3,4,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[10,5,4,1,2,3,6,7,8,9]=>{{1,3,4,6,7,8,9,10},{2,5}}
[10,9,3,4,5,6,8,7,2,1]=>{{1,10},{2,9},{3},{4},{5},{6},{7,8}}
[10,9,4,3,5,6,7,8,2,1]=>{{1,10},{2,9},{3,4},{5},{6},{7},{8}}
[10,3,4,5,6,7,9,8,2,1]=>{{1,10},{2,3,4,5,6,7,9},{8}}
[10,4,3,5,6,7,8,9,2,1]=>{{1,10},{2,4,5,6,7,8,9},{3}}
[1,7,5,6,8,4,9,3,10,2]=>{{1},{2,7,9,10},{3,5,8},{4,6}}
[1,2,3,4,5,8,6,9,7,10]=>{{1},{2},{3},{4},{5},{6,7,8,9},{10}}
[1,2,3,4,5,9,6,10,7,8]=>{{1},{2},{3},{4},{5},{6,7,9},{8,10}}
[10,8,7,6,5,4,3,9,2,1]=>{{1,10},{2,8,9},{3,7},{4,6},{5}}
[10,9,7,6,5,4,8,3,2,1]=>{{1,10},{2,9},{3,7,8},{4,6},{5}}
[1,2,3,4,5,6,7,8,9,11,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[2,1,3,4,5,6,7,8,9,10,11]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[11,1,2,3,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[10,1,2,3,4,5,6,7,8,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,1,2,3,4,5,6,7,10,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,1,2,3,4,5,6,10,7,8,9]=>{{1,2,3,4,5,6,7,9,11},{8,10}}
[10,1,2,3,4,5,11,6,7,8,9]=>{{1,2,3,4,5,6,8,10},{7,9,11}}
[11,1,2,3,4,10,5,6,7,8,9]=>{{1,2,3,4,5,7,9,11},{6,8,10}}
[11,1,2,3,10,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[10,1,2,11,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,1,10,2,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,10,1,2,3,4,5,6,7,8,9]=>{{1,3,5,7,9,11},{2,4,6,8,10}}
[10,9,8,7,6,5,4,3,2,1,11]=>{{1,10},{2,9},{3,8},{4,7},{5,6},{11}}
[1,11,10,9,8,7,6,5,4,3,2]=>{{1},{2,11},{3,10},{4,9},{5,8},{6,7}}
[2,3,4,5,6,7,8,9,10,11,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[3,1,4,5,6,7,8,9,10,11,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,3,4,5,6,7,8,9,1,2,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,1,4,5,6,7,8,9,10,2,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[10,1,2,3,4,5,6,7,8,9,11]=>{{1,2,3,4,5,6,7,8,9,10},{11}}
[1,11,2,3,4,5,6,7,8,9,10]=>{{1},{2,3,4,5,6,7,8,9,10,11}}
[10,9,8,7,6,5,4,3,1,11,2]=>{{1,2,9,10,11},{3,8},{4,7},{5,6}}
[9,11,8,7,6,5,4,3,2,1,10]=>{{1,2,9,10,11},{3,8},{4,7},{5,6}}
[1,9,8,7,6,5,4,3,11,10,2]=>{{1},{2,9,11},{3,8},{4,7},{5,6},{10}}
[1,11,8,7,6,5,4,3,2,10,9]=>{{1},{2,9,11},{3,8},{4,7},{5,6},{10}}
[10,11,9,8,7,6,5,4,3,2,1]=>{{1,2,10,11},{3,9},{4,8},{5,7},{6}}
[11,10,9,8,7,6,5,4,3,1,2]=>{{1,2,10,11},{3,9},{4,8},{5,7},{6}}
[2,3,4,5,6,7,8,9,10,1,11]=>{{1,2,3,4,5,6,7,8,9,10},{11}}
[1,3,4,5,6,7,8,9,10,11,2]=>{{1},{2,3,4,5,6,7,8,9,10,11}}
[2,11,1,3,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,3,1,2,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,4,1,2,3,5,6,7,8,9,10]=>{{1,3,5,6,7,8,9,10,11},{2,4}}
[5,11,1,2,3,4,6,7,8,9,10]=>{{1,3,5},{2,4,6,7,8,9,10,11}}
[11,6,1,2,3,4,5,7,8,9,10]=>{{1,3,5,7,8,9,10,11},{2,4,6}}
[11,7,1,2,3,4,5,6,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[8,11,1,2,3,4,5,6,7,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,9,1,2,3,4,5,6,7,8,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,9,8,7,6,5,4,3,2,1,10]=>{{1,10,11},{2,9},{3,8},{4,7},{5,6}}
[10,9,8,7,6,5,4,3,2,11,1]=>{{1,10,11},{2,9},{3,8},{4,7},{5,6}}
[9,8,10,7,6,5,4,3,2,1,11]=>{{1,2,3,8,9,10},{4,7},{5,6},{11}}
[9,8,7,10,6,5,4,3,2,1,11]=>{{1,2,3,4,7,8,9,10},{5,6},{11}}
[9,8,7,6,11,5,4,3,2,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[9,8,7,6,5,10,4,3,2,1,11]=>{{1,2,3,4,6,7,8,9,10},{5},{11}}
[9,8,7,6,5,4,10,3,2,1,11]=>{{1,2,3,7,8,9,10},{4,6},{5},{11}}
[9,8,7,6,5,4,3,11,2,1,10]=>{{1,2,8,9,10,11},{3,7},{4,6},{5}}
[9,8,7,6,5,4,3,2,10,1,11]=>{{1,9,10},{2,8},{3,7},{4,6},{5},{11}}
[9,8,7,6,5,4,3,2,1,10,11]=>{{1,9},{2,8},{3,7},{4,6},{5},{10},{11}}
[3,4,5,6,7,8,9,10,11,2,1]=>{{1,3,5,7,9,11},{2,4,6,8,10}}
[10,1,11,9,8,7,6,5,4,3,2]=>{{1,2,3,10,11},{4,9},{5,8},{6,7}}
[2,11,10,9,8,7,6,5,4,1,3]=>{{1,2,3,10,11},{4,9},{5,8},{6,7}}
[10,2,1,9,8,7,6,5,4,3,11]=>{{1,3,10},{2},{4,9},{5,8},{6,7},{11}}
[3,2,10,9,8,7,6,5,4,1,11]=>{{1,3,10},{2},{4,9},{5,8},{6,7},{11}}
[2,11,10,9,8,7,6,5,4,3,1]=>{{1,2,11},{3,10},{4,9},{5,8},{6,7}}
[11,1,10,9,8,7,6,5,4,3,2]=>{{1,2,11},{3,10},{4,9},{5,8},{6,7}}
[1,11,10,9,8,7,6,5,2,4,3]=>{{1},{2,3,4,9,10,11},{5,8},{6,7}}
[1,11,10,9,8,7,6,2,5,4,3]=>{{1},{2,3,4,5,8,9,10,11},{6,7}}
[2,11,10,9,8,7,1,6,5,4,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,11,10,9,8,2,7,6,5,4,3]=>{{1},{2,3,4,5,6,8,9,10,11},{7}}
[1,11,10,9,2,8,7,6,5,4,3]=>{{1},{2,3,4,5,9,10,11},{6,8},{7}}
[2,11,10,1,9,8,7,6,5,4,3]=>{{1,2,3,4,10,11},{5,9},{6,8},{7}}
[1,11,2,10,9,8,7,6,5,4,3]=>{{1},{2,3,11},{4,10},{5,9},{6,8},{7}}
[1,2,11,10,9,8,7,6,5,4,3]=>{{1},{2},{3,11},{4,10},{5,9},{6,8},{7}}
[6,7,8,9,10,1,2,3,4,5,11]=>{{1,6},{2,7},{3,8},{4,9},{5,10},{11}}
[1,7,8,9,10,11,2,3,4,5,6]=>{{1},{2,7},{3,8},{4,9},{5,10},{6,11}}
[2,4,1,5,6,7,8,9,10,11,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,2,3,4,6,8,5,7,10,9,11]=>{{1},{2},{3},{4},{5,6,7,8},{9,10},{11}}
[1,2,3,4,7,5,8,6,10,9,11]=>{{1},{2},{3},{4},{5,6,7,8},{9,10},{11}}
[11,10,9,8,7,6,5,4,3,2,1]=>{{1,11},{2,10},{3,9},{4,8},{5,7},{6}}
[2,1,11,10,9,8,7,6,5,4,3]=>{{1,2},{3,11},{4,10},{5,9},{6,8},{7}}
[1,2,3,4,5,6,7,8,10,11,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10,11}}
[2,4,1,3,6,5,8,7,10,9,11]=>{{1,2,3,4},{5,6},{7,8},{9,10},{11}}
[11,3,4,5,6,7,8,9,10,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[10,3,4,5,6,7,8,9,1,11,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[9,3,4,5,6,7,8,1,10,11,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[8,3,4,5,6,7,1,9,10,11,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[7,3,4,5,6,1,8,9,10,11,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[6,3,4,5,1,7,8,9,10,11,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[5,3,4,1,6,7,8,9,10,11,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[4,3,1,5,6,7,8,9,10,11,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,11,4,5,6,7,8,9,10,1,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[10,9,4,5,6,7,8,1,2,11,3]=>{{1,3,4,5,6,7,8,10,11},{2,9}}
[2,11,10,5,6,7,8,9,1,3,4]=>{{1,2,4,5,6,7,8,9,11},{3,10}}
[11,2,3,4,5,6,7,8,9,10,1]=>{{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,1,2,3,4,5,6,7,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,11,10,1,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,4,1,6,3,5,8,7,10,9,11]=>{{1,2,3,4,5,6},{7,8},{9,10},{11}}
[10,1,2,3,4,5,6,7,11,8,9]=>{{1,2,3,4,5,6,7,8,10},{9,11}}
[1,11,2,3,4,5,6,7,8,10,9]=>{{1},{2,3,4,5,6,7,8,9,11},{10}}
[1,2,11,3,4,5,6,7,8,10,9]=>{{1},{2},{3,4,5,6,7,8,9,11},{10}}
[1,2,3,10,4,5,6,7,11,8,9]=>{{1},{2},{3},{4,5,6,7,8,10},{9,11}}
[1,2,3,4,11,5,6,7,8,10,9]=>{{1},{2},{3},{4},{5,6,7,8,9,11},{10}}
[1,2,3,4,5,11,6,7,8,10,9]=>{{1},{2},{3},{4},{5},{6,7,8,9,11},{10}}
[1,2,3,4,5,6,10,7,11,8,9]=>{{1},{2},{3},{4},{5},{6},{7,8,10},{9,11}}
[1,2,3,4,5,6,7,11,8,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,11},{10}}
[1,2,3,4,5,6,7,8,11,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,11},{10}}
[1,2,3,4,5,6,7,8,11,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10,11}}
[11,1,3,4,5,6,7,8,9,10,2]=>{{1,2,11},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,2,3,4,5,6,7,8,11,1,9]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9,11}}
[10,11,3,4,5,6,7,8,9,1,2]=>{{1,10},{2,11},{3},{4},{5},{6},{7},{8},{9}}
[7,1,2,3,4,5,11,6,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,1,2,3,4,5,8,6,7,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,1,2,3,4,5,9,6,7,8,10]=>{{1,2,3,4,5,6,8,10,11},{7,9}}
[11,10,5,1,2,3,4,6,7,8,9]=>{{1,4,7,9,11},{2,3,5,6,8,10}}
[11,10,1,5,2,3,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[5,11,1,2,10,3,4,6,7,8,9]=>{{1,3,5,6,8,10},{2,4,7,9,11}}
[5,11,1,2,3,10,4,6,7,8,9]=>{{1,3,5},{2,4,7,9,11},{6,8,10}}
[2,3,4,5,6,7,8,10,11,1,9]=>{{1,2,3,4,5,6,7,8,10},{9,11}}
[2,4,5,6,7,8,9,10,11,1,3]=>{{1,2,4,6,8,10},{3,5,7,9,11}}
[3,4,5,6,7,8,9,10,11,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[10,11,1,9,2,3,4,5,6,7,8]=>{{1,3,4,6,7,9,10},{2,5,8,11}}
[1,2,3,4,5,6,7,8,9,10,11]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[10,1,11,2,3,4,5,6,7,8,9]=>{{1,2,4,6,8,10},{3,5,7,9,11}}
[10,11,1,2,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[3,1,4,2,6,5,8,7,10,9,11]=>{{1,2,3,4},{5,6},{7,8},{9,10},{11}}
[1,2,3,4,5,6,7,8,10,9,11]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10},{11}}
[11,2,3,4,5,6,7,8,9,1,10]=>{{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}}
[3,11,1,4,5,6,7,8,9,10,2]=>{{1,3},{2,11},{4},{5},{6},{7},{8},{9},{10}}
[9,1,11,3,4,5,6,7,8,2,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,6,7,8,9,11,10,1]=>{{1,2,3,4,5,6,7,8,9,11},{10}}
[3,1,11,5,6,7,8,9,10,2,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,1,4,5,6,7,8,9,10,11]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11}}
[3,1,2,4,5,6,7,8,9,10,11]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11}}
[3,4,5,6,7,8,9,10,1,2,11]=>{{1,3,5,7,9},{2,4,6,8,10},{11}}
[3,4,5,6,7,9,10,11,1,2,8]=>{{1,2,3,4,5,6,7,9,10},{8,11}}
[3,4,6,7,8,9,10,11,1,2,5]=>{{1,3,6,9},{2,4,7,10},{5,8,11}}
[11,1,10,5,6,7,8,9,2,3,4]=>{{1,2,4,5,6,7,8,9,11},{3,10}}
[10,1,11,9,6,7,8,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[9,1,10,11,8,7,2,3,4,5,6]=>{{1,2,4,6,7,9,11},{3,5,8,10}}
[8,1,9,10,11,2,3,4,5,6,7]=>{{1,2,4,6,8,10},{3,5,7,9,11}}
[11,1,10,9,2,3,4,5,6,7,8]=>{{1,2,5,8,11},{3,4,6,7,9,10}}
[9,8,7,6,5,4,3,2,1,11,10]=>{{1,9},{2,8},{3,7},{4,6},{5},{10,11}}
[2,3,4,5,6,7,10,9,11,8,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,6,10,8,9,11,7,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,10,7,8,9,11,1,6]=>{{1,2,3,4,5,10},{6,7,8,9,11}}
[2,3,4,10,6,7,8,9,11,5,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,10,5,6,7,8,9,11,4,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,10,4,5,6,7,8,9,11,1,3]=>{{1,2,10},{3,4,5,6,7,8,9,11}}
[10,3,4,5,6,7,8,9,11,2,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,3,2,5,4,7,6,9,8,11,10]=>{{1},{2,3},{4,5},{6,7},{8,9},{10,11}}
[10,9,11,8,7,6,5,4,3,2,1]=>{{1,2,3,9,10,11},{4,8},{5,7},{6}}
[3,4,5,6,7,8,9,10,1,11,2]=>{{1,3,5,7,9},{2,4,6,8,10,11}}
[6,5,7,4,8,3,9,2,10,1,11]=>{{1,3,6,7,9,10},{2,5,8},{4},{11}}
[1,7,6,8,5,9,4,10,3,11,2]=>{{1},{2,4,7,8,10,11},{3,6,9},{5}}
[2,3,4,5,6,7,8,11,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,3,4,5,6,7,8,10,1,2,9]=>{{1,9,11},{2,3,4,5,6,7,8,10}}
[3,2,4,5,6,7,8,9,10,11,1]=>{{1,3,4,5,6,7,8,9,10,11},{2}}
[3,4,5,6,7,8,1,9,2,11,10]=>{{1,3,5,7},{2,4,6,8,9},{10,11}}
[1,4,5,6,7,11,8,9,2,10,3]=>{{1},{2,3,4,5,6,7,8,9,11},{10}}
[8,9,10,7,6,1,2,3,4,11,5]=>{{1,3,5,6,8,10,11},{2,4,7,9}}
[2,9,10,11,8,7,1,3,4,5,6]=>{{1,2,4,6,7,9,11},{3,5,8,10}}
[7,8,9,10,1,2,3,4,5,11,6]=>{{1,3,5,7,9},{2,4,6,8,10,11}}
[2,8,9,10,11,1,3,4,5,6,7]=>{{1,2,4,6,8,10},{3,5,7,9,11}}
[2,3,4,5,6,7,8,11,1,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,6,7,11,1,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,6,11,1,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,11,1,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,11,1,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,11,1,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[3,1,4,5,6,7,8,9,11,2,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,11,1,3,4,5,6,7,10,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,10,1,3,4,5,6,7,8,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,2,1,3,4,5,6,7,8,9,10]=>{{1,3,4,5,6,7,8,9,10,11},{2}}
[11,10,2,3,4,5,6,7,8,9,1]=>{{1,11},{2,3,4,5,6,7,8,9,10}}
[11,3,4,5,6,7,8,9,10,2,1]=>{{1,11},{2,3,4,5,6,7,8,9,10}}
[9,11,1,2,3,4,5,6,7,8,10]=>{{1,3,5,7,9},{2,4,6,8,10,11}}
[11,10,9,8,6,7,5,4,3,2,1]=>{{1,11},{2,10},{3,9},{4,8},{5,6,7}}
[11,1,2,3,4,5,6,10,8,7,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,1,2,3,4,5,10,7,8,6,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[10,1,2,3,4,11,6,7,8,5,9]=>{{1,2,3,4,5,10},{6,7,8,9,11}}
[11,1,2,3,10,5,6,7,8,4,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,1,2,10,4,5,6,7,8,3,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[10,1,11,3,4,5,6,7,8,2,9]=>{{1,2,10},{3,4,5,6,7,8,9,11}}
[11,10,2,3,4,5,6,7,8,1,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[11,10,2,1,4,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[10,11,8,1,2,3,4,5,6,7,9]=>{{1,4,7,10},{2,3,5,6,8,9,11}}
[6,7,5,4,3,2,1,8,9,10,11]=>{{1,2,6,7},{3,5},{4},{8},{9},{10},{11}}
[7,6,5,4,3,1,2,8,9,10,11]=>{{1,2,6,7},{3,5},{4},{8},{9},{10},{11}}
[9,11,10,8,7,6,5,4,3,2,1]=>{{1,2,3,9,10,11},{4,8},{5,7},{6}}
[11,10,9,8,5,7,6,4,3,2,1]=>{{1,11},{2,10},{3,9},{4,8},{5},{6,7}}
[11,10,9,8,6,5,7,4,3,2,1]=>{{1,11},{2,10},{3,9},{4,8},{5,6},{7}}
[8,9,1,2,3,4,5,6,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,6,7,8,9,1,11,10]=>{{1,2,3,4,5,6,7,8,9},{10,11}}
[3,4,1,5,6,7,8,9,10,11,2]=>{{1,3},{2,4,5,6,7,8,9,10,11}}
[1,3,4,5,6,7,8,9,11,2,10]=>{{1},{2,3,4,5,6,7,8,9,10,11}}
[1,4,2,5,6,7,8,9,11,10,3]=>{{1},{2,3,4,5,6,7,8,9,11},{10}}
[1,2,10,3,4,5,6,7,8,11,9]=>{{1},{2},{3,4,5,6,7,8,9,10,11}}
[1,2,3,4,5,10,6,7,8,11,9]=>{{1},{2},{3},{4},{5},{6,7,8,9,10,11}}
[11,9,10,8,7,6,5,4,3,2,1]=>{{1,11},{2,3,9,10},{4,8},{5,7},{6}}
[10,8,11,9,7,6,5,4,3,2,1]=>{{1,2,3,4,8,9,10,11},{5,7},{6}}
[10,8,6,5,4,3,2,1,11,9,7]=>{{1,2,7,8,9,10,11},{3,6},{4,5}}
[10,8,6,11,9,7,5,4,3,2,1]=>{{1,2,4,8,10,11},{3,5,6,7,9}}
[11,9,7,5,10,8,6,4,3,2,1]=>{{1,11},{2,3,4,5,6,7,8,9,10}}
[11,9,7,5,3,2,1,10,8,6,4]=>{{1,3,4,5,7,11},{2,6,8,9,10}}
[11,9,7,5,3,10,8,6,4,2,1]=>{{1,11},{2,3,4,5,6,7,8,9,10}}
[10,8,6,4,2,11,9,7,5,3,1]=>{{1,3,6,10,11},{2,5,7,8,9},{4}}
[5,6,7,8,9,11,1,2,3,4,10]=>{{1,3,5,7,9},{2,4,6,8,10,11}}
[6,1,7,8,9,10,11,2,3,4,5]=>{{1,2,4,6,8,10},{3,5,7,9,11}}
[3,4,5,6,7,8,9,11,1,10,2]=>{{1,3,5,7,9},{2,4,6,8,11},{10}}
[3,4,5,6,7,8,10,11,1,9,2]=>{{1,3,5,7,9,10},{2,4,6,8,11}}
[3,4,5,6,8,9,10,11,1,7,2]=>{{1,2,3,4,5,6,8,9,11},{7,10}}
[3,4,5,7,8,9,10,11,1,6,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[3,5,6,7,8,9,10,11,1,4,2]=>{{1,3,6,9},{2,5,8,11},{4,7,10}}
[4,5,6,7,8,9,10,11,1,3,2]=>{{1,3,4,6,7,9,10},{2,5,8,11}}
[10,2,3,4,5,6,7,8,9,11,1]=>{{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}}
[2,10,4,5,6,7,8,9,1,11,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[4,3,11,5,6,7,8,9,10,2,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[8,11,1,2,3,4,5,9,10,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[10,11,1,2,3,4,8,9,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[10,11,1,2,3,9,8,4,5,6,7]=>{{1,3,5,6,9,10},{2,4,7,8,11}}
[10,9,1,2,11,8,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[9,8,1,10,11,2,3,4,5,6,7]=>{{1,3,5,7,9,11},{2,4,6,8,10}}
[11,8,9,10,1,2,3,4,5,6,7]=>{{1,3,5,7,9,11},{2,4,6,8,10}}
[2,3,4,5,6,7,11,9,10,1,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,6,11,8,9,10,1,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,5,11,7,8,9,10,1,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,4,11,6,7,8,9,10,1,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[2,3,11,5,6,7,8,9,10,1,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[5,6,7,8,9,11,10,4,3,2,1]=>{{1,2,3,5,6,7,9,10,11},{4,8}}
[6,5,7,8,9,10,11,4,3,2,1]=>{{1,2,3,5,6,7,9,10,11},{4,8}}
[3,4,5,6,7,8,10,11,9,1,2]=>{{1,3,5,7,10},{2,4,6,8,11},{9}}
[3,4,5,6,7,9,10,11,8,1,2]=>{{1,3,5,7,10},{2,4,6,8,9,11}}
[3,4,5,7,8,9,10,11,6,1,2]=>{{1,2,3,4,5,7,8,10,11},{6,9}}
[3,4,6,7,8,9,10,11,5,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[4,5,6,7,8,9,10,11,3,1,2]=>{{1,4,7,10},{2,5,8,11},{3,6,9}}
[4,5,6,7,8,9,10,11,2,1,3]=>{{1,4,7,10},{2,3,5,6,8,9,11}}
[11,10,3,4,5,6,7,9,8,2,1]=>{{1,11},{2,10},{3},{4},{5},{6},{7},{8,9}}
[11,10,4,3,5,6,7,8,9,2,1]=>{{1,11},{2,10},{3,4},{5},{6},{7},{8},{9}}
[2,1,4,3,6,5,8,7,10,9,12,11]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[6,5,4,3,2,1,12,11,10,9,8,7]=>{{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}}
[12,11,10,9,8,7,6,5,4,3,2,1]=>{{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}
[2,4,6,8,10,12,1,3,5,7,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,4,6,8,11,12,1,3,5,7,9,10]=>{{1,2,3,4,6,7,8,10,12},{5,9,11}}
[2,4,6,9,10,12,1,3,5,7,8,11]=>{{1,2,4,5,7,9,10},{3,6,8,11,12}}
[2,4,6,9,11,12,1,3,5,7,8,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,4,6,10,11,12,1,3,5,7,8,9]=>{{1,2,4,7,10},{3,5,6,8,9,11,12}}
[2,4,7,8,10,12,1,3,5,6,9,11]=>{{1,2,3,4,7,8},{5,6,9,10,11,12}}
[2,4,7,8,11,12,1,3,5,6,9,10]=>{{1,2,3,4,7,8},{5,9,11},{6,10,12}}
[2,4,7,9,10,12,1,3,5,6,8,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,4,7,9,11,12,1,3,5,6,8,10]=>{{1,2,3,4,5,7,8,9,11},{6,10,12}}
[2,4,7,10,11,12,1,3,5,6,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,4,8,9,10,12,1,3,5,6,7,11]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}}
[2,4,8,9,11,12,1,3,5,6,7,10]=>{{1,2,4,5,7,9,11},{3,8},{6,10,12}}
[2,4,8,10,11,12,1,3,5,6,7,9]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}}
[2,4,9,10,11,12,1,3,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,5,6,8,10,12,1,3,4,7,9,11]=>{{1,2,5,7,10},{3,4,6,8,9,11,12}}
[2,5,6,8,11,12,1,3,4,7,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,5,6,9,10,12,1,3,4,7,8,11]=>{{1,2,5,7,10},{3,6,8,11,12},{4,9}}
[2,5,6,9,11,12,1,3,4,7,8,10]=>{{1,2,3,5,6,7,8,10,11,12},{4,9}}
[2,5,6,10,11,12,1,3,4,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,5,7,8,10,12,1,3,4,6,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,5,7,8,11,12,1,3,4,6,9,10]=>{{1,2,3,4,5,7,8,9,11},{6,10,12}}
[2,5,7,9,10,12,1,3,4,6,8,11]=>{{1,2,3,5,6,7,8,10,11,12},{4,9}}
[2,5,7,9,11,12,1,3,4,6,8,10]=>{{1,2,3,5,7,8,11},{4,9},{6,10,12}}
[2,5,7,10,11,12,1,3,4,6,8,9]=>{{1,2,3,5,7,8,11},{4,6,9,10,12}}
[2,5,8,9,10,12,1,3,4,6,7,11]=>{{1,2,5,6,7,10,11,12},{3,8},{4,9}}
[2,5,8,9,11,12,1,3,4,6,7,10]=>{{1,2,5,7,11},{3,8},{4,9},{6,10,12}}
[2,5,8,10,11,12,1,3,4,6,7,9]=>{{1,2,5,7,11},{3,8},{4,6,9,10,12}}
[2,5,9,10,11,12,1,3,4,6,7,8]=>{{1,2,5,7,11},{3,4,6,8,9,10,12}}
[2,6,7,8,10,12,1,3,4,5,9,11]=>{{1,2,3,4,6,7,8,9,11,12},{5,10}}
[2,6,7,8,11,12,1,3,4,5,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,6,7,9,10,12,1,3,4,5,8,11]=>{{1,2,3,6,7,8,11,12},{4,9},{5,10}}
[2,6,7,9,11,12,1,3,4,5,8,10]=>{{1,2,3,5,6,7,8,10,11,12},{4,9}}
[2,6,7,10,11,12,1,3,4,5,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,6,8,9,10,12,1,3,4,5,7,11]=>{{1,2,6,7,11,12},{3,8},{4,9},{5,10}}
[2,6,8,9,11,12,1,3,4,5,7,10]=>{{1,2,5,6,7,10,11,12},{3,8},{4,9}}
[2,6,8,10,11,12,1,3,4,5,7,9]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}}
[2,6,9,10,11,12,1,3,4,5,7,8]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,7,8,9,10,12,1,3,4,5,6,11]=>{{1,2,7},{3,8},{4,9},{5,10},{6,11,12}}
[2,7,8,9,11,12,1,3,4,5,6,10]=>{{1,2,7},{3,8},{4,9},{5,6,10,11,12}}
[2,7,8,10,11,12,1,3,4,5,6,9]=>{{1,2,7},{3,8},{4,5,6,9,10,11,12}}
[2,7,9,10,11,12,1,3,4,5,6,8]=>{{1,2,7},{3,4,5,6,8,9,10,11,12}}
[2,8,9,10,11,12,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,4,6,8,10,12,1,2,5,7,9,11]=>{{1,3,5,6,7,9,10,11,12},{2,4,8}}
[3,4,6,8,11,12,1,2,5,7,9,10]=>{{1,3,6,7,10,12},{2,4,8},{5,9,11}}
[3,4,6,9,10,12,1,2,5,7,8,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,4,6,9,11,12,1,2,5,7,8,10]=>{{1,3,6,7,10,12},{2,4,5,8,9,11}}
[3,4,6,10,11,12,1,2,5,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,4,7,8,10,12,1,2,5,6,9,11]=>{{1,3,7},{2,4,8},{5,6,9,10,11,12}}
[3,4,7,8,11,12,1,2,5,6,9,10]=>{{1,3,7},{2,4,8},{5,9,11},{6,10,12}}
[3,4,7,9,10,12,1,2,5,6,8,11]=>{{1,3,7},{2,4,5,6,8,9,10,11,12}}
[3,4,7,9,11,12,1,2,5,6,8,10]=>{{1,3,7},{2,4,5,8,9,11},{6,10,12}}
[3,4,7,10,11,12,1,2,5,6,8,9]=>{{1,3,7},{2,4,5,6,8,9,10,11,12}}
[3,4,8,9,10,12,1,2,5,6,7,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,4,8,9,11,12,1,2,5,6,7,10]=>{{1,2,3,4,5,7,8,9,11},{6,10,12}}
[3,4,8,10,11,12,1,2,5,6,7,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,4,9,10,11,12,1,2,5,6,7,8]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[3,5,6,8,10,12,1,2,4,7,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,5,6,8,11,12,1,2,4,7,9,10]=>{{1,3,6,7,10,12},{2,4,5,8,9,11}}
[3,5,6,9,10,12,1,2,4,7,8,11]=>{{1,2,3,5,6,7,8,10,11,12},{4,9}}
[3,5,6,9,11,12,1,2,4,7,8,10]=>{{1,3,6,7,10,12},{2,5,8,11},{4,9}}
[3,5,6,10,11,12,1,2,4,7,8,9]=>{{1,3,4,6,7,9,10,12},{2,5,8,11}}
[3,5,7,8,10,12,1,2,4,6,9,11]=>{{1,3,7},{2,4,5,6,8,9,10,11,12}}
[3,5,7,8,11,12,1,2,4,6,9,10]=>{{1,3,7},{2,4,5,8,9,11},{6,10,12}}
[3,5,7,9,10,12,1,2,4,6,8,11]=>{{1,3,7},{2,5,6,8,10,11,12},{4,9}}
[3,5,7,9,11,12,1,2,4,6,8,10]=>{{1,3,7},{2,5,8,11},{4,9},{6,10,12}}
[3,5,7,10,11,12,1,2,4,6,8,9]=>{{1,3,7},{2,5,8,11},{4,6,9,10,12}}
[3,5,8,9,10,12,1,2,4,6,7,11]=>{{1,2,3,5,6,7,8,10,11,12},{4,9}}
[3,5,8,9,11,12,1,2,4,6,7,10]=>{{1,2,3,5,7,8,11},{4,9},{6,10,12}}
[3,5,8,10,11,12,1,2,4,6,7,9]=>{{1,2,3,5,7,8,11},{4,6,9,10,12}}
[3,5,9,10,11,12,1,2,4,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,6,7,8,10,12,1,2,4,5,9,11]=>{{1,3,7},{2,4,6,8,9,11,12},{5,10}}
[3,6,7,8,11,12,1,2,4,5,9,10]=>{{1,3,7},{2,4,5,6,8,9,10,11,12}}
[3,6,7,9,10,12,1,2,4,5,8,11]=>{{1,3,7},{2,6,8,11,12},{4,9},{5,10}}
[3,6,7,9,11,12,1,2,4,5,8,10]=>{{1,3,7},{2,5,6,8,10,11,12},{4,9}}
[3,6,7,10,11,12,1,2,4,5,8,9]=>{{1,3,7},{2,4,5,6,8,9,10,11,12}}
[3,6,8,9,10,12,1,2,4,5,7,11]=>{{1,2,3,6,7,8,11,12},{4,9},{5,10}}
[3,6,8,9,11,12,1,2,4,5,7,10]=>{{1,2,3,5,6,7,8,10,11,12},{4,9}}
[3,6,8,10,11,12,1,2,4,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,6,9,10,11,12,1,2,4,5,7,8]=>{{1,3,4,5,7,9,10,11},{2,6,8,12}}
[3,7,8,9,10,12,1,2,4,5,6,11]=>{{1,2,3,7,8},{4,9},{5,10},{6,11,12}}
[3,7,8,9,11,12,1,2,4,5,6,10]=>{{1,2,3,7,8},{4,9},{5,6,10,11,12}}
[3,7,8,10,11,12,1,2,4,5,6,9]=>{{1,2,3,7,8},{4,5,6,9,10,11,12}}
[3,7,9,10,11,12,1,2,4,5,6,8]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,8,9,10,11,12,1,2,4,5,6,7]=>{{1,3,4,5,6,7,9,10,11,12},{2,8}}
[4,5,6,8,10,12,1,2,3,7,9,11]=>{{1,2,4,5,7,8,10},{3,6,9,11,12}}
[4,5,6,8,11,12,1,2,3,7,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,5,6,9,10,12,1,2,3,7,8,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,5,6,9,11,12,1,2,3,7,8,10]=>{{1,3,4,6,7,9,10,12},{2,5,8,11}}
[4,5,6,10,11,12,1,2,3,7,8,9]=>{{1,4,7,10},{2,5,8,11},{3,6,9,12}}
[4,5,7,8,10,12,1,2,3,6,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,5,7,8,11,12,1,2,3,6,9,10]=>{{1,2,3,4,5,7,8,9,11},{6,10,12}}
[4,5,7,9,10,12,1,2,3,6,8,11]=>{{1,3,4,7,9},{2,5,6,8,10,11,12}}
[4,5,7,9,11,12,1,2,3,6,8,10]=>{{1,3,4,7,9},{2,5,8,11},{6,10,12}}
[4,5,7,10,11,12,1,2,3,6,8,9]=>{{1,3,4,6,7,9,10,12},{2,5,8,11}}
[4,5,8,9,10,12,1,2,3,6,7,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,5,8,9,11,12,1,2,3,6,7,10]=>{{1,2,3,4,5,7,8,9,11},{6,10,12}}
[4,5,8,10,11,12,1,2,3,6,7,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,5,9,10,11,12,1,2,3,6,7,8]=>{{1,2,4,5,6,7,8,10,11,12},{3,9}}
[4,6,7,8,10,12,1,2,3,5,9,11]=>{{1,2,3,4,6,7,8,9,11,12},{5,10}}
[4,6,7,8,11,12,1,2,3,5,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,6,7,9,10,12,1,2,3,5,8,11]=>{{1,3,4,7,9},{2,6,8,11,12},{5,10}}
[4,6,7,9,11,12,1,2,3,5,8,10]=>{{1,3,4,7,9},{2,5,6,8,10,11,12}}
[4,6,7,10,11,12,1,2,3,5,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,6,8,9,10,12,1,2,3,5,7,11]=>{{1,2,3,4,6,7,8,9,11,12},{5,10}}
[4,6,8,9,11,12,1,2,3,5,7,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,6,8,10,11,12,1,2,3,5,7,9]=>{{1,4,5,7,10,11},{2,3,6,8,9,12}}
[4,6,9,10,11,12,1,2,3,5,7,8]=>{{1,4,5,7,10,11},{2,6,8,12},{3,9}}
[4,7,8,9,10,12,1,2,3,5,6,11]=>{{1,2,3,4,7,8,9},{5,10},{6,11,12}}
[4,7,8,9,11,12,1,2,3,5,6,10]=>{{1,2,3,4,7,8,9},{5,6,10,11,12}}
[4,7,8,10,11,12,1,2,3,5,6,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,7,9,10,11,12,1,2,3,5,6,8]=>{{1,2,4,5,6,7,8,10,11,12},{3,9}}
[4,8,9,10,11,12,1,2,3,5,6,7]=>{{1,4,5,6,7,10,11,12},{2,8},{3,9}}
[5,6,7,8,10,12,1,2,3,4,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[5,6,7,8,11,12,1,2,3,4,9,10]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[5,6,7,9,10,12,1,2,3,4,8,11]=>{{1,3,4,5,7,9,10},{2,6,8,11,12}}
[5,6,7,9,11,12,1,2,3,4,8,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[5,6,7,10,11,12,1,2,3,4,8,9]=>{{1,2,3,5,6,7,8,9,11,12},{4,10}}
[5,6,8,9,10,12,1,2,3,4,7,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[5,6,8,9,11,12,1,2,3,4,7,10]=>{{1,5,7,11},{2,3,4,6,8,9,10,12}}
[5,6,8,10,11,12,1,2,3,4,7,9]=>{{1,5,7,11},{2,3,6,8,9,12},{4,10}}
[5,6,9,10,11,12,1,2,3,4,7,8]=>{{1,5,7,11},{2,6,8,12},{3,9},{4,10}}
[5,7,8,9,10,12,1,2,3,4,6,11]=>{{1,2,3,4,5,7,8,9,10},{6,11,12}}
[5,7,8,9,11,12,1,2,3,4,6,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[5,7,8,10,11,12,1,2,3,4,6,9]=>{{1,2,3,5,6,7,8,9,11,12},{4,10}}
[5,7,9,10,11,12,1,2,3,4,6,8]=>{{1,2,5,6,7,8,11,12},{3,9},{4,10}}
[5,8,9,10,11,12,1,2,3,4,6,7]=>{{1,5,6,7,11,12},{2,8},{3,9},{4,10}}
[6,7,8,9,10,12,1,2,3,4,5,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,7,8,9,11,12,1,2,3,4,5,10]=>{{1,2,3,4,6,7,8,9,10,12},{5,11}}
[6,7,8,10,11,12,1,2,3,4,5,9]=>{{1,2,3,6,7,8,9,12},{4,10},{5,11}}
[6,7,9,10,11,12,1,2,3,4,5,8]=>{{1,2,6,7,8,12},{3,9},{4,10},{5,11}}
[6,8,9,10,11,12,1,2,3,4,5,7]=>{{1,6,7,12},{2,8},{3,9},{4,10},{5,11}}
[7,8,9,10,11,12,1,2,3,4,5,6]=>{{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}}
[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,1,4,5,6,7,8,9,10,11,12,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,1,4,3,6,5,8,7,11,12,10,9]=>{{1,2},{3,4},{5,6},{7,8},{9,10,11,12}}
[2,1,4,3,6,5,9,10,8,7,12,11]=>{{1,2},{3,4},{5,6},{7,8,9,10},{11,12}}
[2,1,4,3,6,5,9,11,8,12,10,7]=>{{1,2},{3,4},{5,6},{7,8,9,10,11,12}}
[2,1,4,3,6,5,10,11,12,9,8,7]=>{{1,2},{3,4},{5,6},{7,9,10,12},{8,11}}
[2,1,4,3,7,8,6,5,10,9,12,11]=>{{1,2},{3,4},{5,6,7,8},{9,10},{11,12}}
[2,1,4,3,7,8,6,5,11,12,10,9]=>{{1,2},{3,4},{5,6,7,8},{9,10,11,12}}
[2,1,4,3,7,9,6,10,8,5,12,11]=>{{1,2},{3,4},{5,6,7,8,9,10},{11,12}}
[2,1,4,3,7,9,6,11,8,12,10,5]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,3,7,10,6,11,12,9,8,5]=>{{1,2},{3,4},{5,6,7,9,10,12},{8,11}}
[2,1,4,3,8,9,10,7,6,5,12,11]=>{{1,2},{3,4},{5,7,8,10},{6,9},{11,12}}
[2,1,4,3,8,9,11,7,6,12,10,5]=>{{1,2},{3,4},{5,7,8,10,11,12},{6,9}}
[2,1,4,3,8,10,11,7,12,9,6,5]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,3,9,10,11,12,8,7,6,5]=>{{1,2},{3,4},{5,8,9,12},{6,7,10,11}}
[2,1,5,6,4,3,8,7,10,9,12,11]=>{{1,2},{3,4,5,6},{7,8},{9,10},{11,12}}
[2,1,5,6,4,3,8,7,11,12,10,9]=>{{1,2},{3,4,5,6},{7,8},{9,10,11,12}}
[2,1,5,6,4,3,9,10,8,7,12,11]=>{{1,2},{3,4,5,6},{7,8,9,10},{11,12}}
[2,1,5,6,4,3,9,11,8,12,10,7]=>{{1,2},{3,4,5,6},{7,8,9,10,11,12}}
[2,1,5,6,4,3,10,11,12,9,8,7]=>{{1,2},{3,4,5,6},{7,9,10,12},{8,11}}
[2,1,5,7,4,8,6,3,10,9,12,11]=>{{1,2},{3,4,5,6,7,8},{9,10},{11,12}}
[2,1,5,7,4,8,6,3,11,12,10,9]=>{{1,2},{3,4,5,6,7,8},{9,10,11,12}}
[2,1,5,7,4,9,6,10,8,3,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,5,7,4,9,6,11,8,12,10,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,5,7,4,10,6,11,12,9,8,3]=>{{1,2},{3,4,5,6,7,9,10,12},{8,11}}
[2,1,5,8,4,9,10,7,6,3,12,11]=>{{1,2},{3,4,5,7,8,10},{6,9},{11,12}}
[2,1,5,8,4,9,11,7,6,12,10,3]=>{{1,2},{3,4,5,7,8,10,11,12},{6,9}}
[2,1,5,8,4,10,11,7,12,9,6,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,5,9,4,10,11,12,8,7,6,3]=>{{1,2},{3,4,5,8,9,12},{6,7,10,11}}
[2,1,6,7,8,5,4,3,10,9,12,11]=>{{1,2},{3,5,6,8},{4,7},{9,10},{11,12}}
[2,1,6,7,8,5,4,3,11,12,10,9]=>{{1,2},{3,5,6,8},{4,7},{9,10,11,12}}
[2,1,6,7,9,5,4,10,8,3,12,11]=>{{1,2},{3,5,6,8,9,10},{4,7},{11,12}}
[2,1,6,7,9,5,4,11,8,12,10,3]=>{{1,2},{3,5,6,8,9,10,11,12},{4,7}}
[2,1,6,7,10,5,4,11,12,9,8,3]=>{{1,2},{3,5,6,9,10,12},{4,7},{8,11}}
[2,1,6,8,9,5,10,7,4,3,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,6,8,9,5,11,7,4,12,10,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,6,8,10,5,11,7,12,9,4,3]=>{{1,2},{3,5,6,9,10,12},{4,7,8,11}}
[2,1,6,9,10,5,11,12,8,7,4,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,7,8,9,10,6,5,4,3,12,11]=>{{1,2},{3,6,7,10},{4,5,8,9},{11,12}}
[2,1,7,8,9,11,6,5,4,12,10,3]=>{{1,2},{3,6,7,10,11,12},{4,5,8,9}}
[2,1,7,8,10,11,6,5,12,9,4,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,7,9,10,11,6,12,8,5,4,3]=>{{1,2},{3,4,6,7,8,9,11,12},{5,10}}
[2,1,8,9,10,11,12,7,6,5,4,3]=>{{1,2},{3,7,8,12},{4,6,9,11},{5,10}}
[3,4,2,1,6,5,8,7,10,9,12,11]=>{{1,2,3,4},{5,6},{7,8},{9,10},{11,12}}
[3,4,2,1,6,5,8,7,11,12,10,9]=>{{1,2,3,4},{5,6},{7,8},{9,10,11,12}}
[3,4,2,1,6,5,9,10,8,7,12,11]=>{{1,2,3,4},{5,6},{7,8,9,10},{11,12}}
[3,4,2,1,6,5,9,11,8,12,10,7]=>{{1,2,3,4},{5,6},{7,8,9,10,11,12}}
[3,4,2,1,6,5,10,11,12,9,8,7]=>{{1,2,3,4},{5,6},{7,9,10,12},{8,11}}
[3,4,2,1,7,8,6,5,10,9,12,11]=>{{1,2,3,4},{5,6,7,8},{9,10},{11,12}}
[3,4,2,1,7,8,6,5,11,12,10,9]=>{{1,2,3,4},{5,6,7,8},{9,10,11,12}}
[3,4,2,1,7,9,6,10,8,5,12,11]=>{{1,2,3,4},{5,6,7,8,9,10},{11,12}}
[3,4,2,1,7,9,6,11,8,12,10,5]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[3,4,2,1,7,10,6,11,12,9,8,5]=>{{1,2,3,4},{5,6,7,9,10,12},{8,11}}
[3,4,2,1,8,9,10,7,6,5,12,11]=>{{1,2,3,4},{5,7,8,10},{6,9},{11,12}}
[3,4,2,1,8,9,11,7,6,12,10,5]=>{{1,2,3,4},{5,7,8,10,11,12},{6,9}}
[3,4,2,1,8,10,11,7,12,9,6,5]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[3,4,2,1,9,10,11,12,8,7,6,5]=>{{1,2,3,4},{5,8,9,12},{6,7,10,11}}
[3,5,2,6,4,1,8,7,10,9,12,11]=>{{1,2,3,4,5,6},{7,8},{9,10},{11,12}}
[3,5,2,6,4,1,8,7,11,12,10,9]=>{{1,2,3,4,5,6},{7,8},{9,10,11,12}}
[3,5,2,6,4,1,9,10,8,7,12,11]=>{{1,2,3,4,5,6},{7,8,9,10},{11,12}}
[3,5,2,6,4,1,9,11,8,12,10,7]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}}
[3,5,2,6,4,1,10,11,12,9,8,7]=>{{1,2,3,4,5,6},{7,9,10,12},{8,11}}
[3,5,2,7,4,8,6,1,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[3,5,2,7,4,8,6,1,11,12,10,9]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[3,5,2,7,4,9,6,10,8,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[3,5,2,7,4,9,6,11,8,12,10,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,5,2,7,4,10,6,11,12,9,8,1]=>{{1,2,3,4,5,6,7,9,10,12},{8,11}}
[3,5,2,8,4,9,10,7,6,1,12,11]=>{{1,2,3,4,5,7,8,10},{6,9},{11,12}}
[3,5,2,8,4,9,11,7,6,12,10,1]=>{{1,2,3,4,5,7,8,10,11,12},{6,9}}
[3,5,2,8,4,10,11,7,12,9,6,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,5,2,9,4,10,11,12,8,7,6,1]=>{{1,2,3,4,5,8,9,12},{6,7,10,11}}
[3,6,2,7,8,5,4,1,10,9,12,11]=>{{1,2,3,5,6,8},{4,7},{9,10},{11,12}}
[3,6,2,7,8,5,4,1,11,12,10,9]=>{{1,2,3,5,6,8},{4,7},{9,10,11,12}}
[3,6,2,7,9,5,4,10,8,1,12,11]=>{{1,2,3,5,6,8,9,10},{4,7},{11,12}}
[3,6,2,7,9,5,4,11,8,12,10,1]=>{{1,2,3,5,6,8,9,10,11,12},{4,7}}
[3,6,2,7,10,5,4,11,12,9,8,1]=>{{1,2,3,5,6,9,10,12},{4,7},{8,11}}
[3,6,2,8,9,5,10,7,4,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[3,6,2,8,9,5,11,7,4,12,10,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,6,2,8,10,5,11,7,12,9,4,1]=>{{1,2,3,5,6,9,10,12},{4,7,8,11}}
[3,6,2,9,10,5,11,12,8,7,4,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,7,2,8,9,10,6,5,4,1,12,11]=>{{1,2,3,6,7,10},{4,5,8,9},{11,12}}
[3,7,2,8,9,11,6,5,4,12,10,1]=>{{1,2,3,6,7,10,11,12},{4,5,8,9}}
[3,7,2,8,10,11,6,5,12,9,4,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,7,2,9,10,11,6,12,8,5,4,1]=>{{1,2,3,4,6,7,8,9,11,12},{5,10}}
[3,8,2,9,10,11,12,7,6,5,4,1]=>{{1,2,3,7,8,12},{4,6,9,11},{5,10}}
[4,5,6,3,2,1,8,7,10,9,12,11]=>{{1,3,4,6},{2,5},{7,8},{9,10},{11,12}}
[4,5,6,3,2,1,8,7,11,12,10,9]=>{{1,3,4,6},{2,5},{7,8},{9,10,11,12}}
[4,5,6,3,2,1,9,10,8,7,12,11]=>{{1,3,4,6},{2,5},{7,8,9,10},{11,12}}
[4,5,6,3,2,1,9,11,8,12,10,7]=>{{1,3,4,6},{2,5},{7,8,9,10,11,12}}
[4,5,6,3,2,1,10,11,12,9,8,7]=>{{1,3,4,6},{2,5},{7,9,10,12},{8,11}}
[4,5,7,3,2,8,6,1,10,9,12,11]=>{{1,3,4,6,7,8},{2,5},{9,10},{11,12}}
[4,5,7,3,2,8,6,1,11,12,10,9]=>{{1,3,4,6,7,8},{2,5},{9,10,11,12}}
[4,5,7,3,2,9,6,10,8,1,12,11]=>{{1,3,4,6,7,8,9,10},{2,5},{11,12}}
[4,5,7,3,2,9,6,11,8,12,10,1]=>{{1,3,4,6,7,8,9,10,11,12},{2,5}}
[4,5,7,3,2,10,6,11,12,9,8,1]=>{{1,3,4,6,7,9,10,12},{2,5},{8,11}}
[4,5,8,3,2,9,10,7,6,1,12,11]=>{{1,3,4,7,8,10},{2,5},{6,9},{11,12}}
[4,5,8,3,2,9,11,7,6,12,10,1]=>{{1,3,4,7,8,10,11,12},{2,5},{6,9}}
[4,5,8,3,2,10,11,7,12,9,6,1]=>{{1,3,4,6,7,8,9,10,11,12},{2,5}}
[4,5,9,3,2,10,11,12,8,7,6,1]=>{{1,3,4,8,9,12},{2,5},{6,7,10,11}}
[4,6,7,3,8,5,2,1,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[4,6,7,3,8,5,2,1,11,12,10,9]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[4,6,7,3,9,5,2,10,8,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[4,6,7,3,9,5,2,11,8,12,10,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,6,7,3,10,5,2,11,12,9,8,1]=>{{1,2,3,4,5,6,7,9,10,12},{8,11}}
[4,6,8,3,9,5,10,7,2,1,12,11]=>{{1,3,4,7,8,10},{2,5,6,9},{11,12}}
[4,6,8,3,9,5,11,7,2,12,10,1]=>{{1,3,4,7,8,10,11,12},{2,5,6,9}}
[4,6,8,3,10,5,11,7,12,9,2,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,6,9,3,10,5,11,12,8,7,2,1]=>{{1,3,4,8,9,12},{2,5,6,7,10,11}}
[4,7,8,3,9,10,6,5,2,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[4,7,8,3,9,11,6,5,2,12,10,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,7,8,3,10,11,6,5,12,9,2,1]=>{{1,3,4,5,8,9,10,12},{2,6,7,11}}
[4,7,9,3,10,11,6,12,8,5,2,1]=>{{1,3,4,8,9,12},{2,6,7,11},{5,10}}
[4,8,9,3,10,11,12,7,6,5,2,1]=>{{1,2,3,4,6,7,8,9,11,12},{5,10}}
[5,6,7,8,4,3,2,1,10,9,12,11]=>{{1,4,5,8},{2,3,6,7},{9,10},{11,12}}
[5,6,7,8,4,3,2,1,11,12,10,9]=>{{1,4,5,8},{2,3,6,7},{9,10,11,12}}
[5,6,7,9,4,3,2,10,8,1,12,11]=>{{1,4,5,8,9,10},{2,3,6,7},{11,12}}
[5,6,7,9,4,3,2,11,8,12,10,1]=>{{1,4,5,8,9,10,11,12},{2,3,6,7}}
[5,6,7,10,4,3,2,11,12,9,8,1]=>{{1,4,5,9,10,12},{2,3,6,7},{8,11}}
[5,6,8,9,4,3,10,7,2,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[5,6,8,9,4,3,11,7,2,12,10,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[5,6,8,10,4,3,11,7,12,9,2,1]=>{{1,4,5,9,10,12},{2,3,6,7,8,11}}
[5,6,9,10,4,3,11,12,8,7,2,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[5,7,8,9,4,10,6,3,2,1,12,11]=>{{1,2,4,5,6,7,9,10},{3,8},{11,12}}
[5,7,8,9,4,11,6,3,2,12,10,1]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}}
[5,7,8,10,4,11,6,3,12,9,2,1]=>{{1,4,5,9,10,12},{2,6,7,11},{3,8}}
[5,7,9,10,4,11,6,12,8,3,2,1]=>{{1,3,4,5,8,9,10,12},{2,6,7,11}}
[5,8,9,10,4,11,12,7,6,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,7,8,9,10,5,4,3,2,1,12,11]=>{{1,5,6,10},{2,4,7,9},{3,8},{11,12}}
[6,7,8,9,11,5,4,3,2,12,10,1]=>{{1,5,6,10,11,12},{2,4,7,9},{3,8}}
[6,7,8,10,11,5,4,3,12,9,2,1]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}}
[6,7,9,10,11,5,4,12,8,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,8,9,10,11,5,12,7,4,3,2,1]=>{{1,2,5,6,7,8,11,12},{3,4,9,10}}
[7,8,9,10,11,12,6,5,4,3,2,1]=>{{1,6,7,12},{2,5,8,11},{3,4,9,10}}
[11,10,9,8,7,6,5,4,3,1,12,2]=>{{1,2,10,11,12},{3,9},{4,8},{5,7},{6}}
[10,12,9,8,7,6,5,4,3,2,1,11]=>{{1,2,10,11,12},{3,9},{4,8},{5,7},{6}}
[11,12,9,10,7,8,5,6,3,4,1,2]=>{{1,11},{2,12},{3,9},{4,10},{5,7},{6,8}}
[9,10,12,11,7,8,5,6,3,4,1,2]=>{{1,2,3,4,9,10,11,12},{5,7},{6,8}}
[11,12,7,8,10,9,5,6,3,4,1,2]=>{{1,11},{2,12},{3,4,5,6,7,8,9,10}}
[7,10,12,8,11,9,5,6,3,4,1,2]=>{{1,5,7,11},{2,3,4,6,8,9,10,12}}
[7,8,9,12,11,10,5,6,3,4,1,2]=>{{1,5,7,11},{2,4,6,8,10,12},{3,9}}
[11,12,9,10,5,6,8,7,3,4,1,2]=>{{1,11},{2,12},{3,9},{4,10},{5},{6},{7,8}}
[9,10,12,11,5,6,8,7,3,4,1,2]=>{{1,2,3,4,9,10,11,12},{5},{6},{7,8}}
[11,12,5,8,10,6,9,7,3,4,1,2]=>{{1,11},{2,12},{3,4,5,7,8,9,10},{6}}
[5,10,12,8,11,6,9,7,3,4,1,2]=>{{1,5,11},{2,3,4,7,8,9,10,12},{6}}
[5,8,9,12,11,6,10,7,3,4,1,2]=>{{1,5,11},{2,4,7,8,10,12},{3,9},{6}}
[11,12,5,6,7,10,9,8,3,4,1,2]=>{{1,11},{2,12},{3,5,7,9},{4,6,10},{8}}
[5,10,12,6,7,11,9,8,3,4,1,2]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[5,6,9,12,7,11,10,8,3,4,1,2]=>{{1,2,4,5,6,7,10,11,12},{3,9},{8}}
[5,6,7,8,12,11,10,9,3,4,1,2]=>{{1,2,5,6,11,12},{3,4,7,8,9,10}}
[11,12,9,10,7,8,3,4,6,5,1,2]=>{{1,11},{2,12},{3,4,5,6,7,8,9,10}}
[9,10,12,11,7,8,3,4,6,5,1,2]=>{{1,4,6,8,9,11},{2,3,5,7,10,12}}
[11,12,7,8,10,9,3,4,6,5,1,2]=>{{1,11},{2,12},{3,7},{4,8},{5,10},{6,9}}
[7,10,12,8,11,9,3,4,6,5,1,2]=>{{1,2,3,5,7,10,11,12},{4,8},{6,9}}
[7,8,9,12,11,10,3,4,6,5,1,2]=>{{1,3,5,6,7,9,10,11},{2,4,8,12}}
[11,12,9,10,3,6,8,4,7,5,1,2]=>{{1,11},{2,12},{3,4,5,7,8,9,10},{6}}
[9,10,12,11,3,6,8,4,7,5,1,2]=>{{1,4,7,8,9,11},{2,3,5,10,12},{6}}
[11,12,3,8,10,6,9,4,7,5,1,2]=>{{1,11},{2,12},{3},{4,8},{5,10},{6},{7,9}}
[3,10,12,8,11,6,9,4,7,5,1,2]=>{{1,2,3,5,10,11,12},{4,8},{6},{7,9}}
[3,8,9,12,11,6,10,4,7,5,1,2]=>{{1,3,5,7,9,10,11},{2,4,8,12},{6}}
[11,12,3,6,7,10,9,4,8,5,1,2]=>{{1,11},{2,12},{3},{4,5,6,7,8,9,10}}
[3,10,12,6,7,11,9,4,8,5,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,6,9,12,7,11,10,4,8,5,1,2]=>{{1,2,3,4,6,8,9,11,12},{5,7,10}}
[3,6,7,8,12,11,10,4,9,5,1,2]=>{{1,2,3,5,6,7,10,11,12},{4,8},{9}}
[11,12,9,10,3,4,5,8,7,6,1,2]=>{{1,11},{2,12},{3,5,7,9},{4,6,10},{8}}
[9,10,12,11,3,4,5,8,7,6,1,2]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[11,12,3,8,10,4,5,9,7,6,1,2]=>{{1,11},{2,12},{3},{4,5,6,7,8,9,10}}
[3,10,12,8,11,4,5,9,7,6,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,8,9,12,11,4,5,10,7,6,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,3,4,7,10,5,9,8,6,1,2]=>{{1,11},{2,12},{3},{4},{5,7},{6,10},{8,9}}
[3,10,12,4,7,11,5,9,8,6,1,2]=>{{1,2,3,6,10,11,12},{4},{5,7},{8,9}}
[3,4,9,12,7,11,5,10,8,6,1,2]=>{{1,3,6,8,9,10,11},{2,4,12},{5,7}}
[3,4,7,8,12,11,5,10,9,6,1,2]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[11,12,3,4,5,6,10,9,8,7,1,2]=>{{1,11},{2,12},{3},{4},{5},{6},{7,10},{8,9}}
[3,10,12,4,5,6,11,9,8,7,1,2]=>{{1,2,3,7,10,11,12},{4},{5},{6},{8,9}}
[3,4,9,12,5,6,11,10,8,7,1,2]=>{{1,3,7,8,9,10,11},{2,4,12},{5},{6}}
[3,4,5,8,12,6,11,10,9,7,1,2]=>{{1,2,3,4,5,7,8,10,11,12},{6},{9}}
[3,4,5,6,7,12,11,10,9,8,1,2]=>{{1,3,5,7,11},{2,4,6,12},{8,10},{9}}
[11,12,9,10,7,8,5,6,1,2,4,3]=>{{1,2,3,4,9,10,11,12},{5,7},{6,8}}
[9,10,12,11,7,8,5,6,1,2,4,3]=>{{1,9},{2,10},{3,12},{4,11},{5,7},{6,8}}
[11,12,7,8,10,9,5,6,1,2,4,3]=>{{1,4,6,8,9,11},{2,3,5,7,10,12}}
[7,10,12,8,11,9,5,6,1,2,4,3]=>{{1,4,5,6,7,8,9,11},{2,10},{3,12}}
[7,8,9,12,11,10,5,6,1,2,4,3]=>{{1,3,4,5,7,9,11,12},{2,6,8,10}}
[11,12,9,10,5,6,8,7,1,2,4,3]=>{{1,2,3,4,9,10,11,12},{5},{6},{7,8}}
[9,10,12,11,5,6,8,7,1,2,4,3]=>{{1,9},{2,10},{3,12},{4,11},{5},{6},{7,8}}
[11,12,5,8,10,6,9,7,1,2,4,3]=>{{1,4,7,8,9,11},{2,3,5,10,12},{6}}
[5,10,12,8,11,6,9,7,1,2,4,3]=>{{1,4,5,7,8,9,11},{2,10},{3,12},{6}}
[5,8,9,12,11,6,10,7,1,2,4,3]=>{{1,3,4,5,9,11,12},{2,7,8,10},{6}}
[11,12,5,6,7,10,9,8,1,2,4,3]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[5,10,12,6,7,11,9,8,1,2,4,3]=>{{1,5,7,9},{2,10},{3,12},{4,6,11},{8}}
[5,6,9,12,7,11,10,8,1,2,4,3]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[5,6,7,8,12,11,10,9,1,2,4,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,9,10,7,8,1,4,6,2,5,3]=>{{1,5,7,11},{2,3,4,6,8,9,10,12}}
[9,10,12,11,7,8,1,4,6,2,5,3]=>{{1,4,5,6,7,8,9,11},{2,10},{3,12}}
[11,12,7,8,10,9,1,4,6,2,5,3]=>{{1,2,3,5,7,10,11,12},{4,8},{6,9}}
[7,10,12,8,11,9,1,4,6,2,5,3]=>{{1,7},{2,10},{3,12},{4,8},{5,11},{6,9}}
[7,8,9,12,11,10,1,4,6,2,5,3]=>{{1,7},{2,3,4,6,8,9,10,12},{5,11}}
[11,12,9,10,1,6,8,4,7,2,5,3]=>{{1,5,11},{2,3,4,7,8,9,10,12},{6}}
[9,10,12,11,1,6,8,4,7,2,5,3]=>{{1,4,5,7,8,9,11},{2,10},{3,12},{6}}
[11,12,1,8,10,6,9,4,7,2,5,3]=>{{1,2,3,5,10,11,12},{4,8},{6},{7,9}}
[1,10,12,8,11,6,9,4,7,2,5,3]=>{{1},{2,10},{3,12},{4,8},{5,11},{6},{7,9}}
[1,8,9,12,11,6,10,4,7,2,5,3]=>{{1},{2,3,4,7,8,9,10,12},{5,11},{6}}
[11,12,1,6,7,10,9,4,8,2,5,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,10,12,6,7,11,9,4,8,2,5,3]=>{{1},{2,10},{3,12},{4,5,6,7,8,9,11}}
[1,6,9,12,7,11,10,4,8,2,5,3]=>{{1},{2,5,6,7,10,11},{3,4,8,9,12}}
[1,6,7,8,12,11,10,4,9,2,5,3]=>{{1},{2,3,5,6,7,10,11,12},{4,8},{9}}
[11,12,9,10,1,4,5,8,7,2,6,3]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[9,10,12,11,1,4,5,8,7,2,6,3]=>{{1,5,7,9},{2,10},{3,12},{4,6,11},{8}}
[11,12,1,8,10,4,5,9,7,2,6,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,10,12,8,11,4,5,9,7,2,6,3]=>{{1},{2,10},{3,12},{4,5,6,7,8,9,11}}
[1,8,9,12,11,4,5,10,7,2,6,3]=>{{1},{2,8,10},{3,4,5,6,7,9,11,12}}
[11,12,1,4,7,10,5,9,8,2,6,3]=>{{1,2,3,6,10,11,12},{4},{5,7},{8,9}}
[1,10,12,4,7,11,5,9,8,2,6,3]=>{{1},{2,10},{3,12},{4},{5,7},{6,11},{8,9}}
[1,4,9,12,7,11,5,10,8,2,6,3]=>{{1},{2,3,4,8,9,10,12},{5,7},{6,11}}
[1,4,7,8,12,11,5,10,9,2,6,3]=>{{1},{2,4,8,10},{3,5,7,12},{6,11},{9}}
[11,12,1,4,5,6,10,9,8,2,7,3]=>{{1,2,3,7,10,11,12},{4},{5},{6},{8,9}}
[1,10,12,4,5,6,11,9,8,2,7,3]=>{{1},{2,10},{3,12},{4},{5},{6},{7,11},{8,9}}
[1,4,9,12,5,6,11,10,8,2,7,3]=>{{1},{2,3,4,8,9,10,12},{5},{6},{7,11}}
[1,4,5,8,12,6,11,10,9,2,7,3]=>{{1},{2,4,8,10},{3,5,12},{6},{7,11},{9}}
[1,4,5,6,7,12,11,10,9,2,8,3]=>{{1},{2,3,4,5,6,7,8,10,11,12},{9}}
[11,12,9,10,7,8,1,2,3,6,5,4]=>{{1,5,7,11},{2,4,6,8,10,12},{3,9}}
[9,10,12,11,7,8,1,2,3,6,5,4]=>{{1,3,4,5,7,9,11,12},{2,6,8,10}}
[11,12,7,8,10,9,1,2,3,6,5,4]=>{{1,3,5,6,7,9,10,11},{2,4,8,12}}
[7,10,12,8,11,9,1,2,3,6,5,4]=>{{1,7},{2,3,4,6,8,9,10,12},{5,11}}
[7,8,9,12,11,10,1,2,3,6,5,4]=>{{1,7},{2,8},{3,9},{4,12},{5,11},{6,10}}
[11,12,9,10,1,6,8,2,3,7,5,4]=>{{1,5,11},{2,4,7,8,10,12},{3,9},{6}}
[9,10,12,11,1,6,8,2,3,7,5,4]=>{{1,3,4,5,9,11,12},{2,7,8,10},{6}}
[11,12,1,8,10,6,9,2,3,7,5,4]=>{{1,3,5,7,9,10,11},{2,4,8,12},{6}}
[1,10,12,8,11,6,9,2,3,7,5,4]=>{{1},{2,3,4,7,8,9,10,12},{5,11},{6}}
[1,8,9,12,11,6,10,2,3,7,5,4]=>{{1},{2,8},{3,9},{4,12},{5,11},{6},{7,10}}
[11,12,1,6,7,10,9,2,3,8,5,4]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[1,10,12,6,7,11,9,2,3,8,5,4]=>{{1},{2,8,10},{3,4,5,6,7,9,11,12}}
[1,6,9,12,7,11,10,2,3,8,5,4]=>{{1},{2,5,6,7,8,10,11},{3,9},{4,12}}
[1,6,7,8,12,11,10,2,3,9,5,4]=>{{1},{2,4,5,6,8,11,12},{3,7,9,10}}
[11,12,9,10,1,2,5,8,3,7,6,4]=>{{1,2,4,5,6,7,10,11,12},{3,9},{8}}
[9,10,12,11,1,2,5,8,3,7,6,4]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[11,12,1,8,10,2,5,9,3,7,6,4]=>{{1,2,3,4,6,8,9,11,12},{5,7,10}}
[1,10,12,8,11,2,5,9,3,7,6,4]=>{{1},{2,5,6,7,10,11},{3,4,8,9,12}}
[1,8,9,12,11,2,5,10,3,7,6,4]=>{{1},{2,5,6,7,8,10,11},{3,9},{4,12}}
[11,12,1,2,7,10,5,9,3,8,6,4]=>{{1,3,6,8,9,10,11},{2,4,12},{5,7}}
[1,10,12,2,7,11,5,9,3,8,6,4]=>{{1},{2,3,4,8,9,10,12},{5,7},{6,11}}
[1,2,9,12,7,11,5,10,3,8,6,4]=>{{1},{2},{3,9},{4,12},{5,7},{6,11},{8,10}}
[1,2,7,8,12,11,5,10,3,9,6,4]=>{{1},{2},{3,4,5,7,8,9,10,12},{6,11}}
[11,12,1,2,5,6,10,9,3,8,7,4]=>{{1,3,7,8,9,10,11},{2,4,12},{5},{6}}
[1,10,12,2,5,6,11,9,3,8,7,4]=>{{1},{2,3,4,8,9,10,12},{5},{6},{7,11}}
[1,2,9,12,5,6,11,10,3,8,7,4]=>{{1},{2},{3,9},{4,12},{5},{6},{7,11},{8,10}}
[1,2,5,8,12,6,11,10,3,9,7,4]=>{{1},{2},{3,4,5,8,9,10,12},{6},{7,11}}
[1,2,5,6,7,12,11,10,3,9,8,4]=>{{1},{2},{3,5,7,8,9,10,11},{4,6,12}}
[11,12,9,10,1,2,3,4,8,7,6,5]=>{{1,2,5,6,11,12},{3,4,7,8,9,10}}
[9,10,12,11,1,2,3,4,8,7,6,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,1,8,10,2,3,4,9,7,6,5]=>{{1,2,3,5,6,7,10,11,12},{4,8},{9}}
[1,10,12,8,11,2,3,4,9,7,6,5]=>{{1},{2,3,5,6,7,10,11,12},{4,8},{9}}
[1,8,9,12,11,2,3,4,10,7,6,5]=>{{1},{2,4,5,6,8,11,12},{3,7,9,10}}
[11,12,1,2,7,10,3,4,9,8,6,5]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[1,10,12,2,7,11,3,4,9,8,6,5]=>{{1},{2,4,8,10},{3,5,7,12},{6,11},{9}}
[1,2,9,12,7,11,3,4,10,8,6,5]=>{{1},{2},{3,4,5,7,8,9,10,12},{6,11}}
[1,2,7,8,12,11,3,4,10,9,6,5]=>{{1},{2},{3,7},{4,8},{5,12},{6,11},{9,10}}
[11,12,1,2,3,6,10,4,9,8,7,5]=>{{1,2,3,4,5,7,8,10,11,12},{6},{9}}
[1,10,12,2,3,6,11,4,9,8,7,5]=>{{1},{2,4,8,10},{3,5,12},{6},{7,11},{9}}
[1,2,9,12,3,6,11,4,10,8,7,5]=>{{1},{2},{3,4,5,8,9,10,12},{6},{7,11}}
[1,2,3,8,12,6,11,4,10,9,7,5]=>{{1},{2},{3},{4,8},{5,12},{6},{7,11},{9,10}}
[1,2,3,6,7,12,11,4,10,9,8,5]=>{{1},{2},{3},{4,5,6,7,8,11,12},{9,10}}
[11,12,1,2,3,4,5,10,9,8,7,6]=>{{1,3,5,7,11},{2,4,6,12},{8,10},{9}}
[1,10,12,2,3,4,5,11,9,8,7,6]=>{{1},{2,3,4,5,6,7,8,10,11,12},{9}}
[1,2,9,12,3,4,5,11,10,8,7,6]=>{{1},{2},{3,5,7,8,9,10,11},{4,6,12}}
[1,2,3,8,12,4,5,11,10,9,7,6]=>{{1},{2},{3},{4,5,6,7,8,11,12},{9,10}}
[1,2,3,4,7,12,5,11,10,9,8,6]=>{{1},{2},{3},{4},{5,7},{6,12},{8,11},{9,10}}
[1,2,3,4,5,6,12,11,10,9,8,7]=>{{1},{2},{3},{4},{5},{6},{7,12},{8,11},{9,10}}
[10,12,9,11,7,8,5,6,3,4,1,2]=>{{1,4,10,11},{2,12},{3,9},{5,7},{6,8}}
[11,12,8,10,7,9,5,6,3,4,1,2]=>{{1,11},{2,12},{3,6,8,9},{4,10},{5,7}}
[10,12,8,11,7,9,5,6,3,4,1,2]=>{{1,4,10,11},{2,12},{3,6,8,9},{5,7}}
[9,12,8,11,7,10,5,6,3,4,1,2]=>{{1,3,4,6,8,9,10,11},{2,12},{5,7}}
[11,12,9,10,6,8,5,7,3,4,1,2]=>{{1,11},{2,12},{3,9},{4,10},{5,6,7,8}}
[10,12,9,11,6,8,5,7,3,4,1,2]=>{{1,4,10,11},{2,12},{3,9},{5,6,7,8}}
[11,12,8,10,6,9,5,7,3,4,1,2]=>{{1,11},{2,12},{3,5,6,7,8,9},{4,10}}
[10,12,8,11,6,9,5,7,3,4,1,2]=>{{1,4,10,11},{2,12},{3,5,6,7,8,9}}
[9,12,8,11,6,10,5,7,3,4,1,2]=>{{1,3,4,5,6,7,8,9,10,11},{2,12}}
[11,12,7,10,6,9,5,8,3,4,1,2]=>{{1,11},{2,12},{3,5,6,7,9},{4,10},{8}}
[10,12,7,11,6,9,5,8,3,4,1,2]=>{{1,4,10,11},{2,12},{3,5,6,7,9},{8}}
[9,12,7,11,6,10,5,8,3,4,1,2]=>{{1,3,4,5,6,7,9,10,11},{2,12},{8}}
[8,12,7,11,6,10,5,9,3,4,1,2]=>{{1,3,4,5,6,7,8,9,10,11},{2,12}}
[11,12,9,10,7,8,4,6,3,5,1,2]=>{{1,11},{2,12},{3,9},{4,5,7,10},{6,8}}
[10,12,9,11,7,8,4,6,3,5,1,2]=>{{1,4,5,7,10,11},{2,12},{3,9},{6,8}}
[11,12,8,10,7,9,4,6,3,5,1,2]=>{{1,11},{2,12},{3,6,8,9},{4,5,7,10}}
[10,12,8,11,7,9,4,6,3,5,1,2]=>{{1,4,5,7,10,11},{2,12},{3,6,8,9}}
[9,12,8,11,7,10,4,6,3,5,1,2]=>{{1,3,4,5,6,7,8,9,10,11},{2,12}}
[11,12,9,10,6,8,4,7,3,5,1,2]=>{{1,11},{2,12},{3,9},{4,5,6,7,8,10}}
[10,12,9,11,6,8,4,7,3,5,1,2]=>{{1,4,5,6,7,8,10,11},{2,12},{3,9}}
[11,12,8,10,6,9,4,7,3,5,1,2]=>{{1,11},{2,12},{3,4,5,6,7,8,9,10}}
[10,12,8,11,6,9,4,7,3,5,1,2]=>{{1,3,4,5,6,7,8,9,10,11},{2,12}}
[9,12,8,11,6,10,4,7,3,5,1,2]=>{{1,3,4,7,8,9,11},{2,12},{5,6,10}}
[11,12,7,10,6,9,4,8,3,5,1,2]=>{{1,11},{2,12},{3,4,5,6,7,9,10},{8}}
[10,12,7,11,6,9,4,8,3,5,1,2]=>{{1,3,4,5,6,7,9,10,11},{2,12},{8}}
[9,12,7,11,6,10,4,8,3,5,1,2]=>{{1,3,4,7,9,11},{2,12},{5,6,10},{8}}
[8,12,7,11,6,10,4,9,3,5,1,2]=>{{1,3,4,7,8,9,11},{2,12},{5,6,10}}
[11,12,9,10,5,8,4,7,3,6,1,2]=>{{1,11},{2,12},{3,9},{4,6,7,8,10},{5}}
[10,12,9,11,5,8,4,7,3,6,1,2]=>{{1,4,6,7,8,10,11},{2,12},{3,9},{5}}
[11,12,8,10,5,9,4,7,3,6,1,2]=>{{1,11},{2,12},{3,4,6,7,8,9,10},{5}}
[10,12,8,11,5,9,4,7,3,6,1,2]=>{{1,3,4,6,7,8,9,10,11},{2,12},{5}}
[9,12,8,11,5,10,4,7,3,6,1,2]=>{{1,3,4,7,8,9,11},{2,12},{5},{6,10}}
[11,12,7,10,5,9,4,8,3,6,1,2]=>{{1,11},{2,12},{3,4,6,7,9,10},{5},{8}}
[10,12,7,11,5,9,4,8,3,6,1,2]=>{{1,3,4,6,7,9,10,11},{2,12},{5},{8}}
[9,12,7,11,5,10,4,8,3,6,1,2]=>{{1,3,4,7,9,11},{2,12},{5},{6,10},{8}}
[8,12,7,11,5,10,4,9,3,6,1,2]=>{{1,3,4,7,8,9,11},{2,12},{5},{6,10}}
[11,12,6,10,5,9,4,8,3,7,1,2]=>{{1,11},{2,12},{3,6,9},{4,7,10},{5},{8}}
[10,12,6,11,5,9,4,8,3,7,1,2]=>{{1,4,7,10,11},{2,12},{3,6,9},{5},{8}}
[9,12,6,11,5,10,4,8,3,7,1,2]=>{{1,3,4,6,7,9,10,11},{2,12},{5},{8}}
[8,12,6,11,5,10,4,9,3,7,1,2]=>{{1,3,4,6,7,8,9,10,11},{2,12},{5}}
[7,12,6,11,5,10,4,9,3,8,1,2]=>{{1,4,7,11},{2,12},{3,6,8,9,10},{5}}
[11,12,9,10,7,8,5,6,2,4,1,3]=>{{1,11},{2,3,9,12},{4,10},{5,7},{6,8}}
[10,12,9,11,7,8,5,6,2,4,1,3]=>{{1,4,10,11},{2,3,9,12},{5,7},{6,8}}
[11,12,8,10,7,9,5,6,2,4,1,3]=>{{1,11},{2,3,6,8,9,12},{4,10},{5,7}}
[10,12,8,11,7,9,5,6,2,4,1,3]=>{{1,4,10,11},{2,3,6,8,9,12},{5,7}}
[9,12,8,11,7,10,5,6,2,4,1,3]=>{{1,2,3,4,6,8,9,10,11,12},{5,7}}
[11,12,9,10,6,8,5,7,2,4,1,3]=>{{1,11},{2,3,9,12},{4,10},{5,6,7,8}}
[10,12,9,11,6,8,5,7,2,4,1,3]=>{{1,4,10,11},{2,3,9,12},{5,6,7,8}}
[11,12,8,10,6,9,5,7,2,4,1,3]=>{{1,11},{2,3,5,6,7,8,9,12},{4,10}}
[10,12,8,11,6,9,5,7,2,4,1,3]=>{{1,4,10,11},{2,3,5,6,7,8,9,12}}
[9,12,8,11,6,10,5,7,2,4,1,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,7,10,6,9,5,8,2,4,1,3]=>{{1,11},{2,3,5,6,7,9,12},{4,10},{8}}
[10,12,7,11,6,9,5,8,2,4,1,3]=>{{1,4,10,11},{2,3,5,6,7,9,12},{8}}
[9,12,7,11,6,10,5,8,2,4,1,3]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[8,12,7,11,6,10,5,9,2,4,1,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,9,10,7,8,4,6,2,5,1,3]=>{{1,11},{2,3,9,12},{4,5,7,10},{6,8}}
[10,12,9,11,7,8,4,6,2,5,1,3]=>{{1,4,5,7,10,11},{2,3,9,12},{6,8}}
[11,12,8,10,7,9,4,6,2,5,1,3]=>{{1,11},{2,3,6,8,9,12},{4,5,7,10}}
[10,12,8,11,7,9,4,6,2,5,1,3]=>{{1,4,5,7,10,11},{2,3,6,8,9,12}}
[9,12,8,11,7,10,4,6,2,5,1,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,9,10,6,8,4,7,2,5,1,3]=>{{1,11},{2,3,9,12},{4,5,6,7,8,10}}
[10,12,9,11,6,8,4,7,2,5,1,3]=>{{1,4,5,6,7,8,10,11},{2,3,9,12}}
[11,12,8,10,6,9,4,7,2,5,1,3]=>{{1,11},{2,3,4,5,6,7,8,9,10,12}}
[10,12,8,11,6,9,4,7,2,5,1,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[9,12,8,11,6,10,4,7,2,5,1,3]=>{{1,2,3,4,7,8,9,11,12},{5,6,10}}
[11,12,7,10,6,9,4,8,2,5,1,3]=>{{1,11},{2,3,4,5,6,7,9,10,12},{8}}
[10,12,7,11,6,9,4,8,2,5,1,3]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[9,12,7,11,6,10,4,8,2,5,1,3]=>{{1,2,3,4,7,9,11,12},{5,6,10},{8}}
[8,12,7,11,6,10,4,9,2,5,1,3]=>{{1,2,3,4,7,8,9,11,12},{5,6,10}}
[11,12,9,10,5,8,4,7,2,6,1,3]=>{{1,11},{2,3,9,12},{4,6,7,8,10},{5}}
[10,12,9,11,5,8,4,7,2,6,1,3]=>{{1,4,6,7,8,10,11},{2,3,9,12},{5}}
[11,12,8,10,5,9,4,7,2,6,1,3]=>{{1,11},{2,3,4,6,7,8,9,10,12},{5}}
[10,12,8,11,5,9,4,7,2,6,1,3]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[9,12,8,11,5,10,4,7,2,6,1,3]=>{{1,2,3,4,7,8,9,11,12},{5},{6,10}}
[11,12,7,10,5,9,4,8,2,6,1,3]=>{{1,11},{2,3,4,6,7,9,10,12},{5},{8}}
[10,12,7,11,5,9,4,8,2,6,1,3]=>{{1,2,3,4,6,7,9,10,11,12},{5},{8}}
[9,12,7,11,5,10,4,8,2,6,1,3]=>{{1,2,3,4,7,9,11,12},{5},{6,10},{8}}
[8,12,7,11,5,10,4,9,2,6,1,3]=>{{1,2,3,4,7,8,9,11,12},{5},{6,10}}
[11,12,6,10,5,9,4,8,2,7,1,3]=>{{1,11},{2,3,6,9,12},{4,7,10},{5},{8}}
[10,12,6,11,5,9,4,8,2,7,1,3]=>{{1,4,7,10,11},{2,3,6,9,12},{5},{8}}
[9,12,6,11,5,10,4,8,2,7,1,3]=>{{1,2,3,4,6,7,9,10,11,12},{5},{8}}
[8,12,6,11,5,10,4,9,2,7,1,3]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[7,12,6,11,5,10,4,9,2,8,1,3]=>{{1,4,7,11},{2,3,6,8,9,10,12},{5}}
[11,12,9,10,7,8,3,6,2,5,1,4]=>{{1,11},{2,3,4,5,7,9,10,12},{6,8}}
[10,12,9,11,7,8,3,6,2,5,1,4]=>{{1,2,3,4,5,7,9,10,11,12},{6,8}}
[11,12,8,10,7,9,3,6,2,5,1,4]=>{{1,11},{2,3,4,5,6,7,8,9,10,12}}
[10,12,8,11,7,9,3,6,2,5,1,4]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[9,12,8,11,7,10,3,6,2,5,1,4]=>{{1,2,4,9,11,12},{3,5,6,7,8,10}}
[11,12,9,10,6,8,3,7,2,5,1,4]=>{{1,11},{2,3,4,5,6,7,8,9,10,12}}
[10,12,9,11,6,8,3,7,2,5,1,4]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,8,10,6,9,3,7,2,5,1,4]=>{{1,11},{2,4,5,6,9,10,12},{3,7,8}}
[10,12,8,11,6,9,3,7,2,5,1,4]=>{{1,2,4,5,6,9,10,11,12},{3,7,8}}
[9,12,8,11,6,10,3,7,2,5,1,4]=>{{1,2,4,9,11,12},{3,7,8},{5,6,10}}
[11,12,7,10,6,9,3,8,2,5,1,4]=>{{1,11},{2,4,5,6,9,10,12},{3,7},{8}}
[10,12,7,11,6,9,3,8,2,5,1,4]=>{{1,2,4,5,6,9,10,11,12},{3,7},{8}}
[9,12,7,11,6,10,3,8,2,5,1,4]=>{{1,2,4,9,11,12},{3,7},{5,6,10},{8}}
[8,12,7,11,6,10,3,9,2,5,1,4]=>{{1,2,4,8,9,11,12},{3,7},{5,6,10}}
[11,12,9,10,5,8,3,7,2,6,1,4]=>{{1,11},{2,3,4,6,7,8,9,10,12},{5}}
[10,12,9,11,5,8,3,7,2,6,1,4]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[11,12,8,10,5,9,3,7,2,6,1,4]=>{{1,11},{2,4,6,9,10,12},{3,7,8},{5}}
[10,12,8,11,5,9,3,7,2,6,1,4]=>{{1,2,4,6,9,10,11,12},{3,7,8},{5}}
[9,12,8,11,5,10,3,7,2,6,1,4]=>{{1,2,4,9,11,12},{3,7,8},{5},{6,10}}
[11,12,7,10,5,9,3,8,2,6,1,4]=>{{1,11},{2,4,6,9,10,12},{3,7},{5},{8}}
[10,12,7,11,5,9,3,8,2,6,1,4]=>{{1,2,4,6,9,10,11,12},{3,7},{5},{8}}
[9,12,7,11,5,10,3,8,2,6,1,4]=>{{1,2,4,9,11,12},{3,7},{5},{6,10},{8}}
[8,12,7,11,5,10,3,9,2,6,1,4]=>{{1,2,4,8,9,11,12},{3,7},{5},{6,10}}
[11,12,6,10,5,9,3,8,2,7,1,4]=>{{1,11},{2,3,4,6,7,9,10,12},{5},{8}}
[10,12,6,11,5,9,3,8,2,7,1,4]=>{{1,2,3,4,6,7,9,10,11,12},{5},{8}}
[9,12,6,11,5,10,3,8,2,7,1,4]=>{{1,2,4,9,11,12},{3,6,7,10},{5},{8}}
[8,12,6,11,5,10,3,9,2,7,1,4]=>{{1,2,4,8,9,11,12},{3,6,7,10},{5}}
[7,12,6,11,5,10,3,9,2,8,1,4]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[11,12,9,10,4,8,3,7,2,6,1,5]=>{{1,11},{2,3,4,5,6,7,8,9,10,12}}
[10,12,9,11,4,8,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,8,10,4,9,3,7,2,6,1,5]=>{{1,11},{2,4,5,6,9,10,12},{3,7,8}}
[10,12,8,11,4,9,3,7,2,6,1,5]=>{{1,2,4,5,6,9,10,11,12},{3,7,8}}
[9,12,8,11,4,10,3,7,2,6,1,5]=>{{1,2,4,5,9,11,12},{3,7,8},{6,10}}
[11,12,7,10,4,9,3,8,2,6,1,5]=>{{1,11},{2,4,5,6,9,10,12},{3,7},{8}}
[10,12,7,11,4,9,3,8,2,6,1,5]=>{{1,2,4,5,6,9,10,11,12},{3,7},{8}}
[9,12,7,11,4,10,3,8,2,6,1,5]=>{{1,2,4,5,9,11,12},{3,7},{6,10},{8}}
[8,12,7,11,4,10,3,9,2,6,1,5]=>{{1,2,4,5,8,9,11,12},{3,7},{6,10}}
[11,12,6,10,4,9,3,8,2,7,1,5]=>{{1,11},{2,3,4,5,6,7,9,10,12},{8}}
[10,12,6,11,4,9,3,8,2,7,1,5]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[9,12,6,11,4,10,3,8,2,7,1,5]=>{{1,2,4,5,9,11,12},{3,6,7,10},{8}}
[8,12,6,11,4,10,3,9,2,7,1,5]=>{{1,2,4,5,8,9,11,12},{3,6,7,10}}
[7,12,6,11,4,10,3,9,2,8,1,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,5,10,4,9,3,8,2,7,1,6]=>{{1,11},{2,6,9,12},{3,4,5,7,10},{8}}
[10,12,5,11,4,9,3,8,2,7,1,6]=>{{1,3,4,5,7,10,11},{2,6,9,12},{8}}
[9,12,5,11,4,10,3,8,2,7,1,6]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[8,12,5,11,4,10,3,9,2,7,1,6]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[7,12,5,11,4,10,3,9,2,8,1,6]=>{{1,3,4,5,7,11},{2,6,8,9,10,12}}
[6,12,5,11,4,10,3,9,2,8,1,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,9,7,5,3,1,12,10,8,6,4,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,9,7,5,3,1,12,11,8,6,4,2]=>{{1,6,10},{2,3,4,5,7,8,9,11,12}}
[11,8,7,5,3,1,12,10,9,6,4,2]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[10,8,7,5,3,1,12,11,9,6,4,2]=>{{1,6,10},{2,3,4,5,7,8,11,12},{9}}
[9,8,7,5,3,1,12,11,10,6,4,2]=>{{1,6,9,10},{2,3,4,5,7,8,11,12}}
[11,9,6,5,3,1,12,10,8,7,4,2]=>{{1,3,4,5,6,11},{2,7,8,9,10,12}}
[10,9,6,5,3,1,12,11,8,7,4,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,8,6,5,3,1,12,10,9,7,4,2]=>{{1,3,4,5,6,11},{2,7,8,10,12},{9}}
[10,8,6,5,3,1,12,11,9,7,4,2]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[9,8,6,5,3,1,12,11,10,7,4,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,7,6,5,3,1,12,10,9,8,4,2]=>{{1,3,4,5,6,11},{2,7,12},{8,10},{9}}
[10,7,6,5,3,1,12,11,9,8,4,2]=>{{1,3,4,5,6,8,10,11},{2,7,12},{9}}
[9,7,6,5,3,1,12,11,10,8,4,2]=>{{1,3,4,5,6,8,9,10,11},{2,7,12}}
[8,7,6,5,3,1,12,11,10,9,4,2]=>{{1,3,4,5,6,8,11},{2,7,12},{9,10}}
[11,9,7,4,3,1,12,10,8,6,5,2]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[10,9,7,4,3,1,12,11,8,6,5,2]=>{{1,6,10},{2,3,5,7,8,9,11,12},{4}}
[11,8,7,4,3,1,12,10,9,6,5,2]=>{{1,2,3,5,6,7,8,10,11,12},{4},{9}}
[10,8,7,4,3,1,12,11,9,6,5,2]=>{{1,6,10},{2,3,5,7,8,11,12},{4},{9}}
[9,8,7,4,3,1,12,11,10,6,5,2]=>{{1,6,9,10},{2,3,5,7,8,11,12},{4}}
[11,9,6,4,3,1,12,10,8,7,5,2]=>{{1,3,5,6,11},{2,7,8,9,10,12},{4}}
[10,9,6,4,3,1,12,11,8,7,5,2]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[11,8,6,4,3,1,12,10,9,7,5,2]=>{{1,3,5,6,11},{2,7,8,10,12},{4},{9}}
[10,8,6,4,3,1,12,11,9,7,5,2]=>{{1,2,3,5,6,7,8,10,11,12},{4},{9}}
[9,8,6,4,3,1,12,11,10,7,5,2]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[11,7,6,4,3,1,12,10,9,8,5,2]=>{{1,3,5,6,11},{2,7,12},{4},{8,10},{9}}
[10,7,6,4,3,1,12,11,9,8,5,2]=>{{1,3,5,6,8,10,11},{2,7,12},{4},{9}}
[9,7,6,4,3,1,12,11,10,8,5,2]=>{{1,3,5,6,8,9,10,11},{2,7,12},{4}}
[8,7,6,4,3,1,12,11,10,9,5,2]=>{{1,3,5,6,8,11},{2,7,12},{4},{9,10}}
[11,9,5,4,3,1,12,10,8,7,6,2]=>{{1,6,11},{2,7,8,9,10,12},{3,5},{4}}
[10,9,5,4,3,1,12,11,8,7,6,2]=>{{1,2,6,7,8,9,10,11,12},{3,5},{4}}
[11,8,5,4,3,1,12,10,9,7,6,2]=>{{1,6,11},{2,7,8,10,12},{3,5},{4},{9}}
[10,8,5,4,3,1,12,11,9,7,6,2]=>{{1,2,6,7,8,10,11,12},{3,5},{4},{9}}
[9,8,5,4,3,1,12,11,10,7,6,2]=>{{1,2,6,7,8,9,10,11,12},{3,5},{4}}
[11,7,5,4,3,1,12,10,9,8,6,2]=>{{1,6,11},{2,7,12},{3,5},{4},{8,10},{9}}
[10,7,5,4,3,1,12,11,9,8,6,2]=>{{1,6,8,10,11},{2,7,12},{3,5},{4},{9}}
[9,7,5,4,3,1,12,11,10,8,6,2]=>{{1,6,8,9,10,11},{2,7,12},{3,5},{4}}
[8,7,5,4,3,1,12,11,10,9,6,2]=>{{1,6,8,11},{2,7,12},{3,5},{4},{9,10}}
[11,6,5,4,3,1,12,10,9,8,7,2]=>{{1,2,6,7,11,12},{3,5},{4},{8,10},{9}}
[10,6,5,4,3,1,12,11,9,8,7,2]=>{{1,2,6,7,8,10,11,12},{3,5},{4},{9}}
[9,6,5,4,3,1,12,11,10,8,7,2]=>{{1,2,6,7,8,9,10,11,12},{3,5},{4}}
[8,6,5,4,3,1,12,11,10,9,7,2]=>{{1,2,6,7,8,11,12},{3,5},{4},{9,10}}
[7,6,5,4,3,1,12,11,10,9,8,2]=>{{1,2,6,7,12},{3,5},{4},{8,11},{9,10}}
[11,9,7,5,2,1,12,10,8,6,4,3]=>{{1,2,4,5,6,8,9,10,11},{3,7,12}}
[10,9,7,5,2,1,12,11,8,6,4,3]=>{{1,6,10},{2,4,5,8,9,11},{3,7,12}}
[11,8,7,5,2,1,12,10,9,6,4,3]=>{{1,2,4,5,6,8,10,11},{3,7,12},{9}}
[10,8,7,5,2,1,12,11,9,6,4,3]=>{{1,6,10},{2,4,5,8,11},{3,7,12},{9}}
[9,8,7,5,2,1,12,11,10,6,4,3]=>{{1,6,9,10},{2,4,5,8,11},{3,7,12}}
[11,9,6,5,2,1,12,10,8,7,4,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,9,6,5,2,1,12,11,8,7,4,3]=>{{1,3,6,7,10,12},{2,4,5,8,9,11}}
[11,8,6,5,2,1,12,10,9,7,4,3]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[10,8,6,5,2,1,12,11,9,7,4,3]=>{{1,3,6,7,10,12},{2,4,5,8,11},{9}}
[9,8,6,5,2,1,12,11,10,7,4,3]=>{{1,3,6,7,9,10,12},{2,4,5,8,11}}
[11,7,6,5,2,1,12,10,9,8,4,3]=>{{1,2,3,4,5,6,7,11,12},{8,10},{9}}
[10,7,6,5,2,1,12,11,9,8,4,3]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[9,7,6,5,2,1,12,11,10,8,4,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,7,6,5,2,1,12,11,10,9,4,3]=>{{1,2,3,4,5,6,7,8,11,12},{9,10}}
[11,9,7,4,2,1,12,10,8,6,5,3]=>{{1,2,5,6,8,9,10,11},{3,7,12},{4}}
[10,9,7,4,2,1,12,11,8,6,5,3]=>{{1,6,10},{2,5,8,9,11},{3,7,12},{4}}
[11,8,7,4,2,1,12,10,9,6,5,3]=>{{1,2,5,6,8,10,11},{3,7,12},{4},{9}}
[10,8,7,4,2,1,12,11,9,6,5,3]=>{{1,6,10},{2,5,8,11},{3,7,12},{4},{9}}
[9,8,7,4,2,1,12,11,10,6,5,3]=>{{1,6,9,10},{2,5,8,11},{3,7,12},{4}}
[11,9,6,4,2,1,12,10,8,7,5,3]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[10,9,6,4,2,1,12,11,8,7,5,3]=>{{1,3,6,7,10,12},{2,5,8,9,11},{4}}
[11,8,6,4,2,1,12,10,9,7,5,3]=>{{1,2,3,5,6,7,8,10,11,12},{4},{9}}
[10,8,6,4,2,1,12,11,9,7,5,3]=>{{1,3,6,7,10,12},{2,5,8,11},{4},{9}}
[9,8,6,4,2,1,12,11,10,7,5,3]=>{{1,3,6,7,9,10,12},{2,5,8,11},{4}}
[11,7,6,4,2,1,12,10,9,8,5,3]=>{{1,2,3,5,6,7,11,12},{4},{8,10},{9}}
[10,7,6,4,2,1,12,11,9,8,5,3]=>{{1,2,3,5,6,7,8,10,11,12},{4},{9}}
[9,7,6,4,2,1,12,11,10,8,5,3]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[8,7,6,4,2,1,12,11,10,9,5,3]=>{{1,2,3,5,6,7,8,11,12},{4},{9,10}}
[11,9,5,4,2,1,12,10,8,7,6,3]=>{{1,6,11},{2,3,5,7,8,9,10,12},{4}}
[10,9,5,4,2,1,12,11,8,7,6,3]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[11,8,5,4,2,1,12,10,9,7,6,3]=>{{1,6,11},{2,3,5,7,8,10,12},{4},{9}}
[10,8,5,4,2,1,12,11,9,7,6,3]=>{{1,2,3,5,6,7,8,10,11,12},{4},{9}}
[9,8,5,4,2,1,12,11,10,7,6,3]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[11,7,5,4,2,1,12,10,9,8,6,3]=>{{1,6,11},{2,3,5,7,12},{4},{8,10},{9}}
[10,7,5,4,2,1,12,11,9,8,6,3]=>{{1,6,8,10,11},{2,3,5,7,12},{4},{9}}
[9,7,5,4,2,1,12,11,10,8,6,3]=>{{1,6,8,9,10,11},{2,3,5,7,12},{4}}
[8,7,5,4,2,1,12,11,10,9,6,3]=>{{1,6,8,11},{2,3,5,7,12},{4},{9,10}}
[11,6,5,4,2,1,12,10,9,8,7,3]=>{{1,2,3,5,6,7,11,12},{4},{8,10},{9}}
[10,6,5,4,2,1,12,11,9,8,7,3]=>{{1,2,3,5,6,7,8,10,11,12},{4},{9}}
[9,6,5,4,2,1,12,11,10,8,7,3]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[8,6,5,4,2,1,12,11,10,9,7,3]=>{{1,2,3,5,6,7,8,11,12},{4},{9,10}}
[7,6,5,4,2,1,12,11,10,9,8,3]=>{{1,2,3,5,6,7,12},{4},{8,11},{9,10}}
[11,9,7,3,2,1,12,10,8,6,5,4]=>{{1,2,5,6,8,9,10,11},{3,4,7,12}}
[10,9,7,3,2,1,12,11,8,6,5,4]=>{{1,6,10},{2,5,8,9,11},{3,4,7,12}}
[11,8,7,3,2,1,12,10,9,6,5,4]=>{{1,2,5,6,8,10,11},{3,4,7,12},{9}}
[10,8,7,3,2,1,12,11,9,6,5,4]=>{{1,6,10},{2,5,8,11},{3,4,7,12},{9}}
[9,8,7,3,2,1,12,11,10,6,5,4]=>{{1,6,9,10},{2,5,8,11},{3,4,7,12}}
[11,9,6,3,2,1,12,10,8,7,5,4]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,9,6,3,2,1,12,11,8,7,5,4]=>{{1,3,4,6,7,10,12},{2,5,8,9,11}}
[11,8,6,3,2,1,12,10,9,7,5,4]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[10,8,6,3,2,1,12,11,9,7,5,4]=>{{1,3,4,6,7,10,12},{2,5,8,11},{9}}
[9,8,6,3,2,1,12,11,10,7,5,4]=>{{1,3,4,6,7,9,10,12},{2,5,8,11}}
[11,7,6,3,2,1,12,10,9,8,5,4]=>{{1,2,3,4,5,6,7,11,12},{8,10},{9}}
[10,7,6,3,2,1,12,11,9,8,5,4]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[9,7,6,3,2,1,12,11,10,8,5,4]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,7,6,3,2,1,12,11,10,9,5,4]=>{{1,2,3,4,5,6,7,8,11,12},{9,10}}
[11,9,5,3,2,1,12,10,8,7,6,4]=>{{1,6,11},{2,3,4,5,7,8,9,10,12}}
[10,9,5,3,2,1,12,11,8,7,6,4]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,8,5,3,2,1,12,10,9,7,6,4]=>{{1,6,11},{2,3,4,5,7,8,10,12},{9}}
[10,8,5,3,2,1,12,11,9,7,6,4]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[9,8,5,3,2,1,12,11,10,7,6,4]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,7,5,3,2,1,12,10,9,8,6,4]=>{{1,6,11},{2,3,4,5,7,12},{8,10},{9}}
[10,7,5,3,2,1,12,11,9,8,6,4]=>{{1,6,8,10,11},{2,3,4,5,7,12},{9}}
[9,7,5,3,2,1,12,11,10,8,6,4]=>{{1,6,8,9,10,11},{2,3,4,5,7,12}}
[8,7,5,3,2,1,12,11,10,9,6,4]=>{{1,6,8,11},{2,3,4,5,7,12},{9,10}}
[11,6,5,3,2,1,12,10,9,8,7,4]=>{{1,2,3,4,5,6,7,11,12},{8,10},{9}}
[10,6,5,3,2,1,12,11,9,8,7,4]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[9,6,5,3,2,1,12,11,10,8,7,4]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,6,5,3,2,1,12,11,10,9,7,4]=>{{1,2,3,4,5,6,7,8,11,12},{9,10}}
[7,6,5,3,2,1,12,11,10,9,8,4]=>{{1,2,3,4,5,6,7,12},{8,11},{9,10}}
[11,9,4,3,2,1,12,10,8,7,6,5]=>{{1,6,11},{2,5,7,8,9,10,12},{3,4}}
[10,9,4,3,2,1,12,11,8,7,6,5]=>{{1,2,5,6,7,8,9,10,11,12},{3,4}}
[11,8,4,3,2,1,12,10,9,7,6,5]=>{{1,6,11},{2,5,7,8,10,12},{3,4},{9}}
[10,8,4,3,2,1,12,11,9,7,6,5]=>{{1,2,5,6,7,8,10,11,12},{3,4},{9}}
[9,8,4,3,2,1,12,11,10,7,6,5]=>{{1,2,5,6,7,8,9,10,11,12},{3,4}}
[11,7,4,3,2,1,12,10,9,8,6,5]=>{{1,6,11},{2,5,7,12},{3,4},{8,10},{9}}
[10,7,4,3,2,1,12,11,9,8,6,5]=>{{1,6,8,10,11},{2,5,7,12},{3,4},{9}}
[9,7,4,3,2,1,12,11,10,8,6,5]=>{{1,6,8,9,10,11},{2,5,7,12},{3,4}}
[8,7,4,3,2,1,12,11,10,9,6,5]=>{{1,6,8,11},{2,5,7,12},{3,4},{9,10}}
[11,6,4,3,2,1,12,10,9,8,7,5]=>{{1,2,5,6,7,11,12},{3,4},{8,10},{9}}
[10,6,4,3,2,1,12,11,9,8,7,5]=>{{1,2,5,6,7,8,10,11,12},{3,4},{9}}
[9,6,4,3,2,1,12,11,10,8,7,5]=>{{1,2,5,6,7,8,9,10,11,12},{3,4}}
[8,6,4,3,2,1,12,11,10,9,7,5]=>{{1,2,5,6,7,8,11,12},{3,4},{9,10}}
[7,6,4,3,2,1,12,11,10,9,8,5]=>{{1,2,5,6,7,12},{3,4},{8,11},{9,10}}
[11,5,4,3,2,1,12,10,9,8,7,6]=>{{1,6,7,11,12},{2,5},{3,4},{8,10},{9}}
[10,5,4,3,2,1,12,11,9,8,7,6]=>{{1,6,7,8,10,11,12},{2,5},{3,4},{9}}
[9,5,4,3,2,1,12,11,10,8,7,6]=>{{1,6,7,8,9,10,11,12},{2,5},{3,4}}
[8,5,4,3,2,1,12,11,10,9,7,6]=>{{1,6,7,8,11,12},{2,5},{3,4},{9,10}}
[7,5,4,3,2,1,12,11,10,9,8,6]=>{{1,6,7,12},{2,5},{3,4},{8,11},{9,10}}
[7,1,8,2,9,3,10,4,11,5,12,6]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[9,10,11,12,7,8,5,6,3,4,1,2]=>{{1,3,9,11},{2,4,10,12},{5,7},{6,8}}
[11,12,7,8,9,10,5,6,3,4,1,2]=>{{1,11},{2,12},{3,5,7,9},{4,6,8,10}}
[7,10,11,8,9,12,5,6,3,4,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[7,8,9,10,11,12,5,6,3,4,1,2]=>{{1,5,7,11},{2,6,8,12},{3,9},{4,10}}
[11,12,9,10,5,6,7,8,3,4,1,2]=>{{1,11},{2,12},{3,9},{4,10},{5},{6},{7},{8}}
[9,10,11,12,5,6,7,8,3,4,1,2]=>{{1,3,9,11},{2,4,10,12},{5},{6},{7},{8}}
[11,12,5,8,9,6,7,10,3,4,1,2]=>{{1,11},{2,12},{3,5,9},{4,8,10},{6},{7}}
[5,10,11,8,9,6,7,12,3,4,1,2]=>{{1,3,5,9,11},{2,4,8,10,12},{6},{7}}
[5,8,9,10,11,6,7,12,3,4,1,2]=>{{1,5,11},{2,8,12},{3,9},{4,10},{6},{7}}
[11,12,5,6,7,8,9,10,3,4,1,2]=>{{1,11},{2,12},{3,5,7,9},{4,6,8,10}}
[5,10,11,6,7,8,9,12,3,4,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[5,6,9,10,7,8,11,12,3,4,1,2]=>{{1,5,7,11},{2,6,8,12},{3,9},{4,10}}
[5,6,7,8,9,10,11,12,3,4,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,9,10,7,8,3,4,5,6,1,2]=>{{1,11},{2,12},{3,5,7,9},{4,6,8,10}}
[9,10,11,12,7,8,3,4,5,6,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,7,8,9,10,3,4,5,6,1,2]=>{{1,11},{2,12},{3,7},{4,8},{5,9},{6,10}}
[7,10,11,8,9,12,3,4,5,6,1,2]=>{{1,3,7,11},{2,6,10,12},{4,8},{5,9}}
[7,8,9,10,11,12,3,4,5,6,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,9,10,3,6,7,4,5,8,1,2]=>{{1,11},{2,12},{3,5,9},{4,8,10},{6},{7}}
[9,10,11,12,3,6,7,4,5,8,1,2]=>{{1,3,5,9,11},{2,4,8,10,12},{6},{7}}
[11,12,3,8,9,6,7,4,5,10,1,2]=>{{1,11},{2,12},{3},{4,8},{5,9},{6},{7},{10}}
[3,10,11,8,9,6,7,4,5,12,1,2]=>{{1,3,11},{2,10,12},{4,8},{5,9},{6},{7}}
[3,8,9,10,11,6,7,4,5,12,1,2]=>{{1,3,5,9,11},{2,4,8,10,12},{6},{7}}
[11,12,3,6,7,8,9,4,5,10,1,2]=>{{1,11},{2,12},{3},{4,6,8},{5,7,9},{10}}
[3,10,11,6,7,8,9,4,5,12,1,2]=>{{1,3,11},{2,10,12},{4,6,8},{5,7,9}}
[3,6,9,10,7,8,11,4,5,12,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[3,6,7,8,9,10,11,4,5,12,1,2]=>{{1,3,7,11},{2,6,10,12},{4,8},{5,9}}
[11,12,9,10,3,4,5,6,7,8,1,2]=>{{1,11},{2,12},{3,5,7,9},{4,6,8,10}}
[9,10,11,12,3,4,5,6,7,8,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,3,8,9,4,5,6,7,10,1,2]=>{{1,11},{2,12},{3},{4,6,8},{5,7,9},{10}}
[3,10,11,8,9,4,5,6,7,12,1,2]=>{{1,3,11},{2,10,12},{4,6,8},{5,7,9}}
[3,8,9,10,11,4,5,6,7,12,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,3,4,7,8,5,6,9,10,1,2]=>{{1,11},{2,12},{3},{4},{5,7},{6,8},{9},{10}}
[3,10,11,4,7,8,5,6,9,12,1,2]=>{{1,3,11},{2,10,12},{4},{5,7},{6,8},{9}}
[3,4,9,10,7,8,5,6,11,12,1,2]=>{{1,3,9,11},{2,4,10,12},{5,7},{6,8}}
[3,4,7,8,9,10,5,6,11,12,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,3,4,5,6,7,8,9,10,1,2]=>{{1,11},{2,12},{3},{4},{5},{6},{7},{8},{9},{10}}
[3,10,11,4,5,6,7,8,9,12,1,2]=>{{1,3,11},{2,10,12},{4},{5},{6},{7},{8},{9}}
[3,4,9,10,5,6,7,8,11,12,1,2]=>{{1,3,9,11},{2,4,10,12},{5},{6},{7},{8}}
[3,4,5,8,9,6,7,10,11,12,1,2]=>{{1,3,5,9,11},{2,4,8,10,12},{6},{7}}
[3,4,5,6,7,8,9,10,11,12,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,9,10,7,8,5,6,1,2,3,4]=>{{1,3,9,11},{2,4,10,12},{5,7},{6,8}}
[9,10,11,12,7,8,5,6,1,2,3,4]=>{{1,9},{2,10},{3,11},{4,12},{5,7},{6,8}}
[11,12,7,8,9,10,5,6,1,2,3,4]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[7,10,11,8,9,12,5,6,1,2,3,4]=>{{1,5,7,9},{2,10},{3,11},{4,6,8,12}}
[7,8,9,10,11,12,5,6,1,2,3,4]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,9,10,5,6,7,8,1,2,3,4]=>{{1,3,9,11},{2,4,10,12},{5},{6},{7},{8}}
[9,10,11,12,5,6,7,8,1,2,3,4]=>{{1,9},{2,10},{3,11},{4,12},{5},{6},{7},{8}}
[11,12,5,8,9,6,7,10,1,2,3,4]=>{{1,3,5,9,11},{2,4,8,10,12},{6},{7}}
[5,10,11,8,9,6,7,12,1,2,3,4]=>{{1,5,9},{2,10},{3,11},{4,8,12},{6},{7}}
[5,8,9,10,11,6,7,12,1,2,3,4]=>{{1,3,5,9,11},{2,4,8,10,12},{6},{7}}
[11,12,5,6,7,8,9,10,1,2,3,4]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[5,10,11,6,7,8,9,12,1,2,3,4]=>{{1,5,7,9},{2,10},{3,11},{4,6,8,12}}
[5,6,9,10,7,8,11,12,1,2,3,4]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[5,6,7,8,9,10,11,12,1,2,3,4]=>{{1,5,9},{2,6,10},{3,7,11},{4,8,12}}
[11,12,9,10,7,8,1,4,5,2,3,6]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[9,10,11,12,7,8,1,4,5,2,3,6]=>{{1,5,7,9},{2,10},{3,11},{4,6,8,12}}
[11,12,7,8,9,10,1,4,5,2,3,6]=>{{1,3,7,11},{2,6,10,12},{4,8},{5,9}}
[7,10,11,8,9,12,1,4,5,2,3,6]=>{{1,7},{2,10},{3,11},{4,8},{5,9},{6,12}}
[7,8,9,10,11,12,1,4,5,2,3,6]=>{{1,7},{2,4,8,10},{3,5,9,11},{6,12}}
[11,12,9,10,1,6,7,4,5,2,3,8]=>{{1,3,5,9,11},{2,4,8,10,12},{6},{7}}
[9,10,11,12,1,6,7,4,5,2,3,8]=>{{1,5,9},{2,10},{3,11},{4,8,12},{6},{7}}
[11,12,1,8,9,6,7,4,5,2,3,10]=>{{1,3,11},{2,10,12},{4,8},{5,9},{6},{7}}
[1,10,11,8,9,6,7,4,5,2,3,12]=>{{1},{2,10},{3,11},{4,8},{5,9},{6},{7},{12}}
[1,8,9,10,11,6,7,4,5,2,3,12]=>{{1},{2,4,8,10},{3,5,9,11},{6},{7},{12}}
[11,12,1,6,7,8,9,4,5,2,3,10]=>{{1,3,11},{2,10,12},{4,6,8},{5,7,9}}
[1,10,11,6,7,8,9,4,5,2,3,12]=>{{1},{2,10},{3,11},{4,6,8},{5,7,9},{12}}
[1,6,9,10,7,8,11,4,5,2,3,12]=>{{1},{2,4,6,8,10},{3,5,7,9,11},{12}}
[1,6,7,8,9,10,11,4,5,2,3,12]=>{{1},{2,6,10},{3,7,11},{4,8},{5,9},{12}}
[11,12,9,10,1,4,5,6,7,2,3,8]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[9,10,11,12,1,4,5,6,7,2,3,8]=>{{1,5,7,9},{2,10},{3,11},{4,6,8,12}}
[11,12,1,8,9,4,5,6,7,2,3,10]=>{{1,3,11},{2,10,12},{4,6,8},{5,7,9}}
[1,10,11,8,9,4,5,6,7,2,3,12]=>{{1},{2,10},{3,11},{4,6,8},{5,7,9},{12}}
[1,8,9,10,11,4,5,6,7,2,3,12]=>{{1},{2,4,6,8,10},{3,5,7,9,11},{12}}
[11,12,1,4,7,8,5,6,9,2,3,10]=>{{1,3,11},{2,10,12},{4},{5,7},{6,8},{9}}
[1,10,11,4,7,8,5,6,9,2,3,12]=>{{1},{2,10},{3,11},{4},{5,7},{6,8},{9},{12}}
[1,4,9,10,7,8,5,6,11,2,3,12]=>{{1},{2,4,10},{3,9,11},{5,7},{6,8},{12}}
[1,4,7,8,9,10,5,6,11,2,3,12]=>{{1},{2,4,6,8,10},{3,5,7,9,11},{12}}
[11,12,1,4,5,6,7,8,9,2,3,10]=>{{1,3,11},{2,10,12},{4},{5},{6},{7},{8},{9}}
[1,10,11,4,5,6,7,8,9,2,3,12]=>{{1},{2,10},{3,11},{4},{5},{6},{7},{8},{9},{12}}
[1,4,9,10,5,6,7,8,11,2,3,12]=>{{1},{2,4,10},{3,9,11},{5},{6},{7},{8},{12}}
[1,4,5,8,9,6,7,10,11,2,3,12]=>{{1},{2,4,8,10},{3,5,9,11},{6},{7},{12}}
[1,4,5,6,7,8,9,10,11,2,3,12]=>{{1},{2,4,6,8,10},{3,5,7,9,11},{12}}
[11,12,9,10,7,8,1,2,3,4,5,6]=>{{1,5,7,11},{2,6,8,12},{3,9},{4,10}}
[9,10,11,12,7,8,1,2,3,4,5,6]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,7,8,9,10,1,2,3,4,5,6]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[7,10,11,8,9,12,1,2,3,4,5,6]=>{{1,7},{2,4,8,10},{3,5,9,11},{6,12}}
[11,12,9,10,1,6,7,2,3,4,5,8]=>{{1,5,11},{2,8,12},{3,9},{4,10},{6},{7}}
[9,10,11,12,1,6,7,2,3,4,5,8]=>{{1,3,5,9,11},{2,4,8,10,12},{6},{7}}
[11,12,1,8,9,6,7,2,3,4,5,10]=>{{1,3,5,9,11},{2,4,8,10,12},{6},{7}}
[1,10,11,8,9,6,7,2,3,4,5,12]=>{{1},{2,4,8,10},{3,5,9,11},{6},{7},{12}}
[1,8,9,10,11,6,7,2,3,4,5,12]=>{{1},{2,8},{3,9},{4,10},{5,11},{6},{7},{12}}
[11,12,1,6,7,8,9,2,3,4,5,10]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[1,10,11,6,7,8,9,2,3,4,5,12]=>{{1},{2,4,6,8,10},{3,5,7,9,11},{12}}
[1,6,9,10,7,8,11,2,3,4,5,12]=>{{1},{2,6,8},{3,9},{4,10},{5,7,11},{12}}
[1,6,7,8,9,10,11,2,3,4,5,12]=>{{1},{2,4,6,8,10},{3,5,7,9,11},{12}}
[11,12,9,10,1,2,5,6,3,4,7,8]=>{{1,5,7,11},{2,6,8,12},{3,9},{4,10}}
[9,10,11,12,1,2,5,6,3,4,7,8]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,1,8,9,2,5,6,3,4,7,10]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[1,10,11,8,9,2,5,6,3,4,7,12]=>{{1},{2,4,6,8,10},{3,5,7,9,11},{12}}
[1,8,9,10,11,2,5,6,3,4,7,12]=>{{1},{2,6,8},{3,9},{4,10},{5,7,11},{12}}
[11,12,1,2,7,8,5,6,3,4,9,10]=>{{1,3,9,11},{2,4,10,12},{5,7},{6,8}}
[1,10,11,2,7,8,5,6,3,4,9,12]=>{{1},{2,4,10},{3,9,11},{5,7},{6,8},{12}}
[1,2,9,10,7,8,5,6,3,4,11,12]=>{{1},{2},{3,9},{4,10},{5,7},{6,8},{11},{12}}
[1,2,7,8,9,10,5,6,3,4,11,12]=>{{1},{2},{3,5,7,9},{4,6,8,10},{11},{12}}
[11,12,1,2,5,6,7,8,3,4,9,10]=>{{1,3,9,11},{2,4,10,12},{5},{6},{7},{8}}
[1,10,11,2,5,6,7,8,3,4,9,12]=>{{1},{2,4,10},{3,9,11},{5},{6},{7},{8},{12}}
[1,2,9,10,5,6,7,8,3,4,11,12]=>{{1},{2},{3,9},{4,10},{5},{6},{7},{8},{11},{12}}
[1,2,5,8,9,6,7,10,3,4,11,12]=>{{1},{2},{3,5,9},{4,8,10},{6},{7},{11},{12}}
[1,2,5,6,7,8,9,10,3,4,11,12]=>{{1},{2},{3,5,7,9},{4,6,8,10},{11},{12}}
[11,12,9,10,1,2,3,4,5,6,7,8]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[9,10,11,12,1,2,3,4,5,6,7,8]=>{{1,5,9},{2,6,10},{3,7,11},{4,8,12}}
[11,12,1,8,9,2,3,4,5,6,7,10]=>{{1,3,7,11},{2,6,10,12},{4,8},{5,9}}
[1,10,11,8,9,2,3,4,5,6,7,12]=>{{1},{2,6,10},{3,7,11},{4,8},{5,9},{12}}
[1,8,9,10,11,2,3,4,5,6,7,12]=>{{1},{2,4,6,8,10},{3,5,7,9,11},{12}}
[11,12,1,2,7,8,3,4,5,6,9,10]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[1,10,11,2,7,8,3,4,5,6,9,12]=>{{1},{2,4,6,8,10},{3,5,7,9,11},{12}}
[1,2,9,10,7,8,3,4,5,6,11,12]=>{{1},{2},{3,5,7,9},{4,6,8,10},{11},{12}}
[1,2,7,8,9,10,3,4,5,6,11,12]=>{{1},{2},{3,7},{4,8},{5,9},{6,10},{11},{12}}
[11,12,1,2,3,6,7,4,5,8,9,10]=>{{1,3,5,9,11},{2,4,8,10,12},{6},{7}}
[1,10,11,2,3,6,7,4,5,8,9,12]=>{{1},{2,4,8,10},{3,5,9,11},{6},{7},{12}}
[1,2,9,10,3,6,7,4,5,8,11,12]=>{{1},{2},{3,5,9},{4,8,10},{6},{7},{11},{12}}
[1,2,3,8,9,6,7,4,5,10,11,12]=>{{1},{2},{3},{4,8},{5,9},{6},{7},{10},{11},{12}}
[1,2,3,6,7,8,9,4,5,10,11,12]=>{{1},{2},{3},{4,6,8},{5,7,9},{10},{11},{12}}
[11,12,1,2,3,4,5,6,7,8,9,10]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[1,10,11,2,3,4,5,6,7,8,9,12]=>{{1},{2,4,6,8,10},{3,5,7,9,11},{12}}
[1,2,9,10,3,4,5,6,7,8,11,12]=>{{1},{2},{3,5,7,9},{4,6,8,10},{11},{12}}
[1,2,3,8,9,4,5,6,7,10,11,12]=>{{1},{2},{3},{4,6,8},{5,7,9},{10},{11},{12}}
[1,2,3,4,7,8,5,6,9,10,11,12]=>{{1},{2},{3},{4},{5,7},{6,8},{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}}
[11,1,12,10,9,8,7,6,5,4,3,2]=>{{1,2,3,11,12},{4,10},{5,9},{6,8},{7}}
[2,12,11,10,9,8,7,6,5,4,1,3]=>{{1,2,3,11,12},{4,10},{5,9},{6,8},{7}}
[11,1,2,3,4,5,6,7,8,9,12,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,12,1,3,4,5,6,7,8,9,10,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,9,10,7,8,5,6,2,1,3,4]=>{{1,2,3,4,9,10,11,12},{5,7},{6,8}}
[11,12,9,10,7,8,4,3,5,6,1,2]=>{{1,11},{2,12},{3,4,5,6,7,8,9,10}}
[11,12,9,10,7,8,4,2,5,1,3,6]=>{{1,3,4,5,7,9,10,11},{2,6,8,12}}
[11,12,9,10,7,8,3,2,1,4,5,6]=>{{1,3,5,7,9,11},{2,6,8,12},{4,10}}
[11,12,9,10,6,5,7,8,3,4,1,2]=>{{1,11},{2,12},{3,9},{4,10},{5,6},{7},{8}}
[11,12,9,10,6,5,7,8,2,1,3,4]=>{{1,2,3,4,9,10,11,12},{5,6},{7},{8}}
[11,12,9,10,6,4,7,3,5,8,1,2]=>{{1,11},{2,12},{3,4,5,6,8,9,10},{7}}
[11,12,9,10,6,4,7,2,5,1,3,8]=>{{1,3,4,5,6,9,10,11},{2,8,12},{7}}
[11,12,9,10,6,3,7,2,1,4,5,8]=>{{1,3,5,6,9,11},{2,8,12},{4,10},{7}}
[11,12,9,10,5,4,3,6,7,8,1,2]=>{{1,11},{2,12},{3,7,9},{4,6,8,10},{5}}
[11,12,9,10,5,4,2,6,7,1,3,8]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[11,12,9,10,5,3,2,6,1,4,7,8]=>{{1,2,3,6,7,8,9,11,12},{4,10},{5}}
[11,12,9,10,4,3,2,1,5,6,7,8]=>{{1,2,7,8,11,12},{3,4,5,6,9,10}}
[11,12,8,7,9,10,5,6,3,4,1,2]=>{{1,11},{2,12},{3,4,5,6,7,8,9,10}}
[11,12,8,7,9,10,5,6,2,1,3,4]=>{{1,3,6,8,10,11},{2,4,5,7,9,12}}
[11,12,8,7,9,10,4,3,5,6,1,2]=>{{1,11},{2,12},{3,8},{4,7},{5,9},{6,10}}
[11,12,8,7,9,10,4,2,5,1,3,6]=>{{1,2,3,6,8,10,11,12},{4,7},{5,9}}
[11,12,8,7,9,10,3,2,1,4,5,6]=>{{1,5,9,11},{2,3,4,6,7,8,10,12}}
[11,12,8,6,9,5,7,10,3,4,1,2]=>{{1,11},{2,12},{3,4,5,6,8,9,10},{7}}
[11,12,8,6,9,5,7,10,2,1,3,4]=>{{1,3,8,10,11},{2,4,5,6,9,12},{7}}
[11,12,8,6,9,4,7,3,5,10,1,2]=>{{1,11},{2,12},{3,8},{4,6},{5,9},{7},{10}}
[11,12,8,6,9,4,7,2,5,1,3,10]=>{{1,2,3,8,10,11,12},{4,6},{5,9},{7}}
[11,12,8,6,9,3,7,2,1,4,5,10]=>{{1,5,9,11},{2,3,4,6,8,10,12},{7}}
[11,12,8,5,9,4,3,6,7,10,1,2]=>{{1,11},{2,12},{3,4,5,6,7,8,9},{10}}
[11,12,8,5,9,4,2,6,7,1,3,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,8,5,9,3,2,6,1,4,7,10]=>{{1,2,4,5,7,9,10,11,12},{3,6,8}}
[11,12,8,4,9,3,2,1,5,6,7,10]=>{{1,2,3,6,7,8,10,11,12},{4},{5,9}}
[11,12,7,6,5,8,9,10,3,4,1,2]=>{{1,11},{2,12},{3,7,9},{4,6,8,10},{5}}
[11,12,7,6,5,8,9,10,2,1,3,4]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[11,12,7,6,4,8,9,3,5,10,1,2]=>{{1,11},{2,12},{3,4,5,6,7,8,9},{10}}
[11,12,7,6,4,8,9,2,5,1,3,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,7,6,3,8,9,2,1,4,5,10]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[11,12,7,5,4,8,3,6,9,10,1,2]=>{{1,11},{2,12},{3,7},{4,5},{6,8},{9},{10}}
[11,12,7,5,4,8,2,6,9,1,3,10]=>{{1,2,3,7,10,11,12},{4,5},{6,8},{9}}
[11,12,7,5,3,8,2,6,1,4,9,10]=>{{1,9,11},{2,3,4,5,7,10,12},{6,8}}
[11,12,7,4,3,8,2,1,5,6,9,10]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[11,12,6,5,4,3,7,8,9,10,1,2]=>{{1,11},{2,12},{3,6},{4,5},{7},{8},{9},{10}}
[11,12,6,5,4,2,7,8,9,1,3,10]=>{{1,2,3,6,10,11,12},{4,5},{7},{8},{9}}
[11,12,6,5,3,2,7,8,1,4,9,10]=>{{1,9,11},{2,3,4,5,6,10,12},{7},{8}}
[11,12,6,4,3,2,7,1,5,8,9,10]=>{{1,2,3,5,6,8,9,10,11,12},{4},{7}}
[11,12,5,4,3,2,1,6,7,8,9,10]=>{{1,7,9,11},{2,6,8,10,12},{3,5},{4}}
[10,9,11,12,7,8,5,6,3,4,1,2]=>{{1,2,3,4,9,10,11,12},{5,7},{6,8}}
[10,9,11,12,7,8,5,6,2,1,3,4]=>{{1,10},{2,9},{3,11},{4,12},{5,7},{6,8}}
[10,9,11,12,7,8,4,3,5,6,1,2]=>{{1,3,6,8,10,11},{2,4,5,7,9,12}}
[10,9,11,12,7,8,4,2,5,1,3,6]=>{{1,10},{2,4,5,6,7,8,9,12},{3,11}}
[10,9,11,12,7,8,3,2,1,4,5,6]=>{{1,2,4,6,8,9,10,12},{3,5,7,11}}
[10,9,11,12,6,5,7,8,3,4,1,2]=>{{1,2,3,4,9,10,11,12},{5,6},{7},{8}}
[10,9,11,12,6,5,7,8,2,1,3,4]=>{{1,10},{2,9},{3,11},{4,12},{5,6},{7},{8}}
[10,9,11,12,6,4,7,3,5,8,1,2]=>{{1,3,8,10,11},{2,4,5,6,9,12},{7}}
[10,9,11,12,6,4,7,2,5,1,3,8]=>{{1,10},{2,4,5,6,8,9,12},{3,11},{7}}
[10,9,11,12,6,3,7,2,1,4,5,8]=>{{1,2,4,8,9,10,12},{3,5,6,11},{7}}
[10,9,11,12,5,4,3,6,7,8,1,2]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[10,9,11,12,5,4,2,6,7,1,3,8]=>{{1,10},{2,7,9},{3,11},{4,6,8,12},{5}}
[10,9,11,12,5,3,2,6,1,4,7,8]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[10,9,11,12,4,3,2,1,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,8,11,7,9,12,5,6,3,4,1,2]=>{{1,3,4,5,7,9,10,11},{2,6,8,12}}
[10,8,11,7,9,12,5,6,2,1,3,4]=>{{1,10},{2,4,5,6,7,8,9,12},{3,11}}
[10,8,11,7,9,12,4,3,5,6,1,2]=>{{1,2,3,6,8,10,11,12},{4,7},{5,9}}
[10,8,11,7,9,12,4,2,5,1,3,6]=>{{1,10},{2,8},{3,11},{4,7},{5,9},{6,12}}
[10,8,11,7,9,12,3,2,1,4,5,6]=>{{1,3,4,5,7,9,10,11},{2,8},{6,12}}
[10,8,11,6,9,5,7,12,3,4,1,2]=>{{1,3,4,5,6,9,10,11},{2,8,12},{7}}
[10,8,11,6,9,5,7,12,2,1,3,4]=>{{1,10},{2,4,5,6,8,9,12},{3,11},{7}}
[10,8,11,6,9,4,7,3,5,12,1,2]=>{{1,2,3,8,10,11,12},{4,6},{5,9},{7}}
[10,8,11,6,9,4,7,2,5,1,3,12]=>{{1,10},{2,8},{3,11},{4,6},{5,9},{7},{12}}
[10,8,11,6,9,3,7,2,1,4,5,12]=>{{1,3,4,5,6,9,10,11},{2,8},{7},{12}}
[10,8,11,5,9,4,3,6,7,12,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,8,11,5,9,4,2,6,7,1,3,12]=>{{1,10},{2,4,5,6,7,8,9},{3,11},{12}}
[10,8,11,5,9,3,2,6,1,4,7,12]=>{{1,4,5,9,10},{2,3,6,7,8,11},{12}}
[10,8,11,4,9,3,2,1,5,6,7,12]=>{{1,2,3,6,7,8,10,11},{4},{5,9},{12}}
[10,7,11,6,5,8,9,12,3,4,1,2]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[10,7,11,6,5,8,9,12,2,1,3,4]=>{{1,10},{2,7,9},{3,11},{4,6,8,12},{5}}
[10,7,11,6,4,8,9,3,5,12,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,7,11,6,4,8,9,2,5,1,3,12]=>{{1,10},{2,4,5,6,7,8,9},{3,11},{12}}
[10,7,11,6,3,8,9,2,1,4,5,12]=>{{1,2,4,6,7,8,9,10},{3,5,11},{12}}
[10,7,11,5,4,8,3,6,9,12,1,2]=>{{1,2,3,7,10,11,12},{4,5},{6,8},{9}}
[10,7,11,5,4,8,2,6,9,1,3,12]=>{{1,10},{2,7},{3,11},{4,5},{6,8},{9},{12}}
[10,7,11,5,3,8,2,6,1,4,9,12]=>{{1,3,4,5,9,10,11},{2,7},{6,8},{12}}
[10,7,11,4,3,8,2,1,5,6,9,12]=>{{1,6,8,10},{2,7},{3,5,9,11},{4},{12}}
[10,6,11,5,4,3,7,8,9,12,1,2]=>{{1,2,3,6,10,11,12},{4,5},{7},{8},{9}}
[10,6,11,5,4,2,7,8,9,1,3,12]=>{{1,10},{2,6},{3,11},{4,5},{7},{8},{9},{12}}
[10,6,11,5,3,2,7,8,1,4,9,12]=>{{1,3,4,5,9,10,11},{2,6},{7},{8},{12}}
[10,6,11,4,3,2,7,1,5,8,9,12]=>{{1,8,10},{2,6},{3,5,9,11},{4},{7},{12}}
[10,5,11,4,3,2,1,6,7,8,9,12]=>{{1,2,3,5,6,7,8,9,10,11},{4},{12}}
[9,8,7,10,11,12,5,6,3,4,1,2]=>{{1,3,5,7,9,11},{2,6,8,12},{4,10}}
[9,8,7,10,11,12,5,6,2,1,3,4]=>{{1,2,4,6,8,9,10,12},{3,5,7,11}}
[9,8,7,10,11,12,4,3,5,6,1,2]=>{{1,5,9,11},{2,3,4,6,7,8,10,12}}
[9,8,7,10,11,12,4,2,5,1,3,6]=>{{1,3,4,5,7,9,10,11},{2,8},{6,12}}
[9,8,7,10,11,12,3,2,1,4,5,6]=>{{1,9},{2,8},{3,7},{4,10},{5,11},{6,12}}
[9,8,6,10,11,5,7,12,3,4,1,2]=>{{1,3,5,6,9,11},{2,8,12},{4,10},{7}}
[9,8,6,10,11,5,7,12,2,1,3,4]=>{{1,2,4,8,9,10,12},{3,5,6,11},{7}}
[9,8,6,10,11,4,7,3,5,12,1,2]=>{{1,5,9,11},{2,3,4,6,8,10,12},{7}}
[9,8,6,10,11,4,7,2,5,1,3,12]=>{{1,3,4,5,6,9,10,11},{2,8},{7},{12}}
[9,8,6,10,11,3,7,2,1,4,5,12]=>{{1,9},{2,8},{3,6},{4,10},{5,11},{7},{12}}
[9,8,5,10,11,4,3,6,7,12,1,2]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}
[9,8,5,10,11,4,2,6,7,1,3,12]=>{{1,2,4,6,7,8,9,10},{3,5,11},{12}}
[9,8,5,10,11,3,2,6,1,4,7,12]=>{{1,9},{2,3,5,6,7,8,11},{4,10},{12}}
[9,8,4,10,11,3,2,1,5,6,7,12]=>{{1,2,5,7,8,9,11},{3,4,6,10},{12}}
[9,7,6,10,5,8,11,12,3,4,1,2]=>{{1,2,3,6,7,8,9,11,12},{4,10},{5}}
[9,7,6,10,5,8,11,12,2,1,3,4]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[9,7,6,10,4,8,11,3,5,12,1,2]=>{{1,2,4,5,7,9,10,11,12},{3,6,8}}
[9,7,6,10,4,8,11,2,5,1,3,12]=>{{1,4,5,9,10},{2,3,6,7,8,11},{12}}
[9,7,6,10,3,8,11,2,1,4,5,12]=>{{1,9},{2,3,5,6,7,8,11},{4,10},{12}}
[9,7,5,10,4,8,3,6,11,12,1,2]=>{{1,9,11},{2,3,4,5,7,10,12},{6,8}}
[9,7,5,10,4,8,2,6,11,1,3,12]=>{{1,3,4,5,9,10,11},{2,7},{6,8},{12}}
[9,7,5,10,3,8,2,6,1,4,11,12]=>{{1,9},{2,7},{3,5},{4,10},{6,8},{11},{12}}
[9,7,4,10,3,8,2,1,5,6,11,12]=>{{1,3,4,5,6,8,9,10},{2,7},{11},{12}}
[9,6,5,10,4,3,7,8,11,12,1,2]=>{{1,9,11},{2,3,4,5,6,10,12},{7},{8}}
[9,6,5,10,4,2,7,8,11,1,3,12]=>{{1,3,4,5,9,10,11},{2,6},{7},{8},{12}}
[9,6,5,10,3,2,7,8,1,4,11,12]=>{{1,9},{2,6},{3,5},{4,10},{7},{8},{11},{12}}
[9,6,4,10,3,2,7,1,5,8,11,12]=>{{1,3,4,5,8,9,10},{2,6},{7},{11},{12}}
[9,5,4,10,3,2,1,6,7,8,11,12]=>{{1,7,9},{2,3,4,5,6,8,10},{11},{12}}
[8,7,6,5,9,10,11,12,3,4,1,2]=>{{1,2,7,8,11,12},{3,4,5,6,9,10}}
[8,7,6,5,9,10,11,12,2,1,3,4]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,7,6,4,9,10,11,3,5,12,1,2]=>{{1,2,3,6,7,8,10,11,12},{4},{5,9}}
[8,7,6,4,9,10,11,2,5,1,3,12]=>{{1,2,3,6,7,8,10,11},{4},{5,9},{12}}
[8,7,6,3,9,10,11,2,1,4,5,12]=>{{1,2,5,7,8,9,11},{3,4,6,10},{12}}
[8,7,5,4,9,10,3,6,11,12,1,2]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[8,7,5,4,9,10,2,6,11,1,3,12]=>{{1,6,8,10},{2,7},{3,5,9,11},{4},{12}}
[8,7,5,3,9,10,2,6,1,4,11,12]=>{{1,3,4,5,6,8,9,10},{2,7},{11},{12}}
[8,7,4,3,9,10,2,1,5,6,11,12]=>{{1,8},{2,7},{3,4},{5,9},{6,10},{11},{12}}
[8,6,5,4,9,3,7,10,11,12,1,2]=>{{1,2,3,5,6,8,9,10,11,12},{4},{7}}
[8,6,5,4,9,2,7,10,11,1,3,12]=>{{1,8,10},{2,6},{3,5,9,11},{4},{7},{12}}
[8,6,5,3,9,2,7,10,1,4,11,12]=>{{1,3,4,5,8,9,10},{2,6},{7},{11},{12}}
[8,6,4,3,9,2,7,1,5,10,11,12]=>{{1,8},{2,6},{3,4},{5,9},{7},{10},{11},{12}}
[8,5,4,3,9,2,1,6,7,10,11,12]=>{{1,2,5,6,7,8,9},{3,4},{10},{11},{12}}
[7,6,5,4,3,8,9,10,11,12,1,2]=>{{1,7,9,11},{2,6,8,10,12},{3,5},{4}}
[7,6,5,4,2,8,9,10,11,1,3,12]=>{{1,2,3,5,6,7,8,9,10,11},{4},{12}}
[7,6,5,3,2,8,9,10,1,4,11,12]=>{{1,7,9},{2,3,4,5,6,8,10},{11},{12}}
[7,6,4,3,2,8,9,1,5,10,11,12]=>{{1,2,5,6,7,8,9},{3,4},{10},{11},{12}}
[7,5,4,3,2,8,1,6,9,10,11,12]=>{{1,7},{2,5},{3,4},{6,8},{9},{10},{11},{12}}
[6,5,4,3,2,1,7,8,9,10,11,12]=>{{1,6},{2,5},{3,4},{7},{8},{9},{10},{11},{12}}
[12,1,3,2,5,4,7,6,9,8,11,10]=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}
[12,1,2,3,4,5,7,8,9,10,11,6]=>{{1,2,3,4,5,6,12},{7},{8},{9},{10},{11}}
[12,11,2,4,6,8,10,1,3,5,7,9]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[10,9,2,4,6,8,12,1,3,5,7,11]=>{{1,5,6,8,10},{2,3,9},{4},{7,11,12}}
[2,12,9,11,4,6,8,10,1,3,5,7]=>{{1,2,3,7,8,9,10,12},{4,5,11},{6}}
[12,11,10,9,2,4,6,8,1,3,5,7]=>{{1,4,6,7,9,12},{2,5,11},{3,10},{8}}
[8,7,2,4,6,10,12,1,3,5,9,11]=>{{1,8},{2,3,7,9,11,12},{4},{5,6,10}}
[8,12,7,11,2,4,6,10,1,3,5,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,10,7,9,4,6,8,12,1,3,5,11]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[2,4,12,7,9,11,6,8,10,1,3,5]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[12,11,2,10,7,9,4,6,8,1,3,5]=>{{1,4,5,7,10,12},{2,3,11},{6,8,9}}
[10,9,8,7,2,4,6,12,1,3,5,11]=>{{1,2,3,5,8,9,10,11,12},{4,6,7}}
[12,9,2,8,7,11,4,6,10,1,3,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,12,7,11,10,9,2,4,6,1,3,5]=>{{1,2,3,4,5,7,8,10,11,12},{6,9}}
[12,11,10,9,8,7,2,4,6,1,3,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,5,2,4,8,10,12,1,3,7,9,11]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[6,12,5,11,2,4,8,10,1,3,7,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,10,5,9,2,4,8,12,1,3,7,11]=>{{1,4,6,9},{2,3,5,10},{7,8,11,12}}
[6,5,12,9,11,2,4,8,10,1,3,7]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[12,11,6,10,5,9,2,4,8,1,3,7]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[2,8,5,7,4,6,10,12,1,3,9,11]=>{{1,2,8,9,11,12},{3,4,5,7,10},{6}}
[2,8,12,5,7,11,4,6,10,1,3,9]=>{{1,2,3,6,8,9,10,11,12},{4,5,7}}
[10,5,2,4,7,9,6,8,12,1,3,11]=>{{1,10},{2,3,5,6,7,9,11,12},{4},{8}}
[12,5,7,2,4,6,9,11,8,10,1,3]=>{{1,3,7,8,9,11,12},{2,4,5},{6},{10}}
[12,5,11,10,2,4,7,9,6,8,1,3]=>{{1,3,11,12},{2,5},{4,6,8,9,10},{7}}
[10,9,2,8,5,7,4,6,12,1,3,11]=>{{1,10},{2,3,9,11,12},{4,6,7,8},{5}}
[12,5,9,8,2,4,7,11,6,10,1,3]=>{{1,3,4,6,8,9,11,12},{2,5},{7},{10}}
[2,12,5,11,8,10,7,9,4,6,1,3]=>{{1,2,3,4,5,8,9,11,12},{6,10},{7}}
[12,11,10,9,2,8,5,7,4,6,1,3]=>{{1,2,3,5,6,7,8,10,11,12},{4,9}}
[8,7,6,5,2,4,10,12,1,3,9,11]=>{{1,8,9,11,12},{2,3,4,5,6,7,10}}
[8,7,6,12,5,11,2,4,10,1,3,9]=>{{1,4,8,9,10,12},{2,7},{3,6,11},{5}}
[10,7,2,6,5,9,4,8,12,1,3,11]=>{{1,10},{2,3,4,6,7,9,11,12},{5},{8}}
[7,6,12,5,2,4,9,11,8,10,1,3]=>{{1,7,8,9,11},{2,4,5,6},{3,12},{10}}
[2,12,7,11,6,10,5,9,4,8,1,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,10,5,9,8,7,2,4,12,1,3,11]=>{{1,2,6,7,10},{3,4,5,8,9,11,12}}
[2,12,6,9,5,8,7,11,4,10,1,3]=>{{1,2,3,6,8,11,12},{4,9},{5},{7},{10}}
[6,8,12,5,7,11,10,9,2,4,1,3]=>{{1,6,11},{2,8,9},{3,12},{4,5,7,10}}
[12,11,6,10,5,9,8,7,2,4,1,3]=>{{1,2,3,6,9,11,12},{4,10},{5},{7,8}}
[10,9,8,7,6,5,2,4,12,1,3,11]=>{{1,10},{2,3,4,7,8,9,11,12},{5,6}}
[12,9,8,7,2,6,5,11,4,10,1,3]=>{{1,3,8,11,12},{2,4,5,7,9},{6},{10}}
[8,7,6,12,5,11,10,9,2,4,1,3]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[7,12,6,11,10,9,8,5,2,4,1,3]=>{{1,4,5,7,8,10,11},{2,3,6,9,12}}
[12,11,10,9,8,7,6,5,2,4,1,3]=>{{1,2,3,4,9,10,11,12},{5,8},{6,7}}
[4,3,2,6,8,10,12,1,5,7,9,11]=>{{1,4,5,6,7,8,9,10,11,12},{2,3}}
[4,12,3,11,2,6,8,10,1,5,7,9]=>{{1,2,4,5,7,8,9,10,11,12},{3},{6}}
[4,10,3,9,2,6,8,12,1,5,7,11]=>{{1,4,9},{2,5,10},{3},{6},{7,8,11,12}}
[4,3,12,9,11,2,6,8,10,1,5,7]=>{{1,4,9,10},{2,3,6,7,12},{5,11},{8}}
[12,11,4,10,3,9,2,6,8,1,5,7]=>{{1,2,3,4,5,7,10,11,12},{6,8,9}}
[4,8,3,7,2,6,10,12,1,5,9,11]=>{{1,2,4,5,7,8,9,10,11,12},{3},{6}}
[4,8,12,3,7,11,2,6,10,1,5,9]=>{{1,3,4,9,10,12},{2,5,6,7,8,11}}
[4,3,10,7,9,2,6,8,12,1,5,11]=>{{1,2,3,4,6,7,10},{5,9,11,12},{8}}
[4,3,7,9,12,11,2,6,8,10,1,5]=>{{1,4,6,8,9,11},{2,3,7},{5,12},{10}}
[12,4,11,3,10,7,9,2,6,8,1,5]=>{{1,2,3,4,5,8,10,11,12},{6,7,9}}
[10,9,4,8,3,7,2,6,12,1,5,11]=>{{1,10},{2,3,4,5,6,7,8,9,11,12}}
[12,4,9,3,8,7,11,2,6,10,1,5]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}}
[4,8,12,11,10,3,7,9,2,6,1,5]=>{{1,4,11},{2,8,9},{3,5,6,10,12},{7}}
[12,11,10,9,4,8,3,7,2,6,1,5]=>{{1,2,4,5,9,11,12},{3,6,7,8,10}}
[3,6,2,5,4,8,10,12,1,7,9,11]=>{{1,2,3,6,8,9,11,12},{4,5},{7,10}}
[3,6,12,2,5,11,4,8,10,1,7,9]=>{{1,3,9,10,12},{2,4,6,7,11},{5},{8}}
[3,6,10,2,5,9,4,8,12,1,7,11]=>{{1,3,10},{2,4,6,7,9,11,12},{5},{8}}
[3,12,6,2,5,9,11,4,8,10,1,7]=>{{1,2,3,4,6,7,8,9,11,12},{5},{10}}
[12,11,3,6,10,2,5,9,4,8,1,7]=>{{1,2,4,5,6,7,8,9,10,11,12},{3}}
[3,5,8,2,4,7,6,10,12,1,9,11]=>{{1,3,8,10},{2,4,5},{6,7},{9,11,12}}
[3,5,8,12,2,4,7,11,6,10,1,9]=>{{1,3,8,11},{2,5},{4,6,9,12},{7},{10}}
[3,5,7,10,2,4,6,9,8,12,1,11]=>{{1,3,4,6,7,10,11,12},{2,5},{8,9}}
[3,5,7,9,12,2,4,6,8,11,10,1]=>{{1,2,3,4,5,6,7,8,9,12},{10,11}}
[12,11,3,5,7,10,2,4,6,9,8,1]=>{{1,12},{2,4,5,7,8,11},{3},{6,9,10}}
[10,9,3,5,8,2,4,7,6,12,1,11]=>{{1,10,11,12},{2,6,9},{3},{4,5,7,8}}
[9,8,3,5,7,12,2,4,6,11,10,1]=>{{1,6,9,12},{2,4,5,7,8},{3},{10,11}}
[3,5,12,11,8,10,2,4,7,9,6,1]=>{{1,3,12},{2,4,5,6,7,8,9,10,11}}
[12,11,10,9,3,5,8,2,4,7,6,1]=>{{1,12},{2,3,5,6,7,8,10,11},{4,9}}
[8,7,3,6,2,5,4,10,12,1,9,11]=>{{1,8,10},{2,4,5,6,7},{3},{9,11,12}}
[8,7,3,6,12,2,5,11,4,10,1,9]=>{{1,8,11},{2,4,5,6,7,9,12},{3},{10}}
[7,6,3,5,10,2,4,9,8,12,1,11]=>{{1,4,5,7,10,11,12},{2,6},{3},{8,9}}
[7,6,3,5,9,12,2,4,8,11,10,1]=>{{1,2,6,7,12},{3},{4,5,8,9},{10,11}}
[7,12,6,11,3,5,10,2,4,9,8,1]=>{{1,2,4,7,8,9,10,11,12},{3,5,6}}
[3,6,10,9,8,2,5,7,4,12,1,11]=>{{1,3,10,11,12},{2,6},{4,9},{5,7,8}}
[3,9,6,8,5,7,12,2,4,11,10,1]=>{{1,3,6,7,12},{2,4,8,9},{5},{10,11}}
[3,2,12,6,8,11,10,5,7,9,4,1]=>{{1,3,12},{2},{4,6,11},{5,8},{7,9,10}}
[12,11,3,6,10,9,8,2,5,7,4,1]=>{{1,12},{2,4,5,6,7,8,9,10,11},{3}}
[10,9,8,7,3,6,2,5,4,12,1,11]=>{{1,10,11,12},{2,4,7,9},{3,5,8},{6}}
[9,8,7,6,3,5,12,2,4,11,10,1]=>{{1,3,4,5,6,7,9,12},{2,8},{10,11}}
[8,7,3,6,12,11,10,2,5,9,4,1]=>{{1,2,5,7,8,9,10,12},{3},{4,6,11}}
[3,12,7,11,10,9,6,8,2,5,4,1]=>{{1,2,3,6,7,9,12},{4,11},{5,10},{8}}
[12,11,10,9,8,7,3,6,2,5,4,1]=>{{1,12},{2,4,9,11},{3,5,6,7,8,10}}
[6,5,4,3,2,8,10,12,1,7,9,11]=>{{1,6,8,9,11,12},{2,5},{3,4},{7,10}}
[6,5,4,12,3,11,2,8,10,1,7,9]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[6,5,4,10,3,9,2,8,12,1,7,11]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[6,12,5,4,3,9,11,2,8,10,1,7]=>{{1,2,6,7,8,9,11,12},{3,5},{4},{10}}
[5,4,3,8,2,7,6,10,12,1,9,11]=>{{1,2,4,5,8,10},{3},{6,7},{9,11,12}}
[5,4,3,8,12,2,7,11,6,10,1,9]=>{{1,2,4,5,6,8,9,11,12},{3},{7},{10}}
[5,4,3,7,10,2,6,9,8,12,1,11]=>{{1,5,10,11,12},{2,4,6,7},{3},{8,9}}
[5,4,3,7,9,12,2,6,8,11,10,1]=>{{1,5,6,8,9,12},{2,4,7},{3},{10,11}}
[5,12,4,11,3,7,10,2,6,9,8,1]=>{{1,2,3,4,5,8,11,12},{6,7,9,10}}
[5,10,4,9,3,8,2,7,6,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[5,9,4,8,3,7,12,2,6,11,10,1]=>{{1,2,3,4,5,6,7,8,9,12},{10,11}}
[12,11,5,4,3,8,10,2,7,9,6,1]=>{{1,12},{2,6,8,11},{3,5},{4},{7,9,10}}
[12,11,5,10,4,9,3,8,2,7,6,1]=>{{1,12},{2,6,9,11},{3,4,5,7,10},{8}}
[4,8,3,7,6,5,2,10,12,1,9,11]=>{{1,2,4,7,8,10},{3},{5,6},{9,11,12}}
[4,8,3,7,6,12,5,11,2,10,1,9]=>{{1,2,4,5,6,7,8,9,11,12},{3},{10}}
[4,7,3,6,5,10,2,9,8,12,1,11]=>{{1,4,6,10,11,12},{2,7},{3},{5},{8,9}}
[4,7,3,6,5,9,12,2,8,11,10,1]=>{{1,2,4,6,7,8,9,12},{3},{5},{10,11}}
[4,7,12,3,6,11,5,10,2,9,8,1]=>{{1,3,4,12},{2,5,6,7,8,9,10,11}}
[4,6,10,3,5,9,8,7,2,12,1,11]=>{{1,3,4,10,11,12},{2,6,9},{5},{7,8}}
[4,6,9,3,5,8,7,12,2,11,10,1]=>{{1,2,3,4,6,8,9,12},{5},{7},{10,11}}
[4,6,8,12,3,5,7,11,10,9,2,1]=>{{1,4,12},{2,3,5,6,8,11},{7},{9,10}}
[12,11,4,6,10,3,5,9,8,7,2,1]=>{{1,12},{2,11},{3,4,6},{5,7,10},{8,9}}
[10,9,4,8,3,7,6,5,2,12,1,11]=>{{1,10,11,12},{2,9},{3,4,5,8},{6,7}}
[9,8,4,7,3,6,5,12,2,11,10,1]=>{{1,2,8,9,12},{3,4,5,7},{6},{10,11}}
[8,7,4,6,12,3,5,11,10,9,2,1]=>{{1,2,5,7,8,11,12},{3,4,6},{9,10}}
[4,7,12,11,10,3,6,9,8,5,2,1]=>{{1,2,3,4,6,7,11,12},{5,10},{8,9}}
[12,11,10,9,4,8,3,7,6,5,2,1]=>{{1,12},{2,11},{3,4,5,6,7,8,9,10}}
[8,7,6,5,4,3,2,10,12,1,9,11]=>{{1,8,10},{2,7},{3,6},{4,5},{9,11,12}}
[8,7,6,5,4,12,3,11,2,10,1,9]=>{{1,8,11},{2,3,6,7,9,12},{4,5},{10}}
[7,6,5,4,3,10,2,9,8,12,1,11]=>{{1,2,6,7,10,11,12},{3,5},{4},{8,9}}
[7,6,5,4,3,9,12,2,8,11,10,1]=>{{1,7,12},{2,6,8,9},{3,5},{4},{10,11}}
[7,6,5,12,4,11,3,10,2,9,8,1]=>{{1,3,4,5,7,12},{2,6,8,9,10,11}}
[6,5,4,10,3,9,8,7,2,12,1,11]=>{{1,2,3,4,5,6,9,10,11,12},{7,8}}
[6,5,4,9,3,8,7,12,2,11,10,1]=>{{1,6,8,12},{2,3,4,5,9},{7},{10,11}}
[6,5,4,8,12,3,7,11,10,9,2,1]=>{{1,2,3,4,5,6,8,11,12},{7},{9,10}}
[6,12,5,11,4,10,3,9,8,7,2,1]=>{{1,2,3,4,5,6,7,10,11,12},{8,9}}
[5,10,4,9,8,7,6,3,2,12,1,11]=>{{1,2,3,4,5,8,9,10,11,12},{6,7}}
[5,9,4,8,7,6,3,12,2,11,10,1]=>{{1,3,4,5,7,8,12},{2,9},{6},{10,11}}
[5,8,4,7,6,12,3,11,10,9,2,1]=>{{1,5,6,12},{2,8,11},{3,4,7},{9,10}}
[5,7,12,4,6,11,10,9,8,3,2,1]=>{{1,2,3,5,6,7,10,11,12},{4},{8,9}}
[12,11,5,10,4,9,8,7,6,3,2,1]=>{{1,12},{2,11},{3,4,5,10},{6,9},{7,8}}
[10,9,8,7,6,5,4,3,2,12,1,11]=>{{1,10,11,12},{2,9},{3,8},{4,7},{5,6}}
[9,8,7,6,5,4,3,12,2,11,10,1]=>{{1,2,8,9,12},{3,7},{4,6},{5},{10,11}}
[8,7,6,5,4,12,3,11,10,9,2,1]=>{{1,2,3,6,7,8,11,12},{4,5},{9,10}}
[7,6,5,12,4,11,10,9,8,3,2,1]=>{{1,3,4,5,7,10,12},{2,6,11},{8,9}}
[6,12,5,11,10,9,8,7,4,3,2,1]=>{{1,2,4,6,9,11,12},{3,5,10},{7,8}}
[12,10,9,8,7,6,5,4,3,2,1,11]=>{{1,11,12},{2,10},{3,9},{4,8},{5,7},{6}}
[11,3,4,5,6,7,8,9,10,1,12,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,12,4,5,6,7,8,9,10,11,1,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,1,2,4,5,6,7,8,9,10,11,12]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11},{12}}
[1,2,3,4,5,6,7,8,9,12,10,11]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11,12}}
[12,1,3,4,5,6,7,8,9,10,11,2]=>{{1,2,12},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[3,2,5,4,7,6,9,8,11,10,1,12]=>{{1,3,5,7,9,11},{2},{4},{6},{8},{10},{12}}
[3,2,5,4,7,6,9,8,1,12,10,11]=>{{1,3,5,7,9},{2},{4},{6},{8},{10,11,12}}
[3,2,5,4,7,6,11,10,8,9,1,12]=>{{1,3,5,7,11},{2},{4},{6},{8,9,10},{12}}
[3,2,5,4,7,6,1,10,8,12,9,11]=>{{1,3,5,7},{2},{4},{6},{8,9,10,11,12}}
[3,2,5,4,7,6,1,12,11,8,9,10]=>{{1,3,5,7},{2},{4},{6},{8,10,12},{9,11}}
[3,2,5,4,9,8,6,7,11,10,1,12]=>{{1,3,5,9,11},{2},{4},{6,7,8},{10},{12}}
[3,2,5,4,9,8,6,7,1,12,10,11]=>{{1,3,5,9},{2},{4},{6,7,8},{10,11,12}}
[3,2,5,4,11,8,6,10,7,9,1,12]=>{{1,3,5,11},{2},{4},{6,7,8,9,10},{12}}
[3,2,5,4,1,8,6,10,7,12,9,11]=>{{1,3,5},{2},{4},{6,7,8,9,10,11,12}}
[3,2,5,4,1,8,6,12,11,7,9,10]=>{{1,3,5},{2},{4},{6,7,8,10,12},{9,11}}
[3,2,5,4,11,10,9,6,7,8,1,12]=>{{1,3,5,11},{2},{4},{6,8,10},{7,9},{12}}
[3,2,5,4,1,10,9,6,7,12,8,11]=>{{1,3,5},{2},{4},{6,8,10,11,12},{7,9}}
[3,2,5,4,1,12,9,6,11,7,8,10]=>{{1,3,5},{2},{4},{6,7,8,9,10,11,12}}
[3,2,5,4,1,12,11,10,6,7,8,9]=>{{1,3,5},{2},{4},{6,9,12},{7,8,10,11}}
[3,2,7,6,4,5,9,8,11,10,1,12]=>{{1,3,7,9,11},{2},{4,5,6},{8},{10},{12}}
[3,2,7,6,4,5,9,8,1,12,10,11]=>{{1,3,7,9},{2},{4,5,6},{8},{10,11,12}}
[3,2,7,6,4,5,11,10,8,9,1,12]=>{{1,3,7,11},{2},{4,5,6},{8,9,10},{12}}
[3,2,7,6,4,5,1,10,8,12,9,11]=>{{1,3,7},{2},{4,5,6},{8,9,10,11,12}}
[3,2,7,6,4,5,1,12,11,8,9,10]=>{{1,3,7},{2},{4,5,6},{8,10,12},{9,11}}
[3,2,9,6,4,8,5,7,11,10,1,12]=>{{1,3,9,11},{2},{4,5,6,7,8},{10},{12}}
[3,2,9,6,4,8,5,7,1,12,10,11]=>{{1,3,9},{2},{4,5,6,7,8},{10,11,12}}
[3,2,11,6,4,8,5,10,7,9,1,12]=>{{1,3,11},{2},{4,5,6,7,8,9,10},{12}}
[3,2,1,6,4,8,5,10,7,12,9,11]=>{{1,3},{2},{4,5,6,7,8,9,10,11,12}}
[3,2,1,6,4,8,5,12,11,7,9,10]=>{{1,3},{2},{4,5,6,7,8,10,12},{9,11}}
[3,2,11,6,4,10,9,5,7,8,1,12]=>{{1,3,11},{2},{4,5,6,8,10},{7,9},{12}}
[3,2,1,6,4,10,9,5,7,12,8,11]=>{{1,3},{2},{4,5,6,8,10,11,12},{7,9}}
[3,2,1,6,4,12,9,5,11,7,8,10]=>{{1,3},{2},{4,5,6,7,8,9,10,11,12}}
[3,2,1,6,4,12,11,10,5,7,8,9]=>{{1,3},{2},{4,5,6,9,12},{7,8,10,11}}
[3,2,9,8,7,4,5,6,11,10,1,12]=>{{1,3,9,11},{2},{4,6,8},{5,7},{10},{12}}
[3,2,9,8,7,4,5,6,1,12,10,11]=>{{1,3,9},{2},{4,6,8},{5,7},{10,11,12}}
[3,2,11,8,7,4,5,10,6,9,1,12]=>{{1,3,11},{2},{4,6,8,9,10},{5,7},{12}}
[3,2,1,8,7,4,5,10,6,12,9,11]=>{{1,3},{2},{4,6,8,9,10,11,12},{5,7}}
[3,2,1,8,7,4,5,12,11,6,9,10]=>{{1,3},{2},{4,6,8,10,12},{5,7},{9,11}}
[3,2,11,10,7,4,9,5,6,8,1,12]=>{{1,3,11},{2},{4,5,6,7,8,9,10},{12}}
[3,2,1,10,7,4,9,5,6,12,8,11]=>{{1,3},{2},{4,5,6,7,8,9,10,11,12}}
[3,2,1,12,7,4,9,5,11,6,8,10]=>{{1,3},{2},{4,6,10,12},{5,7,8,9,11}}
[3,2,1,12,7,4,11,10,5,6,8,9]=>{{1,3},{2},{4,5,6,7,8,9,10,11,12}}
[3,2,11,10,9,8,4,5,6,7,1,12]=>{{1,3,11},{2},{4,7,10},{5,6,8,9},{12}}
[3,2,1,10,9,8,4,5,6,12,7,11]=>{{1,3},{2},{4,7,10,11,12},{5,6,8,9}}
[3,2,1,12,9,8,4,5,11,6,7,10]=>{{1,3},{2},{4,5,6,7,8,9,10,11,12}}
[3,2,1,12,11,8,4,10,5,6,7,9]=>{{1,3},{2},{4,5,7,9,11,12},{6,8,10}}
[3,2,1,12,11,10,9,4,5,6,7,8]=>{{1,3},{2},{4,8,12},{5,7,9,11},{6,10}}
[5,4,2,3,7,6,9,8,11,10,1,12]=>{{1,5,7,9,11},{2,3,4},{6},{8},{10},{12}}
[5,4,2,3,7,6,9,8,1,12,10,11]=>{{1,5,7,9},{2,3,4},{6},{8},{10,11,12}}
[5,4,2,3,7,6,11,10,8,9,1,12]=>{{1,5,7,11},{2,3,4},{6},{8,9,10},{12}}
[5,4,2,3,7,6,1,10,8,12,9,11]=>{{1,5,7},{2,3,4},{6},{8,9,10,11,12}}
[5,4,2,3,7,6,1,12,11,8,9,10]=>{{1,5,7},{2,3,4},{6},{8,10,12},{9,11}}
[5,4,2,3,9,8,6,7,11,10,1,12]=>{{1,5,9,11},{2,3,4},{6,7,8},{10},{12}}
[5,4,2,3,9,8,6,7,1,12,10,11]=>{{1,5,9},{2,3,4},{6,7,8},{10,11,12}}
[5,4,2,3,11,8,6,10,7,9,1,12]=>{{1,5,11},{2,3,4},{6,7,8,9,10},{12}}
[5,4,2,3,1,8,6,10,7,12,9,11]=>{{1,5},{2,3,4},{6,7,8,9,10,11,12}}
[5,4,2,3,1,8,6,12,11,7,9,10]=>{{1,5},{2,3,4},{6,7,8,10,12},{9,11}}
[5,4,2,3,11,10,9,6,7,8,1,12]=>{{1,5,11},{2,3,4},{6,8,10},{7,9},{12}}
[5,4,2,3,1,10,9,6,7,12,8,11]=>{{1,5},{2,3,4},{6,8,10,11,12},{7,9}}
[5,4,2,3,1,12,9,6,11,7,8,10]=>{{1,5},{2,3,4},{6,7,8,9,10,11,12}}
[5,4,2,3,1,12,11,10,6,7,8,9]=>{{1,5},{2,3,4},{6,9,12},{7,8,10,11}}
[7,4,2,6,3,5,9,8,11,10,1,12]=>{{1,7,9,11},{2,3,4,5,6},{8},{10},{12}}
[7,4,2,6,3,5,9,8,1,12,10,11]=>{{1,7,9},{2,3,4,5,6},{8},{10,11,12}}
[7,4,2,6,3,5,11,10,8,9,1,12]=>{{1,7,11},{2,3,4,5,6},{8,9,10},{12}}
[7,4,2,6,3,5,1,10,8,12,9,11]=>{{1,7},{2,3,4,5,6},{8,9,10,11,12}}
[7,4,2,6,3,5,1,12,11,8,9,10]=>{{1,7},{2,3,4,5,6},{8,10,12},{9,11}}
[9,4,2,6,3,8,5,7,11,10,1,12]=>{{1,9,11},{2,3,4,5,6,7,8},{10},{12}}
[9,4,2,6,3,8,5,7,1,12,10,11]=>{{1,9},{2,3,4,5,6,7,8},{10,11,12}}
[11,4,2,6,3,8,5,10,7,9,1,12]=>{{1,11},{2,3,4,5,6,7,8,9,10},{12}}
[1,4,2,6,3,8,5,10,7,12,9,11]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,4,2,6,3,8,5,12,11,7,9,10]=>{{1},{2,3,4,5,6,7,8,10,12},{9,11}}
[11,4,2,6,3,10,9,5,7,8,1,12]=>{{1,11},{2,3,4,5,6,8,10},{7,9},{12}}
[1,4,2,6,3,10,9,5,7,12,8,11]=>{{1},{2,3,4,5,6,8,10,11,12},{7,9}}
[1,4,2,6,3,12,9,5,11,7,8,10]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,4,2,6,3,12,11,10,5,7,8,9]=>{{1},{2,3,4,5,6,9,12},{7,8,10,11}}
[9,4,2,8,7,3,5,6,11,10,1,12]=>{{1,9,11},{2,3,4,6,8},{5,7},{10},{12}}
[9,4,2,8,7,3,5,6,1,12,10,11]=>{{1,9},{2,3,4,6,8},{5,7},{10,11,12}}
[11,4,2,8,7,3,5,10,6,9,1,12]=>{{1,11},{2,3,4,6,8,9,10},{5,7},{12}}
[1,4,2,8,7,3,5,10,6,12,9,11]=>{{1},{2,3,4,6,8,9,10,11,12},{5,7}}
[1,4,2,8,7,3,5,12,11,6,9,10]=>{{1},{2,3,4,6,8,10,12},{5,7},{9,11}}
[11,4,2,10,7,3,9,5,6,8,1,12]=>{{1,11},{2,3,4,5,6,7,8,9,10},{12}}
[1,4,2,10,7,3,9,5,6,12,8,11]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,4,2,12,7,3,9,5,11,6,8,10]=>{{1},{2,3,4,6,10,12},{5,7,8,9,11}}
[1,4,2,12,7,3,11,10,5,6,8,9]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[11,4,2,10,9,8,3,5,6,7,1,12]=>{{1,11},{2,3,4,7,10},{5,6,8,9},{12}}
[1,4,2,10,9,8,3,5,6,12,7,11]=>{{1},{2,3,4,7,10,11,12},{5,6,8,9}}
[1,4,2,12,9,8,3,5,11,6,7,10]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,4,2,12,11,8,3,10,5,6,7,9]=>{{1},{2,3,4,5,7,9,11,12},{6,8,10}}
[1,4,2,12,11,10,9,3,5,6,7,8]=>{{1},{2,3,4,8,12},{5,7,9,11},{6,10}}
[7,6,5,2,3,4,9,8,11,10,1,12]=>{{1,7,9,11},{2,4,6},{3,5},{8},{10},{12}}
[7,6,5,2,3,4,9,8,1,12,10,11]=>{{1,7,9},{2,4,6},{3,5},{8},{10,11,12}}
[7,6,5,2,3,4,11,10,8,9,1,12]=>{{1,7,11},{2,4,6},{3,5},{8,9,10},{12}}
[7,6,5,2,3,4,1,10,8,12,9,11]=>{{1,7},{2,4,6},{3,5},{8,9,10,11,12}}
[7,6,5,2,3,4,1,12,11,8,9,10]=>{{1,7},{2,4,6},{3,5},{8,10,12},{9,11}}
[9,6,5,2,3,8,4,7,11,10,1,12]=>{{1,9,11},{2,4,6,7,8},{3,5},{10},{12}}
[9,6,5,2,3,8,4,7,1,12,10,11]=>{{1,9},{2,4,6,7,8},{3,5},{10,11,12}}
[11,6,5,2,3,8,4,10,7,9,1,12]=>{{1,11},{2,4,6,7,8,9,10},{3,5},{12}}
[1,6,5,2,3,8,4,10,7,12,9,11]=>{{1},{2,4,6,7,8,9,10,11,12},{3,5}}
[1,6,5,2,3,8,4,12,11,7,9,10]=>{{1},{2,4,6,7,8,10,12},{3,5},{9,11}}
[11,6,5,2,3,10,9,4,7,8,1,12]=>{{1,11},{2,4,6,8,10},{3,5},{7,9},{12}}
[1,6,5,2,3,10,9,4,7,12,8,11]=>{{1},{2,4,6,8,10,11,12},{3,5},{7,9}}
[1,6,5,2,3,12,9,4,11,7,8,10]=>{{1},{2,4,6,7,8,9,10,11,12},{3,5}}
[1,6,5,2,3,12,11,10,4,7,8,9]=>{{1},{2,4,6,9,12},{3,5},{7,8,10,11}}
[9,8,5,2,7,3,4,6,11,10,1,12]=>{{1,9,11},{2,3,4,5,6,7,8},{10},{12}}
[9,8,5,2,7,3,4,6,1,12,10,11]=>{{1,9},{2,3,4,5,6,7,8},{10,11,12}}
[11,8,5,2,7,3,4,10,6,9,1,12]=>{{1,11},{2,3,4,5,6,7,8,9,10},{12}}
[1,8,5,2,7,3,4,10,6,12,9,11]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,5,2,7,3,4,12,11,6,9,10]=>{{1},{2,3,4,5,6,7,8,10,12},{9,11}}
[11,10,5,2,7,3,9,4,6,8,1,12]=>{{1,11},{2,4,8,10},{3,5,6,7,9},{12}}
[1,10,5,2,7,3,9,4,6,12,8,11]=>{{1},{2,4,8,10,11,12},{3,5,6,7,9}}
[1,12,5,2,7,3,9,4,11,6,8,10]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,12,5,2,7,3,11,10,4,6,8,9]=>{{1},{2,4,9,12},{3,5,6,7,8,10,11}}
[11,10,5,2,9,8,3,4,6,7,1,12]=>{{1,11},{2,3,4,5,6,7,8,9,10},{12}}
[1,10,5,2,9,8,3,4,6,12,7,11]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,12,5,2,9,8,3,4,11,6,7,10]=>{{1},{2,4,6,8,10,12},{3,5,7,9,11}}
[1,12,5,2,11,8,3,10,4,6,7,9]=>{{1},{2,4,9,12},{3,5,7,11},{6,8,10}}
[1,12,5,2,11,10,9,3,4,6,7,8]=>{{1},{2,3,4,5,7,8,9,11,12},{6,10}}
[9,8,7,6,2,3,4,5,11,10,1,12]=>{{1,9,11},{2,5,8},{3,4,6,7},{10},{12}}
[9,8,7,6,2,3,4,5,1,12,10,11]=>{{1,9},{2,5,8},{3,4,6,7},{10,11,12}}
[11,8,7,6,2,3,4,10,5,9,1,12]=>{{1,11},{2,5,8,9,10},{3,4,6,7},{12}}
[1,8,7,6,2,3,4,10,5,12,9,11]=>{{1},{2,5,8,9,10,11,12},{3,4,6,7}}
[1,8,7,6,2,3,4,12,11,5,9,10]=>{{1},{2,5,8,10,12},{3,4,6,7},{9,11}}
[11,10,7,6,2,3,9,4,5,8,1,12]=>{{1,11},{2,3,4,5,6,7,8,9,10},{12}}
[1,10,7,6,2,3,9,4,5,12,8,11]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,12,7,6,2,3,9,4,11,5,8,10]=>{{1},{2,5,10,12},{3,4,6,7,8,9,11}}
[1,12,7,6,2,3,11,10,4,5,8,9]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[11,10,9,6,2,8,3,4,5,7,1,12]=>{{1,11},{2,3,5,7,9,10},{4,6,8},{12}}
[1,10,9,6,2,8,3,4,5,12,7,11]=>{{1},{2,3,5,7,9,10,11,12},{4,6,8}}
[1,12,9,6,2,8,3,4,11,5,7,10]=>{{1},{2,5,10,12},{3,7,9,11},{4,6,8}}
[1,12,11,6,2,8,3,10,4,5,7,9]=>{{1},{2,4,5,6,8,9,10,12},{3,7,11}}
[1,12,11,6,2,10,9,3,4,5,7,8]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[11,10,9,8,7,2,3,4,5,6,1,12]=>{{1,11},{2,6,10},{3,5,7,9},{4,8},{12}}
[1,10,9,8,7,2,3,4,5,12,6,11]=>{{1},{2,6,10,11,12},{3,5,7,9},{4,8}}
[1,12,9,8,7,2,3,4,11,5,6,10]=>{{1},{2,3,5,6,7,9,10,11,12},{4,8}}
[1,12,11,8,7,2,3,10,4,5,6,9]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,12,11,10,7,2,9,3,4,5,6,8]=>{{1},{2,3,6,8,11,12},{4,5,7,9,10}}
[1,12,11,10,9,8,2,3,4,5,6,7]=>{{1},{2,7,12},{3,6,8,11},{4,5,9,10}}
[3,2,5,4,7,6,9,8,1,12,11,10]=>{{1,3,5,7,9},{2},{4},{6},{8},{10,12},{11}}
[3,2,5,4,7,6,11,10,9,8,1,12]=>{{1,3,5,7,11},{2},{4},{6},{8,10},{9},{12}}
[3,2,5,4,7,6,1,10,9,12,11,8]=>{{1,3,5,7},{2},{4},{6},{8,10,12},{9},{11}}
[3,2,5,4,7,6,1,12,11,10,9,8]=>{{1,3,5,7},{2},{4},{6},{8,12},{9,11},{10}}
[3,2,5,4,9,8,7,6,11,10,1,12]=>{{1,3,5,9,11},{2},{4},{6,8},{7},{10},{12}}
[3,2,5,4,9,8,7,6,1,12,11,10]=>{{1,3,5,9},{2},{4},{6,8},{7},{10,12},{11}}
[3,2,5,4,11,8,7,10,9,6,1,12]=>{{1,3,5,11},{2},{4},{6,8,10},{7},{9},{12}}
[3,2,5,4,1,8,7,10,9,12,11,6]=>{{1,3,5},{2},{4},{6,8,10,12},{7},{9},{11}}
[3,2,5,4,1,8,7,12,11,10,9,6]=>{{1,3,5},{2},{4},{6,8,12},{7},{9,11},{10}}
[3,2,5,4,11,10,9,8,7,6,1,12]=>{{1,3,5,11},{2},{4},{6,10},{7,9},{8},{12}}
[3,2,5,4,1,10,9,8,7,12,11,6]=>{{1,3,5},{2},{4},{6,10,12},{7,9},{8},{11}}
[3,2,5,4,1,12,9,8,11,10,7,6]=>{{1,3,5},{2},{4},{6,12},{7,9,11},{8},{10}}
[3,2,5,4,1,12,11,10,9,8,7,6]=>{{1,3,5},{2},{4},{6,12},{7,11},{8,10},{9}}
[3,2,7,6,5,4,9,8,11,10,1,12]=>{{1,3,7,9,11},{2},{4,6},{5},{8},{10},{12}}
[3,2,7,6,5,4,9,8,1,12,11,10]=>{{1,3,7,9},{2},{4,6},{5},{8},{10,12},{11}}
[3,2,7,6,5,4,11,10,9,8,1,12]=>{{1,3,7,11},{2},{4,6},{5},{8,10},{9},{12}}
[3,2,7,6,5,4,1,10,9,12,11,8]=>{{1,3,7},{2},{4,6},{5},{8,10,12},{9},{11}}
[3,2,7,6,5,4,1,12,11,10,9,8]=>{{1,3,7},{2},{4,6},{5},{8,12},{9,11},{10}}
[3,2,9,6,5,8,7,4,11,10,1,12]=>{{1,3,9,11},{2},{4,6,8},{5},{7},{10},{12}}
[3,2,9,6,5,8,7,4,1,12,11,10]=>{{1,3,9},{2},{4,6,8},{5},{7},{10,12},{11}}
[3,2,11,6,5,8,7,10,9,4,1,12]=>{{1,3,11},{2},{4,6,8,10},{5},{7},{9},{12}}
[3,2,1,6,5,8,7,10,9,12,11,4]=>{{1,3},{2},{4,6,8,10,12},{5},{7},{9},{11}}
[3,2,1,6,5,8,7,12,11,10,9,4]=>{{1,3},{2},{4,6,8,12},{5},{7},{9,11},{10}}
[3,2,11,6,5,10,9,8,7,4,1,12]=>{{1,3,11},{2},{4,6,10},{5},{7,9},{8},{12}}
[3,2,1,6,5,10,9,8,7,12,11,4]=>{{1,3},{2},{4,6,10,12},{5},{7,9},{8},{11}}
[3,2,1,6,5,12,9,8,11,10,7,4]=>{{1,3},{2},{4,6,12},{5},{7,9,11},{8},{10}}
[3,2,1,6,5,12,11,10,9,8,7,4]=>{{1,3},{2},{4,6,12},{5},{7,11},{8,10},{9}}
[3,2,9,8,7,6,5,4,11,10,1,12]=>{{1,3,9,11},{2},{4,8},{5,7},{6},{10},{12}}
[3,2,9,8,7,6,5,4,1,12,11,10]=>{{1,3,9},{2},{4,8},{5,7},{6},{10,12},{11}}
[3,2,11,8,7,6,5,10,9,4,1,12]=>{{1,3,11},{2},{4,8,10},{5,7},{6},{9},{12}}
[3,2,1,8,7,6,5,10,9,12,11,4]=>{{1,3},{2},{4,8,10,12},{5,7},{6},{9},{11}}
[3,2,1,8,7,6,5,12,11,10,9,4]=>{{1,3},{2},{4,8,12},{5,7},{6},{9,11},{10}}
[3,2,11,10,7,6,9,8,5,4,1,12]=>{{1,3,11},{2},{4,10},{5,7,9},{6},{8},{12}}
[3,2,1,10,7,6,9,8,5,12,11,4]=>{{1,3},{2},{4,10,12},{5,7,9},{6},{8},{11}}
[3,2,1,12,7,6,9,8,11,10,5,4]=>{{1,3},{2},{4,12},{5,7,9,11},{6},{8},{10}}
[3,2,1,12,7,6,11,10,9,8,5,4]=>{{1,3},{2},{4,12},{5,7,11},{6},{8,10},{9}}
[3,2,11,10,9,8,7,6,5,4,1,12]=>{{1,3,11},{2},{4,10},{5,9},{6,8},{7},{12}}
[3,2,1,10,9,8,7,6,5,12,11,4]=>{{1,3},{2},{4,10,12},{5,9},{6,8},{7},{11}}
[3,2,1,12,9,8,7,6,11,10,5,4]=>{{1,3},{2},{4,12},{5,9,11},{6,8},{7},{10}}
[3,2,1,12,11,8,7,10,9,6,5,4]=>{{1,3},{2},{4,12},{5,11},{6,8,10},{7},{9}}
[3,2,1,12,11,10,9,8,7,6,5,4]=>{{1,3},{2},{4,12},{5,11},{6,10},{7,9},{8}}
[5,4,3,2,7,6,9,8,11,10,1,12]=>{{1,5,7,9,11},{2,4},{3},{6},{8},{10},{12}}
[5,4,3,2,7,6,9,8,1,12,11,10]=>{{1,5,7,9},{2,4},{3},{6},{8},{10,12},{11}}
[5,4,3,2,7,6,11,10,9,8,1,12]=>{{1,5,7,11},{2,4},{3},{6},{8,10},{9},{12}}
[5,4,3,2,7,6,1,10,9,12,11,8]=>{{1,5,7},{2,4},{3},{6},{8,10,12},{9},{11}}
[5,4,3,2,7,6,1,12,11,10,9,8]=>{{1,5,7},{2,4},{3},{6},{8,12},{9,11},{10}}
[5,4,3,2,9,8,7,6,11,10,1,12]=>{{1,5,9,11},{2,4},{3},{6,8},{7},{10},{12}}
[5,4,3,2,9,8,7,6,1,12,11,10]=>{{1,5,9},{2,4},{3},{6,8},{7},{10,12},{11}}
[5,4,3,2,11,8,7,10,9,6,1,12]=>{{1,5,11},{2,4},{3},{6,8,10},{7},{9},{12}}
[5,4,3,2,1,8,7,10,9,12,11,6]=>{{1,5},{2,4},{3},{6,8,10,12},{7},{9},{11}}
[5,4,3,2,1,8,7,12,11,10,9,6]=>{{1,5},{2,4},{3},{6,8,12},{7},{9,11},{10}}
[5,4,3,2,11,10,9,8,7,6,1,12]=>{{1,5,11},{2,4},{3},{6,10},{7,9},{8},{12}}
[5,4,3,2,1,10,9,8,7,12,11,6]=>{{1,5},{2,4},{3},{6,10,12},{7,9},{8},{11}}
[5,4,3,2,1,12,9,8,11,10,7,6]=>{{1,5},{2,4},{3},{6,12},{7,9,11},{8},{10}}
[5,4,3,2,1,12,11,10,9,8,7,6]=>{{1,5},{2,4},{3},{6,12},{7,11},{8,10},{9}}
[7,4,3,6,5,2,9,8,11,10,1,12]=>{{1,7,9,11},{2,4,6},{3},{5},{8},{10},{12}}
[7,4,3,6,5,2,9,8,1,12,11,10]=>{{1,7,9},{2,4,6},{3},{5},{8},{10,12},{11}}
[7,4,3,6,5,2,11,10,9,8,1,12]=>{{1,7,11},{2,4,6},{3},{5},{8,10},{9},{12}}
[7,4,3,6,5,2,1,10,9,12,11,8]=>{{1,7},{2,4,6},{3},{5},{8,10,12},{9},{11}}
[7,4,3,6,5,2,1,12,11,10,9,8]=>{{1,7},{2,4,6},{3},{5},{8,12},{9,11},{10}}
[9,4,3,6,5,8,7,2,11,10,1,12]=>{{1,9,11},{2,4,6,8},{3},{5},{7},{10},{12}}
[9,4,3,6,5,8,7,2,1,12,11,10]=>{{1,9},{2,4,6,8},{3},{5},{7},{10,12},{11}}
[11,4,3,6,5,8,7,10,9,2,1,12]=>{{1,11},{2,4,6,8,10},{3},{5},{7},{9},{12}}
[1,4,3,6,5,8,7,10,9,12,11,2]=>{{1},{2,4,6,8,10,12},{3},{5},{7},{9},{11}}
[1,4,3,6,5,8,7,12,11,10,9,2]=>{{1},{2,4,6,8,12},{3},{5},{7},{9,11},{10}}
[11,4,3,6,5,10,9,8,7,2,1,12]=>{{1,11},{2,4,6,10},{3},{5},{7,9},{8},{12}}
[1,4,3,6,5,10,9,8,7,12,11,2]=>{{1},{2,4,6,10,12},{3},{5},{7,9},{8},{11}}
[1,4,3,6,5,12,9,8,11,10,7,2]=>{{1},{2,4,6,12},{3},{5},{7,9,11},{8},{10}}
[1,4,3,6,5,12,11,10,9,8,7,2]=>{{1},{2,4,6,12},{3},{5},{7,11},{8,10},{9}}
[9,4,3,8,7,6,5,2,11,10,1,12]=>{{1,9,11},{2,4,8},{3},{5,7},{6},{10},{12}}
[9,4,3,8,7,6,5,2,1,12,11,10]=>{{1,9},{2,4,8},{3},{5,7},{6},{10,12},{11}}
[11,4,3,8,7,6,5,10,9,2,1,12]=>{{1,11},{2,4,8,10},{3},{5,7},{6},{9},{12}}
[1,4,3,8,7,6,5,10,9,12,11,2]=>{{1},{2,4,8,10,12},{3},{5,7},{6},{9},{11}}
[1,4,3,8,7,6,5,12,11,10,9,2]=>{{1},{2,4,8,12},{3},{5,7},{6},{9,11},{10}}
[11,4,3,10,7,6,9,8,5,2,1,12]=>{{1,11},{2,4,10},{3},{5,7,9},{6},{8},{12}}
[1,4,3,10,7,6,9,8,5,12,11,2]=>{{1},{2,4,10,12},{3},{5,7,9},{6},{8},{11}}
[1,4,3,12,7,6,9,8,11,10,5,2]=>{{1},{2,4,12},{3},{5,7,9,11},{6},{8},{10}}
[1,4,3,12,7,6,11,10,9,8,5,2]=>{{1},{2,4,12},{3},{5,7,11},{6},{8,10},{9}}
[11,4,3,10,9,8,7,6,5,2,1,12]=>{{1,11},{2,4,10},{3},{5,9},{6,8},{7},{12}}
[1,4,3,10,9,8,7,6,5,12,11,2]=>{{1},{2,4,10,12},{3},{5,9},{6,8},{7},{11}}
[1,4,3,12,9,8,7,6,11,10,5,2]=>{{1},{2,4,12},{3},{5,9,11},{6,8},{7},{10}}
[1,4,3,12,11,8,7,10,9,6,5,2]=>{{1},{2,4,12},{3},{5,11},{6,8,10},{7},{9}}
[1,4,3,12,11,10,9,8,7,6,5,2]=>{{1},{2,4,12},{3},{5,11},{6,10},{7,9},{8}}
[7,6,5,4,3,2,9,8,11,10,1,12]=>{{1,7,9,11},{2,6},{3,5},{4},{8},{10},{12}}
[7,6,5,4,3,2,9,8,1,12,11,10]=>{{1,7,9},{2,6},{3,5},{4},{8},{10,12},{11}}
[7,6,5,4,3,2,11,10,9,8,1,12]=>{{1,7,11},{2,6},{3,5},{4},{8,10},{9},{12}}
[7,6,5,4,3,2,1,10,9,12,11,8]=>{{1,7},{2,6},{3,5},{4},{8,10,12},{9},{11}}
[7,6,5,4,3,2,1,12,11,10,9,8]=>{{1,7},{2,6},{3,5},{4},{8,12},{9,11},{10}}
[9,6,5,4,3,8,7,2,11,10,1,12]=>{{1,9,11},{2,6,8},{3,5},{4},{7},{10},{12}}
[9,6,5,4,3,8,7,2,1,12,11,10]=>{{1,9},{2,6,8},{3,5},{4},{7},{10,12},{11}}
[11,6,5,4,3,8,7,10,9,2,1,12]=>{{1,11},{2,6,8,10},{3,5},{4},{7},{9},{12}}
[1,6,5,4,3,8,7,10,9,12,11,2]=>{{1},{2,6,8,10,12},{3,5},{4},{7},{9},{11}}
[1,6,5,4,3,8,7,12,11,10,9,2]=>{{1},{2,6,8,12},{3,5},{4},{7},{9,11},{10}}
[11,6,5,4,3,10,9,8,7,2,1,12]=>{{1,11},{2,6,10},{3,5},{4},{7,9},{8},{12}}
[1,6,5,4,3,10,9,8,7,12,11,2]=>{{1},{2,6,10,12},{3,5},{4},{7,9},{8},{11}}
[1,6,5,4,3,12,9,8,11,10,7,2]=>{{1},{2,6,12},{3,5},{4},{7,9,11},{8},{10}}
[1,6,5,4,3,12,11,10,9,8,7,2]=>{{1},{2,6,12},{3,5},{4},{7,11},{8,10},{9}}
[9,8,5,4,7,6,3,2,11,10,1,12]=>{{1,9,11},{2,8},{3,5,7},{4},{6},{10},{12}}
[9,8,5,4,7,6,3,2,1,12,11,10]=>{{1,9},{2,8},{3,5,7},{4},{6},{10,12},{11}}
[11,8,5,4,7,6,3,10,9,2,1,12]=>{{1,11},{2,8,10},{3,5,7},{4},{6},{9},{12}}
[1,8,5,4,7,6,3,10,9,12,11,2]=>{{1},{2,8,10,12},{3,5,7},{4},{6},{9},{11}}
[1,8,5,4,7,6,3,12,11,10,9,2]=>{{1},{2,8,12},{3,5,7},{4},{6},{9,11},{10}}
[11,10,5,4,7,6,9,8,3,2,1,12]=>{{1,11},{2,10},{3,5,7,9},{4},{6},{8},{12}}
[1,10,5,4,7,6,9,8,3,12,11,2]=>{{1},{2,10,12},{3,5,7,9},{4},{6},{8},{11}}
[1,12,5,4,7,6,9,8,11,10,3,2]=>{{1},{2,12},{3,5,7,9,11},{4},{6},{8},{10}}
[1,12,5,4,7,6,11,10,9,8,3,2]=>{{1},{2,12},{3,5,7,11},{4},{6},{8,10},{9}}
[11,10,5,4,9,8,7,6,3,2,1,12]=>{{1,11},{2,10},{3,5,9},{4},{6,8},{7},{12}}
[1,10,5,4,9,8,7,6,3,12,11,2]=>{{1},{2,10,12},{3,5,9},{4},{6,8},{7},{11}}
[1,12,5,4,9,8,7,6,11,10,3,2]=>{{1},{2,12},{3,5,9,11},{4},{6,8},{7},{10}}
[1,12,5,4,11,8,7,10,9,6,3,2]=>{{1},{2,12},{3,5,11},{4},{6,8,10},{7},{9}}
[1,12,5,4,11,10,9,8,7,6,3,2]=>{{1},{2,12},{3,5,11},{4},{6,10},{7,9},{8}}
[9,8,7,6,5,4,3,2,11,10,1,12]=>{{1,9,11},{2,8},{3,7},{4,6},{5},{10},{12}}
[9,8,7,6,5,4,3,2,1,12,11,10]=>{{1,9},{2,8},{3,7},{4,6},{5},{10,12},{11}}
[11,8,7,6,5,4,3,10,9,2,1,12]=>{{1,11},{2,8,10},{3,7},{4,6},{5},{9},{12}}
[1,8,7,6,5,4,3,10,9,12,11,2]=>{{1},{2,8,10,12},{3,7},{4,6},{5},{9},{11}}
[1,8,7,6,5,4,3,12,11,10,9,2]=>{{1},{2,8,12},{3,7},{4,6},{5},{9,11},{10}}
[11,10,7,6,5,4,9,8,3,2,1,12]=>{{1,11},{2,10},{3,7,9},{4,6},{5},{8},{12}}
[1,10,7,6,5,4,9,8,3,12,11,2]=>{{1},{2,10,12},{3,7,9},{4,6},{5},{8},{11}}
[1,12,7,6,5,4,9,8,11,10,3,2]=>{{1},{2,12},{3,7,9,11},{4,6},{5},{8},{10}}
[1,12,7,6,5,4,11,10,9,8,3,2]=>{{1},{2,12},{3,7,11},{4,6},{5},{8,10},{9}}
[11,10,9,6,5,8,7,4,3,2,1,12]=>{{1,11},{2,10},{3,9},{4,6,8},{5},{7},{12}}
[1,10,9,6,5,8,7,4,3,12,11,2]=>{{1},{2,10,12},{3,9},{4,6,8},{5},{7},{11}}
[1,12,9,6,5,8,7,4,11,10,3,2]=>{{1},{2,12},{3,9,11},{4,6,8},{5},{7},{10}}
[1,12,11,6,5,8,7,10,9,4,3,2]=>{{1},{2,12},{3,11},{4,6,8,10},{5},{7},{9}}
[1,12,11,6,5,10,9,8,7,4,3,2]=>{{1},{2,12},{3,11},{4,6,10},{5},{7,9},{8}}
[11,10,9,8,7,6,5,4,3,2,1,12]=>{{1,11},{2,10},{3,9},{4,8},{5,7},{6},{12}}
[1,10,9,8,7,6,5,4,3,12,11,2]=>{{1},{2,10,12},{3,9},{4,8},{5,7},{6},{11}}
[1,12,9,8,7,6,5,4,11,10,3,2]=>{{1},{2,12},{3,9,11},{4,8},{5,7},{6},{10}}
[1,12,11,8,7,6,5,10,9,4,3,2]=>{{1},{2,12},{3,11},{4,8,10},{5,7},{6},{9}}
[1,12,11,10,7,6,9,8,5,4,3,2]=>{{1},{2,12},{3,11},{4,10},{5,7,9},{6},{8}}
[1,12,11,10,9,8,7,6,5,4,3,2]=>{{1},{2,12},{3,11},{4,10},{5,9},{6,8},{7}}
[2,3,4,5,6,7,8,9,10,11,12,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,3,4,5,6,7,8,9,10,11,12,2]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[2,1,4,3,6,5,8,7,10,12,11,9]=>{{1,2},{3,4},{5,6},{7,8},{9,10,12},{11}}
[2,1,4,3,6,5,8,10,9,7,12,11]=>{{1,2},{3,4},{5,6},{7,8,10},{9},{11,12}}
[2,1,4,3,6,5,10,12,9,11,7,8]=>{{1,2},{3,4},{5,6},{7,10,11},{8,12},{9}}
[2,1,4,3,6,5,8,9,12,10,11,7]=>{{1,2},{3,4},{5,6},{7,8,9,12},{10},{11}}
[2,1,4,3,6,8,7,5,10,9,12,11]=>{{1,2},{3,4},{5,6,8},{7},{9,10},{11,12}}
[2,1,4,3,6,8,7,5,10,12,11,9]=>{{1,2},{3,4},{5,6,8},{7},{9,10,12},{11}}
[2,1,4,3,8,10,7,9,5,6,12,11]=>{{1,2},{3,4},{5,8,9},{6,10},{7},{11,12}}
[2,1,4,3,10,9,7,12,6,11,5,8]=>{{1,2},{3,4},{5,10,11},{6,9},{7},{8,12}}
[2,1,4,3,8,9,7,12,10,6,11,5]=>{{1,2},{3,4},{5,8,12},{6,9,10},{7},{11}}
[2,1,4,3,6,7,10,8,9,5,12,11]=>{{1,2},{3,4},{5,6,7,10},{8},{9},{11,12}}
[2,1,4,3,10,7,12,8,9,11,5,6]=>{{1,2},{3,4},{5,10,11},{6,7,12},{8},{9}}
[2,1,4,3,6,9,12,8,11,10,5,7]=>{{1,2},{3,4},{5,6,9,11},{7,12},{8},{10}}
[2,1,4,3,6,7,8,12,9,10,11,5]=>{{1,2},{3,4},{5,6,7,8,12},{9},{10},{11}}
[2,1,4,6,5,3,8,7,10,9,12,11]=>{{1,2},{3,4,6},{5},{7,8},{9,10},{11,12}}
[2,1,4,6,5,3,8,7,10,12,11,9]=>{{1,2},{3,4,6},{5},{7,8},{9,10,12},{11}}
[2,1,4,6,5,3,8,10,9,7,12,11]=>{{1,2},{3,4,6},{5},{7,8,10},{9},{11,12}}
[2,1,4,6,5,3,10,12,9,11,7,8]=>{{1,2},{3,4,6},{5},{7,10,11},{8,12},{9}}
[2,1,4,6,5,3,8,9,12,10,11,7]=>{{1,2},{3,4,6},{5},{7,8,9,12},{10},{11}}
[2,1,6,8,5,7,3,4,10,9,12,11]=>{{1,2},{3,6,7},{4,8},{5},{9,10},{11,12}}
[2,1,6,8,5,7,3,4,10,12,11,9]=>{{1,2},{3,6,7},{4,8},{5},{9,10,12},{11}}
[2,1,8,7,5,10,4,9,3,6,12,11]=>{{1,2},{3,8,9},{4,7},{5},{6,10},{11,12}}
[2,1,10,7,5,9,4,12,6,11,3,8]=>{{1,2},{3,10,11},{4,7},{5},{6,9},{8,12}}
[2,1,8,7,5,9,4,12,10,6,11,3]=>{{1,2},{3,8,12},{4,7},{5},{6,9,10},{11}}
[2,1,6,7,5,10,8,4,9,3,12,11]=>{{1,2},{3,6,10},{4,7,8},{5},{9},{11,12}}
[2,1,10,8,5,7,12,4,9,11,3,6]=>{{1,2},{3,10,11},{4,8},{5},{6,7,12},{9}}
[2,1,6,9,5,8,12,3,11,10,4,7]=>{{1,2},{3,6,8},{4,9,11},{5},{7,12},{10}}
[2,1,6,7,5,8,12,9,3,10,11,4]=>{{1,2},{3,6,8,9},{4,7,12},{5},{10},{11}}
[2,1,4,5,8,6,7,3,10,9,12,11]=>{{1,2},{3,4,5,8},{6},{7},{9,10},{11,12}}
[2,1,4,5,8,6,7,3,10,12,11,9]=>{{1,2},{3,4,5,8},{6},{7},{9,10,12},{11}}
[2,1,8,5,10,6,7,9,3,4,12,11]=>{{1,2},{3,8,9},{4,5,10},{6},{7},{11,12}}
[2,1,10,5,9,6,7,12,4,11,3,8]=>{{1,2},{3,10,11},{4,5,9},{6},{7},{8,12}}
[2,1,8,5,9,6,7,12,10,4,11,3]=>{{1,2},{3,8,12},{4,5,9,10},{6},{7},{11}}
[2,1,4,7,10,6,9,8,3,5,12,11]=>{{1,2},{3,4,7,9},{5,10},{6},{8},{11,12}}
[2,1,10,7,12,6,9,8,4,11,3,5]=>{{1,2},{3,10,11},{4,7,9},{5,12},{6},{8}}
[2,1,4,9,12,6,10,8,11,7,3,5]=>{{1,2},{3,4,9,11},{5,12},{6},{7,10},{8}}
[2,1,4,7,8,6,12,10,9,5,11,3]=>{{1,2},{3,4,7,12},{5,8,10},{6},{9},{11}}
[2,1,4,5,6,10,7,8,9,3,12,11]=>{{1,2},{3,4,5,6,10},{7},{8},{9},{11,12}}
[2,1,10,5,6,12,7,8,9,11,3,4]=>{{1,2},{3,10,11},{4,5,6,12},{7},{8},{9}}
[2,1,4,9,6,12,7,8,11,10,3,5]=>{{1,2},{3,4,9,11},{5,6,12},{7},{8},{10}}
[2,1,4,5,8,12,7,11,9,10,3,6]=>{{1,2},{3,4,5,8,11},{6,12},{7},{9},{10}}
[2,1,4,5,6,7,12,8,9,10,11,3]=>{{1,2},{3,4,5,6,7,12},{8},{9},{10},{11}}
[2,4,3,1,6,5,8,7,10,9,12,11]=>{{1,2,4},{3},{5,6},{7,8},{9,10},{11,12}}
[2,4,3,1,6,5,8,7,10,12,11,9]=>{{1,2,4},{3},{5,6},{7,8},{9,10,12},{11}}
[2,4,3,1,6,5,8,10,9,7,12,11]=>{{1,2,4},{3},{5,6},{7,8,10},{9},{11,12}}
[2,4,3,1,6,5,10,12,9,11,7,8]=>{{1,2,4},{3},{5,6},{7,10,11},{8,12},{9}}
[2,4,3,1,6,5,8,9,12,10,11,7]=>{{1,2,4},{3},{5,6},{7,8,9,12},{10},{11}}
[2,4,3,1,6,8,7,5,10,9,12,11]=>{{1,2,4},{3},{5,6,8},{7},{9,10},{11,12}}
[2,4,3,1,6,8,7,5,10,12,11,9]=>{{1,2,4},{3},{5,6,8},{7},{9,10,12},{11}}
[2,4,3,1,8,10,7,9,5,6,12,11]=>{{1,2,4},{3},{5,8,9},{6,10},{7},{11,12}}
[2,4,3,1,10,9,7,12,6,11,5,8]=>{{1,2,4},{3},{5,10,11},{6,9},{7},{8,12}}
[2,4,3,1,8,9,7,12,10,6,11,5]=>{{1,2,4},{3},{5,8,12},{6,9,10},{7},{11}}
[2,4,3,1,6,7,10,8,9,5,12,11]=>{{1,2,4},{3},{5,6,7,10},{8},{9},{11,12}}
[2,4,3,1,10,7,12,8,9,11,5,6]=>{{1,2,4},{3},{5,10,11},{6,7,12},{8},{9}}
[2,4,3,1,6,9,12,8,11,10,5,7]=>{{1,2,4},{3},{5,6,9,11},{7,12},{8},{10}}
[2,4,3,1,6,7,8,12,9,10,11,5]=>{{1,2,4},{3},{5,6,7,8,12},{9},{10},{11}}
[4,6,3,5,1,2,8,7,10,9,12,11]=>{{1,4,5},{2,6},{3},{7,8},{9,10},{11,12}}
[4,6,3,5,1,2,8,7,10,12,11,9]=>{{1,4,5},{2,6},{3},{7,8},{9,10,12},{11}}
[4,6,3,5,1,2,8,10,9,7,12,11]=>{{1,4,5},{2,6},{3},{7,8,10},{9},{11,12}}
[4,6,3,5,1,2,10,12,9,11,7,8]=>{{1,4,5},{2,6},{3},{7,10,11},{8,12},{9}}
[4,6,3,5,1,2,8,9,12,10,11,7]=>{{1,4,5},{2,6},{3},{7,8,9,12},{10},{11}}
[6,5,3,8,2,7,1,4,10,9,12,11]=>{{1,6,7},{2,5},{3},{4,8},{9,10},{11,12}}
[6,5,3,8,2,7,1,4,10,12,11,9]=>{{1,6,7},{2,5},{3},{4,8},{9,10,12},{11}}
[8,5,3,7,2,10,4,9,1,6,12,11]=>{{1,8,9},{2,5},{3},{4,7},{6,10},{11,12}}
[10,5,3,7,2,9,4,12,6,11,1,8]=>{{1,10,11},{2,5},{3},{4,7},{6,9},{8,12}}
[8,5,3,7,2,9,4,12,10,6,11,1]=>{{1,8,12},{2,5},{3},{4,7},{6,9,10},{11}}
[6,5,3,7,2,10,8,4,9,1,12,11]=>{{1,6,10},{2,5},{3},{4,7,8},{9},{11,12}}
[10,5,3,8,2,7,12,4,9,11,1,6]=>{{1,10,11},{2,5},{3},{4,8},{6,7,12},{9}}
[6,5,3,9,2,8,12,1,11,10,4,7]=>{{1,6,8},{2,5},{3},{4,9,11},{7,12},{10}}
[6,5,3,7,2,8,12,9,1,10,11,4]=>{{1,6,8,9},{2,5},{3},{4,7,12},{10},{11}}
[4,5,3,8,6,2,7,1,10,9,12,11]=>{{1,4,8},{2,5,6},{3},{7},{9,10},{11,12}}
[4,5,3,8,6,2,7,1,10,12,11,9]=>{{1,4,8},{2,5,6},{3},{7},{9,10,12},{11}}
[8,6,3,5,10,2,7,9,1,4,12,11]=>{{1,8,9},{2,6},{3},{4,5,10},{7},{11,12}}
[10,6,3,5,9,2,7,12,4,11,1,8]=>{{1,10,11},{2,6},{3},{4,5,9},{7},{8,12}}
[8,6,3,5,9,2,7,12,10,4,11,1]=>{{1,8,12},{2,6},{3},{4,5,9,10},{7},{11}}
[4,7,3,6,10,1,9,8,2,5,12,11]=>{{1,4,6},{2,7,9},{3},{5,10},{8},{11,12}}
[10,6,3,7,12,2,9,8,4,11,1,5]=>{{1,10,11},{2,6},{3},{4,7,9},{5,12},{8}}
[4,9,3,6,12,1,10,8,11,7,2,5]=>{{1,4,6},{2,9,11},{3},{5,12},{7,10},{8}}
[4,7,3,6,8,1,12,10,9,5,11,2]=>{{1,4,6},{2,7,12},{3},{5,8,10},{9},{11}}
[4,5,3,6,10,7,1,8,9,2,12,11]=>{{1,4,6,7},{2,5,10},{3},{8},{9},{11,12}}
[10,7,3,5,6,12,2,8,9,11,1,4]=>{{1,10,11},{2,7},{3},{4,5,6,12},{8},{9}}
[4,9,3,7,6,12,1,8,11,10,2,5]=>{{1,4,7},{2,9,11},{3},{5,6,12},{8},{10}}
[4,5,3,8,7,12,2,11,9,10,1,6]=>{{1,4,8,11},{2,5,7},{3},{6,12},{9},{10}}
[4,5,3,6,7,12,8,2,9,10,11,1]=>{{1,4,6,12},{2,5,7,8},{3},{9},{10},{11}}
[2,3,6,4,5,1,8,7,10,9,12,11]=>{{1,2,3,6},{4},{5},{7,8},{9,10},{11,12}}
[2,3,6,4,5,1,8,7,10,12,11,9]=>{{1,2,3,6},{4},{5},{7,8},{9,10,12},{11}}
[2,3,6,4,5,1,8,10,9,7,12,11]=>{{1,2,3,6},{4},{5},{7,8,10},{9},{11,12}}
[2,3,6,4,5,1,10,12,9,11,7,8]=>{{1,2,3,6},{4},{5},{7,10,11},{8,12},{9}}
[2,3,6,4,5,1,8,9,12,10,11,7]=>{{1,2,3,6},{4},{5},{7,8,9,12},{10},{11}}
[6,3,8,4,5,7,1,2,10,9,12,11]=>{{1,6,7},{2,3,8},{4},{5},{9,10},{11,12}}
[6,3,8,4,5,7,1,2,10,12,11,9]=>{{1,6,7},{2,3,8},{4},{5},{9,10,12},{11}}
[8,3,7,4,5,10,2,9,1,6,12,11]=>{{1,8,9},{2,3,7},{4},{5},{6,10},{11,12}}
[10,3,7,4,5,9,2,12,6,11,1,8]=>{{1,10,11},{2,3,7},{4},{5},{6,9},{8,12}}
[8,3,7,4,5,9,2,12,10,6,11,1]=>{{1,8,12},{2,3,7},{4},{5},{6,9,10},{11}}
[6,3,7,4,5,10,8,2,9,1,12,11]=>{{1,6,10},{2,3,7,8},{4},{5},{9},{11,12}}
[10,3,8,4,5,7,12,2,9,11,1,6]=>{{1,10,11},{2,3,8},{4},{5},{6,7,12},{9}}
[6,3,9,4,5,8,12,1,11,10,2,7]=>{{1,6,8},{2,3,9,11},{4},{5},{7,12},{10}}
[6,3,7,4,5,8,12,9,1,10,11,2]=>{{1,6,8,9},{2,3,7,12},{4},{5},{10},{11}}
[2,5,8,4,7,6,1,3,10,9,12,11]=>{{1,2,5,7},{3,8},{4},{6},{9,10},{11,12}}
[2,5,8,4,7,6,1,3,10,12,11,9]=>{{1,2,5,7},{3,8},{4},{6},{9,10,12},{11}}
[8,5,10,4,7,6,2,9,1,3,12,11]=>{{1,8,9},{2,5,7},{3,10},{4},{6},{11,12}}
[10,5,9,4,7,6,2,12,3,11,1,8]=>{{1,10,11},{2,5,7},{3,9},{4},{6},{8,12}}
[8,5,9,4,7,6,2,12,10,3,11,1]=>{{1,8,12},{2,5,7},{3,9,10},{4},{6},{11}}
[2,7,10,4,8,6,9,5,1,3,12,11]=>{{1,2,7,9},{3,10},{4},{5,8},{6},{11,12}}
[10,7,12,4,8,6,9,5,2,11,1,3]=>{{1,10,11},{2,7,9},{3,12},{4},{5,8},{6}}
[2,9,8,4,12,6,10,3,11,7,1,5]=>{{1,2,9,11},{3,8},{4},{5,12},{6},{7,10}}
[2,7,8,4,12,6,9,10,1,3,11,5]=>{{1,2,7,9},{3,8,10},{4},{5,12},{6},{11}}
[2,5,6,4,10,8,7,3,9,1,12,11]=>{{1,2,5,10},{3,6,8},{4},{7},{9},{11,12}}
[10,5,6,4,12,8,7,3,9,11,1,2]=>{{1,10,11},{2,5,12},{3,6,8},{4},{7},{9}}
[2,9,8,4,6,12,7,3,11,10,1,5]=>{{1,2,9,11},{3,8},{4},{5,6,12},{7},{10}}
[2,5,8,4,12,9,7,11,6,10,3,1]=>{{1,2,5,12},{3,8,11},{4},{6,9},{7},{10}}
[2,5,6,4,7,12,9,8,1,10,11,3]=>{{1,2,5,7,9},{3,6,12},{4},{8},{10},{11}}
[2,3,4,8,5,6,7,1,10,9,12,11]=>{{1,2,3,4,8},{5},{6},{7},{9,10},{11,12}}
[2,3,4,8,5,6,7,1,10,12,11,9]=>{{1,2,3,4,8},{5},{6},{7},{9,10,12},{11}}
[8,3,4,10,5,6,7,9,1,2,12,11]=>{{1,8,9},{2,3,4,10},{5},{6},{7},{11,12}}
[10,3,4,9,5,6,7,12,2,11,1,8]=>{{1,10,11},{2,3,4,9},{5},{6},{7},{8,12}}
[8,3,4,9,5,6,7,12,10,2,11,1]=>{{1,8,12},{2,3,4,9,10},{5},{6},{7},{11}}
[2,7,4,10,5,6,9,8,1,3,12,11]=>{{1,2,7,9},{3,4,10},{5},{6},{8},{11,12}}
[10,7,4,12,5,6,9,8,2,11,1,3]=>{{1,10,11},{2,7,9},{3,4,12},{5},{6},{8}}
[2,9,4,12,5,6,10,8,11,7,1,3]=>{{1,2,9,11},{3,4,12},{5},{6},{7,10},{8}}
[2,7,4,8,5,6,12,10,9,3,11,1]=>{{1,2,7,12},{3,4,8,10},{5},{6},{9},{11}}
[2,3,6,10,5,9,7,8,1,4,12,11]=>{{1,2,3,6,9},{4,10},{5},{7},{8},{11,12}}
[10,3,6,12,5,9,7,8,2,11,1,4]=>{{1,10,11},{2,3,6,9},{4,12},{5},{7},{8}}
[2,9,6,12,5,11,7,8,10,1,3,4]=>{{1,2,9,10},{3,6,11},{4,12},{5},{7},{8}}
[2,3,8,12,5,10,7,11,9,6,1,4]=>{{1,2,3,8,11},{4,12},{5},{6,10},{7},{9}}
[2,3,6,7,5,12,10,8,9,4,11,1]=>{{1,2,3,6,12},{4,7,10},{5},{8},{9},{11}}
[2,3,4,5,10,6,7,8,9,1,12,11]=>{{1,2,3,4,5,10},{6},{7},{8},{9},{11,12}}
[10,3,4,5,12,6,7,8,9,11,1,2]=>{{1,10,11},{2,3,4,5,12},{6},{7},{8},{9}}
[2,9,4,5,12,6,7,8,11,10,1,3]=>{{1,2,9,11},{3,4,5,12},{6},{7},{8},{10}}
[2,3,8,5,12,6,7,11,9,10,1,4]=>{{1,2,3,8,11},{4,5,12},{6},{7},{9},{10}}
[2,3,4,7,12,6,11,8,9,10,1,5]=>{{1,2,3,4,7,11},{5,12},{6},{8},{9},{10}}
[2,3,4,5,6,12,7,8,9,10,11,1]=>{{1,2,3,4,5,6,12},{7},{8},{9},{10},{11}}
[2,1,4,3,6,5,8,7,10,11,12,9]=>{{1,2},{3,4},{5,6},{7,8},{9,10,11,12}}
[2,1,4,3,6,5,8,9,10,7,12,11]=>{{1,2},{3,4},{5,6},{7,8,9,10},{11,12}}
[2,1,4,3,6,5,10,9,11,12,7,8]=>{{1,2},{3,4},{5,6},{7,8,9,10,11,12}}
[2,1,4,3,6,5,8,9,10,11,12,7]=>{{1,2},{3,4},{5,6},{7,8,9,10,11,12}}
[2,1,4,3,6,7,8,5,10,9,12,11]=>{{1,2},{3,4},{5,6,7,8},{9,10},{11,12}}
[2,1,4,3,6,7,8,5,10,11,12,9]=>{{1,2},{3,4},{5,6,7,8},{9,10,11,12}}
[2,1,4,3,8,7,9,10,5,6,12,11]=>{{1,2},{3,4},{5,6,7,8,9,10},{11,12}}
[2,1,4,3,10,7,11,9,5,12,8,6]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,3,8,7,9,10,11,12,5,6]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,3,6,7,8,9,10,5,12,11]=>{{1,2},{3,4},{5,6,7,8,9,10},{11,12}}
[2,1,4,3,10,7,8,9,11,12,5,6]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,3,6,9,8,10,11,5,12,7]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,3,6,7,8,9,10,11,12,5]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,5,6,3,8,7,10,9,12,11]=>{{1,2},{3,4,5,6},{7,8},{9,10},{11,12}}
[2,1,4,5,6,3,8,7,10,11,12,9]=>{{1,2},{3,4,5,6},{7,8},{9,10,11,12}}
[2,1,4,5,6,3,8,9,10,7,12,11]=>{{1,2},{3,4,5,6},{7,8,9,10},{11,12}}
[2,1,4,5,6,3,10,9,11,12,7,8]=>{{1,2},{3,4,5,6},{7,8,9,10,11,12}}
[2,1,4,5,6,3,8,9,10,11,12,7]=>{{1,2},{3,4,5,6},{7,8,9,10,11,12}}
[2,1,6,5,7,8,3,4,10,9,12,11]=>{{1,2},{3,4,5,6,7,8},{9,10},{11,12}}
[2,1,6,5,7,8,3,4,10,11,12,9]=>{{1,2},{3,4,5,6,7,8},{9,10,11,12}}
[2,1,8,5,9,7,3,10,6,4,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,10,5,11,7,3,9,6,12,8,4]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,8,5,9,7,3,10,11,12,6,4]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,6,5,7,8,9,10,3,4,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,10,5,11,7,8,9,3,12,6,4]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,6,5,9,10,8,12,11,4,7,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,6,5,7,8,9,10,11,12,3,4]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,4,5,6,7,8,3,10,9,12,11]=>{{1,2},{3,4,5,6,7,8},{9,10},{11,12}}
[2,1,4,5,6,7,8,3,10,11,12,9]=>{{1,2},{3,4,5,6,7,8},{9,10,11,12}}
[2,1,8,5,6,7,9,10,3,4,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,10,5,6,7,11,9,3,12,8,4]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,8,5,6,7,9,10,11,12,3,4]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,4,7,6,8,9,3,10,5,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,10,7,6,8,9,3,11,12,5,4]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,4,9,6,10,8,3,11,7,12,5]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,4,7,6,8,9,10,11,3,12,5]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,4,5,6,7,8,9,10,3,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,10,5,6,7,8,9,11,12,3,4]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,4,9,6,7,8,10,11,3,12,5]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,4,5,8,7,9,10,3,11,12,6]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,4,5,6,7,8,9,10,11,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,3,4,1,6,5,8,7,10,9,12,11]=>{{1,2,3,4},{5,6},{7,8},{9,10},{11,12}}
[2,3,4,1,6,5,8,7,10,11,12,9]=>{{1,2,3,4},{5,6},{7,8},{9,10,11,12}}
[2,3,4,1,6,5,8,9,10,7,12,11]=>{{1,2,3,4},{5,6},{7,8,9,10},{11,12}}
[2,3,4,1,6,5,10,9,11,12,7,8]=>{{1,2,3,4},{5,6},{7,8,9,10,11,12}}
[2,3,4,1,6,5,8,9,10,11,12,7]=>{{1,2,3,4},{5,6},{7,8,9,10,11,12}}
[2,3,4,1,6,7,8,5,10,9,12,11]=>{{1,2,3,4},{5,6,7,8},{9,10},{11,12}}
[2,3,4,1,6,7,8,5,10,11,12,9]=>{{1,2,3,4},{5,6,7,8},{9,10,11,12}}
[2,3,4,1,8,7,9,10,5,6,12,11]=>{{1,2,3,4},{5,6,7,8,9,10},{11,12}}
[2,3,4,1,10,7,11,9,5,12,8,6]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[2,3,4,1,8,7,9,10,11,12,5,6]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[2,3,4,1,6,7,8,9,10,5,12,11]=>{{1,2,3,4},{5,6,7,8,9,10},{11,12}}
[2,3,4,1,10,7,8,9,11,12,5,6]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[2,3,4,1,6,9,8,10,11,5,12,7]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[2,3,4,1,6,7,8,9,10,11,12,5]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[4,3,5,6,1,2,8,7,10,9,12,11]=>{{1,2,3,4,5,6},{7,8},{9,10},{11,12}}
[4,3,5,6,1,2,8,7,10,11,12,9]=>{{1,2,3,4,5,6},{7,8},{9,10,11,12}}
[4,3,5,6,1,2,8,9,10,7,12,11]=>{{1,2,3,4,5,6},{7,8,9,10},{11,12}}
[4,3,5,6,1,2,10,9,11,12,7,8]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}}
[4,3,5,6,1,2,8,9,10,11,12,7]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}}
[6,3,7,5,1,8,4,2,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[6,3,7,5,1,8,4,2,10,11,12,9]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[8,3,9,5,1,7,4,10,6,2,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,3,11,5,1,7,4,9,6,12,8,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,3,9,5,1,7,4,10,11,12,6,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,3,7,5,1,8,9,10,4,2,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,3,11,5,1,7,8,9,4,12,6,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,3,9,5,2,10,8,12,11,4,7,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,3,7,5,1,8,9,10,11,12,4,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,3,5,6,7,8,1,2,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[4,3,5,6,7,8,1,2,10,11,12,9]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[8,3,9,5,6,7,1,10,4,2,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,3,11,5,6,7,1,9,4,12,8,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,3,9,5,6,7,1,10,11,12,4,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,3,7,8,6,10,9,2,5,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,3,11,7,6,8,9,4,1,12,5,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,3,9,10,6,12,8,2,11,7,5,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,3,7,8,6,9,10,12,11,5,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,3,5,6,7,8,9,10,1,2,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,3,11,5,6,7,8,9,1,12,4,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,3,9,10,6,7,8,12,11,2,5,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,3,5,8,9,7,12,10,1,11,6,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,3,5,6,7,8,9,10,11,12,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,3,4,5,6,1,8,7,10,9,12,11]=>{{1,2,3,4,5,6},{7,8},{9,10},{11,12}}
[2,3,4,5,6,1,8,7,10,11,12,9]=>{{1,2,3,4,5,6},{7,8},{9,10,11,12}}
[2,3,4,5,6,1,8,9,10,7,12,11]=>{{1,2,3,4,5,6},{7,8,9,10},{11,12}}
[2,3,4,5,6,1,10,9,11,12,7,8]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}}
[2,3,4,5,6,1,8,9,10,11,12,7]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}}
[6,3,4,5,7,8,1,2,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[6,3,4,5,7,8,1,2,10,11,12,9]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[8,3,4,5,9,7,1,10,6,2,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,3,4,5,11,7,1,9,6,12,8,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,3,4,5,9,7,1,10,11,12,6,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,3,4,5,7,8,9,10,1,2,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,3,4,5,11,7,8,9,1,12,6,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,3,4,5,9,10,8,12,11,2,7,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,3,4,5,7,8,9,10,11,12,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,5,4,6,7,1,8,3,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[2,5,4,6,7,1,8,3,10,11,12,9]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[8,5,4,6,7,1,9,10,3,2,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,5,4,6,7,1,11,9,3,12,8,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,5,4,6,7,1,9,10,11,12,3,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,7,4,8,6,1,9,5,10,3,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,7,4,8,6,1,9,5,11,12,3,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,9,4,10,6,1,8,5,11,7,12,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,7,4,8,6,1,9,10,11,5,12,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,5,4,6,7,8,9,1,10,3,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,5,4,6,7,8,9,1,11,12,3,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,9,4,10,6,7,8,1,11,5,12,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,5,4,8,9,7,11,10,3,6,12,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,5,4,6,7,8,9,10,11,1,12,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,3,4,5,6,7,8,1,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[2,3,4,5,6,7,8,1,10,11,12,9]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[8,3,4,5,6,7,9,10,1,2,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,3,4,5,6,7,11,9,1,12,8,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,3,4,5,6,7,9,10,11,12,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,7,4,5,6,8,9,1,10,3,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,7,4,5,6,8,9,1,11,12,3,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,9,4,5,6,10,8,1,11,7,12,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,7,4,5,6,8,9,10,11,1,12,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,3,6,5,7,8,1,9,10,4,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,3,6,5,7,8,1,9,11,12,4,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,9,6,5,7,8,1,10,11,4,12,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,3,8,5,9,7,1,10,6,11,12,4]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,3,6,5,7,8,9,10,1,11,12,4]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,3,4,5,6,7,8,9,10,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[10,3,4,5,6,7,8,9,11,12,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,9,4,5,6,7,8,10,11,1,12,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,3,8,5,6,7,9,10,1,11,12,4]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,3,4,7,6,8,9,1,10,11,12,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,4,3,6,5,8,7,12,11,9,10,2]=>{{1},{2,4,6,8,12},{3},{5},{7},{9,10,11}}
[1,4,3,6,5,10,9,7,8,12,11,2]=>{{1},{2,4,6,10,12},{3},{5},{7,8,9},{11}}
[1,4,3,6,5,12,9,7,11,8,10,2]=>{{1},{2,4,6,12},{3},{5},{7,8,9,10,11}}
[1,4,3,6,5,12,11,10,7,8,9,2]=>{{1},{2,4,6,12},{3},{5},{7,9,11},{8,10}}
[1,4,3,8,7,5,6,10,9,12,11,2]=>{{1},{2,4,8,10,12},{3},{5,6,7},{9},{11}}
[1,4,3,8,7,5,6,12,11,9,10,2]=>{{1},{2,4,8,12},{3},{5,6,7},{9,10,11}}
[1,4,3,10,7,5,9,6,8,12,11,2]=>{{1},{2,4,10,12},{3},{5,6,7,8,9},{11}}
[1,4,3,12,7,5,9,6,11,8,10,2]=>{{1},{2,4,12},{3},{5,6,7,8,9,10,11}}
[1,4,3,12,7,5,11,10,6,8,9,2]=>{{1},{2,4,12},{3},{5,6,7,9,11},{8,10}}
[1,4,3,10,9,8,5,6,7,12,11,2]=>{{1},{2,4,10,12},{3},{5,7,9},{6,8},{11}}
[1,4,3,12,9,8,5,6,11,7,10,2]=>{{1},{2,4,12},{3},{5,7,9,10,11},{6,8}}
[1,4,3,12,11,8,5,10,6,7,9,2]=>{{1},{2,4,12},{3},{5,6,7,8,9,10,11}}
[1,4,3,12,11,10,9,5,6,7,8,2]=>{{1},{2,4,12},{3},{5,8,11},{6,7,9,10}}
[1,6,5,3,4,8,7,10,9,12,11,2]=>{{1},{2,6,8,10,12},{3,4,5},{7},{9},{11}}
[1,6,5,3,4,8,7,12,11,9,10,2]=>{{1},{2,6,8,12},{3,4,5},{7},{9,10,11}}
[1,6,5,3,4,10,9,7,8,12,11,2]=>{{1},{2,6,10,12},{3,4,5},{7,8,9},{11}}
[1,6,5,3,4,12,9,7,11,8,10,2]=>{{1},{2,6,12},{3,4,5},{7,8,9,10,11}}
[1,6,5,3,4,12,11,10,7,8,9,2]=>{{1},{2,6,12},{3,4,5},{7,9,11},{8,10}}
[1,8,5,3,7,4,6,10,9,12,11,2]=>{{1},{2,8,10,12},{3,4,5,6,7},{9},{11}}
[1,8,5,3,7,4,6,12,11,9,10,2]=>{{1},{2,8,12},{3,4,5,6,7},{9,10,11}}
[1,10,5,3,7,4,9,6,8,12,11,2]=>{{1},{2,10,12},{3,4,5,6,7,8,9},{11}}
[1,12,5,3,7,4,9,6,11,8,10,2]=>{{1},{2,12},{3,4,5,6,7,8,9,10,11}}
[1,12,5,3,7,4,11,10,6,8,9,2]=>{{1},{2,12},{3,4,5,6,7,9,11},{8,10}}
[1,10,5,3,9,8,4,6,7,12,11,2]=>{{1},{2,10,12},{3,4,5,7,9},{6,8},{11}}
[1,12,5,3,9,8,4,6,11,7,10,2]=>{{1},{2,12},{3,4,5,7,9,10,11},{6,8}}
[1,12,5,3,11,8,4,10,6,7,9,2]=>{{1},{2,12},{3,4,5,6,7,8,9,10,11}}
[1,12,5,3,11,10,9,4,6,7,8,2]=>{{1},{2,12},{3,4,5,8,11},{6,7,9,10}}
[1,8,7,6,3,4,5,10,9,12,11,2]=>{{1},{2,8,10,12},{3,5,7},{4,6},{9},{11}}
[1,8,7,6,3,4,5,12,11,9,10,2]=>{{1},{2,8,12},{3,5,7},{4,6},{9,10,11}}
[1,10,7,6,3,4,9,5,8,12,11,2]=>{{1},{2,10,12},{3,5,7,8,9},{4,6},{11}}
[1,12,7,6,3,4,9,5,11,8,10,2]=>{{1},{2,12},{3,5,7,8,9,10,11},{4,6}}
[1,12,7,6,3,4,11,10,5,8,9,2]=>{{1},{2,12},{3,5,7,9,11},{4,6},{8,10}}
[1,10,9,6,3,8,4,5,7,12,11,2]=>{{1},{2,10,12},{3,4,5,6,7,8,9},{11}}
[1,12,9,6,3,8,4,5,11,7,10,2]=>{{1},{2,12},{3,4,5,6,7,8,9,10,11}}
[1,12,11,6,3,8,4,10,5,7,9,2]=>{{1},{2,12},{3,5,9,11},{4,6,7,8,10}}
[1,12,11,6,3,10,9,4,5,7,8,2]=>{{1},{2,12},{3,4,5,6,7,8,9,10,11}}
[1,10,9,8,7,3,4,5,6,12,11,2]=>{{1},{2,10,12},{3,6,9},{4,5,7,8},{11}}
[1,12,9,8,7,3,4,5,11,6,10,2]=>{{1},{2,12},{3,6,9,10,11},{4,5,7,8}}
[1,12,11,8,7,3,4,10,5,6,9,2]=>{{1},{2,12},{3,4,5,6,7,8,9,10,11}}
[1,12,11,10,7,3,9,4,5,6,8,2]=>{{1},{2,12},{3,4,6,8,10,11},{5,7,9}}
[1,12,11,10,9,8,3,4,5,6,7,2]=>{{1},{2,12},{3,7,11},{4,6,8,10},{5,9}}
[3,1,2,6,5,8,7,10,9,12,11,4]=>{{1,2,3},{4,6,8,10,12},{5},{7},{9},{11}}
[3,1,2,6,5,8,7,12,11,9,10,4]=>{{1,2,3},{4,6,8,12},{5},{7},{9,10,11}}
[3,1,2,6,5,10,9,7,8,12,11,4]=>{{1,2,3},{4,6,10,12},{5},{7,8,9},{11}}
[3,1,2,6,5,12,9,7,11,8,10,4]=>{{1,2,3},{4,6,12},{5},{7,8,9,10,11}}
[3,1,2,6,5,12,11,10,7,8,9,4]=>{{1,2,3},{4,6,12},{5},{7,9,11},{8,10}}
[3,1,2,8,7,5,6,10,9,12,11,4]=>{{1,2,3},{4,8,10,12},{5,6,7},{9},{11}}
[3,1,2,8,7,5,6,12,11,9,10,4]=>{{1,2,3},{4,8,12},{5,6,7},{9,10,11}}
[3,1,2,10,7,5,9,6,8,12,11,4]=>{{1,2,3},{4,10,12},{5,6,7,8,9},{11}}
[3,1,2,12,7,5,9,6,11,8,10,4]=>{{1,2,3},{4,12},{5,6,7,8,9,10,11}}
[3,1,2,12,7,5,11,10,6,8,9,4]=>{{1,2,3},{4,12},{5,6,7,9,11},{8,10}}
[3,1,2,10,9,8,5,6,7,12,11,4]=>{{1,2,3},{4,10,12},{5,7,9},{6,8},{11}}
[3,1,2,12,9,8,5,6,11,7,10,4]=>{{1,2,3},{4,12},{5,7,9,10,11},{6,8}}
[3,1,2,12,11,8,5,10,6,7,9,4]=>{{1,2,3},{4,12},{5,6,7,8,9,10,11}}
[3,1,2,12,11,10,9,5,6,7,8,4]=>{{1,2,3},{4,12},{5,8,11},{6,7,9,10}}
[3,1,5,2,4,8,7,10,9,12,11,6]=>{{1,2,3,4,5},{6,8,10,12},{7},{9},{11}}
[3,1,5,2,4,8,7,12,11,9,10,6]=>{{1,2,3,4,5},{6,8,12},{7},{9,10,11}}
[3,1,5,2,4,10,9,7,8,12,11,6]=>{{1,2,3,4,5},{6,10,12},{7,8,9},{11}}
[3,1,5,2,4,12,9,7,11,8,10,6]=>{{1,2,3,4,5},{6,12},{7,8,9,10,11}}
[3,1,5,2,4,12,11,10,7,8,9,6]=>{{1,2,3,4,5},{6,12},{7,9,11},{8,10}}
[3,1,5,2,7,4,6,10,9,12,11,8]=>{{1,2,3,4,5,6,7},{8,10,12},{9},{11}}
[3,1,5,2,7,4,6,12,11,9,10,8]=>{{1,2,3,4,5,6,7},{8,12},{9,10,11}}
[3,1,5,2,7,4,9,6,8,12,11,10]=>{{1,2,3,4,5,6,7,8,9},{10,12},{11}}
[3,1,5,2,7,4,9,6,11,8,10,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[3,1,5,2,7,4,11,10,6,8,9,12]=>{{1,2,3,4,5,6,7,9,11},{8,10},{12}}
[3,1,5,2,9,8,4,6,7,12,11,10]=>{{1,2,3,4,5,7,9},{6,8},{10,12},{11}}
[3,1,5,2,9,8,4,6,11,7,10,12]=>{{1,2,3,4,5,7,9,10,11},{6,8},{12}}
[3,1,5,2,11,8,4,10,6,7,9,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[3,1,5,2,11,10,9,4,6,7,8,12]=>{{1,2,3,4,5,8,11},{6,7,9,10},{12}}
[3,1,7,6,2,4,5,10,9,12,11,8]=>{{1,2,3,5,7},{4,6},{8,10,12},{9},{11}}
[3,1,7,6,2,4,5,12,11,9,10,8]=>{{1,2,3,5,7},{4,6},{8,12},{9,10,11}}
[3,1,7,6,2,4,9,5,8,12,11,10]=>{{1,2,3,5,7,8,9},{4,6},{10,12},{11}}
[3,1,7,6,2,4,9,5,11,8,10,12]=>{{1,2,3,5,7,8,9,10,11},{4,6},{12}}
[3,1,7,6,2,4,11,10,5,8,9,12]=>{{1,2,3,5,7,9,11},{4,6},{8,10},{12}}
[3,1,9,6,2,8,4,5,7,12,11,10]=>{{1,2,3,4,5,6,7,8,9},{10,12},{11}}
[3,1,9,6,2,8,4,5,11,7,10,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[3,1,11,6,2,8,4,10,5,7,9,12]=>{{1,2,3,5,9,11},{4,6,7,8,10},{12}}
[3,1,11,6,2,10,9,4,5,7,8,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[3,1,9,8,7,2,4,5,6,12,11,10]=>{{1,2,3,6,9},{4,5,7,8},{10,12},{11}}
[3,1,9,8,7,2,4,5,11,6,10,12]=>{{1,2,3,6,9,10,11},{4,5,7,8},{12}}
[3,1,11,8,7,2,4,10,5,6,9,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[3,1,11,10,7,2,9,4,5,6,8,12]=>{{1,2,3,4,6,8,10,11},{5,7,9},{12}}
[3,1,11,10,9,8,2,4,5,6,7,12]=>{{1,2,3,7,11},{4,6,8,10},{5,9},{12}}
[5,4,1,2,3,8,7,10,9,12,11,6]=>{{1,3,5},{2,4},{6,8,10,12},{7},{9},{11}}
[5,4,1,2,3,8,7,12,11,9,10,6]=>{{1,3,5},{2,4},{6,8,12},{7},{9,10,11}}
[5,4,1,2,3,10,9,7,8,12,11,6]=>{{1,3,5},{2,4},{6,10,12},{7,8,9},{11}}
[5,4,1,2,3,12,9,7,11,8,10,6]=>{{1,3,5},{2,4},{6,12},{7,8,9,10,11}}
[5,4,1,2,3,12,11,10,7,8,9,6]=>{{1,3,5},{2,4},{6,12},{7,9,11},{8,10}}
[5,4,1,2,7,3,6,10,9,12,11,8]=>{{1,3,5,6,7},{2,4},{8,10,12},{9},{11}}
[5,4,1,2,7,3,6,12,11,9,10,8]=>{{1,3,5,6,7},{2,4},{8,12},{9,10,11}}
[5,4,1,2,7,3,9,6,8,12,11,10]=>{{1,3,5,6,7,8,9},{2,4},{10,12},{11}}
[5,4,1,2,7,3,9,6,11,8,10,12]=>{{1,3,5,6,7,8,9,10,11},{2,4},{12}}
[5,4,1,2,7,3,11,10,6,8,9,12]=>{{1,3,5,6,7,9,11},{2,4},{8,10},{12}}
[5,4,1,2,9,8,3,6,7,12,11,10]=>{{1,3,5,7,9},{2,4},{6,8},{10,12},{11}}
[5,4,1,2,9,8,3,6,11,7,10,12]=>{{1,3,5,7,9,10,11},{2,4},{6,8},{12}}
[5,4,1,2,11,8,3,10,6,7,9,12]=>{{1,3,5,6,7,8,9,10,11},{2,4},{12}}
[5,4,1,2,11,10,9,3,6,7,8,12]=>{{1,3,5,8,11},{2,4},{6,7,9,10},{12}}
[7,4,1,6,2,3,5,10,9,12,11,8]=>{{1,2,3,4,5,6,7},{8,10,12},{9},{11}}
[7,4,1,6,2,3,5,12,11,9,10,8]=>{{1,2,3,4,5,6,7},{8,12},{9,10,11}}
[7,4,1,6,2,3,9,5,8,12,11,10]=>{{1,2,3,4,5,6,7,8,9},{10,12},{11}}
[7,4,1,6,2,3,9,5,11,8,10,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[7,4,1,6,2,3,11,10,5,8,9,12]=>{{1,2,3,4,5,6,7,9,11},{8,10},{12}}
[9,4,1,6,2,8,3,5,7,12,11,10]=>{{1,3,7,9},{2,4,5,6,8},{10,12},{11}}
[9,4,1,6,2,8,3,5,11,7,10,12]=>{{1,3,7,9,10,11},{2,4,5,6,8},{12}}
[11,4,1,6,2,8,3,10,5,7,9,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[11,4,1,6,2,10,9,3,5,7,8,12]=>{{1,3,8,11},{2,4,5,6,7,9,10},{12}}
[9,4,1,8,7,2,3,5,6,12,11,10]=>{{1,2,3,4,5,6,7,8,9},{10,12},{11}}
[9,4,1,8,7,2,3,5,11,6,10,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[11,4,1,8,7,2,3,10,5,6,9,12]=>{{1,3,5,7,9,11},{2,4,6,8,10},{12}}
[11,4,1,10,7,2,9,3,5,6,8,12]=>{{1,3,8,11},{2,4,6,10},{5,7,9},{12}}
[11,4,1,10,9,8,2,3,5,6,7,12]=>{{1,2,3,4,6,7,8,10,11},{5,9},{12}}
[7,6,5,1,2,3,4,10,9,12,11,8]=>{{1,4,7},{2,3,5,6},{8,10,12},{9},{11}}
[7,6,5,1,2,3,4,12,11,9,10,8]=>{{1,4,7},{2,3,5,6},{8,12},{9,10,11}}
[7,6,5,1,2,3,9,4,8,12,11,10]=>{{1,4,7,8,9},{2,3,5,6},{10,12},{11}}
[7,6,5,1,2,3,9,4,11,8,10,12]=>{{1,4,7,8,9,10,11},{2,3,5,6},{12}}
[7,6,5,1,2,3,11,10,4,8,9,12]=>{{1,4,7,9,11},{2,3,5,6},{8,10},{12}}
[9,6,5,1,2,8,3,4,7,12,11,10]=>{{1,2,3,4,5,6,7,8,9},{10,12},{11}}
[9,6,5,1,2,8,3,4,11,7,10,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[11,6,5,1,2,8,3,10,4,7,9,12]=>{{1,4,9,11},{2,3,5,6,7,8,10},{12}}
[11,6,5,1,2,10,9,3,4,7,8,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[9,8,5,1,7,2,3,4,6,12,11,10]=>{{1,2,4,6,8,9},{3,5,7},{10,12},{11}}
[9,8,5,1,7,2,3,4,11,6,10,12]=>{{1,2,4,6,8,9,10,11},{3,5,7},{12}}
[11,8,5,1,7,2,3,10,4,6,9,12]=>{{1,4,9,11},{2,6,8,10},{3,5,7},{12}}
[11,10,5,1,7,2,9,3,4,6,8,12]=>{{1,3,4,5,7,8,9,11},{2,6,10},{12}}
[11,10,5,1,9,8,2,3,4,6,7,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[9,8,7,6,1,2,3,4,5,12,11,10]=>{{1,5,9},{2,4,6,8},{3,7},{10,12},{11}}
[9,8,7,6,1,2,3,4,11,5,10,12]=>{{1,5,9,10,11},{2,4,6,8},{3,7},{12}}
[11,8,7,6,1,2,3,10,4,5,9,12]=>{{1,2,4,5,6,8,9,10,11},{3,7},{12}}
[11,10,7,6,1,2,9,3,4,5,8,12]=>{{1,2,3,4,5,6,7,8,9,10,11},{12}}
[11,10,9,6,1,8,2,3,4,5,7,12]=>{{1,2,5,7,10,11},{3,4,6,8,9},{12}}
[11,10,9,8,7,1,2,3,4,5,6,12]=>{{1,6,11},{2,5,7,10},{3,4,8,9},{12}}
[2,4,3,6,5,8,7,10,9,12,11,1]=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}
[12,2,3,4,5,6,7,8,9,10,1,11]=>{{1,11,12},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[3,12,1,4,5,6,7,8,9,10,11,2]=>{{1,3},{2,12},{4},{5},{6},{7},{8},{9},{10},{11}}
[12,3,4,5,6,7,8,9,10,11,1,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,1,4,3,6,5,8,7,11,10,12,9]=>{{1,2},{3,4},{5,6},{7,8},{9,11,12},{10}}
[2,1,4,3,6,5,9,8,10,7,12,11]=>{{1,2},{3,4},{5,6},{7,9,10},{8},{11,12}}
[2,1,4,3,6,5,9,8,11,10,12,7]=>{{1,2},{3,4},{5,6},{7,9,11,12},{8},{10}}
[2,1,4,3,6,5,10,9,11,8,12,7]=>{{1,2},{3,4},{5,6},{7,8,9,10,11,12}}
[2,1,4,3,7,6,8,5,10,9,12,11]=>{{1,2},{3,4},{5,7,8},{6},{9,10},{11,12}}
[2,1,4,3,7,6,8,5,11,10,12,9]=>{{1,2},{3,4},{5,7,8},{6},{9,11,12},{10}}
[2,1,4,3,7,6,9,8,10,5,12,11]=>{{1,2},{3,4},{5,7,9,10},{6},{8},{11,12}}
[2,1,4,3,7,6,9,8,11,10,12,5]=>{{1,2},{3,4},{5,7,9,11,12},{6},{8},{10}}
[2,1,4,3,7,6,10,9,11,8,12,5]=>{{1,2},{3,4},{5,7,8,9,10,11,12},{6}}
[2,1,4,3,8,7,9,6,10,5,12,11]=>{{1,2},{3,4},{5,6,7,8,9,10},{11,12}}
[2,1,4,3,8,7,9,6,11,10,12,5]=>{{1,2},{3,4},{5,6,7,8,9,11,12},{10}}
[2,1,4,3,8,7,10,9,11,6,12,5]=>{{1,2},{3,4},{5,8,9,11,12},{6,7,10}}
[2,1,4,3,9,8,10,7,11,6,12,5]=>{{1,2},{3,4},{5,9,11,12},{6,7,8,10}}
[2,1,5,4,6,3,8,7,10,9,12,11]=>{{1,2},{3,5,6},{4},{7,8},{9,10},{11,12}}
[2,1,5,4,6,3,8,7,11,10,12,9]=>{{1,2},{3,5,6},{4},{7,8},{9,11,12},{10}}
[2,1,5,4,6,3,9,8,10,7,12,11]=>{{1,2},{3,5,6},{4},{7,9,10},{8},{11,12}}
[2,1,5,4,6,3,9,8,11,10,12,7]=>{{1,2},{3,5,6},{4},{7,9,11,12},{8},{10}}
[2,1,5,4,6,3,10,9,11,8,12,7]=>{{1,2},{3,5,6},{4},{7,8,9,10,11,12}}
[2,1,5,4,7,6,8,3,10,9,12,11]=>{{1,2},{3,5,7,8},{4},{6},{9,10},{11,12}}
[2,1,5,4,7,6,8,3,11,10,12,9]=>{{1,2},{3,5,7,8},{4},{6},{9,11,12},{10}}
[2,1,5,4,7,6,9,8,10,3,12,11]=>{{1,2},{3,5,7,9,10},{4},{6},{8},{11,12}}
[2,1,5,4,7,6,9,8,11,10,12,3]=>{{1,2},{3,5,7,9,11,12},{4},{6},{8},{10}}
[2,1,5,4,7,6,10,9,11,8,12,3]=>{{1,2},{3,5,7,8,9,10,11,12},{4},{6}}
[2,1,5,4,8,7,9,6,10,3,12,11]=>{{1,2},{3,5,6,7,8,9,10},{4},{11,12}}
[2,1,5,4,8,7,9,6,11,10,12,3]=>{{1,2},{3,5,6,7,8,9,11,12},{4},{10}}
[2,1,5,4,8,7,10,9,11,6,12,3]=>{{1,2},{3,5,8,9,11,12},{4},{6,7,10}}
[2,1,5,4,9,8,10,7,11,6,12,3]=>{{1,2},{3,5,9,11,12},{4},{6,7,8,10}}
[2,1,6,5,7,4,8,3,10,9,12,11]=>{{1,2},{3,4,5,6,7,8},{9,10},{11,12}}
[2,1,6,5,7,4,8,3,11,10,12,9]=>{{1,2},{3,4,5,6,7,8},{9,11,12},{10}}
[2,1,6,5,7,4,9,8,10,3,12,11]=>{{1,2},{3,4,5,6,7,9,10},{8},{11,12}}
[2,1,6,5,7,4,9,8,11,10,12,3]=>{{1,2},{3,4,5,6,7,9,11,12},{8},{10}}
[2,1,6,5,7,4,10,9,11,8,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,6,5,8,7,9,4,10,3,12,11]=>{{1,2},{3,6,7,9,10},{4,5,8},{11,12}}
[2,1,6,5,8,7,9,4,11,10,12,3]=>{{1,2},{3,6,7,9,11,12},{4,5,8},{10}}
[2,1,6,5,8,7,10,9,11,4,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,6,5,9,8,10,7,11,4,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,7,6,8,5,9,4,10,3,12,11]=>{{1,2},{3,7,9,10},{4,5,6,8},{11,12}}
[2,1,7,6,8,5,9,4,11,10,12,3]=>{{1,2},{3,7,9,11,12},{4,5,6,8},{10}}
[2,1,7,6,8,5,10,9,11,4,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,7,6,9,8,10,5,11,4,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,8,7,9,6,10,5,11,4,12,3]=>{{1,2},{3,5,8,9,11,12},{4,7,10},{6}}
[3,2,4,1,6,5,8,7,10,9,12,11]=>{{1,3,4},{2},{5,6},{7,8},{9,10},{11,12}}
[3,2,4,1,6,5,8,7,11,10,12,9]=>{{1,3,4},{2},{5,6},{7,8},{9,11,12},{10}}
[3,2,4,1,6,5,9,8,10,7,12,11]=>{{1,3,4},{2},{5,6},{7,9,10},{8},{11,12}}
[3,2,4,1,6,5,9,8,11,10,12,7]=>{{1,3,4},{2},{5,6},{7,9,11,12},{8},{10}}
[3,2,4,1,6,5,10,9,11,8,12,7]=>{{1,3,4},{2},{5,6},{7,8,9,10,11,12}}
[3,2,4,1,7,6,8,5,10,9,12,11]=>{{1,3,4},{2},{5,7,8},{6},{9,10},{11,12}}
[3,2,4,1,7,6,8,5,11,10,12,9]=>{{1,3,4},{2},{5,7,8},{6},{9,11,12},{10}}
[3,2,4,1,7,6,9,8,10,5,12,11]=>{{1,3,4},{2},{5,7,9,10},{6},{8},{11,12}}
[3,2,4,1,7,6,9,8,11,10,12,5]=>{{1,3,4},{2},{5,7,9,11,12},{6},{8},{10}}
[3,2,4,1,7,6,10,9,11,8,12,5]=>{{1,3,4},{2},{5,7,8,9,10,11,12},{6}}
[3,2,4,1,8,7,9,6,10,5,12,11]=>{{1,3,4},{2},{5,6,7,8,9,10},{11,12}}
[3,2,4,1,8,7,9,6,11,10,12,5]=>{{1,3,4},{2},{5,6,7,8,9,11,12},{10}}
[3,2,4,1,8,7,10,9,11,6,12,5]=>{{1,3,4},{2},{5,8,9,11,12},{6,7,10}}
[3,2,4,1,9,8,10,7,11,6,12,5]=>{{1,3,4},{2},{5,9,11,12},{6,7,8,10}}
[3,2,5,4,6,1,8,7,10,9,12,11]=>{{1,3,5,6},{2},{4},{7,8},{9,10},{11,12}}
[3,2,5,4,6,1,8,7,11,10,12,9]=>{{1,3,5,6},{2},{4},{7,8},{9,11,12},{10}}
[3,2,5,4,6,1,9,8,10,7,12,11]=>{{1,3,5,6},{2},{4},{7,9,10},{8},{11,12}}
[3,2,5,4,6,1,9,8,11,10,12,7]=>{{1,3,5,6},{2},{4},{7,9,11,12},{8},{10}}
[3,2,5,4,6,1,10,9,11,8,12,7]=>{{1,3,5,6},{2},{4},{7,8,9,10,11,12}}
[3,2,5,4,7,6,8,1,10,9,12,11]=>{{1,3,5,7,8},{2},{4},{6},{9,10},{11,12}}
[3,2,5,4,7,6,8,1,11,10,12,9]=>{{1,3,5,7,8},{2},{4},{6},{9,11,12},{10}}
[3,2,5,4,7,6,9,8,10,1,12,11]=>{{1,3,5,7,9,10},{2},{4},{6},{8},{11,12}}
[3,2,5,4,7,6,9,8,11,10,12,1]=>{{1,3,5,7,9,11,12},{2},{4},{6},{8},{10}}
[3,2,5,4,7,6,10,9,11,8,12,1]=>{{1,3,5,7,8,9,10,11,12},{2},{4},{6}}
[3,2,5,4,8,7,9,6,10,1,12,11]=>{{1,3,5,6,7,8,9,10},{2},{4},{11,12}}
[3,2,5,4,8,7,9,6,11,10,12,1]=>{{1,3,5,6,7,8,9,11,12},{2},{4},{10}}
[3,2,5,4,8,7,10,9,11,6,12,1]=>{{1,3,5,8,9,11,12},{2},{4},{6,7,10}}
[3,2,5,4,9,8,10,7,11,6,12,1]=>{{1,3,5,9,11,12},{2},{4},{6,7,8,10}}
[3,2,6,5,7,4,8,1,10,9,12,11]=>{{1,3,4,5,6,7,8},{2},{9,10},{11,12}}
[3,2,6,5,7,4,8,1,11,10,12,9]=>{{1,3,4,5,6,7,8},{2},{9,11,12},{10}}
[3,2,6,5,7,4,9,8,10,1,12,11]=>{{1,3,4,5,6,7,9,10},{2},{8},{11,12}}
[3,2,6,5,7,4,9,8,11,10,12,1]=>{{1,3,4,5,6,7,9,11,12},{2},{8},{10}}
[3,2,6,5,7,4,10,9,11,8,12,1]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[3,2,6,5,8,7,9,4,10,1,12,11]=>{{1,3,6,7,9,10},{2},{4,5,8},{11,12}}
[3,2,6,5,8,7,9,4,11,10,12,1]=>{{1,3,6,7,9,11,12},{2},{4,5,8},{10}}
[3,2,6,5,8,7,10,9,11,4,12,1]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[3,2,6,5,9,8,10,7,11,4,12,1]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[3,2,7,6,8,5,9,4,10,1,12,11]=>{{1,3,7,9,10},{2},{4,5,6,8},{11,12}}
[3,2,7,6,8,5,9,4,11,10,12,1]=>{{1,3,7,9,11,12},{2},{4,5,6,8},{10}}
[3,2,7,6,8,5,10,9,11,4,12,1]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[3,2,7,6,9,8,10,5,11,4,12,1]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[3,2,8,7,9,6,10,5,11,4,12,1]=>{{1,3,5,8,9,11,12},{2},{4,7,10},{6}}
[4,3,5,2,6,1,8,7,10,9,12,11]=>{{1,2,3,4,5,6},{7,8},{9,10},{11,12}}
[4,3,5,2,6,1,8,7,11,10,12,9]=>{{1,2,3,4,5,6},{7,8},{9,11,12},{10}}
[4,3,5,2,6,1,9,8,10,7,12,11]=>{{1,2,3,4,5,6},{7,9,10},{8},{11,12}}
[4,3,5,2,6,1,9,8,11,10,12,7]=>{{1,2,3,4,5,6},{7,9,11,12},{8},{10}}
[4,3,5,2,6,1,10,9,11,8,12,7]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}}
[4,3,5,2,7,6,8,1,10,9,12,11]=>{{1,2,3,4,5,7,8},{6},{9,10},{11,12}}
[4,3,5,2,7,6,8,1,11,10,12,9]=>{{1,2,3,4,5,7,8},{6},{9,11,12},{10}}
[4,3,5,2,7,6,9,8,10,1,12,11]=>{{1,2,3,4,5,7,9,10},{6},{8},{11,12}}
[4,3,5,2,7,6,9,8,11,10,12,1]=>{{1,2,3,4,5,7,9,11,12},{6},{8},{10}}
[4,3,5,2,7,6,10,9,11,8,12,1]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[4,3,5,2,8,7,9,6,10,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[4,3,5,2,8,7,9,6,11,10,12,1]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}}
[4,3,5,2,8,7,10,9,11,6,12,1]=>{{1,2,3,4,5,8,9,11,12},{6,7,10}}
[4,3,5,2,9,8,10,7,11,6,12,1]=>{{1,2,3,4,5,9,11,12},{6,7,8,10}}
[4,3,6,5,7,2,8,1,10,9,12,11]=>{{1,4,5,7,8},{2,3,6},{9,10},{11,12}}
[4,3,6,5,7,2,8,1,11,10,12,9]=>{{1,4,5,7,8},{2,3,6},{9,11,12},{10}}
[4,3,6,5,7,2,9,8,10,1,12,11]=>{{1,4,5,7,9,10},{2,3,6},{8},{11,12}}
[4,3,6,5,7,2,9,8,11,10,12,1]=>{{1,4,5,7,9,11,12},{2,3,6},{8},{10}}
[4,3,6,5,7,2,10,9,11,8,12,1]=>{{1,4,5,7,8,9,10,11,12},{2,3,6}}
[4,3,6,5,8,7,9,2,10,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[4,3,6,5,8,7,9,2,11,10,12,1]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}}
[4,3,6,5,8,7,10,9,11,2,12,1]=>{{1,4,5,8,9,11,12},{2,3,6,7,10}}
[4,3,6,5,9,8,10,7,11,2,12,1]=>{{1,4,5,9,11,12},{2,3,6,7,8,10}}
[4,3,7,6,8,5,9,2,10,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[4,3,7,6,8,5,9,2,11,10,12,1]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}}
[4,3,7,6,8,5,10,9,11,2,12,1]=>{{1,4,5,6,8,9,11,12},{2,3,7,10}}
[4,3,7,6,9,8,10,5,11,2,12,1]=>{{1,4,5,6,8,9,11,12},{2,3,7,10}}
[4,3,8,7,9,6,10,5,11,2,12,1]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[5,4,6,3,7,2,8,1,10,9,12,11]=>{{1,5,7,8},{2,3,4,6},{9,10},{11,12}}
[5,4,6,3,7,2,8,1,11,10,12,9]=>{{1,5,7,8},{2,3,4,6},{9,11,12},{10}}
[5,4,6,3,7,2,9,8,10,1,12,11]=>{{1,5,7,9,10},{2,3,4,6},{8},{11,12}}
[5,4,6,3,7,2,9,8,11,10,12,1]=>{{1,5,7,9,11,12},{2,3,4,6},{8},{10}}
[5,4,6,3,7,2,10,9,11,8,12,1]=>{{1,5,7,8,9,10,11,12},{2,3,4,6}}
[5,4,6,3,8,7,9,2,10,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[5,4,6,3,8,7,9,2,11,10,12,1]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}}
[5,4,6,3,8,7,10,9,11,2,12,1]=>{{1,5,8,9,11,12},{2,3,4,6,7,10}}
[5,4,6,3,9,8,10,7,11,2,12,1]=>{{1,5,9,11,12},{2,3,4,6,7,8,10}}
[5,4,7,6,8,3,9,2,10,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[5,4,7,6,8,3,9,2,11,10,12,1]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}}
[5,4,7,6,8,3,10,9,11,2,12,1]=>{{1,5,8,9,11,12},{2,3,4,6,7,10}}
[5,4,7,6,9,8,10,3,11,2,12,1]=>{{1,5,9,11,12},{2,3,4,6,7,8,10}}
[5,4,8,7,9,6,10,3,11,2,12,1]=>{{1,5,9,11,12},{2,4,7,10},{3,8},{6}}
[6,5,7,4,8,3,9,2,10,1,12,11]=>{{1,3,6,7,9,10},{2,5,8},{4},{11,12}}
[6,5,7,4,8,3,9,2,11,10,12,1]=>{{1,3,6,7,9,11,12},{2,5,8},{4},{10}}
[6,5,7,4,8,3,10,9,11,2,12,1]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[6,5,7,4,9,8,10,3,11,2,12,1]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[6,5,8,7,9,4,10,3,11,2,12,1]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}}
[7,6,8,5,9,4,10,3,11,2,12,1]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}}
[2,1,4,3,6,5,8,7,11,9,12,10]=>{{1,2},{3,4},{5,6},{7,8},{9,10,11,12}}
[2,1,4,3,6,5,9,7,10,8,12,11]=>{{1,2},{3,4},{5,6},{7,8,9,10},{11,12}}
[2,1,4,3,6,5,9,7,11,8,12,10]=>{{1,2},{3,4},{5,6},{7,8,9,10,11,12}}
[2,1,4,3,6,5,10,7,11,8,12,9]=>{{1,2},{3,4},{5,6},{7,8,10},{9,11,12}}
[2,1,4,3,7,5,8,6,10,9,12,11]=>{{1,2},{3,4},{5,6,7,8},{9,10},{11,12}}
[2,1,4,3,7,5,8,6,11,9,12,10]=>{{1,2},{3,4},{5,6,7,8},{9,10,11,12}}
[2,1,4,3,7,5,9,6,10,8,12,11]=>{{1,2},{3,4},{5,6,7,8,9,10},{11,12}}
[2,1,4,3,7,5,9,6,11,8,12,10]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,3,7,5,10,6,11,8,12,9]=>{{1,2},{3,4},{5,6,7,8,10},{9,11,12}}
[2,1,4,3,8,5,9,6,10,7,12,11]=>{{1,2},{3,4},{5,6,8},{7,9,10},{11,12}}
[2,1,4,3,8,5,9,6,11,7,12,10]=>{{1,2},{3,4},{5,6,8},{7,9,10,11,12}}
[2,1,4,3,8,5,10,6,11,7,12,9]=>{{1,2},{3,4},{5,6,8},{7,10},{9,11,12}}
[2,1,4,3,9,5,10,6,11,7,12,8]=>{{1,2},{3,4},{5,6,8,9,11,12},{7,10}}
[2,1,5,3,6,4,8,7,10,9,12,11]=>{{1,2},{3,4,5,6},{7,8},{9,10},{11,12}}
[2,1,5,3,6,4,8,7,11,9,12,10]=>{{1,2},{3,4,5,6},{7,8},{9,10,11,12}}
[2,1,5,3,6,4,9,7,10,8,12,11]=>{{1,2},{3,4,5,6},{7,8,9,10},{11,12}}
[2,1,5,3,6,4,9,7,11,8,12,10]=>{{1,2},{3,4,5,6},{7,8,9,10,11,12}}
[2,1,5,3,6,4,10,7,11,8,12,9]=>{{1,2},{3,4,5,6},{7,8,10},{9,11,12}}
[2,1,5,3,7,4,8,6,10,9,12,11]=>{{1,2},{3,4,5,6,7,8},{9,10},{11,12}}
[2,1,5,3,7,4,8,6,11,9,12,10]=>{{1,2},{3,4,5,6,7,8},{9,10,11,12}}
[2,1,5,3,7,4,9,6,10,8,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,5,3,7,4,9,6,11,8,12,10]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,5,3,7,4,10,6,11,8,12,9]=>{{1,2},{3,4,5,6,7,8,10},{9,11,12}}
[2,1,5,3,8,4,9,6,10,7,12,11]=>{{1,2},{3,4,5,6,8},{7,9,10},{11,12}}
[2,1,5,3,8,4,9,6,11,7,12,10]=>{{1,2},{3,4,5,6,8},{7,9,10,11,12}}
[2,1,5,3,8,4,10,6,11,7,12,9]=>{{1,2},{3,4,5,6,8},{7,10},{9,11,12}}
[2,1,5,3,9,4,10,6,11,7,12,8]=>{{1,2},{3,4,5,6,8,9,11,12},{7,10}}
[2,1,6,3,7,4,8,5,10,9,12,11]=>{{1,2},{3,4,6},{5,7,8},{9,10},{11,12}}
[2,1,6,3,7,4,8,5,11,9,12,10]=>{{1,2},{3,4,6},{5,7,8},{9,10,11,12}}
[2,1,6,3,7,4,9,5,10,8,12,11]=>{{1,2},{3,4,6},{5,7,8,9,10},{11,12}}
[2,1,6,3,7,4,9,5,11,8,12,10]=>{{1,2},{3,4,6},{5,7,8,9,10,11,12}}
[2,1,6,3,7,4,10,5,11,8,12,9]=>{{1,2},{3,4,6},{5,7,8,10},{9,11,12}}
[2,1,6,3,8,4,9,5,10,7,12,11]=>{{1,2},{3,4,6},{5,8},{7,9,10},{11,12}}
[2,1,6,3,8,4,9,5,11,7,12,10]=>{{1,2},{3,4,6},{5,8},{7,9,10,11,12}}
[2,1,6,3,8,4,10,5,11,7,12,9]=>{{1,2},{3,4,6},{5,8},{7,10},{9,11,12}}
[2,1,6,3,9,4,10,5,11,7,12,8]=>{{1,2},{3,4,6},{5,8,9,11,12},{7,10}}
[2,1,7,3,8,4,9,5,10,6,12,11]=>{{1,2},{3,4,6,7,9,10},{5,8},{11,12}}
[2,1,7,3,8,4,9,5,11,6,12,10]=>{{1,2},{3,4,6,7,9,10,11,12},{5,8}}
[2,1,7,3,8,4,10,5,11,6,12,9]=>{{1,2},{3,4,6,7,10},{5,8},{9,11,12}}
[2,1,7,3,9,4,10,5,11,6,12,8]=>{{1,2},{3,4,6,7,10},{5,8,9,11,12}}
[2,1,8,3,9,4,10,5,11,6,12,7]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[3,1,4,2,6,5,8,7,10,9,12,11]=>{{1,2,3,4},{5,6},{7,8},{9,10},{11,12}}
[3,1,4,2,6,5,8,7,11,9,12,10]=>{{1,2,3,4},{5,6},{7,8},{9,10,11,12}}
[3,1,4,2,6,5,9,7,10,8,12,11]=>{{1,2,3,4},{5,6},{7,8,9,10},{11,12}}
[3,1,4,2,6,5,9,7,11,8,12,10]=>{{1,2,3,4},{5,6},{7,8,9,10,11,12}}
[3,1,4,2,6,5,10,7,11,8,12,9]=>{{1,2,3,4},{5,6},{7,8,10},{9,11,12}}
[3,1,4,2,7,5,8,6,10,9,12,11]=>{{1,2,3,4},{5,6,7,8},{9,10},{11,12}}
[3,1,4,2,7,5,8,6,11,9,12,10]=>{{1,2,3,4},{5,6,7,8},{9,10,11,12}}
[3,1,4,2,7,5,9,6,10,8,12,11]=>{{1,2,3,4},{5,6,7,8,9,10},{11,12}}
[3,1,4,2,7,5,9,6,11,8,12,10]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[3,1,4,2,7,5,10,6,11,8,12,9]=>{{1,2,3,4},{5,6,7,8,10},{9,11,12}}
[3,1,4,2,8,5,9,6,10,7,12,11]=>{{1,2,3,4},{5,6,8},{7,9,10},{11,12}}
[3,1,4,2,8,5,9,6,11,7,12,10]=>{{1,2,3,4},{5,6,8},{7,9,10,11,12}}
[3,1,4,2,8,5,10,6,11,7,12,9]=>{{1,2,3,4},{5,6,8},{7,10},{9,11,12}}
[3,1,4,2,9,5,10,6,11,7,12,8]=>{{1,2,3,4},{5,6,8,9,11,12},{7,10}}
[3,1,5,2,6,4,8,7,10,9,12,11]=>{{1,2,3,4,5,6},{7,8},{9,10},{11,12}}
[3,1,5,2,6,4,8,7,11,9,12,10]=>{{1,2,3,4,5,6},{7,8},{9,10,11,12}}
[3,1,5,2,6,4,9,7,10,8,12,11]=>{{1,2,3,4,5,6},{7,8,9,10},{11,12}}
[3,1,5,2,6,4,9,7,11,8,12,10]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}}
[3,1,5,2,6,4,10,7,11,8,12,9]=>{{1,2,3,4,5,6},{7,8,10},{9,11,12}}
[3,1,5,2,7,4,8,6,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[3,1,5,2,7,4,8,6,11,9,12,10]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[3,1,5,2,7,4,9,6,10,8,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[3,1,5,2,7,4,9,6,11,8,12,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,1,5,2,7,4,10,6,11,8,12,9]=>{{1,2,3,4,5,6,7,8,10},{9,11,12}}
[3,1,5,2,8,4,9,6,10,7,12,11]=>{{1,2,3,4,5,6,8},{7,9,10},{11,12}}
[3,1,5,2,8,4,9,6,11,7,12,10]=>{{1,2,3,4,5,6,8},{7,9,10,11,12}}
[3,1,5,2,8,4,10,6,11,7,12,9]=>{{1,2,3,4,5,6,8},{7,10},{9,11,12}}
[3,1,5,2,9,4,10,6,11,7,12,8]=>{{1,2,3,4,5,6,8,9,11,12},{7,10}}
[3,1,6,2,7,4,8,5,10,9,12,11]=>{{1,2,3,4,6},{5,7,8},{9,10},{11,12}}
[3,1,6,2,7,4,8,5,11,9,12,10]=>{{1,2,3,4,6},{5,7,8},{9,10,11,12}}
[3,1,6,2,7,4,9,5,10,8,12,11]=>{{1,2,3,4,6},{5,7,8,9,10},{11,12}}
[3,1,6,2,7,4,9,5,11,8,12,10]=>{{1,2,3,4,6},{5,7,8,9,10,11,12}}
[3,1,6,2,7,4,10,5,11,8,12,9]=>{{1,2,3,4,6},{5,7,8,10},{9,11,12}}
[3,1,6,2,8,4,9,5,10,7,12,11]=>{{1,2,3,4,6},{5,8},{7,9,10},{11,12}}
[3,1,6,2,8,4,9,5,11,7,12,10]=>{{1,2,3,4,6},{5,8},{7,9,10,11,12}}
[3,1,6,2,8,4,10,5,11,7,12,9]=>{{1,2,3,4,6},{5,8},{7,10},{9,11,12}}
[3,1,6,2,9,4,10,5,11,7,12,8]=>{{1,2,3,4,6},{5,8,9,11,12},{7,10}}
[3,1,7,2,8,4,9,5,10,6,12,11]=>{{1,2,3,4,6,7,9,10},{5,8},{11,12}}
[3,1,7,2,8,4,9,5,11,6,12,10]=>{{1,2,3,4,6,7,9,10,11,12},{5,8}}
[3,1,7,2,8,4,10,5,11,6,12,9]=>{{1,2,3,4,6,7,10},{5,8},{9,11,12}}
[3,1,7,2,9,4,10,5,11,6,12,8]=>{{1,2,3,4,6,7,10},{5,8,9,11,12}}
[3,1,8,2,9,4,10,5,11,6,12,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,1,5,2,6,3,8,7,10,9,12,11]=>{{1,2,4},{3,5,6},{7,8},{9,10},{11,12}}
[4,1,5,2,6,3,8,7,11,9,12,10]=>{{1,2,4},{3,5,6},{7,8},{9,10,11,12}}
[4,1,5,2,6,3,9,7,10,8,12,11]=>{{1,2,4},{3,5,6},{7,8,9,10},{11,12}}
[4,1,5,2,6,3,9,7,11,8,12,10]=>{{1,2,4},{3,5,6},{7,8,9,10,11,12}}
[4,1,5,2,6,3,10,7,11,8,12,9]=>{{1,2,4},{3,5,6},{7,8,10},{9,11,12}}
[4,1,5,2,7,3,8,6,10,9,12,11]=>{{1,2,4},{3,5,6,7,8},{9,10},{11,12}}
[4,1,5,2,7,3,8,6,11,9,12,10]=>{{1,2,4},{3,5,6,7,8},{9,10,11,12}}
[4,1,5,2,7,3,9,6,10,8,12,11]=>{{1,2,4},{3,5,6,7,8,9,10},{11,12}}
[4,1,5,2,7,3,9,6,11,8,12,10]=>{{1,2,4},{3,5,6,7,8,9,10,11,12}}
[4,1,5,2,7,3,10,6,11,8,12,9]=>{{1,2,4},{3,5,6,7,8,10},{9,11,12}}
[4,1,5,2,8,3,9,6,10,7,12,11]=>{{1,2,4},{3,5,6,8},{7,9,10},{11,12}}
[4,1,5,2,8,3,9,6,11,7,12,10]=>{{1,2,4},{3,5,6,8},{7,9,10,11,12}}
[4,1,5,2,8,3,10,6,11,7,12,9]=>{{1,2,4},{3,5,6,8},{7,10},{9,11,12}}
[4,1,5,2,9,3,10,6,11,7,12,8]=>{{1,2,4},{3,5,6,8,9,11,12},{7,10}}
[4,1,6,2,7,3,8,5,10,9,12,11]=>{{1,2,4},{3,6},{5,7,8},{9,10},{11,12}}
[4,1,6,2,7,3,8,5,11,9,12,10]=>{{1,2,4},{3,6},{5,7,8},{9,10,11,12}}
[4,1,6,2,7,3,9,5,10,8,12,11]=>{{1,2,4},{3,6},{5,7,8,9,10},{11,12}}
[4,1,6,2,7,3,9,5,11,8,12,10]=>{{1,2,4},{3,6},{5,7,8,9,10,11,12}}
[4,1,6,2,7,3,10,5,11,8,12,9]=>{{1,2,4},{3,6},{5,7,8,10},{9,11,12}}
[4,1,6,2,8,3,9,5,10,7,12,11]=>{{1,2,4},{3,6},{5,8},{7,9,10},{11,12}}
[4,1,6,2,8,3,9,5,11,7,12,10]=>{{1,2,4},{3,6},{5,8},{7,9,10,11,12}}
[4,1,6,2,8,3,10,5,11,7,12,9]=>{{1,2,4},{3,6},{5,8},{7,10},{9,11,12}}
[4,1,6,2,9,3,10,5,11,7,12,8]=>{{1,2,4},{3,6},{5,8,9,11,12},{7,10}}
[4,1,7,2,8,3,9,5,10,6,12,11]=>{{1,2,4},{3,6,7,9,10},{5,8},{11,12}}
[4,1,7,2,8,3,9,5,11,6,12,10]=>{{1,2,4},{3,6,7,9,10,11,12},{5,8}}
[4,1,7,2,8,3,10,5,11,6,12,9]=>{{1,2,4},{3,6,7,10},{5,8},{9,11,12}}
[4,1,7,2,9,3,10,5,11,6,12,8]=>{{1,2,4},{3,6,7,10},{5,8,9,11,12}}
[4,1,8,2,9,3,10,5,11,6,12,7]=>{{1,2,4},{3,5,6,7,8,9,10,11,12}}
[5,1,6,2,7,3,8,4,10,9,12,11]=>{{1,2,4,5,7,8},{3,6},{9,10},{11,12}}
[5,1,6,2,7,3,8,4,11,9,12,10]=>{{1,2,4,5,7,8},{3,6},{9,10,11,12}}
[5,1,6,2,7,3,9,4,10,8,12,11]=>{{1,2,4,5,7,8,9,10},{3,6},{11,12}}
[5,1,6,2,7,3,9,4,11,8,12,10]=>{{1,2,4,5,7,8,9,10,11,12},{3,6}}
[5,1,6,2,7,3,10,4,11,8,12,9]=>{{1,2,4,5,7,8,10},{3,6},{9,11,12}}
[5,1,6,2,8,3,9,4,10,7,12,11]=>{{1,2,4,5,8},{3,6},{7,9,10},{11,12}}
[5,1,6,2,8,3,9,4,11,7,12,10]=>{{1,2,4,5,8},{3,6},{7,9,10,11,12}}
[5,1,6,2,8,3,10,4,11,7,12,9]=>{{1,2,4,5,8},{3,6},{7,10},{9,11,12}}
[5,1,6,2,9,3,10,4,11,7,12,8]=>{{1,2,4,5,8,9,11,12},{3,6},{7,10}}
[5,1,7,2,8,3,9,4,10,6,12,11]=>{{1,2,4,5,8},{3,6,7,9,10},{11,12}}
[5,1,7,2,8,3,9,4,11,6,12,10]=>{{1,2,4,5,8},{3,6,7,9,10,11,12}}
[5,1,7,2,8,3,10,4,11,6,12,9]=>{{1,2,4,5,8},{3,6,7,10},{9,11,12}}
[5,1,7,2,9,3,10,4,11,6,12,8]=>{{1,2,4,5,8,9,11,12},{3,6,7,10}}
[5,1,8,2,9,3,10,4,11,6,12,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,1,7,2,8,3,9,4,10,5,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[6,1,7,2,8,3,9,4,11,5,12,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,1,7,2,8,3,10,4,11,5,12,9]=>{{1,2,3,4,5,6,7,8,10},{9,11,12}}
[6,1,7,2,9,3,10,4,11,5,12,8]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,1,8,2,9,3,10,4,11,5,12,7]=>{{1,2,3,4,6,8},{5,7,9,10,11,12}}
[1,8,2,9,3,10,4,11,5,12,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,2,9,3,10,4,11,12,5,6,7]=>{{1},{2,3,5,6,8,10,11},{4,7,9,12}}
[1,8,2,9,3,10,11,4,5,12,6,7]=>{{1},{2,3,4,5,8,9},{6,7,10,11,12}}
[1,8,2,9,3,10,11,4,12,5,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,2,9,3,10,11,12,4,5,6,7]=>{{1},{2,3,5,6,7,8,10,11,12},{4,9}}
[1,8,2,9,10,3,4,11,5,12,6,7]=>{{1},{2,3,6,8,11},{4,5,7,9,10,12}}
[1,8,2,9,10,3,4,11,12,5,6,7]=>{{1},{2,3,6,8,11},{4,7,9,12},{5,10}}
[1,8,2,9,10,3,11,4,5,12,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,2,9,10,3,11,4,12,5,6,7]=>{{1},{2,3,4,6,7,8,9,11,12},{5,10}}
[1,8,2,9,10,3,11,12,4,5,6,7]=>{{1},{2,3,6,7,8,11,12},{4,9},{5,10}}
[1,8,2,9,10,11,3,4,5,12,6,7]=>{{1},{2,3,4,5,7,8,9,10,12},{6,11}}
[1,8,2,9,10,11,3,4,12,5,6,7]=>{{1},{2,3,4,7,8,9,12},{5,10},{6,11}}
[1,8,2,9,10,11,3,12,4,5,6,7]=>{{1},{2,3,7,8,12},{4,9},{5,10},{6,11}}
[1,8,2,9,10,11,12,3,4,5,6,7]=>{{1},{2,3,8},{4,9},{5,10},{6,11},{7,12}}
[1,8,9,2,3,10,4,11,5,12,6,7]=>{{1},{2,4,6,7,8,10,11,12},{3,5,9}}
[1,8,9,2,3,10,4,11,12,5,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,9,2,3,10,11,4,5,12,6,7]=>{{1},{2,4,8},{3,5,9},{6,7,10,11,12}}
[1,8,9,2,3,10,11,4,12,5,6,7]=>{{1},{2,4,8},{3,5,6,7,9,10,11,12}}
[1,8,9,2,3,10,11,12,4,5,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,9,2,10,3,4,11,5,12,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,9,2,10,3,4,11,12,5,6,7]=>{{1},{2,3,4,6,7,8,9,11,12},{5,10}}
[1,8,9,2,10,3,11,4,5,12,6,7]=>{{1},{2,4,8},{3,5,6,7,9,10,11,12}}
[1,8,9,2,10,3,11,4,12,5,6,7]=>{{1},{2,4,8},{3,6,7,9,11,12},{5,10}}
[1,8,9,2,10,3,11,12,4,5,6,7]=>{{1},{2,3,4,6,7,8,9,11,12},{5,10}}
[1,8,9,2,10,11,3,4,5,12,6,7]=>{{1},{2,4,8},{3,5,7,9,10,12},{6,11}}
[1,8,9,2,10,11,3,4,12,5,6,7]=>{{1},{2,4,8},{3,7,9,12},{5,10},{6,11}}
[1,8,9,2,10,11,3,12,4,5,6,7]=>{{1},{2,3,4,7,8,9,12},{5,10},{6,11}}
[1,8,9,2,10,11,12,3,4,5,6,7]=>{{1},{2,3,4,8,9},{5,10},{6,11},{7,12}}
[1,8,9,10,2,3,4,11,5,12,6,7]=>{{1},{2,3,5,6,8,9,11},{4,7,10,12}}
[1,8,9,10,2,3,4,11,12,5,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,9,10,2,3,11,4,5,12,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,9,10,2,3,11,4,12,5,6,7]=>{{1},{2,4,5,8,10},{3,6,7,9,11,12}}
[1,8,9,10,2,3,11,12,4,5,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,9,10,2,11,3,4,5,12,6,7]=>{{1},{2,3,4,5,7,8,9,10,12},{6,11}}
[1,8,9,10,2,11,3,4,12,5,6,7]=>{{1},{2,4,5,8,10},{3,7,9,12},{6,11}}
[1,8,9,10,2,11,3,12,4,5,6,7]=>{{1},{2,3,4,5,7,8,9,10,12},{6,11}}
[1,8,9,10,2,11,12,3,4,5,6,7]=>{{1},{2,3,4,5,8,9,10},{6,11},{7,12}}
[1,8,9,10,11,2,3,4,5,12,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,9,10,11,2,3,4,12,5,6,7]=>{{1},{2,4,5,6,8,10,11},{3,7,9,12}}
[1,8,9,10,11,2,3,12,4,5,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,8,9,10,11,2,12,3,4,5,6,7]=>{{1},{2,3,4,5,6,8,9,10,11},{7,12}}
[1,8,9,10,11,12,2,3,4,5,6,7]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[8,1,2,9,3,10,4,11,5,12,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,2,9,3,10,4,11,12,5,6,7]=>{{1,2,3,5,6,8,10,11},{4,7,9,12}}
[8,1,2,9,3,10,11,4,5,12,6,7]=>{{1,2,3,4,5,8,9},{6,7,10,11,12}}
[8,1,2,9,3,10,11,4,12,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,2,9,3,10,11,12,4,5,6,7]=>{{1,2,3,5,6,7,8,10,11,12},{4,9}}
[8,1,2,9,10,3,4,11,5,12,6,7]=>{{1,2,3,6,8,11},{4,5,7,9,10,12}}
[8,1,2,9,10,3,4,11,12,5,6,7]=>{{1,2,3,6,8,11},{4,7,9,12},{5,10}}
[8,1,2,9,10,3,11,4,5,12,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,2,9,10,3,11,4,12,5,6,7]=>{{1,2,3,4,6,7,8,9,11,12},{5,10}}
[8,1,2,9,10,3,11,12,4,5,6,7]=>{{1,2,3,6,7,8,11,12},{4,9},{5,10}}
[8,1,2,9,10,11,3,4,5,12,6,7]=>{{1,2,3,4,5,7,8,9,10,12},{6,11}}
[8,1,2,9,10,11,3,4,12,5,6,7]=>{{1,2,3,4,7,8,9,12},{5,10},{6,11}}
[8,1,2,9,10,11,3,12,4,5,6,7]=>{{1,2,3,7,8,12},{4,9},{5,10},{6,11}}
[8,1,2,9,10,11,12,3,4,5,6,7]=>{{1,2,3,8},{4,9},{5,10},{6,11},{7,12}}
[8,1,9,2,3,10,4,11,5,12,6,7]=>{{1,2,4,6,7,8,10,11,12},{3,5,9}}
[8,1,9,2,3,10,4,11,12,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,9,2,3,10,11,4,5,12,6,7]=>{{1,2,4,8},{3,5,9},{6,7,10,11,12}}
[8,1,9,2,3,10,11,4,12,5,6,7]=>{{1,2,4,8},{3,5,6,7,9,10,11,12}}
[8,1,9,2,3,10,11,12,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,9,2,10,3,4,11,5,12,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,9,2,10,3,4,11,12,5,6,7]=>{{1,2,3,4,6,7,8,9,11,12},{5,10}}
[8,1,9,2,10,3,11,4,5,12,6,7]=>{{1,2,4,8},{3,5,6,7,9,10,11,12}}
[8,1,9,2,10,3,11,4,12,5,6,7]=>{{1,2,4,8},{3,6,7,9,11,12},{5,10}}
[8,1,9,2,10,3,11,12,4,5,6,7]=>{{1,2,3,4,6,7,8,9,11,12},{5,10}}
[8,1,9,2,10,11,3,4,5,12,6,7]=>{{1,2,4,8},{3,5,7,9,10,12},{6,11}}
[8,1,9,2,10,11,3,4,12,5,6,7]=>{{1,2,4,8},{3,7,9,12},{5,10},{6,11}}
[8,1,9,2,10,11,3,12,4,5,6,7]=>{{1,2,3,4,7,8,9,12},{5,10},{6,11}}
[8,1,9,2,10,11,12,3,4,5,6,7]=>{{1,2,3,4,8,9},{5,10},{6,11},{7,12}}
[8,1,9,10,2,3,4,11,5,12,6,7]=>{{1,2,3,5,6,8,9,11},{4,7,10,12}}
[8,1,9,10,2,3,4,11,12,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,9,10,2,3,11,4,5,12,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,9,10,2,3,11,4,12,5,6,7]=>{{1,2,4,5,8,10},{3,6,7,9,11,12}}
[8,1,9,10,2,3,11,12,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,9,10,2,11,3,4,5,12,6,7]=>{{1,2,3,4,5,7,8,9,10,12},{6,11}}
[8,1,9,10,2,11,3,4,12,5,6,7]=>{{1,2,4,5,8,10},{3,7,9,12},{6,11}}
[8,1,9,10,2,11,3,12,4,5,6,7]=>{{1,2,3,4,5,7,8,9,10,12},{6,11}}
[8,1,9,10,2,11,12,3,4,5,6,7]=>{{1,2,3,4,5,8,9,10},{6,11},{7,12}}
[8,1,9,10,11,2,3,4,5,12,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,9,10,11,2,3,4,12,5,6,7]=>{{1,2,4,5,6,8,10,11},{3,7,9,12}}
[8,1,9,10,11,2,3,12,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,9,10,11,2,12,3,4,5,6,7]=>{{1,2,3,4,5,6,8,9,10,11},{7,12}}
[8,1,9,10,11,12,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,1,2,3,10,4,11,5,12,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,1,2,3,10,4,11,12,5,6,7]=>{{1,3,5,6,8,10,11},{2,4,7,9,12}}
[8,9,1,2,3,10,11,4,5,12,6,7]=>{{1,2,3,4,5,8,9},{6,7,10,11,12}}
[8,9,1,2,3,10,11,4,12,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,1,2,3,10,11,12,4,5,6,7]=>{{1,3,5,6,7,8,10,11,12},{2,4,9}}
[8,9,1,2,10,3,4,11,5,12,6,7]=>{{1,3,6,8,11},{2,4,5,7,9,10,12}}
[8,9,1,2,10,3,4,11,12,5,6,7]=>{{1,3,6,8,11},{2,4,7,9,12},{5,10}}
[8,9,1,2,10,3,11,4,5,12,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,1,2,10,3,11,4,12,5,6,7]=>{{1,2,3,4,6,7,8,9,11,12},{5,10}}
[8,9,1,2,10,3,11,12,4,5,6,7]=>{{1,3,6,7,8,11,12},{2,4,9},{5,10}}
[8,9,1,2,10,11,3,4,5,12,6,7]=>{{1,2,3,4,5,7,8,9,10,12},{6,11}}
[8,9,1,2,10,11,3,4,12,5,6,7]=>{{1,2,3,4,7,8,9,12},{5,10},{6,11}}
[8,9,1,2,10,11,3,12,4,5,6,7]=>{{1,3,7,8,12},{2,4,9},{5,10},{6,11}}
[8,9,1,2,10,11,12,3,4,5,6,7]=>{{1,3,8},{2,4,9},{5,10},{6,11},{7,12}}
[8,9,1,10,2,3,4,11,5,12,6,7]=>{{1,3,6,8,11},{2,5,9},{4,7,10,12}}
[8,9,1,10,2,3,4,11,12,5,6,7]=>{{1,3,6,8,11},{2,4,5,7,9,10,12}}
[8,9,1,10,2,3,11,4,5,12,6,7]=>{{1,3,4,6,7,8,10,11,12},{2,5,9}}
[8,9,1,10,2,3,11,4,12,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,1,10,2,3,11,12,4,5,6,7]=>{{1,3,6,7,8,11,12},{2,4,5,9,10}}
[8,9,1,10,2,11,3,4,5,12,6,7]=>{{1,3,4,7,8,10,12},{2,5,9},{6,11}}
[8,9,1,10,2,11,3,4,12,5,6,7]=>{{1,2,3,4,5,7,8,9,10,12},{6,11}}
[8,9,1,10,2,11,3,12,4,5,6,7]=>{{1,3,7,8,12},{2,4,5,9,10},{6,11}}
[8,9,1,10,2,11,12,3,4,5,6,7]=>{{1,3,8},{2,4,5,9,10},{6,11},{7,12}}
[8,9,1,10,11,2,3,4,5,12,6,7]=>{{1,3,4,7,8,10,12},{2,5,6,9,11}}
[8,9,1,10,11,2,3,4,12,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,1,10,11,2,3,12,4,5,6,7]=>{{1,3,7,8,12},{2,4,5,6,9,10,11}}
[8,9,1,10,11,2,12,3,4,5,6,7]=>{{1,3,8},{2,4,5,6,9,10,11},{7,12}}
[8,9,1,10,11,12,2,3,4,5,6,7]=>{{1,3,8},{2,4,5,6,7,9,10,11,12}}
[8,9,10,1,2,3,4,11,5,12,6,7]=>{{1,3,4,6,7,8,10,11,12},{2,5,9}}
[8,9,10,1,2,3,4,11,12,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,1,2,3,11,4,5,12,6,7]=>{{1,4,8},{2,5,9},{3,6,7,10,11,12}}
[8,9,10,1,2,3,11,4,12,5,6,7]=>{{1,4,8},{2,3,5,6,7,9,10,11,12}}
[8,9,10,1,2,3,11,12,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,1,2,11,3,4,5,12,6,7]=>{{1,4,8},{2,5,9},{3,7,10,12},{6,11}}
[8,9,10,1,2,11,3,4,12,5,6,7]=>{{1,4,8},{2,3,5,7,9,10,12},{6,11}}
[8,9,10,1,2,11,3,12,4,5,6,7]=>{{1,2,3,4,5,7,8,9,10,12},{6,11}}
[8,9,10,1,2,11,12,3,4,5,6,7]=>{{1,2,3,4,5,8,9,10},{6,11},{7,12}}
[8,9,10,1,11,2,3,4,5,12,6,7]=>{{1,4,8},{2,5,6,9,11},{3,7,10,12}}
[8,9,10,1,11,2,3,4,12,5,6,7]=>{{1,4,8},{2,3,5,6,7,9,10,11,12}}
[8,9,10,1,11,2,3,12,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,1,11,2,12,3,4,5,6,7]=>{{1,2,3,4,5,6,8,9,10,11},{7,12}}
[8,9,10,1,11,12,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,11,1,2,3,4,5,12,6,7]=>{{1,2,4,5,6,8,9,11},{3,7,10,12}}
[8,9,10,11,1,2,3,4,12,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,11,1,2,3,12,4,5,6,7]=>{{1,3,5,7,8,10,12},{2,4,6,9,11}}
[8,9,10,11,1,2,12,3,4,5,6,7]=>{{1,3,5,8,10},{2,4,6,9,11},{7,12}}
[8,9,10,11,1,12,2,3,4,5,6,7]=>{{1,3,5,8,10},{2,4,6,7,9,11,12}}
[8,9,10,11,12,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,10,8,6,4,2,1,3,5,7,9,11]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}}
[11,12,8,6,4,2,1,3,5,7,10,9]=>{{1,7,10,11},{2,4,5,6,9,12},{3,8}}
[12,9,10,6,4,2,1,3,5,8,7,11]=>{{1,7,11,12},{2,4,5,6,9},{3,8,10}}
[11,9,12,6,4,2,1,3,5,8,10,7]=>{{1,3,7,8,10,11,12},{2,4,5,6,9}}
[10,11,12,6,4,2,1,3,5,9,8,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,10,7,8,4,2,1,3,6,5,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,7,8,4,2,1,3,6,5,10,9]=>{{1,3,4,5,7,8,10,11},{2,6,9,12}}
[12,9,7,10,4,2,1,3,6,8,5,11]=>{{1,3,4,5,7,8,10,11,12},{2,6,9}}
[11,9,7,12,4,2,1,3,6,8,10,5]=>{{1,3,7,8,10,11},{2,6,9},{4,5,12}}
[10,11,7,12,4,2,1,3,6,9,8,5]=>{{1,2,3,6,7,8,9,10,11},{4,5,12}}
[12,8,9,10,4,2,1,3,7,6,5,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,8,9,12,4,2,1,3,7,6,10,5]=>{{1,2,3,6,7,8,9,10,11},{4,5,12}}
[10,8,11,12,4,2,1,3,7,9,6,5]=>{{1,7,9,10},{2,3,6,8,11},{4,5,12}}
[9,10,11,12,4,2,1,3,8,7,6,5]=>{{1,2,3,6,7,8,9,10,11},{4,5,12}}
[12,10,8,5,6,2,1,4,3,7,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,8,5,6,2,1,4,3,7,10,9]=>{{1,7,10,11},{2,3,4,5,6,8,9,12}}
[12,9,10,5,6,2,1,4,3,8,7,11]=>{{1,7,11,12},{2,3,4,5,6,8,9,10}}
[11,9,12,5,6,2,1,4,3,8,10,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,11,12,5,6,2,1,4,3,9,8,7]=>{{1,3,7,9,10,12},{2,4,5,6,8,11}}
[12,10,7,5,8,2,1,4,6,3,9,11]=>{{1,2,3,6,7,9,10,11,12},{4,5,8}}
[11,12,7,5,8,2,1,4,6,3,10,9]=>{{1,3,7,10,11},{2,6,9,12},{4,5,8}}
[12,9,7,5,10,2,1,4,6,8,3,11]=>{{1,3,7,11,12},{2,6,9},{4,5,8,10}}
[11,9,7,5,12,2,1,4,6,8,10,3]=>{{1,3,4,5,7,8,10,11,12},{2,6,9}}
[10,11,7,5,12,2,1,4,6,9,8,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,8,9,5,10,2,1,4,7,6,3,11]=>{{1,3,7,9,11,12},{2,4,5,6,8,10}}
[11,8,9,5,12,2,1,4,7,6,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,8,11,5,12,2,1,4,7,9,6,3]=>{{1,7,9,10},{2,3,4,5,6,8,11,12}}
[9,10,11,5,12,2,1,4,8,7,6,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,10,6,7,8,2,1,5,4,3,9,11]=>{{1,4,7,9,11,12},{2,3,6,10},{5,8}}
[11,12,6,7,8,2,1,5,4,3,10,9]=>{{1,2,3,4,6,7,9,10,11,12},{5,8}}
[12,9,6,7,10,2,1,5,4,8,3,11]=>{{1,2,3,4,6,7,9,11,12},{5,8,10}}
[11,9,6,7,12,2,1,5,4,8,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,11,6,7,12,2,1,5,4,9,8,3]=>{{1,4,7,9,10},{2,3,5,6,8,11,12}}
[12,8,6,9,10,2,1,5,7,4,3,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,8,6,9,12,2,1,5,7,4,10,3]=>{{1,4,7,9,10,11},{2,3,5,6,8,12}}
[10,8,6,11,12,2,1,5,7,9,4,3]=>{{1,7,9,10},{2,3,5,6,8,12},{4,11}}
[9,10,6,11,12,2,1,5,8,7,4,3]=>{{1,2,3,5,6,7,8,9,10,12},{4,11}}
[12,7,8,9,10,2,1,6,5,4,3,11]=>{{1,2,3,6,7,8,11,12},{4,5,9,10}}
[11,7,8,9,12,2,1,6,5,4,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,7,8,11,12,2,1,6,5,9,4,3]=>{{1,2,3,5,6,7,8,9,10,12},{4,11}}
[9,7,10,11,12,2,1,6,8,5,4,3]=>{{1,2,6,7,8,9},{3,5,10,12},{4,11}}
[8,9,10,11,12,2,1,7,6,5,4,3]=>{{1,7,8},{2,6,9},{3,5,10,12},{4,11}}
[12,10,8,6,3,4,2,1,5,7,9,11]=>{{1,3,5,8,9,11,12},{2,7,10},{4,6}}
[11,12,8,6,3,4,2,1,5,7,10,9]=>{{1,2,3,5,7,8,9,10,11,12},{4,6}}
[12,9,10,6,3,4,2,1,5,8,7,11]=>{{1,2,3,5,7,8,9,10,11,12},{4,6}}
[11,9,12,6,3,4,2,1,5,8,10,7]=>{{1,8,10,11},{2,3,5,7,9,12},{4,6}}
[10,11,12,6,3,4,2,1,5,9,8,7]=>{{1,2,3,5,7,8,9,10,11,12},{4,6}}
[12,10,7,8,3,4,2,1,6,5,9,11]=>{{1,4,6,8,9,11,12},{2,3,5,7,10}}
[11,12,7,8,3,4,2,1,6,5,10,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,9,7,10,3,4,2,1,6,8,5,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,9,7,12,3,4,2,1,6,8,10,5]=>{{1,8,10,11},{2,3,4,5,6,7,9,12}}
[10,11,7,12,3,4,2,1,6,9,8,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,8,9,10,3,4,2,1,7,6,5,11]=>{{1,2,3,5,7,8,9,11,12},{4,6,10}}
[11,8,9,12,3,4,2,1,7,6,10,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,8,11,12,3,4,2,1,7,9,6,5]=>{{1,2,7,8,9,10},{3,4,5,6,11,12}}
[9,10,11,12,3,4,2,1,8,7,6,5]=>{{1,8,9},{2,7,10},{3,4,5,6,11,12}}
[12,10,8,5,3,6,2,4,1,7,9,11]=>{{1,9,11,12},{2,7,10},{3,4,5,8},{6}}
[11,12,8,5,3,6,2,4,1,7,10,9]=>{{1,2,7,9,10,11,12},{3,4,5,8},{6}}
[12,9,10,5,3,6,2,4,1,8,7,11]=>{{1,2,7,9,11,12},{3,4,5,8,10},{6}}
[11,9,12,5,3,6,2,4,1,8,10,7]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[10,11,12,5,3,6,2,4,1,9,8,7]=>{{1,9,10},{2,3,4,5,7,8,11,12},{6}}
[12,10,7,5,3,8,2,4,6,1,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,7,5,3,8,2,4,6,1,10,9]=>{{1,10,11},{2,3,4,5,6,7,8,9,12}}
[12,9,7,5,3,10,2,4,6,8,1,11]=>{{1,11,12},{2,3,4,5,6,7,8,9,10}}
[11,9,7,5,3,12,2,4,6,8,10,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,11,7,5,3,12,2,4,6,9,8,1]=>{{1,6,9,10,12},{2,3,4,5,7,8,11}}
[12,8,9,5,3,10,2,4,7,6,1,11]=>{{1,11,12},{2,3,4,5,7,8,9},{6,10}}
[11,8,9,5,3,12,2,4,7,6,10,1]=>{{1,6,10,11,12},{2,3,4,5,7,8,9}}
[10,8,11,5,3,12,2,4,7,9,6,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[9,10,11,5,3,12,2,4,8,7,6,1]=>{{1,3,4,5,6,8,9,11,12},{2,7,10}}
[12,10,6,7,3,8,2,5,4,1,9,11]=>{{1,2,4,7,9,10,11,12},{3,5,6,8}}
[11,12,6,7,3,8,2,5,4,1,10,9]=>{{1,10,11},{2,4,7,9,12},{3,5,6,8}}
[12,9,6,7,3,10,2,5,4,8,1,11]=>{{1,11,12},{2,4,7,9},{3,5,6,8,10}}
[11,9,6,7,3,12,2,5,4,8,10,1]=>{{1,3,5,6,8,10,11,12},{2,4,7,9}}
[10,11,6,7,3,12,2,5,4,9,8,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,8,6,9,3,10,2,5,7,4,1,11]=>{{1,11,12},{2,3,4,5,6,7,8,9,10}}
[11,8,6,9,3,12,2,5,7,4,10,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,8,6,11,3,12,2,5,7,9,4,1]=>{{1,2,3,5,6,7,8,9,10,12},{4,11}}
[9,10,6,11,3,12,2,5,8,7,4,1]=>{{1,3,5,6,8,9,12},{2,7,10},{4,11}}
[12,7,8,9,3,10,2,6,5,4,1,11]=>{{1,11,12},{2,7},{3,4,5,6,8,9,10}}
[11,7,8,9,3,12,2,6,5,4,10,1]=>{{1,3,4,5,6,8,9,10,11,12},{2,7}}
[10,7,8,11,3,12,2,6,5,9,4,1]=>{{1,3,5,6,8,9,10,12},{2,7},{4,11}}
[9,7,10,11,3,12,2,6,8,5,4,1]=>{{1,6,8,9,12},{2,7},{3,5,10},{4,11}}
[8,9,10,11,3,12,2,7,6,5,4,1]=>{{1,2,6,7,8,9,12},{3,5,10},{4,11}}
[12,10,8,4,5,6,3,2,1,7,9,11]=>{{1,9,11,12},{2,3,7,8,10},{4},{5},{6}}
[11,12,8,4,5,6,3,2,1,7,10,9]=>{{1,2,3,7,8,9,10,11,12},{4},{5},{6}}
[12,9,10,4,5,6,3,2,1,8,7,11]=>{{1,2,3,7,8,9,10,11,12},{4},{5},{6}}
[11,9,12,4,5,6,3,2,1,8,10,7]=>{{1,2,8,9,10,11},{3,7,12},{4},{5},{6}}
[10,11,12,4,5,6,3,2,1,9,8,7]=>{{1,9,10},{2,8,11},{3,7,12},{4},{5},{6}}
[12,10,7,4,5,8,3,2,6,1,9,11]=>{{1,2,6,8,9,10,11,12},{3,7},{4},{5}}
[11,12,7,4,5,8,3,2,6,1,10,9]=>{{1,10,11},{2,6,8,9,12},{3,7},{4},{5}}
[12,9,7,4,5,10,3,2,6,8,1,11]=>{{1,11,12},{2,6,8,9,10},{3,7},{4},{5}}
[11,9,7,4,5,12,3,2,6,8,10,1]=>{{1,2,6,8,9,10,11,12},{3,7},{4},{5}}
[10,11,7,4,5,12,3,2,6,9,8,1]=>{{1,6,9,10,12},{2,8,11},{3,7},{4},{5}}
[12,8,9,4,5,10,3,2,7,6,1,11]=>{{1,11,12},{2,8},{3,7,9},{4},{5},{6,10}}
[11,8,9,4,5,12,3,2,7,6,10,1]=>{{1,6,10,11,12},{2,8},{3,7,9},{4},{5}}
[10,8,11,4,5,12,3,2,7,9,6,1]=>{{1,3,6,7,9,10,11,12},{2,8},{4},{5}}
[9,10,11,4,5,12,3,2,8,7,6,1]=>{{1,2,3,6,7,8,9,10,11,12},{4},{5}}
[12,10,6,4,7,8,3,5,2,1,9,11]=>{{1,2,9,10,11,12},{3,5,6,7,8},{4}}
[11,12,6,4,7,8,3,5,2,1,10,9]=>{{1,10,11},{2,9,12},{3,5,6,7,8},{4}}
[12,9,6,4,7,10,3,5,2,8,1,11]=>{{1,11,12},{2,9},{3,5,6,7,8,10},{4}}
[11,9,6,4,7,12,3,5,2,8,10,1]=>{{1,3,5,6,7,8,10,11,12},{2,9},{4}}
[10,11,6,4,7,12,3,5,2,9,8,1]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[12,8,6,4,9,10,3,5,7,2,1,11]=>{{1,11,12},{2,3,5,6,7,8,9,10},{4}}
[11,8,6,4,9,12,3,5,7,2,10,1]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[10,8,6,4,11,12,3,5,7,9,2,1]=>{{1,3,6,7,9,10,12},{2,5,8,11},{4}}
[9,10,6,4,11,12,3,5,8,7,2,1]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[12,7,8,4,9,10,3,6,5,2,1,11]=>{{1,11,12},{2,3,6,7,8,10},{4},{5,9}}
[11,7,8,4,9,12,3,6,5,2,10,1]=>{{1,2,3,6,7,8,10,11,12},{4},{5,9}}
[10,7,8,4,11,12,3,6,5,9,2,1]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[9,7,10,4,11,12,3,6,8,5,2,1]=>{{1,6,8,9,12},{2,3,5,7,10,11},{4}}
[8,9,10,4,11,12,3,7,6,5,2,1]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[12,10,5,6,7,8,4,3,2,1,9,11]=>{{1,2,9,10,11,12},{3,4,5,6,7,8}}
[11,12,5,6,7,8,4,3,2,1,10,9]=>{{1,10,11},{2,9,12},{3,4,5,6,7,8}}
[12,9,5,6,7,10,4,3,2,8,1,11]=>{{1,11,12},{2,9},{3,4,5,6,7,8,10}}
[11,9,5,6,7,12,4,3,2,8,10,1]=>{{1,3,4,5,6,7,8,10,11,12},{2,9}}
[10,11,5,6,7,12,4,3,2,9,8,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,8,5,6,9,10,4,3,7,2,1,11]=>{{1,11,12},{2,3,4,5,6,7,8,9,10}}
[11,8,5,6,9,12,4,3,7,2,10,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,8,5,6,11,12,4,3,7,9,2,1]=>{{1,4,6,7,9,10,12},{2,3,5,8,11}}
[9,10,5,6,11,12,4,3,8,7,2,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,7,5,8,9,10,4,6,3,2,1,11]=>{{1,11,12},{2,4,6,7,8,10},{3,5,9}}
[11,7,5,8,9,12,4,6,3,2,10,1]=>{{1,2,4,6,7,8,10,11,12},{3,5,9}}
[10,7,5,8,11,12,4,6,3,9,2,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[9,7,5,10,11,12,4,6,8,3,2,1]=>{{1,6,8,9,12},{2,3,4,5,7,10,11}}
[8,9,5,10,11,12,4,7,6,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,6,7,8,9,10,5,4,3,2,1,11]=>{{1,11,12},{2,6,10},{3,5,7,9},{4,8}}
[11,6,7,8,9,12,5,4,3,2,10,1]=>{{1,2,6,10,11,12},{3,5,7,9},{4,8}}
[10,6,7,8,11,12,5,4,3,9,2,1]=>{{1,2,3,5,6,7,9,10,11,12},{4,8}}
[9,6,7,10,11,12,5,4,8,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,6,9,10,11,12,5,7,4,3,2,1]=>{{1,2,5,6,7,8,11,12},{3,4,9,10}}
[2,3,4,5,6,7,8,9,12,11,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,10,8,6,4,2,1,3,5,7,9]=>{{1,3,4,5,6,8,9,10,12},{2,7,11}}
[12,10,9,8,6,4,2,1,3,5,7,11]=>{{1,2,4,5,6,7,8,10,11,12},{3,9}}
[12,9,11,8,6,4,2,1,3,5,10,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,10,9,8,6,4,2,1,3,5,7]=>{{1,4,7,9,12},{2,5,8,11},{3,10},{6}}
[12,10,8,7,6,4,2,1,3,5,9,11]=>{{1,3,8,9,11,12},{2,4,5,6,7,10}}
[12,11,10,8,7,6,4,2,1,3,5,9]=>{{1,9,12},{2,4,5,7,8,11},{3,10},{6}}
[12,10,7,9,6,4,2,1,3,8,5,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,7,11,9,6,4,2,1,3,8,10,5]=>{{1,3,4,5,6,8,9,10,11,12},{2,7}}
[12,11,10,7,9,6,4,2,1,3,8,5]=>{{1,5,9,12},{2,8,11},{3,10},{4,7},{6}}
[12,10,9,8,7,6,4,2,1,3,5,11]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[12,9,11,8,7,6,4,2,1,3,10,5]=>{{1,2,4,5,7,8,9,12},{3,10,11},{6}}
[12,8,11,10,7,9,4,2,1,3,6,5]=>{{1,3,4,5,6,7,9,10,11,12},{2,8}}
[12,11,10,9,8,7,6,4,2,1,3,5]=>{{1,2,3,4,5,8,9,10,11,12},{6,7}}
[12,10,8,6,5,4,2,1,3,7,9,11]=>{{1,3,8,9,11,12},{2,7,10},{4,6},{5}}
[12,11,10,8,6,5,4,2,1,3,7,9]=>{{1,9,12},{2,4,7,8,11},{3,10},{5,6}}
[12,10,9,8,6,5,4,2,1,3,7,11]=>{{1,2,3,4,7,8,9,10,11,12},{5,6}}
[12,9,11,8,6,5,4,2,1,3,10,7]=>{{1,2,4,7,8,9,12},{3,10,11},{5,6}}
[12,11,10,9,8,6,5,4,2,1,3,7]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[12,10,8,5,7,4,2,1,6,3,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,10,8,5,7,4,2,1,6,3,9]=>{{1,9,12},{2,3,4,6,7,8,10,11},{5}}
[12,10,5,9,7,4,2,1,6,8,3,11]=>{{1,2,3,5,7,8,10,11,12},{4,6,9}}
[12,5,11,9,7,4,2,1,6,8,10,3]=>{{1,3,8,10,11,12},{2,5,7},{4,6,9}}
[12,11,10,5,9,7,4,2,1,6,8,3]=>{{1,3,4,5,6,7,9,10,12},{2,8,11}}
[12,10,9,8,5,7,4,2,1,6,3,11]=>{{1,3,9,11,12},{2,4,6,7,8,10},{5}}
[12,9,11,8,5,7,4,2,1,6,10,3]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[12,11,5,10,8,7,4,2,1,9,6,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,10,9,8,5,7,4,2,1,6,3]=>{{1,3,10,12},{2,4,5,6,8,9,11},{7}}
[12,10,8,7,6,5,4,2,1,3,9,11]=>{{1,9,11,12},{2,3,8,10},{4,7},{5,6}}
[12,11,10,8,7,6,5,4,2,1,3,9]=>{{1,2,3,9,10,11,12},{4,8},{5,7},{6}}
[12,10,7,9,6,5,4,2,1,8,3,11]=>{{1,3,4,7,9,11,12},{2,8,10},{5,6}}
[12,7,11,9,6,5,4,2,1,8,10,3]=>{{1,2,3,4,7,8,9,10,11,12},{5,6}}
[12,11,10,7,9,6,5,4,2,1,8,3]=>{{1,3,10,12},{2,4,5,7,8,9,11},{6}}
[12,10,6,9,8,5,7,2,1,4,3,11]=>{{1,2,3,4,5,6,8,9,10,11,12},{7}}
[12,6,11,9,8,5,7,2,1,4,10,3]=>{{1,3,4,9,10,11,12},{2,5,6,8},{7}}
[12,6,11,8,10,5,7,2,1,9,4,3]=>{{1,2,3,4,5,6,8,9,10,11,12},{7}}
[12,11,10,6,9,8,5,7,2,1,4,3]=>{{1,3,10,12},{2,4,5,6,7,8,9,11}}
[12,10,9,8,7,6,5,4,2,1,3,11]=>{{1,2,3,9,10,11,12},{4,8},{5,7},{6}}
[12,9,11,8,7,6,5,4,2,1,10,3]=>{{1,3,10,11,12},{2,9},{4,8},{5,7},{6}}
[12,8,11,10,7,6,5,9,2,1,4,3]=>{{1,3,4,10,11,12},{2,8,9},{5,7},{6}}
[12,7,11,10,9,6,8,5,2,1,4,3]=>{{1,3,4,10,11,12},{2,5,7,8,9},{6}}
[12,11,10,9,8,7,6,5,4,2,1,3]=>{{1,2,3,10,11,12},{4,9},{5,8},{6,7}}
[12,10,8,6,4,3,2,1,5,7,9,11]=>{{1,3,4,5,6,8,9,11,12},{2,7,10}}
[12,11,10,8,6,4,3,2,1,5,7,9]=>{{1,9,12},{2,3,4,5,6,7,8,10,11}}
[12,10,9,8,6,4,3,2,1,5,7,11]=>{{1,3,7,9,11,12},{2,4,5,6,8,10}}
[12,9,11,8,6,4,3,2,1,5,10,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,10,9,8,6,4,3,2,1,5,7]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[12,10,8,7,6,4,3,2,1,5,9,11]=>{{1,9,11,12},{2,3,4,5,6,7,8,10}}
[12,11,10,8,7,6,4,3,2,1,5,9]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[12,10,7,9,6,4,3,2,1,8,5,11]=>{{1,4,5,6,9,11,12},{2,8,10},{3,7}}
[12,7,11,9,6,4,3,2,1,8,10,5]=>{{1,4,5,6,9,12},{2,3,7,8,10,11}}
[12,11,10,7,9,6,4,3,2,1,8,5]=>{{1,2,3,5,8,9,10,11,12},{4,7},{6}}
[12,10,9,8,7,6,4,3,2,1,5,11]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[12,9,11,8,7,6,4,3,2,1,10,5]=>{{1,3,4,5,7,8,10,11,12},{2,9},{6}}
[12,8,11,10,7,9,4,3,2,1,6,5]=>{{1,4,5,7,10,12},{2,3,6,8,9,11}}
[12,11,10,9,8,7,6,4,3,2,1,5]=>{{1,2,3,4,5,8,9,10,11,12},{6,7}}
[12,10,8,6,3,5,2,4,1,7,9,11]=>{{1,9,11,12},{2,7,10},{3,4,5,6,8}}
[12,11,10,8,6,3,5,2,4,1,7,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,10,9,8,6,3,5,2,4,1,7,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,9,11,8,6,3,5,2,4,1,10,7]=>{{1,3,5,6,7,10,11,12},{2,4,8,9}}
[12,11,10,9,8,6,3,5,2,4,1,7]=>{{1,2,3,4,7,9,10,11,12},{5,8},{6}}
[12,10,8,3,7,5,2,4,6,1,9,11]=>{{1,2,5,6,7,9,10,11,12},{3,4,8}}
[12,11,10,8,3,7,5,2,4,6,1,9]=>{{1,2,4,8,9,11,12},{3,5,6,7,10}}
[12,10,3,9,7,5,2,4,6,8,1,11]=>{{1,11,12},{2,4,5,6,7,8,9,10},{3}}
[12,3,11,9,7,5,2,4,6,8,10,1]=>{{1,12},{2,3,4,5,6,7,8,9,10,11}}
[12,11,10,3,9,7,5,2,4,6,8,1]=>{{1,12},{2,8,11},{3,4,5,6,7,9,10}}
[12,10,9,8,3,7,5,2,4,6,1,11]=>{{1,11,12},{2,3,4,5,6,7,8,9,10}}
[12,9,11,8,3,7,5,2,4,6,10,1]=>{{1,12},{2,4,8,9},{3,5,6,7,10,11}}
[12,11,3,10,8,7,5,2,4,9,6,1]=>{{1,12},{2,5,6,7,8,11},{3},{4,9,10}}
[12,11,10,9,8,3,7,5,2,4,6,1]=>{{1,12},{2,3,4,6,9,10,11},{5,8},{7}}
[12,10,8,7,6,3,5,2,4,1,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,10,8,7,6,3,5,2,4,1,9]=>{{1,2,9,11,12},{3,4,5,7,8,10},{6}}
[12,10,7,9,6,3,5,2,4,8,1,11]=>{{1,11,12},{2,8,10},{3,5,6,7},{4,9}}
[12,7,11,9,6,3,5,2,4,8,10,1]=>{{1,12},{2,3,5,6,7,8,10,11},{4,9}}
[12,11,10,7,9,6,3,5,2,4,8,1]=>{{1,12},{2,5,8,9,11},{3,4,7,10},{6}}
[12,10,9,3,8,6,5,2,7,4,1,11]=>{{1,11,12},{2,3,4,5,7,8,9,10},{6}}
[12,9,11,3,8,6,5,2,7,4,10,1]=>{{1,12},{2,5,7,8,9},{3,4,10,11},{6}}
[12,11,3,8,10,6,5,2,7,9,4,1]=>{{1,12},{2,4,8,11},{3},{5,7,9,10},{6}}
[12,11,10,9,3,8,6,5,2,7,4,1]=>{{1,12},{2,4,9,11},{3,5,6,7,8,10}}
[12,10,9,8,7,6,3,5,2,4,1,11]=>{{1,11,12},{2,3,4,5,7,8,9,10},{6}}
[12,9,11,8,7,6,3,5,2,4,10,1]=>{{1,12},{2,9},{3,4,5,7,8,10,11},{6}}
[12,8,11,10,7,6,3,5,2,9,4,1]=>{{1,12},{2,3,4,5,7,8,9,10,11},{6}}
[12,11,10,3,9,7,6,8,2,5,4,1]=>{{1,12},{2,3,4,5,9,10,11},{6,7},{8}}
[12,11,10,9,8,7,6,3,5,2,4,1]=>{{1,12},{2,3,4,5,8,9,10,11},{6,7}}
[12,10,8,6,5,4,3,2,1,7,9,11]=>{{1,9,11,12},{2,3,7,8,10},{4,6},{5}}
[12,11,10,8,6,5,4,3,2,1,7,9]=>{{1,2,3,4,7,8,9,10,11,12},{5,6}}
[12,10,9,8,6,5,4,3,2,1,7,11]=>{{1,2,3,4,7,8,9,10,11,12},{5,6}}
[12,9,11,8,6,5,4,3,2,1,10,7]=>{{1,3,4,7,8,10,11,12},{2,9},{5,6}}
[12,11,10,9,8,6,5,4,3,2,1,7]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[12,10,8,5,7,4,3,2,6,1,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,10,8,5,7,4,3,2,6,1,9]=>{{1,2,9,11,12},{3,4,6,7,8,10},{5}}
[12,10,5,9,7,4,3,2,6,8,1,11]=>{{1,11,12},{2,8,10},{3,5,7},{4,6,9}}
[12,5,11,9,7,4,3,2,6,8,10,1]=>{{1,12},{2,3,5,7,8,10,11},{4,6,9}}
[12,11,10,5,9,7,4,3,2,6,8,1]=>{{1,12},{2,3,4,5,6,7,8,9,10,11}}
[12,10,9,8,5,7,4,3,2,6,1,11]=>{{1,11,12},{2,3,4,6,7,8,9,10},{5}}
[12,9,11,8,5,7,4,3,2,6,10,1]=>{{1,12},{2,9},{3,4,6,7,8,10,11},{5}}
[12,11,5,10,8,7,4,3,2,9,6,1]=>{{1,12},{2,4,6,7,9,10,11},{3,5,8}}
[12,11,10,9,8,5,7,4,3,2,6,1]=>{{1,12},{2,3,4,5,6,8,9,10,11},{7}}
[12,10,8,4,7,6,3,5,2,1,9,11]=>{{1,2,9,10,11,12},{3,5,7,8},{4},{6}}
[12,11,10,8,4,7,6,3,5,2,1,9]=>{{1,2,3,4,5,8,9,10,11,12},{6,7}}
[12,10,4,9,7,6,3,5,2,8,1,11]=>{{1,11,12},{2,3,4,5,7,8,9,10},{6}}
[12,4,11,9,7,6,3,5,2,8,10,1]=>{{1,12},{2,4,9},{3,5,7,8,10,11},{6}}
[12,11,10,4,9,7,6,3,5,2,8,1]=>{{1,12},{2,3,8,10,11},{4},{5,9},{6,7}}
[12,10,4,9,6,8,3,5,7,2,1,11]=>{{1,11,12},{2,10},{3,4,7,9},{5,6,8}}
[12,4,11,9,6,8,3,5,7,2,10,1]=>{{1,12},{2,3,4,7,9,10,11},{5,6,8}}
[12,4,11,6,10,8,3,5,7,9,2,1]=>{{1,12},{2,3,4,5,6,7,8,9,10,11}}
[12,11,10,4,9,6,8,3,5,7,2,1]=>{{1,12},{2,11},{3,7,8,10},{4},{5,9},{6}}
[12,10,9,8,4,7,6,3,5,2,1,11]=>{{1,11,12},{2,10},{3,4,5,8,9},{6,7}}
[12,9,11,8,4,7,6,3,5,2,10,1]=>{{1,12},{2,3,4,5,8,9,10,11},{6,7}}
[12,8,11,10,4,7,6,3,5,9,2,1]=>{{1,12},{2,3,8,11},{4,5,9,10},{6,7}}
[12,11,4,10,7,9,6,3,8,5,2,1]=>{{1,12},{2,11},{3,4,5,6,7,8,9,10}}
[12,11,10,9,8,4,7,6,3,5,2,1]=>{{1,12},{2,11},{3,4,5,6,8,9,10},{7}}
[12,10,8,7,6,5,4,3,2,1,9,11]=>{{1,2,9,10,11,12},{3,8},{4,7},{5,6}}
[12,11,10,8,7,6,5,4,3,2,1,9]=>{{1,2,3,9,10,11,12},{4,8},{5,7},{6}}
[12,10,7,9,6,5,4,3,2,8,1,11]=>{{1,11,12},{2,3,4,7,8,9,10},{5,6}}
[12,7,11,9,6,5,4,3,2,8,10,1]=>{{1,12},{2,4,7,9},{3,8,10,11},{5,6}}
[12,11,10,7,9,6,5,4,3,2,8,1]=>{{1,12},{2,3,4,5,7,8,9,10,11},{6}}
[12,10,6,9,8,5,4,3,7,2,1,11]=>{{1,11,12},{2,10},{3,5,6,8},{4,7,9}}
[12,6,11,9,8,5,4,3,7,2,10,1]=>{{1,12},{2,3,5,6,8,10,11},{4,7,9}}
[12,6,11,8,10,5,4,3,7,9,2,1]=>{{1,12},{2,3,4,5,6,7,8,9,10,11}}
[12,11,10,6,9,8,5,4,3,7,2,1]=>{{1,12},{2,11},{3,5,7,9,10},{4,6,8}}
[12,10,5,9,8,7,4,6,3,2,1,11]=>{{1,11,12},{2,10},{3,4,5,6,7,8,9}}
[12,5,11,9,8,7,4,6,3,2,10,1]=>{{1,12},{2,3,4,5,6,7,8,9,10,11}}
[12,5,11,8,10,7,4,6,3,9,2,1]=>{{1,12},{2,3,5,9,10,11},{4,6,7,8}}
[12,5,11,7,10,9,4,6,8,3,2,1]=>{{1,12},{2,3,5,10,11},{4,7},{6,8,9}}
[12,11,10,5,9,8,7,4,6,3,2,1]=>{{1,12},{2,11},{3,10},{4,5,6,8,9},{7}}
[12,9,11,8,7,6,5,4,3,2,10,1]=>{{1,12},{2,3,9,10,11},{4,8},{5,7},{6}}
[12,8,11,10,7,6,5,4,3,9,2,1]=>{{1,12},{2,3,4,8,9,10,11},{5,7},{6}}
[12,7,11,10,9,6,5,4,8,3,2,1]=>{{1,12},{2,3,4,5,7,8,9,10,11},{6}}
[12,6,11,10,9,8,5,7,4,3,2,1]=>{{1,12},{2,3,4,5,6,7,8,9,10,11}}
[8,9,10,11,7,1,2,3,4,5,12,6]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,9,10,11,12,8,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,2,4,6,8,10,1,3,5,7,9]=>{{1,5,6,7,8,10,11},{2,3,9,12},{4}}
[9,10,2,4,6,8,12,1,3,5,7,11]=>{{1,2,3,5,6,8,9,10},{4},{7,11,12}}
[11,9,12,2,4,6,8,10,1,3,5,7]=>{{1,2,4,5,9,11},{3,7,8,10,12},{6}}
[10,11,12,9,2,4,6,8,1,3,5,7]=>{{1,3,4,6,7,9,10,12},{2,5,11},{8}}
[7,8,2,4,6,10,12,1,3,5,9,11]=>{{1,2,3,7,8,9,11,12},{4},{5,6,10}}
[7,8,11,12,2,4,6,10,1,3,5,9]=>{{1,4,6,7,9,12},{2,3,5,8,10,11}}
[9,7,10,2,4,6,8,12,1,3,5,11]=>{{1,9},{2,4,5,7,8,11,12},{3,10},{6}}
[9,11,7,12,2,4,6,8,10,1,3,5]=>{{1,9,10},{2,3,4,5,6,7,11,12},{8}}
[7,10,11,12,9,2,4,6,8,1,3,5]=>{{1,2,4,5,6,7,8,9,10,12},{3,11}}
[8,9,10,7,2,4,6,12,1,3,5,11]=>{{1,2,5,8,9,11,12},{3,10},{4,6,7}}
[11,8,9,7,12,2,4,6,10,1,3,5]=>{{1,3,9,10,11},{2,6,8},{4,7},{5,12}}
[10,11,8,12,7,9,2,4,6,1,3,5]=>{{1,10},{2,3,4,5,7,8,11,12},{6,9}}
[9,10,11,12,8,7,2,4,6,1,3,5]=>{{1,2,6,7,9,10},{3,11},{4,5,8,12}}
[5,6,2,4,8,10,12,1,3,7,9,11]=>{{1,5,8},{2,3,6,7,9,10,11,12},{4}}
[5,6,11,12,2,4,8,10,1,3,7,9]=>{{1,2,4,5,6,9,12},{3,7,8,10,11}}
[5,6,9,10,2,4,8,12,1,3,7,11]=>{{1,2,3,4,5,6,9,10},{7,8,11,12}}
[11,5,6,9,12,2,4,8,10,1,3,7]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[10,11,12,5,6,9,2,4,8,1,3,7]=>{{1,10},{2,3,7,11,12},{4,5,6,8,9}}
[7,5,8,2,4,6,10,12,1,3,9,11]=>{{1,3,7,8,9,10,11,12},{2,4,5},{6}}
[7,5,8,11,12,2,4,6,10,1,3,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[7,9,5,10,2,4,6,8,12,1,3,11]=>{{1,4,6,7,10},{2,3,5,9,11,12},{8}}
[7,9,11,5,12,2,4,6,8,10,1,3]=>{{1,3,4,5,7,11,12},{2,6,8,9},{10}}
[10,7,11,12,5,9,2,4,6,8,1,3]=>{{1,3,4,8,10,11,12},{2,7},{5},{6,9}}
[5,8,9,10,7,2,4,6,12,1,3,11]=>{{1,4,5,7,10},{2,6,8},{3,9,11,12}}
[11,5,8,9,7,12,2,4,6,10,1,3]=>{{1,11},{2,5,7},{3,4,6,8,9,12},{10}}
[8,10,5,11,12,7,9,2,4,6,1,3]=>{{1,2,4,6,7,8,9,10,11},{3,5,12}}
[9,10,11,12,5,8,7,2,4,6,1,3]=>{{1,3,4,9,11,12},{2,6,8,10},{5},{7}}
[6,7,8,5,2,4,10,12,1,3,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,7,8,5,11,12,2,4,10,1,3,9]=>{{1,6,9,10,12},{2,7},{3,4,5,8,11}}
[9,6,7,5,10,2,4,8,12,1,3,11]=>{{1,3,4,5,7,9,10,11,12},{2,6},{8}}
[9,6,7,11,5,12,2,4,8,10,1,3]=>{{1,4,8,9,11},{2,3,6,7,12},{5},{10}}
[6,10,7,11,12,5,9,2,4,8,1,3]=>{{1,3,4,5,6,7,9,11,12},{2,8,10}}
[8,9,6,10,5,7,2,4,12,1,3,11]=>{{1,4,8,10},{2,3,6,7,9,11,12},{5}}
[8,9,11,6,5,7,12,2,4,10,1,3]=>{{1,2,3,4,6,7,8,9,11,12},{5},{10}}
[10,8,11,6,12,5,7,9,2,4,1,3]=>{{1,3,4,5,6,10,11,12},{2,8,9},{7}}
[9,6,10,11,12,8,5,7,2,4,1,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[7,8,9,10,6,5,2,4,12,1,3,11]=>{{1,2,4,7,8,10},{3,9,11,12},{5,6}}
[11,7,8,9,6,5,12,2,4,10,1,3]=>{{1,11},{2,3,7,8,12},{4,9},{5,6},{10}}
[10,11,7,8,6,12,5,9,2,4,1,3]=>{{1,2,4,8,9,10,11},{3,5,6,7,12}}
[9,10,11,7,12,6,8,5,2,4,1,3]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[8,9,10,11,12,7,6,5,2,4,1,3]=>{{1,3,4,5,8,10,11,12},{2,9},{6,7}}
[3,4,2,6,8,10,12,1,5,7,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[3,4,11,12,2,6,8,10,1,5,7,9]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[3,4,9,10,2,6,8,12,1,5,7,11]=>{{1,3,9},{2,4,5,10},{6},{7,8,11,12}}
[11,3,4,9,12,2,6,8,10,1,5,7]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[10,11,12,3,4,9,2,6,8,1,5,7]=>{{1,10},{2,3,4,5,7,11,12},{6,8,9}}
[3,4,7,8,2,6,10,12,1,5,9,11]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[3,4,7,8,11,12,2,6,10,1,5,9]=>{{1,2,3,4,6,7,8,9,10,12},{5,11}}
[9,3,4,7,10,2,6,8,12,1,5,11]=>{{1,5,9,10,11,12},{2,3,4,6,7},{8}}
[9,11,3,4,7,12,2,6,8,10,1,5]=>{{1,2,5,6,7,8,9,11,12},{3},{4},{10}}
[3,10,11,12,4,7,9,2,6,8,1,5]=>{{1,3,11},{2,8,10},{4,5,12},{6,7,9}}
[8,9,10,3,4,7,2,6,12,1,5,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,8,9,3,4,7,12,2,6,10,1,5]=>{{1,11},{2,8},{3,4,5,6,7,9,12},{10}}
[10,11,8,12,3,4,7,9,2,6,1,5]=>{{1,2,3,4,5,6,8,9,10,11,12},{7}}
[9,10,11,12,8,3,4,7,2,6,1,5]=>{{1,2,3,6,9,10,11},{4,5,7,8,12}}
[5,3,6,2,4,8,10,12,1,7,9,11]=>{{1,2,3,4,5,6,8,9,11,12},{7,10}}
[5,3,6,11,12,2,4,8,10,1,7,9]=>{{1,5,9,10,12},{2,3,6},{4,7,11},{8}}
[5,3,6,9,10,2,4,8,12,1,7,11]=>{{1,5,10},{2,3,6},{4,7,9,11,12},{8}}
[5,11,3,6,9,12,2,4,8,10,1,7]=>{{1,2,4,5,6,7,8,9,11,12},{3},{10}}
[5,10,11,12,3,6,9,2,4,8,1,7]=>{{1,3,5,11},{2,8,10},{4,7,9,12},{6}}
[5,7,3,8,2,4,6,10,12,1,9,11]=>{{1,2,4,5,6,7,8,10},{3},{9,11,12}}
[5,7,3,8,11,12,2,4,6,10,1,9]=>{{1,5,11},{2,7},{3},{4,8},{6,9,12},{10}}
[5,7,9,3,10,2,4,6,8,12,1,11]=>{{1,5,10,11,12},{2,3,4,6,7,8,9}}
[5,7,9,11,3,12,2,4,6,8,10,1]=>{{1,3,5,6,9,12},{2,7},{4,8,10,11}}
[10,5,7,11,12,3,9,2,4,6,8,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,5,9,10,3,7,2,4,6,12,1,11]=>{{1,4,8,10,11,12},{2,3,5,6,7,9}}
[8,11,5,9,3,7,12,2,4,6,10,1]=>{{1,2,6,7,8,10,11,12},{3,5},{4,9}}
[8,10,11,5,12,3,7,9,2,4,6,1]=>{{1,2,4,5,8,9,10,12},{3,6,11},{7}}
[5,9,10,11,12,8,3,7,2,4,6,1]=>{{1,5,12},{2,9},{3,4,6,7,8,10,11}}
[3,6,7,8,5,2,4,10,12,1,9,11]=>{{1,3,4,7,8,10},{2,6},{5},{9,11,12}}
[3,6,7,8,5,11,12,2,4,10,1,9]=>{{1,2,3,4,6,7,8,9,11,12},{5},{10}}
[9,3,6,7,5,10,2,4,8,12,1,11]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[9,3,6,7,11,5,12,2,4,8,10,1]=>{{1,4,7,9,12},{2,3,5,6,8,10,11}}
[6,10,3,7,11,12,5,9,2,4,8,1]=>{{1,6,12},{2,4,5,7,8,9,10,11},{3}}
[6,8,3,9,10,5,7,2,4,12,1,11]=>{{1,5,6,10,11,12},{2,8},{3},{4,9},{7}}
[6,8,9,3,11,5,7,12,2,4,10,1]=>{{1,2,3,4,5,6,8,9,10,11,12},{7}}
[10,6,8,3,11,12,5,7,9,2,4,1]=>{{1,2,6,10,12},{3,4,5,7,8,11},{9}}
[9,6,10,11,12,3,8,5,7,2,4,1]=>{{1,5,7,8,9,12},{2,3,6,10},{4,11}}
[7,8,9,10,3,6,5,2,4,12,1,11]=>{{1,3,4,5,7,9,10,11,12},{2,8},{6}}
[11,7,8,9,3,6,5,12,2,4,10,1]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[10,11,7,8,3,6,12,5,9,2,4,1]=>{{1,2,3,4,5,7,8,10,11,12},{6},{9}}
[9,10,11,7,12,3,6,8,5,2,4,1]=>{{1,5,9,12},{2,10},{3,4,6,7,11},{8}}
[8,9,10,11,12,7,3,6,5,2,4,1]=>{{1,2,3,5,6,7,8,9,10,12},{4,11}}
[4,5,6,3,2,8,10,12,1,7,9,11]=>{{1,3,4,6,8,9,11,12},{2,5},{7,10}}
[4,5,6,3,11,12,2,8,10,1,7,9]=>{{1,3,4,6,9,10,12},{2,5,7,11},{8}}
[4,5,6,3,9,10,2,8,12,1,7,11]=>{{1,3,4,6,10},{2,5,7,9,11,12},{8}}
[4,5,6,11,3,9,12,2,8,10,1,7]=>{{1,4,11},{2,3,5,6,8,9},{7,12},{10}}
[4,5,6,10,11,12,3,9,2,8,1,7]=>{{1,2,4,5,8,9,10,11},{3,6,7,12}}
[7,4,5,3,8,2,6,10,12,1,9,11]=>{{1,2,3,4,5,6,7,8,10},{9,11,12}}
[7,4,5,3,8,11,12,2,6,10,1,9]=>{{1,6,7,9,11,12},{2,3,4,5,8},{10}}
[7,4,5,9,3,10,2,6,8,12,1,11]=>{{1,2,4,6,7,8,9,10,11,12},{3,5}}
[7,4,5,9,11,3,12,2,6,8,10,1]=>{{1,7,12},{2,3,4,5,6,8,9,10,11}}
[7,10,4,5,11,12,3,9,2,6,8,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[4,8,5,9,10,3,7,2,6,12,1,11]=>{{1,3,4,5,6,9,10,11,12},{2,8},{7}}
[4,8,11,5,9,3,7,12,2,6,10,1]=>{{1,2,4,5,8,9,12},{3,6,10,11},{7}}
[4,8,10,11,5,12,3,7,9,2,6,1]=>{{1,4,6,11,12},{2,3,7,8,10},{5},{9}}
[4,5,9,10,11,12,8,3,7,2,6,1]=>{{1,2,4,5,6,10,11,12},{3,7,8,9}}
[6,7,4,8,3,5,2,10,12,1,9,11]=>{{1,3,4,5,6,8,10},{2,7},{9,11,12}}
[6,7,4,8,3,5,11,12,2,10,1,9]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}}
[6,7,9,4,3,5,10,2,8,12,1,11]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[6,7,9,4,11,3,5,12,2,8,10,1]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[10,6,7,4,11,12,3,5,9,2,8,1]=>{{1,2,6,10,12},{3,7},{4},{5,8,11},{9}}
[8,6,9,4,10,3,5,7,2,12,1,11]=>{{1,5,7,8,10,11,12},{2,3,6,9},{4}}
[8,6,9,11,4,3,5,7,12,2,10,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,10,6,11,4,12,3,5,7,9,2,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,9,4,10,11,12,8,3,5,7,2,1]=>{{1,6,12},{2,5,9,11},{3,4,7,8,10}}
[7,4,8,9,10,6,3,5,2,12,1,11]=>{{1,3,5,7,8,10,11,12},{2,4,9},{6}}
[7,11,4,8,9,6,3,5,12,2,10,1]=>{{1,3,4,5,7,8,9,12},{2,10,11},{6}}
[7,8,10,4,11,6,12,3,5,9,2,1]=>{{1,7,12},{2,3,5,8,9,10,11},{4},{6}}
[9,7,10,4,11,12,6,8,3,5,2,1]=>{{1,2,3,5,6,7,9,10,11,12},{4},{8}}
[4,8,9,10,11,12,7,6,3,5,2,1]=>{{1,2,4,5,6,8,10,11,12},{3,9},{7}}
[5,6,7,8,4,3,2,10,12,1,9,11]=>{{1,4,5,8,10},{2,3,6,7},{9,11,12}}
[5,6,7,8,4,3,11,12,2,10,1,9]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}}
[9,5,6,7,4,3,10,2,8,12,1,11]=>{{1,2,4,5,7,8,9,10,11,12},{3,6}}
[9,5,6,7,4,11,3,12,2,8,10,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[5,10,6,7,4,11,12,3,9,2,8,1]=>{{1,4,5,7,12},{2,10},{3,6,8,11},{9}}
[8,9,5,6,4,10,3,7,2,12,1,11]=>{{1,3,4,5,6,7,8,10,11,12},{2,9}}
[8,9,5,6,11,4,3,7,12,2,10,1]=>{{1,2,3,5,7,8,9,10,11,12},{4,6}}
[10,8,5,6,11,4,12,3,7,9,2,1]=>{{1,7,9,10,12},{2,3,5,8,11},{4,6}}
[9,5,10,6,11,12,4,8,3,7,2,1]=>{{1,3,4,6,7,9,10,12},{2,5,11},{8}}
[7,8,9,5,10,4,6,3,2,12,1,11]=>{{1,4,5,6,7,10,11,12},{2,3,8,9}}
[7,8,9,11,5,4,6,3,12,2,10,1]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[10,7,8,11,5,4,6,12,3,9,2,1]=>{{1,3,8,9,10,12},{2,4,6,7,11},{5}}
[9,10,7,11,5,12,4,6,8,3,2,1]=>{{1,6,8,9,12},{2,3,4,7,10,11},{5}}
[8,9,5,10,11,12,7,4,6,3,2,1]=>{{1,2,3,4,5,6,8,9,10,11,12},{7}}
[6,7,8,9,10,5,4,3,2,12,1,11]=>{{1,5,6,10,11,12},{2,4,7,9},{3,8}}
[11,6,7,8,9,5,4,3,12,2,10,1]=>{{1,2,5,6,9,10,11,12},{3,4,7,8}}
[10,11,6,7,8,5,4,12,3,9,2,1]=>{{1,3,5,6,8,9,10,12},{2,11},{4,7}}
[9,10,11,6,7,5,12,4,8,3,2,1]=>{{1,4,5,6,7,8,9,12},{2,3,10,11}}
[8,9,10,11,6,12,5,7,4,3,2,1]=>{{1,5,6,7,8,12},{2,4,9,11},{3,10}}
[6,5,2,1,4,3,12,11,8,7,10,9]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}}
[2,1,4,3,6,5,8,7,9,11,12,10]=>{{1,2},{3,4},{5,6},{7,8},{9},{10,11,12}}
[2,1,4,3,6,5,7,9,10,8,12,11]=>{{1,2},{3,4},{5,6},{7},{8,9,10},{11,12}}
[2,1,4,3,6,5,7,9,8,11,12,10]=>{{1,2},{3,4},{5,6},{7},{8,9},{10,11,12}}
[2,1,4,3,6,5,7,8,10,11,12,9]=>{{1,2},{3,4},{5,6},{7},{8},{9,10,11,12}}
[2,1,4,3,5,7,8,6,10,9,12,11]=>{{1,2},{3,4},{5},{6,7,8},{9,10},{11,12}}
[2,1,4,3,5,7,8,6,9,11,12,10]=>{{1,2},{3,4},{5},{6,7,8},{9},{10,11,12}}
[2,1,4,3,5,7,6,9,10,8,12,11]=>{{1,2},{3,4},{5},{6,7},{8,9,10},{11,12}}
[2,1,4,3,5,7,6,9,8,11,12,10]=>{{1,2},{3,4},{5},{6,7},{8,9},{10,11,12}}
[2,1,4,3,5,7,6,8,10,11,12,9]=>{{1,2},{3,4},{5},{6,7},{8},{9,10,11,12}}
[2,1,4,3,5,6,8,9,10,7,12,11]=>{{1,2},{3,4},{5},{6},{7,8,9,10},{11,12}}
[2,1,4,3,5,6,8,9,7,11,12,10]=>{{1,2},{3,4},{5},{6},{7,8,9},{10,11,12}}
[2,1,4,3,5,6,8,7,10,11,12,9]=>{{1,2},{3,4},{5},{6},{7,8},{9,10,11,12}}
[2,1,4,3,5,6,7,9,10,11,12,8]=>{{1,2},{3,4},{5},{6},{7},{8,9,10,11,12}}
[2,1,3,5,6,4,8,7,10,9,12,11]=>{{1,2},{3},{4,5,6},{7,8},{9,10},{11,12}}
[2,1,3,5,6,4,8,7,9,11,12,10]=>{{1,2},{3},{4,5,6},{7,8},{9},{10,11,12}}
[2,1,3,5,6,4,7,9,10,8,12,11]=>{{1,2},{3},{4,5,6},{7},{8,9,10},{11,12}}
[2,1,3,5,6,4,7,9,8,11,12,10]=>{{1,2},{3},{4,5,6},{7},{8,9},{10,11,12}}
[2,1,3,5,6,4,7,8,10,11,12,9]=>{{1,2},{3},{4,5,6},{7},{8},{9,10,11,12}}
[2,1,3,5,4,7,8,6,10,9,12,11]=>{{1,2},{3},{4,5},{6,7,8},{9,10},{11,12}}
[2,1,3,5,4,7,8,6,9,11,12,10]=>{{1,2},{3},{4,5},{6,7,8},{9},{10,11,12}}
[2,1,3,5,4,7,6,9,10,8,12,11]=>{{1,2},{3},{4,5},{6,7},{8,9,10},{11,12}}
[2,1,3,5,4,7,6,9,8,11,12,10]=>{{1,2},{3},{4,5},{6,7},{8,9},{10,11,12}}
[2,1,3,5,4,7,6,8,10,11,12,9]=>{{1,2},{3},{4,5},{6,7},{8},{9,10,11,12}}
[2,1,3,5,4,6,8,9,10,7,12,11]=>{{1,2},{3},{4,5},{6},{7,8,9,10},{11,12}}
[2,1,3,5,4,6,8,9,7,11,12,10]=>{{1,2},{3},{4,5},{6},{7,8,9},{10,11,12}}
[2,1,3,5,4,6,8,7,10,11,12,9]=>{{1,2},{3},{4,5},{6},{7,8},{9,10,11,12}}
[2,1,3,5,4,6,7,9,10,11,12,8]=>{{1,2},{3},{4,5},{6},{7},{8,9,10,11,12}}
[2,1,3,4,6,7,8,5,10,9,12,11]=>{{1,2},{3},{4},{5,6,7,8},{9,10},{11,12}}
[2,1,3,4,6,7,8,5,9,11,12,10]=>{{1,2},{3},{4},{5,6,7,8},{9},{10,11,12}}
[2,1,3,4,6,7,5,9,10,8,12,11]=>{{1,2},{3},{4},{5,6,7},{8,9,10},{11,12}}
[2,1,3,4,6,7,5,9,8,11,12,10]=>{{1,2},{3},{4},{5,6,7},{8,9},{10,11,12}}
[2,1,3,4,6,7,5,8,10,11,12,9]=>{{1,2},{3},{4},{5,6,7},{8},{9,10,11,12}}
[2,1,3,4,6,5,8,9,10,7,12,11]=>{{1,2},{3},{4},{5,6},{7,8,9,10},{11,12}}
[2,1,3,4,6,5,8,9,7,11,12,10]=>{{1,2},{3},{4},{5,6},{7,8,9},{10,11,12}}
[2,1,3,4,6,5,8,7,10,11,12,9]=>{{1,2},{3},{4},{5,6},{7,8},{9,10,11,12}}
[2,1,3,4,6,5,7,9,10,11,12,8]=>{{1,2},{3},{4},{5,6},{7},{8,9,10,11,12}}
[2,1,3,4,5,7,8,9,10,6,12,11]=>{{1,2},{3},{4},{5},{6,7,8,9,10},{11,12}}
[2,1,3,4,5,7,8,9,6,11,12,10]=>{{1,2},{3},{4},{5},{6,7,8,9},{10,11,12}}
[2,1,3,4,5,7,8,6,10,11,12,9]=>{{1,2},{3},{4},{5},{6,7,8},{9,10,11,12}}
[2,1,3,4,5,7,6,9,10,11,12,8]=>{{1,2},{3},{4},{5},{6,7},{8,9,10,11,12}}
[2,1,3,4,5,6,8,9,10,11,12,7]=>{{1,2},{3},{4},{5},{6},{7,8,9,10,11,12}}
[1,3,4,2,6,5,8,7,10,9,12,11]=>{{1},{2,3,4},{5,6},{7,8},{9,10},{11,12}}
[1,3,4,2,6,5,8,7,9,11,12,10]=>{{1},{2,3,4},{5,6},{7,8},{9},{10,11,12}}
[1,3,4,2,6,5,7,9,10,8,12,11]=>{{1},{2,3,4},{5,6},{7},{8,9,10},{11,12}}
[1,3,4,2,6,5,7,9,8,11,12,10]=>{{1},{2,3,4},{5,6},{7},{8,9},{10,11,12}}
[1,3,4,2,6,5,7,8,10,11,12,9]=>{{1},{2,3,4},{5,6},{7},{8},{9,10,11,12}}
[1,3,4,2,5,7,8,6,10,9,12,11]=>{{1},{2,3,4},{5},{6,7,8},{9,10},{11,12}}
[1,3,4,2,5,7,8,6,9,11,12,10]=>{{1},{2,3,4},{5},{6,7,8},{9},{10,11,12}}
[1,3,4,2,5,7,6,9,10,8,12,11]=>{{1},{2,3,4},{5},{6,7},{8,9,10},{11,12}}
[1,3,4,2,5,7,6,9,8,11,12,10]=>{{1},{2,3,4},{5},{6,7},{8,9},{10,11,12}}
[1,3,4,2,5,7,6,8,10,11,12,9]=>{{1},{2,3,4},{5},{6,7},{8},{9,10,11,12}}
[1,3,4,2,5,6,8,9,10,7,12,11]=>{{1},{2,3,4},{5},{6},{7,8,9,10},{11,12}}
[1,3,4,2,5,6,8,9,7,11,12,10]=>{{1},{2,3,4},{5},{6},{7,8,9},{10,11,12}}
[1,3,4,2,5,6,8,7,10,11,12,9]=>{{1},{2,3,4},{5},{6},{7,8},{9,10,11,12}}
[1,3,4,2,5,6,7,9,10,11,12,8]=>{{1},{2,3,4},{5},{6},{7},{8,9,10,11,12}}
[1,3,2,5,6,4,8,7,10,9,12,11]=>{{1},{2,3},{4,5,6},{7,8},{9,10},{11,12}}
[1,3,2,5,6,4,8,7,9,11,12,10]=>{{1},{2,3},{4,5,6},{7,8},{9},{10,11,12}}
[1,3,2,5,6,4,7,9,10,8,12,11]=>{{1},{2,3},{4,5,6},{7},{8,9,10},{11,12}}
[1,3,2,5,6,4,7,9,8,11,12,10]=>{{1},{2,3},{4,5,6},{7},{8,9},{10,11,12}}
[1,3,2,5,6,4,7,8,10,11,12,9]=>{{1},{2,3},{4,5,6},{7},{8},{9,10,11,12}}
[1,3,2,5,4,7,8,6,10,9,12,11]=>{{1},{2,3},{4,5},{6,7,8},{9,10},{11,12}}
[1,3,2,5,4,7,8,6,9,11,12,10]=>{{1},{2,3},{4,5},{6,7,8},{9},{10,11,12}}
[1,3,2,5,4,7,6,9,10,8,12,11]=>{{1},{2,3},{4,5},{6,7},{8,9,10},{11,12}}
[1,3,2,5,4,7,6,9,8,11,12,10]=>{{1},{2,3},{4,5},{6,7},{8,9},{10,11,12}}
[1,3,2,5,4,7,6,8,10,11,12,9]=>{{1},{2,3},{4,5},{6,7},{8},{9,10,11,12}}
[1,3,2,5,4,6,8,9,10,7,12,11]=>{{1},{2,3},{4,5},{6},{7,8,9,10},{11,12}}
[1,3,2,5,4,6,8,9,7,11,12,10]=>{{1},{2,3},{4,5},{6},{7,8,9},{10,11,12}}
[1,3,2,5,4,6,8,7,10,11,12,9]=>{{1},{2,3},{4,5},{6},{7,8},{9,10,11,12}}
[1,3,2,5,4,6,7,9,10,11,12,8]=>{{1},{2,3},{4,5},{6},{7},{8,9,10,11,12}}
[1,3,2,4,6,7,8,5,10,9,12,11]=>{{1},{2,3},{4},{5,6,7,8},{9,10},{11,12}}
[1,3,2,4,6,7,8,5,9,11,12,10]=>{{1},{2,3},{4},{5,6,7,8},{9},{10,11,12}}
[1,3,2,4,6,7,5,9,10,8,12,11]=>{{1},{2,3},{4},{5,6,7},{8,9,10},{11,12}}
[1,3,2,4,6,7,5,9,8,11,12,10]=>{{1},{2,3},{4},{5,6,7},{8,9},{10,11,12}}
[1,3,2,4,6,7,5,8,10,11,12,9]=>{{1},{2,3},{4},{5,6,7},{8},{9,10,11,12}}
[1,3,2,4,6,5,8,9,10,7,12,11]=>{{1},{2,3},{4},{5,6},{7,8,9,10},{11,12}}
[1,3,2,4,6,5,8,9,7,11,12,10]=>{{1},{2,3},{4},{5,6},{7,8,9},{10,11,12}}
[1,3,2,4,6,5,8,7,10,11,12,9]=>{{1},{2,3},{4},{5,6},{7,8},{9,10,11,12}}
[1,3,2,4,6,5,7,9,10,11,12,8]=>{{1},{2,3},{4},{5,6},{7},{8,9,10,11,12}}
[1,3,2,4,5,7,8,9,10,6,12,11]=>{{1},{2,3},{4},{5},{6,7,8,9,10},{11,12}}
[1,3,2,4,5,7,8,9,6,11,12,10]=>{{1},{2,3},{4},{5},{6,7,8,9},{10,11,12}}
[1,3,2,4,5,7,8,6,10,11,12,9]=>{{1},{2,3},{4},{5},{6,7,8},{9,10,11,12}}
[1,3,2,4,5,7,6,9,10,11,12,8]=>{{1},{2,3},{4},{5},{6,7},{8,9,10,11,12}}
[1,3,2,4,5,6,8,9,10,11,12,7]=>{{1},{2,3},{4},{5},{6},{7,8,9,10,11,12}}
[1,2,4,5,6,3,8,7,10,9,12,11]=>{{1},{2},{3,4,5,6},{7,8},{9,10},{11,12}}
[1,2,4,5,6,3,8,7,9,11,12,10]=>{{1},{2},{3,4,5,6},{7,8},{9},{10,11,12}}
[1,2,4,5,6,3,7,9,10,8,12,11]=>{{1},{2},{3,4,5,6},{7},{8,9,10},{11,12}}
[1,2,4,5,6,3,7,9,8,11,12,10]=>{{1},{2},{3,4,5,6},{7},{8,9},{10,11,12}}
[1,2,4,5,6,3,7,8,10,11,12,9]=>{{1},{2},{3,4,5,6},{7},{8},{9,10,11,12}}
[1,2,4,5,3,7,8,6,10,9,12,11]=>{{1},{2},{3,4,5},{6,7,8},{9,10},{11,12}}
[1,2,4,5,3,7,8,6,9,11,12,10]=>{{1},{2},{3,4,5},{6,7,8},{9},{10,11,12}}
[1,2,4,5,3,7,6,9,10,8,12,11]=>{{1},{2},{3,4,5},{6,7},{8,9,10},{11,12}}
[1,2,4,5,3,7,6,9,8,11,12,10]=>{{1},{2},{3,4,5},{6,7},{8,9},{10,11,12}}
[1,2,4,5,3,7,6,8,10,11,12,9]=>{{1},{2},{3,4,5},{6,7},{8},{9,10,11,12}}
[1,2,4,5,3,6,8,9,10,7,12,11]=>{{1},{2},{3,4,5},{6},{7,8,9,10},{11,12}}
[1,2,4,5,3,6,8,9,7,11,12,10]=>{{1},{2},{3,4,5},{6},{7,8,9},{10,11,12}}
[1,2,4,5,3,6,8,7,10,11,12,9]=>{{1},{2},{3,4,5},{6},{7,8},{9,10,11,12}}
[1,2,4,5,3,6,7,9,10,11,12,8]=>{{1},{2},{3,4,5},{6},{7},{8,9,10,11,12}}
[1,2,4,3,6,7,8,5,10,9,12,11]=>{{1},{2},{3,4},{5,6,7,8},{9,10},{11,12}}
[1,2,4,3,6,7,8,5,9,11,12,10]=>{{1},{2},{3,4},{5,6,7,8},{9},{10,11,12}}
[1,2,4,3,6,7,5,9,10,8,12,11]=>{{1},{2},{3,4},{5,6,7},{8,9,10},{11,12}}
[1,2,4,3,6,7,5,9,8,11,12,10]=>{{1},{2},{3,4},{5,6,7},{8,9},{10,11,12}}
[1,2,4,3,6,7,5,8,10,11,12,9]=>{{1},{2},{3,4},{5,6,7},{8},{9,10,11,12}}
[1,2,4,3,6,5,8,9,10,7,12,11]=>{{1},{2},{3,4},{5,6},{7,8,9,10},{11,12}}
[1,2,4,3,6,5,8,9,7,11,12,10]=>{{1},{2},{3,4},{5,6},{7,8,9},{10,11,12}}
[1,2,4,3,6,5,8,7,10,11,12,9]=>{{1},{2},{3,4},{5,6},{7,8},{9,10,11,12}}
[1,2,4,3,6,5,7,9,10,11,12,8]=>{{1},{2},{3,4},{5,6},{7},{8,9,10,11,12}}
[1,2,4,3,5,7,8,9,10,6,12,11]=>{{1},{2},{3,4},{5},{6,7,8,9,10},{11,12}}
[1,2,4,3,5,7,8,9,6,11,12,10]=>{{1},{2},{3,4},{5},{6,7,8,9},{10,11,12}}
[1,2,4,3,5,7,8,6,10,11,12,9]=>{{1},{2},{3,4},{5},{6,7,8},{9,10,11,12}}
[1,2,4,3,5,7,6,9,10,11,12,8]=>{{1},{2},{3,4},{5},{6,7},{8,9,10,11,12}}
[1,2,4,3,5,6,8,9,10,11,12,7]=>{{1},{2},{3,4},{5},{6},{7,8,9,10,11,12}}
[1,2,3,5,6,7,8,4,10,9,12,11]=>{{1},{2},{3},{4,5,6,7,8},{9,10},{11,12}}
[1,2,3,5,6,7,8,4,9,11,12,10]=>{{1},{2},{3},{4,5,6,7,8},{9},{10,11,12}}
[1,2,3,5,6,7,4,9,10,8,12,11]=>{{1},{2},{3},{4,5,6,7},{8,9,10},{11,12}}
[1,2,3,5,6,7,4,9,8,11,12,10]=>{{1},{2},{3},{4,5,6,7},{8,9},{10,11,12}}
[1,2,3,5,6,7,4,8,10,11,12,9]=>{{1},{2},{3},{4,5,6,7},{8},{9,10,11,12}}
[1,2,3,5,6,4,8,9,10,7,12,11]=>{{1},{2},{3},{4,5,6},{7,8,9,10},{11,12}}
[1,2,3,5,6,4,8,9,7,11,12,10]=>{{1},{2},{3},{4,5,6},{7,8,9},{10,11,12}}
[1,2,3,5,6,4,8,7,10,11,12,9]=>{{1},{2},{3},{4,5,6},{7,8},{9,10,11,12}}
[1,2,3,5,6,4,7,9,10,11,12,8]=>{{1},{2},{3},{4,5,6},{7},{8,9,10,11,12}}
[1,2,3,5,4,7,8,9,10,6,12,11]=>{{1},{2},{3},{4,5},{6,7,8,9,10},{11,12}}
[1,2,3,5,4,7,8,9,6,11,12,10]=>{{1},{2},{3},{4,5},{6,7,8,9},{10,11,12}}
[1,2,3,5,4,7,8,6,10,11,12,9]=>{{1},{2},{3},{4,5},{6,7,8},{9,10,11,12}}
[1,2,3,5,4,7,6,9,10,11,12,8]=>{{1},{2},{3},{4,5},{6,7},{8,9,10,11,12}}
[1,2,3,5,4,6,8,9,10,11,12,7]=>{{1},{2},{3},{4,5},{6},{7,8,9,10,11,12}}
[1,2,3,4,6,7,8,9,10,5,12,11]=>{{1},{2},{3},{4},{5,6,7,8,9,10},{11,12}}
[1,2,3,4,6,7,8,9,5,11,12,10]=>{{1},{2},{3},{4},{5,6,7,8,9},{10,11,12}}
[1,2,3,4,6,7,8,5,10,11,12,9]=>{{1},{2},{3},{4},{5,6,7,8},{9,10,11,12}}
[1,2,3,4,6,7,5,9,10,11,12,8]=>{{1},{2},{3},{4},{5,6,7},{8,9,10,11,12}}
[1,2,3,4,6,5,8,9,10,11,12,7]=>{{1},{2},{3},{4},{5,6},{7,8,9,10,11,12}}
[1,2,3,4,5,7,8,9,10,11,12,6]=>{{1},{2},{3},{4},{5},{6,7,8,9,10,11,12}}
[12,1,2,3,4,5,6,7,8,11,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,1,2,3,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,2,1,3,4,5,6,7,8,9,10,11]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[2,1,4,3,6,5,8,7,12,9,11,10]=>{{1,2},{3,4},{5,6},{7,8},{9,10,12},{11}}
[2,1,4,3,6,5,10,7,9,8,12,11]=>{{1,2},{3,4},{5,6},{7,8,10},{9},{11,12}}
[2,1,4,3,6,5,12,11,9,7,8,10]=>{{1,2},{3,4},{5,6},{7,10,12},{8,11},{9}}
[2,1,4,3,6,5,12,7,8,10,11,9]=>{{1,2},{3,4},{5,6},{7,8,9,12},{10},{11}}
[2,1,4,3,8,5,7,6,10,9,12,11]=>{{1,2},{3,4},{5,6,8},{7},{9,10},{11,12}}
[2,1,4,3,8,5,7,6,12,9,11,10]=>{{1,2},{3,4},{5,6,8},{7},{9,10,12},{11}}
[2,1,4,3,10,9,7,5,6,8,12,11]=>{{1,2},{3,4},{5,8,10},{6,9},{7},{11,12}}
[2,1,4,3,12,9,7,11,6,5,8,10]=>{{1,2},{3,4},{5,10,12},{6,9},{7},{8,11}}
[2,1,4,3,12,10,7,5,8,6,11,9]=>{{1,2},{3,4},{5,8,9,12},{6,10},{7},{11}}
[2,1,4,3,10,5,6,8,9,7,12,11]=>{{1,2},{3,4},{5,6,7,10},{8},{9},{11,12}}
[2,1,4,3,12,11,6,8,9,5,7,10]=>{{1,2},{3,4},{5,10,12},{6,7,11},{8},{9}}
[2,1,4,3,12,5,11,8,6,10,7,9]=>{{1,2},{3,4},{5,6,9,12},{7,11},{8},{10}}
[2,1,4,3,12,5,6,7,9,10,11,8]=>{{1,2},{3,4},{5,6,7,8,12},{9},{10},{11}}
[2,1,6,3,5,4,8,7,10,9,12,11]=>{{1,2},{3,4,6},{5},{7,8},{9,10},{11,12}}
[2,1,6,3,5,4,8,7,12,9,11,10]=>{{1,2},{3,4,6},{5},{7,8},{9,10,12},{11}}
[2,1,6,3,5,4,10,7,9,8,12,11]=>{{1,2},{3,4,6},{5},{7,8,10},{9},{11,12}}
[2,1,6,3,5,4,12,11,9,7,8,10]=>{{1,2},{3,4,6},{5},{7,10,12},{8,11},{9}}
[2,1,6,3,5,4,12,7,8,10,11,9]=>{{1,2},{3,4,6},{5},{7,8,9,12},{10},{11}}
[2,1,8,7,5,3,4,6,10,9,12,11]=>{{1,2},{3,6,8},{4,7},{5},{9,10},{11,12}}
[2,1,8,7,5,3,4,6,12,9,11,10]=>{{1,2},{3,6,8},{4,7},{5},{9,10,12},{11}}
[2,1,10,7,5,9,4,3,6,8,12,11]=>{{1,2},{3,8,10},{4,7},{5},{6,9},{11,12}}
[2,1,12,7,5,9,4,11,6,3,8,10]=>{{1,2},{3,10,12},{4,7},{5},{6,9},{8,11}}
[2,1,12,7,5,10,4,3,8,6,11,9]=>{{1,2},{3,8,9,12},{4,7},{5},{6,10},{11}}
[2,1,10,8,5,3,6,4,9,7,12,11]=>{{1,2},{3,6,7,10},{4,8},{5},{9},{11,12}}
[2,1,12,8,5,11,6,4,9,3,7,10]=>{{1,2},{3,10,12},{4,8},{5},{6,7,11},{9}}
[2,1,12,8,5,3,11,4,6,10,7,9]=>{{1,2},{3,6,9,12},{4,8},{5},{7,11},{10}}
[2,1,12,9,5,3,6,7,4,10,11,8]=>{{1,2},{3,6,7,8,12},{4,9},{5},{10},{11}}
[2,1,8,3,4,6,7,5,10,9,12,11]=>{{1,2},{3,4,5,8},{6},{7},{9,10},{11,12}}
[2,1,8,3,4,6,7,5,12,9,11,10]=>{{1,2},{3,4,5,8},{6},{7},{9,10,12},{11}}
[2,1,10,9,4,6,7,3,5,8,12,11]=>{{1,2},{3,8,10},{4,5,9},{6},{7},{11,12}}
[2,1,12,9,4,6,7,11,5,3,8,10]=>{{1,2},{3,10,12},{4,5,9},{6},{7},{8,11}}
[2,1,12,10,4,6,7,3,8,5,11,9]=>{{1,2},{3,8,9,12},{4,5,10},{6},{7},{11}}
[2,1,10,3,9,6,4,8,5,7,12,11]=>{{1,2},{3,4,7,10},{5,9},{6},{8},{11,12}}
[2,1,12,11,9,6,4,8,5,3,7,10]=>{{1,2},{3,10,12},{4,7,11},{5,9},{6},{8}}
[2,1,12,3,10,6,11,8,4,5,7,9]=>{{1,2},{3,4,9,12},{5,10},{6},{7,11},{8}}
[2,1,12,3,10,6,4,7,9,5,11,8]=>{{1,2},{3,4,7,8,12},{5,10},{6},{9},{11}}
[2,1,10,3,4,5,7,8,9,6,12,11]=>{{1,2},{3,4,5,6,10},{7},{8},{9},{11,12}}
[2,1,12,11,4,5,7,8,9,3,6,10]=>{{1,2},{3,10,12},{4,5,6,11},{7},{8},{9}}
[2,1,12,3,11,5,7,8,4,10,6,9]=>{{1,2},{3,4,9,12},{5,6,11},{7},{8},{10}}
[2,1,12,3,4,11,7,5,9,10,6,8]=>{{1,2},{3,4,5,8,12},{6,11},{7},{9},{10}}
[2,1,12,3,4,5,6,8,9,10,11,7]=>{{1,2},{3,4,5,6,7,12},{8},{9},{10},{11}}
[4,1,3,2,6,5,8,7,10,9,12,11]=>{{1,2,4},{3},{5,6},{7,8},{9,10},{11,12}}
[4,1,3,2,6,5,8,7,12,9,11,10]=>{{1,2,4},{3},{5,6},{7,8},{9,10,12},{11}}
[4,1,3,2,6,5,10,7,9,8,12,11]=>{{1,2,4},{3},{5,6},{7,8,10},{9},{11,12}}
[4,1,3,2,6,5,12,11,9,7,8,10]=>{{1,2,4},{3},{5,6},{7,10,12},{8,11},{9}}
[4,1,3,2,6,5,12,7,8,10,11,9]=>{{1,2,4},{3},{5,6},{7,8,9,12},{10},{11}}
[4,1,3,2,8,5,7,6,10,9,12,11]=>{{1,2,4},{3},{5,6,8},{7},{9,10},{11,12}}
[4,1,3,2,8,5,7,6,12,9,11,10]=>{{1,2,4},{3},{5,6,8},{7},{9,10,12},{11}}
[4,1,3,2,10,9,7,5,6,8,12,11]=>{{1,2,4},{3},{5,8,10},{6,9},{7},{11,12}}
[4,1,3,2,12,9,7,11,6,5,8,10]=>{{1,2,4},{3},{5,10,12},{6,9},{7},{8,11}}
[4,1,3,2,12,10,7,5,8,6,11,9]=>{{1,2,4},{3},{5,8,9,12},{6,10},{7},{11}}
[4,1,3,2,10,5,6,8,9,7,12,11]=>{{1,2,4},{3},{5,6,7,10},{8},{9},{11,12}}
[4,1,3,2,12,11,6,8,9,5,7,10]=>{{1,2,4},{3},{5,10,12},{6,7,11},{8},{9}}
[4,1,3,2,12,5,11,8,6,10,7,9]=>{{1,2,4},{3},{5,6,9,12},{7,11},{8},{10}}
[4,1,3,2,12,5,6,7,9,10,11,8]=>{{1,2,4},{3},{5,6,7,8,12},{9},{10},{11}}
[6,5,3,1,2,4,8,7,10,9,12,11]=>{{1,4,6},{2,5},{3},{7,8},{9,10},{11,12}}
[6,5,3,1,2,4,8,7,12,9,11,10]=>{{1,4,6},{2,5},{3},{7,8},{9,10,12},{11}}
[6,5,3,1,2,4,10,7,9,8,12,11]=>{{1,4,6},{2,5},{3},{7,8,10},{9},{11,12}}
[6,5,3,1,2,4,12,11,9,7,8,10]=>{{1,4,6},{2,5},{3},{7,10,12},{8,11},{9}}
[6,5,3,1,2,4,12,7,8,10,11,9]=>{{1,4,6},{2,5},{3},{7,8,9,12},{10},{11}}
[8,5,3,7,2,1,4,6,10,9,12,11]=>{{1,6,8},{2,5},{3},{4,7},{9,10},{11,12}}
[8,5,3,7,2,1,4,6,12,9,11,10]=>{{1,6,8},{2,5},{3},{4,7},{9,10,12},{11}}
[10,5,3,7,2,9,4,1,6,8,12,11]=>{{1,8,10},{2,5},{3},{4,7},{6,9},{11,12}}
[12,5,3,7,2,9,4,11,6,1,8,10]=>{{1,10,12},{2,5},{3},{4,7},{6,9},{8,11}}
[12,5,3,7,2,10,4,1,8,6,11,9]=>{{1,8,9,12},{2,5},{3},{4,7},{6,10},{11}}
[10,5,3,8,2,1,6,4,9,7,12,11]=>{{1,6,7,10},{2,5},{3},{4,8},{9},{11,12}}
[12,5,3,8,2,11,6,4,9,1,7,10]=>{{1,10,12},{2,5},{3},{4,8},{6,7,11},{9}}
[12,5,3,8,2,1,11,4,6,10,7,9]=>{{1,6,9,12},{2,5},{3},{4,8},{7,11},{10}}
[12,5,3,9,2,1,6,7,4,10,11,8]=>{{1,6,7,8,12},{2,5},{3},{4,9},{10},{11}}
[8,6,3,1,4,2,7,5,10,9,12,11]=>{{1,4,5,8},{2,6},{3},{7},{9,10},{11,12}}
[8,6,3,1,4,2,7,5,12,9,11,10]=>{{1,4,5,8},{2,6},{3},{7},{9,10,12},{11}}
[10,6,3,9,4,2,7,1,5,8,12,11]=>{{1,8,10},{2,6},{3},{4,5,9},{7},{11,12}}
[12,6,3,9,4,2,7,11,5,1,8,10]=>{{1,10,12},{2,6},{3},{4,5,9},{7},{8,11}}
[12,6,3,10,4,2,7,1,8,5,11,9]=>{{1,8,9,12},{2,6},{3},{4,5,10},{7},{11}}
[10,6,3,1,9,2,4,8,5,7,12,11]=>{{1,4,7,10},{2,6},{3},{5,9},{8},{11,12}}
[12,6,3,11,9,2,4,8,5,1,7,10]=>{{1,10,12},{2,6},{3},{4,7,11},{5,9},{8}}
[12,6,3,1,10,2,11,8,4,5,7,9]=>{{1,4,9,12},{2,6},{3},{5,10},{7,11},{8}}
[12,6,3,1,10,2,4,7,9,5,11,8]=>{{1,4,7,8,12},{2,6},{3},{5,10},{9},{11}}
[10,7,3,1,4,5,2,8,9,6,12,11]=>{{1,4,5,6,10},{2,7},{3},{8},{9},{11,12}}
[12,7,3,11,4,5,2,8,9,1,6,10]=>{{1,10,12},{2,7},{3},{4,5,6,11},{8},{9}}
[12,7,3,1,11,5,2,8,4,10,6,9]=>{{1,4,9,12},{2,7},{3},{5,6,11},{8},{10}}
[12,7,3,1,4,11,2,5,9,10,6,8]=>{{1,4,5,8,12},{2,7},{3},{6,11},{9},{10}}
[12,8,3,1,4,5,6,2,9,10,11,7]=>{{1,4,5,6,7,12},{2,8},{3},{9},{10},{11}}
[6,1,2,4,5,3,8,7,10,9,12,11]=>{{1,2,3,6},{4},{5},{7,8},{9,10},{11,12}}
[6,1,2,4,5,3,8,7,12,9,11,10]=>{{1,2,3,6},{4},{5},{7,8},{9,10,12},{11}}
[6,1,2,4,5,3,10,7,9,8,12,11]=>{{1,2,3,6},{4},{5},{7,8,10},{9},{11,12}}
[6,1,2,4,5,3,12,11,9,7,8,10]=>{{1,2,3,6},{4},{5},{7,10,12},{8,11},{9}}
[6,1,2,4,5,3,12,7,8,10,11,9]=>{{1,2,3,6},{4},{5},{7,8,9,12},{10},{11}}
[8,7,2,4,5,1,3,6,10,9,12,11]=>{{1,6,8},{2,3,7},{4},{5},{9,10},{11,12}}
[8,7,2,4,5,1,3,6,12,9,11,10]=>{{1,6,8},{2,3,7},{4},{5},{9,10,12},{11}}
[10,7,2,4,5,9,3,1,6,8,12,11]=>{{1,8,10},{2,3,7},{4},{5},{6,9},{11,12}}
[12,7,2,4,5,9,3,11,6,1,8,10]=>{{1,10,12},{2,3,7},{4},{5},{6,9},{8,11}}
[12,7,2,4,5,10,3,1,8,6,11,9]=>{{1,8,9,12},{2,3,7},{4},{5},{6,10},{11}}
[10,8,2,4,5,1,6,3,9,7,12,11]=>{{1,6,7,10},{2,3,8},{4},{5},{9},{11,12}}
[12,8,2,4,5,11,6,3,9,1,7,10]=>{{1,10,12},{2,3,8},{4},{5},{6,7,11},{9}}
[12,8,2,4,5,1,11,3,6,10,7,9]=>{{1,6,9,12},{2,3,8},{4},{5},{7,11},{10}}
[12,9,2,4,5,1,6,7,3,10,11,8]=>{{1,6,7,8,12},{2,3,9},{4},{5},{10},{11}}
[8,1,7,4,2,6,3,5,10,9,12,11]=>{{1,2,5,8},{3,7},{4},{6},{9,10},{11,12}}
[8,1,7,4,2,6,3,5,12,9,11,10]=>{{1,2,5,8},{3,7},{4},{6},{9,10,12},{11}}
[10,9,7,4,2,6,3,1,5,8,12,11]=>{{1,8,10},{2,5,9},{3,7},{4},{6},{11,12}}
[12,9,7,4,2,6,3,11,5,1,8,10]=>{{1,10,12},{2,5,9},{3,7},{4},{6},{8,11}}
[12,10,7,4,2,6,3,1,8,5,11,9]=>{{1,8,9,12},{2,5,10},{3,7},{4},{6},{11}}
[10,1,8,4,9,6,2,3,5,7,12,11]=>{{1,2,7,10},{3,8},{4},{5,9},{6},{11,12}}
[12,11,8,4,9,6,2,3,5,1,7,10]=>{{1,10,12},{2,7,11},{3,8},{4},{5,9},{6}}
[12,1,8,4,10,6,11,3,2,5,7,9]=>{{1,2,9,12},{3,8},{4},{5,10},{6},{7,11}}
[12,1,9,4,10,6,2,7,3,5,11,8]=>{{1,2,7,8,12},{3,9},{4},{5,10},{6},{11}}
[10,1,8,4,2,5,7,3,9,6,12,11]=>{{1,2,5,6,10},{3,8},{4},{7},{9},{11,12}}
[12,11,8,4,2,5,7,3,9,1,6,10]=>{{1,10,12},{2,5,6,11},{3,8},{4},{7},{9}}
[12,1,8,4,11,5,7,3,2,10,6,9]=>{{1,2,9,12},{3,8},{4},{5,6,11},{7},{10}}
[12,1,9,4,2,11,7,5,3,10,6,8]=>{{1,2,5,8,12},{3,9},{4},{6,11},{7},{10}}
[12,1,9,4,2,5,6,8,3,10,11,7]=>{{1,2,5,6,7,12},{3,9},{4},{8},{10},{11}}
[8,1,2,3,5,6,7,4,10,9,12,11]=>{{1,2,3,4,8},{5},{6},{7},{9,10},{11,12}}
[8,1,2,3,5,6,7,4,12,9,11,10]=>{{1,2,3,4,8},{5},{6},{7},{9,10,12},{11}}
[10,9,2,3,5,6,7,1,4,8,12,11]=>{{1,8,10},{2,3,4,9},{5},{6},{7},{11,12}}
[12,9,2,3,5,6,7,11,4,1,8,10]=>{{1,10,12},{2,3,4,9},{5},{6},{7},{8,11}}
[12,10,2,3,5,6,7,1,8,4,11,9]=>{{1,8,9,12},{2,3,4,10},{5},{6},{7},{11}}
[10,1,9,3,5,6,2,8,4,7,12,11]=>{{1,2,7,10},{3,4,9},{5},{6},{8},{11,12}}
[12,11,9,3,5,6,2,8,4,1,7,10]=>{{1,10,12},{2,7,11},{3,4,9},{5},{6},{8}}
[12,1,10,3,5,6,11,8,2,4,7,9]=>{{1,2,9,12},{3,4,10},{5},{6},{7,11},{8}}
[12,1,10,3,5,6,2,7,9,4,11,8]=>{{1,2,7,8,12},{3,4,10},{5},{6},{9},{11}}
[10,1,2,9,5,3,7,8,4,6,12,11]=>{{1,2,3,6,10},{4,9},{5},{7},{8},{11,12}}
[12,11,2,9,5,3,7,8,4,1,6,10]=>{{1,10,12},{2,3,6,11},{4,9},{5},{7},{8}}
[12,1,11,10,5,3,7,8,2,4,6,9]=>{{1,2,9,12},{3,6,11},{4,10},{5},{7},{8}}
[12,1,2,10,5,11,7,3,9,4,6,8]=>{{1,2,3,8,12},{4,10},{5},{6,11},{7},{9}}
[12,1,2,10,5,3,6,8,9,4,11,7]=>{{1,2,3,6,7,12},{4,10},{5},{8},{9},{11}}
[10,1,2,3,4,6,7,8,9,5,12,11]=>{{1,2,3,4,5,10},{6},{7},{8},{9},{11,12}}
[12,11,2,3,4,6,7,8,9,1,5,10]=>{{1,10,12},{2,3,4,5,11},{6},{7},{8},{9}}
[12,1,11,3,4,6,7,8,2,10,5,9]=>{{1,2,9,12},{3,4,5,11},{6},{7},{8},{10}}
[12,1,2,11,4,6,7,3,9,10,5,8]=>{{1,2,3,8,12},{4,5,11},{6},{7},{9},{10}}
[12,1,2,3,11,6,4,8,9,10,5,7]=>{{1,2,3,4,7,12},{5,11},{6},{8},{9},{10}}
[2,1,4,3,6,5,8,7,12,9,10,11]=>{{1,2},{3,4},{5,6},{7,8},{9,10,11,12}}
[2,1,4,3,6,5,10,7,8,9,12,11]=>{{1,2},{3,4},{5,6},{7,8,9,10},{11,12}}
[2,1,4,3,6,5,12,11,8,7,10,9]=>{{1,2},{3,4},{5,6},{7,8,9,10,11,12}}
[2,1,4,3,6,5,12,7,8,9,10,11]=>{{1,2},{3,4},{5,6},{7,8,9,10,11,12}}
[2,1,4,3,8,5,6,7,10,9,12,11]=>{{1,2},{3,4},{5,6,7,8},{9,10},{11,12}}
[2,1,4,3,8,5,6,7,12,9,10,11]=>{{1,2},{3,4},{5,6,7,8},{9,10,11,12}}
[2,1,4,3,10,9,6,5,8,7,12,11]=>{{1,2},{3,4},{5,6,7,8,9,10},{11,12}}
[2,1,4,3,12,9,6,11,8,5,10,7]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,3,12,11,6,5,8,9,10,7]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,3,10,5,6,7,8,9,12,11]=>{{1,2},{3,4},{5,6,7,8,9,10},{11,12}}
[2,1,4,3,12,11,6,7,8,5,10,9]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,3,12,5,10,7,6,9,8,11]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,4,3,12,5,6,7,8,9,10,11]=>{{1,2},{3,4},{5,6,7,8,9,10,11,12}}
[2,1,6,3,4,5,8,7,10,9,12,11]=>{{1,2},{3,4,5,6},{7,8},{9,10},{11,12}}
[2,1,6,3,4,5,8,7,12,9,10,11]=>{{1,2},{3,4,5,6},{7,8},{9,10,11,12}}
[2,1,6,3,4,5,10,7,8,9,12,11]=>{{1,2},{3,4,5,6},{7,8,9,10},{11,12}}
[2,1,6,3,4,5,12,11,8,7,10,9]=>{{1,2},{3,4,5,6},{7,8,9,10,11,12}}
[2,1,6,3,4,5,12,7,8,9,10,11]=>{{1,2},{3,4,5,6},{7,8,9,10,11,12}}
[2,1,8,7,4,3,6,5,10,9,12,11]=>{{1,2},{3,4,5,6,7,8},{9,10},{11,12}}
[2,1,8,7,4,3,6,5,12,9,10,11]=>{{1,2},{3,4,5,6,7,8},{9,10,11,12}}
[2,1,10,7,4,9,6,3,8,5,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,12,7,4,9,6,11,8,3,10,5]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,12,7,4,11,6,3,8,9,10,5]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,10,9,4,3,6,7,8,5,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,12,9,4,11,6,7,8,3,10,5]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,12,11,4,3,10,7,6,9,8,5]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,12,11,4,3,6,7,8,9,10,5]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,8,3,4,5,6,7,10,9,12,11]=>{{1,2},{3,4,5,6,7,8},{9,10},{11,12}}
[2,1,8,3,4,5,6,7,12,9,10,11]=>{{1,2},{3,4,5,6,7,8},{9,10,11,12}}
[2,1,10,9,4,5,6,3,8,7,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,12,9,4,5,6,11,8,3,10,7]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,12,11,4,5,6,3,8,9,10,7]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,10,3,8,5,4,7,6,9,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,12,11,8,5,4,7,6,3,10,9]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,12,3,8,5,10,7,4,9,6,11]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,12,3,10,5,4,7,8,9,6,11]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,10,3,4,5,6,7,8,9,12,11]=>{{1,2},{3,4,5,6,7,8,9,10},{11,12}}
[2,1,12,11,4,5,6,7,8,3,10,9]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,12,3,10,5,6,7,4,9,8,11]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,12,3,4,9,6,5,8,7,10,11]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,12,3,4,5,6,7,8,9,10,11]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[4,1,2,3,6,5,8,7,10,9,12,11]=>{{1,2,3,4},{5,6},{7,8},{9,10},{11,12}}
[4,1,2,3,6,5,8,7,12,9,10,11]=>{{1,2,3,4},{5,6},{7,8},{9,10,11,12}}
[4,1,2,3,6,5,10,7,8,9,12,11]=>{{1,2,3,4},{5,6},{7,8,9,10},{11,12}}
[4,1,2,3,6,5,12,11,8,7,10,9]=>{{1,2,3,4},{5,6},{7,8,9,10,11,12}}
[4,1,2,3,6,5,12,7,8,9,10,11]=>{{1,2,3,4},{5,6},{7,8,9,10,11,12}}
[4,1,2,3,8,5,6,7,10,9,12,11]=>{{1,2,3,4},{5,6,7,8},{9,10},{11,12}}
[4,1,2,3,8,5,6,7,12,9,10,11]=>{{1,2,3,4},{5,6,7,8},{9,10,11,12}}
[4,1,2,3,10,9,6,5,8,7,12,11]=>{{1,2,3,4},{5,6,7,8,9,10},{11,12}}
[4,1,2,3,12,9,6,11,8,5,10,7]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[4,1,2,3,12,11,6,5,8,9,10,7]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[4,1,2,3,10,5,6,7,8,9,12,11]=>{{1,2,3,4},{5,6,7,8,9,10},{11,12}}
[4,1,2,3,12,11,6,7,8,5,10,9]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[4,1,2,3,12,5,10,7,6,9,8,11]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[4,1,2,3,12,5,6,7,8,9,10,11]=>{{1,2,3,4},{5,6,7,8,9,10,11,12}}
[6,5,2,1,4,3,8,7,10,9,12,11]=>{{1,2,3,4,5,6},{7,8},{9,10},{11,12}}
[6,5,2,1,4,3,8,7,12,9,10,11]=>{{1,2,3,4,5,6},{7,8},{9,10,11,12}}
[6,5,2,1,4,3,10,7,8,9,12,11]=>{{1,2,3,4,5,6},{7,8,9,10},{11,12}}
[6,5,2,1,4,3,12,7,8,9,10,11]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}}
[8,5,2,7,4,1,6,3,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[8,5,2,7,4,1,6,3,12,9,10,11]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[10,5,2,7,4,9,6,1,8,3,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,5,2,7,4,9,6,11,8,1,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,5,2,7,4,11,6,1,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,5,2,9,4,1,6,7,8,3,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,5,2,9,4,11,6,7,8,1,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,5,2,11,4,1,10,7,6,9,8,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,5,2,11,4,1,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,7,2,1,4,5,6,3,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[8,7,2,1,4,5,6,3,12,9,10,11]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[10,7,2,9,4,5,6,1,8,3,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,7,2,9,4,5,6,11,8,1,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,7,2,11,4,5,6,1,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,9,2,1,8,5,4,7,6,3,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,9,2,11,8,5,4,7,6,1,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,2,1,8,5,10,7,4,9,6,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,2,1,10,5,4,7,8,9,6,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,9,2,1,4,5,6,7,8,3,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,9,2,11,4,5,6,7,8,1,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,2,1,10,5,6,7,4,9,8,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,2,1,4,9,6,5,8,7,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,2,1,4,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[6,1,2,3,4,5,8,7,10,9,12,11]=>{{1,2,3,4,5,6},{7,8},{9,10},{11,12}}
[6,1,2,3,4,5,8,7,12,9,10,11]=>{{1,2,3,4,5,6},{7,8},{9,10,11,12}}
[6,1,2,3,4,5,10,7,8,9,12,11]=>{{1,2,3,4,5,6},{7,8,9,10},{11,12}}
[6,1,2,3,4,5,12,11,8,7,10,9]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}}
[6,1,2,3,4,5,12,7,8,9,10,11]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}}
[8,7,2,3,4,1,6,5,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[8,7,2,3,4,1,6,5,12,9,10,11]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[10,7,2,3,4,9,6,1,8,5,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,7,2,3,4,9,6,11,8,1,10,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,7,2,3,4,11,6,1,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,9,2,3,4,1,6,7,8,5,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,9,2,3,4,11,6,7,8,1,10,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,2,3,4,1,10,7,6,9,8,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,2,3,4,1,6,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,6,3,2,5,4,7,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[8,1,6,3,2,5,4,7,12,9,10,11]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[10,9,6,3,2,5,4,1,8,7,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,9,6,3,2,5,4,11,8,1,10,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,6,3,2,5,4,1,8,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,1,6,3,8,5,2,7,4,9,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,11,6,3,8,5,2,7,4,1,10,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,6,3,8,5,10,7,2,9,4,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,6,3,10,5,2,7,8,9,4,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,1,8,3,2,5,6,7,4,9,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,11,8,3,2,5,6,7,4,1,10,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,8,3,10,5,6,7,2,9,4,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,10,3,2,9,6,5,8,7,4,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,10,3,2,5,6,7,8,9,4,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,1,2,3,4,5,6,7,10,9,12,11]=>{{1,2,3,4,5,6,7,8},{9,10},{11,12}}
[8,1,2,3,4,5,6,7,12,9,10,11]=>{{1,2,3,4,5,6,7,8},{9,10,11,12}}
[10,9,2,3,4,5,6,1,8,7,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,9,2,3,4,5,6,11,8,1,10,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,2,3,4,5,6,1,8,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,1,8,3,4,5,2,7,6,9,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,11,8,3,4,5,2,7,6,1,10,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,8,3,4,5,10,7,2,9,6,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,10,3,4,5,2,7,8,9,6,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,1,2,7,4,3,6,5,8,9,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,11,2,7,4,3,6,5,8,1,10,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,10,7,4,3,6,5,2,9,8,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,2,7,4,9,6,3,8,5,10,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,2,9,4,3,6,7,8,5,10,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,1,2,3,4,5,6,7,8,9,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[12,11,2,3,4,5,6,7,8,1,10,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,10,3,4,5,6,7,2,9,8,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,2,9,4,5,6,3,8,7,10,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,2,3,8,5,4,7,6,9,10,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,1,2,3,4,5,6,7,8,9,10,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,1,4,3,6,5,12,7,9,8,11,10]=>{{1,2},{3,4},{5,6},{7,8,10,12},{9},{11}}
[2,1,4,3,6,5,11,8,12,7,10,9]=>{{1,2},{3,4},{5,6},{7,10,11},{8},{9,12}}
[2,1,4,3,10,5,7,6,9,8,12,11]=>{{1,2},{3,4},{5,6,8,10},{7},{9},{11,12}}
[2,1,4,3,12,5,7,6,9,8,11,10]=>{{1,2},{3,4},{5,6,8,10,12},{7},{9},{11}}
[2,1,4,3,11,8,12,5,7,6,10,9]=>{{1,2},{3,4},{5,6,8,10,11},{7,9,12}}
[2,1,4,3,9,6,10,5,8,7,12,11]=>{{1,2},{3,4},{5,8,9},{6},{7,10},{11,12}}
[2,1,4,3,9,6,12,5,8,7,11,10]=>{{1,2},{3,4},{5,8,9},{6},{7,10,12},{11}}
[2,1,4,3,12,5,8,7,11,6,10,9]=>{{1,2},{3,4},{5,6,9,10,11,12},{7,8}}
[2,1,4,3,11,6,10,7,12,5,9,8]=>{{1,2},{3,4},{5,7,8,9,10,11,12},{6}}
[2,1,6,3,5,4,12,7,9,8,11,10]=>{{1,2},{3,4,6},{5},{7,8,10,12},{9},{11}}
[2,1,6,3,5,4,11,8,12,7,10,9]=>{{1,2},{3,4,6},{5},{7,10,11},{8},{9,12}}
[2,1,8,3,5,4,7,6,10,9,12,11]=>{{1,2},{3,4,6,8},{5},{7},{9,10},{11,12}}
[2,1,8,3,5,4,7,6,12,9,11,10]=>{{1,2},{3,4,6,8},{5},{7},{9,10,12},{11}}
[2,1,10,3,5,4,7,6,9,8,12,11]=>{{1,2},{3,4,6,8,10},{5},{7},{9},{11,12}}
[2,1,12,3,5,4,7,6,9,8,11,10]=>{{1,2},{3,4,6,8,10,12},{5},{7},{9},{11}}
[2,1,11,8,12,3,5,4,7,6,10,9]=>{{1,2},{3,6,10,11},{4,8},{5,7,9,12}}
[2,1,9,6,10,3,5,4,8,7,12,11]=>{{1,2},{3,4,6,8,9},{5,7,10},{11,12}}
[2,1,9,6,12,3,5,4,8,7,11,10]=>{{1,2},{3,4,6,8,9},{5,7,10,12},{11}}
[2,1,12,3,5,4,8,7,11,6,10,9]=>{{1,2},{3,4,6,9,10,11,12},{5},{7,8}}
[2,1,11,6,10,7,12,3,5,4,9,8]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}}
[2,1,7,4,8,3,6,5,10,9,12,11]=>{{1,2},{3,6,7},{4},{5,8},{9,10},{11,12}}
[2,1,7,4,8,3,6,5,12,9,11,10]=>{{1,2},{3,6,7},{4},{5,8},{9,10,12},{11}}
[2,1,7,4,10,3,6,5,9,8,12,11]=>{{1,2},{3,6,7},{4},{5,8,10},{9},{11,12}}
[2,1,7,4,12,3,6,5,9,8,11,10]=>{{1,2},{3,6,7},{4},{5,8,10,12},{9},{11}}
[2,1,7,4,11,8,12,3,6,5,10,9]=>{{1,2},{3,6,7,8,9,12},{4},{5,10,11}}
[2,1,10,3,6,5,9,4,8,7,12,11]=>{{1,2},{3,4,7,8,9,10},{5,6},{11,12}}
[2,1,12,3,6,5,9,4,8,7,11,10]=>{{1,2},{3,4,7,8,9,10,12},{5,6},{11}}
[2,1,11,4,8,7,12,3,6,5,10,9]=>{{1,2},{3,5,8,10,11},{4},{6,7,9,12}}
[2,1,12,3,6,5,10,7,11,4,9,8]=>{{1,2},{3,4,7,8,10,12},{5,6},{9,11}}
[2,1,9,4,8,5,10,3,7,6,12,11]=>{{1,2},{3,5,6,7,8,9,10},{4},{11,12}}
[2,1,9,4,8,5,12,3,7,6,11,10]=>{{1,2},{3,5,6,7,8,9,10,12},{4},{11}}
[2,1,12,3,7,6,11,4,8,5,10,9]=>{{1,2},{3,4,8,9,12},{5,7,10,11},{6}}
[2,1,10,5,12,3,7,6,11,4,9,8]=>{{1,2},{3,4,5,6,8,10,12},{7},{9,11}}
[2,1,10,5,11,4,9,6,12,3,8,7]=>{{1,2},{3,10},{4,5,6,8,11},{7,9,12}}
[4,1,3,2,6,5,12,7,9,8,11,10]=>{{1,2,4},{3},{5,6},{7,8,10,12},{9},{11}}
[4,1,3,2,6,5,11,8,12,7,10,9]=>{{1,2,4},{3},{5,6},{7,10,11},{8},{9,12}}
[4,1,3,2,10,5,7,6,9,8,12,11]=>{{1,2,4},{3},{5,6,8,10},{7},{9},{11,12}}
[4,1,3,2,12,5,7,6,9,8,11,10]=>{{1,2,4},{3},{5,6,8,10,12},{7},{9},{11}}
[4,1,3,2,11,8,12,5,7,6,10,9]=>{{1,2,4},{3},{5,6,8,10,11},{7,9,12}}
[4,1,3,2,9,6,10,5,8,7,12,11]=>{{1,2,4},{3},{5,8,9},{6},{7,10},{11,12}}
[4,1,3,2,9,6,12,5,8,7,11,10]=>{{1,2,4},{3},{5,8,9},{6},{7,10,12},{11}}
[4,1,3,2,12,5,8,7,11,6,10,9]=>{{1,2,4},{3},{5,6,9,10,11,12},{7,8}}
[4,1,3,2,11,6,10,7,12,5,9,8]=>{{1,2,4},{3},{5,7,8,9,10,11,12},{6}}
[6,1,3,2,5,4,8,7,10,9,12,11]=>{{1,2,4,6},{3},{5},{7,8},{9,10},{11,12}}
[6,1,3,2,5,4,8,7,12,9,11,10]=>{{1,2,4,6},{3},{5},{7,8},{9,10,12},{11}}
[6,1,3,2,5,4,10,7,9,8,12,11]=>{{1,2,4,6},{3},{5},{7,8,10},{9},{11,12}}
[6,1,3,2,5,4,12,7,9,8,11,10]=>{{1,2,4,6},{3},{5},{7,8,10,12},{9},{11}}
[6,1,3,2,5,4,11,8,12,7,10,9]=>{{1,2,4,6},{3},{5},{7,10,11},{8},{9,12}}
[8,1,3,2,5,4,7,6,10,9,12,11]=>{{1,2,4,6,8},{3},{5},{7},{9,10},{11,12}}
[8,1,3,2,5,4,7,6,12,9,11,10]=>{{1,2,4,6,8},{3},{5},{7},{9,10,12},{11}}
[10,1,3,2,5,4,7,6,9,8,12,11]=>{{1,2,4,6,8,10},{3},{5},{7},{9},{11,12}}
[11,8,12,1,3,2,5,4,7,6,10,9]=>{{1,2,4,6,8,10,11},{3,5,7,9,12}}
[9,6,10,1,3,2,5,4,8,7,12,11]=>{{1,4,8,9},{2,6},{3,5,7,10},{11,12}}
[9,6,12,1,3,2,5,4,8,7,11,10]=>{{1,4,8,9},{2,6},{3,5,7,10,12},{11}}
[12,1,3,2,5,4,8,7,11,6,10,9]=>{{1,2,4,6,9,10,11,12},{3},{5},{7,8}}
[11,6,10,7,12,1,3,2,5,4,9,8]=>{{1,2,5,6,8,9,11,12},{3,4,7,10}}
[7,4,8,1,3,2,6,5,10,9,12,11]=>{{1,2,4,6,7},{3,5,8},{9,10},{11,12}}
[7,4,8,1,3,2,6,5,12,9,11,10]=>{{1,2,4,6,7},{3,5,8},{9,10,12},{11}}
[7,4,10,1,3,2,6,5,9,8,12,11]=>{{1,2,4,6,7},{3,5,8,10},{9},{11,12}}
[7,4,12,1,3,2,6,5,9,8,11,10]=>{{1,2,4,6,7},{3,5,8,10,12},{9},{11}}
[7,4,11,8,12,1,3,2,6,5,10,9]=>{{1,3,5,6,7,9,10,11,12},{2,4,8}}
[10,1,3,2,6,5,9,4,8,7,12,11]=>{{1,2,4,7,8,9,10},{3},{5,6},{11,12}}
[12,1,3,2,6,5,9,4,8,7,11,10]=>{{1,2,4,7,8,9,10,12},{3},{5,6},{11}}
[11,4,8,7,12,1,3,2,6,5,10,9]=>{{1,5,6,9,10,11,12},{2,3,4,7,8}}
[12,1,3,2,6,5,10,7,11,4,9,8]=>{{1,2,4,7,8,10,12},{3},{5,6},{9,11}}
[9,4,8,5,10,1,3,2,7,6,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}}
[9,4,8,5,12,1,3,2,7,6,11,10]=>{{1,2,3,4,5,6,7,8,9,10,12},{11}}
[12,1,3,2,7,6,11,4,8,5,10,9]=>{{1,2,4,8,9,12},{3},{5,7,10,11},{6}}
[10,5,12,1,3,2,7,6,11,4,9,8]=>{{1,4,10},{2,3,5,6,8,12},{7},{9,11}}
[10,5,11,4,9,6,12,1,3,2,8,7]=>{{1,2,3,5,8,9,10,11},{4},{6},{7,12}}
[5,2,6,1,4,3,8,7,10,9,12,11]=>{{1,4,5},{2},{3,6},{7,8},{9,10},{11,12}}
[5,2,6,1,4,3,8,7,12,9,11,10]=>{{1,4,5},{2},{3,6},{7,8},{9,10,12},{11}}
[5,2,6,1,4,3,10,7,9,8,12,11]=>{{1,4,5},{2},{3,6},{7,8,10},{9},{11,12}}
[5,2,6,1,4,3,12,7,9,8,11,10]=>{{1,4,5},{2},{3,6},{7,8,10,12},{9},{11}}
[5,2,6,1,4,3,11,8,12,7,10,9]=>{{1,4,5},{2},{3,6},{7,10,11},{8},{9,12}}
[5,2,8,1,4,3,7,6,10,9,12,11]=>{{1,4,5},{2},{3,6,8},{7},{9,10},{11,12}}
[5,2,8,1,4,3,7,6,12,9,11,10]=>{{1,4,5},{2},{3,6,8},{7},{9,10,12},{11}}
[5,2,10,1,4,3,7,6,9,8,12,11]=>{{1,4,5},{2},{3,6,8,10},{7},{9},{11,12}}
[5,2,12,1,4,3,7,6,9,8,11,10]=>{{1,4,5},{2},{3,6,8,10,12},{7},{9},{11}}
[5,2,11,8,12,1,4,3,7,6,10,9]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[5,2,9,6,10,1,4,3,8,7,12,11]=>{{1,4,5,6,7,10},{2},{3,8,9},{11,12}}
[5,2,9,6,12,1,4,3,8,7,11,10]=>{{1,4,5,6,7,10,12},{2},{3,8,9},{11}}
[5,2,12,1,4,3,8,7,11,6,10,9]=>{{1,4,5},{2},{3,6,9,10,11,12},{7,8}}
[5,2,11,6,10,7,12,1,4,3,9,8]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,1,4,3,7,2,6,5,10,9,12,11]=>{{1,2,5,6,7,8},{3,4},{9,10},{11,12}}
[8,1,4,3,7,2,6,5,12,9,11,10]=>{{1,2,5,6,7,8},{3,4},{9,10,12},{11}}
[10,1,4,3,7,2,6,5,9,8,12,11]=>{{1,2,5,6,7,8,10},{3,4},{9},{11,12}}
[12,1,4,3,7,2,6,5,9,8,11,10]=>{{1,2,5,6,7,8,10,12},{3,4},{9},{11}}
[11,8,12,1,4,3,7,2,6,5,10,9]=>{{1,4,5,10,11},{2,8},{3,6,9,12},{7}}
[9,2,6,5,10,1,4,3,8,7,12,11]=>{{1,3,6,8,9},{2},{4,5,7,10},{11,12}}
[9,2,6,5,12,1,4,3,8,7,11,10]=>{{1,3,6,8,9},{2},{4,5,7,10,12},{11}}
[12,1,4,3,8,7,11,2,6,5,10,9]=>{{1,2,5,6,7,8,9,10,11,12},{3,4}}
[11,2,6,5,10,7,12,1,4,3,9,8]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[10,1,4,3,8,5,9,2,7,6,12,11]=>{{1,2,5,6,8,10},{3,4},{7,9},{11,12}}
[12,1,4,3,8,5,9,2,7,6,11,10]=>{{1,2,5,6,8,10,12},{3,4},{7,9},{11}}
[11,2,7,6,12,1,4,3,8,5,10,9]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[10,5,11,2,7,6,12,1,4,3,9,8]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[10,5,12,1,4,3,9,6,11,2,8,7]=>{{1,2,4,5,10},{3,6,7,8,9,11,12}}
[7,2,6,3,8,1,5,4,10,9,12,11]=>{{1,3,4,5,6,7,8},{2},{9,10},{11,12}}
[7,2,6,3,8,1,5,4,12,9,11,10]=>{{1,3,4,5,6,7,8},{2},{9,10,12},{11}}
[7,2,6,3,10,1,5,4,9,8,12,11]=>{{1,3,4,5,6,7,8,10},{2},{9},{11,12}}
[7,2,6,3,12,1,5,4,9,8,11,10]=>{{1,3,4,5,6,7,8,10,12},{2},{9},{11}}
[7,2,6,3,11,8,12,1,5,4,10,9]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[10,1,5,4,9,2,6,3,8,7,12,11]=>{{1,2,6,7,10},{3,5,8,9},{4},{11,12}}
[12,1,5,4,9,2,6,3,8,7,11,10]=>{{1,2,6,7,10,12},{3,5,8,9},{4},{11}}
[11,2,6,3,8,7,12,1,5,4,10,9]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[12,1,5,4,10,7,11,2,6,3,9,8]=>{{1,2,8,12},{3,5,10},{4},{6,7,9,11}}
[8,3,10,1,5,4,9,2,7,6,12,11]=>{{1,2,3,4,6,8,10},{5},{7,9},{11,12}}
[8,3,12,1,5,4,9,2,7,6,11,10]=>{{1,2,3,4,6,8,10,12},{5},{7,9},{11}}
[8,3,11,2,7,6,12,1,5,4,10,9]=>{{1,8},{2,3,4,10,11},{5,7,9,12},{6}}
[11,2,7,6,12,1,5,4,10,3,9,8]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[12,1,5,4,10,3,9,6,11,2,8,7]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[8,3,9,2,7,4,10,1,6,5,12,11]=>{{1,8},{2,3,4,6,9},{5,7,10},{11,12}}
[8,3,9,2,7,4,12,1,6,5,11,10]=>{{1,8},{2,3,4,6,9},{5,7,10,12},{11}}
[8,3,12,1,6,5,11,2,7,4,10,9]=>{{1,2,3,4,7,8,9,10,11,12},{5,6}}
[12,1,6,5,11,2,7,4,10,3,9,8]=>{{1,2,3,4,5,6,8,9,10,11,12},{7}}
[10,3,9,4,12,1,6,5,11,2,8,7]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[10,3,9,4,11,2,8,5,12,1,7,6]=>{{1,10},{2,3,6,9,12},{4},{5,7,8,11}}
[11,12,8,2,1,6,4,3,5,7,9,10]=>{{1,5,9,11},{2,4,7,10,12},{3,8},{6}}
[12,2,9,1,10,6,4,3,5,7,8,11]=>{{1,3,4,5,7,8,9,10,11,12},{2},{6}}
[11,12,2,1,9,6,4,3,5,7,8,10]=>{{1,2,3,4,7,8,10,11,12},{5,9},{6}}
[10,2,4,1,11,3,12,6,5,7,8,9]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[7,12,10,2,1,8,4,3,5,6,9,11]=>{{1,2,4,5,7,9,11,12},{3,6,8,10}}
[2,11,7,1,12,8,4,3,5,6,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[9,12,2,1,10,7,4,3,5,6,8,11]=>{{1,4,5,6,7,9,10},{2,3,8,11,12}}
[2,11,1,12,9,7,4,3,5,6,8,10]=>{{1,2,3,8,11},{4,6,7,10,12},{5,9}}
[10,11,2,1,4,3,12,7,5,6,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,12,2,1,9,4,3,10,5,6,7,11]=>{{1,4,6,8,10},{2,3,7,11,12},{5,9}}
[2,11,1,12,8,4,3,9,5,6,7,10]=>{{1,2,3,7,11},{4,6,10,12},{5,8,9}}
[2,10,1,11,4,3,12,8,5,6,7,9]=>{{1,2,3,6,10},{4,5,7,9,11,12},{8}}
[2,9,1,10,4,3,11,5,12,6,7,8]=>{{1,2,3,4,5,6,8,9,10,12},{7,11}}
[12,10,8,5,2,1,6,3,4,7,9,11]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}}
[5,11,2,1,12,8,6,3,4,7,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,9,5,2,1,10,6,3,4,7,8,11]=>{{1,3,5,8,11,12},{2,4,9},{6,7,10}}
[11,5,2,1,12,9,6,3,4,7,8,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,11,2,1,5,3,12,6,4,7,8,9]=>{{1,4,7,9,10,12},{2,3,6,8,11},{5}}
[12,10,7,2,1,8,5,3,4,6,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,7,2,1,12,8,5,3,4,6,9,10]=>{{1,4,9,11},{2,3,5,6,7,8,10,12}}
[12,9,2,1,10,7,5,3,4,6,8,11]=>{{1,2,3,4,8,9,11,12},{5,6,7,10}}
[11,2,1,12,9,7,5,3,4,6,8,10]=>{{1,3,8,11},{2},{4,5,6,7,9,10,12}}
[10,11,2,1,3,12,7,5,4,6,8,9]=>{{1,4,6,9,10,12},{2,3,5,8,11},{7}}
[8,9,2,1,12,3,10,5,4,6,7,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,8,2,1,12,3,9,5,4,6,7,10]=>{{1,4,7,9,11},{2,3,5,6,8,10,12}}
[2,10,1,11,3,12,8,5,4,6,7,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[2,9,1,10,3,11,5,4,12,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,10,6,2,1,7,3,8,4,5,9,11]=>{{1,2,4,5,9,10,11,12},{3,6,7},{8}}
[11,6,2,1,12,7,3,8,4,5,9,10]=>{{1,4,9,11},{2,3,6,7},{5,10,12},{8}}
[12,9,2,1,10,6,3,7,4,5,8,11]=>{{1,2,3,4,7,8,9,11,12},{5,10},{6}}
[11,2,1,12,9,6,3,7,4,5,8,10]=>{{1,3,7,8,11},{2},{4,5,9,10,12},{6}}
[10,2,1,11,6,3,12,7,4,5,8,9]=>{{1,3,5,6,10},{2},{4,7,8,9,11,12}}
[12,8,2,1,9,3,10,6,4,5,7,11]=>{{1,4,5,7,9,10,11,12},{2,3,6,8}}
[11,2,1,12,8,3,9,6,4,5,7,10]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[10,2,1,11,3,12,8,6,4,5,7,9]=>{{1,3,5,10},{2},{4,6,7,8,9,11,12}}
[2,9,1,10,3,11,4,12,6,5,7,8]=>{{1,2,3,4,5,6,7,9,10,11},{8,12}}
[12,7,2,1,8,3,9,4,10,5,6,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,2,1,12,7,3,8,4,9,5,6,10]=>{{1,3,6,11},{2},{4,5,7,8,10,12},{9}}
[10,2,1,11,3,12,7,4,8,5,6,9]=>{{1,3,5,10},{2},{4,6,8,9,11,12},{7}}
[9,2,1,10,3,11,4,12,7,5,6,8]=>{{1,3,4,5,7,9,10},{2},{6,11},{8,12}}
[8,2,1,9,3,10,4,11,5,12,6,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[12,10,8,6,3,1,4,2,5,7,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,12,3,1,8,6,4,2,5,7,9,10]=>{{1,2,4,5,7,8,9,10,11,12},{3},{6}}
[9,12,3,1,10,6,4,2,5,7,8,11]=>{{1,4,5,7,9,10},{2,8,11,12},{3},{6}}
[3,11,1,12,9,6,4,2,5,7,8,10]=>{{1,3},{2,8,11},{4,7,10,12},{5,9},{6}}
[3,10,4,1,11,2,12,6,5,7,8,9]=>{{1,3,4},{2,5,6,7,8,9,10,11,12}}
[12,10,7,3,1,8,4,2,5,6,9,11]=>{{1,5,9,11,12},{2,6,8,10},{3,4,7}}
[11,7,3,1,12,8,4,2,5,6,9,10]=>{{1,2,4,5,6,7,8,9,10,11,12},{3}}
[12,9,3,1,10,7,4,2,5,6,8,11]=>{{1,2,4,5,6,7,8,9,10,11,12},{3}}
[11,3,1,12,9,7,4,2,5,6,8,10]=>{{1,2,3,8,11},{4,6,7,10,12},{5,9}}
[3,10,1,11,4,2,12,7,5,6,8,9]=>{{1,3},{2,6,10},{4,5,7,8,9,11,12}}
[12,8,3,1,9,4,2,10,5,6,7,11]=>{{1,2,4,6,7,8,10,11,12},{3},{5,9}}
[11,3,1,12,8,4,2,9,5,6,7,10]=>{{1,2,3,7,11},{4,6,10,12},{5,8,9}}
[10,3,1,11,4,2,12,8,5,6,7,9]=>{{1,2,3,6,10},{4,5,7,9,11,12},{8}}
[9,3,1,10,4,2,11,5,12,6,7,8]=>{{1,2,3,4,5,6,8,9,10,12},{7,11}}
[12,10,8,5,1,6,3,2,4,7,9,11]=>{{1,4,5,9,11,12},{2,3,7,8,10},{6}}
[5,11,1,12,8,6,3,2,4,7,9,10]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[12,9,5,1,10,6,3,2,4,7,8,11]=>{{1,2,4,8,9,11,12},{3,5,7,10},{6}}
[11,5,1,12,9,6,3,2,4,7,8,10]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[3,10,1,11,5,2,12,6,4,7,8,9]=>{{1,3},{2,4,6,7,8,9,10,11,12},{5}}
[12,10,7,1,8,5,3,2,4,6,9,11]=>{{1,4,9,11,12},{2,5,6,8,10},{3,7}}
[11,7,1,12,8,5,3,2,4,6,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,9,1,10,7,5,3,2,4,6,8,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,1,12,9,7,5,3,2,4,6,8,10]=>{{1,2,8,11},{3,5,6,7,10,12},{4,9}}
[3,10,1,11,2,12,7,5,4,6,8,9]=>{{1,3},{2,4,5,6,8,9,10,11,12},{7}}
[8,9,1,12,3,2,10,5,4,6,7,11]=>{{1,3,5,8},{2,4,6,7,9,10,11,12}}
[11,8,1,12,3,2,9,5,4,6,7,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,3,1,11,2,12,8,5,4,6,7,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[9,3,1,10,2,11,5,4,12,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,10,6,1,7,3,2,8,4,5,9,11]=>{{1,4,9,11,12},{2,5,7,10},{3,6},{8}}
[11,6,1,12,7,3,2,8,4,5,9,10]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[12,9,1,10,6,3,2,7,4,5,8,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,1,12,9,6,3,2,7,4,5,8,10]=>{{1,2,7,8,11},{3,5,6,10,12},{4,9}}
[10,1,11,6,3,2,12,7,4,5,8,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,8,1,9,3,2,10,6,4,5,7,11]=>{{1,3,5,7,10,11,12},{2,6,8},{4,9}}
[11,1,12,8,3,2,9,6,4,5,7,10]=>{{1,2,4,6,7,8,9,11},{3,5,10,12}}
[10,1,11,3,2,12,8,6,4,5,7,9]=>{{1,2,5,10},{3,4,6,7,8,9,11,12}}
[9,3,1,10,2,11,4,12,6,5,7,8]=>{{1,2,3,4,5,6,7,9,10,11},{8,12}}
[12,7,1,8,3,2,9,4,10,5,6,11]=>{{1,2,3,5,6,7,9,10,11,12},{4,8}}
[11,1,12,7,3,2,8,4,9,5,6,10]=>{{1,2,6,11},{3,5,10,12},{4,7,8},{9}}
[10,1,11,3,2,12,7,4,8,5,6,9]=>{{1,2,5,10},{3,4,6,8,9,11,12},{7}}
[9,1,10,3,2,11,4,12,7,5,6,8]=>{{1,2,3,4,5,7,9,10},{6,11},{8,12}}
[8,1,9,3,2,10,4,11,5,12,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,10,8,4,1,5,2,6,3,7,9,11]=>{{1,3,5,6,8,9,11,12},{2,7,10},{4}}
[4,11,1,12,8,5,2,6,3,7,9,10]=>{{1,2,3,4,7,9,10,11,12},{5,6,8}}
[12,9,4,1,10,5,2,6,3,7,8,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,4,1,12,9,5,2,6,3,7,8,10]=>{{1,3,5,6,8,9,11},{2,4,7,10,12}}
[10,4,1,11,5,2,12,6,3,7,8,9]=>{{1,3,7,9,10,12},{2,4,6,8,11},{5}}
[12,10,7,1,8,4,2,5,3,6,9,11]=>{{1,2,3,4,6,7,9,10,11,12},{5,8}}
[11,7,1,12,8,4,2,5,3,6,9,10]=>{{1,3,9,11},{2,7},{4,6,10,12},{5,8}}
[12,9,1,10,7,4,2,5,3,6,8,11]=>{{1,2,3,5,7,8,9,11,12},{4,6,10}}
[11,1,12,9,7,4,2,5,3,6,8,10]=>{{1,2,5,7,8,11},{3,4,6,9,10,12}}
[10,4,1,11,2,12,7,5,3,6,8,9]=>{{1,3,6,9,10,12},{2,4,5,8,11},{7}}
[12,8,1,9,4,2,10,5,3,6,7,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,1,12,8,4,2,9,5,3,6,7,10]=>{{1,2,3,6,7,9,10,11,12},{4,5,8}}
[10,1,11,4,2,12,8,5,3,6,7,9]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[9,1,10,4,2,11,5,3,12,6,7,8]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[12,10,6,1,7,2,8,4,3,5,9,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,6,1,12,7,2,8,4,3,5,9,10]=>{{1,3,9,11},{2,6},{4,5,7,8,10,12}}
[12,9,1,10,6,2,7,4,3,5,8,11]=>{{1,2,3,4,5,6,8,9,10,11,12},{7}}
[11,1,12,9,6,2,7,4,3,5,8,10]=>{{1,2,3,4,5,6,8,9,10,11,12},{7}}
[10,1,11,6,2,12,7,4,3,5,8,9]=>{{1,2,5,10},{3,4,6,8,9,11,12},{7}}
[12,8,1,9,2,10,6,4,3,5,7,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,1,12,8,2,9,6,4,3,5,7,10]=>{{1,2,3,5,6,7,9,10,11,12},{4,8}}
[10,1,11,2,12,8,6,4,3,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[9,1,10,4,2,11,3,12,6,5,7,8]=>{{1,2,3,5,6,7,9,10,11},{4},{8,12}}
[12,7,1,8,2,9,4,3,10,5,6,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,1,12,7,2,8,4,3,9,5,6,10]=>{{1,2,3,5,6,8,10,11,12},{4,7},{9}}
[10,1,11,2,12,7,4,3,8,5,6,9]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[9,1,10,2,11,4,3,12,7,5,6,8]=>{{1,2,3,4,5,6,7,9,10,11},{8,12}}
[8,1,9,2,10,4,3,11,5,12,6,7]=>{{1,2,4,6,8,11},{3,5,7,9,10,12}}
[12,10,5,1,6,2,7,3,8,4,9,11]=>{{1,2,3,4,5,6,8,9,10,11,12},{7}}
[11,5,1,12,6,2,7,3,8,4,9,10]=>{{1,3,8,9,11},{2,5,6},{4,10,12},{7}}
[12,9,1,10,5,2,6,3,7,4,8,11]=>{{1,3,8,11,12},{2,6,7,9},{4,10},{5}}
[11,1,12,9,5,2,6,3,7,4,8,10]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[10,1,11,5,2,12,6,3,7,4,8,9]=>{{1,2,4,5,10},{3,8,11},{6,7,9,12}}
[12,8,1,9,2,10,5,3,6,4,7,11]=>{{1,2,3,5,7,8,11,12},{4,6,9,10}}
[11,1,12,8,2,9,5,3,6,4,7,10]=>{{1,2,5,7,11},{3,4,8,10,12},{6,9}}
[10,1,11,2,12,8,5,3,6,4,7,9]=>{{1,2,4,10},{3,5,6,7,8,9,11,12}}
[9,1,10,2,11,5,3,12,6,4,7,8]=>{{1,2,3,4,5,6,7,9,10,11},{8,12}}
[12,7,1,8,2,9,3,10,5,4,6,11]=>{{1,2,3,5,6,7,9,11,12},{4,8,10}}
[11,1,12,7,2,8,3,9,5,4,6,10]=>{{1,2,5,6,8,9,11},{3,4,7,10,12}}
[10,1,11,2,12,7,3,8,5,4,6,9]=>{{1,2,4,10},{3,6,7,11},{5,9,12},{8}}
[9,1,10,2,11,3,12,7,5,4,6,8]=>{{1,2,3,4,5,6,9,10,11},{7,8,12}}
[8,1,9,2,10,3,11,5,4,12,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,6,1,7,2,8,3,9,4,10,5,11]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}}
[11,1,12,6,2,7,3,8,4,9,5,10]=>{{1,2,5,11},{3,4,6,7,9,10,12},{8}}
[10,1,11,2,12,6,3,7,4,8,5,9]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}}
[9,1,10,2,11,3,12,6,4,7,5,8]=>{{1,2,4,9},{3,6,7,8,10,12},{5,11}}
[8,1,9,2,10,3,11,4,12,6,5,7]=>{{1,2,4,8},{3,5,6,7,9,10,11,12}}
[3,2,5,4,7,6,9,8,10,12,11,1]=>{{1,3,5,7,9,10,12},{2},{4},{6},{8},{11}}
[3,2,5,4,7,6,8,11,9,10,12,1]=>{{1,3,5,7,8,11,12},{2},{4},{6},{9},{10}}
[3,2,5,4,7,6,8,10,9,12,11,1]=>{{1,3,5,7,8,10,12},{2},{4},{6},{9},{11}}
[3,2,5,4,7,6,8,9,12,10,11,1]=>{{1,3,5,7,8,9,12},{2},{4},{6},{10},{11}}
[3,2,5,4,6,9,7,8,11,10,12,1]=>{{1,3,5,6,9,11,12},{2},{4},{7},{8},{10}}
[3,2,5,4,6,9,7,8,10,12,11,1]=>{{1,3,5,6,9,10,12},{2},{4},{7},{8},{11}}
[3,2,5,4,6,8,7,11,9,10,12,1]=>{{1,3,5,6,8,11,12},{2},{4},{7},{9},{10}}
[3,2,5,4,6,8,7,10,9,12,11,1]=>{{1,3,5,6,8,10,12},{2},{4},{7},{9},{11}}
[3,2,5,4,6,8,7,9,12,10,11,1]=>{{1,3,5,6,8,9,12},{2},{4},{7},{10},{11}}
[3,2,5,4,6,7,11,8,9,10,12,1]=>{{1,3,5,6,7,11,12},{2},{4},{8},{9},{10}}
[3,2,5,4,6,7,10,8,9,12,11,1]=>{{1,3,5,6,7,10,12},{2},{4},{8},{9},{11}}
[3,2,5,4,6,7,9,8,12,10,11,1]=>{{1,3,5,6,7,9,12},{2},{4},{8},{10},{11}}
[3,2,5,4,6,7,8,12,9,10,11,1]=>{{1,3,5,6,7,8,12},{2},{4},{9},{10},{11}}
[3,2,4,7,5,6,9,8,11,10,12,1]=>{{1,3,4,7,9,11,12},{2},{5},{6},{8},{10}}
[3,2,4,7,5,6,9,8,10,12,11,1]=>{{1,3,4,7,9,10,12},{2},{5},{6},{8},{11}}
[3,2,4,7,5,6,8,11,9,10,12,1]=>{{1,3,4,7,8,11,12},{2},{5},{6},{9},{10}}
[3,2,4,7,5,6,8,10,9,12,11,1]=>{{1,3,4,7,8,10,12},{2},{5},{6},{9},{11}}
[3,2,4,7,5,6,8,9,12,10,11,1]=>{{1,3,4,7,8,9,12},{2},{5},{6},{10},{11}}
[3,2,4,6,5,9,7,8,11,10,12,1]=>{{1,3,4,6,9,11,12},{2},{5},{7},{8},{10}}
[3,2,4,6,5,9,7,8,10,12,11,1]=>{{1,3,4,6,9,10,12},{2},{5},{7},{8},{11}}
[3,2,4,6,5,8,7,11,9,10,12,1]=>{{1,3,4,6,8,11,12},{2},{5},{7},{9},{10}}
[3,2,4,6,5,8,7,10,9,12,11,1]=>{{1,3,4,6,8,10,12},{2},{5},{7},{9},{11}}
[3,2,4,6,5,8,7,9,12,10,11,1]=>{{1,3,4,6,8,9,12},{2},{5},{7},{10},{11}}
[3,2,4,6,5,7,11,8,9,10,12,1]=>{{1,3,4,6,7,11,12},{2},{5},{8},{9},{10}}
[3,2,4,6,5,7,10,8,9,12,11,1]=>{{1,3,4,6,7,10,12},{2},{5},{8},{9},{11}}
[3,2,4,6,5,7,9,8,12,10,11,1]=>{{1,3,4,6,7,9,12},{2},{5},{8},{10},{11}}
[3,2,4,6,5,7,8,12,9,10,11,1]=>{{1,3,4,6,7,8,12},{2},{5},{9},{10},{11}}
[3,2,4,5,9,6,7,8,11,10,12,1]=>{{1,3,4,5,9,11,12},{2},{6},{7},{8},{10}}
[3,2,4,5,9,6,7,8,10,12,11,1]=>{{1,3,4,5,9,10,12},{2},{6},{7},{8},{11}}
[3,2,4,5,8,6,7,11,9,10,12,1]=>{{1,3,4,5,8,11,12},{2},{6},{7},{9},{10}}
[3,2,4,5,8,6,7,10,9,12,11,1]=>{{1,3,4,5,8,10,12},{2},{6},{7},{9},{11}}
[3,2,4,5,8,6,7,9,12,10,11,1]=>{{1,3,4,5,8,9,12},{2},{6},{7},{10},{11}}
[3,2,4,5,7,6,11,8,9,10,12,1]=>{{1,3,4,5,7,11,12},{2},{6},{8},{9},{10}}
[3,2,4,5,7,6,10,8,9,12,11,1]=>{{1,3,4,5,7,10,12},{2},{6},{8},{9},{11}}
[3,2,4,5,7,6,9,8,12,10,11,1]=>{{1,3,4,5,7,9,12},{2},{6},{8},{10},{11}}
[3,2,4,5,7,6,8,12,9,10,11,1]=>{{1,3,4,5,7,8,12},{2},{6},{9},{10},{11}}
[3,2,4,5,6,11,7,8,9,10,12,1]=>{{1,3,4,5,6,11,12},{2},{7},{8},{9},{10}}
[3,2,4,5,6,10,7,8,9,12,11,1]=>{{1,3,4,5,6,10,12},{2},{7},{8},{9},{11}}
[3,2,4,5,6,9,7,8,12,10,11,1]=>{{1,3,4,5,6,9,12},{2},{7},{8},{10},{11}}
[3,2,4,5,6,8,7,12,9,10,11,1]=>{{1,3,4,5,6,8,12},{2},{7},{9},{10},{11}}
[3,2,4,5,6,7,12,8,9,10,11,1]=>{{1,3,4,5,6,7,12},{2},{8},{9},{10},{11}}
[2,5,3,4,7,6,9,8,11,10,12,1]=>{{1,2,5,7,9,11,12},{3},{4},{6},{8},{10}}
[2,5,3,4,7,6,9,8,10,12,11,1]=>{{1,2,5,7,9,10,12},{3},{4},{6},{8},{11}}
[2,5,3,4,7,6,8,11,9,10,12,1]=>{{1,2,5,7,8,11,12},{3},{4},{6},{9},{10}}
[2,5,3,4,7,6,8,10,9,12,11,1]=>{{1,2,5,7,8,10,12},{3},{4},{6},{9},{11}}
[2,5,3,4,7,6,8,9,12,10,11,1]=>{{1,2,5,7,8,9,12},{3},{4},{6},{10},{11}}
[2,5,3,4,6,9,7,8,11,10,12,1]=>{{1,2,5,6,9,11,12},{3},{4},{7},{8},{10}}
[2,5,3,4,6,9,7,8,10,12,11,1]=>{{1,2,5,6,9,10,12},{3},{4},{7},{8},{11}}
[2,5,3,4,6,8,7,11,9,10,12,1]=>{{1,2,5,6,8,11,12},{3},{4},{7},{9},{10}}
[2,5,3,4,6,8,7,10,9,12,11,1]=>{{1,2,5,6,8,10,12},{3},{4},{7},{9},{11}}
[2,5,3,4,6,8,7,9,12,10,11,1]=>{{1,2,5,6,8,9,12},{3},{4},{7},{10},{11}}
[2,5,3,4,6,7,11,8,9,10,12,1]=>{{1,2,5,6,7,11,12},{3},{4},{8},{9},{10}}
[2,5,3,4,6,7,10,8,9,12,11,1]=>{{1,2,5,6,7,10,12},{3},{4},{8},{9},{11}}
[2,5,3,4,6,7,9,8,12,10,11,1]=>{{1,2,5,6,7,9,12},{3},{4},{8},{10},{11}}
[2,5,3,4,6,7,8,12,9,10,11,1]=>{{1,2,5,6,7,8,12},{3},{4},{9},{10},{11}}
[2,4,3,7,5,6,9,8,11,10,12,1]=>{{1,2,4,7,9,11,12},{3},{5},{6},{8},{10}}
[2,4,3,7,5,6,9,8,10,12,11,1]=>{{1,2,4,7,9,10,12},{3},{5},{6},{8},{11}}
[2,4,3,7,5,6,8,11,9,10,12,1]=>{{1,2,4,7,8,11,12},{3},{5},{6},{9},{10}}
[2,4,3,7,5,6,8,10,9,12,11,1]=>{{1,2,4,7,8,10,12},{3},{5},{6},{9},{11}}
[2,4,3,7,5,6,8,9,12,10,11,1]=>{{1,2,4,7,8,9,12},{3},{5},{6},{10},{11}}
[2,4,3,6,5,9,7,8,11,10,12,1]=>{{1,2,4,6,9,11,12},{3},{5},{7},{8},{10}}
[2,4,3,6,5,9,7,8,10,12,11,1]=>{{1,2,4,6,9,10,12},{3},{5},{7},{8},{11}}
[2,4,3,6,5,8,7,11,9,10,12,1]=>{{1,2,4,6,8,11,12},{3},{5},{7},{9},{10}}
[2,4,3,6,5,8,7,9,12,10,11,1]=>{{1,2,4,6,8,9,12},{3},{5},{7},{10},{11}}
[2,4,3,6,5,7,11,8,9,10,12,1]=>{{1,2,4,6,7,11,12},{3},{5},{8},{9},{10}}
[2,4,3,6,5,7,10,8,9,12,11,1]=>{{1,2,4,6,7,10,12},{3},{5},{8},{9},{11}}
[2,4,3,6,5,7,9,8,12,10,11,1]=>{{1,2,4,6,7,9,12},{3},{5},{8},{10},{11}}
[2,4,3,6,5,7,8,12,9,10,11,1]=>{{1,2,4,6,7,8,12},{3},{5},{9},{10},{11}}
[2,4,3,5,9,6,7,8,11,10,12,1]=>{{1,2,4,5,9,11,12},{3},{6},{7},{8},{10}}
[2,4,3,5,9,6,7,8,10,12,11,1]=>{{1,2,4,5,9,10,12},{3},{6},{7},{8},{11}}
[2,4,3,5,8,6,7,11,9,10,12,1]=>{{1,2,4,5,8,11,12},{3},{6},{7},{9},{10}}
[2,4,3,5,8,6,7,10,9,12,11,1]=>{{1,2,4,5,8,10,12},{3},{6},{7},{9},{11}}
[2,4,3,5,8,6,7,9,12,10,11,1]=>{{1,2,4,5,8,9,12},{3},{6},{7},{10},{11}}
[2,4,3,5,7,6,11,8,9,10,12,1]=>{{1,2,4,5,7,11,12},{3},{6},{8},{9},{10}}
[2,4,3,5,7,6,10,8,9,12,11,1]=>{{1,2,4,5,7,10,12},{3},{6},{8},{9},{11}}
[2,4,3,5,7,6,9,8,12,10,11,1]=>{{1,2,4,5,7,9,12},{3},{6},{8},{10},{11}}
[2,4,3,5,7,6,8,12,9,10,11,1]=>{{1,2,4,5,7,8,12},{3},{6},{9},{10},{11}}
[2,4,3,5,6,11,7,8,9,10,12,1]=>{{1,2,4,5,6,11,12},{3},{7},{8},{9},{10}}
[2,4,3,5,6,10,7,8,9,12,11,1]=>{{1,2,4,5,6,10,12},{3},{7},{8},{9},{11}}
[2,4,3,5,6,9,7,8,12,10,11,1]=>{{1,2,4,5,6,9,12},{3},{7},{8},{10},{11}}
[2,4,3,5,6,8,7,12,9,10,11,1]=>{{1,2,4,5,6,8,12},{3},{7},{9},{10},{11}}
[2,4,3,5,6,7,12,8,9,10,11,1]=>{{1,2,4,5,6,7,12},{3},{8},{9},{10},{11}}
[2,3,7,4,5,6,9,8,11,10,12,1]=>{{1,2,3,7,9,11,12},{4},{5},{6},{8},{10}}
[2,3,7,4,5,6,9,8,10,12,11,1]=>{{1,2,3,7,9,10,12},{4},{5},{6},{8},{11}}
[2,3,7,4,5,6,8,11,9,10,12,1]=>{{1,2,3,7,8,11,12},{4},{5},{6},{9},{10}}
[2,3,7,4,5,6,8,10,9,12,11,1]=>{{1,2,3,7,8,10,12},{4},{5},{6},{9},{11}}
[2,3,7,4,5,6,8,9,12,10,11,1]=>{{1,2,3,7,8,9,12},{4},{5},{6},{10},{11}}
[2,3,6,4,5,9,7,8,11,10,12,1]=>{{1,2,3,6,9,11,12},{4},{5},{7},{8},{10}}
[2,3,6,4,5,9,7,8,10,12,11,1]=>{{1,2,3,6,9,10,12},{4},{5},{7},{8},{11}}
[2,3,6,4,5,8,7,11,9,10,12,1]=>{{1,2,3,6,8,11,12},{4},{5},{7},{9},{10}}
[2,3,6,4,5,8,7,10,9,12,11,1]=>{{1,2,3,6,8,10,12},{4},{5},{7},{9},{11}}
[2,3,6,4,5,8,7,9,12,10,11,1]=>{{1,2,3,6,8,9,12},{4},{5},{7},{10},{11}}
[2,3,6,4,5,7,11,8,9,10,12,1]=>{{1,2,3,6,7,11,12},{4},{5},{8},{9},{10}}
[2,3,6,4,5,7,10,8,9,12,11,1]=>{{1,2,3,6,7,10,12},{4},{5},{8},{9},{11}}
[2,3,6,4,5,7,9,8,12,10,11,1]=>{{1,2,3,6,7,9,12},{4},{5},{8},{10},{11}}
[2,3,6,4,5,7,8,12,9,10,11,1]=>{{1,2,3,6,7,8,12},{4},{5},{9},{10},{11}}
[2,3,5,4,9,6,7,8,11,10,12,1]=>{{1,2,3,5,9,11,12},{4},{6},{7},{8},{10}}
[2,3,5,4,9,6,7,8,10,12,11,1]=>{{1,2,3,5,9,10,12},{4},{6},{7},{8},{11}}
[2,3,5,4,8,6,7,11,9,10,12,1]=>{{1,2,3,5,8,11,12},{4},{6},{7},{9},{10}}
[2,3,5,4,8,6,7,10,9,12,11,1]=>{{1,2,3,5,8,10,12},{4},{6},{7},{9},{11}}
[2,3,5,4,8,6,7,9,12,10,11,1]=>{{1,2,3,5,8,9,12},{4},{6},{7},{10},{11}}
[2,3,5,4,7,6,11,8,9,10,12,1]=>{{1,2,3,5,7,11,12},{4},{6},{8},{9},{10}}
[2,3,5,4,7,6,10,8,9,12,11,1]=>{{1,2,3,5,7,10,12},{4},{6},{8},{9},{11}}
[2,3,5,4,7,6,9,8,12,10,11,1]=>{{1,2,3,5,7,9,12},{4},{6},{8},{10},{11}}
[2,3,5,4,7,6,8,12,9,10,11,1]=>{{1,2,3,5,7,8,12},{4},{6},{9},{10},{11}}
[2,3,5,4,6,11,7,8,9,10,12,1]=>{{1,2,3,5,6,11,12},{4},{7},{8},{9},{10}}
[2,3,5,4,6,10,7,8,9,12,11,1]=>{{1,2,3,5,6,10,12},{4},{7},{8},{9},{11}}
[2,3,5,4,6,9,7,8,12,10,11,1]=>{{1,2,3,5,6,9,12},{4},{7},{8},{10},{11}}
[2,3,5,4,6,8,7,12,9,10,11,1]=>{{1,2,3,5,6,8,12},{4},{7},{9},{10},{11}}
[2,3,5,4,6,7,12,8,9,10,11,1]=>{{1,2,3,5,6,7,12},{4},{8},{9},{10},{11}}
[2,3,4,9,5,6,7,8,11,10,12,1]=>{{1,2,3,4,9,11,12},{5},{6},{7},{8},{10}}
[2,3,4,9,5,6,7,8,10,12,11,1]=>{{1,2,3,4,9,10,12},{5},{6},{7},{8},{11}}
[2,3,4,8,5,6,7,11,9,10,12,1]=>{{1,2,3,4,8,11,12},{5},{6},{7},{9},{10}}
[2,3,4,8,5,6,7,10,9,12,11,1]=>{{1,2,3,4,8,10,12},{5},{6},{7},{9},{11}}
[2,3,4,8,5,6,7,9,12,10,11,1]=>{{1,2,3,4,8,9,12},{5},{6},{7},{10},{11}}
[2,3,4,7,5,6,11,8,9,10,12,1]=>{{1,2,3,4,7,11,12},{5},{6},{8},{9},{10}}
[2,3,4,7,5,6,10,8,9,12,11,1]=>{{1,2,3,4,7,10,12},{5},{6},{8},{9},{11}}
[2,3,4,7,5,6,9,8,12,10,11,1]=>{{1,2,3,4,7,9,12},{5},{6},{8},{10},{11}}
[2,3,4,7,5,6,8,12,9,10,11,1]=>{{1,2,3,4,7,8,12},{5},{6},{9},{10},{11}}
[2,3,4,6,5,11,7,8,9,10,12,1]=>{{1,2,3,4,6,11,12},{5},{7},{8},{9},{10}}
[2,3,4,6,5,10,7,8,9,12,11,1]=>{{1,2,3,4,6,10,12},{5},{7},{8},{9},{11}}
[2,3,4,6,5,9,7,8,12,10,11,1]=>{{1,2,3,4,6,9,12},{5},{7},{8},{10},{11}}
[2,3,4,6,5,8,7,12,9,10,11,1]=>{{1,2,3,4,6,8,12},{5},{7},{9},{10},{11}}
[2,3,4,6,5,7,12,8,9,10,11,1]=>{{1,2,3,4,6,7,12},{5},{8},{9},{10},{11}}
[2,3,4,5,11,6,7,8,9,10,12,1]=>{{1,2,3,4,5,11,12},{6},{7},{8},{9},{10}}
[2,3,4,5,10,6,7,8,9,12,11,1]=>{{1,2,3,4,5,10,12},{6},{7},{8},{9},{11}}
[2,3,4,5,9,6,7,8,12,10,11,1]=>{{1,2,3,4,5,9,12},{6},{7},{8},{10},{11}}
[2,3,4,5,8,6,7,12,9,10,11,1]=>{{1,2,3,4,5,8,12},{6},{7},{9},{10},{11}}
[2,3,4,5,7,6,12,8,9,10,11,1]=>{{1,2,3,4,5,7,12},{6},{8},{9},{10},{11}}
[12,11,9,5,10,7,1,2,4,8,3,6]=>{{1,6,7,12},{2,3,4,5,8,9,10,11}}
[11,9,5,12,10,7,1,2,4,8,3,6]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,7,1,2,4,9,5,12,11,8,3,6]=>{{1,3,6,8,9,10,11,12},{2,4,5,7}}
[12,10,7,1,2,4,9,5,11,8,3,6]=>{{1,4,6,12},{2,5,8,10},{3,7,9,11}}
[10,7,1,2,4,12,9,5,11,8,3,6]=>{{1,2,3,4,5,7,8,9,10,11},{6,12}}
[8,3,7,1,2,4,12,11,9,5,10,6]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[8,3,7,1,2,4,11,9,5,12,10,6]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[12,11,8,3,7,1,2,4,9,5,10,6]=>{{1,6,12},{2,5,7,10,11},{3,4,8},{9}}
[11,8,3,7,1,2,4,9,5,12,10,6]=>{{1,2,5,6,8,9,10,11,12},{3},{4,7}}
[12,9,5,11,8,3,7,1,2,4,10,6]=>{{1,3,5,6,8,12},{2,9},{4,10,11},{7}}
[8,3,12,11,7,1,2,4,9,5,10,6]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[8,3,11,7,1,2,4,9,5,12,10,6]=>{{1,5,8,9},{2,3,6,10,11,12},{4,7}}
[8,3,12,9,5,11,7,1,2,4,10,6]=>{{1,8},{2,3,4,6,9,10,11,12},{5},{7}}
[12,8,3,9,5,11,7,1,2,4,10,6]=>{{1,2,4,6,8,9,10,11,12},{3},{5},{7}}
[10,7,1,2,5,12,11,9,4,8,3,6]=>{{1,2,3,4,7,8,9,10,11},{5},{6,12}}
[12,10,7,1,2,5,11,9,4,8,3,6]=>{{1,2,4,5,6,8,9,10,12},{3,7,11}}
[9,4,10,7,1,2,5,12,11,8,3,6]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[9,4,12,10,7,1,2,5,11,8,3,6]=>{{1,3,6,9,11,12},{2,4,5,7,8,10}}
[12,9,4,10,7,1,2,5,11,8,3,6]=>{{1,6,12},{2,3,4,5,7,8,9,10,11}}
[12,11,9,4,8,3,7,1,2,5,10,6]=>{{1,2,3,5,6,8,9,10,11,12},{4},{7}}
[11,9,4,8,3,7,1,2,5,12,10,6]=>{{1,6,7,10,11,12},{2,3,4,5,8,9}}
[9,4,12,11,8,3,7,1,2,5,10,6]=>{{1,2,4,5,8,9,10,11},{3,6,12},{7}}
[9,4,11,8,3,7,1,2,5,12,10,6]=>{{1,3,5,6,7,9,10,11,12},{2,4,8}}
[11,8,3,7,1,2,5,12,9,4,10,6]=>{{1,4,5,7,10,11},{2,6,8,12},{3},{9}}
[8,3,9,4,12,11,7,1,2,5,10,6]=>{{1,8},{2,3,9},{4},{5,6,10,11,12},{7}}
[8,3,9,4,11,7,1,2,5,12,10,6]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[8,3,11,7,1,2,5,12,9,4,10,6]=>{{1,2,3,4,5,6,7,8,10,11,12},{9}}
[11,7,1,2,5,12,8,3,9,4,10,6]=>{{1,2,3,4,7,8,10,11},{5},{6,12},{9}}
[10,5,12,11,9,4,8,3,7,1,2,6]=>{{1,10},{2,3,4,5,6,7,8,9,11,12}}
[12,10,5,11,9,4,8,3,7,1,2,6]=>{{1,2,4,6,10,11,12},{3,5,7,8,9}}
[9,4,10,5,12,11,8,3,7,1,2,6]=>{{1,3,7,8,9,10},{2,4,5,6,11,12}}
[9,4,12,10,5,11,8,3,7,1,2,6]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[12,9,4,10,5,11,8,3,7,1,2,6]=>{{1,2,3,4,6,7,8,9,10,11,12},{5}}
[8,3,9,4,10,5,12,11,7,1,2,6]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[8,3,9,4,12,10,5,11,7,1,2,6]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[8,3,12,9,4,10,5,11,7,1,2,6]=>{{1,2,3,6,8,10,11,12},{4,5,7,9}}
[12,8,3,9,4,10,5,11,7,1,2,6]=>{{1,6,10,12},{2,8,11},{3},{4,5,7,9}}
[7,1,2,8,3,9,4,10,5,12,11,6]=>{{1,2,3,4,5,6,7,8,9,10,12},{11}}
[7,1,2,8,3,9,4,12,10,5,11,6]=>{{1,2,3,4,5,6,7,8,9,10,12},{11}}
[7,1,2,8,3,12,9,4,10,5,11,6]=>{{1,2,3,5,7,9,10},{4,8},{6,12},{11}}
[7,1,2,12,8,3,9,4,10,5,11,6]=>{{1,2,3,4,5,6,7,8,9,10,12},{11}}
[12,7,1,2,8,3,9,4,10,5,11,6]=>{{1,3,6,12},{2,4,5,7,8,9,10},{11}}
[8,2,4,12,11,9,5,10,7,1,3,6]=>{{1,8,10},{2},{3,4,5,6,7,9,11,12}}
[8,2,4,11,9,5,12,10,7,1,3,6]=>{{1,8,10},{2},{3,4,11},{5,6,7,9,12}}
[12,11,8,2,4,9,5,10,7,1,3,6]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[11,8,2,4,9,5,12,10,7,1,3,6]=>{{1,2,3,8,10,11},{4},{5,6,7,9,12}}
[12,9,5,11,8,2,4,10,7,1,3,6]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[7,1,3,8,2,4,12,11,9,5,10,6]=>{{1,2,4,5,6,7,8,10,11,12},{3},{9}}
[7,1,3,8,2,4,11,9,5,12,10,6]=>{{1,2,4,5,6,7,8,9,10,11,12},{3}}
[7,1,3,12,11,8,2,4,9,5,10,6]=>{{1,2,7},{3},{4,6,8,12},{5,10,11},{9}}
[7,1,3,11,8,2,4,9,5,12,10,6]=>{{1,2,4,6,7,10,11,12},{3},{5,8,9}}
[7,1,3,12,9,5,11,8,2,4,10,6]=>{{1,2,4,5,6,7,9,10,11,12},{3},{8}}
[12,11,7,1,3,8,2,4,9,5,10,6]=>{{1,4,6,8,12},{2,3,5,7,10,11},{9}}
[11,7,1,3,8,2,4,9,5,12,10,6]=>{{1,2,3,4,6,7,10,11,12},{5,8,9}}
[12,9,5,11,7,1,3,8,2,4,10,6]=>{{1,6,12},{2,9},{3,5,7},{4,10,11},{8}}
[11,7,1,3,9,5,12,8,2,4,10,6]=>{{1,3,4,10,11},{2,5,6,7,9,12},{8}}
[12,11,9,4,8,2,5,10,7,1,3,6]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[11,9,4,8,2,5,12,10,7,1,3,6]=>{{1,3,4,8,10,11},{2,5,6,7,9,12}}
[9,4,12,11,8,2,5,10,7,1,3,6]=>{{1,5,7,8,9,10},{2,3,4,6,11,12}}
[9,4,11,8,2,5,12,10,7,1,3,6]=>{{1,2,4,5,6,7,8,9,10,12},{3,11}}
[11,8,2,5,12,9,4,10,7,1,3,6]=>{{1,2,3,8,10,11},{4,5,6,7,9,12}}
[7,1,3,12,11,9,4,8,2,5,10,6]=>{{1,2,4,6,7,9,12},{3},{5,10,11},{8}}
[7,1,3,11,9,4,8,2,5,12,10,6]=>{{1,2,7,8},{3},{4,6,10,11,12},{5,9}}
[7,1,3,9,4,12,11,8,2,5,10,6]=>{{1,2,4,5,7,9,10,11},{3},{6,12},{8}}
[7,1,3,9,4,11,8,2,5,12,10,6]=>{{1,2,7,8},{3},{4,5,9},{6,10,11,12}}
[7,1,3,11,8,2,5,12,9,4,10,6]=>{{1,2,5,6,7,8,12},{3},{4,10,11},{9}}
[9,4,12,11,7,1,3,8,2,5,10,6]=>{{1,2,3,4,5,6,7,9,10,11,12},{8}}
[9,4,11,7,1,3,8,2,5,12,10,6]=>{{1,5,9},{2,4,7,8},{3,6,10,11,12}}
[11,7,1,3,8,2,5,12,9,4,10,6]=>{{1,3,4,10,11},{2,5,6,7,8,12},{9}}
[12,8,2,5,11,7,1,3,9,4,10,6]=>{{1,6,7,12},{2,3,8},{4,5,10,11},{9}}
[7,1,3,10,5,12,11,9,4,8,2,6]=>{{1,2,7,11},{3},{4,8,9,10},{5},{6,12}}
[7,1,3,12,10,5,11,9,4,8,2,6]=>{{1,2,7,11},{3},{4,5,6,8,9,10,12}}
[7,1,3,9,4,10,5,12,11,8,2,6]=>{{1,2,4,5,7,9,11},{3},{6,8,10,12}}
[7,1,3,9,4,12,10,5,11,8,2,6]=>{{1,2,4,5,7,8,9,10,11},{3},{6,12}}
[7,1,3,12,9,4,10,5,11,8,2,6]=>{{1,2,5,7,8,9,10,11},{3},{4,6,12}}
[9,4,10,5,12,11,7,1,3,8,2,6]=>{{1,3,8,9,10},{2,4,5,6,11,12},{7}}
[9,4,12,10,5,11,7,1,3,8,2,6]=>{{1,2,3,4,6,8,9,10,11,12},{5},{7}}
[12,9,4,10,5,11,7,1,3,8,2,6]=>{{1,2,3,4,6,8,9,10,11,12},{5},{7}}
[11,7,1,3,9,4,10,5,12,8,2,6]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,2,7,1,3,9,4,10,5,12,11,6]=>{{1,3,4,5,6,7,8,9,10,12},{2},{11}}
[8,2,7,1,3,9,4,12,10,5,11,6]=>{{1,3,4,5,6,7,8,9,10,12},{2},{11}}
[8,2,7,1,3,12,9,4,10,5,11,6]=>{{1,4,8},{2},{3,5,7,9,10},{6,12},{11}}
[12,8,2,7,1,3,9,4,10,5,11,6]=>{{1,2,3,4,5,6,7,8,9,10,12},{11}}
[8,2,12,7,1,3,9,4,10,5,11,6]=>{{1,4,5,7,8,9,10},{2},{3,6,12},{11}}
[10,7,1,4,8,2,5,12,11,9,3,6]=>{{1,3,9,10,11},{2,5,6,7,8,12},{4}}
[12,10,7,1,4,8,2,5,11,9,3,6]=>{{1,4,5,6,8,12},{2,3,7,9,10,11}}
[12,11,8,2,5,10,7,1,4,9,3,6]=>{{1,2,3,4,6,8,9,10,11,12},{5},{7}}
[11,8,2,5,12,10,7,1,4,9,3,6]=>{{1,2,3,8,11},{4,5,6,9,10,12},{7}}
[10,7,1,4,11,8,2,5,12,9,3,6]=>{{1,3,5,6,8,9,10,11,12},{2,7},{4}}
[12,11,9,3,7,1,4,8,2,5,10,6]=>{{1,6,12},{2,3,4,5,7,9,10,11},{8}}
[11,9,3,7,1,4,8,2,5,12,10,6]=>{{1,2,4,5,6,7,8,9,10,11,12},{3}}
[9,3,7,1,4,12,11,8,2,5,10,6]=>{{1,2,3,4,5,7,9,10,11},{6,12},{8}}
[9,3,7,1,4,11,8,2,5,12,10,6]=>{{1,4,5,9},{2,3,7,8},{6,10,11,12}}
[11,8,2,5,12,9,3,7,1,4,10,6]=>{{1,4,5,6,9,10,11,12},{2,3,7,8}}
[12,11,7,1,4,9,3,8,2,5,10,6]=>{{1,2,4,5,6,9,10,11,12},{3,7},{8}}
[11,7,1,4,9,3,8,2,5,12,10,6]=>{{1,3,6,10,11,12},{2,7,8},{4},{5,9}}
[12,9,3,8,2,5,11,7,1,4,10,6]=>{{1,2,5,6,9,12},{3},{4,7,8,10,11}}
[9,3,12,8,2,5,11,7,1,4,10,6]=>{{1,9},{2,3,5,6,12},{4,7,8,10,11}}
[10,5,12,11,9,3,7,1,4,8,2,6]=>{{1,8,10},{2,4,5,9,11},{3,6,12},{7}}
[12,10,5,11,9,3,7,1,4,8,2,6]=>{{1,2,3,4,5,6,8,9,10,11,12},{7}}
[9,3,7,1,4,10,5,12,11,8,2,6]=>{{1,2,3,4,5,7,9,11},{6,8,10,12}}
[9,3,7,1,4,12,10,5,11,8,2,6]=>{{1,2,3,4,5,7,8,9,10,11},{6,12}}
[12,9,3,7,1,4,10,5,11,8,2,6]=>{{1,4,5,6,7,8,10,12},{2,9,11},{3}}
[10,5,12,11,7,1,4,9,3,8,2,6]=>{{1,3,6,8,9,10,12},{2,4,5,7,11}}
[12,10,5,11,7,1,4,9,3,8,2,6]=>{{1,6,12},{2,3,4,5,7,8,9,10,11}}
[11,7,1,4,10,5,12,9,3,8,2,6]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}}
[9,3,11,7,1,4,10,5,12,8,2,6]=>{{1,4,5,6,7,8,9,10,12},{2,3,11}}
[9,3,8,2,7,1,4,10,5,12,11,6]=>{{1,2,3,4,5,6,7,8,9,10,12},{11}}
[9,3,8,2,7,1,4,12,10,5,11,6]=>{{1,2,3,4,5,6,7,8,9,10,12},{11}}
[12,9,3,8,2,7,1,4,10,5,11,6]=>{{1,6,7,12},{2,5,9,10},{3},{4,8},{11}}
[9,3,12,8,2,7,1,4,10,5,11,6]=>{{1,2,3,5,6,7,9,10,12},{4,8},{11}}
[8,2,9,3,12,7,1,4,10,5,11,6]=>{{1,3,4,5,6,7,8,9,10,12},{2},{11}}
[12,11,9,3,7,1,5,10,4,8,2,6]=>{{1,6,12},{2,11},{3,4,9},{5,7},{8,10}}
[11,9,3,7,1,5,12,10,4,8,2,6]=>{{1,2,4,5,6,7,9,11,12},{3},{8,10}}
[10,4,9,3,7,1,5,12,11,8,2,6]=>{{1,6,8,10,12},{2,3,4,9,11},{5,7}}
[12,10,4,9,3,7,1,5,11,8,2,6]=>{{1,6,7,12},{2,3,4,5,8,9,10,11}}
[10,4,12,9,3,7,1,5,11,8,2,6]=>{{1,3,5,6,7,8,10,12},{2,4,9,11}}
[12,11,7,1,5,10,4,9,3,8,2,6]=>{{1,3,4,6,7,8,9,10,12},{2,11},{5}}
[11,7,1,5,12,10,4,9,3,8,2,6]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[10,4,11,7,1,5,12,9,3,8,2,6]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[9,3,10,4,11,7,1,5,12,8,2,6]=>{{1,6,7,9,12},{2,3,5,8,10,11},{4}}
[10,4,9,3,8,2,7,1,5,12,11,6]=>{{1,2,3,4,5,6,8,9,10,12},{7},{11}}
[12,10,4,9,3,8,2,7,1,5,11,6]=>{{1,2,3,4,5,6,7,8,9,10,12},{11}}
[10,4,12,9,3,8,2,7,1,5,11,6]=>{{1,2,3,4,5,6,7,8,9,10,12},{11}}
[9,3,10,4,12,8,2,7,1,5,11,6]=>{{1,9},{2,3,5,6,7,8,10,12},{4},{11}}
[8,2,9,3,10,4,12,7,1,5,11,6]=>{{1,3,4,6,7,8,9,12},{2},{5,10},{11}}
[12,11,5,10,4,9,3,8,2,7,1,6]=>{{1,2,6,9,11,12},{3,4,5,7,10},{8}}
[11,5,12,10,4,9,3,8,2,7,1,6]=>{{1,11},{2,3,4,5,6,7,9,10,12},{8}}
[10,4,11,5,12,9,3,8,2,7,1,6]=>{{1,3,7,10,11},{2,4,5,6,9,12},{8}}
[9,3,10,4,11,5,12,8,2,7,1,6]=>{{1,2,3,5,6,7,9,10,11,12},{4},{8}}
[8,2,9,3,10,4,11,5,12,7,1,6]=>{{1,5,7,8,10,11},{2},{3,4,6,9,12}}
[3,4,1,5,6,7,8,9,10,11,12,2]=>{{1,3},{2,4,5,6,7,8,9,10,11,12}}
[8,2,9,3,10,4,11,5,12,6,1,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,2,9,3,10,4,11,5,12,1,6,7]=>{{1,5,8,10},{2},{3,4,6,7,9,11,12}}
[8,2,9,3,10,4,11,12,5,6,1,7]=>{{1,7,8,11,12},{2},{3,4,5,6,9,10}}
[8,2,9,3,10,4,11,12,5,1,6,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,2,9,3,10,4,11,12,1,5,6,7]=>{{1,3,4,6,7,8,9,11,12},{2},{5,10}}
[8,2,9,3,10,11,4,5,12,6,1,7]=>{{1,5,6,8,10,11},{2},{3,4,7,9,12}}
[8,2,9,3,10,11,4,5,12,1,6,7]=>{{1,5,8,10},{2},{3,4,7,9,12},{6,11}}
[8,2,9,3,10,11,4,12,5,6,1,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,2,9,3,10,11,4,12,5,1,6,7]=>{{1,3,4,5,7,8,9,10,12},{2},{6,11}}
[8,2,9,3,10,11,4,12,1,5,6,7]=>{{1,3,4,7,8,9,12},{2},{5,10},{6,11}}
[8,2,9,3,10,11,12,4,5,6,1,7]=>{{1,3,4,5,6,8,9,10,11},{2},{7,12}}
[8,2,9,3,10,11,12,4,5,1,6,7]=>{{1,3,4,5,8,9,10},{2},{6,11},{7,12}}
[8,2,9,3,10,11,12,4,1,5,6,7]=>{{1,3,4,8,9},{2},{5,10},{6,11},{7,12}}
[8,2,9,3,10,11,12,1,4,5,6,7]=>{{1,8},{2},{3,4,9},{5,10},{6,11},{7,12}}
[8,2,9,10,3,4,11,5,12,6,1,7]=>{{1,3,5,7,8,9,11,12},{2},{4,6,10}}
[8,2,9,10,3,4,11,5,12,1,6,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,2,9,10,3,4,11,12,5,6,1,7]=>{{1,7,8,11,12},{2},{3,5,9},{4,6,10}}
[8,2,9,10,3,4,11,12,5,1,6,7]=>{{1,4,6,7,8,10,11,12},{2},{3,5,9}}
[8,2,9,10,3,4,11,12,1,5,6,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,2,9,10,3,11,4,5,12,6,1,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,2,9,10,3,11,4,5,12,1,6,7]=>{{1,3,4,5,7,8,9,10,12},{2},{6,11}}
[8,2,9,10,3,11,4,12,5,6,1,7]=>{{1,4,6,7,8,10,11,12},{2},{3,5,9}}
[8,2,9,10,3,11,4,12,5,1,6,7]=>{{1,4,7,8,10,12},{2},{3,5,9},{6,11}}
[8,2,9,10,3,11,4,12,1,5,6,7]=>{{1,3,4,5,7,8,9,10,12},{2},{6,11}}
[8,2,9,10,3,11,12,4,5,6,1,7]=>{{1,4,6,8,10,11},{2},{3,5,9},{7,12}}
[8,2,9,10,3,11,12,4,5,1,6,7]=>{{1,4,8,10},{2},{3,5,9},{6,11},{7,12}}
[8,2,9,10,3,11,12,4,1,5,6,7]=>{{1,3,4,5,8,9,10},{2},{6,11},{7,12}}
[8,2,9,10,3,11,12,1,4,5,6,7]=>{{1,8},{2},{3,4,5,9,10},{6,11},{7,12}}
[8,2,9,10,11,3,4,5,12,6,1,7]=>{{1,5,8,11},{2},{3,4,6,7,9,10,12}}
[8,2,9,10,11,3,4,5,12,1,6,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,2,9,10,11,3,4,12,5,6,1,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,2,9,10,11,3,4,12,5,1,6,7]=>{{1,4,7,8,10,12},{2},{3,5,6,9,11}}
[8,2,9,10,11,3,4,12,1,5,6,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,2,9,10,11,3,12,4,5,6,1,7]=>{{1,3,4,5,6,8,9,10,11},{2},{7,12}}
[8,2,9,10,11,3,12,4,5,1,6,7]=>{{1,4,8,10},{2},{3,5,6,9,11},{7,12}}
[8,2,9,10,11,3,12,4,1,5,6,7]=>{{1,3,4,5,6,8,9,10,11},{2},{7,12}}
[8,2,9,10,11,3,12,1,4,5,6,7]=>{{1,8},{2},{3,4,5,6,9,10,11},{7,12}}
[8,2,9,10,11,12,3,4,5,6,1,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,2,9,10,11,12,3,4,5,1,6,7]=>{{1,4,8,10},{2},{3,5,6,7,9,11,12}}
[8,2,9,10,11,12,3,4,1,5,6,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,2,9,10,11,12,3,1,4,5,6,7]=>{{1,8},{2},{3,4,5,6,7,9,10,11,12}}
[8,2,9,10,11,12,1,3,4,5,6,7]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,9,2,3,10,4,11,5,12,6,1,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,2,3,10,4,11,5,12,1,6,7]=>{{1,5,8,10},{2,3,4,6,7,9,11,12}}
[8,9,2,3,10,4,11,12,5,6,1,7]=>{{1,7,8,11,12},{2,3,4,5,6,9,10}}
[8,9,2,3,10,4,11,12,5,1,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,2,3,10,4,11,12,1,5,6,7]=>{{1,2,3,4,6,7,8,9,11,12},{5,10}}
[8,9,2,3,10,11,4,5,12,6,1,7]=>{{1,5,6,8,10,11},{2,3,4,7,9,12}}
[8,9,2,3,10,11,4,5,12,1,6,7]=>{{1,5,8,10},{2,3,4,7,9,12},{6,11}}
[8,9,2,3,10,11,4,12,5,6,1,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,2,3,10,11,4,12,5,1,6,7]=>{{1,2,3,4,5,7,8,9,10,12},{6,11}}
[8,9,2,3,10,11,4,12,1,5,6,7]=>{{1,2,3,4,7,8,9,12},{5,10},{6,11}}
[8,9,2,3,10,11,12,4,5,6,1,7]=>{{1,2,3,4,5,6,8,9,10,11},{7,12}}
[8,9,2,3,10,11,12,4,5,1,6,7]=>{{1,2,3,4,5,8,9,10},{6,11},{7,12}}
[8,9,2,3,10,11,12,4,1,5,6,7]=>{{1,2,3,4,8,9},{5,10},{6,11},{7,12}}
[8,9,2,3,10,11,12,1,4,5,6,7]=>{{1,8},{2,3,4,9},{5,10},{6,11},{7,12}}
[8,9,2,10,3,4,11,5,12,6,1,7]=>{{1,2,3,5,7,8,9,11,12},{4,6,10}}
[8,9,2,10,3,4,11,5,12,1,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,2,10,3,4,11,12,5,6,1,7]=>{{1,7,8,11,12},{2,3,5,9},{4,6,10}}
[8,9,2,10,3,4,11,12,5,1,6,7]=>{{1,4,6,7,8,10,11,12},{2,3,5,9}}
[8,9,2,10,3,4,11,12,1,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,2,10,3,11,4,5,12,6,1,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,2,10,3,11,4,5,12,1,6,7]=>{{1,2,3,4,5,7,8,9,10,12},{6,11}}
[8,9,2,10,3,11,4,12,5,6,1,7]=>{{1,4,6,7,8,10,11,12},{2,3,5,9}}
[8,9,2,10,3,11,4,12,5,1,6,7]=>{{1,4,7,8,10,12},{2,3,5,9},{6,11}}
[8,9,2,10,3,11,4,12,1,5,6,7]=>{{1,2,3,4,5,7,8,9,10,12},{6,11}}
[8,9,2,10,3,11,12,4,5,6,1,7]=>{{1,4,6,8,10,11},{2,3,5,9},{7,12}}
[8,9,2,10,3,11,12,4,5,1,6,7]=>{{1,4,8,10},{2,3,5,9},{6,11},{7,12}}
[8,9,2,10,3,11,12,4,1,5,6,7]=>{{1,2,3,4,5,8,9,10},{6,11},{7,12}}
[8,9,2,10,3,11,12,1,4,5,6,7]=>{{1,8},{2,3,4,5,9,10},{6,11},{7,12}}
[8,9,2,10,11,3,4,5,12,6,1,7]=>{{1,5,8,11},{2,3,4,6,7,9,10,12}}
[8,9,2,10,11,3,4,5,12,1,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,2,10,11,3,4,12,5,6,1,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,2,10,11,3,4,12,5,1,6,7]=>{{1,4,7,8,10,12},{2,3,5,6,9,11}}
[8,9,2,10,11,3,4,12,1,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,2,10,11,3,12,4,5,6,1,7]=>{{1,2,3,4,5,6,8,9,10,11},{7,12}}
[8,9,2,10,11,3,12,4,5,1,6,7]=>{{1,4,8,10},{2,3,5,6,9,11},{7,12}}
[8,9,2,10,11,3,12,4,1,5,6,7]=>{{1,2,3,4,5,6,8,9,10,11},{7,12}}
[8,9,2,10,11,3,12,1,4,5,6,7]=>{{1,8},{2,3,4,5,6,9,10,11},{7,12}}
[8,9,2,10,11,12,3,4,5,6,1,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,2,10,11,12,3,4,5,1,6,7]=>{{1,4,8,10},{2,3,5,6,7,9,11,12}}
[8,9,2,10,11,12,3,4,1,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,2,10,11,12,3,1,4,5,6,7]=>{{1,8},{2,3,4,5,6,7,9,10,11,12}}
[8,9,2,10,11,12,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,2,3,4,11,5,12,6,1,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,2,3,4,11,5,12,1,6,7]=>{{1,3,5,8,10},{2,4,6,7,9,11,12}}
[8,9,10,2,3,4,11,12,5,6,1,7]=>{{1,7,8,11,12},{2,3,4,5,6,9,10}}
[8,9,10,2,3,4,11,12,5,1,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,2,3,4,11,12,1,5,6,7]=>{{1,2,4,6,7,8,9,11,12},{3,5,10}}
[8,9,10,2,3,11,4,5,12,6,1,7]=>{{1,3,5,6,8,10,11},{2,4,7,9,12}}
[8,9,10,2,3,11,4,5,12,1,6,7]=>{{1,3,5,8,10},{2,4,7,9,12},{6,11}}
[8,9,10,2,3,11,4,12,5,6,1,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,2,3,11,4,12,5,1,6,7]=>{{1,2,3,4,5,7,8,9,10,12},{6,11}}
[8,9,10,2,3,11,4,12,1,5,6,7]=>{{1,2,4,7,8,9,12},{3,5,10},{6,11}}
[8,9,10,2,3,11,12,4,5,6,1,7]=>{{1,2,3,4,5,6,8,9,10,11},{7,12}}
[8,9,10,2,3,11,12,4,5,1,6,7]=>{{1,2,3,4,5,8,9,10},{6,11},{7,12}}
[8,9,10,2,3,11,12,4,1,5,6,7]=>{{1,2,4,8,9},{3,5,10},{6,11},{7,12}}
[8,9,10,2,3,11,12,1,4,5,6,7]=>{{1,8},{2,4,9},{3,5,10},{6,11},{7,12}}
[8,9,10,2,11,3,4,5,12,6,1,7]=>{{1,5,8,11},{2,4,7,9,12},{3,6,10}}
[8,9,10,2,11,3,4,5,12,1,6,7]=>{{1,3,5,6,8,10,11},{2,4,7,9,12}}
[8,9,10,2,11,3,4,12,5,6,1,7]=>{{1,2,4,5,7,8,9,11,12},{3,6,10}}
[8,9,10,2,11,3,4,12,5,1,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,2,11,3,4,12,1,5,6,7]=>{{1,2,4,7,8,9,12},{3,5,6,10,11}}
[8,9,10,2,11,3,12,4,5,6,1,7]=>{{1,2,4,5,8,9,11},{3,6,10},{7,12}}
[8,9,10,2,11,3,12,4,5,1,6,7]=>{{1,2,3,4,5,6,8,9,10,11},{7,12}}
[8,9,10,2,11,3,12,4,1,5,6,7]=>{{1,2,4,8,9},{3,5,6,10,11},{7,12}}
[8,9,10,2,11,3,12,1,4,5,6,7]=>{{1,8},{2,4,9},{3,5,6,10,11},{7,12}}
[8,9,10,2,11,12,3,4,5,6,1,7]=>{{1,2,4,5,8,9,11},{3,6,7,10,12}}
[8,9,10,2,11,12,3,4,5,1,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,2,11,12,3,4,1,5,6,7]=>{{1,2,4,8,9},{3,5,6,7,10,11,12}}
[8,9,10,2,11,12,3,1,4,5,6,7]=>{{1,8},{2,4,9},{3,5,6,7,10,11,12}}
[8,9,10,2,11,12,1,3,4,5,6,7]=>{{1,3,5,6,7,8,10,11,12},{2,4,9}}
[8,9,10,11,2,3,4,5,12,6,1,7]=>{{1,2,4,5,7,8,9,11,12},{3,6,10}}
[8,9,10,11,2,3,4,5,12,1,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,11,2,3,4,12,5,6,1,7]=>{{1,4,7,8,11,12},{2,5,9},{3,6,10}}
[8,9,10,11,2,3,4,12,5,1,6,7]=>{{1,3,4,6,7,8,10,11,12},{2,5,9}}
[8,9,10,11,2,3,4,12,1,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,11,2,3,12,4,5,6,1,7]=>{{1,4,8,11},{2,5,9},{3,6,10},{7,12}}
[8,9,10,11,2,3,12,4,5,1,6,7]=>{{1,3,4,6,8,10,11},{2,5,9},{7,12}}
[8,9,10,11,2,3,12,4,1,5,6,7]=>{{1,2,3,4,5,6,8,9,10,11},{7,12}}
[8,9,10,11,2,3,12,1,4,5,6,7]=>{{1,8},{2,3,4,5,6,9,10,11},{7,12}}
[8,9,10,11,2,12,3,4,5,6,1,7]=>{{1,4,8,11},{2,5,9},{3,6,7,10,12}}
[8,9,10,11,2,12,3,4,5,1,6,7]=>{{1,3,4,6,7,8,10,11,12},{2,5,9}}
[8,9,10,11,2,12,3,4,1,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,11,2,12,3,1,4,5,6,7]=>{{1,8},{2,3,4,5,6,7,9,10,11,12}}
[8,9,10,11,2,12,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,11,12,2,3,4,5,6,1,7]=>{{1,4,8,11},{2,3,5,6,7,9,10,12}}
[8,9,10,11,12,2,3,4,5,1,6,7]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[8,9,10,11,12,2,3,4,1,5,6,7]=>{{1,2,4,6,8,9,11},{3,5,7,10,12}}
[8,9,10,11,12,2,3,1,4,5,6,7]=>{{1,8},{2,4,6,9,11},{3,5,7,10,12}}
[8,9,10,11,12,2,1,3,4,5,6,7]=>{{1,3,5,7,8,10,12},{2,4,6,9,11}}
[11,2,3,4,5,6,7,8,9,10,12,1]=>{{1,11,12},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
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(only identities of compositions of up to three maps are shown)
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].
References
Properties
surjective, graded
Sage code
def mapping(pi): return SetPartition(pi.cycle_tuples())
Weight
26
Created
Sep 25, 2020 at 16:52 by Tilman Möller
Updated
Sep 25, 2020 at 16:57 by Christian Stump
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