Identifier
- St000233: Set partitions ⟶ ℤ
Values
=>
Cc0009;cc-rep
{{1}}=>0
{{1,2}}=>0
{{1},{2}}=>0
{{1,2,3}}=>0
{{1,2},{3}}=>0
{{1,3},{2}}=>0
{{1},{2,3}}=>0
{{1},{2},{3}}=>0
{{1,2,3,4}}=>0
{{1,2,3},{4}}=>0
{{1,2,4},{3}}=>0
{{1,2},{3,4}}=>0
{{1,2},{3},{4}}=>0
{{1,3,4},{2}}=>0
{{1,3},{2,4}}=>0
{{1,3},{2},{4}}=>0
{{1,4},{2,3}}=>1
{{1},{2,3,4}}=>0
{{1},{2,3},{4}}=>0
{{1,4},{2},{3}}=>0
{{1},{2,4},{3}}=>0
{{1},{2},{3,4}}=>0
{{1},{2},{3},{4}}=>0
{{1,2,3,4,5}}=>0
{{1,2,3,4},{5}}=>0
{{1,2,3,5},{4}}=>0
{{1,2,3},{4,5}}=>0
{{1,2,3},{4},{5}}=>0
{{1,2,4,5},{3}}=>0
{{1,2,4},{3,5}}=>0
{{1,2,4},{3},{5}}=>0
{{1,2,5},{3,4}}=>1
{{1,2},{3,4,5}}=>0
{{1,2},{3,4},{5}}=>0
{{1,2,5},{3},{4}}=>0
{{1,2},{3,5},{4}}=>0
{{1,2},{3},{4,5}}=>0
{{1,2},{3},{4},{5}}=>0
{{1,3,4,5},{2}}=>0
{{1,3,4},{2,5}}=>1
{{1,3,4},{2},{5}}=>0
{{1,3,5},{2,4}}=>0
{{1,3},{2,4,5}}=>0
{{1,3},{2,4},{5}}=>0
{{1,3,5},{2},{4}}=>0
{{1,3},{2,5},{4}}=>0
{{1,3},{2},{4,5}}=>0
{{1,3},{2},{4},{5}}=>0
{{1,4,5},{2,3}}=>1
{{1,4},{2,3,5}}=>1
{{1,4},{2,3},{5}}=>1
{{1,5},{2,3,4}}=>2
{{1},{2,3,4,5}}=>0
{{1},{2,3,4},{5}}=>0
{{1,5},{2,3},{4}}=>1
{{1},{2,3,5},{4}}=>0
{{1},{2,3},{4,5}}=>0
{{1},{2,3},{4},{5}}=>0
{{1,4,5},{2},{3}}=>0
{{1,4},{2,5},{3}}=>0
{{1,4},{2},{3,5}}=>0
{{1,4},{2},{3},{5}}=>0
{{1,5},{2,4},{3}}=>1
{{1},{2,4,5},{3}}=>0
{{1},{2,4},{3,5}}=>0
{{1},{2,4},{3},{5}}=>0
{{1,5},{2},{3,4}}=>1
{{1},{2,5},{3,4}}=>1
{{1},{2},{3,4,5}}=>0
{{1},{2},{3,4},{5}}=>0
{{1,5},{2},{3},{4}}=>0
{{1},{2,5},{3},{4}}=>0
{{1},{2},{3,5},{4}}=>0
{{1},{2},{3},{4,5}}=>0
{{1},{2},{3},{4},{5}}=>0
{{1,2,3,4,5,6}}=>0
{{1,2,3,4,5},{6}}=>0
{{1,2,3,4,6},{5}}=>0
{{1,2,3,4},{5,6}}=>0
{{1,2,3,4},{5},{6}}=>0
{{1,2,3,5,6},{4}}=>0
{{1,2,3,5},{4,6}}=>0
{{1,2,3,5},{4},{6}}=>0
{{1,2,3,6},{4,5}}=>1
{{1,2,3},{4,5,6}}=>0
{{1,2,3},{4,5},{6}}=>0
{{1,2,3,6},{4},{5}}=>0
{{1,2,3},{4,6},{5}}=>0
{{1,2,3},{4},{5,6}}=>0
{{1,2,3},{4},{5},{6}}=>0
{{1,2,4,5,6},{3}}=>0
{{1,2,4,5},{3,6}}=>1
{{1,2,4,5},{3},{6}}=>0
{{1,2,4,6},{3,5}}=>0
{{1,2,4},{3,5,6}}=>0
{{1,2,4},{3,5},{6}}=>0
{{1,2,4,6},{3},{5}}=>0
{{1,2,4},{3,6},{5}}=>0
{{1,2,4},{3},{5,6}}=>0
{{1,2,4},{3},{5},{6}}=>0
{{1,2,5,6},{3,4}}=>1
{{1,2,5},{3,4,6}}=>1
{{1,2,5},{3,4},{6}}=>1
{{1,2,6},{3,4,5}}=>2
{{1,2},{3,4,5,6}}=>0
{{1,2},{3,4,5},{6}}=>0
{{1,2,6},{3,4},{5}}=>1
{{1,2},{3,4,6},{5}}=>0
{{1,2},{3,4},{5,6}}=>0
{{1,2},{3,4},{5},{6}}=>0
{{1,2,5,6},{3},{4}}=>0
{{1,2,5},{3,6},{4}}=>0
{{1,2,5},{3},{4,6}}=>0
{{1,2,5},{3},{4},{6}}=>0
{{1,2,6},{3,5},{4}}=>1
{{1,2},{3,5,6},{4}}=>0
{{1,2},{3,5},{4,6}}=>0
{{1,2},{3,5},{4},{6}}=>0
{{1,2,6},{3},{4,5}}=>1
{{1,2},{3,6},{4,5}}=>1
{{1,2},{3},{4,5,6}}=>0
{{1,2},{3},{4,5},{6}}=>0
{{1,2,6},{3},{4},{5}}=>0
{{1,2},{3,6},{4},{5}}=>0
{{1,2},{3},{4,6},{5}}=>0
{{1,2},{3},{4},{5,6}}=>0
{{1,2},{3},{4},{5},{6}}=>0
{{1,3,4,5,6},{2}}=>0
{{1,3,4,5},{2,6}}=>2
{{1,3,4,5},{2},{6}}=>0
{{1,3,4,6},{2,5}}=>1
{{1,3,4},{2,5,6}}=>1
{{1,3,4},{2,5},{6}}=>1
{{1,3,4,6},{2},{5}}=>0
{{1,3,4},{2,6},{5}}=>1
{{1,3,4},{2},{5,6}}=>0
{{1,3,4},{2},{5},{6}}=>0
{{1,3,5,6},{2,4}}=>0
{{1,3,5},{2,4,6}}=>0
{{1,3,5},{2,4},{6}}=>0
{{1,3,6},{2,4,5}}=>1
{{1,3},{2,4,5,6}}=>0
{{1,3},{2,4,5},{6}}=>0
{{1,3,6},{2,4},{5}}=>0
{{1,3},{2,4,6},{5}}=>0
{{1,3},{2,4},{5,6}}=>0
{{1,3},{2,4},{5},{6}}=>0
{{1,3,5,6},{2},{4}}=>0
{{1,3,5},{2,6},{4}}=>1
{{1,3,5},{2},{4,6}}=>0
{{1,3,5},{2},{4},{6}}=>0
{{1,3,6},{2,5},{4}}=>0
{{1,3},{2,5,6},{4}}=>0
{{1,3},{2,5},{4,6}}=>0
{{1,3},{2,5},{4},{6}}=>0
{{1,3,6},{2},{4,5}}=>1
{{1,3},{2,6},{4,5}}=>1
{{1,3},{2},{4,5,6}}=>0
{{1,3},{2},{4,5},{6}}=>0
{{1,3,6},{2},{4},{5}}=>0
{{1,3},{2,6},{4},{5}}=>0
{{1,3},{2},{4,6},{5}}=>0
{{1,3},{2},{4},{5,6}}=>0
{{1,3},{2},{4},{5},{6}}=>0
{{1,4,5,6},{2,3}}=>1
{{1,4,5},{2,3,6}}=>2
{{1,4,5},{2,3},{6}}=>1
{{1,4,6},{2,3,5}}=>1
{{1,4},{2,3,5,6}}=>1
{{1,4},{2,3,5},{6}}=>1
{{1,4,6},{2,3},{5}}=>1
{{1,4},{2,3,6},{5}}=>1
{{1,4},{2,3},{5,6}}=>1
{{1,4},{2,3},{5},{6}}=>1
{{1,5,6},{2,3,4}}=>2
{{1,5},{2,3,4,6}}=>2
{{1,5},{2,3,4},{6}}=>2
{{1,6},{2,3,4,5}}=>3
{{1},{2,3,4,5,6}}=>0
{{1},{2,3,4,5},{6}}=>0
{{1,6},{2,3,4},{5}}=>2
{{1},{2,3,4,6},{5}}=>0
{{1},{2,3,4},{5,6}}=>0
{{1},{2,3,4},{5},{6}}=>0
{{1,5,6},{2,3},{4}}=>1
{{1,5},{2,3,6},{4}}=>1
{{1,5},{2,3},{4,6}}=>1
{{1,5},{2,3},{4},{6}}=>1
{{1,6},{2,3,5},{4}}=>2
{{1},{2,3,5,6},{4}}=>0
{{1},{2,3,5},{4,6}}=>0
{{1},{2,3,5},{4},{6}}=>0
{{1,6},{2,3},{4,5}}=>2
{{1},{2,3,6},{4,5}}=>1
{{1},{2,3},{4,5,6}}=>0
{{1},{2,3},{4,5},{6}}=>0
{{1,6},{2,3},{4},{5}}=>1
{{1},{2,3,6},{4},{5}}=>0
{{1},{2,3},{4,6},{5}}=>0
{{1},{2,3},{4},{5,6}}=>0
{{1},{2,3},{4},{5},{6}}=>0
{{1,4,5,6},{2},{3}}=>0
{{1,4,5},{2,6},{3}}=>1
{{1,4,5},{2},{3,6}}=>1
{{1,4,5},{2},{3},{6}}=>0
{{1,4,6},{2,5},{3}}=>0
{{1,4},{2,5,6},{3}}=>0
{{1,4},{2,5},{3,6}}=>0
{{1,4},{2,5},{3},{6}}=>0
{{1,4,6},{2},{3,5}}=>0
{{1,4},{2,6},{3,5}}=>1
{{1,4},{2},{3,5,6}}=>0
{{1,4},{2},{3,5},{6}}=>0
{{1,4,6},{2},{3},{5}}=>0
{{1,4},{2,6},{3},{5}}=>0
{{1,4},{2},{3,6},{5}}=>0
{{1,4},{2},{3},{5,6}}=>0
{{1,4},{2},{3},{5},{6}}=>0
{{1,5,6},{2,4},{3}}=>1
{{1,5},{2,4,6},{3}}=>1
{{1,5},{2,4},{3,6}}=>1
{{1,5},{2,4},{3},{6}}=>1
{{1,6},{2,4,5},{3}}=>2
{{1},{2,4,5,6},{3}}=>0
{{1},{2,4,5},{3,6}}=>1
{{1},{2,4,5},{3},{6}}=>0
{{1,6},{2,4},{3,5}}=>2
{{1},{2,4,6},{3,5}}=>0
{{1},{2,4},{3,5,6}}=>0
{{1},{2,4},{3,5},{6}}=>0
{{1,6},{2,4},{3},{5}}=>1
{{1},{2,4,6},{3},{5}}=>0
{{1},{2,4},{3,6},{5}}=>0
{{1},{2,4},{3},{5,6}}=>0
{{1},{2,4},{3},{5},{6}}=>0
{{1,5,6},{2},{3,4}}=>1
{{1,5},{2,6},{3,4}}=>2
{{1,5},{2},{3,4,6}}=>1
{{1,5},{2},{3,4},{6}}=>1
{{1,6},{2,5},{3,4}}=>3
{{1},{2,5,6},{3,4}}=>1
{{1},{2,5},{3,4,6}}=>1
{{1},{2,5},{3,4},{6}}=>1
{{1,6},{2},{3,4,5}}=>2
{{1},{2,6},{3,4,5}}=>2
{{1},{2},{3,4,5,6}}=>0
{{1},{2},{3,4,5},{6}}=>0
{{1,6},{2},{3,4},{5}}=>1
{{1},{2,6},{3,4},{5}}=>1
{{1},{2},{3,4,6},{5}}=>0
{{1},{2},{3,4},{5,6}}=>0
{{1},{2},{3,4},{5},{6}}=>0
{{1,5,6},{2},{3},{4}}=>0
{{1,5},{2,6},{3},{4}}=>0
{{1,5},{2},{3,6},{4}}=>0
{{1,5},{2},{3},{4,6}}=>0
{{1,5},{2},{3},{4},{6}}=>0
{{1,6},{2,5},{3},{4}}=>1
{{1},{2,5,6},{3},{4}}=>0
{{1},{2,5},{3,6},{4}}=>0
{{1},{2,5},{3},{4,6}}=>0
{{1},{2,5},{3},{4},{6}}=>0
{{1,6},{2},{3,5},{4}}=>1
{{1},{2,6},{3,5},{4}}=>1
{{1},{2},{3,5,6},{4}}=>0
{{1},{2},{3,5},{4,6}}=>0
{{1},{2},{3,5},{4},{6}}=>0
{{1,6},{2},{3},{4,5}}=>1
{{1},{2,6},{3},{4,5}}=>1
{{1},{2},{3,6},{4,5}}=>1
{{1},{2},{3},{4,5,6}}=>0
{{1},{2},{3},{4,5},{6}}=>0
{{1,6},{2},{3},{4},{5}}=>0
{{1},{2,6},{3},{4},{5}}=>0
{{1},{2},{3,6},{4},{5}}=>0
{{1},{2},{3},{4,6},{5}}=>0
{{1},{2},{3},{4},{5,6}}=>0
{{1},{2},{3},{4},{5},{6}}=>0
{{1,2,3,4,5,6,7}}=>0
{{1,2,3,4,5,6},{7}}=>0
{{1,2,3,4,5,7},{6}}=>0
{{1,2,3,4,5},{6,7}}=>0
{{1,2,3,4,5},{6},{7}}=>0
{{1,2,3,4,6,7},{5}}=>0
{{1,2,3,4,6},{5,7}}=>0
{{1,2,3,4,6},{5},{7}}=>0
{{1,2,3,4,7},{5,6}}=>1
{{1,2,3,4},{5,6,7}}=>0
{{1,2,3,4},{5,6},{7}}=>0
{{1,2,3,4,7},{5},{6}}=>0
{{1,2,3,4},{5,7},{6}}=>0
{{1,2,3,4},{5},{6,7}}=>0
{{1,2,3,4},{5},{6},{7}}=>0
{{1,2,3,5,6,7},{4}}=>0
{{1,2,3,5,6},{4,7}}=>1
{{1,2,3,5,6},{4},{7}}=>0
{{1,2,3,5,7},{4,6}}=>0
{{1,2,3,5},{4,6,7}}=>0
{{1,2,3,5},{4,6},{7}}=>0
{{1,2,3,5,7},{4},{6}}=>0
{{1,2,3,5},{4,7},{6}}=>0
{{1,2,3,5},{4},{6,7}}=>0
{{1,2,3,5},{4},{6},{7}}=>0
{{1,2,3,6,7},{4,5}}=>1
{{1,2,3,6},{4,5,7}}=>1
{{1,2,3,6},{4,5},{7}}=>1
{{1,2,3,7},{4,5,6}}=>2
{{1,2,3},{4,5,6,7}}=>0
{{1,2,3},{4,5,6},{7}}=>0
{{1,2,3,7},{4,5},{6}}=>1
{{1,2,3},{4,5,7},{6}}=>0
{{1,2,3},{4,5},{6,7}}=>0
{{1,2,3},{4,5},{6},{7}}=>0
{{1,2,3,6,7},{4},{5}}=>0
{{1,2,3,6},{4,7},{5}}=>0
{{1,2,3,6},{4},{5,7}}=>0
{{1,2,3,6},{4},{5},{7}}=>0
{{1,2,3,7},{4,6},{5}}=>1
{{1,2,3},{4,6,7},{5}}=>0
{{1,2,3},{4,6},{5,7}}=>0
{{1,2,3},{4,6},{5},{7}}=>0
{{1,2,3,7},{4},{5,6}}=>1
{{1,2,3},{4,7},{5,6}}=>1
{{1,2,3},{4},{5,6,7}}=>0
{{1,2,3},{4},{5,6},{7}}=>0
{{1,2,3,7},{4},{5},{6}}=>0
{{1,2,3},{4,7},{5},{6}}=>0
{{1,2,3},{4},{5,7},{6}}=>0
{{1,2,3},{4},{5},{6,7}}=>0
{{1,2,3},{4},{5},{6},{7}}=>0
{{1,2,4,5,6,7},{3}}=>0
{{1,2,4,5,6},{3,7}}=>2
{{1,2,4,5,6},{3},{7}}=>0
{{1,2,4,5,7},{3,6}}=>1
{{1,2,4,5},{3,6,7}}=>1
{{1,2,4,5},{3,6},{7}}=>1
{{1,2,4,5,7},{3},{6}}=>0
{{1,2,4,5},{3,7},{6}}=>1
{{1,2,4,5},{3},{6,7}}=>0
{{1,2,4,5},{3},{6},{7}}=>0
{{1,2,4,6,7},{3,5}}=>0
{{1,2,4,6},{3,5,7}}=>0
{{1,2,4,6},{3,5},{7}}=>0
{{1,2,4,7},{3,5,6}}=>1
{{1,2,4},{3,5,6,7}}=>0
{{1,2,4},{3,5,6},{7}}=>0
{{1,2,4,7},{3,5},{6}}=>0
{{1,2,4},{3,5,7},{6}}=>0
{{1,2,4},{3,5},{6,7}}=>0
{{1,2,4},{3,5},{6},{7}}=>0
{{1,2,4,6,7},{3},{5}}=>0
{{1,2,4,6},{3,7},{5}}=>1
{{1,2,4,6},{3},{5,7}}=>0
{{1,2,4,6},{3},{5},{7}}=>0
{{1,2,4,7},{3,6},{5}}=>0
{{1,2,4},{3,6,7},{5}}=>0
{{1,2,4},{3,6},{5,7}}=>0
{{1,2,4},{3,6},{5},{7}}=>0
{{1,2,4,7},{3},{5,6}}=>1
{{1,2,4},{3,7},{5,6}}=>1
{{1,2,4},{3},{5,6,7}}=>0
{{1,2,4},{3},{5,6},{7}}=>0
{{1,2,4,7},{3},{5},{6}}=>0
{{1,2,4},{3,7},{5},{6}}=>0
{{1,2,4},{3},{5,7},{6}}=>0
{{1,2,4},{3},{5},{6,7}}=>0
{{1,2,4},{3},{5},{6},{7}}=>0
{{1,2,5,6,7},{3,4}}=>1
{{1,2,5,6},{3,4,7}}=>2
{{1,2,5,6},{3,4},{7}}=>1
{{1,2,5,7},{3,4,6}}=>1
{{1,2,5},{3,4,6,7}}=>1
{{1,2,5},{3,4,6},{7}}=>1
{{1,2,5,7},{3,4},{6}}=>1
{{1,2,5},{3,4,7},{6}}=>1
{{1,2,5},{3,4},{6,7}}=>1
{{1,2,5},{3,4},{6},{7}}=>1
{{1,2,6,7},{3,4,5}}=>2
{{1,2,6},{3,4,5,7}}=>2
{{1,2,6},{3,4,5},{7}}=>2
{{1,2,7},{3,4,5,6}}=>3
{{1,2},{3,4,5,6,7}}=>0
{{1,2},{3,4,5,6},{7}}=>0
{{1,2,7},{3,4,5},{6}}=>2
{{1,2},{3,4,5,7},{6}}=>0
{{1,2},{3,4,5},{6,7}}=>0
{{1,2},{3,4,5},{6},{7}}=>0
{{1,2,6,7},{3,4},{5}}=>1
{{1,2,6},{3,4,7},{5}}=>1
{{1,2,6},{3,4},{5,7}}=>1
{{1,2,6},{3,4},{5},{7}}=>1
{{1,2,7},{3,4,6},{5}}=>2
{{1,2},{3,4,6,7},{5}}=>0
{{1,2},{3,4,6},{5,7}}=>0
{{1,2},{3,4,6},{5},{7}}=>0
{{1,2,7},{3,4},{5,6}}=>2
{{1,2},{3,4,7},{5,6}}=>1
{{1,2},{3,4},{5,6,7}}=>0
{{1,2},{3,4},{5,6},{7}}=>0
{{1,2,7},{3,4},{5},{6}}=>1
{{1,2},{3,4,7},{5},{6}}=>0
{{1,2},{3,4},{5,7},{6}}=>0
{{1,2},{3,4},{5},{6,7}}=>0
{{1,2},{3,4},{5},{6},{7}}=>0
{{1,2,5,6,7},{3},{4}}=>0
{{1,2,5,6},{3,7},{4}}=>1
{{1,2,5,6},{3},{4,7}}=>1
{{1,2,5,6},{3},{4},{7}}=>0
{{1,2,5,7},{3,6},{4}}=>0
{{1,2,5},{3,6,7},{4}}=>0
{{1,2,5},{3,6},{4,7}}=>0
{{1,2,5},{3,6},{4},{7}}=>0
{{1,2,5,7},{3},{4,6}}=>0
{{1,2,5},{3,7},{4,6}}=>1
{{1,2,5},{3},{4,6,7}}=>0
{{1,2,5},{3},{4,6},{7}}=>0
{{1,2,5,7},{3},{4},{6}}=>0
{{1,2,5},{3,7},{4},{6}}=>0
{{1,2,5},{3},{4,7},{6}}=>0
{{1,2,5},{3},{4},{6,7}}=>0
{{1,2,5},{3},{4},{6},{7}}=>0
{{1,2,6,7},{3,5},{4}}=>1
{{1,2,6},{3,5,7},{4}}=>1
{{1,2,6},{3,5},{4,7}}=>1
{{1,2,6},{3,5},{4},{7}}=>1
{{1,2,7},{3,5,6},{4}}=>2
{{1,2},{3,5,6,7},{4}}=>0
{{1,2},{3,5,6},{4,7}}=>1
{{1,2},{3,5,6},{4},{7}}=>0
{{1,2,7},{3,5},{4,6}}=>2
{{1,2},{3,5,7},{4,6}}=>0
{{1,2},{3,5},{4,6,7}}=>0
{{1,2},{3,5},{4,6},{7}}=>0
{{1,2,7},{3,5},{4},{6}}=>1
{{1,2},{3,5,7},{4},{6}}=>0
{{1,2},{3,5},{4,7},{6}}=>0
{{1,2},{3,5},{4},{6,7}}=>0
{{1,2},{3,5},{4},{6},{7}}=>0
{{1,2,6,7},{3},{4,5}}=>1
{{1,2,6},{3,7},{4,5}}=>2
{{1,2,6},{3},{4,5,7}}=>1
{{1,2,6},{3},{4,5},{7}}=>1
{{1,2,7},{3,6},{4,5}}=>3
{{1,2},{3,6,7},{4,5}}=>1
{{1,2},{3,6},{4,5,7}}=>1
{{1,2},{3,6},{4,5},{7}}=>1
{{1,2,7},{3},{4,5,6}}=>2
{{1,2},{3,7},{4,5,6}}=>2
{{1,2},{3},{4,5,6,7}}=>0
{{1,2},{3},{4,5,6},{7}}=>0
{{1,2,7},{3},{4,5},{6}}=>1
{{1,2},{3,7},{4,5},{6}}=>1
{{1,2},{3},{4,5,7},{6}}=>0
{{1,2},{3},{4,5},{6,7}}=>0
{{1,2},{3},{4,5},{6},{7}}=>0
{{1,2,6,7},{3},{4},{5}}=>0
{{1,2,6},{3,7},{4},{5}}=>0
{{1,2,6},{3},{4,7},{5}}=>0
{{1,2,6},{3},{4},{5,7}}=>0
{{1,2,6},{3},{4},{5},{7}}=>0
{{1,2,7},{3,6},{4},{5}}=>1
{{1,2},{3,6,7},{4},{5}}=>0
{{1,2},{3,6},{4,7},{5}}=>0
{{1,2},{3,6},{4},{5,7}}=>0
{{1,2},{3,6},{4},{5},{7}}=>0
{{1,2,7},{3},{4,6},{5}}=>1
{{1,2},{3,7},{4,6},{5}}=>1
{{1,2},{3},{4,6,7},{5}}=>0
{{1,2},{3},{4,6},{5,7}}=>0
{{1,2},{3},{4,6},{5},{7}}=>0
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{{1,2},{3,7},{4},{5},{6}}=>0
{{1,2},{3},{4,7},{5},{6}}=>0
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{{1,3,4,7},{2,5},{6}}=>1
{{1,3,4},{2,5,7},{6}}=>1
{{1,3,4},{2,5},{6,7}}=>1
{{1,3,4},{2,5},{6},{7}}=>1
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{{1,3,4,6},{2,7},{5}}=>2
{{1,3,4,6},{2},{5,7}}=>0
{{1,3,4,6},{2},{5},{7}}=>0
{{1,3,4,7},{2,6},{5}}=>1
{{1,3,4},{2,6,7},{5}}=>1
{{1,3,4},{2,6},{5,7}}=>1
{{1,3,4},{2,6},{5},{7}}=>1
{{1,3,4,7},{2},{5,6}}=>1
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{{1,3,4,7},{2},{5},{6}}=>0
{{1,3,4},{2,7},{5},{6}}=>1
{{1,3,4},{2},{5,7},{6}}=>0
{{1,3,4},{2},{5},{6,7}}=>0
{{1,3,4},{2},{5},{6},{7}}=>0
{{1,3,5,6,7},{2,4}}=>0
{{1,3,5,6},{2,4,7}}=>1
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{{1,3,5,7},{2,4,6}}=>0
{{1,3,5},{2,4,6,7}}=>0
{{1,3,5},{2,4,6},{7}}=>0
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{{1,3,5},{2,4,7},{6}}=>0
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{{1,3,5},{2,4},{6},{7}}=>0
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{{1,3,6},{2,4,5,7}}=>1
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{{1,3},{2,4,5,6},{7}}=>0
{{1,3,7},{2,4,5},{6}}=>1
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{{1,3},{2,4,5},{6,7}}=>0
{{1,3},{2,4,5},{6},{7}}=>0
{{1,3,6,7},{2,4},{5}}=>0
{{1,3,6},{2,4,7},{5}}=>0
{{1,3,6},{2,4},{5,7}}=>0
{{1,3,6},{2,4},{5},{7}}=>0
{{1,3,7},{2,4,6},{5}}=>1
{{1,3},{2,4,6,7},{5}}=>0
{{1,3},{2,4,6},{5,7}}=>0
{{1,3},{2,4,6},{5},{7}}=>0
{{1,3,7},{2,4},{5,6}}=>1
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{{1,3},{2,4},{5,6},{7}}=>0
{{1,3,7},{2,4},{5},{6}}=>0
{{1,3},{2,4,7},{5},{6}}=>0
{{1,3},{2,4},{5,7},{6}}=>0
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{{1,3,5},{2,6},{4,7}}=>1
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{{1,3,5},{2},{4,6,7}}=>0
{{1,3,5},{2},{4,6},{7}}=>0
{{1,3,5,7},{2},{4},{6}}=>0
{{1,3,5},{2,7},{4},{6}}=>1
{{1,3,5},{2},{4,7},{6}}=>0
{{1,3,5},{2},{4},{6,7}}=>0
{{1,3,5},{2},{4},{6},{7}}=>0
{{1,3,6,7},{2,5},{4}}=>0
{{1,3,6},{2,5,7},{4}}=>0
{{1,3,6},{2,5},{4,7}}=>0
{{1,3,6},{2,5},{4},{7}}=>0
{{1,3,7},{2,5,6},{4}}=>1
{{1,3},{2,5,6,7},{4}}=>0
{{1,3},{2,5,6},{4,7}}=>1
{{1,3},{2,5,6},{4},{7}}=>0
{{1,3,7},{2,5},{4,6}}=>1
{{1,3},{2,5,7},{4,6}}=>0
{{1,3},{2,5},{4,6,7}}=>0
{{1,3},{2,5},{4,6},{7}}=>0
{{1,3,7},{2,5},{4},{6}}=>0
{{1,3},{2,5,7},{4},{6}}=>0
{{1,3},{2,5},{4,7},{6}}=>0
{{1,3},{2,5},{4},{6,7}}=>0
{{1,3},{2,5},{4},{6},{7}}=>0
{{1,3,6,7},{2},{4,5}}=>1
{{1,3,6},{2,7},{4,5}}=>3
{{1,3,6},{2},{4,5,7}}=>1
{{1,3,6},{2},{4,5},{7}}=>1
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{{1,3},{2,6,7},{4,5}}=>1
{{1,3},{2,6},{4,5,7}}=>1
{{1,3},{2,6},{4,5},{7}}=>1
{{1,3,7},{2},{4,5,6}}=>2
{{1,3},{2,7},{4,5,6}}=>2
{{1,3},{2},{4,5,6,7}}=>0
{{1,3},{2},{4,5,6},{7}}=>0
{{1,3,7},{2},{4,5},{6}}=>1
{{1,3},{2,7},{4,5},{6}}=>1
{{1,3},{2},{4,5,7},{6}}=>0
{{1,3},{2},{4,5},{6,7}}=>0
{{1,3},{2},{4,5},{6},{7}}=>0
{{1,3,6,7},{2},{4},{5}}=>0
{{1,3,6},{2,7},{4},{5}}=>1
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{{1,3,6},{2},{4},{5,7}}=>0
{{1,3,6},{2},{4},{5},{7}}=>0
{{1,3,7},{2,6},{4},{5}}=>0
{{1,3},{2,6,7},{4},{5}}=>0
{{1,3},{2,6},{4,7},{5}}=>0
{{1,3},{2,6},{4},{5,7}}=>0
{{1,3},{2,6},{4},{5},{7}}=>0
{{1,3,7},{2},{4,6},{5}}=>1
{{1,3},{2,7},{4,6},{5}}=>1
{{1,3},{2},{4,6,7},{5}}=>0
{{1,3},{2},{4,6},{5,7}}=>0
{{1,3},{2},{4,6},{5},{7}}=>0
{{1,3,7},{2},{4},{5,6}}=>1
{{1,3},{2,7},{4},{5,6}}=>1
{{1,3},{2},{4,7},{5,6}}=>1
{{1,3},{2},{4},{5,6,7}}=>0
{{1,3},{2},{4},{5,6},{7}}=>0
{{1,3,7},{2},{4},{5},{6}}=>0
{{1,3},{2,7},{4},{5},{6}}=>0
{{1,3},{2},{4,7},{5},{6}}=>0
{{1,3},{2},{4},{5,7},{6}}=>0
{{1,3},{2},{4},{5},{6,7}}=>0
{{1,3},{2},{4},{5},{6},{7}}=>0
{{1,4,5,6,7},{2,3}}=>1
{{1,4,5,6},{2,3,7}}=>3
{{1,4,5,6},{2,3},{7}}=>1
{{1,4,5,7},{2,3,6}}=>2
{{1,4,5},{2,3,6,7}}=>2
{{1,4,5},{2,3,6},{7}}=>2
{{1,4,5,7},{2,3},{6}}=>1
{{1,4,5},{2,3,7},{6}}=>2
{{1,4,5},{2,3},{6,7}}=>1
{{1,4,5},{2,3},{6},{7}}=>1
{{1,4,6,7},{2,3,5}}=>1
{{1,4,6},{2,3,5,7}}=>1
{{1,4,6},{2,3,5},{7}}=>1
{{1,4,7},{2,3,5,6}}=>2
{{1,4},{2,3,5,6,7}}=>1
{{1,4},{2,3,5,6},{7}}=>1
{{1,4,7},{2,3,5},{6}}=>1
{{1,4},{2,3,5,7},{6}}=>1
{{1,4},{2,3,5},{6,7}}=>1
{{1,4},{2,3,5},{6},{7}}=>1
{{1,4,6,7},{2,3},{5}}=>1
{{1,4,6},{2,3,7},{5}}=>2
{{1,4,6},{2,3},{5,7}}=>1
{{1,4,6},{2,3},{5},{7}}=>1
{{1,4,7},{2,3,6},{5}}=>1
{{1,4},{2,3,6,7},{5}}=>1
{{1,4},{2,3,6},{5,7}}=>1
{{1,4},{2,3,6},{5},{7}}=>1
{{1,4,7},{2,3},{5,6}}=>2
{{1,4},{2,3,7},{5,6}}=>2
{{1,4},{2,3},{5,6,7}}=>1
{{1,4},{2,3},{5,6},{7}}=>1
{{1,4,7},{2,3},{5},{6}}=>1
{{1,4},{2,3,7},{5},{6}}=>1
{{1,4},{2,3},{5,7},{6}}=>1
{{1,4},{2,3},{5},{6,7}}=>1
{{1,4},{2,3},{5},{6},{7}}=>1
{{1,5,6,7},{2,3,4}}=>2
{{1,5,6},{2,3,4,7}}=>3
{{1,5,6},{2,3,4},{7}}=>2
{{1,5,7},{2,3,4,6}}=>2
{{1,5},{2,3,4,6,7}}=>2
{{1,5},{2,3,4,6},{7}}=>2
{{1,5,7},{2,3,4},{6}}=>2
{{1,5},{2,3,4,7},{6}}=>2
{{1,5},{2,3,4},{6,7}}=>2
{{1,5},{2,3,4},{6},{7}}=>2
{{1,6,7},{2,3,4,5}}=>3
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{{1,6},{2,3,4,5},{7}}=>3
{{1,7},{2,3,4,5,6}}=>4
{{1},{2,3,4,5,6,7}}=>0
{{1},{2,3,4,5,6},{7}}=>0
{{1,7},{2,3,4,5},{6}}=>3
{{1},{2,3,4,5,7},{6}}=>0
{{1},{2,3,4,5},{6,7}}=>0
{{1},{2,3,4,5},{6},{7}}=>0
{{1,6,7},{2,3,4},{5}}=>2
{{1,6},{2,3,4,7},{5}}=>2
{{1,6},{2,3,4},{5,7}}=>2
{{1,6},{2,3,4},{5},{7}}=>2
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{{1},{2,3,4,6,7},{5}}=>0
{{1},{2,3,4,6},{5,7}}=>0
{{1},{2,3,4,6},{5},{7}}=>0
{{1,7},{2,3,4},{5,6}}=>3
{{1},{2,3,4,7},{5,6}}=>1
{{1},{2,3,4},{5,6,7}}=>0
{{1},{2,3,4},{5,6},{7}}=>0
{{1,7},{2,3,4},{5},{6}}=>2
{{1},{2,3,4,7},{5},{6}}=>0
{{1},{2,3,4},{5,7},{6}}=>0
{{1},{2,3,4},{5},{6,7}}=>0
{{1},{2,3,4},{5},{6},{7}}=>0
{{1,5,6,7},{2,3},{4}}=>1
{{1,5,6},{2,3,7},{4}}=>2
{{1,5,6},{2,3},{4,7}}=>2
{{1,5,6},{2,3},{4},{7}}=>1
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{{1,5},{2,3,6,7},{4}}=>1
{{1,5},{2,3,6},{4,7}}=>1
{{1,5},{2,3,6},{4},{7}}=>1
{{1,5,7},{2,3},{4,6}}=>1
{{1,5},{2,3,7},{4,6}}=>2
{{1,5},{2,3},{4,6,7}}=>1
{{1,5},{2,3},{4,6},{7}}=>1
{{1,5,7},{2,3},{4},{6}}=>1
{{1,5},{2,3,7},{4},{6}}=>1
{{1,5},{2,3},{4,7},{6}}=>1
{{1,5},{2,3},{4},{6,7}}=>1
{{1,5},{2,3},{4},{6},{7}}=>1
{{1,6,7},{2,3,5},{4}}=>2
{{1,6},{2,3,5,7},{4}}=>2
{{1,6},{2,3,5},{4,7}}=>2
{{1,6},{2,3,5},{4},{7}}=>2
{{1,7},{2,3,5,6},{4}}=>3
{{1},{2,3,5,6,7},{4}}=>0
{{1},{2,3,5,6},{4,7}}=>1
{{1},{2,3,5,6},{4},{7}}=>0
{{1,7},{2,3,5},{4,6}}=>3
{{1},{2,3,5,7},{4,6}}=>0
{{1},{2,3,5},{4,6,7}}=>0
{{1},{2,3,5},{4,6},{7}}=>0
{{1,7},{2,3,5},{4},{6}}=>2
{{1},{2,3,5,7},{4},{6}}=>0
{{1},{2,3,5},{4,7},{6}}=>0
{{1},{2,3,5},{4},{6,7}}=>0
{{1},{2,3,5},{4},{6},{7}}=>0
{{1,6,7},{2,3},{4,5}}=>2
{{1,6},{2,3,7},{4,5}}=>3
{{1,6},{2,3},{4,5,7}}=>2
{{1,6},{2,3},{4,5},{7}}=>2
{{1,7},{2,3,6},{4,5}}=>4
{{1},{2,3,6,7},{4,5}}=>1
{{1},{2,3,6},{4,5,7}}=>1
{{1},{2,3,6},{4,5},{7}}=>1
{{1,7},{2,3},{4,5,6}}=>3
{{1},{2,3,7},{4,5,6}}=>2
{{1},{2,3},{4,5,6,7}}=>0
{{1},{2,3},{4,5,6},{7}}=>0
{{1,7},{2,3},{4,5},{6}}=>2
{{1},{2,3,7},{4,5},{6}}=>1
{{1},{2,3},{4,5,7},{6}}=>0
{{1},{2,3},{4,5},{6,7}}=>0
{{1},{2,3},{4,5},{6},{7}}=>0
{{1,6,7},{2,3},{4},{5}}=>1
{{1,6},{2,3,7},{4},{5}}=>1
{{1,6},{2,3},{4,7},{5}}=>1
{{1,6},{2,3},{4},{5,7}}=>1
{{1,6},{2,3},{4},{5},{7}}=>1
{{1,7},{2,3,6},{4},{5}}=>2
{{1},{2,3,6,7},{4},{5}}=>0
{{1},{2,3,6},{4,7},{5}}=>0
{{1},{2,3,6},{4},{5,7}}=>0
{{1},{2,3,6},{4},{5},{7}}=>0
{{1,7},{2,3},{4,6},{5}}=>2
{{1},{2,3,7},{4,6},{5}}=>1
{{1},{2,3},{4,6,7},{5}}=>0
{{1},{2,3},{4,6},{5,7}}=>0
{{1},{2,3},{4,6},{5},{7}}=>0
{{1,7},{2,3},{4},{5,6}}=>2
{{1},{2,3,7},{4},{5,6}}=>1
{{1},{2,3},{4,7},{5,6}}=>1
{{1},{2,3},{4},{5,6,7}}=>0
{{1},{2,3},{4},{5,6},{7}}=>0
{{1,7},{2,3},{4},{5},{6}}=>1
{{1},{2,3,7},{4},{5},{6}}=>0
{{1},{2,3},{4,7},{5},{6}}=>0
{{1},{2,3},{4},{5,7},{6}}=>0
{{1},{2,3},{4},{5},{6,7}}=>0
{{1},{2,3},{4},{5},{6},{7}}=>0
{{1,4,5,6,7},{2},{3}}=>0
{{1,4,5,6},{2,7},{3}}=>2
{{1,4,5,6},{2},{3,7}}=>2
{{1,4,5,6},{2},{3},{7}}=>0
{{1,4,5,7},{2,6},{3}}=>1
{{1,4,5},{2,6,7},{3}}=>1
{{1,4,5},{2,6},{3,7}}=>2
{{1,4,5},{2,6},{3},{7}}=>1
{{1,4,5,7},{2},{3,6}}=>1
{{1,4,5},{2,7},{3,6}}=>3
{{1,4,5},{2},{3,6,7}}=>1
{{1,4,5},{2},{3,6},{7}}=>1
{{1,4,5,7},{2},{3},{6}}=>0
{{1,4,5},{2,7},{3},{6}}=>1
{{1,4,5},{2},{3,7},{6}}=>1
{{1,4,5},{2},{3},{6,7}}=>0
{{1,4,5},{2},{3},{6},{7}}=>0
{{1,4,6,7},{2,5},{3}}=>0
{{1,4,6},{2,5,7},{3}}=>0
{{1,4,6},{2,5},{3,7}}=>1
{{1,4,6},{2,5},{3},{7}}=>0
{{1,4,7},{2,5,6},{3}}=>1
{{1,4},{2,5,6,7},{3}}=>0
{{1,4},{2,5,6},{3,7}}=>1
{{1,4},{2,5,6},{3},{7}}=>0
{{1,4,7},{2,5},{3,6}}=>0
{{1,4},{2,5,7},{3,6}}=>0
{{1,4},{2,5},{3,6,7}}=>0
{{1,4},{2,5},{3,6},{7}}=>0
{{1,4,7},{2,5},{3},{6}}=>0
{{1,4},{2,5,7},{3},{6}}=>0
{{1,4},{2,5},{3,7},{6}}=>0
{{1,4},{2,5},{3},{6,7}}=>0
{{1,4},{2,5},{3},{6},{7}}=>0
{{1,4,6,7},{2},{3,5}}=>0
{{1,4,6},{2,7},{3,5}}=>2
{{1,4,6},{2},{3,5,7}}=>0
{{1,4,6},{2},{3,5},{7}}=>0
{{1,4,7},{2,6},{3,5}}=>1
{{1,4},{2,6,7},{3,5}}=>1
{{1,4},{2,6},{3,5,7}}=>1
{{1,4},{2,6},{3,5},{7}}=>1
{{1,4,7},{2},{3,5,6}}=>1
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{{1,4},{2},{3,5,6,7}}=>0
{{1,4},{2},{3,5,6},{7}}=>0
{{1,4,7},{2},{3,5},{6}}=>0
{{1,4},{2,7},{3,5},{6}}=>1
{{1,4},{2},{3,5,7},{6}}=>0
{{1,4},{2},{3,5},{6,7}}=>0
{{1,4},{2},{3,5},{6},{7}}=>0
{{1,4,6,7},{2},{3},{5}}=>0
{{1,4,6},{2,7},{3},{5}}=>1
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{{1,4,6},{2},{3},{5},{7}}=>0
{{1,4,7},{2,6},{3},{5}}=>0
{{1,4},{2,6,7},{3},{5}}=>0
{{1,4},{2,6},{3,7},{5}}=>0
{{1,4},{2,6},{3},{5,7}}=>0
{{1,4},{2,6},{3},{5},{7}}=>0
{{1,4,7},{2},{3,6},{5}}=>0
{{1,4},{2,7},{3,6},{5}}=>1
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{{1,4},{2},{3,6},{5,7}}=>0
{{1,4},{2},{3,6},{5},{7}}=>0
{{1,4,7},{2},{3},{5,6}}=>1
{{1,4},{2,7},{3},{5,6}}=>1
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{{1,4},{2},{3},{5,6},{7}}=>0
{{1,4,7},{2},{3},{5},{6}}=>0
{{1,4},{2,7},{3},{5},{6}}=>0
{{1,4},{2},{3,7},{5},{6}}=>0
{{1,4},{2},{3},{5,7},{6}}=>0
{{1,4},{2},{3},{5},{6,7}}=>0
{{1,4},{2},{3},{5},{6},{7}}=>0
{{1,5,6,7},{2,4},{3}}=>1
{{1,5,6},{2,4,7},{3}}=>2
{{1,5,6},{2,4},{3,7}}=>2
{{1,5,6},{2,4},{3},{7}}=>1
{{1,5,7},{2,4,6},{3}}=>1
{{1,5},{2,4,6,7},{3}}=>1
{{1,5},{2,4,6},{3,7}}=>2
{{1,5},{2,4,6},{3},{7}}=>1
{{1,5,7},{2,4},{3,6}}=>1
{{1,5},{2,4,7},{3,6}}=>1
{{1,5},{2,4},{3,6,7}}=>1
{{1,5},{2,4},{3,6},{7}}=>1
{{1,5,7},{2,4},{3},{6}}=>1
{{1,5},{2,4,7},{3},{6}}=>1
{{1,5},{2,4},{3,7},{6}}=>1
{{1,5},{2,4},{3},{6,7}}=>1
{{1,5},{2,4},{3},{6},{7}}=>1
{{1,6,7},{2,4,5},{3}}=>2
{{1,6},{2,4,5,7},{3}}=>2
{{1,6},{2,4,5},{3,7}}=>3
{{1,6},{2,4,5},{3},{7}}=>2
{{1,7},{2,4,5,6},{3}}=>3
{{1},{2,4,5,6,7},{3}}=>0
{{1},{2,4,5,6},{3,7}}=>2
{{1},{2,4,5,6},{3},{7}}=>0
{{1,7},{2,4,5},{3,6}}=>4
{{1},{2,4,5,7},{3,6}}=>1
{{1},{2,4,5},{3,6,7}}=>1
{{1},{2,4,5},{3,6},{7}}=>1
{{1,7},{2,4,5},{3},{6}}=>2
{{1},{2,4,5,7},{3},{6}}=>0
{{1},{2,4,5},{3,7},{6}}=>1
{{1},{2,4,5},{3},{6,7}}=>0
{{1},{2,4,5},{3},{6},{7}}=>0
{{1,6,7},{2,4},{3,5}}=>2
{{1,6},{2,4,7},{3,5}}=>2
{{1,6},{2,4},{3,5,7}}=>2
{{1,6},{2,4},{3,5},{7}}=>2
{{1,7},{2,4,6},{3,5}}=>3
{{1},{2,4,6,7},{3,5}}=>0
{{1},{2,4,6},{3,5,7}}=>0
{{1},{2,4,6},{3,5},{7}}=>0
{{1,7},{2,4},{3,5,6}}=>3
{{1},{2,4,7},{3,5,6}}=>1
{{1},{2,4},{3,5,6,7}}=>0
{{1},{2,4},{3,5,6},{7}}=>0
{{1,7},{2,4},{3,5},{6}}=>2
{{1},{2,4,7},{3,5},{6}}=>0
{{1},{2,4},{3,5,7},{6}}=>0
{{1},{2,4},{3,5},{6,7}}=>0
{{1},{2,4},{3,5},{6},{7}}=>0
{{1,6,7},{2,4},{3},{5}}=>1
{{1,6},{2,4,7},{3},{5}}=>1
{{1,6},{2,4},{3,7},{5}}=>1
{{1,6},{2,4},{3},{5,7}}=>1
{{1,6},{2,4},{3},{5},{7}}=>1
{{1,7},{2,4,6},{3},{5}}=>2
{{1},{2,4,6,7},{3},{5}}=>0
{{1},{2,4,6},{3,7},{5}}=>1
{{1},{2,4,6},{3},{5,7}}=>0
{{1},{2,4,6},{3},{5},{7}}=>0
{{1,7},{2,4},{3,6},{5}}=>2
{{1},{2,4,7},{3,6},{5}}=>0
{{1},{2,4},{3,6,7},{5}}=>0
{{1},{2,4},{3,6},{5,7}}=>0
{{1},{2,4},{3,6},{5},{7}}=>0
{{1,7},{2,4},{3},{5,6}}=>2
{{1},{2,4,7},{3},{5,6}}=>1
{{1},{2,4},{3,7},{5,6}}=>1
{{1},{2,4},{3},{5,6,7}}=>0
{{1},{2,4},{3},{5,6},{7}}=>0
{{1,7},{2,4},{3},{5},{6}}=>1
{{1},{2,4,7},{3},{5},{6}}=>0
{{1},{2,4},{3,7},{5},{6}}=>0
{{1},{2,4},{3},{5,7},{6}}=>0
{{1},{2,4},{3},{5},{6,7}}=>0
{{1},{2,4},{3},{5},{6},{7}}=>0
{{1,5,6,7},{2},{3,4}}=>1
{{1,5,6},{2,7},{3,4}}=>3
{{1,5,6},{2},{3,4,7}}=>2
{{1,5,6},{2},{3,4},{7}}=>1
{{1,5,7},{2,6},{3,4}}=>2
{{1,5},{2,6,7},{3,4}}=>2
{{1,5},{2,6},{3,4,7}}=>2
{{1,5},{2,6},{3,4},{7}}=>2
{{1,5,7},{2},{3,4,6}}=>1
{{1,5},{2,7},{3,4,6}}=>3
{{1,5},{2},{3,4,6,7}}=>1
{{1,5},{2},{3,4,6},{7}}=>1
{{1,5,7},{2},{3,4},{6}}=>1
{{1,5},{2,7},{3,4},{6}}=>2
{{1,5},{2},{3,4,7},{6}}=>1
{{1,5},{2},{3,4},{6,7}}=>1
{{1,5},{2},{3,4},{6},{7}}=>1
{{1,6,7},{2,5},{3,4}}=>3
{{1,6},{2,5,7},{3,4}}=>3
{{1,6},{2,5},{3,4,7}}=>3
{{1,6},{2,5},{3,4},{7}}=>3
{{1,7},{2,5,6},{3,4}}=>4
{{1},{2,5,6,7},{3,4}}=>1
{{1},{2,5,6},{3,4,7}}=>2
{{1},{2,5,6},{3,4},{7}}=>1
{{1,7},{2,5},{3,4,6}}=>4
{{1},{2,5,7},{3,4,6}}=>1
{{1},{2,5},{3,4,6,7}}=>1
{{1},{2,5},{3,4,6},{7}}=>1
{{1,7},{2,5},{3,4},{6}}=>3
{{1},{2,5,7},{3,4},{6}}=>1
{{1},{2,5},{3,4,7},{6}}=>1
{{1},{2,5},{3,4},{6,7}}=>1
{{1},{2,5},{3,4},{6},{7}}=>1
{{1,6,7},{2},{3,4,5}}=>2
{{1,6},{2,7},{3,4,5}}=>4
{{1,6},{2},{3,4,5,7}}=>2
{{1,6},{2},{3,4,5},{7}}=>2
{{1,7},{2,6},{3,4,5}}=>5
{{1},{2,6,7},{3,4,5}}=>2
{{1},{2,6},{3,4,5,7}}=>2
{{1},{2,6},{3,4,5},{7}}=>2
{{1,7},{2},{3,4,5,6}}=>3
{{1},{2,7},{3,4,5,6}}=>3
{{1},{2},{3,4,5,6,7}}=>0
{{1},{2},{3,4,5,6},{7}}=>0
{{1,7},{2},{3,4,5},{6}}=>2
{{1},{2,7},{3,4,5},{6}}=>2
{{1},{2},{3,4,5,7},{6}}=>0
{{1},{2},{3,4,5},{6,7}}=>0
{{1},{2},{3,4,5},{6},{7}}=>0
{{1,6,7},{2},{3,4},{5}}=>1
{{1,6},{2,7},{3,4},{5}}=>2
{{1,6},{2},{3,4,7},{5}}=>1
{{1,6},{2},{3,4},{5,7}}=>1
{{1,6},{2},{3,4},{5},{7}}=>1
{{1,7},{2,6},{3,4},{5}}=>3
{{1},{2,6,7},{3,4},{5}}=>1
{{1},{2,6},{3,4,7},{5}}=>1
{{1},{2,6},{3,4},{5,7}}=>1
{{1},{2,6},{3,4},{5},{7}}=>1
{{1,7},{2},{3,4,6},{5}}=>2
{{1},{2,7},{3,4,6},{5}}=>2
{{1},{2},{3,4,6,7},{5}}=>0
{{1},{2},{3,4,6},{5,7}}=>0
{{1},{2},{3,4,6},{5},{7}}=>0
{{1,7},{2},{3,4},{5,6}}=>2
{{1},{2,7},{3,4},{5,6}}=>2
{{1},{2},{3,4,7},{5,6}}=>1
{{1},{2},{3,4},{5,6,7}}=>0
{{1},{2},{3,4},{5,6},{7}}=>0
{{1,7},{2},{3,4},{5},{6}}=>1
{{1},{2,7},{3,4},{5},{6}}=>1
{{1},{2},{3,4,7},{5},{6}}=>0
{{1},{2},{3,4},{5,7},{6}}=>0
{{1},{2},{3,4},{5},{6,7}}=>0
{{1},{2},{3,4},{5},{6},{7}}=>0
{{1,5,6,7},{2},{3},{4}}=>0
{{1,5,6},{2,7},{3},{4}}=>1
{{1,5,6},{2},{3,7},{4}}=>1
{{1,5,6},{2},{3},{4,7}}=>1
{{1,5,6},{2},{3},{4},{7}}=>0
{{1,5,7},{2,6},{3},{4}}=>0
{{1,5},{2,6,7},{3},{4}}=>0
{{1,5},{2,6},{3,7},{4}}=>0
{{1,5},{2,6},{3},{4,7}}=>0
{{1,5},{2,6},{3},{4},{7}}=>0
{{1,5,7},{2},{3,6},{4}}=>0
{{1,5},{2,7},{3,6},{4}}=>1
{{1,5},{2},{3,6,7},{4}}=>0
{{1,5},{2},{3,6},{4,7}}=>0
{{1,5},{2},{3,6},{4},{7}}=>0
{{1,5,7},{2},{3},{4,6}}=>0
{{1,5},{2,7},{3},{4,6}}=>1
{{1,5},{2},{3,7},{4,6}}=>1
{{1,5},{2},{3},{4,6,7}}=>0
{{1,5},{2},{3},{4,6},{7}}=>0
{{1,5,7},{2},{3},{4},{6}}=>0
{{1,5},{2,7},{3},{4},{6}}=>0
{{1,5},{2},{3,7},{4},{6}}=>0
{{1,5},{2},{3},{4,7},{6}}=>0
{{1,5},{2},{3},{4},{6,7}}=>0
{{1,5},{2},{3},{4},{6},{7}}=>0
{{1,6,7},{2,5},{3},{4}}=>1
{{1,6},{2,5,7},{3},{4}}=>1
{{1,6},{2,5},{3,7},{4}}=>1
{{1,6},{2,5},{3},{4,7}}=>1
{{1,6},{2,5},{3},{4},{7}}=>1
{{1,7},{2,5,6},{3},{4}}=>2
{{1},{2,5,6,7},{3},{4}}=>0
{{1},{2,5,6},{3,7},{4}}=>1
{{1},{2,5,6},{3},{4,7}}=>1
{{1},{2,5,6},{3},{4},{7}}=>0
{{1,7},{2,5},{3,6},{4}}=>2
{{1},{2,5,7},{3,6},{4}}=>0
{{1},{2,5},{3,6,7},{4}}=>0
{{1},{2,5},{3,6},{4,7}}=>0
{{1},{2,5},{3,6},{4},{7}}=>0
{{1,7},{2,5},{3},{4,6}}=>2
{{1},{2,5,7},{3},{4,6}}=>0
{{1},{2,5},{3,7},{4,6}}=>1
{{1},{2,5},{3},{4,6,7}}=>0
{{1},{2,5},{3},{4,6},{7}}=>0
{{1,7},{2,5},{3},{4},{6}}=>1
{{1},{2,5,7},{3},{4},{6}}=>0
{{1},{2,5},{3,7},{4},{6}}=>0
{{1},{2,5},{3},{4,7},{6}}=>0
{{1},{2,5},{3},{4},{6,7}}=>0
{{1},{2,5},{3},{4},{6},{7}}=>0
{{1,6,7},{2},{3,5},{4}}=>1
{{1,6},{2,7},{3,5},{4}}=>2
{{1,6},{2},{3,5,7},{4}}=>1
{{1,6},{2},{3,5},{4,7}}=>1
{{1,6},{2},{3,5},{4},{7}}=>1
{{1,7},{2,6},{3,5},{4}}=>3
{{1},{2,6,7},{3,5},{4}}=>1
{{1},{2,6},{3,5,7},{4}}=>1
{{1},{2,6},{3,5},{4,7}}=>1
{{1},{2,6},{3,5},{4},{7}}=>1
{{1,7},{2},{3,5,6},{4}}=>2
{{1},{2,7},{3,5,6},{4}}=>2
{{1},{2},{3,5,6,7},{4}}=>0
{{1},{2},{3,5,6},{4,7}}=>1
{{1},{2},{3,5,6},{4},{7}}=>0
{{1,7},{2},{3,5},{4,6}}=>2
{{1},{2,7},{3,5},{4,6}}=>2
{{1},{2},{3,5,7},{4,6}}=>0
{{1},{2},{3,5},{4,6,7}}=>0
{{1},{2},{3,5},{4,6},{7}}=>0
{{1,7},{2},{3,5},{4},{6}}=>1
{{1},{2,7},{3,5},{4},{6}}=>1
{{1},{2},{3,5,7},{4},{6}}=>0
{{1},{2},{3,5},{4,7},{6}}=>0
{{1},{2},{3,5},{4},{6,7}}=>0
{{1},{2},{3,5},{4},{6},{7}}=>0
{{1,6,7},{2},{3},{4,5}}=>1
{{1,6},{2,7},{3},{4,5}}=>2
{{1,6},{2},{3,7},{4,5}}=>2
{{1,6},{2},{3},{4,5,7}}=>1
{{1,6},{2},{3},{4,5},{7}}=>1
{{1,7},{2,6},{3},{4,5}}=>3
{{1},{2,6,7},{3},{4,5}}=>1
{{1},{2,6},{3,7},{4,5}}=>2
{{1},{2,6},{3},{4,5,7}}=>1
{{1},{2,6},{3},{4,5},{7}}=>1
{{1,7},{2},{3,6},{4,5}}=>3
{{1},{2,7},{3,6},{4,5}}=>3
{{1},{2},{3,6,7},{4,5}}=>1
{{1},{2},{3,6},{4,5,7}}=>1
{{1},{2},{3,6},{4,5},{7}}=>1
{{1,7},{2},{3},{4,5,6}}=>2
{{1},{2,7},{3},{4,5,6}}=>2
{{1},{2},{3,7},{4,5,6}}=>2
{{1},{2},{3},{4,5,6,7}}=>0
{{1},{2},{3},{4,5,6},{7}}=>0
{{1,7},{2},{3},{4,5},{6}}=>1
{{1},{2,7},{3},{4,5},{6}}=>1
{{1},{2},{3,7},{4,5},{6}}=>1
{{1},{2},{3},{4,5,7},{6}}=>0
{{1},{2},{3},{4,5},{6,7}}=>0
{{1},{2},{3},{4,5},{6},{7}}=>0
{{1,6,7},{2},{3},{4},{5}}=>0
{{1,6},{2,7},{3},{4},{5}}=>0
{{1,6},{2},{3,7},{4},{5}}=>0
{{1,6},{2},{3},{4,7},{5}}=>0
{{1,6},{2},{3},{4},{5,7}}=>0
{{1,6},{2},{3},{4},{5},{7}}=>0
{{1,7},{2,6},{3},{4},{5}}=>1
{{1},{2,6,7},{3},{4},{5}}=>0
{{1},{2,6},{3,7},{4},{5}}=>0
{{1},{2,6},{3},{4,7},{5}}=>0
{{1},{2,6},{3},{4},{5,7}}=>0
{{1},{2,6},{3},{4},{5},{7}}=>0
{{1,7},{2},{3,6},{4},{5}}=>1
{{1},{2,7},{3,6},{4},{5}}=>1
{{1},{2},{3,6,7},{4},{5}}=>0
{{1},{2},{3,6},{4,7},{5}}=>0
{{1},{2},{3,6},{4},{5,7}}=>0
{{1},{2},{3,6},{4},{5},{7}}=>0
{{1,7},{2},{3},{4,6},{5}}=>1
{{1},{2,7},{3},{4,6},{5}}=>1
{{1},{2},{3,7},{4,6},{5}}=>1
{{1},{2},{3},{4,6,7},{5}}=>0
{{1},{2},{3},{4,6},{5,7}}=>0
{{1},{2},{3},{4,6},{5},{7}}=>0
{{1,7},{2},{3},{4},{5,6}}=>1
{{1},{2,7},{3},{4},{5,6}}=>1
{{1},{2},{3,7},{4},{5,6}}=>1
{{1},{2},{3},{4,7},{5,6}}=>1
{{1},{2},{3},{4},{5,6,7}}=>0
{{1},{2},{3},{4},{5,6},{7}}=>0
{{1,7},{2},{3},{4},{5},{6}}=>0
{{1},{2,7},{3},{4},{5},{6}}=>0
{{1},{2},{3,7},{4},{5},{6}}=>0
{{1},{2},{3},{4,7},{5},{6}}=>0
{{1},{2},{3},{4},{5,7},{6}}=>0
{{1},{2},{3},{4},{5},{6,7}}=>0
{{1},{2},{3},{4},{5},{6},{7}}=>0
{{1,2},{3,4},{5,6},{7,8}}=>0
{{1,3},{2,4},{5,6},{7,8}}=>0
{{1,4},{2,3},{5,6},{7,8}}=>1
{{1,5},{2,3},{4,6},{7,8}}=>1
{{1,6},{2,3},{4,5},{7,8}}=>2
{{1,7},{2,3},{4,5},{6,8}}=>2
{{1,8},{2,3},{4,5},{6,7}}=>3
{{1,8},{2,4},{3,5},{6,7}}=>3
{{1,7},{2,4},{3,5},{6,8}}=>2
{{1,6},{2,4},{3,5},{7,8}}=>2
{{1,5},{2,4},{3,6},{7,8}}=>1
{{1,4},{2,5},{3,6},{7,8}}=>0
{{1,3},{2,5},{4,6},{7,8}}=>0
{{1,2},{3,5},{4,6},{7,8}}=>0
{{1,2},{3,6},{4,5},{7,8}}=>1
{{1,3},{2,6},{4,5},{7,8}}=>1
{{1,4},{2,6},{3,5},{7,8}}=>1
{{1,5},{2,6},{3,4},{7,8}}=>2
{{1,6},{2,5},{3,4},{7,8}}=>3
{{1,7},{2,5},{3,4},{6,8}}=>3
{{1,8},{2,5},{3,4},{6,7}}=>4
{{1,8},{2,6},{3,4},{5,7}}=>4
{{1,7},{2,6},{3,4},{5,8}}=>3
{{1,6},{2,7},{3,4},{5,8}}=>2
{{1,5},{2,7},{3,4},{6,8}}=>2
{{1,4},{2,7},{3,5},{6,8}}=>1
{{1,3},{2,7},{4,5},{6,8}}=>1
{{1,2},{3,7},{4,5},{6,8}}=>1
{{1,2},{3,8},{4,5},{6,7}}=>2
{{1,3},{2,8},{4,5},{6,7}}=>2
{{1,4},{2,8},{3,5},{6,7}}=>2
{{1,5},{2,8},{3,4},{6,7}}=>3
{{1,6},{2,8},{3,4},{5,7}}=>3
{{1,7},{2,8},{3,4},{5,6}}=>4
{{1,8},{2,7},{3,4},{5,6}}=>5
{{1,8},{2,7},{3,5},{4,6}}=>5
{{1,7},{2,8},{3,5},{4,6}}=>4
{{1,6},{2,8},{3,5},{4,7}}=>3
{{1,5},{2,8},{3,6},{4,7}}=>2
{{1,4},{2,8},{3,6},{5,7}}=>2
{{1,3},{2,8},{4,6},{5,7}}=>2
{{1,2},{3,8},{4,6},{5,7}}=>2
{{1,2},{3,7},{4,6},{5,8}}=>1
{{1,3},{2,7},{4,6},{5,8}}=>1
{{1,4},{2,7},{3,6},{5,8}}=>1
{{1,5},{2,7},{3,6},{4,8}}=>1
{{1,6},{2,7},{3,5},{4,8}}=>2
{{1,7},{2,6},{3,5},{4,8}}=>3
{{1,8},{2,6},{3,5},{4,7}}=>4
{{1,8},{2,5},{3,6},{4,7}}=>3
{{1,7},{2,5},{3,6},{4,8}}=>2
{{1,6},{2,5},{3,7},{4,8}}=>1
{{1,5},{2,6},{3,7},{4,8}}=>0
{{1,4},{2,6},{3,7},{5,8}}=>0
{{1,3},{2,6},{4,7},{5,8}}=>0
{{1,2},{3,6},{4,7},{5,8}}=>0
{{1,2},{3,5},{4,7},{6,8}}=>0
{{1,3},{2,5},{4,7},{6,8}}=>0
{{1,4},{2,5},{3,7},{6,8}}=>0
{{1,5},{2,4},{3,7},{6,8}}=>1
{{1,6},{2,4},{3,7},{5,8}}=>1
{{1,7},{2,4},{3,6},{5,8}}=>2
{{1,8},{2,4},{3,6},{5,7}}=>3
{{1,8},{2,3},{4,6},{5,7}}=>3
{{1,7},{2,3},{4,6},{5,8}}=>2
{{1,6},{2,3},{4,7},{5,8}}=>1
{{1,5},{2,3},{4,7},{6,8}}=>1
{{1,4},{2,3},{5,7},{6,8}}=>1
{{1,3},{2,4},{5,7},{6,8}}=>0
{{1,2},{3,4},{5,7},{6,8}}=>0
{{1,2},{3,4},{5,8},{6,7}}=>1
{{1,3},{2,4},{5,8},{6,7}}=>1
{{1,4},{2,3},{5,8},{6,7}}=>2
{{1,5},{2,3},{4,8},{6,7}}=>2
{{1,6},{2,3},{4,8},{5,7}}=>2
{{1,7},{2,3},{4,8},{5,6}}=>3
{{1,8},{2,3},{4,7},{5,6}}=>4
{{1,8},{2,4},{3,7},{5,6}}=>4
{{1,7},{2,4},{3,8},{5,6}}=>3
{{1,6},{2,4},{3,8},{5,7}}=>2
{{1,5},{2,4},{3,8},{6,7}}=>2
{{1,4},{2,5},{3,8},{6,7}}=>1
{{1,3},{2,5},{4,8},{6,7}}=>1
{{1,2},{3,5},{4,8},{6,7}}=>1
{{1,2},{3,6},{4,8},{5,7}}=>1
{{1,3},{2,6},{4,8},{5,7}}=>1
{{1,4},{2,6},{3,8},{5,7}}=>1
{{1,5},{2,6},{3,8},{4,7}}=>1
{{1,6},{2,5},{3,8},{4,7}}=>2
{{1,7},{2,5},{3,8},{4,6}}=>3
{{1,8},{2,5},{3,7},{4,6}}=>4
{{1,8},{2,6},{3,7},{4,5}}=>5
{{1,7},{2,6},{3,8},{4,5}}=>4
{{1,6},{2,7},{3,8},{4,5}}=>3
{{1,5},{2,7},{3,8},{4,6}}=>2
{{1,4},{2,7},{3,8},{5,6}}=>2
{{1,3},{2,7},{4,8},{5,6}}=>2
{{1,2},{3,7},{4,8},{5,6}}=>2
{{1,2},{3,8},{4,7},{5,6}}=>3
{{1,3},{2,8},{4,7},{5,6}}=>3
{{1,4},{2,8},{3,7},{5,6}}=>3
{{1,5},{2,8},{3,7},{4,6}}=>3
{{1,6},{2,8},{3,7},{4,5}}=>4
{{1,7},{2,8},{3,6},{4,5}}=>5
{{1,8},{2,7},{3,6},{4,5}}=>6
{{1},{2},{3,4,5,6,7,8}}=>0
{{1},{2,4,5,6,7,8},{3}}=>0
{{1},{2,3,5,6,7,8},{4}}=>0
{{1},{2,3,4,6,7,8},{5}}=>0
{{1},{2,3,4,5,8},{6},{7}}=>0
{{1},{2,3,4,5,7,8},{6}}=>0
{{1},{2,3,4,5,6,7},{8}}=>0
{{1},{2,3,4,8},{5,6,7}}=>2
{{1},{2,3,4,5,8},{6,7}}=>1
{{1},{2,3,4,5,6,8},{7}}=>0
{{1},{2,3,4,5,6,7,8}}=>0
{{1,2},{3,4,5,6,7,8}}=>0
{{1,4,5,6,7,8},{2},{3}}=>0
{{1,3,5,6,7,8},{2},{4}}=>0
{{1,3,4,5,6,7,8},{2}}=>0
{{1,4,5,6,7,8},{2,3}}=>1
{{1,2,4,5,6,7,8},{3}}=>0
{{1,2,5,6,7,8},{3,4}}=>1
{{1,2,3,5,6,7},{4},{8}}=>0
{{1,2,3,5,6,7,8},{4}}=>0
{{1,2,3,6,7,8},{4,5}}=>1
{{1,2,3,4,7},{5},{6},{8}}=>0
{{1,2,3,4,6,7},{5},{8}}=>0
{{1,2,3,4,6,7,8},{5}}=>0
{{1,2,3,4,5,6},{7,8}}=>0
{{1,2,3,7},{4,5,6},{8}}=>2
{{1,2,3,4,7},{5,6},{8}}=>1
{{1,2,3,4,7,8},{5,6}}=>1
{{1,2,3,4,5,7},{6},{8}}=>0
{{1,2,3,4,5,7,8},{6}}=>0
{{1,2,3,4,5,6,7},{8}}=>0
{{1,8},{2,3,4,5,6,7}}=>5
{{1,2,3,4,5,8},{6,7}}=>1
{{1,2,3,4,5,6,8},{7}}=>0
{{1,2,3,4,5,6,7,8}}=>0
{{1,3,5,6,7,8},{2,4}}=>0
{{1,3,4,6,7,8},{2,5}}=>1
{{1,2,4,6,7,8},{3,5}}=>0
{{1,3,4,5,7,8},{2,6}}=>2
{{1,2,4,5,7,8},{3,6}}=>1
{{1,2,3,5,7,8},{4,6}}=>0
{{1,3,4,5,6,8},{2,7}}=>3
{{1,2,4,5,6,8},{3,7}}=>2
{{1,2,3,5,6,8},{4,7}}=>1
{{1,2,3,4,6,8},{5,7}}=>0
{{1,3,4,5,6,7},{2,8}}=>4
{{1,2,4,5,6,7},{3,8}}=>3
{{1,2,3,5,6,7},{4,8}}=>2
{{1,2,3,4,6,7},{5,8}}=>1
{{1,2,3,4,5,7},{6,8}}=>0
{{1,3},{2,4,5,6,7,8}}=>0
{{1,4},{2,3,5,6,7,8}}=>1
{{1,5},{2,3,4,6,7,8}}=>2
{{1,6},{2,3,4,5,7,8}}=>3
{{1,7},{2,3,4,5,6,8}}=>4
{{1,2,3,4,5,6,7,8},{9}}=>0
{{1},{2,3,4,5,6,7,8,9}}=>0
{{1,2,3,4,5,6,8},{7},{9}}=>0
{{1},{2,3,4,5,6,7,9},{8}}=>0
{{1,2,3,4,5,8},{6,7},{9}}=>1
{{1,2,3,4,5,7,8},{6},{9}}=>0
{{1},{2,3,4,5,6,9},{7,8}}=>1
{{1},{2,3,4,5,6,8,9},{7}}=>0
{{1,2},{3,4},{5,6},{7,8},{9,10}}=>0
{{1,4},{2,3},{5,6},{7,8},{9,10}}=>1
{{1,6},{2,3},{4,5},{7,8},{9,10}}=>2
{{1,8},{2,3},{4,5},{6,7},{9,10}}=>3
{{1,10},{2,3},{4,5},{6,7},{8,9}}=>4
{{1,2},{3,6},{4,5},{7,8},{9,10}}=>1
{{1,6},{2,5},{3,4},{7,8},{9,10}}=>3
{{1,8},{2,5},{3,4},{6,7},{9,10}}=>4
{{1,10},{2,5},{3,4},{6,7},{8,9}}=>5
{{1,2},{3,8},{4,5},{6,7},{9,10}}=>2
{{1,8},{2,7},{3,4},{5,6},{9,10}}=>5
{{1,10},{2,7},{3,4},{5,6},{8,9}}=>6
{{1,2},{3,10},{4,5},{6,7},{8,9}}=>3
{{1,10},{2,9},{3,4},{5,6},{7,8}}=>7
{{1,2},{3,4},{5,8},{6,7},{9,10}}=>1
{{1,4},{2,3},{5,8},{6,7},{9,10}}=>2
{{1,8},{2,3},{4,7},{5,6},{9,10}}=>4
{{1,10},{2,3},{4,7},{5,6},{8,9}}=>5
{{1,2},{3,8},{4,7},{5,6},{9,10}}=>3
{{1,8},{2,7},{3,6},{4,5},{9,10}}=>6
{{1,10},{2,7},{3,6},{4,5},{8,9}}=>7
{{1,2},{3,10},{4,7},{5,6},{8,9}}=>4
{{1,10},{2,9},{3,6},{4,5},{7,8}}=>8
{{1,2},{3,4},{5,10},{6,7},{8,9}}=>2
{{1,4},{2,3},{5,10},{6,7},{8,9}}=>3
{{1,10},{2,3},{4,9},{5,6},{7,8}}=>6
{{1,2},{3,10},{4,9},{5,6},{7,8}}=>5
{{1,10},{2,9},{3,8},{4,5},{6,7}}=>9
{{1,2},{3,4},{5,6},{7,10},{8,9}}=>1
{{1,4},{2,3},{5,6},{7,10},{8,9}}=>2
{{1,6},{2,3},{4,5},{7,10},{8,9}}=>3
{{1,10},{2,3},{4,5},{6,9},{7,8}}=>5
{{1,2},{3,6},{4,5},{7,10},{8,9}}=>2
{{1,6},{2,5},{3,4},{7,10},{8,9}}=>4
{{1,10},{2,5},{3,4},{6,9},{7,8}}=>6
{{1,2},{3,10},{4,5},{6,9},{7,8}}=>4
{{1,10},{2,9},{3,4},{5,8},{6,7}}=>8
{{1,2},{3,4},{5,10},{6,9},{7,8}}=>3
{{1,4},{2,3},{5,10},{6,9},{7,8}}=>4
{{1,10},{2,3},{4,9},{5,8},{6,7}}=>7
{{1,2},{3,10},{4,9},{5,8},{6,7}}=>6
{{1,10},{2,9},{3,8},{4,7},{5,6}}=>10
{{1,2,3,4,5,6,7,8,9},{10}}=>0
{{1},{2,3,4,5,6,7,8,9,10}}=>0
{{1,2,3,4,5,6,7,9},{8},{10}}=>0
{{1},{2,3,4,5,6,7,8,10},{9}}=>0
{{1,2,3,4,5,6,7,8,9,10},{11}}=>0
{{1},{2,3,4,5,6,7,8,9,10,11}}=>0
{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>0
{{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}}=>1
{{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}}=>1
{{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}}=>2
{{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}}=>3
{{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}}=>1
{{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}}=>2
{{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}}=>2
{{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}}=>3
{{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}}=>4
{{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}}=>3
{{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}}=>4
{{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}}=>5
{{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}}=>6
{{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}}=>1
{{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}}=>2
{{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}}=>2
{{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}}=>3
{{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}}=>4
{{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}}=>2
{{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}}=>3
{{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}}=>3
{{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}}=>4
{{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}}=>5
{{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}}=>4
{{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}}=>5
{{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}}=>6
{{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}}=>7
{{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}}=>3
{{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}}=>4
{{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}}=>4
{{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}}=>5
{{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}}=>6
{{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}}=>5
{{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}}=>6
{{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}}=>7
{{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}}=>8
{{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}}=>6
{{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}}=>7
{{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}}=>8
{{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}}=>9
{{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}}=>10
{{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}}=>1
{{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}}=>2
{{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}}=>2
{{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}}=>3
{{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}}=>4
{{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}}=>2
{{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}}=>3
{{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}}=>3
{{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}}=>4
{{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}}=>5
{{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}}=>4
{{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}}=>5
{{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}}=>6
{{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}}=>7
{{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}}=>2
{{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}}=>3
{{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}}=>3
{{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}}=>4
{{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}}=>5
{{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}}=>3
{{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}}=>4
{{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}}=>4
{{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}}=>5
{{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}}=>6
{{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}}=>5
{{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}}=>6
{{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}}=>7
{{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}}=>8
{{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}}=>4
{{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}}=>5
{{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}}=>5
{{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}}=>6
{{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}}=>7
{{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}}=>6
{{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}}=>7
{{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}}=>8
{{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}}=>9
{{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}}=>7
{{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}}=>8
{{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}}=>9
{{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}}=>10
{{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}}=>11
{{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}}=>3
{{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}}=>4
{{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}}=>4
{{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}}=>5
{{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}}=>6
{{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}}=>4
{{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}}=>5
{{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}}=>5
{{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}}=>6
{{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}}=>7
{{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}}=>6
{{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}}=>7
{{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}}=>8
{{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}}=>9
{{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}}=>5
{{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}}=>6
{{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}}=>6
{{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}}=>7
{{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}}=>8
{{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}}=>7
{{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}}=>8
{{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}}=>9
{{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}}=>10
{{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}}=>8
{{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}}=>9
{{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}}=>10
{{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}}=>11
{{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}}=>12
{{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}}=>6
{{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}}=>7
{{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}}=>7
{{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}}=>8
{{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}}=>9
{{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}}=>8
{{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}}=>9
{{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}}=>10
{{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}}=>11
{{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}}=>9
{{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}}=>10
{{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}}=>11
{{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}}=>12
{{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}}=>13
{{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}}=>10
{{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}}=>11
{{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}}=>12
{{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}}=>13
{{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}}=>14
{{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}=>15
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Description
The number of nestings of a set partition.
This is given by the number of $i < i' < j' < j$ such that $i,j$ are two consecutive entries on one block, and $i',j'$ are consecutive entries in another block.
This is given by the number of $i < i' < j' < j$ such that $i,j$ are two consecutive entries on one block, and $i',j'$ are consecutive entries in another block.
References
[1] Chern, B., Diaconis, P., Kane, D. M., Rhoades, R. C. Central Limit Theorems for some Set Partition Statistics arXiv:1502.00938
[2] Kasraoui, A., Zeng, J. Distribution of crossings, nestings and alignments of two edges in matchings and partitions MathSciNet:2212506
[3] Rubey, M., Stump, C. Crossings and nestings in set partitions of classical types MathSciNet:2729369
[2] Kasraoui, A., Zeng, J. Distribution of crossings, nestings and alignments of two edges in matchings and partitions MathSciNet:2212506
[3] Rubey, M., Stump, C. Crossings and nestings in set partitions of classical types MathSciNet:2729369
Code
def statistic(pi): pi_sorted = sorted([sorted(b) for b in pi]) edges = [(a,b) for block in pi_sorted for (a,b) in zip(block, block[1:])] count = 0 for (i1,j1),(i2,j2) in Subsets(edges, 2): if i1 < i2 < j2 < j1 or i2 < i1 < j1 < j2: count += 1 return count
Created
Feb 04, 2015 at 11:35 by Christian Stump
Updated
Dec 26, 2017 at 17:19 by Martin Rubey
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