Identifier
Values
=>
Cc0020;cc-rep-0 Cc0020;cc-rep-1 Cc0020;cc-rep
([],1)=>([],1)=>([],1)=>1 ([],2)=>([],1)=>([],1)=>1 ([(0,1)],2)=>([(0,1)],2)=>([],2)=>1 ([],3)=>([],1)=>([],1)=>1 ([(1,2)],3)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(0,2),(1,2)],3)=>([(0,1)],2)=>([],2)=>1 ([(0,1),(0,2),(1,2)],3)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([],4)=>([],1)=>([],1)=>1 ([(2,3)],4)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(1,3),(2,3)],4)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(0,3),(1,3),(2,3)],4)=>([(0,1)],2)=>([],2)=>1 ([(0,3),(1,2)],4)=>([(0,3),(1,2)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(1,2),(1,3),(2,3)],4)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,3),(1,2),(1,3),(2,3)],4)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,2),(0,3),(1,2),(1,3)],4)=>([(0,1)],2)=>([],2)=>1 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([],4)=>1 ([],5)=>([],1)=>([],1)=>1 ([(3,4)],5)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(2,4),(3,4)],5)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(1,4),(2,4),(3,4)],5)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1)],2)=>([],2)=>1 ([(0,1),(2,4),(3,4)],5)=>([(0,3),(1,2)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(1,3),(1,4),(2,3),(2,4)],5)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2)=>([],2)=>1 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(1,3),(1,4),(2,3),(2,4)],5)=>3 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>2 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>2 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([],4)=>1 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([],5)=>1 ([],6)=>([],1)=>([],1)=>1 ([(4,5)],6)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(3,5),(4,5)],6)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)=>([],2)=>1 ([(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,1),(2,5),(3,5),(4,5)],6)=>([(0,3),(1,2)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(2,4),(2,5),(3,4),(3,5)],6)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,3),(1,2)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)=>([],2)=>1 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,3),(1,2)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(1,3),(1,4),(2,3),(2,4)],5)=>3 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>2 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>2 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>2 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,1)],2)=>([],2)=>1 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([],4)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(1,3),(1,4),(2,3),(2,4)],5)=>3 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>2 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>3 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>2 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>2 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,4),(3,4),(3,5)],6)=>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)=>([(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)=>([(2,5),(3,4),(4,5)],6)=>2 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>2 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>2 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6)=>2 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>2 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,5),(4,5)],6)=>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)=>([(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)=>([(2,5),(3,5),(4,5)],6)=>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)=>([(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)=>([(3,5),(4,5)],6)=>2 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,4),(3,4)],6)=>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)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>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)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([],4)=>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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([],5)=>1 ([(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)=>([(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)=>([],6)=>1 ([],7)=>([],1)=>([],1)=>1 ([(5,6)],7)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(4,6),(5,6)],7)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1)],2)=>([],2)=>1 ([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,3),(1,2)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(3,5),(3,6),(4,5),(4,6)],7)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,3),(1,2)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1)],2)=>([],2)=>1 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(1,2)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(1,3),(1,4),(2,3),(2,4)],5)=>3 ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>2 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>2 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)=>([(0,3),(1,2)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(1,3),(1,4),(2,3),(2,4)],5)=>3 ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>2 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(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)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>2 ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(1,2)],3)=>([(0,2),(1,2)],3)=>2 ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(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)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4)=>2 ([(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)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(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)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(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)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>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)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 ([(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)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>2 ([(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)=>([(0,1)],2)=>([],2)=>1 ([(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)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(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)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(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)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([],4)=>1 ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(1,3),(1,4),(2,3),(2,4)],5)=>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)=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(1,3),(1,4),(2,3),(2,4)],5)=>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)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>2 ([(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)=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 ([(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)=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>2 ([(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)=>([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>2 ([(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)=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>2 ([(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)=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6)=>2 ([(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)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(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)=>([(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)=>([(2,5),(3,5),(4,5)],6)=>2 ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(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)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(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)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>2 ([(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)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>2 ([(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)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>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)=>([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>2 ([(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)=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>2 ([(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)=>([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>2 ([(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)=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,4),(3,4),(3,5)],6)=>2 ([(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)=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>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)=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>2 ([(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)=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>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)=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6)=>2 ([(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)=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,4),(3,4),(3,5)],6)=>2 ([(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)=>([(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)=>([(2,5),(3,4),(4,5)],6)=>2 ([(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)=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,4),(3,4)],6)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>2 ([(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)=>([(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)=>([(3,5),(4,5)],6)=>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)=>([(1,2),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4)=>2 ([(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)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>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)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 ([(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)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(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)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>2 ([(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)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(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)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(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)=>([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>2 ([(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)=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>2 ([(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)=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,4),(3,4),(3,5)],6)=>2 ([(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)=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>2 ([(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)=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>2 ([(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)=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6)=>2 ([(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)=>([(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)=>([(2,5),(3,4),(4,5)],6)=>2 ([(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)=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>2 ([(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)=>([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>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),(5,6)],7)=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>2 ([(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)=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6)=>2 ([(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)=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>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)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 ([(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)=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 ([(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)=>([(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)=>([(2,5),(3,5),(4,5)],6)=>2 ([(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)=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,4),(3,4)],6)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(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)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>2 ([(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)=>([(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)=>([(3,5),(4,5)],6)=>2 ([(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)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(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)=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(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)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(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)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(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)=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(1,3),(1,4),(2,3),(2,4)],5)=>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)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(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)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(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)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>2 ([(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)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([],4)=>1 ([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([],5)=>1 ([(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)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(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)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>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)=>([(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)=>([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)=>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)=>([(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)=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>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)=>([(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)=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>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)=>([(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)=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>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)=>([(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)=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>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)=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,4),(3,4),(3,5)],6)=>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)=>([(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)=>([(2,5),(3,4),(4,5)],6)=>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)=>([(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)=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>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)=>([(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)=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>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)=>([(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)=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>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)=>([(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)=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>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)=>([(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)=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>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)=>([(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)=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>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)=>([(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)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>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)=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6)=>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)=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,5),(4,5)],6)=>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)=>([(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)=>([(2,5),(3,5),(4,5)],6)=>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)=>([(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)=>([(3,5),(4,5)],6)=>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)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([],4)=>1 ([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([],5)=>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)=>([(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)=>([],6)=>1 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([],5)=>1 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(2,4),(3,4)],5)=>2 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([],4)=>1 ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([],4)=>1 ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(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)=>([],6)=>1 ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([],4)=>1 ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>([(0,3),(1,2)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>([(0,1),(0,2),(1,2)],3)=>([],3)=>1 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(6,7)],8)=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,3),(3,4)],5)=>2 ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(1,3),(2,3)],4)=>2 ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5)=>2 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)=>([(0,1)],2)=>([],2)=>1 ([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8)=>([(0,3),(1,2)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(1,3),(1,4),(2,3),(2,4)],5)=>3 ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,4),(3,4)],6)=>2 ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,4),(3,4)],6)=>2
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Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Map
de-duplicate
Description
The de-duplicate of a graph.
Let $G = (V, E)$ be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods $\{N_v | v \in V\}$ of $G$, and has an edge $(N_a, N_b)$ between two vertices if and only if $(a, b)$ is an edge of $G$. This is well-defined, because if $N_a = N_c$ and $N_b = N_d$, then $(a, b)\in E$ if and only if $(c, d)\in E$.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.
Map
complement
Description
The complement of a graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.