Identifier
Mp00099:
Dyck paths
—bounce path⟶
Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Mp00220: Set partitions —Yip⟶ Set partitions
Mp00174: Set partitions —dual major index to intertwining number⟶ Set partitions
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Mp00220: Set partitions —Yip⟶ Set partitions
Mp00174: Set partitions —dual major index to intertwining number⟶ Set partitions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0009;cc-rep-2Cc0009;cc-rep-3Cc0009;cc-rep-4
[1,0]=>[1,0]=>{{1}}=>{{1}}=>{{1}}
[1,0,1,0]=>[1,0,1,0]=>{{1},{2}}=>{{1},{2}}=>{{1},{2}}
[1,1,0,0]=>[1,1,0,0]=>{{1,2}}=>{{1,2}}=>{{1,2}}
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>{{1},{2},{3}}=>{{1},{2},{3}}=>{{1},{2},{3}}
[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>{{1},{2,3}}=>{{1,3},{2}}=>{{1},{2,3}}
[1,1,0,0,1,0]=>[1,1,0,0,1,0]=>{{1,2},{3}}=>{{1,2},{3}}=>{{1,2},{3}}
[1,1,0,1,0,0]=>[1,0,1,1,0,0]=>{{1},{2,3}}=>{{1,3},{2}}=>{{1},{2,3}}
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>{{1,2,3}}=>{{1,2,3}}=>{{1,2,3}}
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4}}=>{{1},{2},{3},{4}}=>{{1},{2},{3},{4}}
[1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0]=>{{1},{2},{3,4}}=>{{1,4},{2},{3}}=>{{1},{2},{3,4}}
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>{{1},{2,3},{4}}=>{{1,3},{2},{4}}=>{{1},{2,3},{4}}
[1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]=>{{1},{2},{3,4}}=>{{1,4},{2},{3}}=>{{1},{2},{3,4}}
[1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>{{1},{2,3,4}}=>{{1,3,4},{2}}=>{{1},{2,3,4}}
[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]=>{{1,2},{3},{4}}=>{{1,2},{3},{4}}=>{{1,2},{3},{4}}
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>{{1,2},{3,4}}=>{{1,2,4},{3}}=>{{1,2},{3,4}}
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>{{1},{2,3},{4}}=>{{1,3},{2},{4}}=>{{1},{2,3},{4}}
[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>{{1,2},{3,4}}=>{{1,2,4},{3}}=>{{1,2},{3,4}}
[1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>{{1},{2,3,4}}=>{{1,3,4},{2}}=>{{1},{2,3,4}}
[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0]=>{{1,2,3},{4}}=>{{1,2,3},{4}}=>{{1,2,3},{4}}
[1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>{{1,2},{3,4}}=>{{1,2,4},{3}}=>{{1,2},{3,4}}
[1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>{{1},{2,3,4}}=>{{1,3,4},{2}}=>{{1},{2,3,4}}
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>{{1,2,3,4}}=>{{1,2,3,4}}=>{{1,2,3,4}}
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5}}=>{{1,5},{2},{3},{4}}=>{{1},{2},{3},{4,5}}
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5}}=>{{1,4},{2},{3},{5}}=>{{1},{2},{3,4},{5}}
[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5}}=>{{1,5},{2},{3},{4}}=>{{1},{2},{3},{4,5}}
[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}}=>{{1,4,5},{2},{3}}=>{{1},{2},{3,4,5}}
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4},{5}}=>{{1,3},{2},{4},{5}}=>{{1},{2,3},{4},{5}}
[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>{{1,3,5},{2},{4}}=>{{1},{2,3},{4,5}}
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5}}=>{{1,4},{2},{3},{5}}=>{{1},{2},{3,4},{5}}
[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>{{1,3,5},{2},{4}}=>{{1},{2,3},{4,5}}
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}}=>{{1,4,5},{2},{3}}=>{{1},{2},{3,4,5}}
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}}=>{{1,3,4},{2},{5}}=>{{1},{2,3,4},{5}}
[1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>{{1,3,5},{2},{4}}=>{{1},{2,3},{4,5}}
[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}}=>{{1,4,5},{2},{3}}=>{{1},{2},{3,4,5}}
[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}}=>{{1,3,4,5},{2}}=>{{1},{2,3,4,5}}
[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5}}=>{{1,2},{3},{4},{5}}=>{{1,2},{3},{4},{5}}
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3},{4,5}}=>{{1,2,5},{3},{4}}=>{{1,2},{3},{4,5}}
[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5}}=>{{1,2,4},{3},{5}}=>{{1,2},{3,4},{5}}
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3},{4,5}}=>{{1,2,5},{3},{4}}=>{{1,2},{3},{4,5}}
[1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>{{1,2,4,5},{3}}=>{{1,2},{3,4,5}}
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4},{5}}=>{{1,3},{2},{4},{5}}=>{{1},{2,3},{4},{5}}
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>{{1,3,5},{2},{4}}=>{{1},{2,3},{4,5}}
[1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5}}=>{{1,2,4},{3},{5}}=>{{1,2},{3,4},{5}}
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>{{1,3,5},{2},{4}}=>{{1},{2,3},{4,5}}
[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>{{1,2,4,5},{3}}=>{{1,2},{3,4,5}}
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}}=>{{1,3,4},{2},{5}}=>{{1},{2,3,4},{5}}
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>{{1,3,5},{2},{4}}=>{{1},{2,3},{4,5}}
[1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>{{1,2,4,5},{3}}=>{{1,2},{3,4,5}}
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}}=>{{1,3,4,5},{2}}=>{{1},{2,3,4,5}}
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4},{5}}=>{{1,2,3},{4},{5}}=>{{1,2,3},{4},{5}}
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}}=>{{1,2,3,5},{4}}=>{{1,2,3},{4,5}}
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5}}=>{{1,2,4},{3},{5}}=>{{1,2},{3,4},{5}}
[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}}=>{{1,2,3,5},{4}}=>{{1,2,3},{4,5}}
[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>{{1,2,4,5},{3}}=>{{1,2},{3,4,5}}
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}}=>{{1,3,4},{2},{5}}=>{{1},{2,3,4},{5}}
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}}=>{{1,2,3,5},{4}}=>{{1,2,3},{4,5}}
[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>{{1,2,4,5},{3}}=>{{1,2},{3,4,5}}
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}}=>{{1,3,4,5},{2}}=>{{1},{2,3,4,5}}
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4},{5}}=>{{1,2,3,4},{5}}=>{{1,2,3,4},{5}}
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}}=>{{1,2,3,5},{4}}=>{{1,2,3},{4,5}}
[1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>{{1,2,4,5},{3}}=>{{1,2},{3,4,5}}
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}}=>{{1,3,4,5},{2}}=>{{1},{2,3,4,5}}
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}}=>{{1,2,3,4,5}}
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6}}=>{{1,6},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5,6}}
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6}}=>{{1,5},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6}}
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6}}=>{{1,6},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5,6}}
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}}=>{{1,5,6},{2},{3},{4}}=>{{1},{2},{3},{4,5,6}}
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6}}=>{{1,4},{2},{3},{5},{6}}=>{{1},{2},{3,4},{5},{6}}
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>{{1,4,6},{2},{3},{5}}=>{{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6}}=>{{1,5},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6}}
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>{{1,4,6},{2},{3},{5}}=>{{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}}=>{{1,5,6},{2},{3},{4}}=>{{1},{2},{3},{4,5,6}}
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}}=>{{1,4,5},{2},{3},{6}}=>{{1},{2},{3,4,5},{6}}
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>{{1,4,6},{2},{3},{5}}=>{{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}}=>{{1,5,6},{2},{3},{4}}=>{{1},{2},{3},{4,5,6}}
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}}=>{{1,4,5,6},{2},{3}}=>{{1},{2},{3,4,5,6}}
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6}}=>{{1,3},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6}}
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}}=>{{1,3,6},{2},{4},{5}}=>{{1},{2,3},{4},{5,6}}
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>{{1,3,5},{2},{4},{6}}=>{{1},{2,3},{4,5},{6}}
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}}=>{{1,3,6},{2},{4},{5}}=>{{1},{2,3},{4},{5,6}}
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6}}=>{{1,4},{2},{3},{5},{6}}=>{{1},{2},{3,4},{5},{6}}
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>{{1,4,6},{2},{3},{5}}=>{{1},{2},{3,4},{5,6}}
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>{{1,3,5},{2},{4},{6}}=>{{1},{2,3},{4,5},{6}}
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>{{1,4,6},{2},{3},{5}}=>{{1},{2},{3,4},{5,6}}
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}}=>{{1,4,5},{2},{3},{6}}=>{{1},{2},{3,4,5},{6}}
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>{{1,4,6},{2},{3},{5}}=>{{1},{2},{3,4},{5,6}}
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}}=>{{1,4,5,6},{2},{3}}=>{{1},{2},{3,4,5,6}}
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}}=>{{1,3,4},{2},{5},{6}}=>{{1},{2,3,4},{5},{6}}
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>{{1,3,5},{2},{4},{6}}=>{{1},{2,3},{4,5},{6}}
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}}=>{{1,4,5},{2},{3},{6}}=>{{1},{2},{3,4,5},{6}}
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}}=>{{1,4,5,6},{2},{3}}=>{{1},{2},{3,4,5,6}}
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}}=>{{1,3,4,5},{2},{6}}=>{{1},{2,3,4,5},{6}}
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}}=>{{1,4,5,6},{2},{3}}=>{{1},{2},{3,4,5,6}}
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}}=>{{1,3,4,5,6},{2}}=>{{1},{2,3,4,5,6}}
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6}}
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5,6}}=>{{1,2,6},{3},{4},{5}}=>{{1,2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4,5},{6}}=>{{1,2,5},{3},{4},{6}}=>{{1,2},{3},{4,5},{6}}
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5,6}}=>{{1,2,6},{3},{4},{5}}=>{{1,2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}}=>{{1,2,5,6},{3},{4}}=>{{1,2},{3},{4,5,6}}
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5},{6}}=>{{1,2,4},{3},{5},{6}}=>{{1,2},{3,4},{5},{6}}
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,2,4,6},{3},{5}}=>{{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4,5},{6}}=>{{1,2,5},{3},{4},{6}}=>{{1,2},{3},{4,5},{6}}
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,2,4,6},{3},{5}}=>{{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}}=>{{1,2,5,6},{3},{4}}=>{{1,2},{3},{4,5,6}}
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>{{1,2,4,5},{3},{6}}=>{{1,2},{3,4,5},{6}}
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,2,4,6},{3},{5}}=>{{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}}=>{{1,2,5,6},{3},{4}}=>{{1,2},{3},{4,5,6}}
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,4,5,6},{3}}=>{{1,2},{3,4,5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6}}=>{{1,3},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}}=>{{1,3,6},{2},{4},{5}}=>{{1},{2,3},{4},{5,6}}
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>{{1,3,5},{2},{4},{6}}=>{{1},{2,3},{4,5},{6}}
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}}=>{{1,3,6},{2},{4},{5}}=>{{1},{2,3},{4},{5,6}}
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5},{6}}=>{{1,2,4},{3},{5},{6}}=>{{1,2},{3,4},{5},{6}}
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,2,4,6},{3},{5}}=>{{1,2},{3,4},{5,6}}
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>{{1,3,5},{2},{4},{6}}=>{{1},{2,3},{4,5},{6}}
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,2,4,6},{3},{5}}=>{{1,2},{3,4},{5,6}}
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>{{1,2,4,5},{3},{6}}=>{{1,2},{3,4,5},{6}}
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,2,4,6},{3},{5}}=>{{1,2},{3,4},{5,6}}
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,4,5,6},{3}}=>{{1,2},{3,4,5,6}}
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}}=>{{1,3,4},{2},{5},{6}}=>{{1},{2,3,4},{5},{6}}
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>{{1,3,5},{2},{4},{6}}=>{{1},{2,3},{4,5},{6}}
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>{{1,2,4,5},{3},{6}}=>{{1,2},{3,4,5},{6}}
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,4,5,6},{3}}=>{{1,2},{3,4,5,6}}
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}}=>{{1,3,4,5},{2},{6}}=>{{1},{2,3,4,5},{6}}
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}}=>{{1},{2,3},{4,5,6}}
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,4,5,6},{3}}=>{{1,2},{3,4,5,6}}
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}}=>{{1,3,4,5,6},{2}}=>{{1},{2,3,4,5,6}}
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6}}=>{{1,2,3},{4},{5},{6}}=>{{1,2,3},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5,6}}=>{{1,2,3,6},{4},{5}}=>{{1,2,3},{4},{5,6}}
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}}=>{{1,2,3,5},{4},{6}}=>{{1,2,3},{4,5},{6}}
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5,6}}=>{{1,2,3,6},{4},{5}}=>{{1,2,3},{4},{5,6}}
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3,5,6},{4}}=>{{1,2,3},{4,5,6}}
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5},{6}}=>{{1,2,4},{3},{5},{6}}=>{{1,2},{3,4},{5},{6}}
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,2,4,6},{3},{5}}=>{{1,2},{3,4},{5,6}}
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}}=>{{1,2,3,5},{4},{6}}=>{{1,2,3},{4,5},{6}}
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,2,4,6},{3},{5}}=>{{1,2},{3,4},{5,6}}
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3,5,6},{4}}=>{{1,2,3},{4,5,6}}
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>{{1,2,4,5},{3},{6}}=>{{1,2},{3,4,5},{6}}
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,2,4,6},{3},{5}}=>{{1,2},{3,4},{5,6}}
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3,5,6},{4}}=>{{1,2,3},{4,5,6}}
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,4,5,6},{3}}=>{{1,2},{3,4,5,6}}
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}}=>{{1,3,4},{2},{5},{6}}=>{{1},{2,3,4},{5},{6}}
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}}=>{{1,2,3,5},{4},{6}}=>{{1,2,3},{4,5},{6}}
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3,5,6},{4}}=>{{1,2,3},{4,5,6}}
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>{{1,2,4,5},{3},{6}}=>{{1,2},{3,4,5},{6}}
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3,5,6},{4}}=>{{1,2,3},{4,5,6}}
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,4,5,6},{3}}=>{{1,2},{3,4,5,6}}
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}}=>{{1,3,4,5},{2},{6}}=>{{1},{2,3,4,5},{6}}
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1},{2,3,4},{5,6}}
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3,5,6},{4}}=>{{1,2,3},{4,5,6}}
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,4,5,6},{3}}=>{{1,2},{3,4,5,6}}
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}}=>{{1,3,4,5,6},{2}}=>{{1},{2,3,4,5,6}}
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}}
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4,6},{5}}=>{{1,2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}}=>{{1,2,3,5},{4},{6}}=>{{1,2,3},{4,5},{6}}
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4,6},{5}}=>{{1,2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3,5,6},{4}}=>{{1,2,3},{4,5,6}}
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>{{1,2,4,5},{3},{6}}=>{{1,2},{3,4,5},{6}}
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4,6},{5}}=>{{1,2,3,4},{5,6}}
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3,5,6},{4}}=>{{1,2,3},{4,5,6}}
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,4,5,6},{3}}=>{{1,2},{3,4,5,6}}
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}}=>{{1,3,4,5},{2},{6}}=>{{1},{2,3,4,5},{6}}
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4,6},{5}}=>{{1,2,3,4},{5,6}}
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3,5,6},{4}}=>{{1,2,3},{4,5,6}}
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,4,5,6},{3}}=>{{1,2},{3,4,5,6}}
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}}=>{{1,3,4,5,6},{2}}=>{{1},{2,3,4,5,6}}
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}}
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4,6},{5}}=>{{1,2,3,4},{5,6}}
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3,5,6},{4}}=>{{1,2,3},{4,5,6}}
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,4,5,6},{3}}=>{{1,2},{3,4,5,6}}
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}}=>{{1,3,4,5,6},{2}}=>{{1},{2,3,4,5,6}}
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6,7}}=>{{1,7},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5,6},{7}}=>{{1,6},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6,7}}=>{{1,7},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6,7}}=>{{1,6,7},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7}}=>{{1,5},{2},{3},{4},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>{{1,5,7},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5,6},{7}}=>{{1,6},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>{{1,5,7},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6,7}}=>{{1,6,7},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4,5,6},{7}}=>{{1,5,6},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>{{1,5,7},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6,7}}=>{{1,6,7},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5,6,7}}=>{{1,5,6,7},{2},{3},{4}}=>{{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7}}=>{{1,4},{2},{3},{5},{6},{7}}=>{{1},{2},{3,4},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6,7}}=>{{1,4,7},{2},{3},{5},{6}}=>{{1},{2},{3,4},{5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>{{1,4,6},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6,7}}=>{{1,4,7},{2},{3},{5},{6}}=>{{1},{2},{3,4},{5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7}}=>{{1,5},{2},{3},{4},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>{{1,5,7},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>{{1,4,6},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>{{1,5,7},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4,5,6},{7}}=>{{1,5,6},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>{{1,5,7},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5,6,7}}=>{{1,5,6,7},{2},{3},{4}}=>{{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7}}=>{{1,4,5},{2},{3},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>{{1,4,6},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4,5,6},{7}}=>{{1,5,6},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5,6,7}}=>{{1,5,6,7},{2},{3},{4}}=>{{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}}=>{{1,4,5,6},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5,6,7}}=>{{1,5,6,7},{2},{3},{4}}=>{{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}}=>{{1,4,5,6,7},{2},{3}}=>{{1},{2},{3,4,5,6,7}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7}}=>{{1,3},{2},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6,7}}=>{{1,3,7},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5,6},{7}}=>{{1,3,6},{2},{4},{5},{7}}=>{{1},{2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6,7}}=>{{1,3,7},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>{{1,3,6,7},{2},{4},{5}}=>{{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5,6},{7}}=>{{1,3,6},{2},{4},{5},{7}}=>{{1},{2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>{{1,3,6,7},{2},{4},{5}}=>{{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>{{1,3,6,7},{2},{4},{5}}=>{{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7}}=>{{1,4},{2},{3},{5},{6},{7}}=>{{1},{2},{3,4},{5},{6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6,7}}=>{{1,4,7},{2},{3},{5},{6}}=>{{1},{2},{3,4},{5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>{{1,4,6},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6,7}}=>{{1,4,7},{2},{3},{5},{6}}=>{{1},{2},{3,4},{5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>{{1,4,6},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7}}=>{{1,4,5},{2},{3},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>{{1,4,6},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}}=>{{1,4,5,6},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}}=>{{1,4,5,6,7},{2},{3}}=>{{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7}}=>{{1,3,4},{2},{5},{6},{7}}=>{{1},{2,3,4},{5},{6},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>{{1,3,4,7},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>{{1,3,4,7},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7}}=>{{1,4,5},{2},{3},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}}=>{{1,4,5,6},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}}=>{{1,4,5,6,7},{2},{3}}=>{{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}}=>{{1,3,4,5},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}}=>{{1,4,5,6},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}}=>{{1,4,5,6,7},{2},{3}}=>{{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}}=>{{1,3,4,5,6},{2},{7}}=>{{1},{2,3,4,5,6},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}}=>{{1,4,5,6,7},{2},{3}}=>{{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>{{1,3,4,5,6,7},{2}}=>{{1},{2,3,4,5,6,7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7}}=>{{1,2},{3},{4},{5},{6},{7}}=>{{1,2},{3},{4},{5},{6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6,7}}=>{{1,2,7},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5,6},{7}}=>{{1,2,6},{3},{4},{5},{7}}=>{{1,2},{3},{4},{5,6},{7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6,7}}=>{{1,2,7},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}}=>{{1,2,6,7},{3},{4},{5}}=>{{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7}}=>{{1,2,5},{3},{4},{6},{7}}=>{{1,2},{3},{4,5},{6},{7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>{{1,2,5,7},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5,6},{7}}=>{{1,2,6},{3},{4},{5},{7}}=>{{1,2},{3},{4},{5,6},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>{{1,2,5,7},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}}=>{{1,2,6,7},{3},{4},{5}}=>{{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2},{3},{4,5,6},{7}}=>{{1,2,5,6},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>{{1,2,5,7},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}}=>{{1,2,6,7},{3},{4},{5}}=>{{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}}=>{{1,2,5,6,7},{3},{4}}=>{{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7}}=>{{1,2,4},{3},{5},{6},{7}}=>{{1,2},{3,4},{5},{6},{7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>{{1,2,4,7},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>{{1,2,4,6},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>{{1,2,4,7},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7}}=>{{1,2,5},{3},{4},{6},{7}}=>{{1,2},{3},{4,5},{6},{7}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>{{1,2,5,7},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>{{1,2,4,6},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>{{1,2,5,7},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2},{3},{4,5,6},{7}}=>{{1,2,5,6},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>{{1,2,5,7},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}}=>{{1,2,5,6,7},{3},{4}}=>{{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>{{1,2,4,5},{3},{6},{7}}=>{{1,2},{3,4,5},{6},{7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>{{1,2,4,6},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2},{3},{4,5,6},{7}}=>{{1,2,5,6},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}}=>{{1,2,5,6,7},{3},{4}}=>{{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}}=>{{1,2,5,6,7},{3},{4}}=>{{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7}}=>{{1,3},{2},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6,7}}=>{{1,3,7},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6,7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5,6},{7}}=>{{1,3,6},{2},{4},{5},{7}}=>{{1},{2,3},{4},{5,6},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6,7}}=>{{1,3,7},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6,7}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>{{1,3,6,7},{2},{4},{5}}=>{{1},{2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5,6},{7}}=>{{1,3,6},{2},{4},{5},{7}}=>{{1},{2,3},{4},{5,6},{7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>{{1,3,6,7},{2},{4},{5}}=>{{1},{2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>{{1,3,6,7},{2},{4},{5}}=>{{1},{2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7}}=>{{1,2,4},{3},{5},{6},{7}}=>{{1,2},{3,4},{5},{6},{7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>{{1,2,4,7},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>{{1,2,4,6},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>{{1,2,4,7},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>{{1,2,4,6},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>{{1,2,4,5},{3},{6},{7}}=>{{1,2},{3,4,5},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>{{1,2,4,6},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7}}=>{{1,3,4},{2},{5},{6},{7}}=>{{1},{2,3,4},{5},{6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>{{1,3,4,7},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>{{1,3,4,7},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>{{1,2,4,5},{3},{6},{7}}=>{{1,2},{3,4,5},{6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}}=>{{1,3,4,5},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}}=>{{1,3,4,5,6},{2},{7}}=>{{1},{2,3,4,5,6},{7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>{{1,3,4,5,6,7},{2}}=>{{1},{2,3,4,5,6,7}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6,7}}=>{{1,2,3,7},{4},{5},{6}}=>{{1,2,3},{4},{5},{6,7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3},{4},{5,6},{7}}=>{{1,2,3,6},{4},{5},{7}}=>{{1,2,3},{4},{5,6},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6,7}}=>{{1,2,3,7},{4},{5},{6}}=>{{1,2,3},{4},{5},{6,7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3,6,7},{4},{5}}=>{{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7}}=>{{1,2,3,5},{4},{6},{7}}=>{{1,2,3},{4,5},{6},{7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3},{4},{5,6},{7}}=>{{1,2,3,6},{4},{5},{7}}=>{{1,2,3},{4},{5,6},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3,6,7},{4},{5}}=>{{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3,6,7},{4},{5}}=>{{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7}}=>{{1,2,4},{3},{5},{6},{7}}=>{{1,2},{3,4},{5},{6},{7}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>{{1,2,4,7},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>{{1,2,4,6},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>{{1,2,4,7},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7}}=>{{1,2,3,5},{4},{6},{7}}=>{{1,2,3},{4,5},{6},{7}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>{{1,2,4,6},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>{{1,2,4,5},{3},{6},{7}}=>{{1,2},{3,4,5},{6},{7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>{{1,2,4,6},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7}}=>{{1,3,4},{2},{5},{6},{7}}=>{{1},{2,3,4},{5},{6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>{{1,3,4,7},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>{{1,3,4,7},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7}}=>{{1,2,3,5},{4},{6},{7}}=>{{1,2,3},{4,5},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>{{1,2,4,5},{3},{6},{7}}=>{{1,2},{3,4,5},{6},{7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}}=>{{1,3,4,5},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}}=>{{1,3,4,5,6},{2},{7}}=>{{1},{2,3,4,5,6},{7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>{{1,3,4,5,6,7},{2}}=>{{1},{2,3,4,5,6,7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}}=>{{1,2,3,4,7},{5},{6}}=>{{1,2,3,4},{5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4,6},{5},{7}}=>{{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}}=>{{1,2,3,4,7},{5},{6}}=>{{1,2,3,4},{5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7}}=>{{1,2,3,5},{4},{6},{7}}=>{{1,2,3},{4,5},{6},{7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4,6},{5},{7}}=>{{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3},{4,5},{6,7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>{{1,2,4,5},{3},{6},{7}}=>{{1,2},{3,4,5},{6},{7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4,6},{5},{7}}=>{{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}}=>{{1,3,4,5},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4,6},{5},{7}}=>{{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}}=>{{1,3,4,5,6},{2},{7}}=>{{1},{2,3,4,5,6},{7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>{{1,3,4,5,6,7},{2}}=>{{1},{2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5,7},{6}}=>{{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4,6},{5},{7}}=>{{1,2,3,4},{5,6},{7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5,7},{6}}=>{{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5,7},{6}}=>{{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5,7},{6}}=>{{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}}=>{{1,3,4,5,6},{2},{7}}=>{{1},{2,3,4,5,6},{7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5,7},{6}}=>{{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>{{1,3,4,5,6,7},{2}}=>{{1},{2,3,4,5,6,7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5,7},{6}}=>{{1,2,3,4,5},{6,7}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4},{5,6,7}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3},{4,5,6,7}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2},{3,4,5,6,7}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>{{1,3,4,5,6,7},{2}}=>{{1},{2,3,4,5,6,7}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8}}=>{{1,8},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6,7},{8}}=>{{1,7},{2},{3},{4},{5},{6},{8}}=>{{1},{2},{3},{4},{5},{6,7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8}}=>{{1,8},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8}}=>{{1,7,8},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4},{5,6},{7},{8}}=>{{1,6},{2},{3},{4},{5},{7},{8}}=>{{1},{2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1,6,8},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6,7},{8}}=>{{1,7},{2},{3},{4},{5},{6},{8}}=>{{1},{2},{3},{4},{5},{6,7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1,6,8},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8}}=>{{1,7,8},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4},{5,6,7},{8}}=>{{1,6,7},{2},{3},{4},{5},{8}}=>{{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1,6,8},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8}}=>{{1,7,8},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1,6,7,8},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7},{8}}=>{{1,5},{2},{3},{4},{6},{7},{8}}=>{{1},{2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6},{7,8}}=>{{1,5,8},{2},{3},{4},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1,5,7},{2},{3},{4},{6},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6},{7,8}}=>{{1,5,8},{2},{3},{4},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4},{5,6},{7},{8}}=>{{1,6},{2},{3},{4},{5},{7},{8}}=>{{1},{2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1,6,8},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1,5,7},{2},{3},{4},{6},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1,6,8},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4},{5,6,7},{8}}=>{{1,6,7},{2},{3},{4},{5},{8}}=>{{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1,6,8},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1,6,7,8},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3},{4,5,6},{7},{8}}=>{{1,5,6},{2},{3},{4},{7},{8}}=>{{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1,5,7},{2},{3},{4},{6},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4},{5,6,7},{8}}=>{{1,6,7},{2},{3},{4},{5},{8}}=>{{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1,6,7,8},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3},{4,5,6,7},{8}}=>{{1,5,6,7},{2},{3},{4},{8}}=>{{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1,6,7,8},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8}}=>{{1,5,6,7,8},{2},{3},{4}}=>{{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5,6},{7},{8}}=>{{1,4,6},{2},{3},{5},{7},{8}}=>{{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7},{8}}=>{{1,5},{2},{3},{4},{6},{7},{8}}=>{{1},{2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6},{7,8}}=>{{1,5,8},{2},{3},{4},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1,5,7},{2},{3},{4},{6},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6},{7,8}}=>{{1,5,8},{2},{3},{4},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5,6},{7},{8}}=>{{1,4,6},{2},{3},{5},{7},{8}}=>{{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1,5,7},{2},{3},{4},{6},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3},{4,5,6},{7},{8}}=>{{1,5,6},{2},{3},{4},{7},{8}}=>{{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1,5,7},{2},{3},{4},{6},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3},{4,5,6,7},{8}}=>{{1,5,6,7},{2},{3},{4},{8}}=>{{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}}=>{{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8}}=>{{1,5,6,7,8},{2},{3},{4}}=>{{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7},{8}}=>{{1,4,5},{2},{3},{6},{7},{8}}=>{{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5,6},{7},{8}}=>{{1,4,6},{2},{3},{5},{7},{8}}=>{{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3},{4,5,6},{7},{8}}=>{{1,5,6},{2},{3},{4},{7},{8}}=>{{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3},{4,5,6,7},{8}}=>{{1,5,6,7},{2},{3},{4},{8}}=>{{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}}=>{{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8}}=>{{1,5,6,7,8},{2},{3},{4}}=>{{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3},{4,5,6,7},{8}}=>{{1,5,6,7},{2},{3},{4},{8}}=>{{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8}}=>{{1,5,6,7,8},{2},{3},{4}}=>{{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6,7},{8}}=>{{1,4,5,6,7},{2},{3},{8}}=>{{1},{2},{3,4,5,6,7},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8}}=>{{1,5,6,7,8},{2},{3},{4}}=>{{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8}}=>{{1,4,5,6,7,8},{2},{3}}=>{{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7},{8}}=>{{1,3},{2},{4},{5},{6},{7},{8}}=>{{1},{2,3},{4},{5},{6},{7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6},{7,8}}=>{{1,3,8},{2},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1,3,7},{2},{4},{5},{6},{8}}=>{{1},{2,3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6},{7,8}}=>{{1,3,8},{2},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5},{6,7,8}}=>{{1,3,7,8},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1,3,7},{2},{4},{5},{6},{8}}=>{{1},{2,3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5},{6,7,8}}=>{{1,3,7,8},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5},{6,7,8}}=>{{1,3,7,8},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1,3,5},{2},{4},{6},{7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5,6},{7},{8}}=>{{1,4,6},{2},{3},{5},{7},{8}}=>{{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1,3,5},{2},{4},{6},{7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5,6},{7},{8}}=>{{1,4,6},{2},{3},{5},{7},{8}}=>{{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7},{8}}=>{{1,4,5},{2},{3},{6},{7},{8}}=>{{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5,6},{7},{8}}=>{{1,4,6},{2},{3},{5},{7},{8}}=>{{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6,7},{8}}=>{{1,4,5,6,7},{2},{3},{8}}=>{{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8}}=>{{1,4,5,6,7,8},{2},{3}}=>{{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7},{8}}=>{{1,3,4},{2},{5},{6},{7},{8}}=>{{1},{2,3,4},{5},{6},{7},{8}}
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5},{6,7,8}}=>{{1,3,4,7,8},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5},{6,7,8}}=>{{1,3,4,7,8},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5},{6,7,8}}=>{{1,3,4,7,8},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1,3,5},{2},{4},{6},{7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7},{8}}=>{{1,4,5},{2},{3},{6},{7},{8}}=>{{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6,7},{8}}=>{{1,4,5,6,7},{2},{3},{8}}=>{{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8}}=>{{1,4,5,6,7,8},{2},{3}}=>{{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7},{8}}=>{{1,3,4,5},{2},{6},{7},{8}}=>{{1},{2,3,4,5},{6},{7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4,5},{6},{7,8}}=>{{1,3,4,5,8},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4,5},{6},{7,8}}=>{{1,3,4,5,8},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6,7},{8}}=>{{1,4,5,6,7},{2},{3},{8}}=>{{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}}=>{{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8}}=>{{1,4,5,6,7,8},{2},{3}}=>{{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5,6},{7},{8}}=>{{1,3,4,5,6},{2},{7},{8}}=>{{1},{2,3,4,5,6},{7},{8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6,7},{8}}=>{{1,4,5,6,7},{2},{3},{8}}=>{{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8}}=>{{1,4,5,6,7,8},{2},{3}}=>{{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}}=>{{1,3,4,5,6,7},{2},{8}}=>{{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8}}=>{{1,4,5,6,7,8},{2},{3}}=>{{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>{{1,3,4,5,6,7,8},{2}}=>{{1},{2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7},{8}}=>{{1,2},{3},{4},{5},{6},{7},{8}}=>{{1,2},{3},{4},{5},{6},{7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6},{7,8}}=>{{1,2,8},{3},{4},{5},{6},{7}}=>{{1,2},{3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5},{6,7},{8}}=>{{1,2,7},{3},{4},{5},{6},{8}}=>{{1,2},{3},{4},{5},{6,7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6},{7,8}}=>{{1,2,8},{3},{4},{5},{6},{7}}=>{{1,2},{3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5},{6,7,8}}=>{{1,2,7,8},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4},{5,6},{7},{8}}=>{{1,2,6},{3},{4},{5},{7},{8}}=>{{1,2},{3},{4},{5,6},{7},{8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5},{6,7},{8}}=>{{1,2,7},{3},{4},{5},{6},{8}}=>{{1,2},{3},{4},{5},{6,7},{8}}
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5},{6,7,8}}=>{{1,2,7,8},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5},{6,7,8}}=>{{1,2,7,8},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4},{5,6,7,8}}=>{{1,2,6,7,8},{3},{4},{5}}=>{{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7},{8}}=>{{1,2,5},{3},{4},{6},{7},{8}}=>{{1,2},{3},{4,5},{6},{7},{8}}
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4},{5,6},{7},{8}}=>{{1,2,6},{3},{4},{5},{7},{8}}=>{{1,2},{3},{4},{5,6},{7},{8}}
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4},{5,6,7,8}}=>{{1,2,6,7,8},{3},{4},{5}}=>{{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4},{5,6,7,8}}=>{{1,2,6,7,8},{3},{4},{5}}=>{{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3},{4,5,6,7},{8}}=>{{1,2,5,6,7},{3},{4},{8}}=>{{1,2},{3},{4,5,6,7},{8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4},{5,6,7,8}}=>{{1,2,6,7,8},{3},{4},{5}}=>{{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3},{4,5,6,7,8}}=>{{1,2,5,6,7,8},{3},{4}}=>{{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8}}=>{{1,2,4},{3},{5},{6},{7},{8}}=>{{1,2},{3,4},{5},{6},{7},{8}}
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5},{6,7,8}}=>{{1,2,4,7,8},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5},{6,7,8}}=>{{1,2,4,7,8},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5},{6,7,8}}=>{{1,2,4,7,8},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7},{8}}=>{{1,2,5},{3},{4},{6},{7},{8}}=>{{1,2},{3},{4,5},{6},{7},{8}}
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3},{4,5,6,7},{8}}=>{{1,2,5,6,7},{3},{4},{8}}=>{{1,2},{3},{4,5,6,7},{8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}}=>{{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3},{4,5,6,7,8}}=>{{1,2,5,6,7,8},{3},{4}}=>{{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3},{4,5,6,7},{8}}=>{{1,2,5,6,7},{3},{4},{8}}=>{{1,2},{3},{4,5,6,7},{8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3},{4,5,6,7,8}}=>{{1,2,5,6,7,8},{3},{4}}=>{{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3},{4,5,6,7},{8}}=>{{1,2,5,6,7},{3},{4},{8}}=>{{1,2},{3},{4,5,6,7},{8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3},{4,5,6,7,8}}=>{{1,2,5,6,7,8},{3},{4}}=>{{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3},{4,5,6,7,8}}=>{{1,2,5,6,7,8},{3},{4}}=>{{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7},{8}}=>{{1,3},{2},{4},{5},{6},{7},{8}}=>{{1},{2,3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6},{7,8}}=>{{1,3,8},{2},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1,3,7},{2},{4},{5},{6},{8}}=>{{1},{2,3},{4},{5},{6,7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6},{7,8}}=>{{1,3,8},{2},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5},{6,7,8}}=>{{1,3,7,8},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1,3,7},{2},{4},{5},{6},{8}}=>{{1},{2,3},{4},{5},{6,7},{8}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5},{6,7,8}}=>{{1,3,7,8},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5},{6,7,8}}=>{{1,3,7,8},{2},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1,3,5},{2},{4},{6},{7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8}}=>{{1,2,4},{3},{5},{6},{7},{8}}=>{{1,2},{3,4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5},{6,7,8}}=>{{1,2,4,7,8},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5},{6,7,8}}=>{{1,2,4,7,8},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5},{6,7,8}}=>{{1,2,4,7,8},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1,3,5},{2},{4},{6},{7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7},{8}}=>{{1,3,4},{2},{5},{6},{7},{8}}=>{{1},{2,3,4},{5},{6},{7},{8}}
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5},{6,7,8}}=>{{1,3,4,7,8},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7,8}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5},{6,7,8}}=>{{1,3,4,7,8},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7,8}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5},{6,7,8}}=>{{1,3,4,7,8},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7,8}}
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1,3,5},{2},{4},{6},{7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7},{8}}=>{{1,3,4,5},{2},{6},{7},{8}}=>{{1},{2,3,4,5},{6},{7},{8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4,5},{6},{7,8}}=>{{1,3,4,5,8},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4,5},{6},{7,8}}=>{{1,3,4,5,8},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}}=>{{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5,6},{7},{8}}=>{{1,3,4,5,6},{2},{7},{8}}=>{{1},{2,3,4,5,6},{7},{8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}}=>{{1,3,4,5,6,7},{2},{8}}=>{{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>{{1,3,4,5,6,7,8},{2}}=>{{1},{2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7},{8}}=>{{1,2,3},{4},{5},{6},{7},{8}}=>{{1,2,3},{4},{5},{6},{7},{8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6},{7,8}}=>{{1,2,3,8},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6},{7,8}}=>{{1,2,3,8},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5},{6,7,8}}=>{{1,2,3,7,8},{4},{5},{6}}=>{{1,2,3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4},{5,6},{7,8}}=>{{1,2,3,6,8},{4},{5},{7}}=>{{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4},{5,6},{7,8}}=>{{1,2,3,6,8},{4},{5},{7}}=>{{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5},{6,7,8}}=>{{1,2,3,7,8},{4},{5},{6}}=>{{1,2,3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4},{5,6},{7,8}}=>{{1,2,3,6,8},{4},{5},{7}}=>{{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5},{6,7,8}}=>{{1,2,3,7,8},{4},{5},{6}}=>{{1,2,3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4},{5,6,7,8}}=>{{1,2,3,6,7,8},{4},{5}}=>{{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4},{5,6},{7,8}}=>{{1,2,3,6,8},{4},{5},{7}}=>{{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4},{5,6},{7,8}}=>{{1,2,3,6,8},{4},{5},{7}}=>{{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4},{5,6},{7,8}}=>{{1,2,3,6,8},{4},{5},{7}}=>{{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4},{5,6,7,8}}=>{{1,2,3,6,7,8},{4},{5}}=>{{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3,5,6},{4},{7},{8}}=>{{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4},{5,6,7,8}}=>{{1,2,3,6,7,8},{4},{5}}=>{{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4},{5,6,7,8}}=>{{1,2,3,6,7,8},{4},{5}}=>{{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8}}=>{{1,2,4},{3},{5},{6},{7},{8}}=>{{1,2},{3,4},{5},{6},{7},{8}}
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5},{6,7,8}}=>{{1,2,4,7,8},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5},{6,7,8}}=>{{1,2,4,7,8},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5},{6,7,8}}=>{{1,2,4,7,8},{3},{5},{6}}=>{{1,2},{3,4},{5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3,5,6},{4},{7},{8}}=>{{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3,5,6},{4},{7},{8}}=>{{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7},{8}}=>{{1,3,4},{2},{5},{6},{7},{8}}=>{{1},{2,3,4},{5},{6},{7},{8}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5},{6,7,8}}=>{{1,3,4,7,8},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5},{6,7,8}}=>{{1,3,4,7,8},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5},{6,7,8}}=>{{1,3,4,7,8},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3,5,6},{4},{7},{8}}=>{{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3,5,6},{4},{7},{8}}=>{{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7},{8}}=>{{1,3,4,5},{2},{6},{7},{8}}=>{{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4,5},{6},{7,8}}=>{{1,3,4,5,8},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4,5},{6},{7,8}}=>{{1,3,4,5,8},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}}=>{{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3,5,6},{4},{7},{8}}=>{{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5,6},{7},{8}}=>{{1,3,4,5,6},{2},{7},{8}}=>{{1},{2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}}=>{{1,3,4,5,6,7},{2},{8}}=>{{1},{2,3,4,5,6,7},{8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>{{1,3,4,5,6,7,8},{2}}=>{{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7},{8}}=>{{1,2,3,4},{5},{6},{7},{8}}=>{{1,2,3,4},{5},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6},{7,8}}=>{{1,2,3,4,8},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3,4},{5},{6,7},{8}}=>{{1,2,3,4,7},{5},{6},{8}}=>{{1,2,3,4},{5},{6,7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6},{7,8}}=>{{1,2,3,4,8},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3,4},{5},{6,7,8}}=>{{1,2,3,4,7,8},{5},{6}}=>{{1,2,3,4},{5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3,4},{5,6},{7},{8}}=>{{1,2,3,4,6},{5},{7},{8}}=>{{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3,4},{5},{6,7},{8}}=>{{1,2,3,4,7},{5},{6},{8}}=>{{1,2,3,4},{5},{6,7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3,4},{5},{6,7,8}}=>{{1,2,3,4,7,8},{5},{6}}=>{{1,2,3,4},{5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3,4},{5},{6,7,8}}=>{{1,2,3,4,7,8},{5},{6}}=>{{1,2,3,4},{5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3,4},{5,6},{7},{8}}=>{{1,2,3,4,6},{5},{7},{8}}=>{{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3,5,6},{4},{7},{8}}=>{{1,2,3},{4,5,6},{7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3,4},{5,6},{7},{8}}=>{{1,2,3,4,6},{5},{7},{8}}=>{{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3,5,6},{4},{7},{8}}=>{{1,2,3},{4,5,6},{7},{8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7},{8}}=>{{1,3,4,5},{2},{6},{7},{8}}=>{{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4,5},{6},{7,8}}=>{{1,3,4,5,8},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4,5},{6},{7,8}}=>{{1,3,4,5,8},{2},{6},{7}}=>{{1},{2,3,4,5},{6},{7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3,4},{5,6},{7},{8}}=>{{1,2,3,4,6},{5},{7},{8}}=>{{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3,5,6},{4},{7},{8}}=>{{1,2,3},{4,5,6},{7},{8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5,6},{7},{8}}=>{{1,3,4,5,6},{2},{7},{8}}=>{{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}}=>{{1,3,4,5,6,7},{2},{8}}=>{{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}}=>{{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>{{1,3,4,5,6,7,8},{2}}=>{{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7},{8}}=>{{1,2,3,4,5},{6},{7},{8}}=>{{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4,5},{6},{7,8}}=>{{1,2,3,4,5,8},{6},{7}}=>{{1,2,3,4,5},{6},{7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4,5},{6,7},{8}}=>{{1,2,3,4,5,7},{6},{8}}=>{{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4,5},{6},{7,8}}=>{{1,2,3,4,5,8},{6},{7}}=>{{1,2,3,4,5},{6},{7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3,4},{5,6},{7},{8}}=>{{1,2,3,4,6},{5},{7},{8}}=>{{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4,5},{6,7},{8}}=>{{1,2,3,4,5,7},{6},{8}}=>{{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3,5,6},{4},{7},{8}}=>{{1,2,3},{4,5,6},{7},{8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4,5},{6,7},{8}}=>{{1,2,3,4,5,7},{6},{8}}=>{{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}}=>{{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4,5},{6,7},{8}}=>{{1,2,3,4,5,7},{6},{8}}=>{{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5,6},{7},{8}}=>{{1,3,4,5,6},{2},{7},{8}}=>{{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4,5},{6,7},{8}}=>{{1,2,3,4,5,7},{6},{8}}=>{{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}}=>{{1,3,4,5,6,7},{2},{8}}=>{{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}}=>{{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>{{1,3,4,5,6,7,8},{2}}=>{{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5,6},{7},{8}}=>{{1,2,3,4,5,6},{7},{8}}=>{{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>{{1,2,3,4,5,6,8},{7}}=>{{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4,5},{6,7},{8}}=>{{1,2,3,4,5,7},{6},{8}}=>{{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>{{1,2,3,4,5,6,8},{7}}=>{{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>{{1,2,3,4,5,6,8},{7}}=>{{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}}=>{{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>{{1,2,3,4,5,6,8},{7}}=>{{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}}=>{{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>{{1,2,3,4,5,6,8},{7}}=>{{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}}=>{{1,3,4,5,6,7},{2},{8}}=>{{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>{{1,2,3,4,5,6,8},{7}}=>{{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>{{1,3,4,5,6,7,8},{2}}=>{{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7},{8}}=>{{1,2,3,4,5,6,7},{8}}=>{{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>{{1,2,3,4,5,6,8},{7}}=>{{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>{{1,3,4,5,6,7,8},{2}}=>{{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{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}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7,8},{9}}=>{{1,3,4,5,6,7,8},{2},{9}}=>{{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1,4,5,6,7,8,9},{2},{3}}=>{{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7,8,9,10},{11}}=>{{1,2,3,4,5,6,7,8,9,10},{11}}=>{{1,2,3,4,5,6,7,8,9,10},{11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}}=>{{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7,8},{9}}=>{{1,3,4,5,6,7,8},{2},{9}}=>{{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1,4,5,6,7,8,9},{2},{3}}=>{{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}}=>{{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7,8},{9}}=>{{1,3,4,5,6,7,8},{2},{9}}=>{{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1,4,5,6,7,8,9},{2},{3}}=>{{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}}=>{{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}}=>{{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7,8},{9}}=>{{1,3,4,5,6,7,8},{2},{9}}=>{{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1,4,5,6,7,8,9},{2},{3}}=>{{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}}=>{{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}}=>{{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7,8},{9}}=>{{1,3,4,5,6,7,8},{2},{9}}=>{{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1,4,5,6,7,8,9},{2},{3}}=>{{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>{{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}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}}=>{{1,2},{3,4,5,6,7,8},{9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7,8},{9}}=>{{1,3,4,5,6,7,8},{2},{9}}=>{{1},{2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7,9},{8}}=>{{1,2,3,4,5,6,7},{8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1,4,5,6,7,8,9},{2},{3}}=>{{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>{{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}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7,8},{9}}=>{{1,3,4,5,6,7,8},{2},{9}}=>{{1},{2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1,4,5,6,7,8,9},{2},{3}}=>{{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>{{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}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8},{9,10}}=>{{1,2,3,4,5,6,7,8,10},{9}}=>{{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>{{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}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}}=>{{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>{{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}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>{{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}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7,9},{8}}=>{{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7,9},{8}}=>{{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7,9},{8}}=>{{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7,9},{8}}=>{{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7,9},{8}}=>{{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7,9},{8}}=>{{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7,9},{8}}=>{{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}=>{{1,8,9},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6,7},{8,9}}=>{{1,6,7,9},{2},{3},{4},{5},{8}}=>{{1},{2},{3},{4},{5,6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}=>{{1,8,9},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6,7},{8,9}}=>{{1,6,7,9},{2},{3},{4},{5},{8}}=>{{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6,7},{8,9}}=>{{1,6,7,9},{2},{3},{4},{5},{8}}=>{{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6,7},{8,9}}=>{{1,6,7,9},{2},{3},{4},{5},{8}}=>{{1},{2},{3},{4},{5,6,7},{8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,6,8,9},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6,7},{8,9}}=>{{1,6,7,9},{2},{3},{4},{5},{8}}=>{{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7,8},{9}}=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}=>{{1},{2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4},{5},{6,7,8},{9}}=>{{1,7,8},{2},{3},{4},{5},{6},{9}}=>{{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,6,8,9},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6,7},{8,9}}=>{{1,6,7,9},{2},{3},{4},{5},{8}}=>{{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7},{8},{9}}=>{{1,5},{2},{3},{4},{6},{7},{8},{9}}=>{{1},{2},{3},{4,5},{6},{7},{8},{9}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7},{8},{9}}=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}=>{{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5},{6},{7,8},{9}}=>{{1,2,8},{3},{4},{5},{6},{7},{9}}=>{{1,2},{3},{4},{5},{6},{7,8},{9}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7},{8},{9}}=>{{1,2,5},{3},{4},{6},{7},{8},{9}}=>{{1,2},{3},{4,5},{6},{7},{8},{9}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8},{9}}=>{{1,2,4},{3},{5},{6},{7},{8},{9}}=>{{1,2},{3,4},{5},{6},{7},{8},{9}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}}=>{{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}=>{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7},{8},{9}}=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}=>{{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8},{9}}=>{{1,2,4},{3},{5},{6},{7},{8},{9}}=>{{1,2},{3,4},{5},{6},{7},{8},{9}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8},{9,10}}=>{{1,2,3,4,5,6,7,8,10},{9}}=>{{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8,9},{10,11}}=>{{1,2,3,4,5,6,7,8,9,11},{10}}=>{{1,2,3,4,5,6,7,8,9},{10,11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8},{9,10}}=>{{1,2,3,4,5,6,7,8,10},{9}}=>{{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8},{9}}=>{{1,2,4},{3},{5},{6},{7},{8},{9}}=>{{1,2},{3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7},{8},{9}}=>{{1,5},{2},{3},{4},{6},{7},{8},{9}}=>{{1},{2},{3},{4,5},{6},{7},{8},{9}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7},{8},{9}}=>{{1,2,5},{3},{4},{6},{7},{8},{9}}=>{{1,2},{3},{4,5},{6},{7},{8},{9}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}}=>{{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{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}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8,9},{10,11}}=>{{1,2,3,4,5,6,7,8,9,11},{10}}=>{{1,2,3,4,5,6,7,8,9},{10,11}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8},{9,10}}=>{{1,2,3,4,5,6,7,8,10},{9}}=>{{1,2,3,4,5,6,7,8},{9,10}}
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}=>{{1,8,9},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8,9},{10,11}}=>{{1,2,3,4,5,6,7,8,9,11},{10}}=>{{1,2,3,4,5,6,7,8,9},{10,11}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4},{5},{6,7,8},{9}}=>{{1,7,8},{2},{3},{4},{5},{6},{9}}=>{{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7,8},{9}}=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}=>{{1},{2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,6,8,9},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5},{6},{7,8},{9}}=>{{1,2,8},{3},{4},{5},{6},{7},{9}}=>{{1,2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,6,8,9},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,6,8,9},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{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}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,6,8,9},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4},{5},{6,7,8},{9}}=>{{1,7,8},{2},{3},{4},{5},{6},{9}}=>{{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}=>{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,6,8,9},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}}=>{{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>{{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}}
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}}=>{{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8},{9,10}}=>{{1,2,3,4,5,6,7,8,10},{9}}=>{{1,2,3,4,5,6,7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,6,8,9},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,6,8,9},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8,9}}
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6,7},{8,9}}=>{{1,6,7,9},{2},{3},{4},{5},{8}}=>{{1},{2},{3},{4},{5,6,7},{8,9}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8,9},{10,11}}=>{{1,2,3,4,5,6,7,8,9,11},{10}}=>{{1,2,3,4,5,6,7,8,9},{10,11}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8},{9,10}}=>{{1,2,3,4,5,6,7,8,10},{9}}=>{{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,6,8,9},{2},{3},{4},{5},{7}}=>{{1},{2},{3},{4},{5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{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}}
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{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}}
Map
bounce path
Description
Sends a Dyck path $D$ of length $2n$ to its bounce path.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
Yip
Description
A transformation of set partitions due to Yip.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Yip's bijection $\psi$.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Yip's bijection $\psi$.
Map
dual major index to intertwining number
Description
A bijection sending the dual major index of a set partition to its intertwining number.
More precisely, St000493The los statistic of a set partition.$(P) = $St000490The intertwining number of a set partition.$(\phi(P))$ for all set partitions $P$.
This is the inverse of Mp00171intertwining number to dual major index.
More precisely, St000493The los statistic of a set partition.$(P) = $St000490The intertwining number of a set partition.$(\phi(P))$ for all set partitions $P$.
This is the inverse of Mp00171intertwining number to dual major index.
searching the database
Sorry, this map was not found in the database.