Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00217: Set partitions —Wachs-White-rho ⟶ Set partitions
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00217: Set partitions —Wachs-White-rho ⟶ Set partitions
Images
=>
Cc0005;cc-rep-0Cc0009;cc-rep-2Cc0009;cc-rep-3
[1,0]=>[1]=>{{1}}=>{{1}}
[1,0,1,0]=>[2,1]=>{{1,2}}=>{{1,2}}
[1,1,0,0]=>[1,2]=>{{1},{2}}=>{{1},{2}}
[1,0,1,0,1,0]=>[2,3,1]=>{{1,2,3}}=>{{1,2,3}}
[1,0,1,1,0,0]=>[2,1,3]=>{{1,2},{3}}=>{{1,2},{3}}
[1,1,0,0,1,0]=>[1,3,2]=>{{1},{2,3}}=>{{1},{2,3}}
[1,1,0,1,0,0]=>[3,1,2]=>{{1,3},{2}}=>{{1,3},{2}}
[1,1,1,0,0,0]=>[1,2,3]=>{{1},{2},{3}}=>{{1},{2},{3}}
[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>{{1,2,3,4}}=>{{1,2,3,4}}
[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>{{1,2,3},{4}}=>{{1,2,3},{4}}
[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>{{1,2},{3,4}}=>{{1,2},{3,4}}
[1,0,1,1,0,1,0,0]=>[2,4,1,3]=>{{1,2,4},{3}}=>{{1,2,4},{3}}
[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>{{1,2},{3},{4}}=>{{1,2},{3},{4}}
[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>{{1},{2,3,4}}=>{{1},{2,3,4}}
[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>{{1},{2,3},{4}}=>{{1},{2,3},{4}}
[1,1,0,1,0,0,1,0]=>[3,1,4,2]=>{{1,3,4},{2}}=>{{1,3,4},{2}}
[1,1,0,1,0,1,0,0]=>[3,4,1,2]=>{{1,3},{2,4}}=>{{1,4},{2,3}}
[1,1,0,1,1,0,0,0]=>[3,1,2,4]=>{{1,3},{2},{4}}=>{{1,3},{2},{4}}
[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>{{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}}
[1,1,1,0,1,0,0,0]=>[4,1,2,3]=>{{1,4},{2},{3}}=>{{1,4},{2},{3}}
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>{{1},{2},{3},{4}}=>{{1},{2},{3},{4}}
[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}}
[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>{{1,2,3,4},{5}}=>{{1,2,3,4},{5}}
[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>{{1,2,3},{4,5}}=>{{1,2,3},{4,5}}
[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>{{1,2,3,5},{4}}=>{{1,2,3,5},{4}}
[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}}=>{{1,2,3},{4},{5}}
[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>{{1,2},{3,4,5}}=>{{1,2},{3,4,5}}
[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}}=>{{1,2},{3,4},{5}}
[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>{{1,2,4,5},{3}}=>{{1,2,4,5},{3}}
[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>{{1,2,4},{3,5}}=>{{1,2,5},{3,4}}
[1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]=>{{1,2,4},{3},{5}}=>{{1,2,4},{3},{5}}
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}}=>{{1,2},{3},{4,5}}
[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>{{1,2},{3,5},{4}}=>{{1,2},{3,5},{4}}
[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>{{1,2,5},{3},{4}}=>{{1,2,5},{3},{4}}
[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}}=>{{1,2},{3},{4},{5}}
[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}=>{{1},{2,3,4,5}}
[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}=>{{1},{2,3,4},{5}}
[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}=>{{1},{2,3},{4,5}}
[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>{{1},{2,3,5},{4}}=>{{1},{2,3,5},{4}}
[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}=>{{1},{2,3},{4},{5}}
[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>{{1,3,4,5},{2}}=>{{1,3,4,5},{2}}
[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>{{1,3,4},{2},{5}}=>{{1,3,4},{2},{5}}
[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>{{1,3},{2,4,5}}=>{{1,4,5},{2,3}}
[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>{{1,3,5},{2,4}}=>{{1,5},{2,3,4}}
[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>{{1,3},{2,4},{5}}=>{{1,4},{2,3},{5}}
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>{{1,3},{2},{4,5}}=>{{1,3},{2},{4,5}}
[1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]=>{{1,3,5},{2},{4}}=>{{1,3,5},{2},{4}}
[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>{{1,3},{2,5},{4}}=>{{1,5},{2,3},{4}}
[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>{{1,3},{2},{4},{5}}=>{{1,3},{2},{4},{5}}
[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}=>{{1},{2},{3,4,5}}
[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}=>{{1},{2},{3,4},{5}}
[1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]=>{{1},{2,4,5},{3}}=>{{1},{2,4,5},{3}}
[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}=>{{1},{2,5},{3,4}}
[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>{{1},{2,4},{3},{5}}=>{{1},{2,4},{3},{5}}
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>{{1,4,5},{2},{3}}=>{{1,4,5},{2},{3}}
[1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]=>{{1,4},{2},{3,5}}=>{{1,5},{2},{3,4}}
[1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]=>{{1,4},{2,5},{3}}=>{{1,5},{2,4},{3}}
[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>{{1,4},{2},{3},{5}}=>{{1,4},{2},{3},{5}}
[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}=>{{1},{2},{3},{4,5}}
[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>{{1},{2},{3,5},{4}}=>{{1},{2},{3,5},{4}}
[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>{{1},{2,5},{3},{4}}=>{{1},{2,5},{3},{4}}
[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>{{1,5},{2},{3},{4}}=>{{1,5},{2},{3},{4}}
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}}
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4},{5,6}}
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,6},{5}}=>{{1,2,3,4,6},{5}}
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}}
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}=>{{1,2,3},{4,5,6}}
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}=>{{1,2,3},{4,5},{6}}
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>{{1,2,3,5,6},{4}}=>{{1,2,3,5,6},{4}}
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>{{1,2,3,5},{4,6}}=>{{1,2,3,6},{4,5}}
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>{{1,2,3,5},{4},{6}}=>{{1,2,3,5},{4},{6}}
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}=>{{1,2,3},{4},{5,6}}
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>{{1,2,3},{4,6},{5}}=>{{1,2,3},{4,6},{5}}
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>{{1,2,3,6},{4},{5}}=>{{1,2,3,6},{4},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}=>{{1,2,3},{4},{5},{6}}
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}=>{{1,2},{3,4,5,6}}
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}=>{{1,2},{3,4,5},{6}}
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}=>{{1,2},{3,4},{5,6}}
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>{{1,2},{3,4,6},{5}}=>{{1,2},{3,4,6},{5}}
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}=>{{1,2},{3,4},{5},{6}}
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>{{1,2,4,5,6},{3}}=>{{1,2,4,5,6},{3}}
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>{{1,2,4,5},{3},{6}}=>{{1,2,4,5},{3},{6}}
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>{{1,2,4},{3,5,6}}=>{{1,2,5,6},{3,4}}
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>{{1,2,4,6},{3,5}}=>{{1,2,6},{3,4,5}}
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>{{1,2,4},{3,5},{6}}=>{{1,2,5},{3,4},{6}}
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>{{1,2,4},{3},{5,6}}=>{{1,2,4},{3},{5,6}}
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>{{1,2,4,6},{3},{5}}=>{{1,2,4,6},{3},{5}}
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>{{1,2,4},{3,6},{5}}=>{{1,2,6},{3,4},{5}}
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>{{1,2,4},{3},{5},{6}}=>{{1,2,4},{3},{5},{6}}
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}=>{{1,2},{3},{4,5,6}}
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}=>{{1,2},{3},{4,5},{6}}
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>{{1,2},{3,5,6},{4}}=>{{1,2},{3,5,6},{4}}
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}}=>{{1,2},{3,6},{4,5}}
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>{{1,2},{3,5},{4},{6}}=>{{1,2},{3,5},{4},{6}}
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>{{1,2,5,6},{3},{4}}=>{{1,2,5,6},{3},{4}}
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>{{1,2,5},{3},{4,6}}=>{{1,2,6},{3},{4,5}}
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>{{1,2,5},{3,6},{4}}=>{{1,2,6},{3,5},{4}}
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>{{1,2,5},{3},{4},{6}}=>{{1,2,5},{3},{4},{6}}
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}=>{{1,2},{3},{4},{5,6}}
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>{{1,2},{3},{4,6},{5}}=>{{1,2},{3},{4,6},{5}}
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>{{1,2},{3,6},{4},{5}}=>{{1,2},{3,6},{4},{5}}
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>{{1,2,6},{3},{4},{5}}=>{{1,2,6},{3},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6}}
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}}
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}}
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}=>{{1},{2,3,4},{5,6}}
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>{{1},{2,3,4,6},{5}}=>{{1},{2,3,4,6},{5}}
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}=>{{1},{2,3,4},{5},{6}}
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}=>{{1},{2,3},{4,5,6}}
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}=>{{1},{2,3},{4,5},{6}}
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>{{1},{2,3,5,6},{4}}=>{{1},{2,3,5,6},{4}}
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}=>{{1},{2,3,6},{4,5}}
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>{{1},{2,3,5},{4},{6}}=>{{1},{2,3,5},{4},{6}}
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}=>{{1},{2,3},{4},{5,6}}
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>{{1},{2,3},{4,6},{5}}=>{{1},{2,3},{4,6},{5}}
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>{{1},{2,3,6},{4},{5}}=>{{1},{2,3,6},{4},{5}}
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>{{1,3,4,5,6},{2}}=>{{1,3,4,5,6},{2}}
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>{{1,3,4,5},{2},{6}}=>{{1,3,4,5},{2},{6}}
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>{{1,3,4},{2},{5,6}}=>{{1,3,4},{2},{5,6}}
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>{{1,3,4,6},{2},{5}}=>{{1,3,4,6},{2},{5}}
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>{{1,3,4},{2},{5},{6}}=>{{1,3,4},{2},{5},{6}}
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>{{1,3},{2,4,5,6}}=>{{1,4,5,6},{2,3}}
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>{{1,3},{2,4,5},{6}}=>{{1,4,5},{2,3},{6}}
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>{{1,3,5,6},{2,4}}=>{{1,5,6},{2,3,4}}
[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}}=>{{1,6},{2,3,4,5}}
[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>{{1,3,5},{2,4},{6}}=>{{1,5},{2,3,4},{6}}
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}}=>{{1,4},{2,3},{5,6}}
[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>{{1,3},{2,4,6},{5}}=>{{1,4,6},{2,3},{5}}
[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>{{1,3,6},{2,4},{5}}=>{{1,6},{2,3,4},{5}}
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>{{1,3},{2,4},{5},{6}}=>{{1,4},{2,3},{5},{6}}
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>{{1,3},{2},{4,5,6}}=>{{1,3},{2},{4,5,6}}
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>{{1,3},{2},{4,5},{6}}=>{{1,3},{2},{4,5},{6}}
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>{{1,3,5,6},{2},{4}}=>{{1,3,5,6},{2},{4}}
[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>{{1,3,5},{2},{4,6}}=>{{1,3,6},{2},{4,5}}
[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>{{1,3,5},{2},{4},{6}}=>{{1,3,5},{2},{4},{6}}
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>{{1,3},{2,5,6},{4}}=>{{1,5,6},{2,3},{4}}
[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3},{4,5}}
[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>{{1,3,6},{2,5},{4}}=>{{1,6},{2,3,5},{4}}
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>{{1,3},{2,5},{4},{6}}=>{{1,5},{2,3},{4},{6}}
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>{{1,3},{2},{4},{5,6}}=>{{1,3},{2},{4},{5,6}}
[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>{{1,3},{2},{4,6},{5}}=>{{1,3},{2},{4,6},{5}}
[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>{{1,3,6},{2},{4},{5}}=>{{1,3,6},{2},{4},{5}}
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>{{1,3},{2,6},{4},{5}}=>{{1,6},{2,3},{4},{5}}
[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>{{1,3},{2},{4},{5},{6}}=>{{1,3},{2},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}=>{{1},{2},{3,4,5,6}}
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}=>{{1},{2},{3,4,5},{6}}
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}=>{{1},{2},{3,4},{5,6}}
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>{{1},{2},{3,4,6},{5}}=>{{1},{2},{3,4,6},{5}}
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}=>{{1},{2},{3,4},{5},{6}}
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>{{1},{2,4,5,6},{3}}=>{{1},{2,4,5,6},{3}}
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>{{1},{2,4,5},{3},{6}}=>{{1},{2,4,5},{3},{6}}
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}=>{{1},{2,5,6},{3,4}}
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>{{1},{2,4,6},{3,5}}=>{{1},{2,6},{3,4,5}}
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}=>{{1},{2,5},{3,4},{6}}
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>{{1},{2,4},{3},{5,6}}=>{{1},{2,4},{3},{5,6}}
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>{{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},{2,4},{3,6},{5}}=>{{1},{2,6},{3,4},{5}}
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>{{1},{2,4},{3},{5},{6}}=>{{1},{2,4},{3},{5},{6}}
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>{{1,4,5,6},{2},{3}}=>{{1,4,5,6},{2},{3}}
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>{{1,4,5},{2},{3},{6}}=>{{1,4,5},{2},{3},{6}}
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>{{1,4},{2},{3,5,6}}=>{{1,5,6},{2},{3,4}}
[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>{{1,4,6},{2},{3,5}}=>{{1,6},{2},{3,4,5}}
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>{{1,4},{2},{3,5},{6}}=>{{1,5},{2},{3,4},{6}}
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>{{1,4},{2,5,6},{3}}=>{{1,5,6},{2,4},{3}}
[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>{{1,4,6},{2,5},{3}}=>{{1,6},{2,4,5},{3}}
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}}
[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>{{1,4},{2,5},{3},{6}}=>{{1,5},{2,4},{3},{6}}
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>{{1,4},{2},{3},{5,6}}=>{{1,4},{2},{3},{5,6}}
[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>{{1,4,6},{2},{3},{5}}=>{{1,4,6},{2},{3},{5}}
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>{{1,4},{2},{3,6},{5}}=>{{1,6},{2},{3,4},{5}}
[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>{{1,4},{2,6},{3},{5}}=>{{1,6},{2,4},{3},{5}}
[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>{{1,4},{2},{3},{5},{6}}=>{{1,4},{2},{3},{5},{6}}
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}=>{{1},{2},{3},{4,5,6}}
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}=>{{1},{2},{3},{4,5},{6}}
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>{{1},{2},{3,5,6},{4}}=>{{1},{2},{3,5,6},{4}}
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}=>{{1},{2},{3,6},{4,5}}
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>{{1},{2},{3,5},{4},{6}}=>{{1},{2},{3,5},{4},{6}}
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>{{1},{2,5,6},{3},{4}}=>{{1},{2,5,6},{3},{4}}
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>{{1},{2,5},{3},{4,6}}=>{{1},{2,6},{3},{4,5}}
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>{{1},{2,5},{3,6},{4}}=>{{1},{2,6},{3,5},{4}}
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>{{1},{2,5},{3},{4},{6}}=>{{1},{2,5},{3},{4},{6}}
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>{{1,5,6},{2},{3},{4}}=>{{1,5,6},{2},{3},{4}}
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>{{1,5},{2},{3},{4,6}}=>{{1,6},{2},{3},{4,5}}
[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>{{1,5},{2},{3,6},{4}}=>{{1,6},{2},{3,5},{4}}
[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>{{1,5},{2,6},{3},{4}}=>{{1,6},{2,5},{3},{4}}
[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>{{1,5},{2},{3},{4},{6}}=>{{1,5},{2},{3},{4},{6}}
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}=>{{1},{2},{3},{4},{5,6}}
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>{{1},{2},{3},{4,6},{5}}=>{{1},{2},{3},{4,6},{5}}
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>{{1},{2},{3,6},{4},{5}}=>{{1},{2},{3,6},{4},{5}}
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>{{1},{2,6},{3},{4},{5}}=>{{1},{2,6},{3},{4},{5}}
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>{{1,6},{2},{3},{4},{5}}=>{{1,6},{2},{3},{4},{5}}
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]=>{{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]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,7},{6}}=>{{1,2,3,4,5,7},{6}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4},{5,6,7}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,7]=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4},{5,6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4,6,7},{5}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,6,7,1,5]=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,6,1,5,7]=>{{1,2,3,4,6},{5},{7}}=>{{1,2,3,4,6},{5},{7}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>{{1,2,3,4},{5},{6,7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,6]=>{{1,2,3,4},{5,7},{6}}=>{{1,2,3,4},{5,7},{6}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,7},{5},{6}}=>{{1,2,3,4,7},{5},{6}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3},{4,5,6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3},{4,5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,7,4,6]=>{{1,2,3},{4,5,7},{6}}=>{{1,2,3},{4,5,7},{6}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}=>{{1,2,3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,5,6,7},{4}}=>{{1,2,3,5,6,7},{4}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,7]=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3,5,6},{4},{7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,1,7,4]=>{{1,2,3,5},{4,6,7}}=>{{1,2,3,6,7},{4,5}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,1,4]=>{{1,2,3,5,7},{4,6}}=>{{1,2,3,7},{4,5,6}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,1,4,7]=>{{1,2,3,5},{4,6},{7}}=>{{1,2,3,6},{4,5},{7}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,7,6]=>{{1,2,3,5},{4},{6,7}}=>{{1,2,3,5},{4},{6,7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3,5,7},{4},{6}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,7,1,4,6]=>{{1,2,3,5},{4,7},{6}}=>{{1,2,3,7},{4,5},{6}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,1,4,6,7]=>{{1,2,3,5},{4},{6},{7}}=>{{1,2,3,5},{4},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6,7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}=>{{1,2,3},{4},{5,6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5]=>{{1,2,3},{4,6,7},{5}}=>{{1,2,3},{4,6,7},{5}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,7,4,5]=>{{1,2,3},{4,6},{5,7}}=>{{1,2,3},{4,7},{5,6}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,5,7]=>{{1,2,3},{4,6},{5},{7}}=>{{1,2,3},{4,6},{5},{7}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,6,1,4,7,5]=>{{1,2,3,6,7},{4},{5}}=>{{1,2,3,6,7},{4},{5}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,5]=>{{1,2,3,6},{4},{5,7}}=>{{1,2,3,7},{4},{5,6}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,6,7,1,4,5]=>{{1,2,3,6},{4,7},{5}}=>{{1,2,3,7},{4,6},{5}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,6,1,4,5,7]=>{{1,2,3,6},{4},{5},{7}}=>{{1,2,3,6},{4},{5},{7}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}=>{{1,2,3},{4},{5},{6,7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>{{1,2,3},{4},{5,7},{6}}=>{{1,2,3},{4},{5,7},{6}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,5,6]=>{{1,2,3},{4,7},{5},{6}}=>{{1,2,3},{4,7},{5},{6}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,7,1,4,5,6]=>{{1,2,3,7},{4},{5},{6}}=>{{1,2,3,7},{4},{5},{6}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}}=>{{1,2},{3,4,5,6,7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}}=>{{1,2},{3,4,5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>{{1,2},{3,4,5},{6,7}}=>{{1,2},{3,4,5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,7,3,6]=>{{1,2},{3,4,5,7},{6}}=>{{1,2},{3,4,5,7},{6}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,3,6,7]=>{{1,2},{3,4,5},{6},{7}}=>{{1,2},{3,4,5},{6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>{{1,2},{3,4},{5,6,7}}=>{{1,2},{3,4},{5,6,7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,7]=>{{1,2},{3,4},{5,6},{7}}=>{{1,2},{3,4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>{{1,2},{3,4,6,7},{5}}=>{{1,2},{3,4,6,7},{5}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,6,7,3,5]=>{{1,2},{3,4,6},{5,7}}=>{{1,2},{3,4,7},{5,6}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5,7]=>{{1,2},{3,4,6},{5},{7}}=>{{1,2},{3,4,6},{5},{7}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>{{1,2},{3,4},{5},{6,7}}=>{{1,2},{3,4},{5},{6,7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,6]=>{{1,2},{3,4},{5,7},{6}}=>{{1,2},{3,4},{5,7},{6}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,7,3,5,6]=>{{1,2},{3,4,7},{5},{6}}=>{{1,2},{3,4,7},{5},{6}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}}=>{{1,2},{3,4},{5},{6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,3]=>{{1,2,4,5,6,7},{3}}=>{{1,2,4,5,6,7},{3}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,6,3,7]=>{{1,2,4,5,6},{3},{7}}=>{{1,2,4,5,6},{3},{7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6]=>{{1,2,4,5},{3},{6,7}}=>{{1,2,4,5},{3},{6,7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,7,3,6]=>{{1,2,4,5,7},{3},{6}}=>{{1,2,4,5,7},{3},{6}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,6,7]=>{{1,2,4,5},{3},{6},{7}}=>{{1,2,4,5},{3},{6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,7,3]=>{{1,2,4},{3,5,6,7}}=>{{1,2,5,6,7},{3,4}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,1,6,3,7]=>{{1,2,4},{3,5,6},{7}}=>{{1,2,5,6},{3,4},{7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,1,7,3]=>{{1,2,4,6,7},{3,5}}=>{{1,2,6,7},{3,4,5}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,1,3]=>{{1,2,4,6},{3,5,7}}=>{{1,2,7},{3,4,5,6}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,1,3,7]=>{{1,2,4,6},{3,5},{7}}=>{{1,2,6},{3,4,5},{7}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,1,3,7,6]=>{{1,2,4},{3,5},{6,7}}=>{{1,2,5},{3,4},{6,7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,6]=>{{1,2,4},{3,5,7},{6}}=>{{1,2,5,7},{3,4},{6}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,7,1,3,6]=>{{1,2,4,7},{3,5},{6}}=>{{1,2,7},{3,4,5},{6}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,1,3,6,7]=>{{1,2,4},{3,5},{6},{7}}=>{{1,2,5},{3,4},{6},{7}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,6,7,5]=>{{1,2,4},{3},{5,6,7}}=>{{1,2,4},{3},{5,6,7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>{{1,2,4},{3},{5,6},{7}}=>{{1,2,4},{3},{5,6},{7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5]=>{{1,2,4,6,7},{3},{5}}=>{{1,2,4,6,7},{3},{5}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,7,3,5]=>{{1,2,4,6},{3},{5,7}}=>{{1,2,4,7},{3},{5,6}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5,7]=>{{1,2,4,6},{3},{5},{7}}=>{{1,2,4,6},{3},{5},{7}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,6,1,3,7,5]=>{{1,2,4},{3,6,7},{5}}=>{{1,2,6,7},{3,4},{5}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,5]=>{{1,2,4},{3,6},{5,7}}=>{{1,2,7},{3,4},{5,6}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,6,7,1,3,5]=>{{1,2,4,7},{3,6},{5}}=>{{1,2,7},{3,4,6},{5}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5,7]=>{{1,2,4},{3,6},{5},{7}}=>{{1,2,6},{3,4},{5},{7}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,1,3,5,7,6]=>{{1,2,4},{3},{5},{6,7}}=>{{1,2,4},{3},{5},{6,7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,3,7,5,6]=>{{1,2,4},{3},{5,7},{6}}=>{{1,2,4},{3},{5,7},{6}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,5,6]=>{{1,2,4,7},{3},{5},{6}}=>{{1,2,4,7},{3},{5},{6}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,7,1,3,5,6]=>{{1,2,4},{3,7},{5},{6}}=>{{1,2,7},{3,4},{5},{6}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,3,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}=>{{1,2,4},{3},{5},{6},{7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}}=>{{1,2},{3},{4,5,6,7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>{{1,2},{3},{4,5,6},{7}}=>{{1,2},{3},{4,5,6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}}=>{{1,2},{3},{4,5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,3,5,7,4,6]=>{{1,2},{3},{4,5,7},{6}}=>{{1,2},{3},{4,5,7},{6}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}}=>{{1,2},{3},{4,5},{6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>{{1,2},{3,5,6,7},{4}}=>{{1,2},{3,5,6,7},{4}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,7]=>{{1,2},{3,5,6},{4},{7}}=>{{1,2},{3,5,6},{4},{7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>{{1,2},{3,5},{4,6,7}}=>{{1,2},{3,6,7},{4,5}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,3,4]=>{{1,2},{3,5,7},{4,6}}=>{{1,2},{3,7},{4,5,6}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,6,3,4,7]=>{{1,2},{3,5},{4,6},{7}}=>{{1,2},{3,6},{4,5},{7}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,4,7,6]=>{{1,2},{3,5},{4},{6,7}}=>{{1,2},{3,5},{4},{6,7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,6]=>{{1,2},{3,5,7},{4},{6}}=>{{1,2},{3,5,7},{4},{6}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,7,3,4,6]=>{{1,2},{3,5},{4,7},{6}}=>{{1,2},{3,7},{4,5},{6}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,4,6,7]=>{{1,2},{3,5},{4},{6},{7}}=>{{1,2},{3,5},{4},{6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,7,4]=>{{1,2,5,6,7},{3},{4}}=>{{1,2,5,6,7},{3},{4}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>{{1,2,5,6},{3},{4},{7}}=>{{1,2,5,6},{3},{4},{7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4]=>{{1,2,5},{3},{4,6,7}}=>{{1,2,6,7},{3},{4,5}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,7,3,4]=>{{1,2,5,7},{3},{4,6}}=>{{1,2,7},{3},{4,5,6}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,4,7]=>{{1,2,5},{3},{4,6},{7}}=>{{1,2,6},{3},{4,5},{7}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,1,3,7,4]=>{{1,2,5},{3,6,7},{4}}=>{{1,2,6,7},{3,5},{4}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,4]=>{{1,2,5,7},{3,6},{4}}=>{{1,2,7},{3,5,6},{4}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,1,3,4]=>{{1,2,5},{3,6},{4,7}}=>{{1,2,7},{3,6},{4,5}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,1,3,4,7]=>{{1,2,5},{3,6},{4},{7}}=>{{1,2,6},{3,5},{4},{7}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,7,6]=>{{1,2,5},{3},{4},{6,7}}=>{{1,2,5},{3},{4},{6,7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,5,1,3,7,4,6]=>{{1,2,5,7},{3},{4},{6}}=>{{1,2,5,7},{3},{4},{6}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,4,6]=>{{1,2,5},{3},{4,7},{6}}=>{{1,2,7},{3},{4,5},{6}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,5,7,1,3,4,6]=>{{1,2,5},{3,7},{4},{6}}=>{{1,2,7},{3,5},{4},{6}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,5,1,3,4,6,7]=>{{1,2,5},{3},{4},{6},{7}}=>{{1,2,5},{3},{4},{6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}}=>{{1,2},{3},{4},{5,6,7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}}=>{{1,2},{3},{4},{5,6},{7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>{{1,2},{3},{4,6,7},{5}}=>{{1,2},{3},{4,6,7},{5}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,6,7,4,5]=>{{1,2},{3},{4,6},{5,7}}=>{{1,2},{3},{4,7},{5,6}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,6,4,5,7]=>{{1,2},{3},{4,6},{5},{7}}=>{{1,2},{3},{4,6},{5},{7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,6,3,4,7,5]=>{{1,2},{3,6,7},{4},{5}}=>{{1,2},{3,6,7},{4},{5}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,5]=>{{1,2},{3,6},{4},{5,7}}=>{{1,2},{3,7},{4},{5,6}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,7,3,4,5]=>{{1,2},{3,6},{4,7},{5}}=>{{1,2},{3,7},{4,6},{5}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,4,5,7]=>{{1,2},{3,6},{4},{5},{7}}=>{{1,2},{3,6},{4},{5},{7}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,1,3,4,7,5]=>{{1,2,6,7},{3},{4},{5}}=>{{1,2,6,7},{3},{4},{5}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,1,3,7,4,5]=>{{1,2,6},{3},{4},{5,7}}=>{{1,2,7},{3},{4},{5,6}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,4,5]=>{{1,2,6},{3},{4,7},{5}}=>{{1,2,7},{3},{4,6},{5}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6,7,1,3,4,5]=>{{1,2,6},{3,7},{4},{5}}=>{{1,2,7},{3,6},{4},{5}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6,1,3,4,5,7]=>{{1,2,6},{3},{4},{5},{7}}=>{{1,2,6},{3},{4},{5},{7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5},{6,7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,3,4,7,5,6]=>{{1,2},{3},{4},{5,7},{6}}=>{{1,2},{3},{4},{5,7},{6}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,3,7,4,5,6]=>{{1,2},{3},{4,7},{5},{6}}=>{{1,2},{3},{4,7},{5},{6}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,4,5,6]=>{{1,2},{3,7},{4},{5},{6}}=>{{1,2},{3,7},{4},{5},{6}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>{{1,2,7},{3},{4},{5},{6}}=>{{1,2,7},{3},{4},{5},{6}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}}=>{{1,2},{3},{4},{5},{6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]=>{{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]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}=>{{1},{2,3,4,5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,7,2,6]=>{{1},{2,3,4,5,7},{6}}=>{{1},{2,3,4,5,7},{6}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}=>{{1},{2,3,4,5},{6},{7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}=>{{1},{2,3,4},{5,6,7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}=>{{1},{2,3,4},{5,6},{7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,6,2,7,5]=>{{1},{2,3,4,6,7},{5}}=>{{1},{2,3,4,6,7},{5}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}=>{{1},{2,3,4,7},{5,6}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,6,2,5,7]=>{{1},{2,3,4,6},{5},{7}}=>{{1},{2,3,4,6},{5},{7}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}=>{{1},{2,3,4},{5},{6,7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,6]=>{{1},{2,3,4},{5,7},{6}}=>{{1},{2,3,4},{5,7},{6}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,7,2,5,6]=>{{1},{2,3,4,7},{5},{6}}=>{{1},{2,3,4,7},{5},{6}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}=>{{1},{2,3,4},{5},{6},{7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}=>{{1},{2,3},{4,5,6,7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}=>{{1},{2,3},{4,5,6},{7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}=>{{1},{2,3},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,7,4,6]=>{{1},{2,3},{4,5,7},{6}}=>{{1},{2,3},{4,5,7},{6}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,7,4]=>{{1},{2,3,5,6,7},{4}}=>{{1},{2,3,5,6,7},{4}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,7]=>{{1},{2,3,5,6},{4},{7}}=>{{1},{2,3,5,6},{4},{7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}=>{{1},{2,3,6,7},{4,5}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,2,4]=>{{1},{2,3,5,7},{4,6}}=>{{1},{2,3,7},{4,5,6}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}=>{{1},{2,3,6},{4,5},{7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,7,6]=>{{1},{2,3,5},{4},{6,7}}=>{{1},{2,3,5},{4},{6,7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,6]=>{{1},{2,3,5,7},{4},{6}}=>{{1},{2,3,5,7},{4},{6}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,7,2,4,6]=>{{1},{2,3,5},{4,7},{6}}=>{{1},{2,3,7},{4,5},{6}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,5,2,4,6,7]=>{{1},{2,3,5},{4},{6},{7}}=>{{1},{2,3,5},{4},{6},{7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}=>{{1},{2,3},{4},{5,6,7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,6},{7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5]=>{{1},{2,3},{4,6,7},{5}}=>{{1},{2,3},{4,6,7},{5}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}=>{{1},{2,3},{4,7},{5,6}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,5,7]=>{{1},{2,3},{4,6},{5},{7}}=>{{1},{2,3},{4,6},{5},{7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,6,2,4,7,5]=>{{1},{2,3,6,7},{4},{5}}=>{{1},{2,3,6,7},{4},{5}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,5]=>{{1},{2,3,6},{4},{5,7}}=>{{1},{2,3,7},{4},{5,6}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,6,7,2,4,5]=>{{1},{2,3,6},{4,7},{5}}=>{{1},{2,3,7},{4,6},{5}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,6,2,4,5,7]=>{{1},{2,3,6},{4},{5},{7}}=>{{1},{2,3,6},{4},{5},{7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}=>{{1},{2,3},{4},{5},{6,7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>{{1},{2,3},{4},{5,7},{6}}=>{{1},{2,3},{4},{5,7},{6}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,5,6]=>{{1},{2,3},{4,7},{5},{6}}=>{{1},{2,3},{4,7},{5},{6}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,7,2,4,5,6]=>{{1},{2,3,7},{4},{5},{6}}=>{{1},{2,3,7},{4},{5},{6}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,2]=>{{1,3,4,5,6,7},{2}}=>{{1,3,4,5,6,7},{2}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,2,7]=>{{1,3,4,5,6},{2},{7}}=>{{1,3,4,5,6},{2},{7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>{{1,3,4,5},{2},{6,7}}=>{{1,3,4,5},{2},{6,7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,7,2,6]=>{{1,3,4,5,7},{2},{6}}=>{{1,3,4,5,7},{2},{6}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,2,6,7]=>{{1,3,4,5},{2},{6},{7}}=>{{1,3,4,5},{2},{6},{7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>{{1,3,4},{2},{5,6,7}}=>{{1,3,4},{2},{5,6,7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,7]=>{{1,3,4},{2},{5,6},{7}}=>{{1,3,4},{2},{5,6},{7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>{{1,3,4,6,7},{2},{5}}=>{{1,3,4,6,7},{2},{5}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,6,7,2,5]=>{{1,3,4,6},{2},{5,7}}=>{{1,3,4,7},{2},{5,6}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,6,2,5,7]=>{{1,3,4,6},{2},{5},{7}}=>{{1,3,4,6},{2},{5},{7}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,5,7,6]=>{{1,3,4},{2},{5},{6,7}}=>{{1,3,4},{2},{5},{6,7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,6]=>{{1,3,4},{2},{5,7},{6}}=>{{1,3,4},{2},{5,7},{6}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,7,2,5,6]=>{{1,3,4,7},{2},{5},{6}}=>{{1,3,4,7},{2},{5},{6}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}=>{{1,3,4},{2},{5},{6},{7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,2]=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,6,2,7]=>{{1,3},{2,4,5,6},{7}}=>{{1,4,5,6},{2,3},{7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6]=>{{1,3},{2,4,5},{6,7}}=>{{1,4,5},{2,3},{6,7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,7,2,6]=>{{1,3},{2,4,5,7},{6}}=>{{1,4,5,7},{2,3},{6}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,6,7]=>{{1,3},{2,4,5},{6},{7}}=>{{1,4,5},{2,3},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,7,2]=>{{1,3,5,6,7},{2,4}}=>{{1,5,6,7},{2,3,4}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,7]=>{{1,3,5,6},{2,4},{7}}=>{{1,5,6},{2,3,4},{7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,1,7,2]=>{{1,3,5},{2,4,6,7}}=>{{1,6,7},{2,3,4,5}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,1,2]=>{{1,3,5,7},{2,4,6}}=>{{1,7},{2,3,4,5,6}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,1,2,7]=>{{1,3,5},{2,4,6},{7}}=>{{1,6},{2,3,4,5},{7}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,1,2,7,6]=>{{1,3,5},{2,4},{6,7}}=>{{1,5},{2,3,4},{6,7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,6]=>{{1,3,5,7},{2,4},{6}}=>{{1,5,7},{2,3,4},{6}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,7,1,2,6]=>{{1,3,5},{2,4,7},{6}}=>{{1,7},{2,3,4,5},{6}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6,7]=>{{1,3,5},{2,4},{6},{7}}=>{{1,5},{2,3,4},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,2,6,7,5]=>{{1,3},{2,4},{5,6,7}}=>{{1,4},{2,3},{5,6,7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>{{1,3},{2,4},{5,6},{7}}=>{{1,4},{2,3},{5,6},{7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5]=>{{1,3},{2,4,6,7},{5}}=>{{1,4,6,7},{2,3},{5}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,7,2,5]=>{{1,3},{2,4,6},{5,7}}=>{{1,4,7},{2,3},{5,6}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5,7]=>{{1,3},{2,4,6},{5},{7}}=>{{1,4,6},{2,3},{5},{7}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,6,1,2,7,5]=>{{1,3,6,7},{2,4},{5}}=>{{1,6,7},{2,3,4},{5}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,5]=>{{1,3,6},{2,4},{5,7}}=>{{1,7},{2,3,4},{5,6}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,6,7,1,2,5]=>{{1,3,6},{2,4,7},{5}}=>{{1,7},{2,3,4,6},{5}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5,7]=>{{1,3,6},{2,4},{5},{7}}=>{{1,6},{2,3,4},{5},{7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,1,2,5,7,6]=>{{1,3},{2,4},{5},{6,7}}=>{{1,4},{2,3},{5},{6,7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,2,7,5,6]=>{{1,3},{2,4},{5,7},{6}}=>{{1,4},{2,3},{5,7},{6}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,5,6]=>{{1,3},{2,4,7},{5},{6}}=>{{1,4,7},{2,3},{5},{6}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,7,1,2,5,6]=>{{1,3,7},{2,4},{5},{6}}=>{{1,7},{2,3,4},{5},{6}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>{{1,3},{2,4},{5},{6},{7}}=>{{1,4},{2,3},{5},{6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,4]=>{{1,3},{2},{4,5,6,7}}=>{{1,3},{2},{4,5,6,7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}}=>{{1,3},{2},{4,5,6},{7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}}=>{{1,3},{2},{4,5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,7,4,6]=>{{1,3},{2},{4,5,7},{6}}=>{{1,3},{2},{4,5,7},{6}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}}=>{{1,3},{2},{4,5},{6},{7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>{{1,3,5,6,7},{2},{4}}=>{{1,3,5,6,7},{2},{4}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,7]=>{{1,3,5,6},{2},{4},{7}}=>{{1,3,5,6},{2},{4},{7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>{{1,3,5},{2},{4,6,7}}=>{{1,3,6,7},{2},{4,5}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,2,4]=>{{1,3,5,7},{2},{4,6}}=>{{1,3,7},{2},{4,5,6}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,6,2,4,7]=>{{1,3,5},{2},{4,6},{7}}=>{{1,3,6},{2},{4,5},{7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,7,6]=>{{1,3,5},{2},{4},{6,7}}=>{{1,3,5},{2},{4},{6,7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,6]=>{{1,3,5,7},{2},{4},{6}}=>{{1,3,5,7},{2},{4},{6}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,7,2,4,6]=>{{1,3,5},{2},{4,7},{6}}=>{{1,3,7},{2},{4,5},{6}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,4,6,7]=>{{1,3,5},{2},{4},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,5,1,2,6,7,4]=>{{1,3},{2,5,6,7},{4}}=>{{1,5,6,7},{2,3},{4}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>{{1,3},{2,5,6},{4},{7}}=>{{1,5,6},{2,3},{4},{7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4]=>{{1,3},{2,5},{4,6,7}}=>{{1,6,7},{2,3},{4,5}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,7,2,4]=>{{1,3},{2,5,7},{4,6}}=>{{1,7},{2,3},{4,5,6}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,4,7]=>{{1,3},{2,5},{4,6},{7}}=>{{1,6},{2,3},{4,5},{7}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,1,2,7,4]=>{{1,3,6,7},{2,5},{4}}=>{{1,6,7},{2,3,5},{4}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,4]=>{{1,3,6},{2,5,7},{4}}=>{{1,7},{2,3,5,6},{4}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,1,2,4]=>{{1,3,6},{2,5},{4,7}}=>{{1,7},{2,3,6},{4,5}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,1,2,4,7]=>{{1,3,6},{2,5},{4},{7}}=>{{1,6},{2,3,5},{4},{7}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,7,6]=>{{1,3},{2,5},{4},{6,7}}=>{{1,5},{2,3},{4},{6,7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,7,4,6]=>{{1,3},{2,5,7},{4},{6}}=>{{1,5,7},{2,3},{4},{6}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,4,6]=>{{1,3},{2,5},{4,7},{6}}=>{{1,7},{2,3},{4,5},{6}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,7,1,2,4,6]=>{{1,3,7},{2,5},{4},{6}}=>{{1,7},{2,3,5},{4},{6}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,5,1,2,4,6,7]=>{{1,3},{2,5},{4},{6},{7}}=>{{1,5},{2,3},{4},{6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}}=>{{1,3},{2},{4},{5,6,7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,4,6,5,7]=>{{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]=>[3,1,2,6,4,7,5]=>{{1,3},{2},{4,6,7},{5}}=>{{1,3},{2},{4,6,7},{5}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,6,7,4,5]=>{{1,3},{2},{4,6},{5,7}}=>{{1,3},{2},{4,7},{5,6}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,6,4,5,7]=>{{1,3},{2},{4,6},{5},{7}}=>{{1,3},{2},{4,6},{5},{7}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,6,2,4,7,5]=>{{1,3,6,7},{2},{4},{5}}=>{{1,3,6,7},{2},{4},{5}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,5]=>{{1,3,6},{2},{4},{5,7}}=>{{1,3,7},{2},{4},{5,6}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,6,7,2,4,5]=>{{1,3,6},{2},{4,7},{5}}=>{{1,3,7},{2},{4,6},{5}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,4,5,7]=>{{1,3,6},{2},{4},{5},{7}}=>{{1,3,6},{2},{4},{5},{7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1,2,4,7,5]=>{{1,3},{2,6,7},{4},{5}}=>{{1,6,7},{2,3},{4},{5}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,2,7,4,5]=>{{1,3},{2,6},{4},{5,7}}=>{{1,7},{2,3},{4},{5,6}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,4,5]=>{{1,3},{2,6},{4,7},{5}}=>{{1,7},{2,3},{4,6},{5}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,6,7,1,2,4,5]=>{{1,3,7},{2,6},{4},{5}}=>{{1,7},{2,3,6},{4},{5}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,6,1,2,4,5,7]=>{{1,3},{2,6},{4},{5},{7}}=>{{1,6},{2,3},{4},{5},{7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}}=>{{1,3},{2},{4},{5},{6,7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,2,4,7,5,6]=>{{1,3},{2},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,7},{6}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,2,7,4,5,6]=>{{1,3},{2},{4,7},{5},{6}}=>{{1,3},{2},{4,7},{5},{6}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,7,2,4,5,6]=>{{1,3,7},{2},{4},{5},{6}}=>{{1,3,7},{2},{4},{5},{6}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>{{1,3},{2,7},{4},{5},{6}}=>{{1,7},{2,3},{4},{5},{6}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}=>{{1,3},{2},{4},{5},{6},{7}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,3]=>{{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]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}=>{{1},{2},{3,4,5,6},{7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}=>{{1},{2},{3,4,5},{6,7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,7,3,6]=>{{1},{2},{3,4,5,7},{6}}=>{{1},{2},{3,4,5,7},{6}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}=>{{1},{2},{3,4},{5,6,7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}=>{{1},{2},{3,4},{5,6},{7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,6,3,7,5]=>{{1},{2},{3,4,6,7},{5}}=>{{1},{2},{3,4,6,7},{5}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}=>{{1},{2},{3,4,7},{5,6}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5,7]=>{{1},{2},{3,4,6},{5},{7}}=>{{1},{2},{3,4,6},{5},{7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}=>{{1},{2},{3,4},{5},{6,7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,6]=>{{1},{2},{3,4},{5,7},{6}}=>{{1},{2},{3,4},{5,7},{6}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,7,3,5,6]=>{{1},{2},{3,4,7},{5},{6}}=>{{1},{2},{3,4,7},{5},{6}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}=>{{1},{2},{3,4},{5},{6},{7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,3]=>{{1},{2,4,5,6,7},{3}}=>{{1},{2,4,5,6,7},{3}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,6,3,7]=>{{1},{2,4,5,6},{3},{7}}=>{{1},{2,4,5,6},{3},{7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6]=>{{1},{2,4,5},{3},{6,7}}=>{{1},{2,4,5},{3},{6,7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,7,3,6]=>{{1},{2,4,5,7},{3},{6}}=>{{1},{2,4,5,7},{3},{6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,6,7]=>{{1},{2,4,5},{3},{6},{7}}=>{{1},{2,4,5},{3},{6},{7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}=>{{1},{2,5,6,7},{3,4}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}=>{{1},{2,5,6},{3,4},{7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,2,7,3]=>{{1},{2,4,6,7},{3,5}}=>{{1},{2,6,7},{3,4,5}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}=>{{1},{2,7},{3,4,5,6}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,2,3,7]=>{{1},{2,4,6},{3,5},{7}}=>{{1},{2,6},{3,4,5},{7}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}=>{{1},{2,5},{3,4},{6,7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,6]=>{{1},{2,4},{3,5,7},{6}}=>{{1},{2,5,7},{3,4},{6}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,7,2,3,6]=>{{1},{2,4,7},{3,5},{6}}=>{{1},{2,7},{3,4,5},{6}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}=>{{1},{2,5},{3,4},{6},{7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,6,7,5]=>{{1},{2,4},{3},{5,6,7}}=>{{1},{2,4},{3},{5,6,7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}=>{{1},{2,4},{3},{5,6},{7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5]=>{{1},{2,4,6,7},{3},{5}}=>{{1},{2,4,6,7},{3},{5}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,7,3,5]=>{{1},{2,4,6},{3},{5,7}}=>{{1},{2,4,7},{3},{5,6}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5,7]=>{{1},{2,4,6},{3},{5},{7}}=>{{1},{2,4,6},{3},{5},{7}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,6,2,3,7,5]=>{{1},{2,4},{3,6,7},{5}}=>{{1},{2,6,7},{3,4},{5}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}=>{{1},{2,7},{3,4},{5,6}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,7,2,3,5]=>{{1},{2,4,7},{3,6},{5}}=>{{1},{2,7},{3,4,6},{5}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5,7]=>{{1},{2,4},{3,6},{5},{7}}=>{{1},{2,6},{3,4},{5},{7}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,3,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}=>{{1},{2,4},{3},{5},{6,7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>{{1},{2,4},{3},{5,7},{6}}=>{{1},{2,4},{3},{5,7},{6}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,5,6]=>{{1},{2,4,7},{3},{5},{6}}=>{{1},{2,4,7},{3},{5},{6}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,7,2,3,5,6]=>{{1},{2,4},{3,7},{5},{6}}=>{{1},{2,7},{3,4},{5},{6}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,3,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}=>{{1},{2,4},{3},{5},{6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,3]=>{{1,4,5,6,7},{2},{3}}=>{{1,4,5,6,7},{2},{3}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2,5,6,3,7]=>{{1,4,5,6},{2},{3},{7}}=>{{1,4,5,6},{2},{3},{7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>{{1,4,5},{2},{3},{6,7}}=>{{1,4,5},{2},{3},{6,7}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,7,3,6]=>{{1,4,5,7},{2},{3},{6}}=>{{1,4,5,7},{2},{3},{6}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,6,7]=>{{1,4,5},{2},{3},{6},{7}}=>{{1,4,5},{2},{3},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>{{1,4},{2},{3,5,6,7}}=>{{1,5,6,7},{2},{3,4}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,7]=>{{1,4},{2},{3,5,6},{7}}=>{{1,5,6},{2},{3,4},{7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>{{1,4,6,7},{2},{3,5}}=>{{1,6,7},{2},{3,4,5}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,2,3]=>{{1,4,6},{2},{3,5,7}}=>{{1,7},{2},{3,4,5,6}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,6,2,3,7]=>{{1,4,6},{2},{3,5},{7}}=>{{1,6},{2},{3,4,5},{7}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,3,7,6]=>{{1,4},{2},{3,5},{6,7}}=>{{1,5},{2},{3,4},{6,7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,6]=>{{1,4},{2},{3,5,7},{6}}=>{{1,5,7},{2},{3,4},{6}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,7,2,3,6]=>{{1,4,7},{2},{3,5},{6}}=>{{1,7},{2},{3,4,5},{6}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,3,6,7]=>{{1,4},{2},{3,5},{6},{7}}=>{{1,5},{2},{3,4},{6},{7}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,1,2,6,7,3]=>{{1,4},{2,5,6,7},{3}}=>{{1,5,6,7},{2,4},{3}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>{{1,4},{2,5,6},{3},{7}}=>{{1,5,6},{2,4},{3},{7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3]=>{{1,4,6,7},{2,5},{3}}=>{{1,6,7},{2,4,5},{3}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,7,2,3]=>{{1,4,6},{2,5,7},{3}}=>{{1,7},{2,4,5,6},{3}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,3,7]=>{{1,4,6},{2,5},{3},{7}}=>{{1,6},{2,4,5},{3},{7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,1,2,7,3]=>{{1,4},{2,5},{3,6,7}}=>{{1,6,7},{2,5},{3,4}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,3]=>{{1,4},{2,5,7},{3,6}}=>{{1,7},{2,5,6},{3,4}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,1,2,3]=>{{1,4,7},{2,5},{3,6}}=>{{1,7},{2,6},{3,4,5}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>{{1,4},{2,5},{3,6},{7}}=>{{1,6},{2,5},{3,4},{7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,1,2,3,7,6]=>{{1,4},{2,5},{3},{6,7}}=>{{1,5},{2,4},{3},{6,7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,1,2,7,3,6]=>{{1,4},{2,5,7},{3},{6}}=>{{1,5,7},{2,4},{3},{6}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,3,6]=>{{1,4,7},{2,5},{3},{6}}=>{{1,7},{2,4,5},{3},{6}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,7,1,2,3,6]=>{{1,4},{2,5},{3,7},{6}}=>{{1,7},{2,5},{3,4},{6}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7]=>{{1,4},{2,5},{3},{6},{7}}=>{{1,5},{2,4},{3},{6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,6,7,5]=>{{1,4},{2},{3},{5,6,7}}=>{{1,4},{2},{3},{5,6,7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5,7]=>{{1,4},{2},{3},{5,6},{7}}=>{{1,4},{2},{3},{5,6},{7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>{{1,4,6,7},{2},{3},{5}}=>{{1,4,6,7},{2},{3},{5}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,6,7,3,5]=>{{1,4,6},{2},{3},{5,7}}=>{{1,4,7},{2},{3},{5,6}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5,7]=>{{1,4,6},{2},{3},{5},{7}}=>{{1,4,6},{2},{3},{5},{7}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,3,7,5]=>{{1,4},{2},{3,6,7},{5}}=>{{1,6,7},{2},{3,4},{5}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,5]=>{{1,4},{2},{3,6},{5,7}}=>{{1,7},{2},{3,4},{5,6}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,1,6,7,2,3,5]=>{{1,4,7},{2},{3,6},{5}}=>{{1,7},{2},{3,4,6},{5}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5,7]=>{{1,4},{2},{3,6},{5},{7}}=>{{1,6},{2},{3,4},{5},{7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,6,1,2,3,7,5]=>{{1,4},{2,6,7},{3},{5}}=>{{1,6,7},{2,4},{3},{5}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,2,7,3,5]=>{{1,4},{2,6},{3},{5,7}}=>{{1,7},{2,4},{3},{5,6}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,3,5]=>{{1,4,7},{2,6},{3},{5}}=>{{1,7},{2,4,6},{3},{5}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,6,7,1,2,3,5]=>{{1,4},{2,6},{3,7},{5}}=>{{1,7},{2,6},{3,4},{5}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5,7]=>{{1,4},{2,6},{3},{5},{7}}=>{{1,6},{2,4},{3},{5},{7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>{{1,4},{2},{3},{5},{6,7}}=>{{1,4},{2},{3},{5},{6,7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,3,7,5,6]=>{{1,4},{2},{3},{5,7},{6}}=>{{1,4},{2},{3},{5,7},{6}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,7,3,5,6]=>{{1,4,7},{2},{3},{5},{6}}=>{{1,4,7},{2},{3},{5},{6}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,3,5,6]=>{{1,4},{2},{3,7},{5},{6}}=>{{1,7},{2},{3,4},{5},{6}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>{{1,4},{2,7},{3},{5},{6}}=>{{1,7},{2,4},{3},{5},{6}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}=>{{1,4},{2},{3},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,4]=>{{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]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}=>{{1},{2},{3},{4,5,6},{7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}=>{{1},{2},{3},{4,5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,5,7,4,6]=>{{1},{2},{3},{4,5,7},{6}}=>{{1},{2},{3},{4,5,7},{6}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,2,5,3,6,7,4]=>{{1},{2},{3,5,6,7},{4}}=>{{1},{2},{3,5,6,7},{4}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,7]=>{{1},{2},{3,5,6},{4},{7}}=>{{1},{2},{3,5,6},{4},{7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}=>{{1},{2},{3,6,7},{4,5}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,3,4]=>{{1},{2},{3,5,7},{4,6}}=>{{1},{2},{3,7},{4,5,6}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}=>{{1},{2},{3,6},{4,5},{7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,4,7,6]=>{{1},{2},{3,5},{4},{6,7}}=>{{1},{2},{3,5},{4},{6,7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,6]=>{{1},{2},{3,5,7},{4},{6}}=>{{1},{2},{3,5,7},{4},{6}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,2,5,7,3,4,6]=>{{1},{2},{3,5},{4,7},{6}}=>{{1},{2},{3,7},{4,5},{6}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,4,6,7]=>{{1},{2},{3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4},{6},{7}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,3,6,7,4]=>{{1},{2,5,6,7},{3},{4}}=>{{1},{2,5,6,7},{3},{4}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,3,6,4,7]=>{{1},{2,5,6},{3},{4},{7}}=>{{1},{2,5,6},{3},{4},{7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4]=>{{1},{2,5},{3},{4,6,7}}=>{{1},{2,6,7},{3},{4,5}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,7,3,4]=>{{1},{2,5,7},{3},{4,6}}=>{{1},{2,7},{3},{4,5,6}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,4,7]=>{{1},{2,5},{3},{4,6},{7}}=>{{1},{2,6},{3},{4,5},{7}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,6,2,3,7,4]=>{{1},{2,5},{3,6,7},{4}}=>{{1},{2,6,7},{3,5},{4}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,4]=>{{1},{2,5,7},{3,6},{4}}=>{{1},{2,7},{3,5,6},{4}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}=>{{1},{2,7},{3,6},{4,5}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,6,2,3,4,7]=>{{1},{2,5},{3,6},{4},{7}}=>{{1},{2,6},{3,5},{4},{7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,7,6]=>{{1},{2,5},{3},{4},{6,7}}=>{{1},{2,5},{3},{4},{6,7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>{{1},{2,5,7},{3},{4},{6}}=>{{1},{2,5,7},{3},{4},{6}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,4,6]=>{{1},{2,5},{3},{4,7},{6}}=>{{1},{2,7},{3},{4,5},{6}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,7,2,3,4,6]=>{{1},{2,5},{3,7},{4},{6}}=>{{1},{2,7},{3,5},{4},{6}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,3,4,6,7]=>{{1},{2,5},{3},{4},{6},{7}}=>{{1},{2,5},{3},{4},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,2,3,6,7,4]=>{{1,5,6,7},{2},{3},{4}}=>{{1,5,6,7},{2},{3},{4}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,1,2,3,6,4,7]=>{{1,5,6},{2},{3},{4},{7}}=>{{1,5,6},{2},{3},{4},{7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>{{1,5},{2},{3},{4,6,7}}=>{{1,6,7},{2},{3},{4,5}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,1,2,6,7,3,4]=>{{1,5,7},{2},{3},{4,6}}=>{{1,7},{2},{3},{4,5,6}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,1,2,6,3,4,7]=>{{1,5},{2},{3},{4,6},{7}}=>{{1,6},{2},{3},{4,5},{7}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,3,7,4]=>{{1,5},{2},{3,6,7},{4}}=>{{1,6,7},{2},{3,5},{4}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,4]=>{{1,5,7},{2},{3,6},{4}}=>{{1,7},{2},{3,5,6},{4}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,7,2,3,4]=>{{1,5},{2},{3,6},{4,7}}=>{{1,7},{2},{3,6},{4,5}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,3,4,7]=>{{1,5},{2},{3,6},{4},{7}}=>{{1,6},{2},{3,5},{4},{7}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,4]=>{{1,5},{2,6,7},{3},{4}}=>{{1,6,7},{2,5},{3},{4}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,1,2,7,3,4]=>{{1,5,7},{2,6},{3},{4}}=>{{1,7},{2,5,6},{3},{4}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,3,4]=>{{1,5},{2,6},{3},{4,7}}=>{{1,7},{2,6},{3},{4,5}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,1,2,3,4]=>{{1,5},{2,6},{3,7},{4}}=>{{1,7},{2,6},{3,5},{4}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,1,2,3,4,7]=>{{1,5},{2,6},{3},{4},{7}}=>{{1,6},{2,5},{3},{4},{7}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>{{1,5},{2},{3},{4},{6,7}}=>{{1,5},{2},{3},{4},{6,7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,7,4,6]=>{{1,5,7},{2},{3},{4},{6}}=>{{1,5,7},{2},{3},{4},{6}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,7,3,4,6]=>{{1,5},{2},{3},{4,7},{6}}=>{{1,7},{2},{3},{4,5},{6}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,3,4,6]=>{{1,5},{2},{3,7},{4},{6}}=>{{1,7},{2},{3,5},{4},{6}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>{{1,5},{2,7},{3},{4},{6}}=>{{1,7},{2,5},{3},{4},{6}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7]=>{{1,5},{2},{3},{4},{6},{7}}=>{{1,5},{2},{3},{4},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,6,7,5]=>{{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]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}=>{{1},{2},{3},{4},{5,6},{7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5]=>{{1},{2},{3},{4,6,7},{5}}=>{{1},{2},{3},{4,6,7},{5}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}=>{{1},{2},{3},{4,7},{5,6}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,3,6,4,5,7]=>{{1},{2},{3},{4,6},{5},{7}}=>{{1},{2},{3},{4,6},{5},{7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,6,3,4,7,5]=>{{1},{2},{3,6,7},{4},{5}}=>{{1},{2},{3,6,7},{4},{5}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,5]=>{{1},{2},{3,6},{4},{5,7}}=>{{1},{2},{3,7},{4},{5,6}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,7,3,4,5]=>{{1},{2},{3,6},{4,7},{5}}=>{{1},{2},{3,7},{4,6},{5}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,3,4,5,7]=>{{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]=>[1,6,2,3,4,7,5]=>{{1},{2,6,7},{3},{4},{5}}=>{{1},{2,6,7},{3},{4},{5}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>{{1},{2,6},{3},{4},{5,7}}=>{{1},{2,7},{3},{4},{5,6}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,4,5]=>{{1},{2,6},{3},{4,7},{5}}=>{{1},{2,7},{3},{4,6},{5}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,7,2,3,4,5]=>{{1},{2,6},{3,7},{4},{5}}=>{{1},{2,7},{3,6},{4},{5}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,3,4,5,7]=>{{1},{2,6},{3},{4},{5},{7}}=>{{1},{2,6},{3},{4},{5},{7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>{{1,6,7},{2},{3},{4},{5}}=>{{1,6,7},{2},{3},{4},{5}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,1,2,3,7,4,5]=>{{1,6},{2},{3},{4},{5,7}}=>{{1,7},{2},{3},{4},{5,6}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,1,2,7,3,4,5]=>{{1,6},{2},{3},{4,7},{5}}=>{{1,7},{2},{3},{4,6},{5}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,3,4,5]=>{{1,6},{2},{3,7},{4},{5}}=>{{1,7},{2},{3,6},{4},{5}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>{{1,6},{2,7},{3},{4},{5}}=>{{1,7},{2,6},{3},{4},{5}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5,7]=>{{1,6},{2},{3},{4},{5},{7}}=>{{1,6},{2},{3},{4},{5},{7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>{{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]=>[1,2,3,4,7,5,6]=>{{1},{2},{3},{4},{5,7},{6}}=>{{1},{2},{3},{4},{5,7},{6}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,3,7,4,5,6]=>{{1},{2},{3},{4,7},{5},{6}}=>{{1},{2},{3},{4,7},{5},{6}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,7,3,4,5,6]=>{{1},{2},{3,7},{4},{5},{6}}=>{{1},{2},{3,7},{4},{5},{6}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>{{1},{2,7},{3},{4},{5},{6}}=>{{1},{2,7},{3},{4},{5},{6}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>{{1,7},{2},{3},{4},{5},{6}}=>{{1,7},{2},{3},{4},{5},{6}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,6,7,5,8]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4},{5,6,7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,8,5,7]=>{{1,2,3,4},{5,6,8},{7}}=>{{1,2,3,4},{5,6,8},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}}=>{{1,2,3,4},{5,6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,4,1,7,5,8,6]=>{{1,2,3,4},{5,7,8},{6}}=>{{1,2,3,4},{5,7,8},{6}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,1,7,8,5,6]=>{{1,2,3,4},{5,7},{6,8}}=>{{1,2,3,4},{5,8},{6,7}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>{{1,2,3,4,8},{5},{6},{7}}=>{{1,2,3,4,8},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}=>{{1,2,3,4},{5},{6},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,1,4]=>{{1,2,3,5,7},{4,6,8}}=>{{1,2,3,8},{4,5,6,7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,5,7,8},{4},{6}}=>{{1,2,3,5,7,8},{4},{6}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,4,6,7,8,5]=>{{1,2,3},{4},{5,6,7,8}}=>{{1,2,3},{4},{5,6,7,8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,8,7]=>{{1,2,3,6},{4},{5},{7,8}}=>{{1,2,3,6},{4},{5},{7,8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>{{1,2},{3,4,5,7,8},{6}}=>{{1,2},{3,4,5,7,8},{6}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4,5,8,3,6,7]=>{{1,2},{3,4,5,8},{6},{7}}=>{{1,2},{3,4,5,8},{6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2},{3,4},{5,6,7,8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,8,5,7]=>{{1,2},{3,4},{5,6,8},{7}}=>{{1,2},{3,4},{5,6,8},{7}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>{{1,2},{3,4,6},{5},{7,8}}=>{{1,2},{3,4,6},{5},{7,8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,8,5,7]=>{{1,2},{3,4,6,8},{5},{7}}=>{{1,2},{3,4,6,8},{5},{7}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,8,3,5,7]=>{{1,2},{3,4,6},{5,8},{7}}=>{{1,2},{3,4,8},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,3,7,5,8,6]=>{{1,2},{3,4},{5,7,8},{6}}=>{{1,2},{3,4},{5,7,8},{6}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,4,3,7,8,5,6]=>{{1,2},{3,4},{5,7},{6,8}}=>{{1,2},{3,4},{5,8},{6,7}}
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,3,8,5,6,7]=>{{1,2},{3,4},{5,8},{6},{7}}=>{{1,2},{3,4},{5,8},{6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,4,1,5,6,3,8,7]=>{{1,2,4,5,6},{3},{7,8}}=>{{1,2,4,5,6},{3},{7,8}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,6,7,8,5]=>{{1,2,4},{3},{5,6,7,8}}=>{{1,2,4},{3},{5,6,7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,8,7]=>{{1,2,4},{3},{5,6},{7,8}}=>{{1,2,4},{3},{5,6},{7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,8,5,7]=>{{1,2,4},{3},{5,6,8},{7}}=>{{1,2,4},{3},{5,6,8},{7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2,4,6,7,8},{3},{5}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,6,7,3,8,5]=>{{1,2,4,6},{3},{5,7,8}}=>{{1,2,4,7,8},{3},{5,6}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,8,7]=>{{1,2,4,6},{3},{5},{7,8}}=>{{1,2,4,6},{3},{5},{7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,2,4,6,8},{3},{5},{7}}
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,8,3,5,7]=>{{1,2,4,6},{3},{5,8},{7}}=>{{1,2,4,8},{3},{5,6},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,6,1,7,3,8,5]=>{{1,2,4},{3,6},{5,7,8}}=>{{1,2,7,8},{3,4},{5,6}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,6,7,1,8,3,5]=>{{1,2,4,7},{3,6,8},{5}}=>{{1,2,8},{3,4,6,7},{5}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,8,7]=>{{1,2,4},{3,6},{5},{7,8}}=>{{1,2,6},{3,4},{5},{7,8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,8,5,7]=>{{1,2,4},{3,6,8},{5},{7}}=>{{1,2,6,8},{3,4},{5},{7}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>{{1,2,4},{3,6},{5,8},{7}}=>{{1,2,8},{3,4},{5,6},{7}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>{{1,2,4,8},{3,6},{5},{7}}=>{{1,2,8},{3,4,6},{5},{7}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,7,1,3,5,8,6]=>{{1,2,4},{3,7,8},{5},{6}}=>{{1,2,7,8},{3,4},{5},{6}}
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1,3,8,5,6,7]=>{{1,2,4},{3},{5,8},{6},{7}}=>{{1,2,4},{3},{5,8},{6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,3,6,4,8,7]=>{{1,2},{3,5,6},{4},{7,8}}=>{{1,2},{3,5,6},{4},{7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,3,4]=>{{1,2},{3,5,7},{4,6,8}}=>{{1,2},{3,8},{4,5,6,7}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>{{1,2},{3,5},{4,6},{7,8}}=>{{1,2},{3,6},{4,5},{7,8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,5,7,3,8,4,6]=>{{1,2},{3,5},{4,7},{6,8}}=>{{1,2},{3,8},{4,5},{6,7}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,1,5,7,8,3,4,6]=>{{1,2},{3,5,8},{4,7},{6}}=>{{1,2},{3,8},{4,5,7},{6}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,5,1,6,7,3,8,4]=>{{1,2,5,7,8},{3},{4,6}}=>{{1,2,7,8},{3},{4,5,6}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>{{1,2,5,7},{3},{4,6,8}}=>{{1,2,8},{3},{4,5,6,7}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,1,3,4]=>{{1,2,5,8},{3,6},{4,7}}=>{{1,2,8},{3,7},{4,5,6}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,7,3,4,8,6]=>{{1,2,5},{3},{4,7,8},{6}}=>{{1,2,7,8},{3},{4,5},{6}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>{{1,2},{3,6,7,8},{4},{5}}=>{{1,2},{3,6,7,8},{4},{5}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,3,4,5]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2},{3,8},{4,7},{5,6}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,8,5,7]=>{{1,2},{3,6,8},{4},{5},{7}}=>{{1,2},{3,6,8},{4},{5},{7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}=>{{1},{2,3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}=>{{1},{2,3,8},{4,5,6,7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1},{2,3},{4},{5},{6,7},{8}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}=>{{1},{2,3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>{{1,3,4},{2},{5,6,7,8}}=>{{1,3,4},{2},{5,6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7]=>{{1,3,4},{2},{5,6},{7,8}}=>{{1,3,4},{2},{5,6},{7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,7,5,8,6]=>{{1,3,4},{2},{5,7,8},{6}}=>{{1,3,4},{2},{5,7,8},{6}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,6,7,8,5]=>{{1,3},{2,4},{5,6,7,8}}=>{{1,4},{2,3},{5,6,7,8}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}=>{{1,4},{2,3},{5,6},{7,8}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,6,1,2,7,8,5]=>{{1,3,6,7,8},{2,4},{5}}=>{{1,6,7,8},{2,3,4},{5}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,2,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,4},{2,3},{5,8},{6,7}}
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>{{1,3,7},{2,4},{5,8},{6}}=>{{1,8},{2,3,4},{5,7},{6}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,5,6,2,8,4,7]=>{{1,3,5},{2},{4,6,8},{7}}=>{{1,3,6,8},{2},{4,5},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6,8]=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1,3,5,7},{2},{4},{6},{8}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,7,2,8,4,6]=>{{1,3,5},{2},{4,7},{6,8}}=>{{1,3,8},{2},{4,5},{6,7}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,5,1,6,2,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>{{1,6},{2,3},{4,5},{7,8}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,5,6,1,7,8,2,4]=>{{1,3,6,8},{2,5,7},{4}}=>{{1,8},{2,3,5,6,7},{4}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,8,1,2,4]=>{{1,3,6},{2,5,8},{4,7}}=>{{1,8},{2,3,7},{4,5,6}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,7,8,2,4,6]=>{{1,3},{2,5,8},{4,7},{6}}=>{{1,8},{2,3},{4,5,7},{6}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,6,7,8,5]=>{{1,3},{2},{4},{5,6,7,8}}=>{{1,3},{2},{4},{5,6,7,8}}
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,1,6,7,2,4,5,8]=>{{1,3,6},{2},{4,7},{5},{8}}=>{{1,3,7},{2},{4,6},{5},{8}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,1,6,2,8,4,5,7]=>{{1,3,6},{2},{4},{5,8},{7}}=>{{1,3,8},{2},{4},{5,6},{7}}
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,1,6,8,2,4,5,7]=>{{1,3,6},{2},{4,8},{5},{7}}=>{{1,3,8},{2},{4,6},{5},{7}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,6,1,7,8,2,4,5]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,6,7,1,2,8,4,5]=>{{1,3,7},{2,6,8},{4},{5}}=>{{1,8},{2,3,6,7},{4},{5}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}=>{{1},{2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>{{1},{2,4,6,8},{3},{5,7}}=>{{1},{2,4,8},{3},{5,6,7}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>{{1},{2,4,6,8},{3},{5},{7}}=>{{1},{2,4,6,8},{3},{5},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}=>{{1},{2,7,8},{3,4},{5,6}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>{{1,4,5,6},{2},{3},{7,8}}=>{{1,4,5,6},{2},{3},{7,8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,5,2,7,3,8,6]=>{{1,4},{2},{3,5,7,8},{6}}=>{{1,5,7,8},{2},{3,4},{6}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[4,1,5,7,2,8,3,6]=>{{1,4,7},{2},{3,5},{6,8}}=>{{1,8},{2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,7,1,2,8,3]=>{{1,4,7,8},{2,5},{3,6}}=>{{1,7,8},{2,6},{3,4,5}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,1,8,2,3]=>{{1,4,7},{2,5},{3,6,8}}=>{{1,8},{2,6,7},{3,4,5}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,1,2,3]=>{{1,4,7},{2,5,8},{3,6}}=>{{1,8},{2,7},{3,4,5,6}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>{{1,4,7},{2,5},{3,6},{8}}=>{{1,7},{2,6},{3,4,5},{8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4},{7,8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,5,7,1,2,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,6,7,5,8]=>{{1,4},{2},{3},{5,6,7},{8}}=>{{1,4},{2},{3},{5,6,7},{8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>{{1,4},{2},{3},{5,6},{7,8}}=>{{1,4},{2},{3},{5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,8,5,7]=>{{1,4},{2},{3},{5,6,8},{7}}=>{{1,4},{2},{3},{5,6,8},{7}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,6,5,7,8]=>{{1,4},{2},{3},{5,6},{7},{8}}=>{{1,4},{2},{3},{5,6},{7},{8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,8,5,7]=>{{1,4,6,8},{2},{3},{5},{7}}=>{{1,4,6,8},{2},{3},{5},{7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,6,2,7,3,8,5]=>{{1,4},{2},{3,6},{5,7,8}}=>{{1,7,8},{2},{3,4},{5,6}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,6,1,7,2,3,5,8]=>{{1,4,7},{2,6},{3},{5},{8}}=>{{1,7},{2,4,6},{3},{5},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,1,2,3,7,5,6,8]=>{{1,4},{2},{3},{5,7},{6},{8}}=>{{1,4},{2},{3},{5,7},{6},{8}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,7,1,8,2,3,5,6]=>{{1,4,8},{2,7},{3},{5},{6}}=>{{1,8},{2,4,7},{3},{5},{6}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,1,2,3,8,5,6,7]=>{{1,4},{2},{3},{5,8},{6},{7}}=>{{1,4},{2},{3},{5,8},{6},{7}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>{{1,4},{2},{3},{5},{6},{7},{8}}=>{{1,4},{2},{3},{5},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,4]=>{{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]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5},{6},{7},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,8,2,3,4]=>{{1},{2,5,8},{3,6},{4,7}}=>{{1},{2,8},{3,7},{4,5,6}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,6,7,8,4]=>{{1,5,6,7,8},{2},{3},{4}}=>{{1,5,6,7,8},{2},{3},{4}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,6,2,7,3,8,4]=>{{1,5,7,8},{2},{3,6},{4}}=>{{1,7,8},{2},{3,5,6},{4}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>{{1,5},{2,6},{3,7},{4},{8}}=>{{1,7},{2,6},{3,5},{4},{8}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,7,1,2,8,3,4,6]=>{{1,5,8},{2,7},{3},{4},{6}}=>{{1,8},{2,5,7},{3},{4},{6}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]=>{{1,5},{2,7},{3,8},{4},{6}}=>{{1,8},{2,7},{3,5},{4},{6}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1},{2},{3},{4},{5,6,7,8}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>{{1},{2,6},{3,7},{4,8},{5}}=>{{1},{2,8},{3,7},{4,6},{5}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>{{1,6},{2,7},{3,8},{4},{5}}=>{{1,8},{2,7},{3,6},{4},{5}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}=>{{1},{2},{3},{4},{5},{6,7},{8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5},{6},{7},{8}}
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
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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