- FindStat

Identifier
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
St000496: Set partitions ⟶ ℤ
Values
=>
                            Cc0005;cc-rep-0
                            
                            Cc0009;cc-rep
                            
                            
                            

                        [1,0]=>{{1}}=>0
[1,0,1,0]=>{{1},{2}}=>0
[1,1,0,0]=>{{1,2}}=>0
[1,0,1,0,1,0]=>{{1},{2},{3}}=>0
[1,0,1,1,0,0]=>{{1},{2,3}}=>0
[1,1,0,0,1,0]=>{{1,2},{3}}=>0
[1,1,0,1,0,0]=>{{1,3},{2}}=>1
[1,1,1,0,0,0]=>{{1,2,3}}=>0
[1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4}}=>0
[1,0,1,0,1,1,0,0]=>{{1},{2},{3,4}}=>0
[1,0,1,1,0,0,1,0]=>{{1},{2,3},{4}}=>0
[1,0,1,1,0,1,0,0]=>{{1},{2,4},{3}}=>1
[1,0,1,1,1,0,0,0]=>{{1},{2,3,4}}=>0
[1,1,0,0,1,0,1,0]=>{{1,2},{3},{4}}=>0
[1,1,0,0,1,1,0,0]=>{{1,2},{3,4}}=>0
[1,1,0,1,0,0,1,0]=>{{1,3},{2},{4}}=>1
[1,1,0,1,0,1,0,0]=>{{1,4},{2},{3}}=>2
[1,1,0,1,1,0,0,0]=>{{1,3,4},{2}}=>2
[1,1,1,0,0,0,1,0]=>{{1,2,3},{4}}=>0
[1,1,1,0,0,1,0,0]=>{{1,4},{2,3}}=>1
[1,1,1,0,1,0,0,0]=>{{1,2,4},{3}}=>1
[1,1,1,1,0,0,0,0]=>{{1,2,3,4}}=>0
[1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5}}=>0
[1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5}}=>0
[1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5}}=>0
[1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3,5},{4}}=>1
[1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}}=>0
[1,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4},{5}}=>0
[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>0
[1,0,1,1,0,1,0,0,1,0]=>{{1},{2,4},{3},{5}}=>1
[1,0,1,1,0,1,0,1,0,0]=>{{1},{2,5},{3},{4}}=>2
[1,0,1,1,0,1,1,0,0,0]=>{{1},{2,4,5},{3}}=>2
[1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}}=>0
[1,0,1,1,1,0,0,1,0,0]=>{{1},{2,5},{3,4}}=>1
[1,0,1,1,1,0,1,0,0,0]=>{{1},{2,3,5},{4}}=>1
[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}}=>0
[1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5}}=>0
[1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3},{4,5}}=>0
[1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5}}=>0
[1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,5},{4}}=>1
[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>0
[1,1,0,1,0,0,1,0,1,0]=>{{1,3},{2},{4},{5}}=>1
[1,1,0,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5}}=>1
[1,1,0,1,0,1,0,0,1,0]=>{{1,4},{2},{3},{5}}=>2
[1,1,0,1,0,1,0,1,0,0]=>{{1,5},{2},{3},{4}}=>3
[1,1,0,1,0,1,1,0,0,0]=>{{1,4,5},{2},{3}}=>4
[1,1,0,1,1,0,0,0,1,0]=>{{1,3,4},{2},{5}}=>2
[1,1,0,1,1,0,0,1,0,0]=>{{1,5},{2},{3,4}}=>2
[1,1,0,1,1,0,1,0,0,0]=>{{1,3,5},{2},{4}}=>3
[1,1,0,1,1,1,0,0,0,0]=>{{1,3,4,5},{2}}=>3
[1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4},{5}}=>0
[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}}=>0
[1,1,1,0,0,1,0,0,1,0]=>{{1,4},{2,3},{5}}=>1
[1,1,1,0,0,1,0,1,0,0]=>{{1,5},{2,3},{4}}=>2
[1,1,1,0,0,1,1,0,0,0]=>{{1,4,5},{2,3}}=>2
[1,1,1,0,1,0,0,0,1,0]=>{{1,2,4},{3},{5}}=>1
[1,1,1,0,1,0,0,1,0,0]=>{{1,5},{2,4},{3}}=>3
[1,1,1,0,1,0,1,0,0,0]=>{{1,2,5},{3},{4}}=>2
[1,1,1,0,1,1,0,0,0,0]=>{{1,2,4,5},{3}}=>2
[1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4},{5}}=>0
[1,1,1,1,0,0,0,1,0,0]=>{{1,5},{2,3,4}}=>1
[1,1,1,1,0,0,1,0,0,0]=>{{1,2,5},{3,4}}=>1
[1,1,1,1,0,1,0,0,0,0]=>{{1,2,3,5},{4}}=>1
[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}}=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6}}=>0
[1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6}}=>0
[1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6}}=>0
[1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4,6},{5}}=>1
[1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}}=>0
[1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6}}=>0
[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>0
[1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3,5},{4},{6}}=>1
[1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3,6},{4},{5}}=>2
[1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3,5,6},{4}}=>2
[1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}}=>0
[1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3,6},{4,5}}=>1
[1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3,4,6},{5}}=>1
[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}}=>0
[1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6}}=>0
[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}}=>0
[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>0
[1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2,3},{4,6},{5}}=>1
[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>0
[1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6}}=>1
[1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2,4},{3},{5,6}}=>1
[1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2,5},{3},{4},{6}}=>2
[1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2,6},{3},{4},{5}}=>3
[1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2,5,6},{3},{4}}=>4
[1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2,4,5},{3},{6}}=>2
[1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2,6},{3},{4,5}}=>2
[1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2,4,6},{3},{5}}=>3
[1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2,4,5,6},{3}}=>3
[1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}}=>0
[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>0
[1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2,5},{3,4},{6}}=>1
[1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2,6},{3,4},{5}}=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2,5,6},{3,4}}=>2
[1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2,3,5},{4},{6}}=>1
[1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2,6},{3,5},{4}}=>3
[1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2,3,6},{4},{5}}=>2
[1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2,3,5,6},{4}}=>2
[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}}=>0
[1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2,6},{3,4,5}}=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2,3,6},{4,5}}=>1
[1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2,3,4,6},{5}}=>1
[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}}=>0
[1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6}}=>0
[1,1,0,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5,6}}=>0
[1,1,0,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4,5},{6}}=>0
[1,1,0,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4,6},{5}}=>1
[1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}}=>0
[1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5},{6}}=>0
[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>0
[1,1,0,0,1,1,0,1,0,0,1,0]=>{{1,2},{3,5},{4},{6}}=>1
[1,1,0,0,1,1,0,1,0,1,0,0]=>{{1,2},{3,6},{4},{5}}=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>{{1,2},{3,5,6},{4}}=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>0
[1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,6},{4,5}}=>1
[1,1,0,0,1,1,1,0,1,0,0,0]=>{{1,2},{3,4,6},{5}}=>1
[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>0
[1,1,0,1,0,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6}}=>1
[1,1,0,1,0,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5,6}}=>1
[1,1,0,1,0,0,1,1,0,0,1,0]=>{{1,3},{2},{4,5},{6}}=>1
[1,1,0,1,0,0,1,1,0,1,0,0]=>{{1,3},{2},{4,6},{5}}=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>{{1,3},{2},{4,5,6}}=>1
[1,1,0,1,0,1,0,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6}}=>2
[1,1,0,1,0,1,0,0,1,1,0,0]=>{{1,4},{2},{3},{5,6}}=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>{{1,5},{2},{3},{4},{6}}=>3
[1,1,0,1,0,1,0,1,0,1,0,0]=>{{1,6},{2},{3},{4},{5}}=>4
[1,1,0,1,0,1,0,1,1,0,0,0]=>{{1,5,6},{2},{3},{4}}=>6
[1,1,0,1,0,1,1,0,0,0,1,0]=>{{1,4,5},{2},{3},{6}}=>4
[1,1,0,1,0,1,1,0,0,1,0,0]=>{{1,6},{2},{3},{4,5}}=>3
[1,1,0,1,0,1,1,0,1,0,0,0]=>{{1,4,6},{2},{3},{5}}=>5
[1,1,0,1,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2},{3}}=>6
[1,1,0,1,1,0,0,0,1,0,1,0]=>{{1,3,4},{2},{5},{6}}=>2
[1,1,0,1,1,0,0,0,1,1,0,0]=>{{1,3,4},{2},{5,6}}=>2
[1,1,0,1,1,0,0,1,0,0,1,0]=>{{1,5},{2},{3,4},{6}}=>2
[1,1,0,1,1,0,0,1,0,1,0,0]=>{{1,6},{2},{3,4},{5}}=>3
[1,1,0,1,1,0,0,1,1,0,0,0]=>{{1,5,6},{2},{3,4}}=>4
[1,1,0,1,1,0,1,0,0,0,1,0]=>{{1,3,5},{2},{4},{6}}=>3
[1,1,0,1,1,0,1,0,0,1,0,0]=>{{1,6},{2},{3,5},{4}}=>4
[1,1,0,1,1,0,1,0,1,0,0,0]=>{{1,3,6},{2},{4},{5}}=>4
[1,1,0,1,1,0,1,1,0,0,0,0]=>{{1,3,5,6},{2},{4}}=>5
[1,1,0,1,1,1,0,0,0,0,1,0]=>{{1,3,4,5},{2},{6}}=>3
[1,1,0,1,1,1,0,0,0,1,0,0]=>{{1,6},{2},{3,4,5}}=>2
[1,1,0,1,1,1,0,0,1,0,0,0]=>{{1,3,6},{2},{4,5}}=>3
[1,1,0,1,1,1,0,1,0,0,0,0]=>{{1,3,4,6},{2},{5}}=>4
[1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,3,4,5,6},{2}}=>4
[1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6}}=>0
[1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5,6}}=>0
[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}}=>0
[1,1,1,0,0,0,1,1,0,1,0,0]=>{{1,2,3},{4,6},{5}}=>1
[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>0
[1,1,1,0,0,1,0,0,1,0,1,0]=>{{1,4},{2,3},{5},{6}}=>1
[1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6}}=>1
[1,1,1,0,0,1,0,1,0,0,1,0]=>{{1,5},{2,3},{4},{6}}=>2
[1,1,1,0,0,1,0,1,0,1,0,0]=>{{1,6},{2,3},{4},{5}}=>3
[1,1,1,0,0,1,0,1,1,0,0,0]=>{{1,5,6},{2,3},{4}}=>4
[1,1,1,0,0,1,1,0,0,0,1,0]=>{{1,4,5},{2,3},{6}}=>2
[1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,6},{2,3},{4,5}}=>2
[1,1,1,0,0,1,1,0,1,0,0,0]=>{{1,4,6},{2,3},{5}}=>3
[1,1,1,0,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2,3}}=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>{{1,2,4},{3},{5},{6}}=>1
[1,1,1,0,1,0,0,0,1,1,0,0]=>{{1,2,4},{3},{5,6}}=>1
[1,1,1,0,1,0,0,1,0,0,1,0]=>{{1,5},{2,4},{3},{6}}=>3
[1,1,1,0,1,0,0,1,0,1,0,0]=>{{1,6},{2,4},{3},{5}}=>4
[1,1,1,0,1,0,0,1,1,0,0,0]=>{{1,5,6},{2,4},{3}}=>5
[1,1,1,0,1,0,1,0,0,0,1,0]=>{{1,2,5},{3},{4},{6}}=>2
[1,1,1,0,1,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3},{4}}=>5
[1,1,1,0,1,0,1,0,1,0,0,0]=>{{1,2,6},{3},{4},{5}}=>3
[1,1,1,0,1,0,1,1,0,0,0,0]=>{{1,2,5,6},{3},{4}}=>4
[1,1,1,0,1,1,0,0,0,0,1,0]=>{{1,2,4,5},{3},{6}}=>2
[1,1,1,0,1,1,0,0,0,1,0,0]=>{{1,6},{2,4,5},{3}}=>4
[1,1,1,0,1,1,0,0,1,0,0,0]=>{{1,2,6},{3},{4,5}}=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>{{1,2,4,6},{3},{5}}=>3
[1,1,1,0,1,1,1,0,0,0,0,0]=>{{1,2,4,5,6},{3}}=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5},{6}}=>0
[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}}=>0
[1,1,1,1,0,0,0,1,0,0,1,0]=>{{1,5},{2,3,4},{6}}=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>{{1,6},{2,3,4},{5}}=>2
[1,1,1,1,0,0,0,1,1,0,0,0]=>{{1,5,6},{2,3,4}}=>2
[1,1,1,1,0,0,1,0,0,0,1,0]=>{{1,2,5},{3,4},{6}}=>1
[1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3,4}}=>3
[1,1,1,1,0,0,1,0,1,0,0,0]=>{{1,2,6},{3,4},{5}}=>2
[1,1,1,1,0,0,1,1,0,0,0,0]=>{{1,2,5,6},{3,4}}=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>{{1,2,3,5},{4},{6}}=>1
[1,1,1,1,0,1,0,0,0,1,0,0]=>{{1,6},{2,3,5},{4}}=>3
[1,1,1,1,0,1,0,0,1,0,0,0]=>{{1,2,6},{3,5},{4}}=>3
[1,1,1,1,0,1,0,1,0,0,0,0]=>{{1,2,3,6},{4},{5}}=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>{{1,2,3,5,6},{4}}=>2
[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}}=>0
[1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,6},{2,3,4,5}}=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>{{1,2,6},{3,4,5}}=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>{{1,2,3,6},{4,5}}=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>{{1,2,3,4,6},{5}}=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}}=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7}}=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6,7}}=>0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5,6},{7}}=>0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4},{5,7},{6}}=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6,7}}=>0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7}}=>0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3},{4,6},{5},{7}}=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3},{4,7},{5},{6}}=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3},{4,6,7},{5}}=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4,5,6},{7}}=>0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3},{4,7},{5,6}}=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3},{4,5,7},{6}}=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5,6,7}}=>0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7}}=>0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6,7}}=>0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2},{3,4},{5,7},{6}}=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2},{3,5},{4},{6},{7}}=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2},{3,5},{4},{6,7}}=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2},{3,6},{4},{5},{7}}=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2},{3,7},{4},{5},{6}}=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4},{5}}=>4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2},{3,5,6},{4},{7}}=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2},{3,7},{4},{5,6}}=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2},{3,5,7},{4},{6}}=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2},{3,5,6,7},{4}}=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7}}=>0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2},{3,6},{4,5},{7}}=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2},{3,7},{4,5},{6}}=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4,5}}=>2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2},{3,4,6},{5},{7}}=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2},{3,7},{4,6},{5}}=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2},{3,4,7},{5},{6}}=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2},{3,4,6,7},{5}}=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}}=>0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2},{3,7},{4,5,6}}=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2},{3,4,7},{5,6}}=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2},{3,4,5,7},{6}}=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}}=>0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7}}=>0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6,7}}=>0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5,6},{7}}=>0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>{{1},{2,3},{4},{5,7},{6}}=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>{{1},{2,3},{4,6},{5},{7}}=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>{{1},{2,3},{4,7},{5},{6}}=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>{{1},{2,3},{4,6,7},{5}}=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1},{2,3},{4,7},{5,6}}=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>{{1},{2,3},{4,5,7},{6}}=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6},{7}}=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>{{1},{2,4},{3},{5},{6,7}}=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>{{1},{2,4},{3},{5,6},{7}}=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>{{1},{2,4},{3},{5,7},{6}}=>2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>{{1},{2,4},{3},{5,6,7}}=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>{{1},{2,5},{3},{4},{6},{7}}=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3},{4},{6,7}}=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3},{4},{5},{7}}=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3},{4},{5},{6}}=>4
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4},{5}}=>6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3},{4},{7}}=>4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3},{4},{5,6}}=>3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3},{4},{6}}=>5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3},{4}}=>6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>{{1},{2,4,5},{3},{6},{7}}=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>{{1},{2,4,5},{3},{6,7}}=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3},{4,5},{7}}=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3},{4,5},{6}}=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4,5}}=>4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>{{1},{2,4,6},{3},{5},{7}}=>3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3},{4,6},{5}}=>4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>{{1},{2,4,7},{3},{5},{6}}=>4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>{{1},{2,4,6,7},{3},{5}}=>5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>{{1},{2,4,5,6},{3},{7}}=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3},{4,5,6}}=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>{{1},{2,4,7},{3},{5,6}}=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>{{1},{2,4,5,7},{3},{6}}=>4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,4,5,6,7},{3}}=>4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7}}=>0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>{{1},{2,3,4},{5,7},{6}}=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>{{1},{2,5},{3,4},{6},{7}}=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3,4},{6,7}}=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3,4},{5},{7}}=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3,4},{5},{6}}=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4},{5}}=>4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3,4},{7}}=>2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3,4},{5,6}}=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3,4},{6}}=>3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3,4}}=>3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>{{1},{2,3,5},{4},{6},{7}}=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>{{1},{2,3,5},{4},{6,7}}=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3,5},{4},{7}}=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3,5},{4},{6}}=>4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,5},{4}}=>5
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4},{5},{7}}=>2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4},{5}}=>5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4},{5},{6}}=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4},{5}}=>4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>{{1},{2,3,5,6},{4},{7}}=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3,5,6},{4}}=>4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4},{5,6}}=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>{{1},{2,3,5,7},{4},{6}}=>3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>{{1},{2,3,5,6,7},{4}}=>3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}}=>0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>{{1},{2,6},{3,4,5},{7}}=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>{{1},{2,7},{3,4,5},{6}}=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4,5}}=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4,5},{7}}=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4,5}}=>3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4,5},{6}}=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4,5}}=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>{{1},{2,3,4,6},{5},{7}}=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>{{1},{2,7},{3,4,6},{5}}=>3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4,6},{5}}=>3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5},{6}}=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>{{1},{2,3,4,6,7},{5}}=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}}=>0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>{{1},{2,7},{3,4,5,6}}=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>{{1},{2,3,7},{4,5,6}}=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5,6}}=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>{{1},{2,3,4,5,7},{6}}=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7}}=>0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6,7}}=>0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5,6},{7}}=>0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4},{5,7},{6}}=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}}=>0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7}}=>0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>{{1,2},{3},{4,6},{5},{7}}=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>{{1,2},{3},{4,7},{5},{6}}=>2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>{{1,2},{3},{4,6,7},{5}}=>2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2},{3},{4,5,6},{7}}=>0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>{{1,2},{3},{4,7},{5,6}}=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>{{1,2},{3},{4,5,7},{6}}=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}}=>0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7}}=>0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,4},{5,7},{6}}=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>{{1,2},{3,5},{4},{6},{7}}=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>{{1,2},{3,5},{4},{6,7}}=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>{{1,2},{3,6},{4},{5},{7}}=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>{{1,2},{3,7},{4},{5},{6}}=>3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4},{5}}=>4
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>{{1,2},{3,5,6},{4},{7}}=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>{{1,2},{3,7},{4},{5,6}}=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>{{1,2},{3,5,7},{4},{6}}=>3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>{{1,2},{3,5,6,7},{4}}=>3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>{{1,2},{3,6},{4,5},{7}}=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>{{1,2},{3,7},{4,5},{6}}=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4,5}}=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>{{1,2},{3,4,6},{5},{7}}=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>{{1,2},{3,7},{4,6},{5}}=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>{{1,2},{3,4,7},{5},{6}}=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>{{1,2},{3,4,6,7},{5}}=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>{{1,2},{3,7},{4,5,6}}=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>{{1,2},{3,4,7},{5,6}}=>1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>{{1,2},{3,4,5,7},{6}}=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6},{7}}=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5},{6,7}}=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>{{1,3},{2},{4},{5,6},{7}}=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>{{1,3},{2},{4},{5,7},{6}}=>2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>{{1,3},{2},{4},{5,6,7}}=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>{{1,3},{2},{4,5},{6},{7}}=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5},{6,7}}=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>{{1,3},{2},{4,6},{5},{7}}=>2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>{{1,3},{2},{4,7},{5},{6}}=>3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>{{1,3},{2},{4,6,7},{5}}=>3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>{{1,3},{2},{4,5,6},{7}}=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,3},{2},{4,7},{5,6}}=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>{{1,3},{2},{4,5,7},{6}}=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>{{1,3},{2},{4,5,6,7}}=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6},{7}}=>2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2},{3},{5},{6,7}}=>2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2},{3},{5,6},{7}}=>2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2},{3},{5,7},{6}}=>3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2},{3},{5,6,7}}=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3},{4},{6},{7}}=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3},{4},{6,7}}=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3},{4},{5},{7}}=>4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3},{4},{5},{6}}=>5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4},{5}}=>8
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3},{4},{7}}=>6
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3},{4},{5,6}}=>4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3},{4},{6}}=>7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3},{4}}=>9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2},{3},{6},{7}}=>4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2},{3},{6,7}}=>4
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3},{4,5},{7}}=>3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3},{4,5},{6}}=>4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4,5}}=>6
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2},{3},{5},{7}}=>5
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3},{4,6},{5}}=>5
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2},{3},{5},{6}}=>6
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2},{3},{5}}=>8
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2},{3},{7}}=>6
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3},{4,5,6}}=>3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2},{3},{5,6}}=>5
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2},{3},{6}}=>7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2},{3}}=>8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>{{1,3,4},{2},{5},{6},{7}}=>2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>{{1,3,4},{2},{5},{6,7}}=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>{{1,3,4},{2},{5,6},{7}}=>2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>{{1,3,4},{2},{5,7},{6}}=>3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>{{1,3,4},{2},{5,6,7}}=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3,4},{6},{7}}=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3,4},{6,7}}=>2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3,4},{5},{7}}=>3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3,4},{5},{6}}=>4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4},{5}}=>6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3,4},{7}}=>4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3,4},{5,6}}=>3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3,4},{6}}=>5
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3,4}}=>6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>{{1,3,5},{2},{4},{6},{7}}=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>{{1,3,5},{2},{4},{6,7}}=>3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3,5},{4},{7}}=>4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3,5},{4},{6}}=>5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,5},{4}}=>7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4},{5},{7}}=>4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4},{5}}=>6
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4},{5},{6}}=>5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4},{5}}=>7
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>{{1,3,5,6},{2},{4},{7}}=>5
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3,5,6},{4}}=>5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4},{5,6}}=>4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>{{1,3,5,7},{2},{4},{6}}=>6
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>{{1,3,5,6,7},{2},{4}}=>7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>{{1,3,4,5},{2},{6},{7}}=>3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,3,4,5},{2},{6,7}}=>3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2},{3,4,5},{7}}=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2},{3,4,5},{6}}=>3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4,5}}=>4
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4,5},{7}}=>3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4,5}}=>4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4,5},{6}}=>4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4,5}}=>5
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>{{1,3,4,6},{2},{5},{7}}=>4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2},{3,4,6},{5}}=>4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4,6},{5}}=>5
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5},{6}}=>5
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>{{1,3,4,6,7},{2},{5}}=>6
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,3,4,5,6},{2},{7}}=>4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2},{3,4,5,6}}=>2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>{{1,3,7},{2},{4,5,6}}=>3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5,6}}=>4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>{{1,3,4,5,7},{2},{6}}=>5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}}=>5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7}}=>0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6,7}}=>0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3},{4},{5,6},{7}}=>0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>{{1,2,3},{4},{5,7},{6}}=>1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}}=>0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7}}=>0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>{{1,2,3},{4,6},{5},{7}}=>1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>{{1,2,3},{4,7},{5},{6}}=>2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>{{1,2,3},{4,6,7},{5}}=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>{{1,2,3},{4,7},{5,6}}=>1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>{{1,2,3},{4,5,7},{6}}=>1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2,3},{5},{6},{7}}=>1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2,3},{5},{6,7}}=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2,3},{5,6},{7}}=>1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2,3},{5,7},{6}}=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2,3},{5,6,7}}=>1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2,3},{4},{6},{7}}=>2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2,3},{4},{6,7}}=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2,3},{4},{5},{7}}=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2,3},{4},{5},{6}}=>4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4},{5}}=>6
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3},{4},{7}}=>4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2,3},{4},{5,6}}=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3},{4},{6}}=>5
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3},{4}}=>6
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2,3},{6},{7}}=>2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2,3},{6,7}}=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2,3},{4,5},{7}}=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2,3},{4,5},{6}}=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4,5}}=>4
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2,3},{5},{7}}=>3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2,3},{4,6},{5}}=>4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2,3},{5},{6}}=>4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2,3},{5}}=>5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2,3},{7}}=>3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2,3},{4,5,6}}=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2,3},{5,6}}=>3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2,3},{6}}=>4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2,3}}=>4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>{{1,2,4},{3},{5},{6},{7}}=>1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>{{1,2,4},{3},{5},{6,7}}=>1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>{{1,2,4},{3},{5,6},{7}}=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>{{1,2,4},{3},{5,7},{6}}=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>{{1,2,4},{3},{5,6,7}}=>1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,4},{3},{6},{7}}=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,4},{3},{6,7}}=>3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,4},{3},{5},{7}}=>4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,4},{3},{5},{6}}=>5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,4},{3},{5}}=>7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,4},{3},{7}}=>5
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,4},{3},{5,6}}=>4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,4},{3},{6}}=>6
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,4},{3}}=>7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3},{4},{6},{7}}=>2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3},{4},{6,7}}=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3},{4},{7}}=>5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3},{4},{6}}=>6
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3},{4}}=>8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4},{5},{7}}=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4},{5}}=>7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4},{5},{6}}=>4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4},{5}}=>6
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3},{4},{7}}=>4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3},{4}}=>7
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4},{5,6}}=>3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3},{4},{6}}=>5
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3},{4}}=>6
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>{{1,2,4,5},{3},{6},{7}}=>2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>{{1,2,4,5},{3},{6,7}}=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,4,5},{3},{7}}=>4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,4,5},{3},{6}}=>5
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,4,5},{3}}=>6
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4,5},{7}}=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4,5}}=>5
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4,5},{6}}=>3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4,5}}=>4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>{{1,2,4,6},{3},{5},{7}}=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,4,6},{3},{5}}=>6
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4,6},{5}}=>4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5},{6}}=>4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>{{1,2,4,6,7},{3},{5}}=>5
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>{{1,2,4,5,6},{3},{7}}=>3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,4,5,6},{3}}=>5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3},{4,5,6}}=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5,6}}=>3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>{{1,2,4,5,7},{3},{6}}=>4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1,2,4,5,6,7},{3}}=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7}}=>0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}}=>0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}}=>0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>{{1,2,3,4},{5,7},{6}}=>1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,3,4},{6},{7}}=>1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,3,4},{6,7}}=>1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,3,4},{5},{7}}=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,3,4},{5},{6}}=>3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3,4},{5}}=>4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3,4},{7}}=>2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,3,4},{5,6}}=>2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3,4},{6}}=>3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3,4}}=>3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3,4},{6},{7}}=>1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3,4},{6,7}}=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3,4},{7}}=>3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3,4},{6}}=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3,4}}=>5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3,4},{5},{7}}=>2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4},{5}}=>5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3,4},{5},{6}}=>3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4},{5}}=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3,4},{7}}=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3,4}}=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3,4},{5,6}}=>2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3,4},{6}}=>3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3,4}}=>3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>{{1,2,3,5},{4},{6},{7}}=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>{{1,2,3,5},{4},{6,7}}=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,5},{4},{7}}=>3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,5},{4},{6}}=>4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,5},{4}}=>5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,5},{4},{7}}=>3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,5},{4}}=>6
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,5},{4},{6}}=>4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,5},{4}}=>5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4},{5},{7}}=>2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4},{5}}=>5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4},{5}}=>5
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5},{6}}=>3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4},{5}}=>4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>{{1,2,3,5,6},{4},{7}}=>2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,5,6},{4}}=>4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,5,6},{4}}=>4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5,6}}=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>{{1,2,3,5,7},{4},{6}}=>3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>{{1,2,3,5,6,7},{4}}=>3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}}=>0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,4,5},{7}}=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,4,5},{6}}=>2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,4,5}}=>2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,4,5},{7}}=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4,5}}=>3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,4,5},{6}}=>2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4,5}}=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4,5},{7}}=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4,5}}=>3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4,5}}=>3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4,5},{6}}=>2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4,5}}=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>{{1,2,3,4,6},{5},{7}}=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,6},{5}}=>3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,6},{5}}=>3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,6},{5}}=>3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5},{6}}=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>{{1,2,3,4,6,7},{5}}=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}}=>0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}}=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,5,6}}=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,5,6}}=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5,6}}=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,7},{6}}=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}}=>0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8}}=>0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,4,5,6,7,8},{3}}=>5
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,5,6,7,8},{4}}=>4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,6,7,8},{5}}=>3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>{{1},{2,3,4,5,8},{6},{7}}=>2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,7,8},{6}}=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}}=>0
[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
[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
[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
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,4},{5,8},{6,7}}=>1
[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
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,8},{4,5},{6,7}}=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,8},{4,7},{5,6}}=>3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,4,5,6,7,8},{2},{3}}=>10
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1,3,5,6,7,8},{2},{4}}=>9
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,3,4,5,6,7,8},{2}}=>6
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6},{7,8}}=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,4},{2,3},{5,8},{6,7}}=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,3},{4,5},{7,8}}=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,8},{2,3},{4,5},{6,7}}=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,3},{4,7},{5,6}}=>4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,4,5,6,7,8},{2,3}}=>5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,4,5,6,7,8},{3}}=>5
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,5},{3,4},{7,8}}=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,8},{2,5},{3,4},{6,7}}=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,4},{5,6}}=>5
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>{{1,2,5,6,7,8},{3,4}}=>4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,5,6,7},{4},{8}}=>3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,5,6,7,8},{4}}=>4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,6},{4,5}}=>6
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>{{1,2,3,6,7,8},{4,5}}=>3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>{{1,2,3,4,7},{5},{6},{8}}=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,6,7},{5},{8}}=>2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,6,7,8},{5}}=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>{{1,2,3,7},{4,5,6},{8}}=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>{{1,2,3,4,7},{5,6},{8}}=>1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>{{1,2,3,4,7,8},{5,6}}=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,7},{6},{8}}=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,7,8},{6}}=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7},{8}}=>0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>{{1,8},{2,3,4,5,6,7}}=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,8},{6,7}}=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,8},{7}}=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}}=>0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7,8},{9}}=>0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8,9}}=>0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7,8,9},{10}}=>0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,8},{7},{9}}=>1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,9},{8}}=>1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8,9,10}}=>0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7,8,9,10},{11}}=>0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7,9},{8},{10}}=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,8},{6,7},{9}}=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,7,8},{6},{9}}=>2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,9},{7,8}}=>1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,8,9},{7}}=>2
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8,10},{9}}=>1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8,9,10,11}}=>0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6},{7,8},{9,10}}=>1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,6},{2,3},{4,5},{7,8},{9,10}}=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,8},{2,3},{4,5},{6,7},{9,10}}=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,10},{2,3},{4,5},{6,7},{8,9}}=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,4},{5,6},{7,10},{8,9}}=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,4},{5,10},{6,7},{8,9}}=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,10},{4,5},{6,7},{8,9}}=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,6},{2,5},{3,4},{7,8},{9,10}}=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,6},{4,5},{7,8},{9,10}}=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,8},{4,7},{5,6},{9,10}}=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,8},{2,3},{4,7},{5,6},{9,10}}=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,8},{2,7},{3,4},{5,6},{9,10}}=>5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,8},{2,7},{3,6},{4,5},{9,10}}=>6
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,8},{6,7},{9,10}}=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,8},{6,7},{9,10}}=>2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,8},{2,5},{3,4},{6,7},{9,10}}=>4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,8},{4,5},{6,7},{9,10}}=>2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,4},{5,10},{6,9},{7,8}}=>3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,4},{2,3},{5,10},{6,9},{7,8}}=>4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,10},{2,5},{3,4},{6,9},{7,8}}=>6
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,10},{4,5},{6,9},{7,8}}=>4
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,10},{2,3},{4,5},{6,9},{7,8}}=>5
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,10},{2,9},{3,4},{5,6},{7,8}}=>7
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,10},{2,9},{3,6},{4,5},{7,8}}=>8
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,10},{2,9},{3,4},{5,8},{6,7}}=>8
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,10},{2,9},{3,8},{4,5},{6,7}}=>9
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,10},{4,9},{5,6},{7,8}}=>5
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,10},{2,3},{4,9},{5,6},{7,8}}=>6
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,10},{2,9},{3,8},{4,7},{5,6}}=>10
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,10},{4,9},{5,8},{6,7}}=>6
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,10},{2,3},{4,9},{5,8},{6,7}}=>7
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,4},{2,3},{5,6},{7,10},{8,9}}=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,6},{2,5},{3,4},{7,10},{8,9}}=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,6},{4,5},{7,10},{8,9}}=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,6},{2,3},{4,5},{7,10},{8,9}}=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,10},{4,7},{5,6},{8,9}}=>4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,10},{2,3},{4,7},{5,6},{8,9}}=>5
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,10},{2,7},{3,4},{5,6},{8,9}}=>6
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,10},{2,7},{3,6},{4,5},{8,9}}=>7
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,4},{2,3},{5,10},{6,7},{8,9}}=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,10},{2,5},{3,4},{6,7},{8,9}}=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}}=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}}=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}}=>1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}}=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}}=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}}=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}}=>5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}}=>6
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}}=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}}=>2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}}=>4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}}=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}}=>3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}}=>3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}}=>4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}}=>6
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}}=>4
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}}=>5
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}}=>7
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}}=>8
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}}=>8
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}}=>9
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}}=>5
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}}=>6
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}}=>10
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}}=>6
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}}=>7
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}}=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}}=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}}=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}}=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}}=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}}=>4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}}=>5
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}}=>6
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}}=>7
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}}=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}}=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}}=>5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}}=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}}=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}}=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}}=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}}=>6
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}}=>4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}}=>5
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}}=>6
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}}=>7
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}}=>8
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}}=>9
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}}=>4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}}=>5
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}}=>7
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}}=>5
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}}=>6
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}}=>7
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}}=>8
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}}=>12
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}}=>8
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}}=>9
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}}=>8
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}}=>9
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}}=>13
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}}=>9
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}}=>10
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}}=>9
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}}=>10
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}}=>10
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}}=>11
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}}=>14
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}=>15
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}}=>10
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}}=>11
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}}=>11
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}}=>12
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}}=>5
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}}=>6
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}}=>8
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}}=>6
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}}=>7
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}}=>10
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}}=>11
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}}=>12
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}}=>13
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}}=>6
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}}=>7
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}}=>9
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}}=>7
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}}=>8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}}=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}}=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}}=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}}=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}}=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}}=>4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}}=>5
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}}=>6
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}}=>7
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}}=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}}=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}}=>5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}}=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}}=>4
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}}=>4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}}=>5
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}}=>7
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}}=>5
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}}=>6
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}}=>8
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}}=>9
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}}=>9
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}}=>10
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}}=>6
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}}=>7
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}}=>11
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}}=>7
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}}=>8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}}=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}}=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}}=>5
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}}=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}}=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}}=>5
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}}=>6
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}}=>7
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}}=>8
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}}=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}}=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}}=>6
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}}=>4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}}=>5
                    
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$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 4\ q + 2\ q^{2}$
$F_{5} = 16 + 12\ q + 9\ q^{2} + 4\ q^{3} + q^{4}$
$F_{6} = 32 + 32\ q + 30\ q^{2} + 20\ q^{3} + 12\ q^{4} + 4\ q^{5} + 2\ q^{6}$
$F_{7} = 64 + 80\ q + 88\ q^{2} + 73\ q^{3} + 56\ q^{4} + 34\ q^{5} + 20\ q^{6} + 9\ q^{7} + 4\ q^{8} + q^{9}$
Description
The rcs statistic of a set partition.
Let
$S = B_1,\ldots,B_k$ be a set partition with ordered blocks
$B_i$ and with
$\operatorname{min} B_a < \operatorname{min} B_b$ for
$a < b$ .
According to [1, Definition 3], a rcs (right-closer-smaller) of
$S$ is given by a pair
$i > j$ such that
$j = \operatorname{max} B_b$ and
$i \in B_a$ for
$a < b$ .
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.