Identifier
Mp00138:
Dyck paths
—to noncrossing partition⟶
Set partitions
Mp00221: Set partitions —conjugate⟶ Set partitions
Mp00115: Set partitions —Kasraoui-Zeng⟶ Set partitions
Mp00217: Set partitions —Wachs-White-rho ⟶ Set partitions
Mp00221: Set partitions —conjugate⟶ Set partitions
Mp00115: Set partitions —Kasraoui-Zeng⟶ Set partitions
Mp00217: Set partitions —Wachs-White-rho ⟶ Set partitions
Images
=>
Cc0005;cc-rep-0Cc0009;cc-rep-1Cc0009;cc-rep-2Cc0009;cc-rep-3Cc0009;cc-rep-4
[1,0]=>{{1}}=>{{1}}=>{{1}}=>{{1}}
[1,0,1,0]=>{{1},{2}}=>{{1,2}}=>{{1,2}}=>{{1,2}}
[1,1,0,0]=>{{1,2}}=>{{1},{2}}=>{{1},{2}}=>{{1},{2}}
[1,0,1,0,1,0]=>{{1},{2},{3}}=>{{1,2,3}}=>{{1,2,3}}=>{{1,2,3}}
[1,0,1,1,0,0]=>{{1},{2,3}}=>{{1,3},{2}}=>{{1,3},{2}}=>{{1,3},{2}}
[1,1,0,0,1,0]=>{{1,2},{3}}=>{{1,2},{3}}=>{{1,2},{3}}=>{{1,2},{3}}
[1,1,0,1,0,0]=>{{1,3},{2}}=>{{1},{2,3}}=>{{1},{2,3}}=>{{1},{2,3}}
[1,1,1,0,0,0]=>{{1,2,3}}=>{{1},{2},{3}}=>{{1},{2},{3}}=>{{1},{2},{3}}
[1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4}}=>{{1,2,3,4}}=>{{1,2,3,4}}=>{{1,2,3,4}}
[1,0,1,0,1,1,0,0]=>{{1},{2},{3,4}}=>{{1,3,4},{2}}=>{{1,3,4},{2}}=>{{1,3,4},{2}}
[1,0,1,1,0,0,1,0]=>{{1},{2,3},{4}}=>{{1,2,4},{3}}=>{{1,2,4},{3}}=>{{1,2,4},{3}}
[1,0,1,1,0,1,0,0]=>{{1},{2,4},{3}}=>{{1,4},{2,3}}=>{{1,3},{2,4}}=>{{1,4},{2,3}}
[1,0,1,1,1,0,0,0]=>{{1},{2,3,4}}=>{{1,4},{2},{3}}=>{{1,4},{2},{3}}=>{{1,4},{2},{3}}
[1,1,0,0,1,0,1,0]=>{{1,2},{3},{4}}=>{{1,2,3},{4}}=>{{1,2,3},{4}}=>{{1,2,3},{4}}
[1,1,0,0,1,1,0,0]=>{{1,2},{3,4}}=>{{1,3},{2},{4}}=>{{1,3},{2},{4}}=>{{1,3},{2},{4}}
[1,1,0,1,0,0,1,0]=>{{1,3},{2},{4}}=>{{1,2},{3,4}}=>{{1,2},{3,4}}=>{{1,2},{3,4}}
[1,1,0,1,0,1,0,0]=>{{1,4},{2},{3}}=>{{1},{2,3,4}}=>{{1},{2,3,4}}=>{{1},{2,3,4}}
[1,1,0,1,1,0,0,0]=>{{1,3,4},{2}}=>{{1},{2},{3,4}}=>{{1},{2},{3,4}}=>{{1},{2},{3,4}}
[1,1,1,0,0,0,1,0]=>{{1,2,3},{4}}=>{{1,2},{3},{4}}=>{{1,2},{3},{4}}=>{{1,2},{3},{4}}
[1,1,1,0,0,1,0,0]=>{{1,4},{2,3}}=>{{1},{2,4},{3}}=>{{1},{2,4},{3}}=>{{1},{2,4},{3}}
[1,1,1,0,1,0,0,0]=>{{1,2,4},{3}}=>{{1},{2,3},{4}}=>{{1},{2,3},{4}}=>{{1},{2,3},{4}}
[1,1,1,1,0,0,0,0]=>{{1,2,3,4}}=>{{1},{2},{3},{4}}=>{{1},{2},{3},{4}}=>{{1},{2},{3},{4}}
[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}}=>{{1,2,3,4,5}}
[1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5}}=>{{1,3,4,5},{2}}=>{{1,3,4,5},{2}}=>{{1,3,4,5},{2}}
[1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5}}=>{{1,2,4,5},{3}}=>{{1,2,4,5},{3}}=>{{1,2,4,5},{3}}
[1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3,5},{4}}=>{{1,4,5},{2,3}}=>{{1,3},{2,4,5}}=>{{1,4,5},{2,3}}
[1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}}=>{{1,4,5},{2},{3}}=>{{1,4,5},{2},{3}}=>{{1,4,5},{2},{3}}
[1,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4},{5}}=>{{1,2,3,5},{4}}=>{{1,2,3,5},{4}}=>{{1,2,3,5},{4}}
[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>{{1,3,5},{2},{4}}=>{{1,3,5},{2},{4}}=>{{1,3,5},{2},{4}}
[1,0,1,1,0,1,0,0,1,0]=>{{1},{2,4},{3},{5}}=>{{1,2,5},{3,4}}=>{{1,2,4},{3,5}}=>{{1,2,5},{3,4}}
[1,0,1,1,0,1,0,1,0,0]=>{{1},{2,5},{3},{4}}=>{{1,5},{2,3,4}}=>{{1,3,5},{2,4}}=>{{1,5},{2,3,4}}
[1,0,1,1,0,1,1,0,0,0]=>{{1},{2,4,5},{3}}=>{{1,5},{2},{3,4}}=>{{1,4},{2},{3,5}}=>{{1,5},{2},{3,4}}
[1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}}=>{{1,2,5},{3},{4}}=>{{1,2,5},{3},{4}}=>{{1,2,5},{3},{4}}
[1,0,1,1,1,0,0,1,0,0]=>{{1},{2,5},{3,4}}=>{{1,5},{2,4},{3}}=>{{1,4},{2,5},{3}}=>{{1,5},{2,4},{3}}
[1,0,1,1,1,0,1,0,0,0]=>{{1},{2,3,5},{4}}=>{{1,5},{2,3},{4}}=>{{1,3},{2,5},{4}}=>{{1,5},{2,3},{4}}
[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}}=>{{1,5},{2},{3},{4}}=>{{1,5},{2},{3},{4}}=>{{1,5},{2},{3},{4}}
[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}}=>{{1,2,3,4},{5}}
[1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3},{4,5}}=>{{1,3,4},{2},{5}}=>{{1,3,4},{2},{5}}=>{{1,3,4},{2},{5}}
[1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5}}=>{{1,2,4},{3},{5}}=>{{1,2,4},{3},{5}}=>{{1,2,4},{3},{5}}
[1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,5},{4}}=>{{1,4},{2,3},{5}}=>{{1,3},{2,4},{5}}=>{{1,4},{2,3},{5}}
[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>{{1,4},{2},{3},{5}}=>{{1,4},{2},{3},{5}}=>{{1,4},{2},{3},{5}}
[1,1,0,1,0,0,1,0,1,0]=>{{1,3},{2},{4},{5}}=>{{1,2,3},{4,5}}=>{{1,2,3},{4,5}}=>{{1,2,3},{4,5}}
[1,1,0,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5}}=>{{1,3},{2},{4,5}}=>{{1,3},{2},{4,5}}=>{{1,3},{2},{4,5}}
[1,1,0,1,0,1,0,0,1,0]=>{{1,4},{2},{3},{5}}=>{{1,2},{3,4,5}}=>{{1,2},{3,4,5}}=>{{1,2},{3,4,5}}
[1,1,0,1,0,1,0,1,0,0]=>{{1,5},{2},{3},{4}}=>{{1},{2,3,4,5}}=>{{1},{2,3,4,5}}=>{{1},{2,3,4,5}}
[1,1,0,1,0,1,1,0,0,0]=>{{1,4,5},{2},{3}}=>{{1},{2},{3,4,5}}=>{{1},{2},{3,4,5}}=>{{1},{2},{3,4,5}}
[1,1,0,1,1,0,0,0,1,0]=>{{1,3,4},{2},{5}}=>{{1,2},{3},{4,5}}=>{{1,2},{3},{4,5}}=>{{1,2},{3},{4,5}}
[1,1,0,1,1,0,0,1,0,0]=>{{1,5},{2},{3,4}}=>{{1},{2,4,5},{3}}=>{{1},{2,4,5},{3}}=>{{1},{2,4,5},{3}}
[1,1,0,1,1,0,1,0,0,0]=>{{1,3,5},{2},{4}}=>{{1},{2,3},{4,5}}=>{{1},{2,3},{4,5}}=>{{1},{2,3},{4,5}}
[1,1,0,1,1,1,0,0,0,0]=>{{1,3,4,5},{2}}=>{{1},{2},{3},{4,5}}=>{{1},{2},{3},{4,5}}=>{{1},{2},{3},{4,5}}
[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}}=>{{1,2,3},{4},{5}}
[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}}=>{{1,3},{2},{4},{5}}=>{{1,3},{2},{4},{5}}=>{{1,3},{2},{4},{5}}
[1,1,1,0,0,1,0,0,1,0]=>{{1,4},{2,3},{5}}=>{{1,2},{3,5},{4}}=>{{1,2},{3,5},{4}}=>{{1,2},{3,5},{4}}
[1,1,1,0,0,1,0,1,0,0]=>{{1,5},{2,3},{4}}=>{{1},{2,3,5},{4}}=>{{1},{2,3,5},{4}}=>{{1},{2,3,5},{4}}
[1,1,1,0,0,1,1,0,0,0]=>{{1,4,5},{2,3}}=>{{1},{2},{3,5},{4}}=>{{1},{2},{3,5},{4}}=>{{1},{2},{3,5},{4}}
[1,1,1,0,1,0,0,0,1,0]=>{{1,2,4},{3},{5}}=>{{1,2},{3,4},{5}}=>{{1,2},{3,4},{5}}=>{{1,2},{3,4},{5}}
[1,1,1,0,1,0,0,1,0,0]=>{{1,5},{2,4},{3}}=>{{1},{2,5},{3,4}}=>{{1},{2,4},{3,5}}=>{{1},{2,5},{3,4}}
[1,1,1,0,1,0,1,0,0,0]=>{{1,2,5},{3},{4}}=>{{1},{2,3,4},{5}}=>{{1},{2,3,4},{5}}=>{{1},{2,3,4},{5}}
[1,1,1,0,1,1,0,0,0,0]=>{{1,2,4,5},{3}}=>{{1},{2},{3,4},{5}}=>{{1},{2},{3,4},{5}}=>{{1},{2},{3,4},{5}}
[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}}=>{{1,2},{3},{4},{5}}
[1,1,1,1,0,0,0,1,0,0]=>{{1,5},{2,3,4}}=>{{1},{2,5},{3},{4}}=>{{1},{2,5},{3},{4}}=>{{1},{2,5},{3},{4}}
[1,1,1,1,0,0,1,0,0,0]=>{{1,2,5},{3,4}}=>{{1},{2,4},{3},{5}}=>{{1},{2,4},{3},{5}}=>{{1},{2,4},{3},{5}}
[1,1,1,1,0,1,0,0,0,0]=>{{1,2,3,5},{4}}=>{{1},{2,3},{4},{5}}=>{{1},{2,3},{4},{5}}=>{{1},{2,3},{4},{5}}
[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},{2},{3},{4},{5}}
[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}}=>{{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6}}=>{{1,3,4,5,6},{2}}=>{{1,3,4,5,6},{2}}=>{{1,3,4,5,6},{2}}
[1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6}}=>{{1,2,4,5,6},{3}}=>{{1,2,4,5,6},{3}}=>{{1,2,4,5,6},{3}}
[1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4,6},{5}}=>{{1,4,5,6},{2,3}}=>{{1,3},{2,4,5,6}}=>{{1,4,5,6},{2,3}}
[1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}}=>{{1,4,5,6},{2},{3}}=>{{1,4,5,6},{2},{3}}=>{{1,4,5,6},{2},{3}}
[1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6}}=>{{1,2,3,5,6},{4}}=>{{1,2,3,5,6},{4}}=>{{1,2,3,5,6},{4}}
[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>{{1,3,5,6},{2},{4}}=>{{1,3,5,6},{2},{4}}=>{{1,3,5,6},{2},{4}}
[1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3,5},{4},{6}}=>{{1,2,5,6},{3,4}}=>{{1,2,4},{3,5,6}}=>{{1,2,5,6},{3,4}}
[1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3,6},{4},{5}}=>{{1,5,6},{2,3,4}}=>{{1,3,5,6},{2,4}}=>{{1,5,6},{2,3,4}}
[1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3,5,6},{4}}=>{{1,5,6},{2},{3,4}}=>{{1,4},{2},{3,5,6}}=>{{1,5,6},{2},{3,4}}
[1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}}=>{{1,2,5,6},{3},{4}}=>{{1,2,5,6},{3},{4}}=>{{1,2,5,6},{3},{4}}
[1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3,6},{4,5}}=>{{1,5,6},{2,4},{3}}=>{{1,4},{2,5,6},{3}}=>{{1,5,6},{2,4},{3}}
[1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3,4,6},{5}}=>{{1,5,6},{2,3},{4}}=>{{1,3},{2,5,6},{4}}=>{{1,5,6},{2,3},{4}}
[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}}=>{{1,5,6},{2},{3},{4}}=>{{1,5,6},{2},{3},{4}}=>{{1,5,6},{2},{3},{4}}
[1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6}}=>{{1,2,3,4,6},{5}}=>{{1,2,3,4,6},{5}}=>{{1,2,3,4,6},{5}}
[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}}=>{{1,3,4,6},{2},{5}}=>{{1,3,4,6},{2},{5}}=>{{1,3,4,6},{2},{5}}
[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>{{1,2,4,6},{3},{5}}=>{{1,2,4,6},{3},{5}}=>{{1,2,4,6},{3},{5}}
[1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2,3},{4,6},{5}}=>{{1,4,6},{2,3},{5}}=>{{1,3},{2,4,6},{5}}=>{{1,4,6},{2,3},{5}}
[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,4,6},{2},{3},{5}}=>{{1,4,6},{2},{3},{5}}=>{{1,4,6},{2},{3},{5}}
[1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6}}=>{{1,2,3,6},{4,5}}=>{{1,2,3,5},{4,6}}=>{{1,2,3,6},{4,5}}
[1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2,4},{3},{5,6}}=>{{1,3,6},{2},{4,5}}=>{{1,3,5},{2},{4,6}}=>{{1,3,6},{2},{4,5}}
[1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2,5},{3},{4},{6}}=>{{1,2,6},{3,4,5}}=>{{1,2,4,6},{3,5}}=>{{1,2,6},{3,4,5}}
[1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2,6},{3},{4},{5}}=>{{1,6},{2,3,4,5}}=>{{1,3,5},{2,4,6}}=>{{1,6},{2,3,4,5}}
[1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2,5,6},{3},{4}}=>{{1,6},{2},{3,4,5}}=>{{1,4,6},{2},{3,5}}=>{{1,6},{2},{3,4,5}}
[1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2,4,5},{3},{6}}=>{{1,2,6},{3},{4,5}}=>{{1,2,5},{3},{4,6}}=>{{1,2,6},{3},{4,5}}
[1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2,6},{3},{4,5}}=>{{1,6},{2,4,5},{3}}=>{{1,4,6},{2,5},{3}}=>{{1,6},{2,4,5},{3}}
[1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2,4,6},{3},{5}}=>{{1,6},{2,3},{4,5}}=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3},{4,5}}
[1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2,4,5,6},{3}}=>{{1,6},{2},{3},{4,5}}=>{{1,5},{2},{3},{4,6}}=>{{1,6},{2},{3},{4,5}}
[1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}}=>{{1,2,3,6},{4},{5}}=>{{1,2,3,6},{4},{5}}=>{{1,2,3,6},{4},{5}}
[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,6},{2},{4},{5}}=>{{1,3,6},{2},{4},{5}}=>{{1,3,6},{2},{4},{5}}
[1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2,5},{3,4},{6}}=>{{1,2,6},{3,5},{4}}=>{{1,2,5},{3,6},{4}}=>{{1,2,6},{3,5},{4}}
[1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2,6},{3,4},{5}}=>{{1,6},{2,3,5},{4}}=>{{1,3,6},{2,5},{4}}=>{{1,6},{2,3,5},{4}}
[1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2,5,6},{3,4}}=>{{1,6},{2},{3,5},{4}}=>{{1,5},{2},{3,6},{4}}=>{{1,6},{2},{3,5},{4}}
[1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2,3,5},{4},{6}}=>{{1,2,6},{3,4},{5}}=>{{1,2,4},{3,6},{5}}=>{{1,2,6},{3,4},{5}}
[1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2,6},{3,5},{4}}=>{{1,6},{2,5},{3,4}}=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}}
[1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2,3,6},{4},{5}}=>{{1,6},{2,3,4},{5}}=>{{1,3,6},{2,4},{5}}=>{{1,6},{2,3,4},{5}}
[1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2,3,5,6},{4}}=>{{1,6},{2},{3,4},{5}}=>{{1,4},{2},{3,6},{5}}=>{{1,6},{2},{3,4},{5}}
[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}}=>{{1,2,6},{3},{4},{5}}=>{{1,2,6},{3},{4},{5}}=>{{1,2,6},{3},{4},{5}}
[1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2,6},{3,4,5}}=>{{1,6},{2,5},{3},{4}}=>{{1,5},{2,6},{3},{4}}=>{{1,6},{2,5},{3},{4}}
[1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2,3,6},{4,5}}=>{{1,6},{2,4},{3},{5}}=>{{1,4},{2,6},{3},{5}}=>{{1,6},{2,4},{3},{5}}
[1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2,3,4,6},{5}}=>{{1,6},{2,3},{4},{5}}=>{{1,3},{2,6},{4},{5}}=>{{1,6},{2,3},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}}=>{{1,6},{2},{3},{4},{5}}=>{{1,6},{2},{3},{4},{5}}=>{{1,6},{2},{3},{4},{5}}
[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}}=>{{1,2,3,4,5},{6}}
[1,1,0,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5,6}}=>{{1,3,4,5},{2},{6}}=>{{1,3,4,5},{2},{6}}=>{{1,3,4,5},{2},{6}}
[1,1,0,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4,5},{6}}=>{{1,2,4,5},{3},{6}}=>{{1,2,4,5},{3},{6}}=>{{1,2,4,5},{3},{6}}
[1,1,0,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4,6},{5}}=>{{1,4,5},{2,3},{6}}=>{{1,3},{2,4,5},{6}}=>{{1,4,5},{2,3},{6}}
[1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}}=>{{1,4,5},{2},{3},{6}}=>{{1,4,5},{2},{3},{6}}=>{{1,4,5},{2},{3},{6}}
[1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5},{6}}=>{{1,2,3,5},{4},{6}}=>{{1,2,3,5},{4},{6}}=>{{1,2,3,5},{4},{6}}
[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,3,5},{2},{4},{6}}=>{{1,3,5},{2},{4},{6}}=>{{1,3,5},{2},{4},{6}}
[1,1,0,0,1,1,0,1,0,0,1,0]=>{{1,2},{3,5},{4},{6}}=>{{1,2,5},{3,4},{6}}=>{{1,2,4},{3,5},{6}}=>{{1,2,5},{3,4},{6}}
[1,1,0,0,1,1,0,1,0,1,0,0]=>{{1,2},{3,6},{4},{5}}=>{{1,5},{2,3,4},{6}}=>{{1,3,5},{2,4},{6}}=>{{1,5},{2,3,4},{6}}
[1,1,0,0,1,1,0,1,1,0,0,0]=>{{1,2},{3,5,6},{4}}=>{{1,5},{2},{3,4},{6}}=>{{1,4},{2},{3,5},{6}}=>{{1,5},{2},{3,4},{6}}
[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>{{1,2,5},{3},{4},{6}}=>{{1,2,5},{3},{4},{6}}=>{{1,2,5},{3},{4},{6}}
[1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,6},{4,5}}=>{{1,5},{2,4},{3},{6}}=>{{1,4},{2,5},{3},{6}}=>{{1,5},{2,4},{3},{6}}
[1,1,0,0,1,1,1,0,1,0,0,0]=>{{1,2},{3,4,6},{5}}=>{{1,5},{2,3},{4},{6}}=>{{1,3},{2,5},{4},{6}}=>{{1,5},{2,3},{4},{6}}
[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,5},{2},{3},{4},{6}}=>{{1,5},{2},{3},{4},{6}}=>{{1,5},{2},{3},{4},{6}}
[1,1,0,1,0,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6}}=>{{1,2,3,4},{5,6}}=>{{1,2,3,4},{5,6}}=>{{1,2,3,4},{5,6}}
[1,1,0,1,0,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5,6}}=>{{1,3,4},{2},{5,6}}=>{{1,3,4},{2},{5,6}}=>{{1,3,4},{2},{5,6}}
[1,1,0,1,0,0,1,1,0,0,1,0]=>{{1,3},{2},{4,5},{6}}=>{{1,2,4},{3},{5,6}}=>{{1,2,4},{3},{5,6}}=>{{1,2,4},{3},{5,6}}
[1,1,0,1,0,0,1,1,0,1,0,0]=>{{1,3},{2},{4,6},{5}}=>{{1,4},{2,3},{5,6}}=>{{1,3},{2,4},{5,6}}=>{{1,4},{2,3},{5,6}}
[1,1,0,1,0,0,1,1,1,0,0,0]=>{{1,3},{2},{4,5,6}}=>{{1,4},{2},{3},{5,6}}=>{{1,4},{2},{3},{5,6}}=>{{1,4},{2},{3},{5,6}}
[1,1,0,1,0,1,0,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6}}=>{{1,2,3},{4,5,6}}=>{{1,2,3},{4,5,6}}=>{{1,2,3},{4,5,6}}
[1,1,0,1,0,1,0,0,1,1,0,0]=>{{1,4},{2},{3},{5,6}}=>{{1,3},{2},{4,5,6}}=>{{1,3},{2},{4,5,6}}=>{{1,3},{2},{4,5,6}}
[1,1,0,1,0,1,0,1,0,0,1,0]=>{{1,5},{2},{3},{4},{6}}=>{{1,2},{3,4,5,6}}=>{{1,2},{3,4,5,6}}=>{{1,2},{3,4,5,6}}
[1,1,0,1,0,1,0,1,0,1,0,0]=>{{1,6},{2},{3},{4},{5}}=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}}
[1,1,0,1,0,1,0,1,1,0,0,0]=>{{1,5,6},{2},{3},{4}}=>{{1},{2},{3,4,5,6}}=>{{1},{2},{3,4,5,6}}=>{{1},{2},{3,4,5,6}}
[1,1,0,1,0,1,1,0,0,0,1,0]=>{{1,4,5},{2},{3},{6}}=>{{1,2},{3},{4,5,6}}=>{{1,2},{3},{4,5,6}}=>{{1,2},{3},{4,5,6}}
[1,1,0,1,0,1,1,0,0,1,0,0]=>{{1,6},{2},{3},{4,5}}=>{{1},{2,4,5,6},{3}}=>{{1},{2,4,5,6},{3}}=>{{1},{2,4,5,6},{3}}
[1,1,0,1,0,1,1,0,1,0,0,0]=>{{1,4,6},{2},{3},{5}}=>{{1},{2,3},{4,5,6}}=>{{1},{2,3},{4,5,6}}=>{{1},{2,3},{4,5,6}}
[1,1,0,1,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2},{3}}=>{{1},{2},{3},{4,5,6}}=>{{1},{2},{3},{4,5,6}}=>{{1},{2},{3},{4,5,6}}
[1,1,0,1,1,0,0,0,1,0,1,0]=>{{1,3,4},{2},{5},{6}}=>{{1,2,3},{4},{5,6}}=>{{1,2,3},{4},{5,6}}=>{{1,2,3},{4},{5,6}}
[1,1,0,1,1,0,0,0,1,1,0,0]=>{{1,3,4},{2},{5,6}}=>{{1,3},{2},{4},{5,6}}=>{{1,3},{2},{4},{5,6}}=>{{1,3},{2},{4},{5,6}}
[1,1,0,1,1,0,0,1,0,0,1,0]=>{{1,5},{2},{3,4},{6}}=>{{1,2},{3,5,6},{4}}=>{{1,2},{3,5,6},{4}}=>{{1,2},{3,5,6},{4}}
[1,1,0,1,1,0,0,1,0,1,0,0]=>{{1,6},{2},{3,4},{5}}=>{{1},{2,3,5,6},{4}}=>{{1},{2,3,5,6},{4}}=>{{1},{2,3,5,6},{4}}
[1,1,0,1,1,0,0,1,1,0,0,0]=>{{1,5,6},{2},{3,4}}=>{{1},{2},{3,5,6},{4}}=>{{1},{2},{3,5,6},{4}}=>{{1},{2},{3,5,6},{4}}
[1,1,0,1,1,0,1,0,0,0,1,0]=>{{1,3,5},{2},{4},{6}}=>{{1,2},{3,4},{5,6}}=>{{1,2},{3,4},{5,6}}=>{{1,2},{3,4},{5,6}}
[1,1,0,1,1,0,1,0,0,1,0,0]=>{{1,6},{2},{3,5},{4}}=>{{1},{2,5,6},{3,4}}=>{{1},{2,4},{3,5,6}}=>{{1},{2,5,6},{3,4}}
[1,1,0,1,1,0,1,0,1,0,0,0]=>{{1,3,6},{2},{4},{5}}=>{{1},{2,3,4},{5,6}}=>{{1},{2,3,4},{5,6}}=>{{1},{2,3,4},{5,6}}
[1,1,0,1,1,0,1,1,0,0,0,0]=>{{1,3,5,6},{2},{4}}=>{{1},{2},{3,4},{5,6}}=>{{1},{2},{3,4},{5,6}}=>{{1},{2},{3,4},{5,6}}
[1,1,0,1,1,1,0,0,0,0,1,0]=>{{1,3,4,5},{2},{6}}=>{{1,2},{3},{4},{5,6}}=>{{1,2},{3},{4},{5,6}}=>{{1,2},{3},{4},{5,6}}
[1,1,0,1,1,1,0,0,0,1,0,0]=>{{1,6},{2},{3,4,5}}=>{{1},{2,5,6},{3},{4}}=>{{1},{2,5,6},{3},{4}}=>{{1},{2,5,6},{3},{4}}
[1,1,0,1,1,1,0,0,1,0,0,0]=>{{1,3,6},{2},{4,5}}=>{{1},{2,4},{3},{5,6}}=>{{1},{2,4},{3},{5,6}}=>{{1},{2,4},{3},{5,6}}
[1,1,0,1,1,1,0,1,0,0,0,0]=>{{1,3,4,6},{2},{5}}=>{{1},{2,3},{4},{5,6}}=>{{1},{2,3},{4},{5,6}}=>{{1},{2,3},{4},{5,6}}
[1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,3,4,5,6},{2}}=>{{1},{2},{3},{4},{5,6}}=>{{1},{2},{3},{4},{5,6}}=>{{1},{2},{3},{4},{5,6}}
[1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6}}=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}}
[1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5,6}}=>{{1,3,4},{2},{5},{6}}=>{{1,3,4},{2},{5},{6}}=>{{1,3,4},{2},{5},{6}}
[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}}=>{{1,2,4},{3},{5},{6}}=>{{1,2,4},{3},{5},{6}}=>{{1,2,4},{3},{5},{6}}
[1,1,1,0,0,0,1,1,0,1,0,0]=>{{1,2,3},{4,6},{5}}=>{{1,4},{2,3},{5},{6}}=>{{1,3},{2,4},{5},{6}}=>{{1,4},{2,3},{5},{6}}
[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,4},{2},{3},{5},{6}}=>{{1,4},{2},{3},{5},{6}}=>{{1,4},{2},{3},{5},{6}}
[1,1,1,0,0,1,0,0,1,0,1,0]=>{{1,4},{2,3},{5},{6}}=>{{1,2,3},{4,6},{5}}=>{{1,2,3},{4,6},{5}}=>{{1,2,3},{4,6},{5}}
[1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6}}=>{{1,3},{2},{4,6},{5}}=>{{1,3},{2},{4,6},{5}}=>{{1,3},{2},{4,6},{5}}
[1,1,1,0,0,1,0,1,0,0,1,0]=>{{1,5},{2,3},{4},{6}}=>{{1,2},{3,4,6},{5}}=>{{1,2},{3,4,6},{5}}=>{{1,2},{3,4,6},{5}}
[1,1,1,0,0,1,0,1,0,1,0,0]=>{{1,6},{2,3},{4},{5}}=>{{1},{2,3,4,6},{5}}=>{{1},{2,3,4,6},{5}}=>{{1},{2,3,4,6},{5}}
[1,1,1,0,0,1,0,1,1,0,0,0]=>{{1,5,6},{2,3},{4}}=>{{1},{2},{3,4,6},{5}}=>{{1},{2},{3,4,6},{5}}=>{{1},{2},{3,4,6},{5}}
[1,1,1,0,0,1,1,0,0,0,1,0]=>{{1,4,5},{2,3},{6}}=>{{1,2},{3},{4,6},{5}}=>{{1,2},{3},{4,6},{5}}=>{{1,2},{3},{4,6},{5}}
[1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,6},{2,3},{4,5}}=>{{1},{2,4,6},{3},{5}}=>{{1},{2,4,6},{3},{5}}=>{{1},{2,4,6},{3},{5}}
[1,1,1,0,0,1,1,0,1,0,0,0]=>{{1,4,6},{2,3},{5}}=>{{1},{2,3},{4,6},{5}}=>{{1},{2,3},{4,6},{5}}=>{{1},{2,3},{4,6},{5}}
[1,1,1,0,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2,3}}=>{{1},{2},{3},{4,6},{5}}=>{{1},{2},{3},{4,6},{5}}=>{{1},{2},{3},{4,6},{5}}
[1,1,1,0,1,0,0,0,1,0,1,0]=>{{1,2,4},{3},{5},{6}}=>{{1,2,3},{4,5},{6}}=>{{1,2,3},{4,5},{6}}=>{{1,2,3},{4,5},{6}}
[1,1,1,0,1,0,0,0,1,1,0,0]=>{{1,2,4},{3},{5,6}}=>{{1,3},{2},{4,5},{6}}=>{{1,3},{2},{4,5},{6}}=>{{1,3},{2},{4,5},{6}}
[1,1,1,0,1,0,0,1,0,0,1,0]=>{{1,5},{2,4},{3},{6}}=>{{1,2},{3,6},{4,5}}=>{{1,2},{3,5},{4,6}}=>{{1,2},{3,6},{4,5}}
[1,1,1,0,1,0,0,1,0,1,0,0]=>{{1,6},{2,4},{3},{5}}=>{{1},{2,3,6},{4,5}}=>{{1},{2,3,5},{4,6}}=>{{1},{2,3,6},{4,5}}
[1,1,1,0,1,0,0,1,1,0,0,0]=>{{1,5,6},{2,4},{3}}=>{{1},{2},{3,6},{4,5}}=>{{1},{2},{3,5},{4,6}}=>{{1},{2},{3,6},{4,5}}
[1,1,1,0,1,0,1,0,0,0,1,0]=>{{1,2,5},{3},{4},{6}}=>{{1,2},{3,4,5},{6}}=>{{1,2},{3,4,5},{6}}=>{{1,2},{3,4,5},{6}}
[1,1,1,0,1,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3},{4}}=>{{1},{2,6},{3,4,5}}=>{{1},{2,4,6},{3,5}}=>{{1},{2,6},{3,4,5}}
[1,1,1,0,1,0,1,0,1,0,0,0]=>{{1,2,6},{3},{4},{5}}=>{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}}
[1,1,1,0,1,0,1,1,0,0,0,0]=>{{1,2,5,6},{3},{4}}=>{{1},{2},{3,4,5},{6}}=>{{1},{2},{3,4,5},{6}}=>{{1},{2},{3,4,5},{6}}
[1,1,1,0,1,1,0,0,0,0,1,0]=>{{1,2,4,5},{3},{6}}=>{{1,2},{3},{4,5},{6}}=>{{1,2},{3},{4,5},{6}}=>{{1,2},{3},{4,5},{6}}
[1,1,1,0,1,1,0,0,0,1,0,0]=>{{1,6},{2,4,5},{3}}=>{{1},{2,6},{3},{4,5}}=>{{1},{2,5},{3},{4,6}}=>{{1},{2,6},{3},{4,5}}
[1,1,1,0,1,1,0,0,1,0,0,0]=>{{1,2,6},{3},{4,5}}=>{{1},{2,4,5},{3},{6}}=>{{1},{2,4,5},{3},{6}}=>{{1},{2,4,5},{3},{6}}
[1,1,1,0,1,1,0,1,0,0,0,0]=>{{1,2,4,6},{3},{5}}=>{{1},{2,3},{4,5},{6}}=>{{1},{2,3},{4,5},{6}}=>{{1},{2,3},{4,5},{6}}
[1,1,1,0,1,1,1,0,0,0,0,0]=>{{1,2,4,5,6},{3}}=>{{1},{2},{3},{4,5},{6}}=>{{1},{2},{3},{4,5},{6}}=>{{1},{2},{3},{4,5},{6}}
[1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5},{6}}=>{{1,2,3},{4},{5},{6}}=>{{1,2,3},{4},{5},{6}}=>{{1,2,3},{4},{5},{6}}
[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}}=>{{1,3},{2},{4},{5},{6}}=>{{1,3},{2},{4},{5},{6}}=>{{1,3},{2},{4},{5},{6}}
[1,1,1,1,0,0,0,1,0,0,1,0]=>{{1,5},{2,3,4},{6}}=>{{1,2},{3,6},{4},{5}}=>{{1,2},{3,6},{4},{5}}=>{{1,2},{3,6},{4},{5}}
[1,1,1,1,0,0,0,1,0,1,0,0]=>{{1,6},{2,3,4},{5}}=>{{1},{2,3,6},{4},{5}}=>{{1},{2,3,6},{4},{5}}=>{{1},{2,3,6},{4},{5}}
[1,1,1,1,0,0,0,1,1,0,0,0]=>{{1,5,6},{2,3,4}}=>{{1},{2},{3,6},{4},{5}}=>{{1},{2},{3,6},{4},{5}}=>{{1},{2},{3,6},{4},{5}}
[1,1,1,1,0,0,1,0,0,0,1,0]=>{{1,2,5},{3,4},{6}}=>{{1,2},{3,5},{4},{6}}=>{{1,2},{3,5},{4},{6}}=>{{1,2},{3,5},{4},{6}}
[1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3,4}}=>{{1},{2,6},{3,5},{4}}=>{{1},{2,5},{3,6},{4}}=>{{1},{2,6},{3,5},{4}}
[1,1,1,1,0,0,1,0,1,0,0,0]=>{{1,2,6},{3,4},{5}}=>{{1},{2,3,5},{4},{6}}=>{{1},{2,3,5},{4},{6}}=>{{1},{2,3,5},{4},{6}}
[1,1,1,1,0,0,1,1,0,0,0,0]=>{{1,2,5,6},{3,4}}=>{{1},{2},{3,5},{4},{6}}=>{{1},{2},{3,5},{4},{6}}=>{{1},{2},{3,5},{4},{6}}
[1,1,1,1,0,1,0,0,0,0,1,0]=>{{1,2,3,5},{4},{6}}=>{{1,2},{3,4},{5},{6}}=>{{1,2},{3,4},{5},{6}}=>{{1,2},{3,4},{5},{6}}
[1,1,1,1,0,1,0,0,0,1,0,0]=>{{1,6},{2,3,5},{4}}=>{{1},{2,6},{3,4},{5}}=>{{1},{2,4},{3,6},{5}}=>{{1},{2,6},{3,4},{5}}
[1,1,1,1,0,1,0,0,1,0,0,0]=>{{1,2,6},{3,5},{4}}=>{{1},{2,5},{3,4},{6}}=>{{1},{2,4},{3,5},{6}}=>{{1},{2,5},{3,4},{6}}
[1,1,1,1,0,1,0,1,0,0,0,0]=>{{1,2,3,6},{4},{5}}=>{{1},{2,3,4},{5},{6}}=>{{1},{2,3,4},{5},{6}}=>{{1},{2,3,4},{5},{6}}
[1,1,1,1,0,1,1,0,0,0,0,0]=>{{1,2,3,5,6},{4}}=>{{1},{2},{3,4},{5},{6}}=>{{1},{2},{3,4},{5},{6}}=>{{1},{2},{3,4},{5},{6}}
[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}}=>{{1,2},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6}}
[1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,6},{2,3,4,5}}=>{{1},{2,6},{3},{4},{5}}=>{{1},{2,6},{3},{4},{5}}=>{{1},{2,6},{3},{4},{5}}
[1,1,1,1,1,0,0,0,1,0,0,0]=>{{1,2,6},{3,4,5}}=>{{1},{2,5},{3},{4},{6}}=>{{1},{2,5},{3},{4},{6}}=>{{1},{2,5},{3},{4},{6}}
[1,1,1,1,1,0,0,1,0,0,0,0]=>{{1,2,3,6},{4,5}}=>{{1},{2,4},{3},{5},{6}}=>{{1},{2,4},{3},{5},{6}}=>{{1},{2,4},{3},{5},{6}}
[1,1,1,1,1,0,1,0,0,0,0,0]=>{{1,2,3,4,6},{5}}=>{{1},{2,3},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6}}
[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},{2},{3},{4},{5},{6}}
[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}}=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6,7}}=>{{1,3,4,5,6,7},{2}}=>{{1,3,4,5,6,7},{2}}=>{{1,3,4,5,6,7},{2}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5,6},{7}}=>{{1,2,4,5,6,7},{3}}=>{{1,2,4,5,6,7},{3}}=>{{1,2,4,5,6,7},{3}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4},{5,7},{6}}=>{{1,4,5,6,7},{2,3}}=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6,7}}=>{{1,4,5,6,7},{2},{3}}=>{{1,4,5,6,7},{2},{3}}=>{{1,4,5,6,7},{2},{3}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3,5,6,7},{4}}=>{{1,2,3,5,6,7},{4}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>{{1,3,5,6,7},{2},{4}}=>{{1,3,5,6,7},{2},{4}}=>{{1,3,5,6,7},{2},{4}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3},{4,6},{5},{7}}=>{{1,2,5,6,7},{3,4}}=>{{1,2,4},{3,5,6,7}}=>{{1,2,5,6,7},{3,4}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3},{4,7},{5},{6}}=>{{1,5,6,7},{2,3,4}}=>{{1,3,5,6,7},{2,4}}=>{{1,5,6,7},{2,3,4}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3},{4,6,7},{5}}=>{{1,5,6,7},{2},{3,4}}=>{{1,4},{2},{3,5,6,7}}=>{{1,5,6,7},{2},{3,4}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4,5,6},{7}}=>{{1,2,5,6,7},{3},{4}}=>{{1,2,5,6,7},{3},{4}}=>{{1,2,5,6,7},{3},{4}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3},{4,7},{5,6}}=>{{1,5,6,7},{2,4},{3}}=>{{1,4},{2,5,6,7},{3}}=>{{1,5,6,7},{2,4},{3}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3},{4,5,7},{6}}=>{{1,5,6,7},{2,3},{4}}=>{{1,3},{2,5,6,7},{4}}=>{{1,5,6,7},{2,3},{4}}
[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}}=>{{1,5,6,7},{2},{3},{4}}=>{{1,5,6,7},{2},{3},{4}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4,6,7},{5}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6,7}}=>{{1,3,4,6,7},{2},{5}}=>{{1,3,4,6,7},{2},{5}}=>{{1,3,4,6,7},{2},{5}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2,4,6,7},{3},{5}}=>{{1,2,4,6,7},{3},{5}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2},{3,4},{5,7},{6}}=>{{1,4,6,7},{2,3},{5}}=>{{1,3},{2,4,6,7},{5}}=>{{1,4,6,7},{2,3},{5}}
[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}}=>{{1,4,6,7},{2},{3},{5}}=>{{1,4,6,7},{2},{3},{5}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2},{3,5},{4},{6},{7}}=>{{1,2,3,6,7},{4,5}}=>{{1,2,3,5},{4,6,7}}=>{{1,2,3,6,7},{4,5}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2},{3,5},{4},{6,7}}=>{{1,3,6,7},{2},{4,5}}=>{{1,3,5},{2},{4,6,7}}=>{{1,3,6,7},{2},{4,5}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2},{3,6},{4},{5},{7}}=>{{1,2,6,7},{3,4,5}}=>{{1,2,4,6,7},{3,5}}=>{{1,2,6,7},{3,4,5}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2},{3,7},{4},{5},{6}}=>{{1,6,7},{2,3,4,5}}=>{{1,3,5},{2,4,6,7}}=>{{1,6,7},{2,3,4,5}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4},{5}}=>{{1,6,7},{2},{3,4,5}}=>{{1,4,6,7},{2},{3,5}}=>{{1,6,7},{2},{3,4,5}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2},{3,5,6},{4},{7}}=>{{1,2,6,7},{3},{4,5}}=>{{1,2,5},{3},{4,6,7}}=>{{1,2,6,7},{3},{4,5}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2},{3,7},{4},{5,6}}=>{{1,6,7},{2,4,5},{3}}=>{{1,4,6,7},{2,5},{3}}=>{{1,6,7},{2,4,5},{3}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2},{3,5,7},{4},{6}}=>{{1,6,7},{2,3},{4,5}}=>{{1,3},{2,5},{4,6,7}}=>{{1,6,7},{2,3},{4,5}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2},{3,5,6,7},{4}}=>{{1,6,7},{2},{3},{4,5}}=>{{1,5},{2},{3},{4,6,7}}=>{{1,6,7},{2},{3},{4,5}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7}}=>{{1,2,3,6,7},{4},{5}}=>{{1,2,3,6,7},{4},{5}}=>{{1,2,3,6,7},{4},{5}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,3,6,7},{2},{4},{5}}=>{{1,3,6,7},{2},{4},{5}}=>{{1,3,6,7},{2},{4},{5}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2},{3,6},{4,5},{7}}=>{{1,2,6,7},{3,5},{4}}=>{{1,2,5},{3,6,7},{4}}=>{{1,2,6,7},{3,5},{4}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2},{3,7},{4,5},{6}}=>{{1,6,7},{2,3,5},{4}}=>{{1,3,6,7},{2,5},{4}}=>{{1,6,7},{2,3,5},{4}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4,5}}=>{{1,6,7},{2},{3,5},{4}}=>{{1,5},{2},{3,6,7},{4}}=>{{1,6,7},{2},{3,5},{4}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2},{3,4,6},{5},{7}}=>{{1,2,6,7},{3,4},{5}}=>{{1,2,4},{3,6,7},{5}}=>{{1,2,6,7},{3,4},{5}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2},{3,7},{4,6},{5}}=>{{1,6,7},{2,5},{3,4}}=>{{1,4},{2,5},{3,6,7}}=>{{1,6,7},{2,5},{3,4}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2},{3,4,7},{5},{6}}=>{{1,6,7},{2,3,4},{5}}=>{{1,3,6,7},{2,4},{5}}=>{{1,6,7},{2,3,4},{5}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2},{3,4,6,7},{5}}=>{{1,6,7},{2},{3,4},{5}}=>{{1,4},{2},{3,6,7},{5}}=>{{1,6,7},{2},{3,4},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}}=>{{1,2,6,7},{3},{4},{5}}=>{{1,2,6,7},{3},{4},{5}}=>{{1,2,6,7},{3},{4},{5}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2},{3,7},{4,5,6}}=>{{1,6,7},{2,5},{3},{4}}=>{{1,5},{2,6,7},{3},{4}}=>{{1,6,7},{2,5},{3},{4}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2},{3,4,7},{5,6}}=>{{1,6,7},{2,4},{3},{5}}=>{{1,4},{2,6,7},{3},{5}}=>{{1,6,7},{2,4},{3},{5}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2},{3,4,5,7},{6}}=>{{1,6,7},{2,3},{4},{5}}=>{{1,3},{2,6,7},{4},{5}}=>{{1,6,7},{2,3},{4},{5}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}}=>{{1,6,7},{2},{3},{4},{5}}=>{{1,6,7},{2},{3},{4},{5}}=>{{1,6,7},{2},{3},{4},{5}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7}}=>{{1,2,3,4,5,7},{6}}=>{{1,2,3,4,5,7},{6}}=>{{1,2,3,4,5,7},{6}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6,7}}=>{{1,3,4,5,7},{2},{6}}=>{{1,3,4,5,7},{2},{6}}=>{{1,3,4,5,7},{2},{6}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5,6},{7}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2,4,5,7},{3},{6}}=>{{1,2,4,5,7},{3},{6}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>{{1},{2,3},{4},{5,7},{6}}=>{{1,4,5,7},{2,3},{6}}=>{{1,3},{2,4,5,7},{6}}=>{{1,4,5,7},{2,3},{6}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>{{1,4,5,7},{2},{3},{6}}=>{{1,4,5,7},{2},{3},{6}}=>{{1,4,5,7},{2},{3},{6}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3,5,7},{4},{6}}
[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}}=>{{1,3,5,7},{2},{4},{6}}=>{{1,3,5,7},{2},{4},{6}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>{{1},{2,3},{4,6},{5},{7}}=>{{1,2,5,7},{3,4},{6}}=>{{1,2,4},{3,5,7},{6}}=>{{1,2,5,7},{3,4},{6}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>{{1},{2,3},{4,7},{5},{6}}=>{{1,5,7},{2,3,4},{6}}=>{{1,3,5,7},{2,4},{6}}=>{{1,5,7},{2,3,4},{6}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>{{1},{2,3},{4,6,7},{5}}=>{{1,5,7},{2},{3,4},{6}}=>{{1,4},{2},{3,5,7},{6}}=>{{1,5,7},{2},{3,4},{6}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,2,5,7},{3},{4},{6}}=>{{1,2,5,7},{3},{4},{6}}=>{{1,2,5,7},{3},{4},{6}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1},{2,3},{4,7},{5,6}}=>{{1,5,7},{2,4},{3},{6}}=>{{1,4},{2,5,7},{3},{6}}=>{{1,5,7},{2,4},{3},{6}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>{{1},{2,3},{4,5,7},{6}}=>{{1,5,7},{2,3},{4},{6}}=>{{1,3},{2,5,7},{4},{6}}=>{{1,5,7},{2,3},{4},{6}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,5,7},{2},{3},{4},{6}}=>{{1,5,7},{2},{3},{4},{6}}=>{{1,5,7},{2},{3},{4},{6}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6},{7}}=>{{1,2,3,4,7},{5,6}}=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>{{1},{2,4},{3},{5},{6,7}}=>{{1,3,4,7},{2},{5,6}}=>{{1,3,4,6},{2},{5,7}}=>{{1,3,4,7},{2},{5,6}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>{{1},{2,4},{3},{5,6},{7}}=>{{1,2,4,7},{3},{5,6}}=>{{1,2,4,6},{3},{5,7}}=>{{1,2,4,7},{3},{5,6}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>{{1},{2,4},{3},{5,7},{6}}=>{{1,4,7},{2,3},{5,6}}=>{{1,3},{2,4,6},{5,7}}=>{{1,4,7},{2,3},{5,6}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>{{1},{2,4},{3},{5,6,7}}=>{{1,4,7},{2},{3},{5,6}}=>{{1,4,6},{2},{3},{5,7}}=>{{1,4,7},{2},{3},{5,6}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>{{1},{2,5},{3},{4},{6},{7}}=>{{1,2,3,7},{4,5,6}}=>{{1,2,3,5,7},{4,6}}=>{{1,2,3,7},{4,5,6}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3},{4},{6,7}}=>{{1,3,7},{2},{4,5,6}}=>{{1,3,5,7},{2},{4,6}}=>{{1,3,7},{2},{4,5,6}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3},{4},{5},{7}}=>{{1,2,7},{3,4,5,6}}=>{{1,2,4,6},{3,5,7}}=>{{1,2,7},{3,4,5,6}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3},{4},{5},{6}}=>{{1,7},{2,3,4,5,6}}=>{{1,3,5,7},{2,4,6}}=>{{1,7},{2,3,4,5,6}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4},{5}}=>{{1,7},{2},{3,4,5,6}}=>{{1,4,6},{2},{3,5,7}}=>{{1,7},{2},{3,4,5,6}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3},{4},{7}}=>{{1,2,7},{3},{4,5,6}}=>{{1,2,5,7},{3},{4,6}}=>{{1,2,7},{3},{4,5,6}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3},{4},{5,6}}=>{{1,7},{2,4,5,6},{3}}=>{{1,4,6},{2,5,7},{3}}=>{{1,7},{2,4,5,6},{3}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3},{4},{6}}=>{{1,7},{2,3},{4,5,6}}=>{{1,3},{2,5,7},{4,6}}=>{{1,7},{2,3},{4,5,6}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3},{4}}=>{{1,7},{2},{3},{4,5,6}}=>{{1,5,7},{2},{3},{4,6}}=>{{1,7},{2},{3},{4,5,6}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>{{1},{2,4,5},{3},{6},{7}}=>{{1,2,3,7},{4},{5,6}}=>{{1,2,3,6},{4},{5,7}}=>{{1,2,3,7},{4},{5,6}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>{{1},{2,4,5},{3},{6,7}}=>{{1,3,7},{2},{4},{5,6}}=>{{1,3,6},{2},{4},{5,7}}=>{{1,3,7},{2},{4},{5,6}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3},{4,5},{7}}=>{{1,2,7},{3,5,6},{4}}=>{{1,2,5,7},{3,6},{4}}=>{{1,2,7},{3,5,6},{4}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3},{4,5},{6}}=>{{1,7},{2,3,5,6},{4}}=>{{1,3,6},{2,5,7},{4}}=>{{1,7},{2,3,5,6},{4}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4,5}}=>{{1,7},{2},{3,5,6},{4}}=>{{1,5,7},{2},{3,6},{4}}=>{{1,7},{2},{3,5,6},{4}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>{{1},{2,4,6},{3},{5},{7}}=>{{1,2,7},{3,4},{5,6}}=>{{1,2,4},{3,6},{5,7}}=>{{1,2,7},{3,4},{5,6}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3},{4,6},{5}}=>{{1,7},{2,5,6},{3,4}}=>{{1,4},{2,5,7},{3,6}}=>{{1,7},{2,5,6},{3,4}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>{{1},{2,4,7},{3},{5},{6}}=>{{1,7},{2,3,4},{5,6}}=>{{1,3,6},{2,4},{5,7}}=>{{1,7},{2,3,4},{5,6}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>{{1},{2,4,6,7},{3},{5}}=>{{1,7},{2},{3,4},{5,6}}=>{{1,4},{2},{3,6},{5,7}}=>{{1,7},{2},{3,4},{5,6}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>{{1},{2,4,5,6},{3},{7}}=>{{1,2,7},{3},{4},{5,6}}=>{{1,2,6},{3},{4},{5,7}}=>{{1,2,7},{3},{4},{5,6}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3},{4,5,6}}=>{{1,7},{2,5,6},{3},{4}}=>{{1,5,7},{2,6},{3},{4}}=>{{1,7},{2,5,6},{3},{4}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>{{1},{2,4,7},{3},{5,6}}=>{{1,7},{2,4},{3},{5,6}}=>{{1,4},{2,6},{3},{5,7}}=>{{1,7},{2,4},{3},{5,6}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>{{1},{2,4,5,7},{3},{6}}=>{{1,7},{2,3},{4},{5,6}}=>{{1,3},{2,6},{4},{5,7}}=>{{1,7},{2,3},{4},{5,6}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,4,5,6,7},{3}}=>{{1,7},{2},{3},{4},{5,6}}=>{{1,6},{2},{3},{4},{5,7}}=>{{1,7},{2},{3},{4},{5,6}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7}}=>{{1,2,3,4,7},{5},{6}}=>{{1,2,3,4,7},{5},{6}}=>{{1,2,3,4,7},{5},{6}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>{{1,3,4,7},{2},{5},{6}}=>{{1,3,4,7},{2},{5},{6}}=>{{1,3,4,7},{2},{5},{6}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,2,4,7},{3},{5},{6}}=>{{1,2,4,7},{3},{5},{6}}=>{{1,2,4,7},{3},{5},{6}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>{{1},{2,3,4},{5,7},{6}}=>{{1,4,7},{2,3},{5},{6}}=>{{1,3},{2,4,7},{5},{6}}=>{{1,4,7},{2,3},{5},{6}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,4,7},{2},{3},{5},{6}}=>{{1,4,7},{2},{3},{5},{6}}=>{{1,4,7},{2},{3},{5},{6}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>{{1},{2,5},{3,4},{6},{7}}=>{{1,2,3,7},{4,6},{5}}=>{{1,2,3,6},{4,7},{5}}=>{{1,2,3,7},{4,6},{5}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3,4},{6,7}}=>{{1,3,7},{2},{4,6},{5}}=>{{1,3,6},{2},{4,7},{5}}=>{{1,3,7},{2},{4,6},{5}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3,4},{5},{7}}=>{{1,2,7},{3,4,6},{5}}=>{{1,2,4,7},{3,6},{5}}=>{{1,2,7},{3,4,6},{5}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3,4},{5},{6}}=>{{1,7},{2,3,4,6},{5}}=>{{1,3,6},{2,4,7},{5}}=>{{1,7},{2,3,4,6},{5}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4},{5}}=>{{1,7},{2},{3,4,6},{5}}=>{{1,4,7},{2},{3,6},{5}}=>{{1,7},{2},{3,4,6},{5}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3,4},{7}}=>{{1,2,7},{3},{4,6},{5}}=>{{1,2,6},{3},{4,7},{5}}=>{{1,2,7},{3},{4,6},{5}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3,4},{5,6}}=>{{1,7},{2,4,6},{3},{5}}=>{{1,4,7},{2,6},{3},{5}}=>{{1,7},{2,4,6},{3},{5}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3,4},{6}}=>{{1,7},{2,3},{4,6},{5}}=>{{1,3},{2,6},{4,7},{5}}=>{{1,7},{2,3},{4,6},{5}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3,4}}=>{{1,7},{2},{3},{4,6},{5}}=>{{1,6},{2},{3},{4,7},{5}}=>{{1,7},{2},{3},{4,6},{5}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>{{1},{2,3,5},{4},{6},{7}}=>{{1,2,3,7},{4,5},{6}}=>{{1,2,3,5},{4,7},{6}}=>{{1,2,3,7},{4,5},{6}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>{{1},{2,3,5},{4},{6,7}}=>{{1,3,7},{2},{4,5},{6}}=>{{1,3,5},{2},{4,7},{6}}=>{{1,3,7},{2},{4,5},{6}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3,5},{4},{7}}=>{{1,2,7},{3,6},{4,5}}=>{{1,2,5},{3,6},{4,7}}=>{{1,2,7},{3,6},{4,5}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3,5},{4},{6}}=>{{1,7},{2,3,6},{4,5}}=>{{1,3,6},{2,5},{4,7}}=>{{1,7},{2,3,6},{4,5}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,5},{4}}=>{{1,7},{2},{3,6},{4,5}}=>{{1,5},{2},{3,6},{4,7}}=>{{1,7},{2},{3,6},{4,5}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4},{5},{7}}=>{{1,2,7},{3,4,5},{6}}=>{{1,2,4,7},{3,5},{6}}=>{{1,2,7},{3,4,5},{6}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4},{5}}=>{{1,7},{2,6},{3,4,5}}=>{{1,4,7},{2,5},{3,6}}=>{{1,7},{2,6},{3,4,5}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4},{5},{6}}=>{{1,7},{2,3,4,5},{6}}=>{{1,3,5},{2,4,7},{6}}=>{{1,7},{2,3,4,5},{6}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4},{5}}=>{{1,7},{2},{3,4,5},{6}}=>{{1,4,7},{2},{3,5},{6}}=>{{1,7},{2},{3,4,5},{6}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>{{1},{2,3,5,6},{4},{7}}=>{{1,2,7},{3},{4,5},{6}}=>{{1,2,5},{3},{4,7},{6}}=>{{1,2,7},{3},{4,5},{6}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3,5,6},{4}}=>{{1,7},{2,6},{3},{4,5}}=>{{1,5},{2,6},{3},{4,7}}=>{{1,7},{2,6},{3},{4,5}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4},{5,6}}=>{{1,7},{2,4,5},{3},{6}}=>{{1,4,7},{2,5},{3},{6}}=>{{1,7},{2,4,5},{3},{6}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>{{1},{2,3,5,7},{4},{6}}=>{{1,7},{2,3},{4,5},{6}}=>{{1,3},{2,5},{4,7},{6}}=>{{1,7},{2,3},{4,5},{6}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>{{1},{2,3,5,6,7},{4}}=>{{1,7},{2},{3},{4,5},{6}}=>{{1,5},{2},{3},{4,7},{6}}=>{{1,7},{2},{3},{4,5},{6}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}}=>{{1,2,3,7},{4},{5},{6}}=>{{1,2,3,7},{4},{5},{6}}=>{{1,2,3,7},{4},{5},{6}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,7},{2},{4},{5},{6}}=>{{1,3,7},{2},{4},{5},{6}}=>{{1,3,7},{2},{4},{5},{6}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>{{1},{2,6},{3,4,5},{7}}=>{{1,2,7},{3,6},{4},{5}}=>{{1,2,6},{3,7},{4},{5}}=>{{1,2,7},{3,6},{4},{5}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>{{1},{2,7},{3,4,5},{6}}=>{{1,7},{2,3,6},{4},{5}}=>{{1,3,7},{2,6},{4},{5}}=>{{1,7},{2,3,6},{4},{5}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4,5}}=>{{1,7},{2},{3,6},{4},{5}}=>{{1,6},{2},{3,7},{4},{5}}=>{{1,7},{2},{3,6},{4},{5}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4,5},{7}}=>{{1,2,7},{3,5},{4},{6}}=>{{1,2,5},{3,7},{4},{6}}=>{{1,2,7},{3,5},{4},{6}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4,5}}=>{{1,7},{2,6},{3,5},{4}}=>{{1,5},{2,6},{3,7},{4}}=>{{1,7},{2,6},{3,5},{4}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4,5},{6}}=>{{1,7},{2,3,5},{4},{6}}=>{{1,3,7},{2,5},{4},{6}}=>{{1,7},{2,3,5},{4},{6}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4,5}}=>{{1,7},{2},{3,5},{4},{6}}=>{{1,5},{2},{3,7},{4},{6}}=>{{1,7},{2},{3,5},{4},{6}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>{{1},{2,3,4,6},{5},{7}}=>{{1,2,7},{3,4},{5},{6}}=>{{1,2,4},{3,7},{5},{6}}=>{{1,2,7},{3,4},{5},{6}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>{{1},{2,7},{3,4,6},{5}}=>{{1,7},{2,6},{3,4},{5}}=>{{1,4},{2,6},{3,7},{5}}=>{{1,7},{2,6},{3,4},{5}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4,6},{5}}=>{{1,7},{2,5},{3,4},{6}}=>{{1,4},{2,5},{3,7},{6}}=>{{1,7},{2,5},{3,4},{6}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5},{6}}=>{{1,7},{2,3,4},{5},{6}}=>{{1,3,7},{2,4},{5},{6}}=>{{1,7},{2,3,4},{5},{6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>{{1},{2,3,4,6,7},{5}}=>{{1,7},{2},{3,4},{5},{6}}=>{{1,4},{2},{3,7},{5},{6}}=>{{1,7},{2},{3,4},{5},{6}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}}=>{{1,2,7},{3},{4},{5},{6}}=>{{1,2,7},{3},{4},{5},{6}}=>{{1,2,7},{3},{4},{5},{6}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>{{1},{2,7},{3,4,5,6}}=>{{1,7},{2,6},{3},{4},{5}}=>{{1,6},{2,7},{3},{4},{5}}=>{{1,7},{2,6},{3},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>{{1},{2,3,7},{4,5,6}}=>{{1,7},{2,5},{3},{4},{6}}=>{{1,5},{2,7},{3},{4},{6}}=>{{1,7},{2,5},{3},{4},{6}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5,6}}=>{{1,7},{2,4},{3},{5},{6}}=>{{1,4},{2,7},{3},{5},{6}}=>{{1,7},{2,4},{3},{5},{6}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>{{1},{2,3,4,5,7},{6}}=>{{1,7},{2,3},{4},{5},{6}}=>{{1,3},{2,7},{4},{5},{6}}=>{{1,7},{2,3},{4},{5},{6}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>{{1,7},{2},{3},{4},{5},{6}}=>{{1,7},{2},{3},{4},{5},{6}}=>{{1,7},{2},{3},{4},{5},{6}}
[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}}=>{{1,2,3,4,5,6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6,7}}=>{{1,3,4,5,6},{2},{7}}=>{{1,3,4,5,6},{2},{7}}=>{{1,3,4,5,6},{2},{7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5,6},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2,4,5,6},{3},{7}}=>{{1,2,4,5,6},{3},{7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4},{5,7},{6}}=>{{1,4,5,6},{2,3},{7}}=>{{1,3},{2,4,5,6},{7}}=>{{1,4,5,6},{2,3},{7}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}}=>{{1,4,5,6},{2},{3},{7}}=>{{1,4,5,6},{2},{3},{7}}=>{{1,4,5,6},{2},{3},{7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3,5,6},{4},{7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1,3,5,6},{2},{4},{7}}=>{{1,3,5,6},{2},{4},{7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>{{1,2},{3},{4,6},{5},{7}}=>{{1,2,5,6},{3,4},{7}}=>{{1,2,4},{3,5,6},{7}}=>{{1,2,5,6},{3,4},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>{{1,2},{3},{4,7},{5},{6}}=>{{1,5,6},{2,3,4},{7}}=>{{1,3,5,6},{2,4},{7}}=>{{1,5,6},{2,3,4},{7}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>{{1,2},{3},{4,6,7},{5}}=>{{1,5,6},{2},{3,4},{7}}=>{{1,4},{2},{3,5,6},{7}}=>{{1,5,6},{2},{3,4},{7}}
[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}}=>{{1,2,5,6},{3},{4},{7}}=>{{1,2,5,6},{3},{4},{7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>{{1,2},{3},{4,7},{5,6}}=>{{1,5,6},{2,4},{3},{7}}=>{{1,4},{2,5,6},{3},{7}}=>{{1,5,6},{2,4},{3},{7}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>{{1,2},{3},{4,5,7},{6}}=>{{1,5,6},{2,3},{4},{7}}=>{{1,3},{2,5,6},{4},{7}}=>{{1,5,6},{2,3},{4},{7}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}}=>{{1,5,6},{2},{3},{4},{7}}=>{{1,5,6},{2},{3},{4},{7}}=>{{1,5,6},{2},{3},{4},{7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7}}=>{{1,2,3,4,6},{5},{7}}=>{{1,2,3,4,6},{5},{7}}=>{{1,2,3,4,6},{5},{7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1,3,4,6},{2},{5},{7}}=>{{1,3,4,6},{2},{5},{7}}
[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}}=>{{1,2,4,6},{3},{5},{7}}=>{{1,2,4,6},{3},{5},{7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,4},{5,7},{6}}=>{{1,4,6},{2,3},{5},{7}}=>{{1,3},{2,4,6},{5},{7}}=>{{1,4,6},{2,3},{5},{7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,4,6},{2},{3},{5},{7}}=>{{1,4,6},{2},{3},{5},{7}}=>{{1,4,6},{2},{3},{5},{7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>{{1,2},{3,5},{4},{6},{7}}=>{{1,2,3,6},{4,5},{7}}=>{{1,2,3,5},{4,6},{7}}=>{{1,2,3,6},{4,5},{7}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>{{1,2},{3,5},{4},{6,7}}=>{{1,3,6},{2},{4,5},{7}}=>{{1,3,5},{2},{4,6},{7}}=>{{1,3,6},{2},{4,5},{7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>{{1,2},{3,6},{4},{5},{7}}=>{{1,2,6},{3,4,5},{7}}=>{{1,2,4,6},{3,5},{7}}=>{{1,2,6},{3,4,5},{7}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>{{1,2},{3,7},{4},{5},{6}}=>{{1,6},{2,3,4,5},{7}}=>{{1,3,5},{2,4,6},{7}}=>{{1,6},{2,3,4,5},{7}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4},{5}}=>{{1,6},{2},{3,4,5},{7}}=>{{1,4,6},{2},{3,5},{7}}=>{{1,6},{2},{3,4,5},{7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>{{1,2},{3,5,6},{4},{7}}=>{{1,2,6},{3},{4,5},{7}}=>{{1,2,5},{3},{4,6},{7}}=>{{1,2,6},{3},{4,5},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>{{1,2},{3,7},{4},{5,6}}=>{{1,6},{2,4,5},{3},{7}}=>{{1,4,6},{2,5},{3},{7}}=>{{1,6},{2,4,5},{3},{7}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>{{1,2},{3,5,7},{4},{6}}=>{{1,6},{2,3},{4,5},{7}}=>{{1,3},{2,5},{4,6},{7}}=>{{1,6},{2,3},{4,5},{7}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>{{1,2},{3,5,6,7},{4}}=>{{1,6},{2},{3},{4,5},{7}}=>{{1,5},{2},{3},{4,6},{7}}=>{{1,6},{2},{3},{4,5},{7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>{{1,2,3,6},{4},{5},{7}}=>{{1,2,3,6},{4},{5},{7}}=>{{1,2,3,6},{4},{5},{7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,3,6},{2},{4},{5},{7}}=>{{1,3,6},{2},{4},{5},{7}}=>{{1,3,6},{2},{4},{5},{7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>{{1,2},{3,6},{4,5},{7}}=>{{1,2,6},{3,5},{4},{7}}=>{{1,2,5},{3,6},{4},{7}}=>{{1,2,6},{3,5},{4},{7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>{{1,2},{3,7},{4,5},{6}}=>{{1,6},{2,3,5},{4},{7}}=>{{1,3,6},{2,5},{4},{7}}=>{{1,6},{2,3,5},{4},{7}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4,5}}=>{{1,6},{2},{3,5},{4},{7}}=>{{1,5},{2},{3,6},{4},{7}}=>{{1,6},{2},{3,5},{4},{7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>{{1,2},{3,4,6},{5},{7}}=>{{1,2,6},{3,4},{5},{7}}=>{{1,2,4},{3,6},{5},{7}}=>{{1,2,6},{3,4},{5},{7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>{{1,2},{3,7},{4,6},{5}}=>{{1,6},{2,5},{3,4},{7}}=>{{1,4},{2,5},{3,6},{7}}=>{{1,6},{2,5},{3,4},{7}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>{{1,2},{3,4,7},{5},{6}}=>{{1,6},{2,3,4},{5},{7}}=>{{1,3,6},{2,4},{5},{7}}=>{{1,6},{2,3,4},{5},{7}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>{{1,2},{3,4,6,7},{5}}=>{{1,6},{2},{3,4},{5},{7}}=>{{1,4},{2},{3,6},{5},{7}}=>{{1,6},{2},{3,4},{5},{7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,6},{3},{4},{5},{7}}=>{{1,2,6},{3},{4},{5},{7}}=>{{1,2,6},{3},{4},{5},{7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>{{1,2},{3,7},{4,5,6}}=>{{1,6},{2,5},{3},{4},{7}}=>{{1,5},{2,6},{3},{4},{7}}=>{{1,6},{2,5},{3},{4},{7}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>{{1,2},{3,4,7},{5,6}}=>{{1,6},{2,4},{3},{5},{7}}=>{{1,4},{2,6},{3},{5},{7}}=>{{1,6},{2,4},{3},{5},{7}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>{{1,2},{3,4,5,7},{6}}=>{{1,6},{2,3},{4},{5},{7}}=>{{1,3},{2,6},{4},{5},{7}}=>{{1,6},{2,3},{4},{5},{7}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,6},{2},{3},{4},{5},{7}}=>{{1,6},{2},{3},{4},{5},{7}}=>{{1,6},{2},{3},{4},{5},{7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6},{7}}=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5},{6,7}}=>{{1,3,4,5},{2},{6,7}}=>{{1,3,4,5},{2},{6,7}}=>{{1,3,4,5},{2},{6,7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>{{1,3},{2},{4},{5,6},{7}}=>{{1,2,4,5},{3},{6,7}}=>{{1,2,4,5},{3},{6,7}}=>{{1,2,4,5},{3},{6,7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>{{1,3},{2},{4},{5,7},{6}}=>{{1,4,5},{2,3},{6,7}}=>{{1,3},{2,4,5},{6,7}}=>{{1,4,5},{2,3},{6,7}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>{{1,3},{2},{4},{5,6,7}}=>{{1,4,5},{2},{3},{6,7}}=>{{1,4,5},{2},{3},{6,7}}=>{{1,4,5},{2},{3},{6,7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>{{1,3},{2},{4,5},{6},{7}}=>{{1,2,3,5},{4},{6,7}}=>{{1,2,3,5},{4},{6,7}}=>{{1,2,3,5},{4},{6,7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5},{6,7}}=>{{1,3,5},{2},{4},{6,7}}=>{{1,3,5},{2},{4},{6,7}}=>{{1,3,5},{2},{4},{6,7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>{{1,3},{2},{4,6},{5},{7}}=>{{1,2,5},{3,4},{6,7}}=>{{1,2,4},{3,5},{6,7}}=>{{1,2,5},{3,4},{6,7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>{{1,3},{2},{4,7},{5},{6}}=>{{1,5},{2,3,4},{6,7}}=>{{1,3,5},{2,4},{6,7}}=>{{1,5},{2,3,4},{6,7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>{{1,3},{2},{4,6,7},{5}}=>{{1,5},{2},{3,4},{6,7}}=>{{1,4},{2},{3,5},{6,7}}=>{{1,5},{2},{3,4},{6,7}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>{{1,3},{2},{4,5,6},{7}}=>{{1,2,5},{3},{4},{6,7}}=>{{1,2,5},{3},{4},{6,7}}=>{{1,2,5},{3},{4},{6,7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,3},{2},{4,7},{5,6}}=>{{1,5},{2,4},{3},{6,7}}=>{{1,4},{2,5},{3},{6,7}}=>{{1,5},{2,4},{3},{6,7}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>{{1,3},{2},{4,5,7},{6}}=>{{1,5},{2,3},{4},{6,7}}=>{{1,3},{2,5},{4},{6,7}}=>{{1,5},{2,3},{4},{6,7}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>{{1,3},{2},{4,5,6,7}}=>{{1,5},{2},{3},{4},{6,7}}=>{{1,5},{2},{3},{4},{6,7}}=>{{1,5},{2},{3},{4},{6,7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6},{7}}=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4},{5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2},{3},{5},{6,7}}=>{{1,3,4},{2},{5,6,7}}=>{{1,3,4},{2},{5,6,7}}=>{{1,3,4},{2},{5,6,7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2},{3},{5,6},{7}}=>{{1,2,4},{3},{5,6,7}}=>{{1,2,4},{3},{5,6,7}}=>{{1,2,4},{3},{5,6,7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2},{3},{5,7},{6}}=>{{1,4},{2,3},{5,6,7}}=>{{1,3},{2,4},{5,6,7}}=>{{1,4},{2,3},{5,6,7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2},{3},{5,6,7}}=>{{1,4},{2},{3},{5,6,7}}=>{{1,4},{2},{3},{5,6,7}}=>{{1,4},{2},{3},{5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3},{4},{6},{7}}=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3},{4},{6,7}}=>{{1,3},{2},{4,5,6,7}}=>{{1,3},{2},{4,5,6,7}}=>{{1,3},{2},{4,5,6,7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3},{4},{5},{7}}=>{{1,2},{3,4,5,6,7}}=>{{1,2},{3,4,5,6,7}}=>{{1,2},{3,4,5,6,7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3},{4},{5},{6}}=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4},{5}}=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3},{4},{7}}=>{{1,2},{3},{4,5,6,7}}=>{{1,2},{3},{4,5,6,7}}=>{{1,2},{3},{4,5,6,7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3},{4},{5,6}}=>{{1},{2,4,5,6,7},{3}}=>{{1},{2,4,5,6,7},{3}}=>{{1},{2,4,5,6,7},{3}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3},{4},{6}}=>{{1},{2,3},{4,5,6,7}}=>{{1},{2,3},{4,5,6,7}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3},{4}}=>{{1},{2},{3},{4,5,6,7}}=>{{1},{2},{3},{4,5,6,7}}=>{{1},{2},{3},{4,5,6,7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2},{3},{6},{7}}=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6,7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2},{3},{6,7}}=>{{1,3},{2},{4},{5,6,7}}=>{{1,3},{2},{4},{5,6,7}}=>{{1,3},{2},{4},{5,6,7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3},{4,5},{7}}=>{{1,2},{3,5,6,7},{4}}=>{{1,2},{3,5,6,7},{4}}=>{{1,2},{3,5,6,7},{4}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3},{4,5},{6}}=>{{1},{2,3,5,6,7},{4}}=>{{1},{2,3,5,6,7},{4}}=>{{1},{2,3,5,6,7},{4}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4,5}}=>{{1},{2},{3,5,6,7},{4}}=>{{1},{2},{3,5,6,7},{4}}=>{{1},{2},{3,5,6,7},{4}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2},{3},{5},{7}}=>{{1,2},{3,4},{5,6,7}}=>{{1,2},{3,4},{5,6,7}}=>{{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3},{4,6},{5}}=>{{1},{2,5,6,7},{3,4}}=>{{1},{2,4},{3,5,6,7}}=>{{1},{2,5,6,7},{3,4}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2},{3},{5},{6}}=>{{1},{2,3,4},{5,6,7}}=>{{1},{2,3,4},{5,6,7}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2},{3},{5}}=>{{1},{2},{3,4},{5,6,7}}=>{{1},{2},{3,4},{5,6,7}}=>{{1},{2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2},{3},{7}}=>{{1,2},{3},{4},{5,6,7}}=>{{1,2},{3},{4},{5,6,7}}=>{{1,2},{3},{4},{5,6,7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3},{4,5,6}}=>{{1},{2,5,6,7},{3},{4}}=>{{1},{2,5,6,7},{3},{4}}=>{{1},{2,5,6,7},{3},{4}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2},{3},{5,6}}=>{{1},{2,4},{3},{5,6,7}}=>{{1},{2,4},{3},{5,6,7}}=>{{1},{2,4},{3},{5,6,7}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2},{3},{6}}=>{{1},{2,3},{4},{5,6,7}}=>{{1},{2,3},{4},{5,6,7}}=>{{1},{2,3},{4},{5,6,7}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2},{3}}=>{{1},{2},{3},{4},{5,6,7}}=>{{1},{2},{3},{4},{5,6,7}}=>{{1},{2},{3},{4},{5,6,7}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>{{1,3,4},{2},{5},{6},{7}}=>{{1,2,3,4},{5},{6,7}}=>{{1,2,3,4},{5},{6,7}}=>{{1,2,3,4},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>{{1,3,4},{2},{5},{6,7}}=>{{1,3,4},{2},{5},{6,7}}=>{{1,3,4},{2},{5},{6,7}}=>{{1,3,4},{2},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>{{1,3,4},{2},{5,6},{7}}=>{{1,2,4},{3},{5},{6,7}}=>{{1,2,4},{3},{5},{6,7}}=>{{1,2,4},{3},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>{{1,3,4},{2},{5,7},{6}}=>{{1,4},{2,3},{5},{6,7}}=>{{1,3},{2,4},{5},{6,7}}=>{{1,4},{2,3},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>{{1,3,4},{2},{5,6,7}}=>{{1,4},{2},{3},{5},{6,7}}=>{{1,4},{2},{3},{5},{6,7}}=>{{1,4},{2},{3},{5},{6,7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3,4},{6},{7}}=>{{1,2,3},{4,6,7},{5}}=>{{1,2,3},{4,6,7},{5}}=>{{1,2,3},{4,6,7},{5}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3,4},{6,7}}=>{{1,3},{2},{4,6,7},{5}}=>{{1,3},{2},{4,6,7},{5}}=>{{1,3},{2},{4,6,7},{5}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3,4},{5},{7}}=>{{1,2},{3,4,6,7},{5}}=>{{1,2},{3,4,6,7},{5}}=>{{1,2},{3,4,6,7},{5}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3,4},{5},{6}}=>{{1},{2,3,4,6,7},{5}}=>{{1},{2,3,4,6,7},{5}}=>{{1},{2,3,4,6,7},{5}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4},{5}}=>{{1},{2},{3,4,6,7},{5}}=>{{1},{2},{3,4,6,7},{5}}=>{{1},{2},{3,4,6,7},{5}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3,4},{7}}=>{{1,2},{3},{4,6,7},{5}}=>{{1,2},{3},{4,6,7},{5}}=>{{1,2},{3},{4,6,7},{5}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3,4},{5,6}}=>{{1},{2,4,6,7},{3},{5}}=>{{1},{2,4,6,7},{3},{5}}=>{{1},{2,4,6,7},{3},{5}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3,4},{6}}=>{{1},{2,3},{4,6,7},{5}}=>{{1},{2,3},{4,6,7},{5}}=>{{1},{2,3},{4,6,7},{5}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3,4}}=>{{1},{2},{3},{4,6,7},{5}}=>{{1},{2},{3},{4,6,7},{5}}=>{{1},{2},{3},{4,6,7},{5}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>{{1,3,5},{2},{4},{6},{7}}=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3},{4,5},{6,7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>{{1,3,5},{2},{4},{6,7}}=>{{1,3},{2},{4,5},{6,7}}=>{{1,3},{2},{4,5},{6,7}}=>{{1,3},{2},{4,5},{6,7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3,5},{4},{7}}=>{{1,2},{3,6,7},{4,5}}=>{{1,2},{3,5},{4,6,7}}=>{{1,2},{3,6,7},{4,5}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3,5},{4},{6}}=>{{1},{2,3,6,7},{4,5}}=>{{1},{2,3,5},{4,6,7}}=>{{1},{2,3,6,7},{4,5}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,5},{4}}=>{{1},{2},{3,6,7},{4,5}}=>{{1},{2},{3,5},{4,6,7}}=>{{1},{2},{3,6,7},{4,5}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4},{5},{7}}=>{{1,2},{3,4,5},{6,7}}=>{{1,2},{3,4,5},{6,7}}=>{{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4},{5}}=>{{1},{2,6,7},{3,4,5}}=>{{1},{2,4,6,7},{3,5}}=>{{1},{2,6,7},{3,4,5}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4},{5},{6}}=>{{1},{2,3,4,5},{6,7}}=>{{1},{2,3,4,5},{6,7}}=>{{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4},{5}}=>{{1},{2},{3,4,5},{6,7}}=>{{1},{2},{3,4,5},{6,7}}=>{{1},{2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>{{1,3,5,6},{2},{4},{7}}=>{{1,2},{3},{4,5},{6,7}}=>{{1,2},{3},{4,5},{6,7}}=>{{1,2},{3},{4,5},{6,7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3,5,6},{4}}=>{{1},{2,6,7},{3},{4,5}}=>{{1},{2,5},{3},{4,6,7}}=>{{1},{2,6,7},{3},{4,5}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4},{5,6}}=>{{1},{2,4,5},{3},{6,7}}=>{{1},{2,4,5},{3},{6,7}}=>{{1},{2,4,5},{3},{6,7}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>{{1,3,5,7},{2},{4},{6}}=>{{1},{2,3},{4,5},{6,7}}=>{{1},{2,3},{4,5},{6,7}}=>{{1},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>{{1,3,5,6,7},{2},{4}}=>{{1},{2},{3},{4,5},{6,7}}=>{{1},{2},{3},{4,5},{6,7}}=>{{1},{2},{3},{4,5},{6,7}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>{{1,3,4,5},{2},{6},{7}}=>{{1,2,3},{4},{5},{6,7}}=>{{1,2,3},{4},{5},{6,7}}=>{{1,2,3},{4},{5},{6,7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,3,4,5},{2},{6,7}}=>{{1,3},{2},{4},{5},{6,7}}=>{{1,3},{2},{4},{5},{6,7}}=>{{1,3},{2},{4},{5},{6,7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2},{3,4,5},{7}}=>{{1,2},{3,6,7},{4},{5}}=>{{1,2},{3,6,7},{4},{5}}=>{{1,2},{3,6,7},{4},{5}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2},{3,4,5},{6}}=>{{1},{2,3,6,7},{4},{5}}=>{{1},{2,3,6,7},{4},{5}}=>{{1},{2,3,6,7},{4},{5}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4,5}}=>{{1},{2},{3,6,7},{4},{5}}=>{{1},{2},{3,6,7},{4},{5}}=>{{1},{2},{3,6,7},{4},{5}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4,5},{7}}=>{{1,2},{3,5},{4},{6,7}}=>{{1,2},{3,5},{4},{6,7}}=>{{1,2},{3,5},{4},{6,7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4,5}}=>{{1},{2,6,7},{3,5},{4}}=>{{1},{2,5},{3,6,7},{4}}=>{{1},{2,6,7},{3,5},{4}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4,5},{6}}=>{{1},{2,3,5},{4},{6,7}}=>{{1},{2,3,5},{4},{6,7}}=>{{1},{2,3,5},{4},{6,7}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4,5}}=>{{1},{2},{3,5},{4},{6,7}}=>{{1},{2},{3,5},{4},{6,7}}=>{{1},{2},{3,5},{4},{6,7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>{{1,3,4,6},{2},{5},{7}}=>{{1,2},{3,4},{5},{6,7}}=>{{1,2},{3,4},{5},{6,7}}=>{{1,2},{3,4},{5},{6,7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2},{3,4,6},{5}}=>{{1},{2,6,7},{3,4},{5}}=>{{1},{2,4},{3,6,7},{5}}=>{{1},{2,6,7},{3,4},{5}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4,6},{5}}=>{{1},{2,5},{3,4},{6,7}}=>{{1},{2,4},{3,5},{6,7}}=>{{1},{2,5},{3,4},{6,7}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5},{6}}=>{{1},{2,3,4},{5},{6,7}}=>{{1},{2,3,4},{5},{6,7}}=>{{1},{2,3,4},{5},{6,7}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>{{1,3,4,6,7},{2},{5}}=>{{1},{2},{3,4},{5},{6,7}}=>{{1},{2},{3,4},{5},{6,7}}=>{{1},{2},{3,4},{5},{6,7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,3,4,5,6},{2},{7}}=>{{1,2},{3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5},{6,7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2},{3,4,5,6}}=>{{1},{2,6,7},{3},{4},{5}}=>{{1},{2,6,7},{3},{4},{5}}=>{{1},{2,6,7},{3},{4},{5}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>{{1,3,7},{2},{4,5,6}}=>{{1},{2,5},{3},{4},{6,7}}=>{{1},{2,5},{3},{4},{6,7}}=>{{1},{2,5},{3},{4},{6,7}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5,6}}=>{{1},{2,4},{3},{5},{6,7}}=>{{1},{2,4},{3},{5},{6,7}}=>{{1},{2,4},{3},{5},{6,7}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>{{1,3,4,5,7},{2},{6}}=>{{1},{2,3},{4},{5},{6,7}}=>{{1},{2,3},{4},{5},{6,7}}=>{{1},{2,3},{4},{5},{6,7}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}}=>{{1},{2},{3},{4},{5},{6,7}}=>{{1},{2},{3},{4},{5},{6,7}}=>{{1},{2},{3},{4},{5},{6,7}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7}}=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6,7}}=>{{1,3,4,5},{2},{6},{7}}=>{{1,3,4,5},{2},{6},{7}}=>{{1,3,4,5},{2},{6},{7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3},{4},{5,6},{7}}=>{{1,2,4,5},{3},{6},{7}}=>{{1,2,4,5},{3},{6},{7}}=>{{1,2,4,5},{3},{6},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>{{1,2,3},{4},{5,7},{6}}=>{{1,4,5},{2,3},{6},{7}}=>{{1,3},{2,4,5},{6},{7}}=>{{1,4,5},{2,3},{6},{7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}}=>{{1,4,5},{2},{3},{6},{7}}=>{{1,4,5},{2},{3},{6},{7}}=>{{1,4,5},{2},{3},{6},{7}}
[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}}=>{{1,2,3,5},{4},{6},{7}}=>{{1,2,3,5},{4},{6},{7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,3,5},{2},{4},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>{{1,2,3},{4,6},{5},{7}}=>{{1,2,5},{3,4},{6},{7}}=>{{1,2,4},{3,5},{6},{7}}=>{{1,2,5},{3,4},{6},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>{{1,2,3},{4,7},{5},{6}}=>{{1,5},{2,3,4},{6},{7}}=>{{1,3,5},{2,4},{6},{7}}=>{{1,5},{2,3,4},{6},{7}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>{{1,2,3},{4,6,7},{5}}=>{{1,5},{2},{3,4},{6},{7}}=>{{1,4},{2},{3,5},{6},{7}}=>{{1,5},{2},{3,4},{6},{7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,5},{3},{4},{6},{7}}=>{{1,2,5},{3},{4},{6},{7}}=>{{1,2,5},{3},{4},{6},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>{{1,2,3},{4,7},{5,6}}=>{{1,5},{2,4},{3},{6},{7}}=>{{1,4},{2,5},{3},{6},{7}}=>{{1,5},{2,4},{3},{6},{7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>{{1,2,3},{4,5,7},{6}}=>{{1,5},{2,3},{4},{6},{7}}=>{{1,3},{2,5},{4},{6},{7}}=>{{1,5},{2,3},{4},{6},{7}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,5},{2},{3},{4},{6},{7}}=>{{1,5},{2},{3},{4},{6},{7}}=>{{1,5},{2},{3},{4},{6},{7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2,3},{5},{6},{7}}=>{{1,2,3,4},{5,7},{6}}=>{{1,2,3,4},{5,7},{6}}=>{{1,2,3,4},{5,7},{6}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2,3},{5},{6,7}}=>{{1,3,4},{2},{5,7},{6}}=>{{1,3,4},{2},{5,7},{6}}=>{{1,3,4},{2},{5,7},{6}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2,3},{5,6},{7}}=>{{1,2,4},{3},{5,7},{6}}=>{{1,2,4},{3},{5,7},{6}}=>{{1,2,4},{3},{5,7},{6}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2,3},{5,7},{6}}=>{{1,4},{2,3},{5,7},{6}}=>{{1,3},{2,4},{5,7},{6}}=>{{1,4},{2,3},{5,7},{6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2,3},{5,6,7}}=>{{1,4},{2},{3},{5,7},{6}}=>{{1,4},{2},{3},{5,7},{6}}=>{{1,4},{2},{3},{5,7},{6}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2,3},{4},{6},{7}}=>{{1,2,3},{4,5,7},{6}}=>{{1,2,3},{4,5,7},{6}}=>{{1,2,3},{4,5,7},{6}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2,3},{4},{6,7}}=>{{1,3},{2},{4,5,7},{6}}=>{{1,3},{2},{4,5,7},{6}}=>{{1,3},{2},{4,5,7},{6}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2,3},{4},{5},{7}}=>{{1,2},{3,4,5,7},{6}}=>{{1,2},{3,4,5,7},{6}}=>{{1,2},{3,4,5,7},{6}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2,3},{4},{5},{6}}=>{{1},{2,3,4,5,7},{6}}=>{{1},{2,3,4,5,7},{6}}=>{{1},{2,3,4,5,7},{6}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4},{5}}=>{{1},{2},{3,4,5,7},{6}}=>{{1},{2},{3,4,5,7},{6}}=>{{1},{2},{3,4,5,7},{6}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3},{4},{7}}=>{{1,2},{3},{4,5,7},{6}}=>{{1,2},{3},{4,5,7},{6}}=>{{1,2},{3},{4,5,7},{6}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2,3},{4},{5,6}}=>{{1},{2,4,5,7},{3},{6}}=>{{1},{2,4,5,7},{3},{6}}=>{{1},{2,4,5,7},{3},{6}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3},{4},{6}}=>{{1},{2,3},{4,5,7},{6}}=>{{1},{2,3},{4,5,7},{6}}=>{{1},{2,3},{4,5,7},{6}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3},{4}}=>{{1},{2},{3},{4,5,7},{6}}=>{{1},{2},{3},{4,5,7},{6}}=>{{1},{2},{3},{4,5,7},{6}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2,3},{6},{7}}=>{{1,2,3},{4},{5,7},{6}}=>{{1,2,3},{4},{5,7},{6}}=>{{1,2,3},{4},{5,7},{6}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2,3},{6,7}}=>{{1,3},{2},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,7},{6}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2,3},{4,5},{7}}=>{{1,2},{3,5,7},{4},{6}}=>{{1,2},{3,5,7},{4},{6}}=>{{1,2},{3,5,7},{4},{6}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2,3},{4,5},{6}}=>{{1},{2,3,5,7},{4},{6}}=>{{1},{2,3,5,7},{4},{6}}=>{{1},{2,3,5,7},{4},{6}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4,5}}=>{{1},{2},{3,5,7},{4},{6}}=>{{1},{2},{3,5,7},{4},{6}}=>{{1},{2},{3,5,7},{4},{6}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2,3},{5},{7}}=>{{1,2},{3,4},{5,7},{6}}=>{{1,2},{3,4},{5,7},{6}}=>{{1,2},{3,4},{5,7},{6}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2,3},{4,6},{5}}=>{{1},{2,5,7},{3,4},{6}}=>{{1},{2,4},{3,5,7},{6}}=>{{1},{2,5,7},{3,4},{6}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2,3},{5},{6}}=>{{1},{2,3,4},{5,7},{6}}=>{{1},{2,3,4},{5,7},{6}}=>{{1},{2,3,4},{5,7},{6}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2,3},{5}}=>{{1},{2},{3,4},{5,7},{6}}=>{{1},{2},{3,4},{5,7},{6}}=>{{1},{2},{3,4},{5,7},{6}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2,3},{7}}=>{{1,2},{3},{4},{5,7},{6}}=>{{1,2},{3},{4},{5,7},{6}}=>{{1,2},{3},{4},{5,7},{6}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2,3},{4,5,6}}=>{{1},{2,5,7},{3},{4},{6}}=>{{1},{2,5,7},{3},{4},{6}}=>{{1},{2,5,7},{3},{4},{6}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2,3},{5,6}}=>{{1},{2,4},{3},{5,7},{6}}=>{{1},{2,4},{3},{5,7},{6}}=>{{1},{2,4},{3},{5,7},{6}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2,3},{6}}=>{{1},{2,3},{4},{5,7},{6}}=>{{1},{2,3},{4},{5,7},{6}}=>{{1},{2,3},{4},{5,7},{6}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2,3}}=>{{1},{2},{3},{4},{5,7},{6}}=>{{1},{2},{3},{4},{5,7},{6}}=>{{1},{2},{3},{4},{5,7},{6}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>{{1,2,4},{3},{5},{6},{7}}=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4},{5,6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>{{1,2,4},{3},{5},{6,7}}=>{{1,3,4},{2},{5,6},{7}}=>{{1,3,4},{2},{5,6},{7}}=>{{1,3,4},{2},{5,6},{7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>{{1,2,4},{3},{5,6},{7}}=>{{1,2,4},{3},{5,6},{7}}=>{{1,2,4},{3},{5,6},{7}}=>{{1,2,4},{3},{5,6},{7}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>{{1,2,4},{3},{5,7},{6}}=>{{1,4},{2,3},{5,6},{7}}=>{{1,3},{2,4},{5,6},{7}}=>{{1,4},{2,3},{5,6},{7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>{{1,2,4},{3},{5,6,7}}=>{{1,4},{2},{3},{5,6},{7}}=>{{1,4},{2},{3},{5,6},{7}}=>{{1,4},{2},{3},{5,6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,4},{3},{6},{7}}=>{{1,2,3},{4,7},{5,6}}=>{{1,2,3},{4,6},{5,7}}=>{{1,2,3},{4,7},{5,6}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,4},{3},{6,7}}=>{{1,3},{2},{4,7},{5,6}}=>{{1,3},{2},{4,6},{5,7}}=>{{1,3},{2},{4,7},{5,6}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,4},{3},{5},{7}}=>{{1,2},{3,4,7},{5,6}}=>{{1,2},{3,4,6},{5,7}}=>{{1,2},{3,4,7},{5,6}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,4},{3},{5},{6}}=>{{1},{2,3,4,7},{5,6}}=>{{1},{2,3,4,6},{5,7}}=>{{1},{2,3,4,7},{5,6}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,4},{3},{5}}=>{{1},{2},{3,4,7},{5,6}}=>{{1},{2},{3,4,6},{5,7}}=>{{1},{2},{3,4,7},{5,6}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,4},{3},{7}}=>{{1,2},{3},{4,7},{5,6}}=>{{1,2},{3},{4,6},{5,7}}=>{{1,2},{3},{4,7},{5,6}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,4},{3},{5,6}}=>{{1},{2,4,7},{3},{5,6}}=>{{1},{2,4,6},{3},{5,7}}=>{{1},{2,4,7},{3},{5,6}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,4},{3},{6}}=>{{1},{2,3},{4,7},{5,6}}=>{{1},{2,3},{4,6},{5,7}}=>{{1},{2,3},{4,7},{5,6}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,4},{3}}=>{{1},{2},{3},{4,7},{5,6}}=>{{1},{2},{3},{4,6},{5,7}}=>{{1},{2},{3},{4,7},{5,6}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3},{4},{6},{7}}=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3},{4},{6,7}}=>{{1,3},{2},{4,5,6},{7}}=>{{1,3},{2},{4,5,6},{7}}=>{{1,3},{2},{4,5,6},{7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3},{4},{7}}=>{{1,2},{3,7},{4,5,6}}=>{{1,2},{3,5,7},{4,6}}=>{{1,2},{3,7},{4,5,6}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3},{4},{6}}=>{{1},{2,3,7},{4,5,6}}=>{{1},{2,3,5,7},{4,6}}=>{{1},{2,3,7},{4,5,6}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3},{4}}=>{{1},{2},{3,7},{4,5,6}}=>{{1},{2},{3,5,7},{4,6}}=>{{1},{2},{3,7},{4,5,6}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4},{5},{7}}=>{{1,2},{3,4,5,6},{7}}=>{{1,2},{3,4,5,6},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4},{5}}=>{{1},{2,7},{3,4,5,6}}=>{{1},{2,4,6},{3,5,7}}=>{{1},{2,7},{3,4,5,6}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4},{5},{6}}=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4},{5}}=>{{1},{2},{3,4,5,6},{7}}=>{{1},{2},{3,4,5,6},{7}}=>{{1},{2},{3,4,5,6},{7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3},{4},{7}}=>{{1,2},{3},{4,5,6},{7}}=>{{1,2},{3},{4,5,6},{7}}=>{{1,2},{3},{4,5,6},{7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3},{4}}=>{{1},{2,7},{3},{4,5,6}}=>{{1},{2,5,7},{3},{4,6}}=>{{1},{2,7},{3},{4,5,6}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4},{5,6}}=>{{1},{2,4,5,6},{3},{7}}=>{{1},{2,4,5,6},{3},{7}}=>{{1},{2,4,5,6},{3},{7}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3},{4},{6}}=>{{1},{2,3},{4,5,6},{7}}=>{{1},{2,3},{4,5,6},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3},{4}}=>{{1},{2},{3},{4,5,6},{7}}=>{{1},{2},{3},{4,5,6},{7}}=>{{1},{2},{3},{4,5,6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>{{1,2,4,5},{3},{6},{7}}=>{{1,2,3},{4},{5,6},{7}}=>{{1,2,3},{4},{5,6},{7}}=>{{1,2,3},{4},{5,6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>{{1,2,4,5},{3},{6,7}}=>{{1,3},{2},{4},{5,6},{7}}=>{{1,3},{2},{4},{5,6},{7}}=>{{1,3},{2},{4},{5,6},{7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,4,5},{3},{7}}=>{{1,2},{3,7},{4},{5,6}}=>{{1,2},{3,6},{4},{5,7}}=>{{1,2},{3,7},{4},{5,6}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,4,5},{3},{6}}=>{{1},{2,3,7},{4},{5,6}}=>{{1},{2,3,6},{4},{5,7}}=>{{1},{2,3,7},{4},{5,6}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,4,5},{3}}=>{{1},{2},{3,7},{4},{5,6}}=>{{1},{2},{3,6},{4},{5,7}}=>{{1},{2},{3,7},{4},{5,6}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4,5},{7}}=>{{1,2},{3,5,6},{4},{7}}=>{{1,2},{3,5,6},{4},{7}}=>{{1,2},{3,5,6},{4},{7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4,5}}=>{{1},{2,7},{3,5,6},{4}}=>{{1},{2,5,7},{3,6},{4}}=>{{1},{2,7},{3,5,6},{4}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4,5},{6}}=>{{1},{2,3,5,6},{4},{7}}=>{{1},{2,3,5,6},{4},{7}}=>{{1},{2,3,5,6},{4},{7}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4,5}}=>{{1},{2},{3,5,6},{4},{7}}=>{{1},{2},{3,5,6},{4},{7}}=>{{1},{2},{3,5,6},{4},{7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>{{1,2,4,6},{3},{5},{7}}=>{{1,2},{3,4},{5,6},{7}}=>{{1,2},{3,4},{5,6},{7}}=>{{1,2},{3,4},{5,6},{7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,4,6},{3},{5}}=>{{1},{2,7},{3,4},{5,6}}=>{{1},{2,4},{3,6},{5,7}}=>{{1},{2,7},{3,4},{5,6}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4,6},{5}}=>{{1},{2,5,6},{3,4},{7}}=>{{1},{2,4},{3,5,6},{7}}=>{{1},{2,5,6},{3,4},{7}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5},{6}}=>{{1},{2,3,4},{5,6},{7}}=>{{1},{2,3,4},{5,6},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>{{1,2,4,6,7},{3},{5}}=>{{1},{2},{3,4},{5,6},{7}}=>{{1},{2},{3,4},{5,6},{7}}=>{{1},{2},{3,4},{5,6},{7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>{{1,2,4,5,6},{3},{7}}=>{{1,2},{3},{4},{5,6},{7}}=>{{1,2},{3},{4},{5,6},{7}}=>{{1,2},{3},{4},{5,6},{7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,4,5,6},{3}}=>{{1},{2,7},{3},{4},{5,6}}=>{{1},{2,6},{3},{4},{5,7}}=>{{1},{2,7},{3},{4},{5,6}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3},{4,5,6}}=>{{1},{2,5,6},{3},{4},{7}}=>{{1},{2,5,6},{3},{4},{7}}=>{{1},{2,5,6},{3},{4},{7}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5,6}}=>{{1},{2,4},{3},{5,6},{7}}=>{{1},{2,4},{3},{5,6},{7}}=>{{1},{2,4},{3},{5,6},{7}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>{{1,2,4,5,7},{3},{6}}=>{{1},{2,3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,6},{7}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1,2,4,5,6,7},{3}}=>{{1},{2},{3},{4},{5,6},{7}}=>{{1},{2},{3},{4},{5,6},{7}}=>{{1},{2},{3},{4},{5,6},{7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}}=>{{1,3,4},{2},{5},{6},{7}}=>{{1,3,4},{2},{5},{6},{7}}=>{{1,3,4},{2},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}}=>{{1,2,4},{3},{5},{6},{7}}=>{{1,2,4},{3},{5},{6},{7}}=>{{1,2,4},{3},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>{{1,2,3,4},{5,7},{6}}=>{{1,4},{2,3},{5},{6},{7}}=>{{1,3},{2,4},{5},{6},{7}}=>{{1,4},{2,3},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,4},{2},{3},{5},{6},{7}}=>{{1,4},{2},{3},{5},{6},{7}}=>{{1,4},{2},{3},{5},{6},{7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,3,4},{6},{7}}=>{{1,2,3},{4,7},{5},{6}}=>{{1,2,3},{4,7},{5},{6}}=>{{1,2,3},{4,7},{5},{6}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,3,4},{6,7}}=>{{1,3},{2},{4,7},{5},{6}}=>{{1,3},{2},{4,7},{5},{6}}=>{{1,3},{2},{4,7},{5},{6}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,3,4},{5},{7}}=>{{1,2},{3,4,7},{5},{6}}=>{{1,2},{3,4,7},{5},{6}}=>{{1,2},{3,4,7},{5},{6}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,3,4},{5},{6}}=>{{1},{2,3,4,7},{5},{6}}=>{{1},{2,3,4,7},{5},{6}}=>{{1},{2,3,4,7},{5},{6}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3,4},{5}}=>{{1},{2},{3,4,7},{5},{6}}=>{{1},{2},{3,4,7},{5},{6}}=>{{1},{2},{3,4,7},{5},{6}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3,4},{7}}=>{{1,2},{3},{4,7},{5},{6}}=>{{1,2},{3},{4,7},{5},{6}}=>{{1,2},{3},{4,7},{5},{6}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,3,4},{5,6}}=>{{1},{2,4,7},{3},{5},{6}}=>{{1},{2,4,7},{3},{5},{6}}=>{{1},{2,4,7},{3},{5},{6}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3,4},{6}}=>{{1},{2,3},{4,7},{5},{6}}=>{{1},{2,3},{4,7},{5},{6}}=>{{1},{2,3},{4,7},{5},{6}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3,4}}=>{{1},{2},{3},{4,7},{5},{6}}=>{{1},{2},{3},{4,7},{5},{6}}=>{{1},{2},{3},{4,7},{5},{6}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3,4},{6},{7}}=>{{1,2,3},{4,6},{5},{7}}=>{{1,2,3},{4,6},{5},{7}}=>{{1,2,3},{4,6},{5},{7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3,4},{6,7}}=>{{1,3},{2},{4,6},{5},{7}}=>{{1,3},{2},{4,6},{5},{7}}=>{{1,3},{2},{4,6},{5},{7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3,4},{7}}=>{{1,2},{3,7},{4,6},{5}}=>{{1,2},{3,6},{4,7},{5}}=>{{1,2},{3,7},{4,6},{5}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3,4},{6}}=>{{1},{2,3,7},{4,6},{5}}=>{{1},{2,3,6},{4,7},{5}}=>{{1},{2,3,7},{4,6},{5}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3,4}}=>{{1},{2},{3,7},{4,6},{5}}=>{{1},{2},{3,6},{4,7},{5}}=>{{1},{2},{3,7},{4,6},{5}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3,4},{5},{7}}=>{{1,2},{3,4,6},{5},{7}}=>{{1,2},{3,4,6},{5},{7}}=>{{1,2},{3,4,6},{5},{7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4},{5}}=>{{1},{2,7},{3,4,6},{5}}=>{{1},{2,4,7},{3,6},{5}}=>{{1},{2,7},{3,4,6},{5}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3,4},{5},{6}}=>{{1},{2,3,4,6},{5},{7}}=>{{1},{2,3,4,6},{5},{7}}=>{{1},{2,3,4,6},{5},{7}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4},{5}}=>{{1},{2},{3,4,6},{5},{7}}=>{{1},{2},{3,4,6},{5},{7}}=>{{1},{2},{3,4,6},{5},{7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3,4},{7}}=>{{1,2},{3},{4,6},{5},{7}}=>{{1,2},{3},{4,6},{5},{7}}=>{{1,2},{3},{4,6},{5},{7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3,4}}=>{{1},{2,7},{3},{4,6},{5}}=>{{1},{2,6},{3},{4,7},{5}}=>{{1},{2,7},{3},{4,6},{5}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3,4},{5,6}}=>{{1},{2,4,6},{3},{5},{7}}=>{{1},{2,4,6},{3},{5},{7}}=>{{1},{2,4,6},{3},{5},{7}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3,4},{6}}=>{{1},{2,3},{4,6},{5},{7}}=>{{1},{2,3},{4,6},{5},{7}}=>{{1},{2,3},{4,6},{5},{7}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3,4}}=>{{1},{2},{3},{4,6},{5},{7}}=>{{1},{2},{3},{4,6},{5},{7}}=>{{1},{2},{3},{4,6},{5},{7}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>{{1,2,3,5},{4},{6},{7}}=>{{1,2,3},{4,5},{6},{7}}=>{{1,2,3},{4,5},{6},{7}}=>{{1,2,3},{4,5},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>{{1,2,3,5},{4},{6,7}}=>{{1,3},{2},{4,5},{6},{7}}=>{{1,3},{2},{4,5},{6},{7}}=>{{1,3},{2},{4,5},{6},{7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,5},{4},{7}}=>{{1,2},{3,7},{4,5},{6}}=>{{1,2},{3,5},{4,7},{6}}=>{{1,2},{3,7},{4,5},{6}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,5},{4},{6}}=>{{1},{2,3,7},{4,5},{6}}=>{{1},{2,3,5},{4,7},{6}}=>{{1},{2,3,7},{4,5},{6}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,5},{4}}=>{{1},{2},{3,7},{4,5},{6}}=>{{1},{2},{3,5},{4,7},{6}}=>{{1},{2},{3,7},{4,5},{6}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,5},{4},{7}}=>{{1,2},{3,6},{4,5},{7}}=>{{1,2},{3,5},{4,6},{7}}=>{{1,2},{3,6},{4,5},{7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,5},{4}}=>{{1},{2,7},{3,6},{4,5}}=>{{1},{2,5},{3,6},{4,7}}=>{{1},{2,7},{3,6},{4,5}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,5},{4},{6}}=>{{1},{2,3,6},{4,5},{7}}=>{{1},{2,3,5},{4,6},{7}}=>{{1},{2,3,6},{4,5},{7}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,5},{4}}=>{{1},{2},{3,6},{4,5},{7}}=>{{1},{2},{3,5},{4,6},{7}}=>{{1},{2},{3,6},{4,5},{7}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4},{5},{7}}=>{{1,2},{3,4,5},{6},{7}}=>{{1,2},{3,4,5},{6},{7}}=>{{1,2},{3,4,5},{6},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4},{5}}=>{{1},{2,7},{3,4,5},{6}}=>{{1},{2,4,7},{3,5},{6}}=>{{1},{2,7},{3,4,5},{6}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4},{5}}=>{{1},{2,6},{3,4,5},{7}}=>{{1},{2,4,6},{3,5},{7}}=>{{1},{2,6},{3,4,5},{7}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5},{6}}=>{{1},{2,3,4,5},{6},{7}}=>{{1},{2,3,4,5},{6},{7}}=>{{1},{2,3,4,5},{6},{7}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4},{5}}=>{{1},{2},{3,4,5},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>{{1,2,3,5,6},{4},{7}}=>{{1,2},{3},{4,5},{6},{7}}=>{{1,2},{3},{4,5},{6},{7}}=>{{1,2},{3},{4,5},{6},{7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,5,6},{4}}=>{{1},{2,7},{3},{4,5},{6}}=>{{1},{2,5},{3},{4,7},{6}}=>{{1},{2,7},{3},{4,5},{6}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,5,6},{4}}=>{{1},{2,6},{3},{4,5},{7}}=>{{1},{2,5},{3},{4,6},{7}}=>{{1},{2,6},{3},{4,5},{7}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5,6}}=>{{1},{2,4,5},{3},{6},{7}}=>{{1},{2,4,5},{3},{6},{7}}=>{{1},{2,4,5},{3},{6},{7}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>{{1,2,3,5,7},{4},{6}}=>{{1},{2,3},{4,5},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>{{1,2,3,5,6,7},{4}}=>{{1},{2},{3},{4,5},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>{{1,3},{2},{4},{5},{6},{7}}=>{{1,3},{2},{4},{5},{6},{7}}=>{{1,3},{2},{4},{5},{6},{7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,4,5},{7}}=>{{1,2},{3,7},{4},{5},{6}}=>{{1,2},{3,7},{4},{5},{6}}=>{{1,2},{3,7},{4},{5},{6}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,4,5},{6}}=>{{1},{2,3,7},{4},{5},{6}}=>{{1},{2,3,7},{4},{5},{6}}=>{{1},{2,3,7},{4},{5},{6}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,4,5}}=>{{1},{2},{3,7},{4},{5},{6}}=>{{1},{2},{3,7},{4},{5},{6}}=>{{1},{2},{3,7},{4},{5},{6}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,4,5},{7}}=>{{1,2},{3,6},{4},{5},{7}}=>{{1,2},{3,6},{4},{5},{7}}=>{{1,2},{3,6},{4},{5},{7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4,5}}=>{{1},{2,7},{3,6},{4},{5}}=>{{1},{2,6},{3,7},{4},{5}}=>{{1},{2,7},{3,6},{4},{5}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,4,5},{6}}=>{{1},{2,3,6},{4},{5},{7}}=>{{1},{2,3,6},{4},{5},{7}}=>{{1},{2,3,6},{4},{5},{7}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4,5}}=>{{1},{2},{3,6},{4},{5},{7}}=>{{1},{2},{3,6},{4},{5},{7}}=>{{1},{2},{3,6},{4},{5},{7}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4,5},{7}}=>{{1,2},{3,5},{4},{6},{7}}=>{{1,2},{3,5},{4},{6},{7}}=>{{1,2},{3,5},{4},{6},{7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4,5}}=>{{1},{2,7},{3,5},{4},{6}}=>{{1},{2,5},{3,7},{4},{6}}=>{{1},{2,7},{3,5},{4},{6}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4,5}}=>{{1},{2,6},{3,5},{4},{7}}=>{{1},{2,5},{3,6},{4},{7}}=>{{1},{2,6},{3,5},{4},{7}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4,5},{6}}=>{{1},{2,3,5},{4},{6},{7}}=>{{1},{2,3,5},{4},{6},{7}}=>{{1},{2,3,5},{4},{6},{7}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4,5}}=>{{1},{2},{3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4},{6},{7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>{{1,2,3,4,6},{5},{7}}=>{{1,2},{3,4},{5},{6},{7}}=>{{1,2},{3,4},{5},{6},{7}}=>{{1,2},{3,4},{5},{6},{7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,6},{5}}=>{{1},{2,7},{3,4},{5},{6}}=>{{1},{2,4},{3,7},{5},{6}}=>{{1},{2,7},{3,4},{5},{6}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,6},{5}}=>{{1},{2,6},{3,4},{5},{7}}=>{{1},{2,4},{3,6},{5},{7}}=>{{1},{2,6},{3,4},{5},{7}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,6},{5}}=>{{1},{2,5},{3,4},{6},{7}}=>{{1},{2,4},{3,5},{6},{7}}=>{{1},{2,5},{3,4},{6},{7}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5},{6}}=>{{1},{2,3,4},{5},{6},{7}}=>{{1},{2,3,4},{5},{6},{7}}=>{{1},{2,3,4},{5},{6},{7}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>{{1,2,3,4,6,7},{5}}=>{{1},{2},{3,4},{5},{6},{7}}=>{{1},{2},{3,4},{5},{6},{7}}=>{{1},{2},{3,4},{5},{6},{7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}}=>{{1,2},{3},{4},{5},{6},{7}}=>{{1,2},{3},{4},{5},{6},{7}}=>{{1,2},{3},{4},{5},{6},{7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}}=>{{1},{2,7},{3},{4},{5},{6}}=>{{1},{2,7},{3},{4},{5},{6}}=>{{1},{2,7},{3},{4},{5},{6}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,5,6}}=>{{1},{2,6},{3},{4},{5},{7}}=>{{1},{2,6},{3},{4},{5},{7}}=>{{1},{2,6},{3},{4},{5},{7}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,5,6}}=>{{1},{2,5},{3},{4},{6},{7}}=>{{1},{2,5},{3},{4},{6},{7}}=>{{1},{2,5},{3},{4},{6},{7}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5,6}}=>{{1},{2,4},{3},{5},{6},{7}}=>{{1},{2,4},{3},{5},{6},{7}}=>{{1},{2,4},{3},{5},{6},{7}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,7},{6}}=>{{1},{2,3},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}}=>{{1},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7}}
[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}}=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8}}=>{{1,3,4,5,6,7,8},{2}}=>{{1,3,4,5,6,7,8},{2}}=>{{1,3,4,5,6,7,8},{2}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6,7},{8}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2,4,5,6,7,8},{3}}=>{{1,2,4,5,6,7,8},{3}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8}}=>{{1,4,5,6,7,8},{2},{3}}=>{{1,4,5,6,7,8},{2},{3}}=>{{1,4,5,6,7,8},{2},{3}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1,3,5,6,7,8},{2},{4}}=>{{1,3,5,6,7,8},{2},{4}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1,5,6,7,8},{2},{3},{4}}=>{{1,5,6,7,8},{2},{3},{4}}=>{{1,5,6,7,8},{2},{3},{4}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7},{8}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,4,6,7,8},{5}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2,4,6,7,8},{3},{5}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2},{3},{4,8},{5,7},{6}}=>{{1,6,7,8},{2,5},{3,4}}=>{{1,4},{2,5},{3,6,7,8}}=>{{1,6,7,8},{2,5},{3,4}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8}}=>{{1,6,7,8},{2},{3},{4},{5}}=>{{1,6,7,8},{2},{3},{4},{5}}=>{{1,6,7,8},{2},{3},{4},{5}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8}}=>{{1,7,8},{2},{3},{4},{5},{6}}=>{{1,7,8},{2},{3},{4},{5},{6}}=>{{1,7,8},{2},{3},{4},{5},{6}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7},{8}}=>{{1,2,3,4,5,6,8},{7}}=>{{1,2,3,4,5,6,8},{7}}=>{{1,2,3,4,5,6,8},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2,4,5,6,8},{3},{7}}=>{{1,2,4,5,6,8},{3},{7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4,6,8},{5},{7}}=>{{1,2,3,4,6,8},{5},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2,4,6,8},{3},{5},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1,4,6,8},{2},{3},{5},{7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6},{7},{8}}=>{{1,2,3,4,5,8},{6,7}}=>{{1,2,3,4,5,7},{6,8}}=>{{1,2,3,4,5,8},{6,7}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1},{2,4},{3},{5,8},{6,7}}=>{{1,5,8},{2,4},{3},{6,7}}=>{{1,4},{2,5,7},{3},{6,8}}=>{{1,5,8},{2,4},{3},{6,7}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>{{1},{2,4,6,8},{3},{5},{7}}=>{{1,8},{2,3},{4,5},{6,7}}=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7},{8}}=>{{1,2,3,4,5,8},{6},{7}}=>{{1,2,3,4,5,8},{6},{7}}=>{{1,2,3,4,5,8},{6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7},{8}}=>{{1,2,3,4,8},{5},{6},{7}}=>{{1,2,3,4,8},{5},{6},{7}}=>{{1,2,3,4,8},{5},{6},{7}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}}=>{{1,2,8},{3},{4},{5},{6},{7}}=>{{1,2,8},{3},{4},{5},{6},{7}}=>{{1,2,8},{3},{4},{5},{6},{7}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>{{1,8},{2},{3},{4},{5},{6},{7}}=>{{1,8},{2},{3},{4},{5},{6},{7}}=>{{1,8},{2},{3},{4},{5},{6},{7}}
[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}}=>{{1,2,3,4,5,6,7},{8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8}}=>{{1,2,3,4,5,7},{6},{8}}=>{{1,2,3,4,5,7},{6},{8}}=>{{1,2,3,4,5,7},{6},{8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>{{1,2},{3,4},{5,8},{6},{7}}=>{{1,5,7},{2,3,4},{6},{8}}=>{{1,3,5,7},{2,4},{6},{8}}=>{{1,5,7},{2,3,4},{6},{8}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,5,7},{2},{3},{4},{6},{8}}=>{{1,5,7},{2},{3},{4},{6},{8}}=>{{1,5,7},{2},{3},{4},{6},{8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>{{1,2},{3,6},{4},{5},{7,8}}=>{{1,3,7},{2},{4,5,6},{8}}=>{{1,3,5,7},{2},{4,6},{8}}=>{{1,3,7},{2},{4,5,6},{8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,6},{4,5},{7,8}}=>{{1,3,7},{2},{4,6},{5},{8}}=>{{1,3,6},{2},{4,7},{5},{8}}=>{{1,3,7},{2},{4,6},{5},{8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,8},{4,5},{6,7}}=>{{1,7},{2,4,6},{3},{5},{8}}=>{{1,4,7},{2,6},{3},{5},{8}}=>{{1,7},{2,4,6},{3},{5},{8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,3,7},{2},{4},{5},{6},{8}}=>{{1,3,7},{2},{4},{5},{6},{8}}=>{{1,3,7},{2},{4},{5},{6},{8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,8},{4,7},{5,6}}=>{{1,7},{2,6},{3,5},{4},{8}}=>{{1,5},{2,6},{3,7},{4},{8}}=>{{1,7},{2,6},{3,5},{4},{8}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,7},{2},{3},{4},{5},{6},{8}}=>{{1,7},{2},{3},{4},{5},{6},{8}}=>{{1,7},{2},{3},{4},{5},{6},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6},{7},{8}}=>{{1,2,3,4,5,6},{7,8}}=>{{1,2,3,4,5,6},{7,8}}=>{{1,2,3,4,5,6},{7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>{{1,3},{2},{4},{5,7},{6},{8}}=>{{1,2,5,6},{3,4},{7,8}}=>{{1,2,4},{3,5,6},{7,8}}=>{{1,2,5,6},{3,4},{7,8}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,3},{2},{4,5},{6},{7},{8}}=>{{1,2,3,4,6},{5},{7,8}}=>{{1,2,3,4,6},{5},{7,8}}=>{{1,2,3,4,6},{5},{7,8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,3},{2},{4,5},{6,7},{8}}=>{{1,2,4,6},{3},{5},{7,8}}=>{{1,2,4,6},{3},{5},{7,8}}=>{{1,2,4,6},{3},{5},{7,8}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>{{1,3},{2},{4,6},{5},{7},{8}}=>{{1,2,3,6},{4,5},{7,8}}=>{{1,2,3,5},{4,6},{7,8}}=>{{1,2,3,6},{4,5},{7,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>{{1,3},{2},{4,7},{5},{6},{8}}=>{{1,2,6},{3,4,5},{7,8}}=>{{1,2,4,6},{3,5},{7,8}}=>{{1,2,6},{3,4,5},{7,8}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,3},{2},{4,5,6},{7},{8}}=>{{1,2,3,6},{4},{5},{7,8}}=>{{1,2,3,6},{4},{5},{7,8}}=>{{1,2,3,6},{4},{5},{7,8}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,3},{2},{4,5,6,7,8}}=>{{1,6},{2},{3},{4},{5},{7,8}}=>{{1,6},{2},{3},{4},{5},{7,8}}=>{{1,6},{2},{3},{4},{5},{7,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6},{7},{8}}=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>{{1,4},{2},{3},{5,6},{7},{8}}=>{{1,2,3,5},{4},{6,7,8}}=>{{1,2,3,5},{4},{6,7,8}}=>{{1,2,3,5},{4},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,4},{2},{3},{5,6},{7,8}}=>{{1,3,5},{2},{4},{6,7,8}}=>{{1,3,5},{2},{4},{6,7,8}}=>{{1,3,5},{2},{4},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>{{1,4},{2},{3},{5,6,7},{8}}=>{{1,2,5},{3},{4},{6,7,8}}=>{{1,2,5},{3},{4},{6,7,8}}=>{{1,2,5},{3},{4},{6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>{{1,5},{2},{3},{4},{6},{7},{8}}=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>{{1,5},{2},{3},{4},{6,7},{8}}=>{{1,2,4},{3},{5,6,7,8}}=>{{1,2,4},{3},{5,6,7,8}}=>{{1,2,4},{3},{5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>{{1,5},{2},{3},{4},{6,8},{7}}=>{{1,4},{2,3},{5,6,7,8}}=>{{1,3},{2,4},{5,6,7,8}}=>{{1,4},{2,3},{5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>{{1,6},{2},{3},{4},{5},{7},{8}}=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>{{1,6},{2},{3},{4},{5},{7,8}}=>{{1,3},{2},{4,5,6,7,8}}=>{{1,3},{2},{4,5,6,7,8}}=>{{1,3},{2},{4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>{{1,7},{2},{3},{4},{5},{6},{8}}=>{{1,2},{3,4,5,6,7,8}}=>{{1,2},{3,4,5,6,7,8}}=>{{1,2},{3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,8},{2},{3},{4},{5},{6},{7}}=>{{1},{2,3,4,5,6,7,8}}=>{{1},{2,3,4,5,6,7,8}}=>{{1},{2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,7,8},{2},{3},{4},{5},{6}}=>{{1},{2},{3,4,5,6,7,8}}=>{{1},{2},{3,4,5,6,7,8}}=>{{1},{2},{3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,6,7,8},{2},{3},{4},{5}}=>{{1},{2},{3},{4,5,6,7,8}}=>{{1},{2},{3},{4,5,6,7,8}}=>{{1},{2},{3},{4,5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,5,6,7,8},{2},{3},{4}}=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1},{2},{3},{4},{5,6,7,8}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>{{1,6,7,8},{2},{3},{4,5}}=>{{1},{2},{3},{4,6,7,8},{5}}=>{{1},{2},{3},{4,6,7,8},{5}}=>{{1},{2},{3},{4,6,7,8},{5}}
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1},{2,3},{4,5},{6,7,8}}=>{{1},{2,3},{4,5},{6,7,8}}=>{{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>{{1,4,7,8},{2},{3},{5,6}}=>{{1},{2},{3,5},{4},{6,7,8}}=>{{1},{2},{3,5},{4},{6,7,8}}=>{{1},{2},{3,5},{4},{6,7,8}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,4,5,6,7,8},{2},{3}}=>{{1},{2},{3},{4},{5},{6,7,8}}=>{{1},{2},{3},{4},{5},{6,7,8}}=>{{1},{2},{3},{4},{5},{6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>{{1,3,5},{2},{4},{6,7,8}}=>{{1,4},{2},{3},{5,6},{7,8}}=>{{1,4},{2},{3},{5,6},{7,8}}=>{{1,4},{2},{3},{5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1,3,5,6,7,8},{2},{4}}=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1},{2},{3},{4},{5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>{{1,3,7},{2},{4,5,6},{8}}=>{{1,2},{3,6},{4},{5},{7,8}}=>{{1,2},{3,6},{4},{5},{7,8}}=>{{1,2},{3,6},{4},{5},{7,8}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,3,4,5,6,7,8},{2}}=>{{1},{2},{3},{4},{5},{6},{7,8}}=>{{1},{2},{3},{4},{5},{6},{7,8}}=>{{1},{2},{3},{4},{5},{6},{7,8}}
[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}}=>{{1,2,3,4,5,6},{7},{8}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7},{8}}=>{{1,2,3,4,6},{5},{7},{8}}=>{{1,2,3,4,6},{5},{7},{8}}=>{{1,2,3,4,6},{5},{7},{8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,4,6},{3},{5},{7},{8}}=>{{1,2,4,6},{3},{5},{7},{8}}=>{{1,2,4,6},{3},{5},{7},{8}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,6},{2},{3},{4},{5},{7},{8}}=>{{1,6},{2},{3},{4},{5},{7},{8}}=>{{1,6},{2},{3},{4},{5},{7},{8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,4},{2,3},{5},{6},{7},{8}}=>{{1,2,3,4,5},{6,8},{7}}=>{{1,2,3,4,5},{6,8},{7}}=>{{1,2,3,4,5},{6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6},{7,8}}=>{{1,3,5},{2},{4},{6,8},{7}}=>{{1,3,5},{2},{4},{6,8},{7}}=>{{1,3,5},{2},{4},{6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>{{1,4},{2,3},{5,6,7,8}}=>{{1,5},{2},{3},{4},{6,8},{7}}=>{{1,5},{2},{3},{4},{6,8},{7}}=>{{1,5},{2},{3},{4},{6,8},{7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,3},{4,5},{7,8}}=>{{1,3},{2},{4,6,8},{5},{7}}=>{{1,3},{2},{4,6,8},{5},{7}}=>{{1,3},{2},{4,6,8},{5},{7}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,8},{2,3},{4,5},{6,7}}=>{{1},{2,4,6,8},{3},{5},{7}}=>{{1},{2,4,6,8},{3},{5},{7}}=>{{1},{2,4,6,8},{3},{5},{7}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,4},{3},{5,6,7,8}}=>{{1,5},{2},{3},{4},{6,7},{8}}=>{{1,5},{2},{3},{4},{6,7},{8}}=>{{1,5},{2},{3},{4},{6,7},{8}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>{{1,5},{2,4},{3},{6},{7},{8}}=>{{1,2,3,4},{5,8},{6,7}}=>{{1,2,3,4},{5,7},{6,8}}=>{{1,2,3,4},{5,8},{6,7}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>{{1,2,5},{3},{4},{6,7,8}}=>{{1,4},{2},{3},{5,6,7},{8}}=>{{1,4},{2},{3},{5,6,7},{8}}=>{{1,4},{2},{3},{5,6,7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>{{1,2,8},{3},{4},{5},{6},{7}}=>{{1},{2,3,4,5,6,7},{8}}=>{{1},{2,3,4,5,6,7},{8}}=>{{1},{2,3,4,5,6,7},{8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>{{1,2,4,6},{3},{5},{7},{8}}=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>{{1,2,4,6},{3},{5},{7,8}}=>{{1,3},{2},{4,5},{6,7},{8}}=>{{1,3},{2},{4,5},{6,7},{8}}=>{{1,3},{2},{4,5},{6,7},{8}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>{{1,2,4,6,8},{3},{5},{7}}=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>{{1,2,4,6,7,8},{3},{5}}=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>{{1,2,4,5,6,8},{3},{7}}=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1},{2,3},{4},{5},{6,7},{8}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,4,5,6,7,8},{3}}=>{{1},{2},{3},{4},{5},{6,7},{8}}=>{{1},{2},{3},{4},{5},{6,7},{8}}=>{{1},{2},{3},{4},{5},{6,7},{8}}
[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}}=>{{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,3,5},{2},{4},{6},{7},{8}}=>{{1,3,5},{2},{4},{6},{7},{8}}=>{{1,3,5},{2},{4},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>{{1,2,3,4},{5,8},{6,7}}=>{{1,5},{2,4},{3},{6},{7},{8}}=>{{1,4},{2,5},{3},{6},{7},{8}}=>{{1,5},{2,4},{3},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,5},{2},{3},{4},{6},{7},{8}}=>{{1,5},{2},{3},{4},{6},{7},{8}}=>{{1,5},{2},{3},{4},{6},{7},{8}}
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>{{1,5},{2,3,4},{6,7,8}}=>{{1,4},{2},{3},{5,8},{6},{7}}=>{{1,4},{2},{3},{5,8},{6},{7}}=>{{1,4},{2},{3},{5,8},{6},{7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>{{1,5,7},{2,3,4},{6},{8}}=>{{1,2},{3,4},{5,8},{6},{7}}=>{{1,2},{3,4},{5,8},{6},{7}}=>{{1,2},{3,4},{5,8},{6},{7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,5},{3,4},{7,8}}=>{{1,3},{2},{4,8},{5,7},{6}}=>{{1,3},{2},{4,7},{5,8},{6}}=>{{1,3},{2},{4,8},{5,7},{6}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>{{1,6,7,8},{2,5},{3,4}}=>{{1},{2},{3},{4,8},{5,7},{6}}=>{{1},{2},{3},{4,7},{5,8},{6}}=>{{1},{2},{3},{4,8},{5,7},{6}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>{{1,2,5,6},{3,4},{7,8}}=>{{1,3},{2},{4},{5,7},{6},{8}}=>{{1,3},{2},{4},{5,7},{6},{8}}=>{{1,3},{2},{4},{5,7},{6},{8}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,5},{4},{6,7,8}}=>{{1,4},{2},{3},{5,6},{7},{8}}=>{{1,4},{2},{3},{5,6},{7},{8}}=>{{1,4},{2},{3},{5,6},{7},{8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>{{1,2,3,6},{4},{5},{7,8}}=>{{1,3},{2},{4,5,6},{7},{8}}=>{{1,3},{2},{4,5,6},{7},{8}}=>{{1,3},{2},{4,5,6},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7},{8}}=>{{1,2,3,4},{5},{6},{7},{8}}=>{{1,2,3,4},{5},{6},{7},{8}}=>{{1,2,3,4},{5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>{{1,2,3,4,5},{6,8},{7}}=>{{1,4},{2,3},{5},{6},{7},{8}}=>{{1,3},{2,4},{5},{6},{7},{8}}=>{{1,4},{2,3},{5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,4},{2},{3},{5},{6},{7},{8}}=>{{1,4},{2},{3},{5},{6},{7},{8}}=>{{1,4},{2},{3},{5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>{{1,2,6},{3,4,5},{7,8}}=>{{1,3},{2},{4,7},{5},{6},{8}}=>{{1,3},{2},{4,7},{5},{6},{8}}=>{{1,3},{2},{4,7},{5},{6},{8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>{{1,2,3,6},{4,5},{7,8}}=>{{1,3},{2},{4,6},{5},{7},{8}}=>{{1,3},{2},{4,6},{5},{7},{8}}=>{{1,3},{2},{4,6},{5},{7},{8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,6},{4,5}}=>{{1},{2,8},{3,7},{4,6},{5}}=>{{1},{2,6},{3,7},{4,8},{5}}=>{{1},{2,8},{3,7},{4,6},{5}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,6},{5},{7},{8}}=>{{1,2,3},{4,5},{6},{7},{8}}=>{{1,2,3},{4,5},{6},{7},{8}}=>{{1,2,3},{4,5},{6},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,6},{5},{7,8}}=>{{1,3},{2},{4,5},{6},{7},{8}}=>{{1,3},{2},{4,5},{6},{7},{8}}=>{{1,3},{2},{4,5},{6},{7},{8}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>{{1,2,3,4,8},{5},{6},{7}}=>{{1},{2,3,4,5},{6},{7},{8}}=>{{1},{2,3,4,5},{6},{7},{8}}=>{{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>{{1,2,3,4,6,8},{5},{7}}=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,6,7,8},{5}}=>{{1},{2},{3},{4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5},{6},{7},{8}}
[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}}=>{{1,2,3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>{{1,3},{2},{4},{5},{6},{7},{8}}=>{{1,3},{2},{4},{5},{6},{7},{8}}=>{{1,3},{2},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,7},{6},{8}}=>{{1,2},{3,4},{5},{6},{7},{8}}=>{{1,2},{3,4},{5},{6},{7},{8}}=>{{1,2},{3,4},{5},{6},{7},{8}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,8},{6},{7}}=>{{1},{2,3,4},{5},{6},{7},{8}}=>{{1},{2,3,4},{5},{6},{7},{8}}=>{{1},{2,3,4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7},{8}}=>{{1,2},{3},{4},{5},{6},{7},{8}}=>{{1,2},{3},{4},{5},{6},{7},{8}}=>{{1,2},{3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,8},{6,7}}=>{{1},{2,4},{3},{5},{6},{7},{8}}=>{{1},{2,4},{3},{5},{6},{7},{8}}=>{{1},{2,4},{3},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,8},{7}}=>{{1},{2,3},{4},{5},{6},{7},{8}}=>{{1},{2,3},{4},{5},{6},{7},{8}}=>{{1},{2,3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{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},{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]=>{{1,2,3,4,5,6,7,8},{9}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8,9}}=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>{{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}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
[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}}=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8,9}}=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}
[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}}=>{{1,2,3},{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},{2},{3,4,5,6,7,8,9}}=>{{1,8,9},{2},{3},{4},{5},{6},{7}}=>{{1,8,9},{2},{3},{4},{5},{6},{7}}=>{{1,8,9},{2},{3},{4},{5},{6},{7}}
[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}}=>{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}=>{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}=>{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}
[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}}=>{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}=>{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}=>{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9,10}}=>{{1,9,10},{2},{3},{4},{5},{6},{7},{8}}=>{{1,9,10},{2},{3},{4},{5},{6},{7},{8}}=>{{1,9,10},{2},{3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}=>{{1},{2,3,4,5,6,7,8,9}}=>{{1},{2,3,4,5,6,7,8,9}}=>{{1},{2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,8,9},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1},{2},{3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,7,8,9},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4,5,6,7,8,9}}=>{{1},{2},{3},{4,5,6,7,8,9}}=>{{1},{2},{3},{4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,6,7,8,9},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5,6,7,8,9}}=>{{1},{2},{3},{4},{5,6,7,8,9}}=>{{1},{2},{3},{4},{5,6,7,8,9}}
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,5,6,7,8,9},{2},{3},{4}}=>{{1},{2},{3},{4},{5},{6,7,8,9}}=>{{1},{2},{3},{4},{5},{6,7,8,9}}=>{{1},{2},{3},{4},{5},{6,7,8,9}}
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,4,5,6,7,8,9},{2},{3}}=>{{1},{2},{3},{4},{5},{6},{7,8,9}}=>{{1},{2},{3},{4},{5},{6},{7,8,9}}=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,3,4,5,6,7,8,9},{2}}=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}=>{{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]=>{{1,2,3,4,5,6,7,9},{8}}=>{{1},{2,3},{4},{5},{6},{7},{8},{9}}=>{{1},{2,3},{4},{5},{6},{7},{8},{9}}=>{{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{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},{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},{2},{3},{4},{5},{6},{7},{8},{9}}=>{{1,2,3,4,5,6,7,8,9}}=>{{1,2,3,4,5,6,7,8,9}}=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}=>{{1,3,4,5,6,7,8,9},{2}}=>{{1,3,4,5,6,7,8,9},{2}}=>{{1,3,4,5,6,7,8,9},{2}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}=>{{1,3,4,5,6,7,8,9,10},{2}}=>{{1,3,4,5,6,7,8,9,10},{2}}=>{{1,3,4,5,6,7,8,9,10},{2}}
[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}}=>{{1,4,5,6,7,8,9},{2},{3}}=>{{1,4,5,6,7,8,9},{2},{3}}=>{{1,4,5,6,7,8,9},{2},{3}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}=>{{1},{2,3,4,5,6,7,8,9,10}}=>{{1},{2,3,4,5,6,7,8,9,10}}=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}=>{{1,4,5,6,7,8,9,10},{2},{3}}=>{{1,4,5,6,7,8,9,10},{2},{3}}=>{{1,4,5,6,7,8,9,10},{2},{3}}
[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}}=>{{1,5,6,7,8,9},{2},{3},{4}}=>{{1,5,6,7,8,9},{2},{3},{4}}=>{{1,5,6,7,8,9},{2},{3},{4}}
[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}}=>{{1,5,6,7,8,9,10},{2},{3},{4}}=>{{1,5,6,7,8,9,10},{2},{3},{4}}=>{{1,5,6,7,8,9,10},{2},{3},{4}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8,9}}=>{{1,6,7,8,9},{2},{3},{4},{5}}=>{{1,6,7,8,9},{2},{3},{4},{5}}=>{{1,6,7,8,9},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}=>{{1,6,7,8,9,10},{2},{3},{4},{5}}=>{{1,6,7,8,9,10},{2},{3},{4},{5}}=>{{1,6,7,8,9,10},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8,9}}=>{{1,7,8,9},{2},{3},{4},{5},{6}}=>{{1,7,8,9},{2},{3},{4},{5},{6}}=>{{1,7,8,9},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}=>{{1,7,8,9,10},{2},{3},{4},{5},{6}}=>{{1,7,8,9,10},{2},{3},{4},{5},{6}}=>{{1,7,8,9,10},{2},{3},{4},{5},{6}}
[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}}=>{{1,2,3,4,5,6,7,9},{8}}=>{{1,2,3,4,5,6,7,9},{8}}=>{{1,2,3,4,5,6,7,9},{8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{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}}=>{{1,2,3,4,5,6,7,8},{9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7},{8},{9}}=>{{1,2,3,4,5,6,7},{8},{9}}=>{{1,2,3,4,5,6,7},{8},{9}}=>{{1,2,3,4,5,6,7},{8},{9}}
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8,9}}=>{{1,7},{2},{3},{4},{5},{6},{8},{9}}=>{{1,7},{2},{3},{4},{5},{6},{8},{9}}=>{{1,7},{2},{3},{4},{5},{6},{8},{9}}
[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}}=>{{1,6},{2},{3},{4},{5},{7},{8},{9}}=>{{1,6},{2},{3},{4},{5},{7},{8},{9}}=>{{1,6},{2},{3},{4},{5},{7},{8},{9}}
[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}}=>{{1,5},{2},{3},{4},{6},{7},{8},{9}}=>{{1,5},{2},{3},{4},{6},{7},{8},{9}}=>{{1,5},{2},{3},{4},{6},{7},{8},{9}}
[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}}=>{{1,4},{2},{3},{5},{6},{7},{8},{9}}=>{{1,4},{2},{3},{5},{6},{7},{8},{9}}=>{{1,4},{2},{3},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8,9,10}}=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}
[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}}=>{{1,2,3,4,5,6,7,8,9},{10}}
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8,9,10}}=>{{1,8},{2},{3},{4},{5},{6},{7},{9},{10}}=>{{1,8},{2},{3},{4},{5},{6},{7},{9},{10}}=>{{1,8},{2},{3},{4},{5},{6},{7},{9},{10}}
[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}}=>{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}}=>{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}}=>{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}}
[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}}=>{{1,6},{2},{3},{4},{5},{7},{8},{9},{10}}=>{{1,6},{2},{3},{4},{5},{7},{8},{9},{10}}=>{{1,6},{2},{3},{4},{5},{7},{8},{9},{10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4,5,6},{7,8,9,10}}=>{{1,5},{2},{3},{4},{6},{7},{8},{9},{10}}=>{{1,5},{2},{3},{4},{6},{7},{8},{9},{10}}=>{{1,5},{2},{3},{4},{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]=>{{1,2,3,4,5,6,7},{8,9,10}}=>{{1,4},{2},{3},{5},{6},{7},{8},{9},{10}}=>{{1,4},{2},{3},{5},{6},{7},{8},{9},{10}}=>{{1,4},{2},{3},{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]=>{{1,2,3,4,5,6,7,8,9,10}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7},{8,9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6},{7},{8},{9}}=>{{1,2,3,4,5,6},{7,8,9}}=>{{1,2,3,4,5,6},{7,8,9}}=>{{1,2,3,4,5,6},{7,8,9}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,5},{2},{3},{4},{6},{7},{8},{9}}=>{{1,2,3,4,5},{6,7,8,9}}=>{{1,2,3,4,5},{6,7,8,9}}=>{{1,2,3,4,5},{6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>{{1,6},{2},{3},{4},{5},{7},{8},{9}}=>{{1,2,3,4},{5,6,7,8,9}}=>{{1,2,3,4},{5,6,7,8,9}}=>{{1,2,3,4},{5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>{{1,7},{2},{3},{4},{5},{6},{8},{9}}=>{{1,2,3},{4,5,6,7,8,9}}=>{{1,2,3},{4,5,6,7,8,9}}=>{{1,2,3},{4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}=>{{1,2},{3,4,5,6,7,8,9}}=>{{1,2},{3,4,5,6,7,8,9}}=>{{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}=>{{1,2,3,4,5,6,7,8},{9,10}}=>{{1,2,3,4,5,6,7,8},{9,10}}=>{{1,2,3,4,5,6,7,8},{9,10}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6},{7},{8},{9},{10}}=>{{1,2,3,4,5,6,7},{8,9,10}}=>{{1,2,3,4,5,6,7},{8,9,10}}=>{{1,2,3,4,5,6,7},{8,9,10}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,5},{2},{3},{4},{6},{7},{8},{9},{10}}=>{{1,2,3,4,5,6},{7,8,9,10}}=>{{1,2,3,4,5,6},{7,8,9,10}}=>{{1,2,3,4,5,6},{7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,6},{2},{3},{4},{5},{7},{8},{9},{10}}=>{{1,2,3,4,5},{6,7,8,9,10}}=>{{1,2,3,4,5},{6,7,8,9,10}}=>{{1,2,3,4,5},{6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}}=>{{1,2,3,4},{5,6,7,8,9,10}}=>{{1,2,3,4},{5,6,7,8,9,10}}=>{{1,2,3,4},{5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>{{1,8},{2},{3},{4},{5},{6},{7},{9},{10}}=>{{1,2,3},{4,5,6,7,8,9,10}}=>{{1,2,3},{4,5,6,7,8,9,10}}=>{{1,2,3},{4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}=>{{1,2},{3,4,5,6,7,8,9,10}}=>{{1,2},{3,4,5,6,7,8,9,10}}=>{{1,2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,9,10},{2},{3},{4},{5},{6},{7},{8}}=>{{1},{2},{3,4,5,6,7,8,9,10}}=>{{1},{2},{3,4,5,6,7,8,9,10}}=>{{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{1,3,4,5,6,7,8,9,10},{2}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4,5,6,7,8,9,10}}=>{{1},{2},{3},{4,5,6,7,8,9,10}}=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,4,5,6,7,8,9,10},{2},{3}}=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,5,6,7,8,9,10},{2},{3},{4}}=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,6,7,8,9,10},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,7,8,9,10},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5,6,7,8,9,10}}=>{{1},{2},{3},{4},{5,6,7,8,9,10}}=>{{1},{2},{3},{4},{5,6,7,8,9,10}}
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
conjugate
Description
The conjugate of a set partition.
This is an involution exchanging singletons and circular adjacencies due to [1].
This is an involution exchanging singletons and circular adjacencies due to [1].
Map
Kasraoui-Zeng
Description
The Kasraoui-Zeng involution.
This is defined in [1] and yields the set partition with the number of nestings and crossings exchanged.
This is defined in [1] and yields the set partition with the number of nestings and crossings exchanged.
Map
Wachs-White-rho
Description
A transformation of set partitions due to Wachs and White.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection $\rho$.
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with $(i,j)$ to the cell in the $i$-th column from the right and the $j$-th row from the top.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection $\rho$.
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with $(i,j)$ to the cell in the $i$-th column from the right and the $j$-th row from the top.
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