Identifier
Mp00324:
Graphs
—chromatic difference sequence⟶
Integer compositions
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00315: Integer compositions —inverse Foata bijection⟶ Integer compositions
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00315: Integer compositions —inverse Foata bijection⟶ Integer compositions
Images
=>
Cc0020;cc-rep-0
([],1)=>[1]=>[1]=>[1]
([],2)=>[2]=>[2]=>[2]
([(0,1)],2)=>[1,1]=>[1,1]=>[1,1]
([],3)=>[3]=>[3]=>[3]
([(1,2)],3)=>[2,1]=>[1,2]=>[1,2]
([(0,2),(1,2)],3)=>[2,1]=>[1,2]=>[1,2]
([(0,1),(0,2),(1,2)],3)=>[1,1,1]=>[1,1,1]=>[1,1,1]
([],4)=>[4]=>[4]=>[4]
([(2,3)],4)=>[3,1]=>[1,3]=>[1,3]
([(1,3),(2,3)],4)=>[3,1]=>[1,3]=>[1,3]
([(0,3),(1,3),(2,3)],4)=>[3,1]=>[1,3]=>[1,3]
([(0,3),(1,2)],4)=>[2,2]=>[2,2]=>[2,2]
([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2]=>[2,2]
([(1,2),(1,3),(2,3)],4)=>[2,1,1]=>[1,1,2]=>[1,1,2]
([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]=>[1,1,2]=>[1,1,2]
([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]=>[2,2]=>[2,2]
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]=>[1,1,2]=>[1,1,2]
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]=>[1,1,1,1]=>[1,1,1,1]
([],5)=>[5]=>[5]=>[5]
([(3,4)],5)=>[4,1]=>[1,4]=>[1,4]
([(2,4),(3,4)],5)=>[4,1]=>[1,4]=>[1,4]
([(1,4),(2,4),(3,4)],5)=>[4,1]=>[1,4]=>[1,4]
([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]=>[1,4]=>[1,4]
([(1,4),(2,3)],5)=>[3,2]=>[2,3]=>[2,3]
([(1,4),(2,3),(3,4)],5)=>[3,2]=>[2,3]=>[2,3]
([(0,1),(2,4),(3,4)],5)=>[3,2]=>[2,3]=>[2,3]
([(2,3),(2,4),(3,4)],5)=>[3,1,1]=>[1,1,3]=>[1,1,3]
([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[2,3]=>[2,3]
([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]=>[1,1,3]=>[1,1,3]
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]=>[1,1,3]=>[1,1,3]
([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]=>[2,3]=>[2,3]
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]=>[2,3]=>[2,3]
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]=>[1,1,3]=>[1,1,3]
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[3,1,1]=>[1,1,3]=>[1,1,3]
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]=>[1,1,3]=>[1,1,3]
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]=>[2,3]=>[2,3]
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]=>[1,1,3]=>[1,1,3]
([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[2,3]=>[2,3]
([(0,1),(2,3),(2,4),(3,4)],5)=>[2,2,1]=>[2,1,2]=>[2,1,2]
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>[2,2,1]=>[2,1,2]=>[2,1,2]
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>[2,2,1]=>[2,1,2]=>[2,1,2]
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>[2,2,1]=>[2,1,2]=>[2,1,2]
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]=>[2,1,2]=>[2,1,2]
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>[2,2,1]=>[2,1,2]=>[2,1,2]
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]=>[2,1,2]=>[2,1,2]
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]=>[1,1,1,2]=>[1,1,1,2]
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]=>[1,1,1,2]=>[1,1,1,2]
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]=>[1,1,1,2]=>[1,1,1,2]
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]=>[2,1,2]=>[2,1,2]
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]=>[2,1,2]=>[2,1,2]
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]=>[1,1,1,2]=>[1,1,1,2]
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[1,1,1,1,1]=>[1,1,1,1,1]=>[1,1,1,1,1]
([],6)=>[6]=>[6]=>[6]
([(4,5)],6)=>[5,1]=>[1,5]=>[1,5]
([(3,5),(4,5)],6)=>[5,1]=>[1,5]=>[1,5]
([(2,5),(3,5),(4,5)],6)=>[5,1]=>[1,5]=>[1,5]
([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]=>[1,5]=>[1,5]
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]=>[1,5]=>[1,5]
([(2,5),(3,4)],6)=>[4,2]=>[2,4]=>[2,4]
([(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(1,2),(3,5),(4,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(0,1),(2,5),(3,5),(4,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(0,5),(1,5),(2,4),(3,4)],6)=>[4,2]=>[2,4]=>[2,4]
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1,4]=>[1,1,4]
([(0,5),(1,4),(2,3)],6)=>[3,3]=>[3,3]=>[3,3]
([(1,5),(2,4),(3,4),(3,5)],6)=>[4,2]=>[2,4]=>[2,4]
([(0,1),(2,5),(3,4),(4,5)],6)=>[3,3]=>[3,3]=>[3,3]
([(1,2),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3]=>[3,3]
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]=>[3,3]=>[3,3]
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3]=>[3,3]
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>[3,3]=>[3,3]=>[3,3]
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>[3,3]=>[3,3]=>[3,3]
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]=>[3,3]=>[3,3]
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>[3,3]=>[3,3]=>[3,3]
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>[3,3]=>[3,3]=>[3,3]
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,3]=>[3,3]=>[3,3]
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[3,1,2]=>[1,2,3]=>[1,2,3]
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]=>[3,3]=>[3,3]
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1,3]=>[1,1,1,3]
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>[3,2,1]=>[2,1,3]=>[2,1,3]
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]=>[1,1,1,1,2]=>[1,1,1,1,2]
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]=>[1,1,1,1,2]=>[1,1,1,1,2]
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]=>[1,1,1,1,2]=>[1,1,1,1,2]
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]=>[1,1,1,1,2]=>[1,1,1,1,2]
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]=>[2,2,2]=>[2,2,2]
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>[2,1,1,2]=>[1,2,1,2]
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]=>[1,1,1,1,2]=>[1,1,1,1,2]
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
([],7)=>[7]=>[7]=>[7]
([(5,6)],7)=>[6,1]=>[1,6]=>[1,6]
([(4,6),(5,6)],7)=>[6,1]=>[1,6]=>[1,6]
([(3,6),(4,6),(5,6)],7)=>[6,1]=>[1,6]=>[1,6]
([(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1,6]=>[1,6]
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1,6]=>[1,6]
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1,6]=>[1,6]
([(3,6),(4,5)],7)=>[5,2]=>[2,5]=>[2,5]
([(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(2,3),(4,6),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(1,2),(3,6),(4,6),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(1,6),(2,6),(3,5),(4,5)],7)=>[5,2]=>[2,5]=>[2,5]
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>[5,2]=>[2,5]=>[2,5]
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1,5]=>[1,1,5]
([(1,6),(2,5),(3,4)],7)=>[4,3]=>[3,4]=>[3,4]
([(2,6),(3,5),(4,5),(4,6)],7)=>[5,2]=>[2,5]=>[2,5]
([(1,2),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,3),(1,2),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(2,3),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(0,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,5),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,4),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,3),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,1,2]=>[1,2,4]=>[1,2,4]
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,1,2]=>[1,2,4]=>[1,2,4]
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[4,1,2]=>[1,2,4]=>[1,2,4]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,3),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,5),(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1,4]=>[1,1,1,4]
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(1,5),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,3),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,3),(1,4),(1,5),(2,4),(2,6),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(1,2),(1,5),(2,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,6),(1,2),(1,6),(2,4),(3,4),(3,5),(4,5),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,2),(1,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,2),(1,6),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,6),(1,2),(1,6),(2,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,3),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,3),(1,5),(2,3),(2,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,3),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,5),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,2),(1,4),(1,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,5),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,2),(0,3),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,5),(2,3),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(1,3),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,6),(1,3),(1,5),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,6),(1,5),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7)=>[4,2,1]=>[2,1,4]=>[2,1,4]
([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,3),(1,4),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,2),(1,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,3),(0,4),(1,2),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,5),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,5),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,4),(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,4),(0,6),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,2),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,5),(0,6),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,6),(1,3),(1,5),(2,4),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,3),(1,6),(2,3),(2,4),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,4),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)=>[4,3]=>[3,4]=>[3,4]
([(0,2),(0,6),(1,2),(1,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(1,2),(1,3),(1,5),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,6),(1,2),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,6),(1,2),(1,5),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,2),(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,5),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,2),(1,5),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,6),(3,5),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,4),(0,6),(1,2),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,2),(0,3),(1,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,5),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,2),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,2),(0,4),(1,3),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,2),(0,6),(1,3),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,2),(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,2),(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,2),(0,6),(1,2),(1,4),(1,5),(2,3),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,2),(0,5),(1,4),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,2),(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,5),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,2),(0,4),(0,5),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,2,1]=>[1,2,1,3]=>[2,1,1,3]
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,2,1]=>[1,2,1,3]=>[2,1,1,3]
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,3),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>[3,1,3]=>[3,1,3]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,2),(0,3),(0,4),(0,6),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,1,1,1,3]
([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,4),(0,5),(1,2),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,3),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,2),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1,3]=>[1,2,1,3]
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,1),(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,2),(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,4),(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,3),(0,4),(1,2),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,2),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,5),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,4),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,3),(0,6),(1,2),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,3),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,1),(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>[3,2,2]=>[2,2,3]=>[2,2,3]
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,2),(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,2),(0,3),(0,6),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,2),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,1,1,1,1,2]
([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,1,1,1,1,2]
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,1,1,1,1,2]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,1,1,1,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,1,1,1,1,2]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,1),(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,1),(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,2,2,1]=>[2,2,1,2]=>[2,2,1,2]
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>[2,1,1,1,2]=>[1,1,2,1,2]
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,1,1,1,1,2]
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
Map
chromatic difference sequence
Description
The chromatic difference sequence of a graph.
Let $G$ be a simple graph with chromatic number $\kappa$. Let $\alpha_m$ be the maximum number of vertices in a $m$-colorable subgraph of $G$. Set $\delta_m=\alpha_m-\alpha_{m-1}$. The sequence $\delta_1,\delta_2,\dots\delta_\kappa$ is the chromatic difference sequence of $G$.
All entries of the chromatic difference sequence are positive: $\alpha_m > \alpha_{m-1}$ for $m < \kappa$, because we can assign any uncolored vertex of a partial coloring with $m-1$ colors the color $m$. Therefore, the chromatic difference sequence is a composition of the number of vertices of $G$ into $\kappa$ parts.
Let $G$ be a simple graph with chromatic number $\kappa$. Let $\alpha_m$ be the maximum number of vertices in a $m$-colorable subgraph of $G$. Set $\delta_m=\alpha_m-\alpha_{m-1}$. The sequence $\delta_1,\delta_2,\dots\delta_\kappa$ is the chromatic difference sequence of $G$.
All entries of the chromatic difference sequence are positive: $\alpha_m > \alpha_{m-1}$ for $m < \kappa$, because we can assign any uncolored vertex of a partial coloring with $m-1$ colors the color $m$. Therefore, the chromatic difference sequence is a composition of the number of vertices of $G$ into $\kappa$ parts.
Map
rotate front to back
Description
The front to back rotation of the entries of an integer composition.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00314Foata bijection.
See Mp00314Foata bijection.
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