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Cc0029;cc-rep-0Cc0020;cc-rep-1
([],1)=>([],0)
([(0,1)],2)=>([],0)
([(0,2),(2,1)],3)=>([],0)
([(0,1),(0,2),(1,3),(2,3)],4)=>([(0,1)],2)
([(0,3),(2,1),(3,2)],4)=>([],0)
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>([(0,2),(1,2)],3)
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([],0)
([(0,4),(2,3),(3,1),(4,2)],5)=>([],0)
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,1)],2)
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>([],0)
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>([],0)
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([],0)
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([],0)
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,1)],2)
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>([(0,1),(0,2),(1,2)],3)
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(1,2)],3)
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([],0)
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>([(0,2),(1,2)],3)
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(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)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>([],0)
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)=>([],0)
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)=>([],0)
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)=>([],0)
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>([],0)
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([],0)
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>([],0)
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>([],0)
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>([],0)
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,1)],2)
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)=>([(0,1),(0,2),(1,2)],3)
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>([(0,1)],2)
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)=>([(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>([(0,2),(1,2)],3)
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)=>([(0,3),(1,3),(2,3)],4)
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>([],0)
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>([(0,3),(1,3),(2,3)],4)
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([],0)
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>([],0)
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>([(0,2),(1,2)],3)
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>([],0)
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>([(0,3),(1,3),(2,3)],4)
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([],0)
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([],0)
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(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)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8)=>([(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)
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)=>([],0)
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5)],8)=>([],0)
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8)=>([],0)
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,4),(7,6)],8)=>([],0)
([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)=>([],0)
([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5)],8)=>([],0)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,2),(5,3),(6,7)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)=>([],0)
([(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,3),(5,4),(6,7)],8)=>([],0)
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8)=>([],0)
([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)=>([],0)
([(0,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7),(7,1)],8)=>([],0)
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,4),(7,3)],8)=>([],0)
([(0,6),(1,7),(2,7),(3,7),(4,3),(5,2),(6,1),(6,4),(6,5)],8)=>([],0)
([(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4),(6,7)],8)=>([],0)
([(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(6,1),(6,5)],8)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(5,3),(6,1),(6,5)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,7),(2,7),(3,7),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3)],8)=>([],0)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,7)],8)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([],0)
([(0,3),(0,6),(1,7),(2,7),(3,7),(4,2),(5,1),(6,4),(6,5)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(1,7),(2,6),(3,7),(4,1),(4,6),(5,2),(5,4),(6,7)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8)=>([],0)
([(0,6),(1,7),(2,7),(3,7),(4,3),(5,1),(5,2),(6,4),(6,5)],8)=>([],0)
([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)=>([],0)
([(0,5),(1,7),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7)],8)=>([],0)
([(0,2),(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,1),(6,5)],8)=>([(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)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2)],8)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)=>([],0)
([(0,2),(0,3),(0,6),(1,7),(2,7),(3,7),(4,5),(5,1),(6,4)],8)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)=>([],0)
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1)],8)=>([(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),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)=>([(0,1)],2)
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,6),(7,1)],8)=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)=>([(0,1),(0,2),(1,2)],3)
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(7,6)],8)=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)=>([(0,1),(0,2),(1,2)],3)
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,6),(6,1),(7,6)],8)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(0,6),(1,7),(3,7),(4,7),(5,7),(6,1),(7,2)],8)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(6,7)],8)=>([(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)
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,7),(6,7)],8)=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(1,6),(2,7),(3,5),(4,5),(4,7),(5,6),(7,1)],8)=>([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(5,7),(6,7),(7,1)],8)=>([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(7,5)],8)=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(2,7),(3,6),(4,6),(5,1),(6,7),(7,5)],8)=>([(0,3),(1,2),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1)],8)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,1)],2)
([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,6),(6,7)],8)=>([(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),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,7),(7,2)],8)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(0,5),(1,6),(2,7),(3,7),(4,1),(5,4),(5,7),(7,6)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(6,7)],8)=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)=>([(0,1)],2)
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,7),(5,7),(7,6)],8)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,5),(1,7),(2,6),(3,6),(4,2),(5,1),(5,4),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(1,7),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4),(6,7)],8)=>([],0)
([(0,6),(1,7),(2,7),(4,2),(5,1),(6,4),(6,5),(7,3)],8)=>([],0)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,7),(5,1),(5,2),(7,6)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,4),(0,6),(1,7),(2,7),(4,7),(5,2),(6,1),(6,5),(7,3)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,6),(1,7),(2,7),(3,7),(5,2),(5,3),(6,1),(6,5),(7,4)],8)=>([],0)
([(0,4),(0,5),(0,6),(1,7),(2,7),(4,7),(5,7),(6,1),(6,2),(7,3)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(7,6)],8)=>([(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),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,6),(4,1),(5,4),(6,7)],8)=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)=>([(0,1)],2)
([(0,3),(0,4),(0,5),(2,7),(3,6),(4,6),(5,2),(6,7),(7,1)],8)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(1,7),(2,6),(3,6),(4,5),(5,1),(5,2),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(1,7),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3),(6,7)],8)=>([],0)
([(0,2),(0,3),(0,5),(1,6),(2,7),(3,7),(4,1),(4,7),(5,4),(7,6)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,6),(1,7),(3,7),(4,7),(5,1),(6,5),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,4),(0,5),(1,7),(2,7),(4,7),(5,6),(6,1),(6,2),(7,3)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)=>([],0)
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(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)
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,7),(3,5),(4,5),(4,7),(5,6),(7,6)],8)=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(2,7),(3,6),(4,6),(5,7),(6,2),(7,1)],8)=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,1)],2)
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,6),(5,6),(6,7),(7,1)],8)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(6,1)],8)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,7)],8)=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,5),(1,7),(2,7),(3,6),(4,1),(5,4),(5,6),(6,7)],8)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(1,7),(2,7),(3,6),(4,5),(4,6),(5,1),(5,2),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,6),(4,1),(4,5),(5,7),(7,6)],8)=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)=>([(0,2),(1,2)],3)
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,4),(5,7),(7,1)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2)],8)=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)=>([(0,2),(1,2)],3)
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2)],8)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,6),(6,7)],8)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,5),(1,7),(2,7),(3,6),(4,2),(5,1),(5,4),(5,6),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(1,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(7,6)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6),(5,7),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,6),(6,3)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3)],8)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,6),(1,7),(2,7),(3,7),(4,5),(5,3),(6,1),(6,2),(6,4)],8)=>([],0)
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(1,7),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4),(6,7)],8)=>([],0)
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,7),(5,1),(5,2),(5,3),(7,6)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,6),(1,7),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5),(7,4)],8)=>([],0)
([(0,5),(0,6),(1,7),(2,7),(3,7),(5,7),(6,1),(6,2),(6,3),(7,4)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,3),(5,1),(5,2),(5,6),(6,7)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,6),(1,7),(2,7),(3,7),(4,5),(5,2),(6,1),(6,4)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,7),(2,7),(3,7),(4,5),(5,2),(5,3),(6,1),(6,4)],8)=>([],0)
([(0,6),(1,7),(2,7),(3,4),(4,1),(5,2),(6,3),(6,5)],8)=>([],0)
([(0,5),(1,7),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4),(6,7)],8)=>([],0)
([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)=>([],0)
([(0,5),(1,7),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4),(6,7)],8)=>([],0)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,6),(5,1),(5,2),(6,7)],8)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,3),(7,2)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,4),(6,7)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(2,7),(3,7),(4,3),(5,1),(6,2),(6,4),(7,5)],8)=>([],0)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(7,6)],8)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(7,5)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,4),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(1,5),(2,5),(2,6),(3,6),(4,1),(4,2),(5,7),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(2,7),(3,6),(4,6),(5,2),(5,3),(6,7),(7,1)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,5),(1,7),(2,6),(3,6),(4,1),(4,3),(5,2),(5,4),(6,7)],8)=>([],0)
([(0,3),(0,5),(1,7),(2,6),(3,7),(4,2),(4,7),(5,1),(5,4),(7,6)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(0,6),(1,7),(2,7),(3,7),(4,3),(5,1),(6,2),(6,4)],8)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,6),(1,7),(2,7),(3,7),(4,3),(5,2),(5,4),(6,1),(6,5)],8)=>([],0)
([(0,3),(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,4),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,3),(5,1),(5,2),(6,7)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,6),(1,7),(2,7),(4,5),(5,2),(6,1),(6,4),(7,3)],8)=>([],0)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,3),(6,7)],8)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(0,6),(1,7),(2,7),(3,7),(5,3),(6,1),(6,2),(7,4)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)=>([],0)
([(0,4),(0,5),(2,6),(3,6),(4,7),(5,2),(5,3),(6,7),(7,1)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,2),(4,6),(5,1),(5,6),(6,7)],8)=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,2),(4,6),(5,1),(5,6),(6,3)],8)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,4),(0,5),(1,7),(2,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(1,6),(2,7),(3,1),(3,5),(4,2),(4,5),(5,7),(7,6)],8)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,4),(0,5),(1,7),(2,7),(4,2),(4,6),(5,1),(5,6),(6,7),(7,3)],8)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2)],8)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,3),(4,6),(5,1),(5,2),(5,6),(6,7)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,3),(6,7)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(1,7),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3),(6,7)],8)=>([],0)
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(7,6)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,2),(5,1),(5,6),(6,7)],8)=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,1),(5,3),(5,7),(7,2)],8)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,4),(0,5),(1,7),(2,6),(3,1),(4,2),(5,3),(5,6),(6,7)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,4),(0,5),(1,7),(3,6),(4,3),(5,1),(5,6),(6,7),(7,2)],8)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,5),(0,6),(1,7),(2,7),(3,7),(4,3),(5,4),(6,1),(6,2)],8)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,2),(6,4)],8)=>([],0)
([(0,4),(1,7),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5)],8)=>([],0)
([(0,4),(0,5),(1,7),(2,7),(3,2),(3,6),(4,3),(5,1),(5,6),(6,7)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,6),(5,1),(6,7)],8)=>([(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),(0,5),(1,7),(2,6),(3,7),(4,6),(5,1),(7,2)],8)=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,2),(1,2)],3)
([(0,3),(0,5),(0,6),(1,7),(2,7),(3,7),(4,1),(5,2),(6,4)],8)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(1,7),(2,7),(3,7),(4,2),(5,6),(6,1),(6,4)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,2),(0,3),(0,5),(1,7),(2,7),(3,6),(4,1),(4,6),(5,4),(6,7)],8)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(4,7),(5,4),(7,1)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2)],8)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(1,7),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4)],8)=>([],0)
([(0,3),(0,4),(1,7),(2,7),(3,6),(4,5),(5,1),(5,2),(5,6),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,2),(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,4)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)=>([],0)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(6,7)],8)=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,5),(0,6),(2,7),(3,7),(4,1),(5,3),(6,2),(7,4)],8)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,5),(1,7),(2,7),(3,4),(4,1),(5,6),(6,2),(6,3)],8)=>([],0)
([(0,4),(0,5),(1,7),(2,6),(3,1),(3,6),(4,2),(5,3),(6,7)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,2),(0,3),(0,5),(1,6),(2,7),(3,6),(4,1),(5,4),(6,7)],8)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,5),(5,1),(5,2),(6,7)],8)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)=>([],0)
([(0,3),(0,6),(2,7),(3,7),(4,2),(5,1),(6,4),(7,5)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,3),(5,2),(6,1)],8)=>([(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)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,2),(5,1),(5,6),(6,7)],8)=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,1),(4,5),(4,6),(5,7),(6,7)],8)=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,5),(1,7),(2,6),(3,4),(4,1),(5,3),(5,6),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,5),(2,7),(3,6),(4,2),(5,4),(5,6),(6,7),(7,1)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,6),(5,7),(6,7)],8)=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(1,6),(3,6),(4,7),(5,1),(5,7),(6,2),(7,3)],8)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(1,7),(3,7),(4,6),(5,1),(5,6),(6,7),(7,2)],8)=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,7),(7,4)],8)=>([(0,2),(1,2)],3)
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,7),(4,1),(4,5),(5,7),(7,6)],8)=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,5),(3,6),(4,1),(4,6),(5,7),(6,7)],8)=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)=>([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,6),(6,7)],8)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(5,7),(6,7)],8)=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,6),(3,2),(4,3),(5,1),(5,6),(6,7)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)=>([],0)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,1),(5,2),(5,7),(7,6)],8)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
([(0,5),(0,6),(1,7),(2,7),(3,4),(4,2),(5,3),(6,1)],8)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(1,7),(2,7),(3,2),(4,1),(5,6),(6,3),(6,4)],8)=>([],0)
([(0,2),(0,5),(1,7),(2,6),(3,1),(4,3),(4,6),(5,4),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8)=>([(0,3),(1,3),(2,3)],4)
([(0,5),(1,7),(2,7),(3,6),(4,1),(5,3),(6,2),(6,4)],8)=>([],0)
([(0,2),(0,5),(1,7),(2,6),(3,4),(4,1),(4,6),(5,3),(6,7)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)=>([],0)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(6,7)],8)=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,2),(0,3),(0,4),(1,5),(1,6),(2,6),(3,5),(4,1),(5,7),(6,7)],8)=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(7,5)],8)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(2,6),(3,7),(4,6),(5,2),(6,7),(7,1)],8)=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,6),(1,7),(3,7),(4,5),(5,1),(6,4),(7,2)],8)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)=>([],0)
([(0,5),(0,6),(1,7),(2,7),(4,1),(5,2),(6,4),(7,3)],8)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(1,7),(2,7),(4,2),(5,6),(6,1),(6,4),(7,3)],8)=>([],0)
([(0,4),(0,5),(0,6),(1,7),(2,7),(4,7),(5,2),(6,1),(7,3)],8)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2)],9)=>([(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)
([(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3)],9)=>([(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)
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)=>([],0)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,5),(7,1),(7,2),(7,3),(7,4),(7,6)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5),(8,7)],9)=>([],0)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)=>([],0)
([(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,4),(7,1),(7,2),(7,3),(7,6)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,4),(6,5),(7,1),(7,2),(7,3),(7,6)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,8),(6,1),(6,2),(6,3),(6,4),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,7),(5,8),(6,1),(6,2),(6,3),(6,4),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,4),(8,7)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5),(8,7)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,8),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5),(8,7)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(8,5)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,3),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,5),(1,8),(2,7),(3,6),(4,6),(4,7),(5,1),(5,2),(5,3),(5,4),(6,8),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,7),(6,1),(6,3),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,8),(7,8)],9)=>([],0)
([(0,5),(1,8),(2,8),(3,6),(4,6),(4,8),(5,1),(5,2),(5,3),(5,4),(6,7),(8,7)],9)=>([],0)
([(0,6),(1,8),(2,8),(4,7),(5,7),(6,1),(6,2),(6,4),(6,5),(7,8),(8,3)],9)=>([],0)
([(0,5),(1,6),(2,6),(3,7),(4,8),(5,1),(5,2),(5,3),(5,4),(6,8),(8,7)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,8),(6,1),(6,2),(6,3),(6,4),(7,5)],9)=>([],0)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,3),(7,1),(7,2),(7,5),(7,6)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,4),(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,3),(7,1),(7,2),(7,6)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,3),(6,4),(7,1),(7,2),(7,6)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,3),(6,4),(6,5),(7,1),(7,2),(7,6)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,8),(6,1),(6,2),(6,3),(7,8)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,8),(5,8),(6,1),(6,2),(6,3),(7,8)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)=>([],0)
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(6,2),(6,3),(6,5),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,4),(0,5),(1,7),(2,6),(3,6),(3,7),(4,8),(5,1),(5,2),(5,3),(6,8),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,5),(1,7),(2,8),(3,6),(4,6),(4,8),(5,2),(5,3),(5,4),(6,7),(8,1)],9)=>([],0)
([(0,5),(2,7),(3,6),(4,6),(4,7),(5,2),(5,3),(5,4),(6,8),(7,8),(8,1)],9)=>([],0)
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(5,7),(6,2),(6,3),(6,5),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,8),(6,1),(6,2),(6,5),(8,4)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(6,3),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,5),(1,6),(2,6),(3,7),(4,3),(4,8),(5,1),(5,2),(5,4),(6,8),(8,7)],9)=>([],0)
([(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(3,7),(4,7),(5,2),(6,1),(6,3),(6,4),(7,8),(8,5)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(6,5),(8,3)],9)=>([],0)
([(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(5,3),(5,4),(6,7),(8,1),(8,6)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,8),(6,1),(6,2),(6,3),(7,4)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,7),(3,7),(4,8),(5,8),(6,1),(6,2),(6,3),(7,4),(7,5)],9)=>([],0)
([(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,2),(7,1),(7,5),(7,6)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(5,7),(6,1),(6,3),(6,5),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(5,7),(6,1),(6,3),(6,5),(7,4)],9)=>([],0)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,2),(6,3),(7,1),(7,5),(7,6)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,3),(5,7),(6,1),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,8),(4,3),(4,7),(5,2),(5,7),(6,1),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,7),(1,8),(2,8),(3,8),(4,3),(5,2),(6,1),(7,4),(7,5),(7,6)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(5,7),(6,3),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,5),(1,8),(2,7),(3,6),(4,1),(4,6),(4,7),(5,2),(5,3),(5,4),(6,8),(7,8)],9)=>([],0)
([(0,5),(1,8),(2,6),(3,6),(3,7),(4,1),(4,7),(5,2),(5,3),(5,4),(6,8),(7,8)],9)=>([],0)
([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(5,7),(6,3),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,5),(1,6),(2,8),(3,7),(4,3),(4,6),(5,1),(5,2),(5,4),(6,8),(8,7)],9)=>([],0)
([(0,3),(0,4),(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,2),(7,1),(7,6)],9)=>([(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)
([(0,4),(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,2),(6,3),(7,1),(7,6)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,4),(6,7),(7,1),(7,2),(7,3)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,5),(6,7),(7,1),(7,2),(7,3),(7,4)],9)=>([],0)
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,8)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)=>([],0)
([(0,3),(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,2),(6,1),(7,5),(7,6)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(5,7),(6,2),(6,5),(7,8)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(5,7),(6,2),(6,5),(7,3)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(5,7),(6,2),(6,5),(7,3),(7,4)],9)=>([],0)
([(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,1),(6,2),(7,5),(7,6)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,1),(5,2),(5,7),(6,3),(6,5),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,7),(4,8),(5,1),(5,2),(5,7),(6,3),(6,5),(7,4)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,4),(6,5),(6,7),(7,1),(7,2),(7,3)],9)=>([],0)
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)=>([],0)
([(0,3),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,3)],9)=>([],0)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(5,4),(6,1),(6,2),(7,5),(7,6)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,8),(4,3),(4,7),(5,1),(5,2),(5,7),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,3),(0,4),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(6,5),(7,8)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([],0)
([(0,2),(0,3),(0,4),(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,1),(7,6)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)=>([],0)
([(0,2),(0,3),(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,1),(7,5)],9)=>([(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)
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)=>([],0)
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,1)],9)=>([(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),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,1),(7,2)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,1),(7,2),(7,3)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,1),(7,2),(7,3),(7,4)],9)=>([(0,1)],2)
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,7),(8,1)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,7),(8,1),(8,2)],9)=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,8),(5,8),(6,8),(8,1),(8,2),(8,3)],9)=>([(0,1),(0,2),(1,2)],3)
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(8,7)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,8),(6,7),(8,1)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,8),(8,1),(8,2)],9)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(8,7)],9)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8),(8,1)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,8),(6,1),(8,7)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(2,8),(3,8),(4,8),(5,8),(6,1),(7,6),(8,7)],9)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(8,7)],9)=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,8),(6,1),(6,8),(8,7)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(3,8),(4,8),(5,8),(6,8),(7,1),(8,2)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,7),(6,1),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(8,6)],9)=>([(0,6),(1,6),(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),(1,7),(2,8),(3,8),(4,8),(5,6),(6,7),(8,6)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(8,2)],9)=>([(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)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(8,2),(8,6)],9)=>([(0,1),(0,2),(1,2)],3)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,8),(5,6),(6,7),(8,1),(8,6)],9)=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(6,8),(8,7)],9)=>([(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),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,8),(8,2)],9)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(0,6),(1,7),(2,8),(3,8),(4,8),(5,1),(6,5),(6,8),(8,7)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(1,7),(3,8),(4,8),(5,8),(6,1),(6,8),(7,2),(8,7)],9)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,7),(6,1),(6,2),(7,8)],9)=>([(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)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(8,6)],9)=>([(0,1),(0,2),(1,2)],3)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,8),(5,1),(5,6),(6,7),(8,6)],9)=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(6,8),(8,7)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(8,7)],9)=>([(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)
([(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(4,8),(5,8),(6,8),(7,1),(7,2),(8,3)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(8,7)],9)=>([(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),(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(8,6)],9)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(0,6),(1,7),(2,8),(3,8),(4,8),(5,1),(6,5),(8,7)],9)=>([(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)
([(0,2),(0,3),(0,4),(2,8),(3,8),(4,8),(5,6),(6,1),(7,5),(8,7)],9)=>([(0,1),(0,2),(1,2)],3)
([(0,2),(0,3),(0,4),(0,5),(2,8),(3,8),(4,8),(5,7),(6,1),(7,6),(8,7)],9)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(0,6),(1,7),(3,8),(4,8),(5,8),(6,1),(7,2),(8,7)],9)=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,2),(0,3),(0,4),(0,6),(1,7),(2,8),(3,8),(4,8),(5,1),(5,8),(6,5),(8,7)],9)=>([(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)
([(0,3),(0,4),(0,7),(1,8),(3,8),(4,8),(5,6),(6,1),(7,5),(8,2)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,6),(1,8),(2,8),(4,8),(5,7),(6,5),(7,1),(7,2),(8,3)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,8),(3,8),(5,7),(6,5),(7,1),(7,2),(7,3),(8,4)],9)=>([],0)
([(0,3),(0,4),(0,5),(0,7),(1,8),(3,8),(4,8),(5,8),(6,1),(7,6),(8,2)],9)=>([(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),(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,6),(6,7),(8,7)],9)=>([(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)
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,7),(5,8),(7,6),(8,6)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(1,7),(3,8),(4,8),(5,8),(6,7),(7,2),(8,1)],9)=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(0,6),(1,7),(2,7),(4,8),(5,8),(6,8),(7,3),(8,1),(8,2)],9)=>([(0,1),(0,2),(1,2)],3)
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8),(8,1)],9)=>([(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),(1,8),(2,8),(3,8),(4,6),(5,6),(5,8),(6,7),(8,7)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,8),(5,7),(6,7),(7,2),(8,1)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(0,6),(2,8),(3,8),(4,8),(5,7),(6,7),(7,2),(7,3),(8,1)],9)=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
([(0,5),(0,6),(2,8),(3,8),(4,8),(5,7),(6,7),(7,2),(7,3),(7,4),(8,1)],9)=>([(0,1)],2)
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8),(8,1)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,8)],9)=>([(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)
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,8),(4,6),(5,6),(5,7),(6,8),(7,1)],9)=>([(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)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,6),(5,7),(6,8),(7,1),(7,2)],9)=>([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)=>([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(2,7),(3,6),(4,6),(4,7),(5,1),(6,8),(7,8),(8,5)],9)=>([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,7),(5,8),(7,2),(8,1)],9)=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,8),(4,5),(4,8),(5,7),(7,6),(8,1),(8,7)],9)=>([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(4,7),(5,1),(6,8),(7,8)],9)=>([(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)
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(4,7),(5,8),(6,8),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(1,8),(2,6),(3,7),(4,6),(4,7),(5,1),(6,8),(7,5)],9)=>([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,5),(3,6),(4,5),(4,6),(5,8),(6,7),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(2,8),(3,6),(4,7),(5,6),(5,7),(6,8),(7,2),(8,1)],9)=>([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(2,8),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8),(8,1)],9)=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(4,7),(5,1),(5,7),(6,8),(7,8)],9)=>([(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)
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)=>([(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(4,8),(5,1),(6,7),(8,7)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,6)],9)=>([(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)
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,6),(6,7),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,8),(3,6),(4,7),(5,7),(7,8),(8,1)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,7),(7,8),(8,1),(8,2)],9)=>([(0,3),(1,2),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,2)],9)=>([(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),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,2),(7,6)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,8),(5,6),(6,8),(7,1),(7,6)],9)=>([(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),(0,5),(1,6),(2,6),(3,8),(4,7),(5,7),(7,1),(7,8),(8,2)],9)=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,2),(7,3)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,2),(7,3),(7,6)],9)=>([(0,1)],2)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,1),(7,2),(7,6)],9)=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,7),(7,8)],9)=>([(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),(0,6),(1,7),(2,7),(3,8),(4,8),(5,7),(6,2),(6,8),(8,1)],9)=>([(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),(0,5),(0,6),(1,7),(2,7),(3,7),(4,8),(5,8),(6,3),(6,8),(8,1),(8,2)],9)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(6,5),(6,7),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,8),(4,8),(5,1),(5,8),(6,7),(8,6)],9)=>([(0,6),(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),(0,6),(1,7),(2,7),(3,8),(4,8),(5,1),(6,5),(6,8),(8,2)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,2),(5,8),(6,7),(8,1),(8,6)],9)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(5,7),(6,1),(6,2),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,5),(1,7),(2,8),(3,8),(4,1),(4,6),(5,4),(5,8),(6,7),(8,6)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,6),(1,7),(2,8),(3,8),(4,5),(5,1),(6,4),(6,8),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,6),(2,7),(3,8),(4,8),(5,1),(6,2),(6,8),(7,5),(8,7)],9)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,3),(0,4),(0,6),(1,7),(3,8),(4,8),(5,1),(6,5),(6,8),(7,2),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(7,8)],9)=>([(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),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(7,6)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(5,1),(5,7),(6,7),(7,8)],9)=>([(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),(0,5),(1,6),(2,6),(3,7),(4,7),(5,2),(5,8),(7,8),(8,1)],9)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(7,3)],9)=>([(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)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(7,3),(7,6)],9)=>([(0,1)],2)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,2),(5,6),(6,8),(7,1),(7,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,7),(7,8)],9)=>([(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),(0,6),(1,7),(2,7),(3,7),(4,8),(5,8),(6,2),(6,3),(6,8),(8,1)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,1),(5,2),(5,8),(6,7),(8,6)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,8),(5,1),(5,2),(5,8),(6,7),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(0,6),(2,8),(3,8),(4,7),(5,7),(6,2),(6,3),(6,7),(7,8),(8,1)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(7,8)],9)=>([(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)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(7,6)],9)=>([(0,1)],2)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(5,1),(5,2),(5,7),(6,7),(7,8)],9)=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,7),(3,7),(4,3),(5,2),(6,1),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(6,1),(6,3),(6,5),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,3),(6,1),(6,4),(6,5),(8,7)],9)=>([],0)
([(0,7),(1,8),(2,8),(3,8),(5,3),(6,2),(7,1),(7,5),(7,6),(8,4)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,8),(6,1),(6,2),(6,3),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,5),(0,7),(1,8),(2,8),(3,8),(5,8),(6,3),(7,1),(7,2),(7,6),(8,4)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,7),(1,8),(2,8),(3,8),(4,8),(6,3),(6,4),(7,1),(7,2),(7,6),(8,5)],9)=>([],0)
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(5,8),(6,8),(7,1),(7,2),(7,3),(8,4)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,7),(5,7),(6,1),(6,2),(7,8)],9)=>([(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),(0,6),(1,8),(2,7),(3,7),(4,8),(5,8),(6,1),(6,2),(8,3)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(8,7)],9)=>([(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),(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(8,6)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(7,8)],9)=>([(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),(0,4),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(6,5),(8,6)],9)=>([(0,1)],2)
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,6),(4,1),(5,4),(5,8),(6,8),(8,7)],9)=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(2,8),(3,6),(4,6),(5,2),(5,7),(6,7),(7,8),(8,1)],9)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,6),(5,1),(5,2),(6,8),(8,7)],9)=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,3),(6,1),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,8),(2,8),(3,7),(4,7),(5,2),(5,6),(6,1),(6,3),(6,4),(7,8)],9)=>([],0)
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,7),(6,1),(6,5),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,6),(1,8),(2,7),(3,7),(4,1),(5,2),(6,4),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,6),(2,8),(3,7),(4,7),(5,3),(6,2),(6,5),(7,8),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,6),(1,8),(2,7),(3,8),(4,1),(5,2),(5,8),(6,4),(6,5),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,8),(3,7),(4,3),(4,8),(5,1),(5,2),(6,4),(6,5),(8,7)],9)=>([],0)
([(0,6),(1,8),(2,7),(3,7),(4,3),(5,1),(5,2),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8),(8,3)],9)=>([],0)
([(0,6),(1,8),(2,7),(3,7),(4,1),(5,2),(5,3),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,6),(1,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,5),(7,8),(8,2)],9)=>([],0)
([(0,5),(1,7),(2,6),(3,6),(4,2),(4,3),(4,7),(5,1),(5,4),(6,8),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(4,7),(5,1),(5,2),(5,7),(6,4),(6,5),(7,8),(8,3)],9)=>([],0)
([(0,3),(0,5),(1,7),(2,6),(3,6),(4,2),(4,7),(5,1),(5,4),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,6),(1,8),(3,7),(4,8),(5,1),(5,7),(6,3),(6,5),(7,8),(8,2)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9)=>([],0)
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,8),(5,2),(6,1),(6,5),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(0,6),(1,8),(2,7),(4,8),(5,8),(6,1),(6,2),(7,3),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(5,3),(6,1),(6,5),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,3),(5,6),(6,1),(6,2),(6,4),(8,7)],9)=>([],0)
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,8),(5,2),(5,8),(6,1),(6,5),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(0,7),(1,8),(2,8),(4,8),(5,8),(6,2),(7,1),(7,6),(8,3)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,5),(0,7),(1,8),(2,8),(3,8),(5,8),(6,2),(6,3),(7,1),(7,6),(8,4)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,8),(3,8),(4,8),(6,4),(6,7),(7,1),(7,2),(7,3),(8,5)],9)=>([],0)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,8),(7,8)],9)=>([(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)
([(0,4),(0,5),(2,8),(3,8),(4,7),(5,7),(6,2),(6,3),(7,6),(8,1)],9)=>([(0,1)],2)
([(0,4),(0,5),(0,6),(1,8),(2,8),(4,7),(5,7),(6,1),(6,2),(7,8),(8,3)],9)=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,6),(2,6),(2,8),(3,8),(4,8),(5,1),(5,2),(6,7),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,5),(0,6),(1,7),(2,7),(4,8),(5,8),(6,1),(6,2),(7,4),(8,3)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([],0)
([(0,4),(0,5),(0,6),(2,7),(3,7),(4,8),(5,8),(6,2),(6,3),(7,8),(8,1)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(6,2),(6,5),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,1),(5,2),(6,3),(6,5),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(8,7)],9)=>([],0)
([(0,4),(0,7),(1,8),(2,8),(4,8),(5,2),(6,1),(7,5),(7,6),(8,3)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,7),(1,8),(2,8),(3,8),(5,3),(6,1),(6,2),(7,5),(7,6),(8,4)],9)=>([],0)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,7),(5,7),(6,1),(7,8)],9)=>([(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),(0,6),(1,8),(2,7),(3,8),(4,8),(5,7),(6,1),(8,2)],9)=>([(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),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,8),(6,1),(8,2),(8,3)],9)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(6,5),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(1,8),(2,7),(3,7),(4,8),(5,1),(6,5),(7,6)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(6,8),(8,7)],9)=>([(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),(0,6),(1,8),(3,7),(4,7),(5,2),(6,1),(7,8),(8,5)],9)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(6,5),(8,1)],9)=>([(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),(0,4),(1,7),(2,7),(3,8),(4,8),(5,6),(6,2),(8,1),(8,5)],9)=>([(0,1)],2)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,2),(6,7),(8,1),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,7),(6,5),(7,8)],9)=>([(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),(0,6),(1,7),(2,7),(3,8),(4,8),(5,1),(5,8),(6,5),(8,2)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,6),(1,7),(2,8),(3,8),(4,1),(5,4),(5,8),(6,5),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,6),(1,7),(3,8),(4,8),(5,1),(5,8),(6,5),(7,2),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(7,8)],9)=>([(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),(0,4),(1,7),(2,7),(3,8),(4,8),(5,6),(6,1),(6,2),(8,5)],9)=>([(0,1)],2)
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,6),(4,1),(4,8),(5,4),(6,8),(8,7)],9)=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4),(7,8)],9)=>([],0)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,8),(2,7),(3,8),(4,8),(5,6),(6,1),(6,2),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,8),(5,6),(6,1),(6,2),(6,3),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4),(8,7)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(4,8),(5,8),(6,7),(7,1),(7,2),(8,3)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,8),(5,8),(6,7),(7,1),(7,2),(7,3),(8,4)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,8),(3,8),(4,8),(6,7),(7,1),(7,2),(7,3),(7,4),(8,5)],9)=>([],0)
([(0,2),(0,3),(0,6),(1,7),(2,8),(3,7),(4,5),(5,1),(6,4),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,7),(2,8),(3,8),(4,2),(5,4),(6,1),(7,5),(8,6)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,5),(1,7),(2,7),(3,8),(4,6),(5,4),(6,1),(6,2),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)=>([],0)
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(6,5),(8,7)],9)=>([(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),(0,7),(2,8),(3,8),(4,8),(5,2),(6,1),(7,5),(8,6)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,6),(1,8),(2,7),(3,7),(4,5),(5,1),(6,4),(7,8)],9)=>([(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)
([(0,2),(0,3),(2,8),(3,8),(4,6),(5,4),(6,1),(7,5),(8,7)],9)=>([(0,1)],2)
([(0,3),(0,4),(0,6),(2,8),(3,7),(4,7),(5,2),(6,5),(7,8),(8,1)],9)=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,5),(1,8),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,8),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3),(7,8)],9)=>([],0)
([(0,2),(0,3),(0,6),(1,7),(2,8),(3,8),(4,5),(5,1),(5,8),(6,4),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)=>([(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)
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,8),(4,8),(5,7),(5,8),(7,1),(8,6)],9)=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(2,8),(3,8),(4,6),(5,6),(5,8),(6,7),(7,1),(8,7)],9)=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,6),(5,8),(6,7),(8,1)],9)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,8),(4,8),(5,6),(6,7),(8,1)],9)=>([(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),(0,5),(1,6),(2,6),(3,7),(4,8),(5,8),(6,7),(8,1),(8,2)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(2,7),(3,8),(4,8),(5,7),(6,1),(7,6),(8,2)],9)=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)=>([(0,1)],2)
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(5,7),(6,8),(8,7)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(2,8),(3,8),(4,7),(5,7),(6,1),(7,8),(8,6)],9)=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,6),(6,7),(8,1)],9)=>([(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)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,6),(6,7),(8,1),(8,2)],9)=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,8),(6,7),(8,1),(8,2),(8,3)],9)=>([(0,1)],2)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,8),(5,8),(7,1),(7,8),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8),(8,1)],9)=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(7,8)],9)=>([(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),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(8,5)],9)=>([(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),(0,4),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(8,5),(8,6)],9)=>([(0,1)],2)
([(0,2),(0,3),(0,4),(1,7),(2,6),(3,6),(4,8),(5,1),(6,5),(6,8),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,1),(6,8),(8,7)],9)=>([(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)
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(2,8),(3,7),(4,7),(5,1),(6,5),(7,8),(8,6)],9)=>([(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,8),(4,6),(5,6),(6,7),(7,8),(8,1)],9)=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,7),(7,8)],9)=>([(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)
([(0,3),(0,4),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(6,8),(8,5)],9)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,1),(5,8),(6,7),(8,6)],9)=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,8),(3,8),(4,6),(5,1),(5,8),(6,7),(8,7)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,7),(2,7),(4,8),(5,8),(6,1),(6,8),(7,3),(8,2)],9)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,7),(5,7),(6,2),(6,7),(7,8),(8,1)],9)=>([(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),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(5,8),(6,1),(6,8),(8,7)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(4,7),(5,1),(5,6),(6,8),(7,8)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(6,2),(6,8),(8,7)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,8),(3,8),(4,6),(4,8),(5,1),(6,7),(8,7)],9)=>([(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),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(6,8),(7,8)],9)=>([(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),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,7),(4,6),(4,7),(5,8),(6,8),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)=>([(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)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)=>([(0,1)],2)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,6),(5,1),(5,8),(6,8),(8,7)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,1),(5,6),(5,7),(6,8),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,1),(5,6),(6,7),(8,7)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,3),(8,2)],9)=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,3),(7,4),(8,2)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(0,6),(1,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,8),(8,2)],9)=>([(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),(0,5),(1,7),(2,6),(3,8),(4,6),(5,1),(5,8),(6,7),(8,2)],9)=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,1),(5,8),(6,7),(8,2),(8,3)],9)=>([(0,2),(1,2)],3)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>([(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),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(6,2),(8,7)],9)=>([(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)
([(0,3),(0,4),(0,7),(2,8),(3,8),(4,8),(5,1),(6,5),(7,2),(8,6)],9)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(0,6),(1,8),(3,8),(4,8),(5,7),(6,1),(7,2),(8,7)],9)=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(4,8),(5,8),(6,2),(7,1),(8,3)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(6,8),(7,8)],9)=>([(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)
([(0,3),(0,4),(0,5),(2,8),(3,8),(4,7),(5,7),(6,2),(7,6),(8,1)],9)=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(0,6),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,1)],2)
([(0,3),(0,4),(0,5),(2,8),(3,6),(4,7),(5,7),(6,8),(7,2),(7,6),(8,1)],9)=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(0,6),(1,8),(3,8),(4,7),(5,7),(6,1),(7,8),(8,2)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,6),(1,8),(2,8),(3,8),(4,6),(5,1),(6,7),(8,7)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(3,7),(4,7),(5,8),(6,1),(7,2),(8,3)],9)=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(0,6),(2,7),(3,8),(4,8),(5,7),(6,2),(7,8),(8,1)],9)=>([(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),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,2),(7,1)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(6,5),(6,7),(7,8)],9)=>([(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),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(5,7),(6,1),(6,2),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(5,7),(6,1),(6,2),(6,3),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(1,8),(2,8),(3,6),(4,5),(4,6),(5,1),(5,2),(5,7),(6,7),(7,8)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,2),(0,3),(0,5),(1,8),(2,8),(3,6),(4,1),(4,7),(5,4),(5,6),(6,7),(7,8)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(4,8),(5,4),(5,7),(7,8),(8,1)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(5,7),(6,1),(6,2),(7,3)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,5),(1,8),(2,8),(3,7),(4,2),(4,6),(5,4),(5,7),(6,8),(7,1),(7,6)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,1),(5,6),(6,7),(7,8)],9)=>([(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),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2)],9)=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(6,5),(6,7),(7,2)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,8),(5,2),(5,7),(6,8),(7,1),(7,6)],9)=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(6,5),(6,7),(7,2),(7,3)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,3),(5,7),(6,8),(7,1),(7,2),(7,6)],9)=>([(0,2),(1,2)],3)
([(0,2),(0,3),(0,6),(1,8),(2,8),(3,7),(4,5),(5,1),(6,4),(6,7),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,5),(1,8),(2,6),(3,7),(4,1),(5,4),(5,6),(6,8),(8,7)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,6),(2,8),(3,7),(4,2),(5,1),(6,4),(6,7),(7,8),(8,5)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,5),(5,2),(6,4),(6,8),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,2),(7,8),(8,3)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,5),(1,7),(2,6),(3,8),(4,2),(5,4),(5,8),(6,7),(8,1),(8,6)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,5),(1,8),(2,8),(3,7),(4,6),(5,4),(5,7),(6,1),(6,2),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,2),(0,5),(1,7),(2,6),(3,4),(4,1),(4,8),(5,3),(5,6),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,2)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,2),(7,3)],9)=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,2),(7,3),(7,4)],9)=>([(0,2),(1,2)],3)
([(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,3),(7,1),(7,2)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,7),(7,8)],9)=>([(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),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,5),(6,7),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,3),(6,1),(6,5),(6,7),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(1,8),(2,8),(3,6),(4,2),(4,7),(5,1),(5,4),(5,6),(6,7),(7,8)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,1),(5,2),(5,6),(6,7),(7,8)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,3),(5,7),(7,8),(8,2)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,5),(6,7),(7,3)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,2),(5,3),(5,7),(6,8),(7,1),(7,6)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,1),(5,2),(5,7),(6,8),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,1),(5,2),(5,6),(6,8),(8,7)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(2,8),(3,8),(4,7),(5,1),(6,2),(6,3),(6,7),(7,8),(8,5)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,2),(5,3),(5,8),(6,7),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,1),(5,2),(5,7),(7,3),(7,8),(8,6)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(5,3),(5,6),(6,7),(8,1)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(2,6),(3,6),(4,7),(5,2),(5,3),(5,7),(6,8),(7,8),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(6,4),(6,5),(6,7),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,4),(5,6),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(1,5),(2,5),(2,7),(3,6),(4,1),(4,2),(4,6),(5,8),(6,7),(7,8)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,8),(5,1),(5,4),(5,6),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(5,1),(5,4),(5,6),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(1,7),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,7),(7,3)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,7),(7,3),(7,4)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,4),(7,1),(7,2),(7,3)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,7),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,5),(6,7),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7),(7,8)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,2),(5,3),(5,7),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,8),(5,7),(6,1),(6,2),(6,3),(6,7),(7,8),(8,4)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,7),(7,4)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,5),(7,1),(7,2),(7,3),(7,4)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,4),(6,7),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,4),(7,1),(7,2),(7,3),(7,5)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5),(7,8)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,4),(6,5),(8,7)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,8),(6,1),(6,2),(6,3),(6,4),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,7),(1,8),(2,8),(3,8),(4,8),(6,4),(7,1),(7,2),(7,3),(7,6),(8,5)],9)=>([],0)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(6,8),(7,1),(7,2),(7,3),(7,4),(8,5)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(6,1),(6,2),(6,3),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,3),(7,1),(7,2),(7,5)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,3),(6,4),(7,1),(7,2),(7,5)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,7),(6,1),(6,2),(6,3),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,7),(6,1),(6,2),(6,3),(7,4)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,3),(6,1),(6,2),(6,5),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,4),(6,5),(8,3)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,7),(6,1),(6,2),(6,3),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,8),(6,1),(6,2),(6,3),(8,4)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,5),(8,7)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,7),(2,8),(3,8),(4,8),(5,4),(6,1),(7,2),(7,3),(7,5),(8,6)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(8,7)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(8,6)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,3),(6,1),(6,2),(6,5),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,7),(5,8),(6,1),(6,2),(6,3),(7,4),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5),(8,7)],9)=>([],0)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,3),(5,8),(6,1),(6,2),(6,5),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,3),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,6),(2,7),(3,8),(4,6),(5,1),(5,2),(5,3),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,4),(6,1),(6,3),(6,5),(7,8)],9)=>([],0)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,7),(6,1),(6,3),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,7),(3,7),(4,3),(5,1),(6,2),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,6),(2,8),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5),(7,8),(8,1)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,2),(5,3),(5,8),(6,1),(6,4),(6,5),(8,7)],9)=>([],0)
([(0,5),(1,6),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(6,8),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(4,7),(5,2),(5,7),(6,1),(6,4),(6,5),(7,8),(8,3)],9)=>([],0)
([(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(5,3),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,8),(2,8),(3,6),(3,8),(4,6),(5,1),(5,2),(5,3),(6,7),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,8),(4,7),(5,7),(6,1),(6,2),(6,4),(7,8),(8,3)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(1,8),(2,6),(3,6),(3,8),(4,8),(5,1),(5,2),(5,3),(6,7),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,7),(2,7),(3,8),(5,8),(6,1),(6,2),(6,3),(7,5),(8,4)],9)=>([],0)
([(0,5),(0,6),(1,8),(3,7),(4,7),(5,8),(6,1),(6,3),(6,4),(7,8),(8,2)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,1),(7,2),(7,3),(7,5)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,3),(6,5),(7,1),(7,2),(7,6)],9)=>([],0)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,6),(1,8),(2,7),(3,7),(4,5),(5,3),(6,1),(6,2),(6,4),(7,8)],9)=>([],0)
([(0,7),(1,8),(2,8),(3,8),(4,2),(5,6),(6,3),(7,1),(7,4),(7,5)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,3),(5,1),(5,7),(6,2),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,2),(5,4),(5,7),(6,1),(6,3),(6,5),(7,8)],9)=>([],0)
([(0,5),(1,6),(2,7),(3,8),(4,3),(4,6),(5,1),(5,2),(5,4),(6,8),(8,7)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,3),(6,4),(7,8)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,4),(0,5),(1,8),(2,6),(3,6),(3,7),(4,7),(5,1),(5,2),(5,3),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,6),(2,7),(3,6),(3,7),(4,2),(5,1),(5,3),(5,4),(6,8),(7,8)],9)=>([],0)
([(0,4),(0,5),(1,6),(2,6),(3,7),(4,3),(5,1),(5,2),(5,7),(6,8),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(0,6),(1,8),(2,8),(4,7),(5,4),(6,1),(6,2),(6,7),(7,8),(8,3)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,4),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,7),(1,8),(2,8),(3,8),(5,6),(6,3),(7,1),(7,2),(7,5),(8,4)],9)=>([],0)
([(0,6),(1,8),(2,7),(3,7),(4,5),(5,1),(6,2),(6,3),(6,4),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,3),(5,4),(5,8),(6,1),(6,2),(6,5),(8,7)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(5,3),(5,8),(6,1),(6,2),(6,5),(7,4),(8,7)],9)=>([],0)
([(0,6),(2,8),(3,7),(4,7),(5,2),(6,3),(6,4),(6,5),(7,8),(8,1)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(6,1),(6,2),(6,3),(8,7)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(6,4),(7,1),(7,2),(7,3),(8,5)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,7),(2,8),(3,8),(4,8),(5,1),(6,5),(7,2),(7,3),(7,4),(8,6)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,8),(5,7),(6,1),(6,2),(6,3),(7,4),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,7),(2,8),(3,8),(4,7),(5,4),(6,1),(6,2),(6,3),(8,5)],9)=>([],0)
([(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,1),(5,2),(5,3),(6,8),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,3),(6,1),(6,2),(6,7),(7,8)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,3),(6,1),(6,2),(6,7),(7,4)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,3),(6,1),(6,4),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(1,6),(2,7),(3,8),(4,1),(5,2),(5,3),(5,6),(6,8),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,5),(7,1),(7,2),(7,3)],9)=>([(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)
([(0,7),(1,8),(2,8),(3,8),(4,6),(5,3),(6,5),(7,1),(7,2),(7,4)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,3),(4,7),(5,4),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,3),(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,2),(7,1),(7,5)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,2),(6,3),(7,1),(7,5)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,4),(6,5),(7,1),(7,2),(7,3)],9)=>([],0)
([(0,3),(0,7),(1,8),(2,8),(3,8),(4,1),(5,6),(6,2),(7,4),(7,5)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,3),(0,6),(1,8),(2,7),(3,8),(4,1),(5,4),(5,7),(6,2),(6,5),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(6,3),(6,4),(7,8)],9)=>([],0)
([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)=>([],0)
([(0,3),(0,5),(1,6),(2,8),(3,7),(4,2),(4,6),(5,1),(5,4),(6,8),(8,7)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)=>([],0)
([(0,6),(1,8),(2,7),(3,7),(4,5),(4,8),(5,3),(6,1),(6,4),(8,2)],9)=>([],0)
([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)=>([],0)
([(0,3),(0,6),(1,8),(2,7),(3,8),(4,5),(5,1),(5,7),(6,2),(6,4),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,7),(3,7),(4,5),(5,3),(5,8),(6,1),(6,4),(8,2)],9)=>([],0)
([(0,7),(1,8),(2,8),(3,8),(4,3),(5,6),(6,1),(6,2),(7,4),(7,5)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,5),(5,1),(5,2),(5,7),(6,3),(6,4),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,4),(4,1),(4,7),(5,2),(5,7),(6,3),(6,5),(7,8)],9)=>([],0)
([(0,3),(0,6),(1,8),(2,7),(3,8),(4,2),(5,1),(5,7),(6,4),(6,5),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,7),(3,7),(4,1),(5,3),(5,8),(6,4),(6,5),(8,2)],9)=>([],0)
([(0,7),(1,8),(2,8),(3,8),(4,5),(5,3),(6,1),(6,2),(7,4),(7,6)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,3),(5,1),(5,2),(5,7),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,7),(6,1),(6,2),(7,8)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,7),(6,1),(6,2),(7,3)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,7),(6,1),(6,2),(7,3),(7,4)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,7),(6,1),(6,2),(7,8)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,7),(6,1),(6,2),(8,3)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,8),(6,1),(6,2),(8,3),(8,4)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,1),(7,2),(7,5)],9)=>([(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)
([(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,2),(6,5),(7,1),(7,6)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,7),(6,1),(6,5),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,7),(6,1),(6,5),(7,3)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,2),(6,3),(7,1),(7,6)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,4),(6,3),(6,7),(7,1),(7,2),(7,5)],9)=>([],0)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,3),(5,7),(6,1),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,8),(4,1),(5,2),(6,4),(6,7),(7,8)],9)=>([(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)
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,3),(5,6),(5,7),(6,1),(6,2),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(1,6),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(6,8),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(0,5),(1,6),(2,8),(3,7),(4,1),(5,2),(5,6),(6,8),(8,7)],9)=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(3,7),(4,2),(5,3),(6,1),(6,7),(7,8),(8,4)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,2),(5,1),(6,4),(6,8),(8,3)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,4),(0,5),(1,7),(2,8),(3,6),(4,2),(5,3),(5,8),(6,7),(8,1),(8,6)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,3),(6,1),(6,2),(7,8)],9)=>([(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),(0,6),(1,7),(2,7),(3,8),(4,5),(5,2),(6,1),(6,4),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,7),(2,8),(3,8),(4,5),(5,3),(6,1),(7,2),(7,4),(8,6)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,1),(5,2),(6,3),(6,4),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,6),(1,8),(2,7),(3,7),(4,3),(5,1),(5,4),(6,2),(6,5),(7,8)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,3),(4,8),(5,1),(6,2),(6,4),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(0,6),(2,8),(3,7),(4,7),(5,4),(6,2),(6,3),(7,8),(8,1)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,4),(8,3)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,2),(5,3),(6,4),(7,1),(7,5)],9)=>([(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)
([(0,7),(1,8),(2,8),(3,8),(4,5),(5,3),(6,2),(6,4),(7,1),(7,6)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,3),(6,1),(6,4),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(1,8),(2,8),(3,8),(4,3),(5,6),(6,2),(6,7),(7,1),(7,4)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,1),(4,2),(4,7),(5,4),(6,3),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,4),(0,5),(1,8),(2,7),(3,2),(3,6),(4,3),(5,1),(5,6),(6,8),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,4),(6,1),(6,3),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,6),(1,8),(2,7),(3,5),(4,3),(5,1),(5,7),(6,2),(6,4),(7,8)],9)=>([],0)
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,7),(5,1),(6,2),(6,5),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(5,3),(6,2),(6,5),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,4),(6,1),(6,5),(8,3)],9)=>([],0)
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,7),(5,1),(5,7),(6,2),(6,5),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,2),(5,8),(6,1),(6,5),(8,3)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(6,3),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(1,8),(2,8),(3,7),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(7,8)],9)=>([],0)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(1,6),(2,7),(3,6),(4,2),(4,8),(5,1),(5,4),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,6),(2,8),(3,6),(4,7),(5,1),(5,2),(6,8),(8,7)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(3,7),(4,7),(5,2),(6,1),(6,3),(7,8),(8,5)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,3),(6,1),(6,5),(8,2)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(1,7),(2,8),(3,6),(4,8),(5,2),(5,3),(6,7),(8,1),(8,6)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(1,6),(2,6),(2,7),(3,8),(4,7),(5,1),(5,2),(6,8),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,7),(2,6),(3,6),(3,8),(4,8),(5,2),(5,3),(6,7),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(2,6),(3,6),(3,7),(4,7),(5,2),(5,3),(6,8),(7,8),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(1,7),(2,8),(3,6),(3,8),(4,6),(5,2),(5,3),(6,7),(8,1)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,5),(8,7)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,3),(6,1),(6,5),(8,7)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,7),(2,8),(3,8),(4,8),(5,1),(6,3),(6,4),(7,2),(7,6),(8,5)],9)=>([],0)
([(0,4),(0,7),(2,8),(3,8),(4,8),(5,3),(6,1),(7,2),(7,5),(8,6)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(6,2),(6,3),(7,8)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(8,7)],9)=>([(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)
([(0,6),(0,7),(2,8),(3,8),(4,8),(5,1),(6,2),(7,3),(7,4),(8,5)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,8)],9)=>([(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)
([(0,4),(1,8),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5),(7,8)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,3),(4,8),(5,4),(6,1),(6,2),(8,7)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)=>([],0)
([(0,5),(0,6),(2,8),(3,7),(4,7),(5,2),(6,3),(6,4),(7,8),(8,1)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(6,1),(6,2),(8,5)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,1),(5,2),(6,8),(8,7)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(2,7),(3,7),(4,8),(5,1),(6,2),(6,3),(7,8),(8,5)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([],0)
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(5,3),(6,7),(8,1),(8,6)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,3),(5,2),(6,1),(7,4),(7,5)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,7),(1,8),(2,8),(3,8),(4,2),(5,3),(6,1),(6,5),(7,4),(7,6)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(5,4),(5,7),(6,3),(6,5),(7,8)],9)=>([],0)
([(0,5),(1,6),(2,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(8,7)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,2),(4,3),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,5),(1,7),(2,8),(3,1),(3,6),(4,2),(4,6),(5,3),(5,4),(6,8),(8,7)],9)=>([],0)
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(5,7),(6,4),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,6),(5,1),(5,4),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(5,3),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(1,8),(2,6),(2,7),(3,6),(4,1),(4,7),(5,2),(5,4),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,3),(0,5),(1,8),(2,6),(3,7),(4,1),(4,6),(4,7),(5,2),(5,4),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,6),(2,7),(3,6),(3,7),(4,2),(5,1),(5,3),(6,8),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,6),(1,7),(2,8),(3,7),(4,3),(4,8),(5,1),(6,2),(6,4),(8,5)],9)=>([],0)
([(0,3),(0,5),(1,6),(2,7),(3,8),(4,2),(4,6),(5,1),(5,4),(6,8),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,7),(5,2),(6,1),(6,5),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,2),(5,3),(6,1),(6,5),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(6,3),(6,5),(8,4)],9)=>([],0)
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(6,3),(6,5),(8,2)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,2),(5,1),(6,4),(6,5),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,7),(2,8),(3,8),(4,3),(5,2),(6,1),(7,4),(7,5),(8,6)],9)=>([],0)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,8)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,3)],9)=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,3),(7,4)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,8),(4,1),(5,2),(5,7),(6,4),(6,7),(7,8)],9)=>([(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),(0,5),(1,7),(2,8),(3,8),(4,1),(4,6),(5,2),(5,6),(6,7),(7,8)],9)=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,3),(4,7),(5,1),(5,7),(7,8),(8,2)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,1),(5,2),(5,7),(6,4),(6,7),(7,3)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,4),(0,5),(1,8),(2,8),(3,6),(4,2),(4,7),(5,3),(5,7),(6,8),(7,1),(7,6)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,3),(4,7),(5,6),(5,7),(6,1),(6,2),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(1,8),(2,8),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7),(7,8)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,2),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(0,6),(2,8),(3,8),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8),(8,4)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,4),(0,5),(1,8),(2,8),(3,6),(4,2),(4,7),(5,1),(5,7),(7,3),(7,8),(8,6)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,5),(0,6),(1,8),(2,8),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,4),(0,5),(1,8),(2,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,4),(0,5),(1,8),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,3),(6,4),(7,1),(7,2)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,3),(5,7),(6,1),(6,2),(6,7),(7,8)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,3),(5,1),(5,7),(6,2),(6,4),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,3),(4,6),(5,1),(5,2),(5,6),(6,7),(7,8)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,1),(4,7),(5,2),(5,3),(5,7),(6,8),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,3),(4,6),(5,1),(5,2),(5,6),(6,8),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,8),(5,3),(5,7),(6,1),(6,2),(6,7),(7,8),(8,4)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,2),(4,6),(5,1),(5,3),(5,6),(6,8),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,3),(5,7),(6,1),(6,2),(6,7),(7,4)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,3),(5,4),(5,7),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,1),(4,6),(5,2),(5,3),(5,6),(6,7),(7,8)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,4),(6,5),(7,1),(7,2),(7,3)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,4),(5,7),(6,1),(6,2),(6,3),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(6,4),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,6),(1,8),(2,8),(3,7),(4,5),(5,1),(5,7),(6,2),(6,3),(6,4),(7,8)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,7),(6,1),(6,3),(6,4),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,6),(1,8),(2,8),(3,7),(4,5),(5,3),(5,8),(6,1),(6,2),(6,4),(8,7)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(1,7),(2,6),(3,6),(3,7),(4,3),(5,1),(5,2),(5,4),(6,8),(7,8)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,3),(5,4),(5,7),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,4),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(5,7),(6,1),(6,3),(7,8)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(5,7),(6,1),(6,3),(7,4)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(5,7),(6,2),(6,3),(7,8)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,8),(6,1),(6,2),(8,4)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,3),(5,4),(5,8),(6,1),(6,2),(8,7)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,7),(5,3),(5,8),(6,1),(6,2),(7,4),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(5,7),(6,3),(6,4),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(1,6),(2,8),(3,7),(4,3),(4,6),(5,1),(5,2),(6,8),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(5,4),(6,3),(6,5),(7,8)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(5,7),(6,3),(6,4),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(0,6),(1,8),(2,8),(4,7),(5,2),(5,7),(6,1),(6,4),(7,8),(8,3)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,4),(5,7),(6,1),(6,3),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,4),(0,5),(1,6),(2,7),(3,8),(4,3),(4,6),(5,1),(5,2),(6,8),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,6),(1,8),(2,7),(3,5),(4,1),(5,4),(5,7),(6,2),(6,3),(7,8)],9)=>([],0)
([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9)=>([],0)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,2),(6,3),(7,1),(7,5)],9)=>([(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)
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,2),(5,6),(6,3),(6,4),(7,1),(7,5)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,3),(4,7),(5,1),(5,7),(6,2),(6,4),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,3),(6,1),(6,4),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(6,3),(6,4),(7,8)],9)=>([(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)
([(0,4),(0,5),(1,8),(2,6),(3,6),(3,7),(4,1),(4,7),(5,2),(5,3),(6,8),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(5,2),(6,3),(6,4),(8,7)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(6,3),(6,4),(7,1),(7,2),(8,5)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(8,5)],9)=>([],0)
([(0,4),(0,5),(1,6),(2,6),(3,7),(4,3),(4,8),(5,1),(5,2),(6,8),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,2),(6,1),(6,7),(7,8)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,2),(6,1),(6,7),(7,3)],9)=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,2),(6,1),(6,7),(7,3),(7,4)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,4),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,5),(7,1),(7,2)],9)=>([(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)
([(0,3),(0,7),(1,8),(2,8),(3,8),(4,6),(5,2),(6,5),(7,1),(7,4)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,7),(1,8),(2,8),(3,8),(4,5),(5,6),(6,2),(6,3),(7,1),(7,4)],9)=>([],0)
([(0,7),(1,8),(2,8),(3,5),(4,3),(5,2),(6,1),(7,4),(7,6)],9)=>([],0)
([(0,6),(1,8),(2,7),(3,4),(4,1),(5,3),(5,7),(6,2),(6,5),(7,8)],9)=>([],0)
([(0,6),(2,8),(3,7),(4,2),(5,4),(5,7),(6,3),(6,5),(7,8),(8,1)],9)=>([],0)
([(0,6),(1,8),(2,7),(3,2),(4,3),(5,1),(5,7),(6,4),(6,5),(7,8)],9)=>([],0)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,8),(5,7),(6,2),(6,3),(7,1),(7,6)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,5),(1,8),(2,8),(3,8),(4,8),(5,6),(6,4),(6,7),(7,1),(7,2),(7,3)],9)=>([],0)
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,4),(6,1),(6,7),(7,8)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,4),(6,1),(6,7),(7,3)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,3),(6,4),(7,1),(7,2)],9)=>([(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)
([(0,5),(1,8),(2,8),(3,8),(4,8),(5,7),(6,3),(6,4),(7,1),(7,2),(7,6)],9)=>([],0)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,1),(5,7),(6,2),(6,3),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,8),(4,2),(5,4),(6,1),(6,7),(7,8)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,1),(5,4),(6,3),(6,8),(8,2)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,5),(1,8),(2,7),(3,8),(4,1),(4,7),(5,6),(6,2),(6,4),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,5),(1,8),(2,7),(3,7),(4,3),(4,8),(5,6),(6,1),(6,4),(8,2)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,7),(3,2),(4,1),(5,3),(6,4),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,5),(0,6),(1,8),(3,7),(4,3),(5,4),(6,1),(6,7),(7,8),(8,2)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(1,8),(2,7),(3,1),(4,3),(4,7),(5,6),(6,2),(6,4),(7,8)],9)=>([],0)
([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)=>([],0)
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(7,8)],9)=>([(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),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(7,2)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(7,2),(7,3)],9)=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(7,2),(7,3),(7,4)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,1),(6,2),(7,5)],9)=>([(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)
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(6,7),(7,1),(7,5)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,8),(4,8),(5,6),(6,1),(6,2),(7,8)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)=>([],0)
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(5,7),(6,5),(7,8)],9)=>([(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),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(5,7),(6,5),(7,2)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(5,7),(6,5),(7,2),(7,3)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,2),(0,3),(0,6),(1,8),(2,8),(3,7),(4,1),(5,4),(5,7),(6,5),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,5),(1,8),(2,6),(3,7),(4,1),(4,6),(5,4),(6,8),(8,7)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,4),(7,8),(8,5)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,5),(4,8),(5,2),(6,4),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,5),(1,7),(2,6),(3,8),(4,2),(4,8),(5,4),(6,7),(8,1),(8,6)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,5),(1,8),(2,8),(3,7),(4,6),(4,7),(5,4),(6,1),(6,2),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,2),(0,5),(1,7),(2,6),(3,4),(3,6),(4,1),(4,8),(5,3),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,3),(6,7),(7,1),(7,2)],9)=>([(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)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,8),(5,3),(6,7),(7,1),(7,2),(7,5)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(6,7),(7,3)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(7,3)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(7,3),(7,5)],9)=>([],0)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,8),(2,7),(3,8),(4,7),(5,6),(6,1),(6,2),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,8),(2,7),(3,7),(4,8),(5,6),(6,1),(6,2),(6,3),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(6,4),(8,3)],9)=>([],0)
([(0,4),(0,5),(1,8),(2,7),(3,7),(4,8),(5,6),(6,1),(6,3),(8,2)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(8,7)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(6,3),(8,7)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(2,8),(3,8),(4,8),(5,1),(6,7),(7,2),(7,3),(7,4),(8,5)],9)=>([],0)
([(0,4),(0,6),(2,8),(3,8),(4,8),(5,1),(6,7),(7,2),(7,3),(8,5)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,2),(0,3),(0,7),(1,8),(2,8),(3,8),(4,6),(5,4),(6,1),(7,5)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,6),(1,8),(2,8),(3,8),(4,5),(5,7),(6,4),(7,1),(7,2)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,8),(4,5),(5,7),(6,4),(7,1),(7,2),(7,3)],9)=>([],0)
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(7,8)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(8,3)],9)=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,3),(0,6),(0,7),(1,8),(2,8),(3,8),(4,2),(5,1),(6,4),(7,5)],9)=>([(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)
([(0,3),(0,6),(1,8),(2,8),(3,8),(4,5),(5,2),(6,7),(7,1),(7,4)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,8),(4,1),(4,7),(5,2),(6,4),(7,8)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,2),(4,8),(5,1),(6,4),(8,3)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3)],9)=>([(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)
([(0,6),(1,8),(2,8),(3,8),(4,5),(5,3),(6,7),(7,1),(7,2),(7,4)],9)=>([],0)
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,3),(5,6),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,3),(6,4),(7,1),(7,2)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,2),(3,7),(4,1),(4,7),(5,3),(6,4),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,3),(0,5),(0,6),(1,7),(2,7),(3,8),(4,1),(5,2),(6,4),(7,8)],9)=>([(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),(0,5),(1,7),(2,7),(3,8),(4,2),(5,6),(6,1),(6,4),(7,8)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(2,8),(3,8),(4,3),(5,1),(6,7),(7,2),(7,4),(8,5)],9)=>([],0)
([(0,6),(0,7),(2,8),(3,8),(4,2),(5,1),(6,4),(7,3),(8,5)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,2),(0,3),(0,4),(0,6),(1,7),(2,8),(3,8),(4,7),(5,1),(6,5),(7,8)],9)=>([(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),(0,6),(1,8),(2,7),(3,8),(4,7),(5,1),(6,5),(8,2)],9)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(6,5),(8,2),(8,3)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,2),(7,1)],9)=>([(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)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,7),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,1),(5,6),(5,7),(6,8),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(5,4),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,6),(4,1),(4,5),(4,6),(5,8),(6,7),(7,8)],9)=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,8),(3,7),(4,6),(5,1),(5,6),(5,7),(6,8),(7,8),(8,2)],9)=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,2),(5,6),(5,7),(6,8),(7,1)],9)=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,1),(4,5),(4,6),(5,8),(6,8),(8,7)],9)=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,8),(3,6),(4,7),(5,1),(5,7),(6,8),(7,8)],9)=>([(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)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,2),(5,8),(6,7),(8,1)],9)=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,1),(5,6),(6,8),(8,7)],9)=>([(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),(0,6),(2,8),(3,8),(4,7),(5,1),(6,2),(6,7),(7,8),(8,5)],9)=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,6),(5,2),(5,8),(6,7),(8,1)],9)=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,3),(5,8),(6,7),(8,1),(8,2)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,8),(5,1),(5,7),(7,2),(7,8),(8,6)],9)=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(2,6),(3,6),(4,7),(5,2),(5,7),(6,8),(7,8),(8,1)],9)=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(5,6),(6,7),(8,1)],9)=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(2,7),(3,7),(4,8),(5,1),(6,2),(6,8),(7,5),(8,3)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,7),(4,1),(5,2),(6,4),(6,7),(7,8)],9)=>([(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),(0,5),(1,8),(2,8),(3,7),(4,2),(5,6),(5,7),(6,1),(6,4),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(1,7),(2,8),(3,6),(4,5),(4,6),(5,1),(5,2),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,2),(0,5),(1,7),(2,6),(3,1),(4,3),(4,8),(5,4),(5,6),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,2),(0,3),(0,5),(1,8),(2,6),(3,7),(4,1),(4,7),(5,4),(5,6),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,5),(1,7),(2,6),(3,8),(4,1),(4,6),(5,4),(5,8),(6,7),(8,2)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,2),(0,3),(0,5),(1,7),(2,8),(3,6),(4,1),(4,8),(5,4),(5,6),(6,8),(8,7)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(1,5),(1,7),(2,5),(3,6),(4,1),(4,6),(5,8),(6,7),(7,8)],9)=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,2),(5,1),(6,4),(6,8),(8,5)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(5,1),(5,6),(6,4),(6,8),(8,7)],9)=>([(0,2),(1,2)],3)
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,8),(4,1),(5,4),(5,6),(6,8),(8,7)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,6),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(2,8),(3,7),(4,6),(5,2),(5,6),(6,7),(7,8),(8,1)],9)=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,1),(5,2),(5,6),(6,8),(8,7)],9)=>([(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),(0,5),(2,7),(3,8),(4,6),(5,2),(5,6),(6,7),(7,8),(8,1)],9)=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,8),(4,2),(5,1),(6,4),(6,8),(8,7)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(0,6),(1,8),(2,7),(4,8),(5,1),(6,2),(6,8),(7,3),(8,7)],9)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,7),(4,1),(5,4),(5,6),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,5),(4,7),(5,1),(5,2),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(1,8),(2,8),(4,7),(5,6),(5,7),(6,1),(6,2),(7,8),(8,3)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,6),(1,7),(3,7),(4,8),(5,1),(6,5),(6,8),(7,2),(8,3)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,6),(1,8),(3,8),(4,7),(5,1),(6,5),(6,7),(7,8),(8,2)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,7),(7,5)],9)=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,8),(4,6),(5,1),(5,6),(6,7),(7,8)],9)=>([(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),(1,6),(2,6),(3,8),(4,7),(5,2),(5,7),(7,8),(8,1)],9)=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,7),(7,3)],9)=>([(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)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,7),(7,3),(7,5)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,2),(5,7),(6,8),(7,1),(7,6)],9)=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(4,7),(5,1),(5,7),(6,8),(7,8)],9)=>([(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)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(4,7),(5,2),(5,7),(6,8),(7,1)],9)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,1),(0,2),(0,3),(0,4),(1,8),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(1,8),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,1)],9)=>([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)=>([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(4,7),(5,2),(5,6),(6,8),(7,1)],9)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,5),(3,6),(4,1),(4,6),(5,8),(6,8),(8,7)],9)=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,2),(0,3),(0,5),(1,8),(2,6),(3,6),(3,7),(4,1),(5,4),(5,7),(6,8),(7,8)],9)=>([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,5),(3,6),(4,1),(4,6),(5,8),(6,7),(7,8)],9)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,8),(3,6),(4,6),(4,7),(5,1),(5,7),(6,8),(7,8),(8,2)],9)=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,7),(6,1),(6,7),(7,8)],9)=>([(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),(0,5),(0,6),(1,8),(2,8),(3,7),(4,1),(5,2),(5,7),(6,4),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,1),(4,8),(5,2),(5,8),(6,7),(8,6)],9)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(0,6),(2,8),(3,8),(4,7),(5,3),(5,7),(6,2),(6,7),(7,8),(8,1)],9)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,8),(5,3),(5,8),(6,2),(6,8),(8,1)],9)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(7,8)],9)=>([(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),(0,4),(0,5),(1,8),(2,6),(3,7),(4,1),(4,6),(5,2),(5,7),(6,8),(7,8)],9)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,2),(4,8),(5,1),(5,6),(6,8),(8,7)],9)=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(7,6)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,2),(4,7),(5,1),(5,6),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(4,7),(5,1),(5,2),(5,7),(6,8),(7,8)],9)=>([(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),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,6),(4,7),(5,1),(5,2),(6,8),(7,8)],9)=>([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,5),(1,6),(2,6),(2,7),(3,7),(4,2),(5,1),(5,4),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(4,8),(5,1),(5,2),(6,7),(8,7)],9)=>([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,6),(2,7),(3,6),(3,7),(4,2),(4,3),(5,1),(5,4),(6,8),(7,8)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,3),(5,1),(5,7),(6,2),(6,4),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,3),(5,4),(6,1),(6,5),(7,8)],9)=>([],0)
([(0,6),(1,8),(2,7),(3,5),(4,2),(5,1),(5,7),(6,3),(6,4),(7,8)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,7),(6,1),(6,3),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,3),(5,8),(6,1),(6,4),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,6),(1,8),(2,8),(3,7),(4,3),(4,8),(5,2),(5,4),(6,1),(6,5),(8,7)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,3),(5,8),(6,1),(6,2),(8,7)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,6),(4,7),(5,1),(6,8),(7,8)],9)=>([(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)
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,6),(4,8),(5,2),(6,7),(8,1)],9)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,6),(4,8),(5,2),(6,7),(8,1)],9)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(2,6),(3,7),(4,6),(4,7),(5,2),(6,8),(7,8),(8,1)],9)=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,7),(5,2),(6,1),(6,7),(7,8)],9)=>([(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),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(6,2),(6,8),(8,3)],9)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8)],9)=>([(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)
([(0,2),(0,6),(1,8),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,6),(2,8),(3,7),(4,5),(5,2),(6,4),(6,7),(7,8),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,7),(6,8),(7,8)],9)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,4),(0,6),(1,8),(3,8),(4,7),(5,3),(6,1),(6,7),(7,5),(8,2)],9)=>([(0,2),(1,2)],3)
([(0,4),(0,5),(0,6),(1,8),(2,8),(4,7),(5,2),(6,1),(6,7),(7,8),(8,3)],9)=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,2),(5,4),(6,1),(6,8),(8,5)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,2),(5,1),(5,6),(6,8),(8,7)],9)=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,3),(0,5),(1,8),(2,8),(3,7),(4,2),(4,7),(5,6),(6,1),(6,4),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,2),(0,3),(0,5),(1,8),(2,6),(3,6),(3,7),(4,1),(4,7),(5,4),(6,8),(7,8)],9)=>([(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),(0,5),(1,8),(2,8),(3,7),(4,6),(5,1),(5,7),(6,2),(6,3),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(1,8),(2,8),(3,7),(4,2),(4,7),(5,6),(6,1),(6,3),(6,4),(7,8)],9)=>([],0)
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,4),(6,1),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,6),(3,7),(4,1),(5,4),(6,8),(7,8)],9)=>([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(1,6),(2,6),(2,7),(3,7),(4,5),(5,1),(5,2),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(1,7),(2,6),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,8),(7,8)],9)=>([],0)
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,8),(4,1),(5,4),(6,2),(6,8),(8,7)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(1,8),(2,7),(3,8),(4,2),(4,8),(5,6),(6,1),(6,4),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,3),(5,8),(6,1),(6,2),(8,7)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(1,8),(2,8),(3,7),(4,3),(4,8),(5,6),(6,1),(6,2),(6,4),(8,7)],9)=>([],0)
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,3),(7,1),(7,2)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,7),(7,8)],9)=>([(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),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,1),(5,2),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,5),(5,2),(6,1),(6,4),(6,7),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(1,7),(2,8),(3,6),(4,2),(5,1),(5,4),(5,6),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,2),(5,7),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,1),(5,3),(5,8),(6,7),(8,2)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(1,8),(2,7),(3,8),(4,6),(5,1),(5,2),(5,6),(6,8),(8,7)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,4),(5,7),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(2,7),(3,8),(4,6),(5,2),(5,3),(5,6),(6,7),(7,8),(8,1)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,6),(1,8),(2,8),(4,7),(5,2),(6,1),(6,5),(6,7),(7,8),(8,3)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,1),(5,2),(5,6),(6,7),(8,7)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(4,8),(5,7),(6,1),(6,2),(6,7),(7,4),(8,3)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(0,6),(1,8),(2,8),(4,8),(5,7),(6,1),(6,2),(6,7),(7,8),(8,3)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,7),(7,5)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,8)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,2),(5,1),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,3),(5,4),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,4),(1,8),(2,8),(3,7),(4,5),(5,3),(5,6),(6,1),(6,2),(6,7),(7,8)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,5),(5,3),(6,1),(7,2),(7,4)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,7),(1,8),(2,8),(3,8),(4,3),(5,2),(6,4),(6,5),(7,1),(7,6)],9)=>([],0)
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,2),(5,4),(5,7),(6,1),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(1,7),(2,8),(3,6),(4,2),(4,6),(5,1),(5,4),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,7),(1,8),(2,8),(3,8),(4,6),(5,3),(6,2),(6,5),(7,1),(7,4)],9)=>([],0)
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,5),(5,1),(5,7),(6,2),(6,4),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,7),(1,8),(2,8),(3,5),(4,6),(5,2),(6,1),(7,3),(7,4)],9)=>([],0)
([(0,6),(1,8),(2,7),(3,2),(4,1),(5,4),(5,7),(6,3),(6,5),(7,8)],9)=>([],0)
([(0,6),(1,8),(3,7),(4,3),(5,1),(5,7),(6,4),(6,5),(7,8),(8,2)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,3),(7,8)],9)=>([(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),(0,4),(0,5),(1,8),(2,6),(2,7),(3,7),(4,6),(5,1),(5,2),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,5),(1,6),(2,6),(2,7),(3,7),(4,1),(5,2),(5,4),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,6),(1,7),(2,8),(3,7),(4,8),(5,3),(6,1),(6,2),(8,5)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(0,5),(1,6),(2,7),(3,6),(4,8),(5,1),(5,2),(6,8),(8,7)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,3),(5,4),(6,1),(6,2),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,4),(1,8),(2,7),(3,7),(4,6),(5,1),(5,3),(6,2),(6,5),(7,8)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(4,2),(4,7),(5,4),(6,1),(6,7),(7,8),(8,3)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,7),(1,8),(2,8),(4,6),(5,2),(6,5),(7,1),(7,4),(8,3)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(6,1),(6,3),(8,7)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,6),(0,7),(1,8),(2,8),(3,8),(5,3),(6,1),(7,2),(7,5),(8,4)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,7),(1,8),(2,8),(3,8),(5,3),(6,2),(6,5),(7,1),(7,6),(8,4)],9)=>([],0)
([(0,4),(0,7),(1,8),(2,8),(4,8),(5,6),(6,2),(7,1),(7,5),(8,3)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,7),(1,8),(2,8),(3,8),(5,6),(6,2),(6,3),(7,1),(7,5),(8,4)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,3),(5,1),(6,2),(6,4),(7,8)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,7),(2,8),(3,8),(4,1),(5,3),(6,4),(7,2),(7,5),(8,6)],9)=>([],0)
([(0,4),(0,6),(2,7),(3,7),(4,8),(5,3),(6,2),(6,5),(7,8),(8,1)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,7),(3,7),(4,1),(5,3),(5,4),(6,2),(6,5),(7,8)],9)=>([],0)
([(0,6),(2,8),(3,7),(4,7),(5,2),(5,4),(6,3),(6,5),(7,8),(8,1)],9)=>([],0)
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(4,7),(5,1),(5,4),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,6),(1,8),(2,8),(4,7),(5,2),(5,7),(6,1),(6,5),(7,8),(8,3)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,3),(6,1),(6,2),(8,7)],9)=>([(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)
([(0,4),(0,7),(2,8),(3,8),(4,8),(5,1),(6,5),(7,2),(7,3),(8,6)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(0,6),(1,8),(2,8),(4,8),(5,7),(6,1),(6,2),(7,3),(8,7)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,6),(0,7),(1,8),(2,8),(3,8),(5,3),(6,5),(7,1),(7,2),(8,4)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,5),(1,8),(2,8),(3,8),(5,7),(6,2),(6,3),(7,1),(7,6),(8,4)],9)=>([],0)
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,6),(1,8),(2,7),(3,7),(4,5),(5,1),(6,2),(6,4),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,6),(2,8),(3,7),(4,7),(5,2),(6,3),(6,5),(7,8),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,6),(1,8),(2,7),(3,7),(4,5),(5,1),(5,3),(6,2),(6,4),(7,8)],9)=>([],0)
([(0,3),(0,6),(1,8),(2,7),(3,8),(4,5),(5,2),(5,8),(6,1),(6,4),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,6),(1,8),(2,7),(3,8),(4,2),(5,4),(5,8),(6,1),(6,5),(8,7)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,6),(1,8),(2,7),(4,8),(5,2),(5,8),(6,1),(6,5),(7,3),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,2),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,8),(2,6),(2,8),(3,8),(4,6),(5,1),(5,2),(6,7),(8,7)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,7),(2,8),(4,7),(5,8),(6,1),(6,2),(7,3),(8,4)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,4),(0,5),(0,6),(1,8),(3,7),(4,8),(5,7),(6,1),(6,3),(7,8),(8,2)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)=>([(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),(0,4),(0,5),(1,8),(2,8),(3,6),(4,2),(4,7),(5,1),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,1),(5,3),(5,7),(6,2),(6,7),(7,4)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,2),(4,6),(5,1),(5,6),(6,7),(7,8)],9)=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(1,7),(2,8),(3,2),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,1),(4,7),(5,2),(5,7),(6,8),(7,8)],9)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,3),(4,8),(5,1),(5,8),(6,7),(8,2)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,3),(0,4),(0,5),(1,8),(2,7),(3,8),(4,1),(4,6),(5,2),(5,6),(6,8),(8,7)],9)=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(2,7),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(7,8),(8,1)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,5),(0,6),(1,8),(2,8),(4,1),(5,2),(5,7),(6,4),(6,7),(7,8),(8,3)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(0,6),(1,8),(2,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,4),(8,3)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,4),(0,5),(0,6),(1,8),(2,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,8),(8,3)],9)=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,3),(4,7),(5,2),(5,7),(6,1),(6,7),(7,8)],9)=>([(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)
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(3,7),(4,2),(4,6),(5,1),(5,7),(6,8),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(1,8),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,8),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,7),(4,1),(4,7),(5,8),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,8),(3,4),(4,2),(4,7),(5,3),(6,1),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(1,8),(2,8),(3,2),(3,7),(4,1),(4,7),(5,6),(6,3),(6,4),(7,8)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,3),(5,2),(5,7),(6,1),(6,7),(7,8)],9)=>([(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)
([(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(3,7),(4,2),(5,1),(5,6),(6,8),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(5,8),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,3),(6,1),(6,7),(7,8)],9)=>([(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)
([(0,5),(0,6),(1,7),(2,7),(3,8),(4,2),(5,3),(6,1),(6,8),(8,4)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,3),(0,4),(0,5),(1,6),(2,7),(3,8),(4,1),(5,2),(5,6),(6,8),(8,7)],9)=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,7),(4,2),(5,1),(5,6),(6,8),(7,8)],9)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,7),(3,4),(4,1),(4,7),(5,3),(6,2),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(6,3),(6,8),(8,7)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,7),(3,2),(4,3),(5,4),(6,1),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)=>([],0)
([(0,5),(1,8),(2,7),(3,2),(4,1),(4,7),(5,6),(6,3),(6,4),(7,8)],9)=>([],0)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,6),(3,7),(4,2),(5,1),(6,8),(7,8)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,7),(3,4),(4,1),(5,2),(6,3),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(0,6),(1,8),(3,7),(4,1),(5,3),(6,4),(6,7),(7,8),(8,2)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,2),(5,1),(5,6),(6,8),(7,8)],9)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(0,6),(1,8),(2,7),(4,8),(5,2),(6,1),(6,7),(7,4),(8,3)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,4),(0,5),(0,6),(1,8),(3,7),(4,8),(5,3),(6,1),(6,7),(7,8),(8,2)],9)=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,5),(5,3),(6,4),(7,1),(7,2)],9)=>([(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)
([(0,7),(1,8),(2,8),(3,4),(4,6),(5,3),(6,1),(7,2),(7,5)],9)=>([],0)
([(0,5),(1,8),(2,8),(3,8),(4,3),(5,7),(6,1),(6,2),(7,4),(7,6)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,8),(3,1),(4,3),(4,7),(5,4),(6,2),(6,7),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,5),(1,7),(2,8),(3,2),(3,6),(4,3),(5,1),(5,6),(6,8),(8,7)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(6,2),(6,3),(7,1),(7,6)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(6,1),(6,2),(7,8)],9)=>([(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),(0,6),(1,8),(2,7),(3,7),(4,5),(5,2),(6,1),(6,4),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,7),(3,7),(4,5),(5,2),(5,3),(6,1),(6,4),(7,8)],9)=>([],0)
([(0,7),(1,8),(2,8),(4,1),(5,6),(6,2),(7,4),(7,5),(8,3)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,3),(5,2),(6,1),(6,4),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,6),(1,8),(2,7),(3,7),(4,3),(5,2),(5,4),(6,1),(6,5),(7,8)],9)=>([],0)
([(0,4),(0,5),(1,7),(2,7),(3,8),(4,8),(5,3),(6,1),(6,2),(8,6)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(1,6),(2,7),(3,6),(4,1),(5,2),(5,8),(6,8),(8,7)],9)=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,3),(0,6),(0,7),(1,8),(2,8),(3,8),(4,5),(5,2),(6,4),(7,1)],9)=>([(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)
([(0,3),(0,6),(1,8),(2,8),(3,8),(4,2),(5,1),(6,7),(7,4),(7,5)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,3),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,4),(7,1),(7,5)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,2),(0,3),(0,6),(1,8),(2,8),(3,7),(4,5),(5,1),(5,7),(6,4),(7,8)],9)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,5),(5,2),(5,8),(6,4),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,4),(7,1),(7,2)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,4),(7,1),(7,2),(7,5)],9)=>([],0)
([(0,3),(0,5),(1,8),(2,8),(3,7),(4,6),(5,4),(6,1),(6,2),(6,7),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,2),(0,7),(1,8),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5)],9)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(0,6),(1,8),(2,8),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],9)=>([],0)
([(0,6),(0,7),(1,8),(2,8),(3,4),(4,1),(5,2),(6,5),(7,3)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,7),(3,1),(4,3),(4,7),(5,4),(6,2),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(0,6),(1,8),(3,7),(4,1),(4,7),(5,3),(6,4),(7,8),(8,2)],9)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
([(0,6),(1,8),(2,8),(3,7),(4,5),(5,1),(6,3),(7,2),(7,4)],9)=>([],0)
([(0,6),(1,8),(2,8),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],9)=>([],0)
([(0,5),(0,6),(1,8),(2,7),(3,2),(4,1),(4,7),(5,3),(6,4),(7,8)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,5),(1,8),(2,7),(3,4),(4,1),(4,7),(5,6),(6,2),(6,3),(7,8)],9)=>([],0)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,7),(5,1),(6,2),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,8),(3,7),(4,6),(5,1),(6,8),(7,8)],9)=>([(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)
([(0,3),(0,4),(0,5),(1,7),(2,6),(2,8),(3,8),(4,6),(5,2),(6,7),(8,1)],9)=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(2,6),(2,7),(3,7),(4,6),(5,2),(6,8),(7,8),(8,1)],9)=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,2),(6,1),(8,5)],9)=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,1),(6,8),(8,7)],9)=>([(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)
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,3),(6,1),(8,2)],9)=>([(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)
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,3),(6,1),(8,2),(8,5)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(6,7),(8,1),(8,6)],9)=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(8,7)],9)=>([(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),(0,6),(0,7),(2,8),(3,8),(4,8),(5,1),(6,3),(7,2),(8,5)],9)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,3),(5,4),(6,2),(7,1)],9)=>([(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)
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,1),(5,3),(6,7),(7,2),(7,4)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,6),(1,8),(2,8),(3,8),(4,3),(5,2),(6,7),(7,1),(7,4),(7,5)],9)=>([],0)
([(0,3),(0,5),(1,8),(2,8),(3,7),(4,2),(5,6),(6,1),(6,4),(6,7),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(1,7),(2,8),(3,6),(4,5),(5,1),(5,2),(5,6),(6,8),(8,7)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,7),(4,1),(4,7),(5,2),(6,4),(7,8)],9)=>([(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)
([(0,2),(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,6),(4,7),(5,4),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,2),(4,8),(5,1),(6,4),(8,5)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,8),(4,1),(4,6),(5,4),(6,8),(8,7)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,7),(4,1),(4,7),(5,4),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,6),(1,7),(3,7),(4,8),(5,1),(5,8),(6,5),(7,2),(8,3)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(0,6),(1,8),(3,8),(4,7),(5,1),(5,7),(6,5),(7,8),(8,2)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,6),(0,7),(1,8),(2,8),(3,5),(4,3),(5,2),(6,4),(7,1)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(6,3),(7,4),(7,5)],9)=>([],0)
([(0,2),(0,6),(1,8),(2,7),(3,5),(4,1),(5,4),(5,7),(6,3),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,4),(7,8),(8,2)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,6),(1,8),(2,8),(3,4),(4,7),(5,1),(6,3),(7,2),(7,5)],9)=>([],0)
([(0,2),(0,6),(1,8),(2,7),(3,5),(4,3),(5,1),(5,7),(6,4),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,8),(3,4),(4,1),(5,2),(6,7),(7,3),(7,5)],9)=>([],0)
([(0,2),(0,6),(1,8),(2,7),(3,4),(4,1),(5,3),(5,7),(6,5),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,6),(2,8),(3,7),(4,2),(5,4),(5,7),(6,5),(7,8),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)=>([],0)
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,7),(4,1),(5,2),(6,4),(7,8)],9)=>([(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),(0,5),(1,8),(2,7),(3,7),(4,2),(5,6),(6,1),(6,4),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,8),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(7,8)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,5),(1,8),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4),(7,8)],9)=>([],0)
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,8),(4,2),(4,8),(5,1),(6,4),(8,7)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(0,5),(1,6),(2,6),(2,7),(3,7),(4,1),(5,2),(6,8),(7,8)],9)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,3),(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(8,6)],9)=>([(0,2),(1,2)],3)
([(0,3),(0,4),(0,6),(2,7),(3,8),(4,7),(5,1),(6,2),(7,8),(8,5)],9)=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,4),(0,5),(0,6),(2,8),(3,7),(4,7),(5,2),(6,3),(7,8),(8,1)],9)=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
([(0,4),(0,6),(0,7),(1,8),(2,8),(4,8),(5,1),(6,2),(7,5),(8,3)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,4),(0,6),(1,8),(2,8),(4,8),(5,2),(6,7),(7,1),(7,5),(8,3)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,5),(0,6),(1,8),(2,8),(3,8),(5,3),(6,7),(7,1),(7,2),(8,4)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,6),(1,8),(2,8),(3,8),(5,3),(6,7),(7,1),(7,2),(7,5),(8,4)],9)=>([],0)
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,3),(5,2),(6,1),(7,8)],9)=>([(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)
([(0,6),(0,7),(1,8),(2,8),(4,5),(5,2),(6,4),(7,1),(8,3)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
([(0,6),(1,8),(2,8),(4,7),(5,2),(6,4),(7,1),(7,5),(8,3)],9)=>([],0)
([(0,6),(1,8),(2,8),(4,2),(5,1),(6,7),(7,4),(7,5),(8,3)],9)=>([],0)
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(5,3),(6,2),(7,1),(8,4)],9)=>([(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)
([(0,6),(0,7),(2,8),(3,8),(4,1),(5,4),(6,3),(7,2),(8,5)],9)=>([(0,2),(0,3),(1,2),(1,3)],4)
([(0,4),(0,5),(0,6),(2,7),(3,7),(4,8),(5,3),(6,2),(7,8),(8,1)],9)=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,7),(4,2),(5,1),(6,4),(7,8)],9)=>([(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)
([(0,4),(0,5),(1,8),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,8)],9)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
([(0,5),(1,8),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(6,4),(7,8)],9)=>([],0)
([(0,5),(2,8),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4),(7,8),(8,1)],9)=>([],0)
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,5),(5,1),(5,2),(5,7),(6,8),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(1,8),(2,8),(4,7),(5,6),(6,1),(6,2),(6,7),(7,8),(8,3)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)=>([],0)
([(0,4),(0,5),(2,7),(3,7),(4,8),(5,6),(6,2),(6,3),(7,8),(8,1)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,3),(0,5),(1,8),(2,7),(3,7),(4,1),(5,6),(6,2),(6,4),(7,8)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,4),(0,5),(2,8),(3,7),(4,7),(5,6),(6,2),(6,3),(7,8),(8,1)],9)=>([(0,4),(1,4),(2,4),(3,4)],5)
([(0,3),(0,7),(2,8),(3,8),(4,2),(5,1),(6,5),(7,4),(8,6)],9)=>([(0,3),(1,3),(2,3)],4)
([(0,3),(0,4),(0,6),(2,7),(3,8),(4,7),(5,2),(6,5),(7,8),(8,1)],9)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,7),(1,8),(3,8),(4,6),(5,4),(6,1),(7,5),(8,2)],9)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(0,6),(1,8),(2,8),(4,5),(5,7),(6,4),(7,1),(7,2),(8,3)],9)=>([],0)
([(0,6),(0,7),(1,8),(2,8),(4,2),(5,1),(6,4),(7,5),(8,3)],9)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
([(0,6),(1,8),(2,8),(4,5),(5,2),(6,7),(7,1),(7,4),(8,3)],9)=>([],0)
([(0,2),(0,3),(0,5),(1,6),(1,7),(2,7),(3,6),(4,1),(5,4),(6,8),(7,8)],9)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
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(only identities of compositions of up to three maps are shown)
Description
The zero divisor graph of a lattice.
Let $0$ be the bottom element of a lattice. A zero divisor of a lattice is an element $a\neq 0$ such that there is another element $b\neq 0$ with $a\wedge b = 0$.
Two zero divisors are adjacent in the zero divisor graph if their join is $0$.
Let $0$ be the bottom element of a lattice. A zero divisor of a lattice is an element $a\neq 0$ such that there is another element $b\neq 0$ with $a\wedge b = 0$.
Two zero divisors are adjacent in the zero divisor graph if their join is $0$.
References
[1] Lu, D., Wu, T. The zero-divisor graphs of posets and an application to semigroups MathSciNet:2729023
[2] Halaš, Radomír, Jukl, M. On Beck's coloring of posets MathSciNet:2519197
[2] Halaš, Radomír, Jukl, M. On Beck's coloring of posets MathSciNet:2519197
Sage code
def mapping(L):
z = L.bottom()
non_bottom = [a for a in L if a != z]
V = [a for a in non_bottom if any(L.meet(a, b) == z for b in non_bottom)]
return Graph([V, lambda a, b: L.meet(a, b) == z])
Weight
40
Created
Dec 01, 2025 at 16:49 by Martin Rubey
Updated
Dec 01, 2025 at 16:49 by Martin Rubey
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