Identifier
Mp00030:
Dyck paths
—zeta map⟶
Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Mp00079: Set partitions —shape⟶ Integer partitions
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Mp00079: Set partitions —shape⟶ Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0009;cc-rep-2Cc0002;cc-rep-3
[1,0]=>[1,0]=>{{1}}=>[1]
[1,0,1,0]=>[1,1,0,0]=>{{1,2}}=>[2]
[1,1,0,0]=>[1,0,1,0]=>{{1},{2}}=>[1,1]
[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>{{1,2,3}}=>[3]
[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>{{1},{2,3}}=>[2,1]
[1,1,0,0,1,0]=>[1,1,0,1,0,0]=>{{1,3},{2}}=>[2,1]
[1,1,0,1,0,0]=>[1,1,0,0,1,0]=>{{1,2},{3}}=>[2,1]
[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>{{1},{2},{3}}=>[1,1,1]
[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>{{1,2,3,4}}=>[4]
[1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0]=>{{1},{2,3,4}}=>[3,1]
[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>{{1,3,4},{2}}=>[3,1]
[1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>{{1,2},{3,4}}=>[2,2]
[1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>{{1},{2},{3,4}}=>[2,1,1]
[1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0]=>{{1,2,4},{3}}=>[3,1]
[1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]=>{{1,4},{2},{3}}=>[2,1,1]
[1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>{{1,4},{2,3}}=>[2,2]
[1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0]=>{{1,2,3},{4}}=>[3,1]
[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>{{1},{2,3},{4}}=>[2,1,1]
[1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>{{1},{2,4},{3}}=>[2,1,1]
[1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>{{1,3},{2},{4}}=>[2,1,1]
[1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>{{1,2},{3},{4}}=>[2,1,1]
[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4}}=>[1,1,1,1]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}}=>[5]
[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}}=>[4,1]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>{{1,3,4,5},{2}}=>[4,1]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>[3,2]
[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}}=>[3,1,1]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>{{1,2,4,5},{3}}=>[4,1]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>{{1,4,5},{2},{3}}=>[3,1,1]
[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>{{1,4,5},{2,3}}=>[3,2]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}}=>[3,2]
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>[2,2,1]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>{{1},{2,4,5},{3}}=>[3,1,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5}}=>[2,2,1]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3},{4,5}}=>[2,2,1]
[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5}}=>[2,1,1,1]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]=>{{1,2,3,5},{4}}=>[4,1]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>{{1,3,5},{2},{4}}=>[3,1,1]
[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]=>{{1,2,5},{3},{4}}=>[3,1,1]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>{{1,5},{2,3},{4}}=>[2,2,1]
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>{{1},{2,5},{3},{4}}=>[2,1,1,1]
[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>{{1,2,5},{3,4}}=>[3,2]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>{{1,5},{2,4},{3}}=>[2,2,1]
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>{{1,5},{2,3,4}}=>[3,2]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4},{5}}=>[4,1]
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}}=>[3,1,1]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>{{1},{2,5},{3,4}}=>[2,2,1]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>{{1,3,4},{2},{5}}=>[3,1,1]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5}}=>[2,2,1]
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5}}=>[2,1,1,1]
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>{{1},{2,3,5},{4}}=>[3,1,1]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>{{1,5},{2},{3},{4}}=>[2,1,1,1]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>{{1,5},{2},{3,4}}=>[2,2,1]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>{{1,2,4},{3},{5}}=>[3,1,1]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>{{1,4},{2},{3},{5}}=>[2,1,1,1]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,5},{4}}=>[2,2,1]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>{{1,4},{2,3},{5}}=>[2,2,1]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4},{5}}=>[3,1,1]
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4},{5}}=>[2,1,1,1]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3,5},{4}}=>[2,1,1,1]
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>{{1},{2,4},{3},{5}}=>[2,1,1,1]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>{{1,3},{2},{4},{5}}=>[2,1,1,1]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5}}=>[2,1,1,1]
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5}}=>[1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}}=>[6]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}}=>[5,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,3,4,5,6},{2}}=>[5,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>[4,2]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}}=>[4,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>{{1,2,4,5,6},{3}}=>[5,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2},{3}}=>[4,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2,3}}=>[4,2]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>[3,3]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>[3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2,4,5,6},{3}}=>[4,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>{{1,3},{2},{4,5,6}}=>[3,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}}=>[3,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}}=>[3,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>{{1,2,3,5,6},{4}}=>[5,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>{{1,3,5,6},{2},{4}}=>[4,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>{{1,2,5,6},{3},{4}}=>[4,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>{{1,5,6},{2,3},{4}}=>[3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2,5,6},{3},{4}}=>[3,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>{{1,2,5,6},{3,4}}=>[4,2]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>{{1,5,6},{2,4},{3}}=>[3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>{{1,5,6},{2,3,4}}=>[3,3]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}}=>[4,2]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>[3,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2,5,6},{3,4}}=>[3,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>{{1,3,4},{2},{5,6}}=>[3,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>[2,2,2]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>[2,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2,3,5,6},{4}}=>[4,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>{{1,5,6},{2},{3},{4}}=>[3,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>{{1,5,6},{2},{3,4}}=>[3,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>{{1,2,4},{3},{5,6}}=>[3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>{{1,4},{2},{3},{5,6}}=>[2,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>{{1,2},{3,5,6},{4}}=>[3,2,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6}}=>[2,2,2]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5,6}}=>[3,2,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}}=>[2,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3,5,6},{4}}=>[3,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2,4},{3},{5,6}}=>[2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5,6}}=>[2,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5,6}}=>[2,2,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6}}=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>{{1,2,3,4,6},{5}}=>[5,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>{{1,3,4,6},{2},{5}}=>[4,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>{{1,2,4,6},{3},{5}}=>[4,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>{{1,4,6},{2,3},{5}}=>[3,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2,4,6},{3},{5}}=>[3,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>{{1,2,3,6},{4},{5}}=>[4,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>{{1,2,6},{3},{4},{5}}=>[3,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>{{1,2,6},{3,4},{5}}=>[3,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>{{1,6},{2,3,4},{5}}=>[3,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2,6},{3,4},{5}}=>[2,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2,3,6},{4},{5}}=>[3,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>{{1,6},{2},{3,4},{5}}=>[2,2,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>{{1,2},{3,6},{4},{5}}=>[2,2,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3,6},{4},{5}}=>[2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>{{1,2,3,6},{4,5}}=>[4,2]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>{{1,2,6},{3},{4,5}}=>[3,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>{{1,2,6},{3,5},{4}}=>[3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3,4}}=>[2,2,2]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2,6},{3,5},{4}}=>[2,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>{{1,2,6},{3,4,5}}=>[3,3]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>{{1,6},{2,3,5},{4}}=>[3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,6},{2,3,4,5}}=>[4,2]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}}=>[5,1]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}}=>[4,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2,6},{3,4,5}}=>[3,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>{{1,3,4,5},{2},{6}}=>[4,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>[3,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}}=>[3,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2,3,6},{4,5}}=>[3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>{{1,6},{2},{3,5},{4}}=>[2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>{{1,6},{2},{3,4,5}}=>[3,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>{{1,2,4,5},{3},{6}}=>[4,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>{{1,4,5},{2},{3},{6}}=>[3,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,6},{4,5}}=>[2,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>{{1,4,5},{2,3},{6}}=>[3,2,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}}=>[3,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>[2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3,6},{4,5}}=>[2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2,4,5},{3},{6}}=>[3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>{{1,3},{2},{4,5},{6}}=>[2,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4,5},{6}}=>[2,2,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6}}=>[2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2,3,4,6},{5}}=>[4,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>{{1,4,6},{2},{3},{5}}=>[3,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>{{1,3,6},{2},{4},{5}}=>[3,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>{{1,6},{2,4},{3},{5}}=>[2,2,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>{{1,6},{2},{3},{4},{5}}=>[2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>{{1,3,6},{2},{4,5}}=>[3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3},{4}}=>[2,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>{{1,6},{2,4,5},{3}}=>[3,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>{{1,2,3,5},{4},{6}}=>[4,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>{{1,3,5},{2},{4},{6}}=>[3,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>{{1,6},{2},{3},{4,5}}=>[2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>{{1,2,5},{3},{4},{6}}=>[3,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>{{1,5},{2,3},{4},{6}}=>[2,2,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2,5},{3},{4},{6}}=>[2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>{{1,2},{3,4,6},{5}}=>[3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>{{1,6},{2,3},{4},{5}}=>[2,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,6},{2,3},{4,5}}=>[2,2,2]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>{{1,2,5},{3,4},{6}}=>[3,2,1]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>{{1,5},{2,4},{3},{6}}=>[2,2,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>{{1,2,3},{4,6},{5}}=>[3,2,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>{{1,5},{2,3,4},{6}}=>[3,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5},{6}}=>[4,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}}=>[3,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2,3},{4,6},{5}}=>[2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2,5},{3,4},{6}}=>[2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>{{1,3,4},{2},{5},{6}}=>[3,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5},{6}}=>[2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6}}=>[2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3,4,6},{5}}=>[3,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2,6},{3},{4},{5}}=>[2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2,6},{3},{4,5}}=>[2,2,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2,3,5},{4},{6}}=>[3,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>{{1,5},{2},{3},{4},{6}}=>[2,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>{{1,3},{2},{4,6},{5}}=>[2,2,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>{{1,5},{2},{3,4},{6}}=>[2,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>{{1,2,4},{3},{5},{6}}=>[3,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6}}=>[2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4,6},{5}}=>[2,2,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>{{1,2},{3,5},{4},{6}}=>[2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>{{1,4},{2,3},{5},{6}}=>[2,2,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6}}=>[3,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6}}=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4,6},{5}}=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3,5},{4},{6}}=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6}}=>[2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6}}=>[2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6}}=>[2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>{{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]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}}=>[7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>[6,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}}=>[6,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>[5,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}}=>[5,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1,2,4,5,6,7},{3}}=>[6,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2},{3}}=>[5,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2,3}}=>[5,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>[4,3]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>[4,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,4,5,6,7},{3}}=>[5,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>{{1,3},{2},{4,5,6,7}}=>[4,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}}=>[4,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5,6,7}}=>[4,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>{{1,2,3,5,6,7},{4}}=>[6,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>{{1,3,5,6,7},{2},{4}}=>[5,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3},{4}}=>[5,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3},{4}}=>[4,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3},{4}}=>[4,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3,4}}=>[5,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,4},{3}}=>[4,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3,4}}=>[4,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>[4,3]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>[3,3,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3,4}}=>[4,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>{{1,3,4},{2},{5,6,7}}=>[3,3,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>[3,2,2]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>[3,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>{{1},{2,3,5,6,7},{4}}=>[5,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3},{4}}=>[4,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3,4}}=>[4,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>{{1,2,4},{3},{5,6,7}}=>[3,3,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2},{3},{5,6,7}}=>[3,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>{{1,2},{3,5,6,7},{4}}=>[4,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2,3},{5,6,7}}=>[3,2,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}}=>[3,3,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>[3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2},{3,5,6,7},{4}}=>[4,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>{{1},{2,4},{3},{5,6,7}}=>[3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>{{1,3},{2},{4},{5,6,7}}=>[3,2,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}}=>[3,2,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{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]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>{{1,2,3,4,6,7},{5}}=>[6,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>{{1,3,4,6,7},{2},{5}}=>[5,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>{{1,2,4,6,7},{3},{5}}=>[5,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2,3},{5}}=>[4,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>{{1},{2,4,6,7},{3},{5}}=>[4,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4},{5}}=>[5,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4},{5}}=>[4,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4},{5}}=>[4,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3,4},{5}}=>[3,3,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4},{5}}=>[3,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4},{5}}=>[4,1,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4},{5}}=>[3,2,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4},{5}}=>[3,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4},{5}}=>[3,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4,5}}=>[5,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4,5}}=>[4,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,5},{4}}=>[4,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3,4}}=>[3,2,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,5},{4}}=>[3,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4,5}}=>[4,3]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,5},{4}}=>[3,3,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,4,5}}=>[4,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>[5,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>[4,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4,5}}=>[3,3,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,3,4,5},{2},{6,7}}=>[4,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>[3,2,2]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>[3,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4,5}}=>[4,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,5},{4}}=>[3,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4,5}}=>[3,3,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>{{1,2,4,5},{3},{6,7}}=>[4,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2},{3},{6,7}}=>[3,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4,5}}=>[3,2,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2,3},{6,7}}=>[3,2,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>[3,2,2]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>[2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4,5}}=>[3,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>{{1},{2,4,5},{3},{6,7}}=>[3,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5},{6,7}}=>[2,2,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>[2,2,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>[2,2,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>{{1},{2,3,4,6,7},{5}}=>[5,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2},{3},{5}}=>[4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4},{5}}=>[4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,4},{3},{5}}=>[3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4},{5}}=>[3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4,5}}=>[4,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3},{4}}=>[3,2,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,4,5},{3}}=>[3,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>{{1,2,3,5},{4},{6,7}}=>[4,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>{{1,3,5},{2},{4},{6,7}}=>[3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4,5}}=>[3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3},{4},{6,7}}=>[3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2,3},{4},{6,7}}=>[2,2,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3},{4},{6,7}}=>[2,2,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>{{1,2},{3,4,6,7},{5}}=>[4,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4},{5}}=>[3,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4,5}}=>[3,2,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3,4},{6,7}}=>[3,2,2]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,4},{3},{6,7}}=>[2,2,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>{{1,2,3},{4,6,7},{5}}=>[3,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,3,4},{6,7}}=>[3,2,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}}=>[4,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>[3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>{{1},{2,3},{4,6,7},{5}}=>[3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3,4},{6,7}}=>[2,2,2,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>{{1,3,4},{2},{5},{6,7}}=>[3,2,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>[2,2,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6,7}}=>[2,2,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2},{3,4,6,7},{5}}=>[4,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4},{5}}=>[3,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4,5}}=>[3,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>{{1},{2,3,5},{4},{6,7}}=>[3,2,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3},{4},{6,7}}=>[2,2,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>{{1,3},{2},{4,6,7},{5}}=>[3,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3,4},{6,7}}=>[2,2,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>{{1,2,4},{3},{5},{6,7}}=>[3,2,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2},{3},{5},{6,7}}=>[2,2,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>{{1,2},{3},{4,6,7},{5}}=>[3,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>{{1,2},{3,5},{4},{6,7}}=>[2,2,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2,3},{5},{6,7}}=>[2,2,2,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6,7}}=>[3,2,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6,7}}=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3},{4,6,7},{5}}=>[3,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2},{3,5},{4},{6,7}}=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>{{1},{2,4},{3},{5},{6,7}}=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5},{6,7}}=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6,7}}=>[2,2,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,7},{6}}=>[6,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>{{1,3,4,5,7},{2},{6}}=>[5,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>{{1,2,4,5,7},{3},{6}}=>[5,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2,3},{6}}=>[4,2,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>{{1},{2,4,5,7},{3},{6}}=>[4,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>{{1,2,3,5,7},{4},{6}}=>[5,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3},{4},{6}}=>[4,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3,4},{6}}=>[4,2,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3,4},{6}}=>[3,3,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3,4},{6}}=>[3,2,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>{{1},{2,3,5,7},{4},{6}}=>[4,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3,4},{6}}=>[3,2,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>{{1,2},{3,5,7},{4},{6}}=>[3,2,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2},{3,5,7},{4},{6}}=>[3,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5},{6}}=>[5,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5},{6}}=>[4,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5},{6}}=>[4,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3,4},{5},{6}}=>[3,2,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4},{5},{6}}=>[3,1,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4,5},{6}}=>[4,2,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,5},{4},{6}}=>[3,2,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,4,5},{6}}=>[3,3,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,4,5},{6}}=>[4,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>{{1},{2,7},{3,4,5},{6}}=>[3,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4,5},{6}}=>[3,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2},{3,4,5},{6}}=>[3,2,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>{{1,2},{3,7},{4,5},{6}}=>[2,2,2,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2},{3,7},{4,5},{6}}=>[2,2,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5},{6}}=>[4,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4},{5},{6}}=>[3,1,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4,5},{6}}=>[3,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,4,5},{3},{6}}=>[3,2,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3},{4,5},{6}}=>[2,2,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>{{1,2},{3,4,7},{5},{6}}=>[3,2,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2,3},{4,5},{6}}=>[2,2,2,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>{{1,2,3},{4,7},{5},{6}}=>[3,2,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>{{1},{2,3},{4,7},{5},{6}}=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2},{3,4,7},{5},{6}}=>[3,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3},{4,5},{6}}=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>{{1,3},{2},{4,7},{5},{6}}=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>{{1,2},{3},{4,7},{5},{6}}=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3},{4,7},{5},{6}}=>[2,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5,6}}=>[5,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5,6}}=>[4,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5,6}}=>[4,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3,4},{5,6}}=>[3,2,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4},{5,6}}=>[3,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,6},{5}}=>[4,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4},{5}}=>[3,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4,5}}=>[3,2,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4,5}}=>[3,2,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4,5}}=>[2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4,6},{5}}=>[3,2,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4,5}}=>[2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>{{1,2},{3,7},{4,6},{5}}=>[2,2,2,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2},{3,7},{4,6},{5}}=>[2,2,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,5,6}}=>[4,3]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,5,6},{4}}=>[3,3,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,6},{5}}=>[3,3,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4,5}}=>[3,2,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>{{1},{2,7},{3,4,6},{5}}=>[3,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,5,6}}=>[4,3]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,6},{5}}=>[4,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}}=>[5,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}}=>[6,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}}=>[5,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>{{1},{2,7},{3,4,5,6}}=>[4,2,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,3,4,5,6},{2},{7}}=>[5,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>[4,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}}=>[4,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>{{1},{2,3,7},{4,5,6}}=>[3,3,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2},{3,4,6},{5}}=>[3,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2},{3,4,5,6}}=>[4,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>{{1,2,4,5,6},{3},{7}}=>[5,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2},{3},{7}}=>[4,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>{{1,2},{3,7},{4,5,6}}=>[3,2,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2,3},{7}}=>[4,2,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>[3,3,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>[3,2,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2},{3,7},{4,5,6}}=>[3,2,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>{{1},{2,4,5,6},{3},{7}}=>[4,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>{{1,3},{2},{4,5,6},{7}}=>[3,2,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2},{3},{4,5,6},{7}}=>[3,2,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4,5,6},{7}}=>[3,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5,6}}=>[4,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4},{5,6}}=>[3,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4,6},{5}}=>[3,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4,5}}=>[2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3},{4,6},{5}}=>[2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>{{1,3,7},{2},{4,5,6}}=>[3,3,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,4,6},{3},{5}}=>[3,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,4,5,6},{3}}=>[4,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>{{1,2,3,5,6},{4},{7}}=>[5,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>{{1,3,5,6},{2},{4},{7}}=>[4,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3},{4,5,6}}=>[3,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3},{4},{7}}=>[4,1,1,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3},{4},{7}}=>[3,2,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3},{4},{7}}=>[3,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>{{1,2},{3,4,7},{5,6}}=>[3,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2,3},{4,6},{5}}=>[2,2,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2,3},{4,5,6}}=>[3,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3,4},{7}}=>[4,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,4},{3},{7}}=>[3,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>{{1,2,3},{4,7},{5,6}}=>[3,2,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3,4},{7}}=>[3,3,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}}=>[4,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>[3,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1},{2,3},{4,7},{5,6}}=>[2,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3,4},{7}}=>[3,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>{{1,3,4},{2},{5,6},{7}}=>[3,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>[2,2,2,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>[2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2},{3,4,7},{5,6}}=>[3,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3},{4,6},{5}}=>[2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3},{4,5,6}}=>[3,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>{{1},{2,3,5,6},{4},{7}}=>[4,1,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3},{4},{7}}=>[3,1,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,3},{2},{4,7},{5,6}}=>[2,2,2,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3,4},{7}}=>[3,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>{{1,2,4},{3},{5,6},{7}}=>[3,2,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2},{3},{5,6},{7}}=>[2,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>{{1,2},{3},{4,7},{5,6}}=>[2,2,2,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>{{1,2},{3,5,6},{4},{7}}=>[3,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2,3},{5,6},{7}}=>[2,2,2,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3},{4},{5,6},{7}}=>[3,2,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5,6},{7}}=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3},{4,7},{5,6}}=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2},{3,5,6},{4},{7}}=>[3,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>{{1},{2,4},{3},{5,6},{7}}=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>{{1,3},{2},{4},{5,6},{7}}=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5,6},{7}}=>[2,2,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5,6},{7}}=>[2,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>{{1},{2,3,4,5,7},{6}}=>[5,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2},{3},{6}}=>[4,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>{{1,3,5,7},{2},{4},{6}}=>[4,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,4},{3},{6}}=>[3,2,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3},{4},{6}}=>[3,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5},{6}}=>[4,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4},{5},{6}}=>[3,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4,5},{6}}=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,5},{4},{6}}=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3,5},{4},{6}}=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2},{3},{5},{6}}=>[3,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3},{4},{6}}=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2,3},{4},{5},{6}}=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3},{4},{5},{6}}=>[2,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5,6}}=>[4,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4},{5,6}}=>[3,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4,6},{5}}=>[3,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,5},{4}}=>[2,2,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4},{5}}=>[2,2,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3},{4,5,6}}=>[3,3,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4},{5}}=>[3,2,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,5,6},{4}}=>[4,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>{{1,2,3,4,6},{5},{7}}=>[5,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>{{1,3,4,6},{2},{5},{7}}=>[4,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3,5,6},{4}}=>[3,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>{{1,2,4,6},{3},{5},{7}}=>[4,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2,3},{5},{7}}=>[3,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>{{1},{2,4,6},{3},{5},{7}}=>[3,1,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2},{3},{5,6}}=>[3,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4},{5}}=>[2,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3},{4}}=>[3,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4},{5},{7}}=>[4,1,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4},{5},{7}}=>[3,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2,3},{4},{5,6}}=>[2,2,2,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3,4},{5},{7}}=>[3,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,3,4},{5},{7}}=>[3,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3,4},{5},{7}}=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3},{4},{5,6}}=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4},{5},{7}}=>[3,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3,4},{5},{7}}=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>{{1,2},{3,6},{4},{5},{7}}=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2},{3,6},{4},{5},{7}}=>[2,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>{{1,2},{3,4,5,7},{6}}=>[4,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3},{4},{6}}=>[3,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2,3},{5},{6}}=>[3,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3,4},{6}}=>[2,2,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,4},{3},{5},{6}}=>[2,2,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2,3},{5,6}}=>[3,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4},{5}}=>[2,2,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3,4}}=>[3,2,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4,5},{7}}=>[4,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4,5},{7}}=>[3,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,4},{3},{5,6}}=>[2,2,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,5},{4},{7}}=>[3,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3,4},{7}}=>[2,2,2,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3,5},{4},{7}}=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>{{1,2,3},{4,5,7},{6}}=>[3,3,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,3,4},{5},{6}}=>[3,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,3,4},{5,6}}=>[3,2,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,4,5},{7}}=>[3,3,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,5},{4},{7}}=>[3,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>{{1,2,3,4},{5,7},{6}}=>[4,2,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,4,5},{7}}=>[4,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}}=>[5,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}}=>[4,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>{{1},{2,3,4},{5,7},{6}}=>[3,2,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>{{1},{2,6},{3,4,5},{7}}=>[3,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>{{1,3,4,5},{2},{6},{7}}=>[4,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>[3,2,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7}}=>[3,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>{{1},{2,3},{4,5,7},{6}}=>[3,2,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3,4},{5},{6}}=>[2,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3,4},{5,6}}=>[2,2,2,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4,5},{7}}=>[3,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3,5},{4},{7}}=>[2,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>{{1,3,4},{2},{5,7},{6}}=>[3,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2},{3,4,5},{7}}=>[3,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>{{1,2,4,5},{3},{6},{7}}=>[4,1,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2},{3},{6},{7}}=>[3,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,4},{5,7},{6}}=>[2,2,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>{{1,2},{3,6},{4,5},{7}}=>[2,2,2,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2,3},{6},{7}}=>[3,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7}}=>[3,2,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2},{3,4},{5,7},{6}}=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2},{3,6},{4,5},{7}}=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>{{1},{2,4,5},{3},{6},{7}}=>[3,1,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>{{1,3},{2},{4,5},{6},{7}}=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7}}=>[2,2,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2},{3,4,5,7},{6}}=>[4,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3},{4},{6}}=>[3,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>{{1},{2,4,7},{3},{5},{6}}=>[3,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3,5},{4},{6}}=>[2,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3},{4},{5},{6}}=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>{{1},{2,4,7},{3},{5,6}}=>[3,2,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4},{5}}=>[2,2,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3,5,6},{4}}=>[3,2,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>{{1},{2,3,4,6},{5},{7}}=>[4,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2},{3},{5},{7}}=>[3,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3},{4},{5,6}}=>[2,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4},{5},{7}}=>[3,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,4},{3},{5},{7}}=>[2,2,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3},{4},{5},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>{{1,3},{2},{4,5,7},{6}}=>[3,2,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3,4},{5},{6}}=>[2,2,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3,4},{5,6}}=>[2,2,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4,5},{7}}=>[3,2,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3},{4},{7}}=>[2,2,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>{{1,2,4},{3},{5,7},{6}}=>[3,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,4,5},{3},{7}}=>[3,2,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>{{1,2,3,5},{4},{6},{7}}=>[4,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>{{1,3,5},{2},{4},{6},{7}}=>[3,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2},{3},{5,7},{6}}=>[2,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3},{4,5},{7}}=>[2,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3},{4},{6},{7}}=>[3,1,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2,3},{4},{6},{7}}=>[2,2,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>{{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]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>{{1,2},{3},{4,5,7},{6}}=>[3,2,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>{{1,2},{3,7},{4},{5},{6}}=>[2,2,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>{{1,2},{3,7},{4},{5,6}}=>[2,2,2,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>{{1,2},{3,4,6},{5},{7}}=>[3,2,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2,3},{4},{5},{7}}=>[2,2,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2,3},{5,7},{6}}=>[2,2,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2,3},{4,5},{7}}=>[2,2,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3,4},{6},{7}}=>[3,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,4},{3},{6},{7}}=>[2,2,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>{{1,2,3},{4},{5,7},{6}}=>[3,2,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>{{1,2,3},{4,6},{5},{7}}=>[3,2,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,3,4},{6},{7}}=>[3,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7}}=>[4,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7}}=>[3,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>{{1},{2,3},{4},{5,7},{6}}=>[2,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>{{1},{2,3},{4,6},{5},{7}}=>[2,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>{{1},{2,5},{3,4},{6},{7}}=>[2,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>{{1,3,4},{2},{5},{6},{7}}=>[3,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7}}=>[2,2,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3},{4,5,7},{6}}=>[3,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2},{3,7},{4},{5},{6}}=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2},{3,7},{4},{5,6}}=>[2,2,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2},{3,4,6},{5},{7}}=>[3,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3},{4},{5},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>{{1},{2,4},{3},{5,7},{6}}=>[2,2,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3},{4,5},{7}}=>[2,2,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>{{1},{2,3,5},{4},{6},{7}}=>[3,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3},{4},{6},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>{{1,3},{2},{4},{5,7},{6}}=>[2,2,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>{{1,3},{2},{4,6},{5},{7}}=>[2,2,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3,4},{6},{7}}=>[2,2,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>{{1,2,4},{3},{5},{6},{7}}=>[3,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4},{5,7},{6}}=>[2,2,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>{{1,2},{3},{4,6},{5},{7}}=>[2,2,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>{{1,2},{3,5},{4},{6},{7}}=>[2,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2,3},{5},{6},{7}}=>[2,2,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7}}=>[3,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4},{5,7},{6}}=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3},{4,6},{5},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2},{3,5},{4},{6},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7}}=>[2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7}}=>[1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}}=>[8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,3,4,5,6,7,8},{2}}=>[7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>[6,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,4,5,6,7,8},{3}}=>[7,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,4,5,6,7,8},{2,3}}=>[6,2]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>[5,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>{{1,5,6,7,8},{2,3,4}}=>[5,3]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>[4,4]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,3,4},{2},{5,6,7,8}}=>[4,3,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>[4,2,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,5,6,7,8},{2},{3},{4}}=>[5,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,4},{3},{5,6,7,8}}=>[4,3,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,5,6,7,8},{4}}=>[5,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>{{1,4},{2,3},{5,6,7,8}}=>[4,2,2]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,6,7,8},{5}}=>[7,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>{{1,2,4,6,7,8},{3},{5}}=>[6,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>{{1,4,6,7,8},{2,3},{5}}=>[5,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>{{1,2,3,6,7,8},{4},{5}}=>[6,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>{{1,2},{3,6,7,8},{4},{5}}=>[4,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>{{1,2,3,6,7,8},{4,5}}=>[6,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>{{1,6,7,8},{2,5},{3,4}}=>[4,2,2]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>{{1,2,6,7,8},{3,4,5}}=>[5,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>{{1,6,7,8},{2,3,4,5}}=>[4,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>[5,3]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>{{1,2},{3,6,7,8},{4,5}}=>[4,2,2]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,6,7,8},{5}}=>[5,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>{{1,6,7,8},{2,3},{4,5}}=>[4,2,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,7,8},{6}}=>[7,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>{{1,7,8},{2,6},{3,4,5}}=>[3,3,2]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>{{1,2,3,7,8},{4,5,6}}=>[5,3]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>{{1,2,7,8},{3,4,5,6}}=>[4,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>[6,2]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>[4,2,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,4,5,6},{3},{7,8}}=>[5,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,4,5,6},{2},{3},{7,8}}=>[4,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,4,5,6},{2,3},{7,8}}=>[4,2,2]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,5,6},{4},{7,8}}=>[5,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>[4,2,2]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,3,4},{2},{5,6},{7,8}}=>[3,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>[2,2,2,2]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,4},{3},{5,6},{7,8}}=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,5,6},{4},{7,8}}=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6},{7,8}}=>[2,2,2,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,6},{5},{7,8}}=>[5,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>{{1,2,4,6},{3},{5},{7,8}}=>[4,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,7,8},{6}}=>[5,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>{{1,7,8},{2,5,6},{3,4}}=>[3,3,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>{{1,2,3,6},{4,5},{7,8}}=>[4,2,2]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,5},{3,4},{7,8}}=>[2,2,2,2]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>{{1,2,6},{3,4,5},{7,8}}=>[3,3,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>{{1,2,3,4},{5,7,8},{6}}=>[4,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>{{1,3,4},{2},{5,7,8},{6}}=>[3,3,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>{{1,2},{3,4},{5,7,8},{6}}=>[3,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,6},{4,5},{7,8}}=>[2,2,2,2]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,6},{5},{7,8}}=>[3,2,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,3},{4,5},{7,8}}=>[2,2,2,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,8},{7}}=>[7,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>{{1,2,4,5,6,8},{3},{7}}=>[6,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>{{1,4,5,6,8},{2,3},{7}}=>[5,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>{{1,5,6,8},{2,3,4},{7}}=>[4,3,1]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>{{1,2},{3,5,6,8},{4},{7}}=>[4,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>{{1,2,3,4,6,8},{5},{7}}=>[6,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>{{1,2,4,6,8},{3},{5},{7}}=>[5,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>{{1,2,3,6,8},{4,5},{7}}=>[5,2,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>{{1,2},{3,4,6,8},{5},{7}}=>[4,2,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>{{1,2,3,8},{4,5,6},{7}}=>[4,3,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,8},{6,7}}=>[6,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>{{1,2,4,5,8},{3},{6,7}}=>[5,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>{{1,2,3,8},{4,5},{6,7}}=>[4,2,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>{{1,2,8},{3,4,5},{6,7}}=>[3,3,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>{{1,2,3,4,8},{5,7},{6}}=>[5,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>{{1,2,3,8},{4,7},{5,6}}=>[4,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>{{1,2,8},{3,7},{4,6},{5}}=>[3,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>{{1,2,8},{3,7},{4,5,6}}=>[3,3,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,8},{4,7},{5,6}}=>[2,2,2,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,3},{4,7},{5,6}}=>[2,2,2,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>{{1,2,3,4,8},{5,6,7}}=>[5,3]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>{{1,2,3,8},{4,5,7},{6}}=>[4,3,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>{{1,2,8},{3,4,7},{5,6}}=>[3,3,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>{{1,2,3,8},{4,5,6,7}}=>[4,4]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>{{1,2,8},{3,4,5,7},{6}}=>[4,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>{{1,8},{2,3,4,5,6,7}}=>[6,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>{{1,2},{3,4,8},{5,6,7}}=>[3,3,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>{{1,2},{3,4,5,8},{6,7}}=>[4,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,4},{5,6}}=>[2,2,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>{{1,4,8},{2,3},{5,6,7}}=>[3,3,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>{{1,2,3},{4,5,8},{6,7}}=>[3,3,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>{{1,2,3,4},{5,8},{6,7}}=>[4,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,4},{5,8},{6,7}}=>[2,2,2,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,4},{2,3},{5,8},{6,7}}=>[2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,4,6},{5}}=>[3,2,2,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>{{1,8},{2,3,7},{4,6},{5}}=>[3,2,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>{{1,8},{2,3,4,6,7},{5}}=>[5,2,1]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>{{1,3,7},{2},{4},{5},{6},{8}}=>[3,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,8},{7}}=>[5,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>{{1,4,6,8},{2,3},{5},{7}}=>[4,2,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>{{1,6,8},{2,5},{3,4},{7}}=>[3,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>{{1,4,5,8},{2,3},{6,7}}=>[4,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,6},{4,5}}=>[2,2,2,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>{{1,8},{2,3,6,7},{4,5}}=>[4,2,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,8},{2,5},{3,4},{6,7}}=>[2,2,2,2]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>{{1,5,8},{2,3,4},{6,7}}=>[3,3,2]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>{{1,2,3,4},{5,6,8},{7}}=>[4,3,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2,3},{4,5,6,8},{7}}=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>{{1,2},{3,4},{5,6,8},{7}}=>[3,2,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,8},{4,5},{6,7}}=>[2,2,2,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>{{1,3,5,7},{2},{4},{6},{8}}=>[4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>{{1,5,7},{2},{3},{4},{6},{8}}=>[3,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>{{1,2,4},{3},{5,6,8},{7}}=>[3,3,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,8},{2,3},{4,5},{6,7}}=>[2,2,2,2]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>{{1,7},{2},{3},{4},{5},{6},{8}}=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>{{1,3,5},{2},{4},{6},{7},{8}}=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>{{1,5},{2},{3},{4},{6},{7},{8}}=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>[1,1,1,1,1,1,1,1]
Map
zeta map
Description
The zeta map on Dyck paths.
The zeta map $\zeta$ is a bijection on Dyck paths of semilength $n$.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path $D$ with corresponding area sequence $a=(a_1,\ldots,a_n)$ to a Dyck path as follows:
The zeta map $\zeta$ is a bijection on Dyck paths of semilength $n$.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path $D$ with corresponding area sequence $a=(a_1,\ldots,a_n)$ to a Dyck path as follows:
- First, build an intermediate Dyck path consisting of $d_1$ north steps, followed by $d_1$ east steps, followed by $d_2$ north steps and $d_2$ east steps, and so on, where $d_i$ is the number of $i-1$'s within the sequence $a$.
For example, given $a=(0,1,2,2,2,3,1,2)$, we build the path
$$NE\ NNEE\ NNNNEEEE\ NE.$$ - Next, the rectangles between two consecutive peaks are filled. Observe that such the rectangle between the $k$th and the $(k+1)$st peak must be filled by $d_k$ east steps and $d_{k+1}$ north steps. In the above example, the rectangle between the second and the third peak must be filled by $2$ east and $4$ north steps, the $2$ being the number of $1$'s in $a$, and $4$ being the number of $2$'s. To fill such a rectangle, scan through the sequence a from left to right, and add east or north steps whenever you see a $k-1$ or $k$, respectively. So to fill the $2\times 4$ rectangle, we look for $1$'s and $2$'s in the sequence and see $122212$, so this rectangle gets filled with $ENNNEN$.
The complete path we obtain in thus
$$NENNENNNENEEENEE.$$
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.
searching the database
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