Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00079: Set partitions —shape⟶ Integer partitions
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00079: Set partitions —shape⟶ Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0009;cc-rep-2Cc0002;cc-rep-3
[1,0]=>[1]=>{{1}}=>[1]
[1,0,1,0]=>[2,1]=>{{1,2}}=>[2]
[1,1,0,0]=>[1,2]=>{{1},{2}}=>[1,1]
[1,0,1,0,1,0]=>[2,3,1]=>{{1,2,3}}=>[3]
[1,0,1,1,0,0]=>[2,1,3]=>{{1,2},{3}}=>[2,1]
[1,1,0,0,1,0]=>[1,3,2]=>{{1},{2,3}}=>[2,1]
[1,1,0,1,0,0]=>[3,1,2]=>{{1,3},{2}}=>[2,1]
[1,1,1,0,0,0]=>[1,2,3]=>{{1},{2},{3}}=>[1,1,1]
[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>{{1,2,3,4}}=>[4]
[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>{{1,2,3},{4}}=>[3,1]
[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>{{1,2},{3,4}}=>[2,2]
[1,0,1,1,0,1,0,0]=>[2,4,1,3]=>{{1,2,4},{3}}=>[3,1]
[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>{{1,2},{3},{4}}=>[2,1,1]
[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>{{1},{2,3,4}}=>[3,1]
[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>{{1},{2,3},{4}}=>[2,1,1]
[1,1,0,1,0,0,1,0]=>[3,1,4,2]=>{{1,3,4},{2}}=>[3,1]
[1,1,0,1,0,1,0,0]=>[3,4,1,2]=>{{1,3},{2,4}}=>[2,2]
[1,1,0,1,1,0,0,0]=>[3,1,2,4]=>{{1,3},{2},{4}}=>[2,1,1]
[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>{{1},{2},{3,4}}=>[2,1,1]
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>{{1},{2,4},{3}}=>[2,1,1]
[1,1,1,0,1,0,0,0]=>[4,1,2,3]=>{{1,4},{2},{3}}=>[2,1,1]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>{{1},{2},{3},{4}}=>[1,1,1,1]
[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>{{1,2,3,4,5}}=>[5]
[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>{{1,2,3,4},{5}}=>[4,1]
[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>{{1,2,3},{4,5}}=>[3,2]
[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>{{1,2,3,5},{4}}=>[4,1]
[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}}=>[3,1,1]
[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>{{1,2},{3,4,5}}=>[3,2]
[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}}=>[2,2,1]
[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>{{1,2,4,5},{3}}=>[4,1]
[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>{{1,2,4},{3,5}}=>[3,2]
[1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]=>{{1,2,4},{3},{5}}=>[3,1,1]
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}}=>[2,2,1]
[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>{{1,2},{3,5},{4}}=>[2,2,1]
[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>{{1,2,5},{3},{4}}=>[3,1,1]
[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}}=>[2,1,1,1]
[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}=>[4,1]
[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}=>[3,1,1]
[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}=>[2,2,1]
[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>{{1},{2,3,5},{4}}=>[3,1,1]
[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}=>[2,1,1,1]
[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>{{1,3,4,5},{2}}=>[4,1]
[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>{{1,3,4},{2},{5}}=>[3,1,1]
[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>{{1,3},{2,4,5}}=>[3,2]
[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>{{1,3,5},{2,4}}=>[3,2]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>{{1,3},{2,4},{5}}=>[2,2,1]
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>{{1,3},{2},{4,5}}=>[2,2,1]
[1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]=>{{1,3,5},{2},{4}}=>[3,1,1]
[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>{{1,3},{2,5},{4}}=>[2,2,1]
[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>{{1,3},{2},{4},{5}}=>[2,1,1,1]
[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}=>[3,1,1]
[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}=>[2,1,1,1]
[1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]=>{{1},{2,4,5},{3}}=>[3,1,1]
[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}=>[2,2,1]
[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>{{1},{2,4},{3},{5}}=>[2,1,1,1]
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>{{1,4,5},{2},{3}}=>[3,1,1]
[1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]=>{{1,4},{2},{3,5}}=>[2,2,1]
[1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]=>{{1,4},{2,5},{3}}=>[2,2,1]
[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>{{1,4},{2},{3},{5}}=>[2,1,1,1]
[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}=>[2,1,1,1]
[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>{{1},{2},{3,5},{4}}=>[2,1,1,1]
[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>{{1},{2,5},{3},{4}}=>[2,1,1,1]
[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>{{1,5},{2},{3},{4}}=>[2,1,1,1]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}=>[1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}=>[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}}=>[5,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}=>[4,2]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,6},{5}}=>[5,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}=>[4,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}=>[3,3]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}=>[3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>{{1,2,3,5,6},{4}}=>[5,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>{{1,2,3,5},{4,6}}=>[4,2]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>{{1,2,3,5},{4},{6}}=>[4,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}=>[3,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>{{1,2,3},{4,6},{5}}=>[3,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>{{1,2,3,6},{4},{5}}=>[4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}=>[3,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}=>[4,2]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}=>[3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}=>[2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>{{1,2},{3,4,6},{5}}=>[3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}=>[2,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>{{1,2,4,5,6},{3}}=>[5,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>{{1,2,4,5},{3},{6}}=>[4,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>{{1,2,4},{3,5,6}}=>[3,3]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>{{1,2,4,6},{3,5}}=>[4,2]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>{{1,2,4},{3,5},{6}}=>[3,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>{{1,2,4},{3},{5,6}}=>[3,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>{{1,2,4,6},{3},{5}}=>[4,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>{{1,2,4},{3,6},{5}}=>[3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>{{1,2,4},{3},{5},{6}}=>[3,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}=>[3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}=>[2,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>{{1,2},{3,5,6},{4}}=>[3,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}}=>[2,2,2]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>{{1,2},{3,5},{4},{6}}=>[2,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>{{1,2,5,6},{3},{4}}=>[4,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>{{1,2,5},{3},{4,6}}=>[3,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>{{1,2,5},{3,6},{4}}=>[3,2,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>{{1,2,5},{3},{4},{6}}=>[3,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}=>[2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>{{1,2},{3},{4,6},{5}}=>[2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>{{1,2},{3,6},{4},{5}}=>[2,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>{{1,2,6},{3},{4},{5}}=>[3,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}=>[5,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}=>[4,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}=>[3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>{{1},{2,3,4,6},{5}}=>[4,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}=>[3,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}=>[3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}=>[2,2,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>{{1},{2,3,5,6},{4}}=>[4,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}=>[3,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>{{1},{2,3,5},{4},{6}}=>[3,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}=>[2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>{{1},{2,3},{4,6},{5}}=>[2,2,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>{{1},{2,3,6},{4},{5}}=>[3,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}=>[2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>{{1,3,4,5,6},{2}}=>[5,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>{{1,3,4,5},{2},{6}}=>[4,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>{{1,3,4},{2},{5,6}}=>[3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>{{1,3,4,6},{2},{5}}=>[4,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>{{1,3,4},{2},{5},{6}}=>[3,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>{{1,3},{2,4,5,6}}=>[4,2]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>{{1,3},{2,4,5},{6}}=>[3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>{{1,3,5,6},{2,4}}=>[4,2]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}}=>[3,3]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>{{1,3,5},{2,4},{6}}=>[3,2,1]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}}=>[2,2,2]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>{{1,3},{2,4,6},{5}}=>[3,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>{{1,3,6},{2,4},{5}}=>[3,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>{{1,3},{2,4},{5},{6}}=>[2,2,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>{{1,3},{2},{4,5,6}}=>[3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>{{1,3},{2},{4,5},{6}}=>[2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>{{1,3,5,6},{2},{4}}=>[4,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>{{1,3,5},{2},{4,6}}=>[3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>{{1,3,5},{2},{4},{6}}=>[3,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>{{1,3},{2,5,6},{4}}=>[3,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}}=>[2,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>{{1,3,6},{2,5},{4}}=>[3,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>{{1,3},{2,5},{4},{6}}=>[2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>{{1,3},{2},{4},{5,6}}=>[2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>{{1,3},{2},{4,6},{5}}=>[2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>{{1,3,6},{2},{4},{5}}=>[3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>{{1,3},{2,6},{4},{5}}=>[2,2,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>{{1,3},{2},{4},{5},{6}}=>[2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}=>[4,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}=>[3,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}=>[2,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>{{1},{2},{3,4,6},{5}}=>[3,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}=>[2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>{{1},{2,4,5,6},{3}}=>[4,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>{{1},{2,4,5},{3},{6}}=>[3,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}=>[3,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>{{1},{2,4,6},{3,5}}=>[3,2,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}=>[2,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>{{1},{2,4},{3},{5,6}}=>[2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>{{1},{2,4,6},{3},{5}}=>[3,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]=>{{1},{2,4},{3,6},{5}}=>[2,2,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>{{1},{2,4},{3},{5},{6}}=>[2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>{{1,4,5,6},{2},{3}}=>[4,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>{{1,4,5},{2},{3},{6}}=>[3,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>{{1,4},{2},{3,5,6}}=>[3,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>{{1,4,6},{2},{3,5}}=>[3,2,1]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>{{1,4},{2},{3,5},{6}}=>[2,2,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>{{1,4},{2,5,6},{3}}=>[3,2,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>{{1,4,6},{2,5},{3}}=>[3,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}}=>[2,2,2]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>{{1,4},{2,5},{3},{6}}=>[2,2,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>{{1,4},{2},{3},{5,6}}=>[2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>{{1,4,6},{2},{3},{5}}=>[3,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>{{1,4},{2},{3,6},{5}}=>[2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>{{1,4},{2,6},{3},{5}}=>[2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>{{1,4},{2},{3},{5},{6}}=>[2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}=>[3,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}=>[2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>{{1},{2},{3,5,6},{4}}=>[3,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}=>[2,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>{{1},{2},{3,5},{4},{6}}=>[2,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>{{1},{2,5,6},{3},{4}}=>[3,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>{{1},{2,5},{3},{4,6}}=>[2,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>{{1},{2,5},{3,6},{4}}=>[2,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>{{1},{2,5},{3},{4},{6}}=>[2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>{{1,5,6},{2},{3},{4}}=>[3,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>{{1,5},{2},{3},{4,6}}=>[2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>{{1,5},{2},{3,6},{4}}=>[2,2,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>{{1,5},{2,6},{3},{4}}=>[2,2,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>{{1,5},{2},{3},{4},{6}}=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>{{1},{2},{3},{4,6},{5}}=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>{{1},{2},{3,6},{4},{5}}=>[2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>{{1},{2,6},{3},{4},{5}}=>[2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>{{1,6},{2},{3},{4},{5}}=>[2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}=>[1,1,1,1,1,1]
[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}}=>[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}}=>[6,1]
[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}}=>[5,2]
[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}}=>[6,1]
[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}}=>[5,1,1]
[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}}=>[4,3]
[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}}=>[4,2,1]
[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}}=>[6,1]
[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}}=>[5,2]
[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}}=>[5,1,1]
[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}}=>[4,2,1]
[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}}=>[4,2,1]
[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}}=>[5,1,1]
[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}}=>[4,1,1,1]
[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}}=>[4,3]
[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}}=>[3,3,1]
[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}}=>[3,2,2]
[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}}=>[3,3,1]
[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}}=>[3,2,1,1]
[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}}=>[6,1]
[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}}=>[5,1,1]
[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}}=>[4,3]
[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}}=>[5,2]
[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}}=>[4,2,1]
[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}}=>[4,2,1]
[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}}=>[5,1,1]
[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}}=>[4,2,1]
[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}}=>[4,1,1,1]
[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}}=>[3,3,1]
[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}}=>[3,2,1,1]
[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}}=>[3,3,1]
[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}}=>[3,2,2]
[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}}=>[3,2,1,1]
[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}}=>[5,1,1]
[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}}=>[4,2,1]
[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}}=>[4,2,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[5,2]
[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}}=>[4,2,1]
[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}}=>[3,2,2]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,2]
[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}}=>[2,2,2,1]
[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}}=>[4,2,1]
[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}}=>[3,2,2]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[6,1]
[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}}=>[5,1,1]
[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}}=>[4,2,1]
[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}}=>[5,1,1]
[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}}=>[4,1,1,1]
[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}}=>[4,3]
[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}}=>[3,3,1]
[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}}=>[5,2]
[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}}=>[4,3]
[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}}=>[4,2,1]
[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}}=>[3,2,2]
[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}}=>[3,3,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,3,1]
[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}}=>[3,2,1,1]
[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}}=>[5,1,1]
[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}}=>[4,2,1]
[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}}=>[4,1,1,1]
[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}}=>[3,3,1]
[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}}=>[3,2,2]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,2]
[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}}=>[3,2,2]
[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}}=>[2,2,2,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,1,1,1]
[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}}=>[5,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,3,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,3,1]
[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}}=>[4,2,1]
[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}}=>[3,2,2]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,1,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[6,1]
[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}}=>[5,1,1]
[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}}=>[4,2,1]
[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}}=>[5,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,3,1]
[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}}=>[3,2,1,1]
[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}}=>[5,1,1]
[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}}=>[4,2,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[5,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,3,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,1,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[6,1]
[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}}=>[5,1,1]
[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}}=>[4,2,1]
[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}}=>[5,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,3,1]
[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}}=>[3,2,1,1]
[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}}=>[5,1,1]
[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}}=>[4,2,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[5,2]
[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}}=>[4,2,1]
[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}}=>[3,2,2]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[5,2]
[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}}=>[4,2,1]
[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}}=>[4,3]
[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}}=>[4,3]
[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}}=>[3,3,1]
[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}}=>[3,2,2]
[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}}=>[4,2,1]
[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}}=>[3,3,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,2]
[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}}=>[2,2,2,1]
[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}}=>[4,2,1]
[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}}=>[3,2,2]
[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}}=>[3,2,1,1]
[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}}=>[4,2,1]
[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}}=>[3,2,2]
[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}}=>[3,3,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[5,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,3,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,2]
[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}}=>[3,2,2]
[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}}=>[2,2,2,1]
[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}}=>[4,2,1]
[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}}=>[3,3,1]
[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}}=>[3,2,2]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,1,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[5,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[5,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[4,2,1]
[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}}=>[3,3,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[5,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[4,2,1]
[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}}=>[3,3,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[4,2,1]
[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}}=>[3,2,1,1]
[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}}=>[4,2,1]
[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}}=>[3,3,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,2]
[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}}=>[3,2,2]
[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}}=>[3,2,2]
[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}}=>[2,2,2,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[4,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,2,1,1]
[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}}=>[3,2,1,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,2,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[3,1,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,2,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[2,1,1,1,1,1]
[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}}=>[1,1,1,1,1,1,1]
[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}}=>[4,4]
[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}}=>[4,2,2]
[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}}=>[4,3,1]
[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}}=>[4,3,1]
[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}}=>[5,2,1]
[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}}=>[4,2,2]
[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}}=>[2,2,2,2]
[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}}=>[3,2,2,1]
[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}}=>[3,2,2,1]
[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}}=>[4,2,1,1]
[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}}=>[3,2,2,1]
[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}}=>[3,2,2,1]
[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}}=>[2,2,2,2]
[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}}=>[5,2,1]
[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}}=>[4,3,1]
[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}}=>[3,2,2,1]
[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}}=>[3,3,1,1]
[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}}=>[6,1,1]
[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}}=>[4,3,1]
[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}}=>[4,2,1,1]
[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}}=>[5,1,1,1]
[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}}=>[4,2,1,1]
[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}}=>[3,3,2]
[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}}=>[4,3,1]
[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}}=>[3,2,2,1]
[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}}=>[3,3,1,1]
[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}}=>[3,2,2,1]
[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}}=>[4,2,1,1]
[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}}=>[3,3,1,1]
[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}}=>[3,2,2,1]
[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}}=>[2,2,2,2]
[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}}=>[2,2,2,2]
[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}}=>[3,2,2,1]
[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}}=>[5,2,1]
[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}}=>[4,2,1,1]
[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}}=>[2,2,2,2]
[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}}=>[4,3,1]
[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}}=>[3,2,2,1]
[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}}=>[3,3,1,1]
[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}}=>[2,2,2,2]
[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}}=>[5,2,1]
[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}}=>[2,2,2,2]
[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}}=>[4,1,1,1,1]
[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}}=>[3,2,2,1]
[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}}=>[2,2,2,2]
[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}}=>[4,3,1]
[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}}=>[2,2,2,2]
[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}}=>[3,2,2,1]
[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}}=>[3,2,1,1,1]
[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}}=>[3,2,1,1,1]
[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}}=>[2,2,2,2]
[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}}=>[4,2,1,1]
[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}}=>[3,2,2,1]
[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}}=>[2,2,2,2]
[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}}=>[2,2,2,2]
[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}}=>[2,2,2,2]
[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}}=>[5,1,1,1]
[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}}=>[2,2,2,2]
[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}}=>[2,2,2,1,1]
[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}}=>[2,2,2,1,1]
[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}}=>[1,1,1,1,1,1,1,1]
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
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.
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