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------------------------------------------------------------------------
Map identifier: Mp00138
------------------------------------------------------------------------
Map name: to noncrossing partition
------------------------------------------------------------------------
Domain: Dyck paths
------------------------------------------------------------------------
Codomain: Set partitions
------------------------------------------------------------------------
Description: Biane's map to noncrossing set partitions.
------------------------------------------------------------------------
References:
------------------------------------------------------------------------
Code:
def mapping(D):
return SetPartition(D.to_noncrossing_partition())
------------------------------------------------------------------------
Map images:
[1,0] => {{1}}
[1,0,1,0] => {{1},{2}}
[1,1,0,0] => {{1,2}}
[1,0,1,0,1,0] => {{1},{2},{3}}
[1,0,1,1,0,0] => {{1},{2,3}}
[1,1,0,0,1,0] => {{1,2},{3}}
[1,1,0,1,0,0] => {{1,3},{2}}
[1,1,1,0,0,0] => {{1,2,3}}
[1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}}
[1,0,1,0,1,1,0,0] => {{1},{2},{3,4}}
[1,0,1,1,0,0,1,0] => {{1},{2,3},{4}}
[1,0,1,1,0,1,0,0] => {{1},{2,4},{3}}
[1,0,1,1,1,0,0,0] => {{1},{2,3,4}}
[1,1,0,0,1,0,1,0] => {{1,2},{3},{4}}
[1,1,0,0,1,1,0,0] => {{1,2},{3,4}}
[1,1,0,1,0,0,1,0] => {{1,3},{2},{4}}
[1,1,0,1,0,1,0,0] => {{1,4},{2},{3}}
[1,1,0,1,1,0,0,0] => {{1,3,4},{2}}
[1,1,1,0,0,0,1,0] => {{1,2,3},{4}}
[1,1,1,0,0,1,0,0] => {{1,4},{2,3}}
[1,1,1,0,1,0,0,0] => {{1,2,4},{3}}
[1,1,1,1,0,0,0,0] => {{1,2,3,4}}
[1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}}
[1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}}
[1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}}
[1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}}
[1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}}
[1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}}
[1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}}
[1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}}
[1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}}
[1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}}
[1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}}
[1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}}
[1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}}
[1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}}
[1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}}
[1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}}
[1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}}
[1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}}
[1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}}
[1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}}
[1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}}
[1,1,0,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4}}
[1,1,0,1,0,1,1,0,0,0] => {{1,4,5},{2},{3}}
[1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}}
[1,1,0,1,1,0,0,1,0,0] => {{1,5},{2},{3,4}}
[1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4}}
[1,1,0,1,1,1,0,0,0,0] => {{1,3,4,5},{2}}
[1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}}
[1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}}
[1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}}
[1,1,1,0,0,1,0,1,0,0] => {{1,5},{2,3},{4}}
[1,1,1,0,0,1,1,0,0,0] => {{1,4,5},{2,3}}
[1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}}
[1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3}}
[1,1,1,0,1,0,1,0,0,0] => {{1,2,5},{3},{4}}
[1,1,1,0,1,1,0,0,0,0] => {{1,2,4,5},{3}}
[1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}}
[1,1,1,1,0,0,0,1,0,0] => {{1,5},{2,3,4}}
[1,1,1,1,0,0,1,0,0,0] => {{1,2,5},{3,4}}
[1,1,1,1,0,1,0,0,0,0] => {{1,2,3,5},{4}}
[1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}}
[1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}}
[1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}}
[1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}}
[1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}}
[1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}}
[1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}}
[1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}}
[1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}}
[1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}}
[1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}}
[1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}}
[1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}}
[1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}}
[1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}}
[1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}}
[1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}}
[1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}}
[1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}}
[1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}}
[1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}}
[1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}}
[1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}}
[1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}}
[1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}}
[1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}}
[1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}}
[1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}}
[1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}}
[1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}}
[1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}}
[1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}}
[1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}}
[1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}}
[1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}}
[1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}}
[1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}}
[1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}}
[1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}}
[1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}}
[1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}}
[1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}}
[1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}}
[1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}}
[1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}}
[1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}}
[1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}}
[1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}}
[1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}}
[1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}}
[1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}}
[1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}}
[1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}}
[1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}}
[1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}}
[1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}}
[1,1,0,1,0,1,0,1,0,1,0,0] => {{1,6},{2},{3},{4},{5}}
[1,1,0,1,0,1,0,1,1,0,0,0] => {{1,5,6},{2},{3},{4}}
[1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}}
[1,1,0,1,0,1,1,0,0,1,0,0] => {{1,6},{2},{3},{4,5}}
[1,1,0,1,0,1,1,0,1,0,0,0] => {{1,4,6},{2},{3},{5}}
[1,1,0,1,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2},{3}}
[1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}}
[1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}}
[1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}}
[1,1,0,1,1,0,0,1,0,1,0,0] => {{1,6},{2},{3,4},{5}}
[1,1,0,1,1,0,0,1,1,0,0,0] => {{1,5,6},{2},{3,4}}
[1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}}
[1,1,0,1,1,0,1,0,0,1,0,0] => {{1,6},{2},{3,5},{4}}
[1,1,0,1,1,0,1,0,1,0,0,0] => {{1,3,6},{2},{4},{5}}
[1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,5,6},{2},{4}}
[1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}}
[1,1,0,1,1,1,0,0,0,1,0,0] => {{1,6},{2},{3,4,5}}
[1,1,0,1,1,1,0,0,1,0,0,0] => {{1,3,6},{2},{4,5}}
[1,1,0,1,1,1,0,1,0,0,0,0] => {{1,3,4,6},{2},{5}}
[1,1,0,1,1,1,1,0,0,0,0,0] => {{1,3,4,5,6},{2}}
[1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}}
[1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}}
[1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}}
[1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}}
[1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}}
[1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}}
[1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}}
[1,1,1,0,0,1,0,1,0,1,0,0] => {{1,6},{2,3},{4},{5}}
[1,1,1,0,0,1,0,1,1,0,0,0] => {{1,5,6},{2,3},{4}}
[1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}}
[1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5}}
[1,1,1,0,0,1,1,0,1,0,0,0] => {{1,4,6},{2,3},{5}}
[1,1,1,0,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2,3}}
[1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}}
[1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}}
[1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}}
[1,1,1,0,1,0,0,1,0,1,0,0] => {{1,6},{2,4},{3},{5}}
[1,1,1,0,1,0,0,1,1,0,0,0] => {{1,5,6},{2,4},{3}}
[1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}}
[1,1,1,0,1,0,1,0,0,1,0,0] => {{1,6},{2,5},{3},{4}}
[1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,6},{3},{4},{5}}
[1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2,5,6},{3},{4}}
[1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}}
[1,1,1,0,1,1,0,0,0,1,0,0] => {{1,6},{2,4,5},{3}}
[1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2,6},{3},{4,5}}
[1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2,4,6},{3},{5}}
[1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,4,5,6},{3}}
[1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}}
[1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}}
[1,1,1,1,0,0,0,1,0,1,0,0] => {{1,6},{2,3,4},{5}}
[1,1,1,1,0,0,0,1,1,0,0,0] => {{1,5,6},{2,3,4}}
[1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}}
[1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4}}
[1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2,6},{3,4},{5}}
[1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2,5,6},{3,4}}
[1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}}
[1,1,1,1,0,1,0,0,0,1,0,0] => {{1,6},{2,3,5},{4}}
[1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2,6},{3,5},{4}}
[1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2,3,6},{4},{5}}
[1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2,3,5,6},{4}}
[1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}}
[1,1,1,1,1,0,0,0,0,1,0,0] => {{1,6},{2,3,4,5}}
[1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2,6},{3,4,5}}
[1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2,3,6},{4,5}}
[1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3,4,6},{5}}
[1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3},{4},{7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4},{5,6}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3},{4},{6}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3},{4}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,7},{3},{4,5},{6}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4,5}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,7},{3},{4,6},{5}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,7},{3,4},{5},{6}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,7},{3,5},{4},{6}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,5},{4}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4,5}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,7},{3,4,6},{5}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4,7},{5},{6}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4,7},{5,6}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4,5,7},{6}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,7},{6}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6,7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3,6},{4},{5},{7}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3,6,7},{4},{5}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,5,6},{4},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,7},{4},{5,6}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3,5,7},{4},{6}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3,5,6,7},{4}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3,7},{4,5},{6}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,6,7},{4,5}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4,6},{5},{7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3,7},{4,6},{5}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4,6,7},{5}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3,7},{4,5,6}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6,7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4,6},{5},{7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4,7},{5},{6}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4,6,7},{5}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,5,6},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4,7},{5,6}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4,5,7},{6}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6,7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5,7},{6}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2},{3},{4},{5},{6}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4},{5}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3},{4},{7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2},{3},{4},{5,6}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3},{4},{6}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3},{4}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2},{3},{4,5},{7}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2},{3},{4,5},{6}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4,5}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2},{3},{4,6},{5}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2},{3},{5},{6}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2},{3},{5}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2},{3},{7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2},{3},{4,5,6}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2},{3},{5,6}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2},{3},{6}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2},{3}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3,4},{2},{5,7},{6}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,3,4},{2},{5,6,7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2},{3,4},{5},{7}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2},{3,4},{5},{6}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3,4},{5}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3,4},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2},{3,4},{5,6}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3,4},{6}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3,4}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,3,5},{2},{4},{6,7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2},{3,5},{4},{6}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,5},{4}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4},{5}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,3,7},{2},{4},{5},{6}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4},{5}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5,6},{2},{4},{7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2},{3,5,6},{4}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,3,7},{2},{4},{5,6}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3,5,7},{2},{4},{6}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,3,5,6,7},{2},{4}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3,4,5},{2},{6,7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2},{3,4,5},{7}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2},{3,4,5},{6}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,4,5}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4,5}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,3,7},{2},{4,5},{6}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4,5}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3,4,6},{2},{5},{7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2},{3,4,6},{5}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3,7},{2},{4,6},{5}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,3,4,7},{2},{5},{6}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,3,4,6,7},{2},{5}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2},{3,4,5,6}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,3,7},{2},{4,5,6}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,3,4,7},{2},{5,6}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,3,4,5,7},{2},{6}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,3,4,5,6,7},{2}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5,7},{6}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4,6},{5},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4,7},{5},{6}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,6,7},{5}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4,7},{5,6}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6,7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2,3},{5,7},{6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2,3},{5,6,7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2,3},{4},{6,7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2,3},{4},{5},{6}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3},{4},{5}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2,3},{4},{5,6}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3},{4},{6}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3},{4}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2,3},{4,5},{6}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2,3},{4,5}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2,3},{5},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2,3},{4,6},{5}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2,3},{5},{6}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2,3},{5}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2,3},{7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2,3},{4,5,6}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2,3},{5,6}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2,3},{6}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2,3}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6,7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,4},{3},{5,7},{6}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,4},{3},{5,6,7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,4},{3},{5},{7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2,4},{3},{5},{6}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,4},{3},{5}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2,4},{3},{5,6}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,4},{3},{6}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,4},{3}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3},{4},{6}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3},{4}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4},{5}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4},{5}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3},{4},{7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3},{4}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3},{4},{5,6}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3},{4},{6}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3},{4}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2,4,5},{3},{6}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,4,5},{3}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3},{4,5},{7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4,5}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3},{4,5},{6}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4,5}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,4,6},{3},{5},{7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3},{4,6},{5}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,4,7},{3},{5},{6}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,4,6,7},{3},{5}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2,4,5,6},{3}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3},{4,5,6}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,4,7},{3},{5,6}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,4,5,7},{3},{6}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,4,5,6,7},{3}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,6},{2,3,4},{5},{7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,7},{2,3,4},{5},{6}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3,4},{5}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,7},{2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3,4},{6}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3,4}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3,4},{6}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3,4}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4},{5},{7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4},{5}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3,4},{5},{6}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4},{5}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3,4}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3,4},{5,6}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3,4},{6}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3,4}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,7},{2,3,5},{4},{6}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,5},{4}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3,5},{4},{6}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,5},{4}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4},{5}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4},{5}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4},{5},{6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4},{5}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,7},{2,3,5,6},{4}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3,5,6},{4}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4},{5,6}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,5,7},{4},{6}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,5,6,7},{4}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,7},{2,3,4,5},{6}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,4,5}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4,5}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,7},{3,4,5},{6}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4,5}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4,5}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4,5}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4,5},{6}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4,5}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,7},{2,3,4,6},{5}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,7},{3,4,6},{5}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4,6},{5}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5},{6}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,6,7},{5}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,7},{2,3,4,5,6}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,7},{3,4,5,6}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,7},{4,5,6}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5,6}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,7},{6}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,8},{7}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5,7},{6},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5,7,8},{6}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6,7}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5,6,8},{7}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3},{4,5},{6,8},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3},{4,6},{5},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3},{4,6},{5},{7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3},{4,7},{5},{6},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4,7,8},{5},{6}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3},{4,6,7},{5},{8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3},{4,8},{5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3},{4,6,8},{5},{7}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3},{4,6,7,8},{5}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3},{4,7},{5,6},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5,6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3},{4,7,8},{5,6}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3},{4,5,7},{6},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,7},{6}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3},{4,5,8},{6},{7}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3},{4,5,7,8},{6}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,6,7}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3},{4,5,8},{6,7}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3},{4,5,6,8},{7}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7},{8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6},{7,8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5},{6,7},{8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5},{6,8},{7}}
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5},{6,7,8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,4},{5,7},{6},{8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,4},{5,8},{6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,4},{5,7,8},{6}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,4},{5,8},{6,7}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4},{5,6,8},{7}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,5},{4},{6},{7,8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,5},{4},{6,7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4},{6,8},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,5},{4},{6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,6},{4},{5},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,6},{4},{5},{7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,7},{4},{5},{6},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4},{5},{6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4},{5},{6}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,6,7},{4},{5},{8}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,8},{4},{5},{6,7}}
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,6,8},{4},{5},{7}}
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,6,7,8},{4},{5}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,5,6},{4},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,5,6},{4},{7,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,7},{4},{5,6},{8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4},{5,6},{7}}
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4},{5,6}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,5,7},{4},{6},{8}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4},{5,7},{6}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,5,8},{4},{6},{7}}
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,5,7,8},{4},{6}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,5,6,7},{4},{8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4},{5,6,7}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,5,8},{4},{6,7}}
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,5,6,8},{4},{7}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,5,6,7,8},{4}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2},{3,4,5},{6},{7,8}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2},{3,4,5},{6,8},{7}}
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2},{3,6},{4,5},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2},{3,6},{4,5},{7,8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2},{3,7},{4,5},{6},{8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5},{6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,5},{6}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2},{3,6,7},{4,5},{8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2},{3,8},{4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2},{3,6,8},{4,5},{7}}
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2},{3,6,7,8},{4,5}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,6},{5},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,6},{5},{7,8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2},{3,7},{4,6},{5},{8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,6},{5},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,6},{5}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,7},{5},{6},{8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5},{6}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,8},{5},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,7,8},{5},{6}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,6,7},{5},{8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4,6,7},{5}}
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5},{6,7}}
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,6,8},{5},{7}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,6,7,8},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2},{3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2},{3,7},{4,5,6},{8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5,6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,5,6}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2},{3,4,7},{5,6},{8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5,6}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2},{3,4,8},{5,6},{7}}
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2},{3,4,7,8},{5,6}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,7},{6},{8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4,5,7},{6}}
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5,7},{6}}
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,8},{6},{7}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,7,8},{6}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2},{3,8},{4,5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2},{3,4,5,8},{6,7}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,8},{7}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5},{6,8},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5,6},{7},{8}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4},{5,6},{7,8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4},{5,7},{6},{8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4},{5,8},{6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4},{5,7,8},{6}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4},{5,6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4},{5,8},{6,7}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4},{5,6,8},{7}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4},{5,6,7,8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4,5},{6},{7,8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5},{6,8},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,3},{4,6},{5},{7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,3},{4,6},{5},{7,8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,3},{4,7},{5},{6},{8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,3},{4,8},{5},{6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,3},{4,7,8},{5},{6}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,3},{4,6,7},{5},{8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,3},{4,8},{5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,3},{4,6,8},{5},{7}}
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,3},{4,6,7,8},{5}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3},{4,5,6},{7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,3},{4,7},{5,6},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,3},{4,8},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,3},{4,7,8},{5,6}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3},{4,5,7},{6},{8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3},{4,8},{5,7},{6}}
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3},{4,5,8},{6},{7}}
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3},{4,5,7,8},{6}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,3},{4,8},{5,6,7}}
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3},{4,5,8},{6,7}}
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3},{4,5,6,8},{7}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6},{7,8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5},{6,7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5},{6,8},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5},{6,7,8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5,6},{7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5,7},{6},{8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,4},{3},{5,8},{6},{7}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,4},{3},{5,7,8},{6}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,4},{3},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,4},{3},{5,8},{6,7}}
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,4},{3},{5,6,8},{7}}
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,4},{3},{5,6,7,8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,5},{3},{4},{6},{7,8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,5},{3},{4},{6,7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3},{4},{6,8},{7}}
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,5},{3},{4},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,6},{3},{4},{5},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,6},{3},{4},{5},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,7},{3},{4},{5},{6},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3},{4},{5},{6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4},{5},{6}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3},{4},{5},{8}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,8},{3},{4},{5},{6,7}}
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3},{4},{5},{7}}
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3},{4},{5}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,5,6},{3},{4},{7},{8}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,5,6},{3},{4},{7,8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,7},{3},{4},{5,6},{8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,8},{3},{4},{5,6},{7}}
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4},{5,6}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,5,7},{3},{4},{6},{8}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4},{5,7},{6}}
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,5,8},{3},{4},{6},{7}}
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,5,7,8},{3},{4},{6}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,5,6,7},{3},{4},{8}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4},{5,6,7}}
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,5,8},{3},{4},{6,7}}
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,5,6,8},{3},{4},{7}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3},{4}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7},{8}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,4,5},{3},{6},{7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,4,5},{3},{6,7},{8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,4,5},{3},{6,8},{7}}
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,4,5},{3},{6,7,8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,6},{3},{4,5},{7},{8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3},{4,5},{7,8}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,7},{3},{4,5},{6},{8}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3},{4,5},{6},{7}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,5},{6}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3},{4,5},{8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3},{4,5},{6,7}}
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3},{4,5},{7}}
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3},{4,5}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,4,6},{3},{5},{7},{8}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,4,6},{3},{5},{7,8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3},{4,6},{5},{8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3},{4,6},{5},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,6},{5}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,4,7},{3},{5},{6},{8}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4,7},{5},{6}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,4,8},{3},{5},{6},{7}}
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,4,7,8},{3},{5},{6}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,4,6,7},{3},{5},{8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4,6,7},{5}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5},{6,7}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,4,6,8},{3},{5},{7}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,4,6,7,8},{3},{5}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,4,5,6},{3},{7},{8}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,4,5,6},{3},{7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3},{4,5,6},{8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3},{4,5,6},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,5,6}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,4,7},{3},{5,6},{8}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4,7},{5,6}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,4,8},{3},{5,6},{7}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,4,7,8},{3},{5,6}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,4,5,7},{3},{6},{8}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4,5,7},{6}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,7},{6}}
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,4,5,8},{3},{6},{7}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,4,5,7,8},{3},{6}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,4,5,6,7},{3},{8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3},{4,5,6,7}}
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,6,7}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,4,5,8},{3},{6,7}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,4,5,6,8},{3},{7}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8},{3}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6},{7,8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3,4},{5},{6,7},{8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3,4},{5},{6,8},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3,4},{5,6},{7},{8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3,4},{5,7},{6},{8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3,4},{5,8},{6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3,4},{5,7,8},{6}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3,4},{5,8},{6,7}}
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3,4},{5,6,8},{7}}
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1},{2,5},{3,4},{6},{7,8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2,5},{3,4},{6,7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3,4},{6,8},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1},{2,5},{3,4},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1},{2,6},{3,4},{5},{7},{8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,4},{5},{7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1},{2,7},{3,4},{5},{6},{8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5},{6},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3,4},{5},{6}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,4},{5},{8}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,4},{5},{6,7}}
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,4},{5},{7}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,4},{5}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1},{2,5,6},{3,4},{7},{8}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1},{2,5,6},{3,4},{7,8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,4},{5,6},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5,6},{7}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4},{5,6}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1},{2,5,7},{3,4},{6},{8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,4},{5,7},{6}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1},{2,5,8},{3,4},{6},{7}}
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1},{2,5,7,8},{3,4},{6}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1},{2,5,6,7},{3,4},{8}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1},{2,5,8},{3,4},{6,7}}
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1},{2,5,6,8},{3,4},{7}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3,4}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7},{8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,5},{4},{6},{7,8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,5},{4},{6,7},{8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,5},{4},{6,8},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,5},{4},{6,7,8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1},{2,6},{3,5},{4},{7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,5},{4},{7,8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1},{2,7},{3,5},{4},{6},{8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,5},{4},{6},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3,5},{4},{6}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,5},{4},{8}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,5},{4},{6,7}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,5},{4},{7}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,5},{4}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,6},{4},{5},{7},{8}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,6},{4},{5},{7,8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,6},{4},{5},{8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,6},{4},{5},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,6},{4},{5}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,7},{4},{5},{6},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5},{6}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,8},{4},{5},{6},{7}}
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4},{5},{6}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,6,7},{4},{5},{8}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,6,7},{4},{5}}
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5},{6,7}}
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,6,8},{4},{5},{7}}
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,6,7,8},{4},{5}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,5,6},{4},{7},{8}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,5,6},{4},{7,8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,5,6},{4},{8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,5,6},{4},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,5,6},{4}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4},{5,6},{8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5,6}}
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4},{5,6},{7}}
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4},{5,6}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,5,7},{4},{6},{8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,5,7},{4},{6}}
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5,7},{6}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6},{7}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,5,7,8},{4},{6}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,5,6,7},{4},{8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,5,6,7},{4}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5,6,7}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6,7}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,5,6,8},{4},{7}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8},{4}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4,5},{6,7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4,5},{6,8},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1},{2,6},{3,4,5},{7},{8}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,4,5},{7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1},{2,7},{3,4,5},{6},{8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4,5},{6},{7}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,5},{6}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,4,5},{8}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,4,5},{7}}
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,4,5}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1},{2,3,6},{4,5},{7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1},{2,3,6},{4,5},{7,8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,6},{4,5},{8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,6},{4,5},{7}}
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,6},{4,5}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1},{2,3,7},{4,5},{6},{8}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5},{6}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,5},{6},{7}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,5},{6}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1},{2,3,6,7},{4,5},{8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,6,7},{4,5}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,5},{6,7}}
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,3,6,8},{4,5},{7}}
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1},{2,3,6,7,8},{4,5}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,6},{5},{7},{8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,6},{5},{7,8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,4,6},{5},{8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,4,6},{5},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,6},{5}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4,6},{5},{8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,6},{5}}
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,6},{5},{7}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,6},{5}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,7},{5},{6},{8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,4,7},{5},{6}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,7},{5},{6}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,8},{5},{6},{7}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,7,8},{5},{6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,6,7},{5},{8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,6,7},{5}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,6,7},{5}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5},{6,7}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,6,8},{5},{7}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,4,5,6},{8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,4,5,6},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,5,6}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4,5,6},{8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5,6}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,5,6},{7}}
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,5,6}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1},{2,3,4,7},{5,6},{8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,4,7},{5,6}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,7},{5,6}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6},{7}}
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1},{2,3,4,7,8},{5,6}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,7},{6},{8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,5,7},{6}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,5,7},{6}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,7},{6}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8},{6}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,5,6,7}}
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,5,6,7}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6,7}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8},{7}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6,7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5},{6,8},{7}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4},{5,6},{7},{8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4},{5,6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4},{5,7},{6},{8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4},{5,8},{6},{7}}
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4},{5,7,8},{6}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4},{5,6,7},{8}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4},{5,8},{6,7}}
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4},{5,6,8},{7}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6,7},{8}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3},{4,5},{6,8},{7}}
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3},{4,6},{5},{7},{8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3},{4,6},{5},{7,8}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3},{4,7},{5},{6},{8}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3},{4,8},{5},{6},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3},{4,7,8},{5},{6}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3},{4,6,7},{5},{8}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3},{4,8},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3},{4,6,8},{5},{7}}
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3},{4,6,7,8},{5}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3},{4,5,6},{7},{8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3},{4,7},{5,6},{8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3},{4,8},{5,6},{7}}
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3},{4,7,8},{5,6}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3},{4,5,7},{6},{8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3},{4,8},{5,7},{6}}
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3},{4,5,8},{6},{7}}
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3},{4,5,7,8},{6}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3},{4,5,6,7},{8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3},{4,8},{5,6,7}}
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3},{4,5,8},{6,7}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3},{4,5,6,8},{7}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6},{7,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3,4},{5},{6,7},{8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3,4},{5},{6,8},{7}}
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,4},{5,7},{6},{8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,4},{5,8},{6},{7}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,4},{5,7,8},{6}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4},{5,6,7},{8}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,8},{6,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4},{5,6,8},{7}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7},{8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1,2},{3,5},{4},{6},{7,8}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1,2},{3,5},{4},{6,7},{8}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4},{6,8},{7}}
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1,2},{3,5},{4},{6,7,8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1,2},{3,6},{4},{5},{7},{8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4},{5},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1,2},{3,7},{4},{5},{6},{8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3,8},{4},{5},{6},{7}}
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1,2},{3,7,8},{4},{5},{6}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1,2},{3,6,7},{4},{5},{8}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1,2},{3,8},{4},{5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1,2},{3,6,8},{4},{5},{7}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4},{5}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1,2},{3,5,6},{4},{7},{8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,5,6},{4},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1,2},{3,7},{4},{5,6},{8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1,2},{3,8},{4},{5,6},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4},{5,6}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1,2},{3,5,7},{4},{6},{8}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1,2},{3,8},{4},{5,7},{6}}
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1,2},{3,5,8},{4},{6},{7}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,5,7,8},{4},{6}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1,2},{3,5,6,7},{4},{8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4},{5,6,7}}
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1,2},{3,5,8},{4},{6,7}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1,2},{3,5,6,8},{4},{7}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1,2},{3,5,6,7,8},{4}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2},{3,4,5},{6,7},{8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2},{3,4,5},{6,8},{7}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1,2},{3,6},{4,5},{7},{8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1,2},{3,7},{4,5},{6},{8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1,2},{3,8},{4,5},{6},{7}}
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,5},{6}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1,2},{3,6,7},{4,5},{8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,8},{4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1,2},{3,6,8},{4,5},{7}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4,5}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2},{3,4,6},{5},{7},{8}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2},{3,4,6},{5},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1,2},{3,7},{4,6},{5},{8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1,2},{3,8},{4,6},{5},{7}}
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,6},{5}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2},{3,4,7},{5},{6},{8}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5},{6}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2},{3,4,8},{5},{6},{7}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2},{3,4,7,8},{5},{6}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2},{3,4,6,7},{5},{8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,6,7},{5}}
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5},{6,7}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2},{3,4,6,8},{5},{7}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2},{3,4,6,7,8},{5}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2},{3,4,5,6},{7},{8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1,2},{3,7},{4,5,6},{8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1,2},{3,8},{4,5,6},{7}}
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,5,6}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2},{3,4,7},{5,6},{8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5,6}}
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2},{3,4,8},{5,6},{7}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2},{3,4,7,8},{5,6}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2},{3,4,5,7},{6},{8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,7},{6}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,7},{6}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6},{7}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2},{3,4,5,7,8},{6}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,6,7}}
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,6,7}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6,7}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2},{3,4,5,6,8},{7}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5},{6,7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5},{6,8},{7}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5,6},{7},{8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4},{5,6},{7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4},{5,7},{6},{8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4},{5,8},{6},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4},{5,7,8},{6}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4},{5,6,7},{8}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4},{5,8},{6,7}}
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4},{5,6,8},{7}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4},{5,6,7,8}}
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Created: Jan 29, 2020 at 13:26 by FindStatCrew
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Last Updated: Jan 29, 2020 at 13:26 by Martin Rubey