Values
=>
Cc0020;cc-rep
([],1)=>0
([],2)=>0
([(0,1)],2)=>1
([],3)=>0
([(1,2)],3)=>0
([(0,2),(1,2)],3)=>1
([(0,1),(0,2),(1,2)],3)=>1
([],4)=>0
([(2,3)],4)=>0
([(1,3),(2,3)],4)=>0
([(0,3),(1,3),(2,3)],4)=>1
([(0,3),(1,2)],4)=>1
([(0,3),(1,2),(2,3)],4)=>1
([(1,2),(1,3),(2,3)],4)=>0
([(0,3),(1,2),(1,3),(2,3)],4)=>1
([(0,2),(0,3),(1,2),(1,3)],4)=>2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>1
([],5)=>0
([(3,4)],5)=>0
([(2,4),(3,4)],5)=>0
([(1,4),(2,4),(3,4)],5)=>0
([(0,4),(1,4),(2,4),(3,4)],5)=>1
([(1,4),(2,3)],5)=>0
([(1,4),(2,3),(3,4)],5)=>0
([(0,1),(2,4),(3,4)],5)=>1
([(2,3),(2,4),(3,4)],5)=>0
([(0,4),(1,4),(2,3),(3,4)],5)=>1
([(1,4),(2,3),(2,4),(3,4)],5)=>0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>1
([(1,3),(1,4),(2,3),(2,4)],5)=>1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
([(0,4),(1,3),(2,3),(2,4)],5)=>1
([(0,1),(2,3),(2,4),(3,4)],5)=>1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
([],6)=>0
([(4,5)],6)=>0
([(3,5),(4,5)],6)=>0
([(2,5),(3,5),(4,5)],6)=>0
([(1,5),(2,5),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>1
([(2,5),(3,4)],6)=>0
([(2,5),(3,4),(4,5)],6)=>0
([(1,2),(3,5),(4,5)],6)=>0
([(3,4),(3,5),(4,5)],6)=>0
([(1,5),(2,5),(3,4),(4,5)],6)=>0
([(0,1),(2,5),(3,5),(4,5)],6)=>1
([(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(2,4),(2,5),(3,4),(3,5)],6)=>0
([(0,5),(1,5),(2,4),(3,4)],6)=>1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,4),(2,3)],6)=>1
([(1,5),(2,4),(3,4),(3,5)],6)=>0
([(0,1),(2,5),(3,4),(4,5)],6)=>1
([(1,2),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>0
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>4
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>5
([(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)=>1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>1
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([],7)=>0
([(5,6)],7)=>0
([(4,6),(5,6)],7)=>0
([(3,6),(4,6),(5,6)],7)=>0
([(2,6),(3,6),(4,6),(5,6)],7)=>0
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>1
([(3,6),(4,5)],7)=>0
([(3,6),(4,5),(5,6)],7)=>0
([(2,3),(4,6),(5,6)],7)=>0
([(4,5),(4,6),(5,6)],7)=>0
([(2,6),(3,6),(4,5),(5,6)],7)=>0
([(1,2),(3,6),(4,6),(5,6)],7)=>0
([(3,6),(4,5),(4,6),(5,6)],7)=>0
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>0
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(3,5),(3,6),(4,5),(4,6)],7)=>0
([(1,6),(2,6),(3,5),(4,5)],7)=>0
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>0
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>0
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>0
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>2
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>3
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>3
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>4
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>5
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,6),(2,5),(3,4)],7)=>0
([(2,6),(3,5),(4,5),(4,6)],7)=>0
([(1,2),(3,6),(4,5),(5,6)],7)=>0
([(0,3),(1,2),(4,6),(5,6)],7)=>1
([(2,3),(4,5),(4,6),(5,6)],7)=>0
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>0
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>0
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>0
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>0
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>2
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)=>2
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>1
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>0
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>0
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>0
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)=>0
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>0
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>2
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>0
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)=>1
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>1
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>1
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>1
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)=>2
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>3
([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>3
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)=>2
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)=>3
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>4
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>4
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(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)=>1
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>0
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>3
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>0
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7)=>2
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>0
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)=>2
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>0
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>0
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>2
([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>3
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>0
([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>0
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)=>2
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)=>1
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)=>1
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)=>2
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)=>3
([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7)=>1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>3
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>4
([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>3
([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)=>3
([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>4
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>4
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>5
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(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)=>1
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(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)=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>5
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>5
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>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
([(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)=>1
([(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)=>1
([(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)=>1
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(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)=>1
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>7
([(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)=>1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)=>1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)=>1
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>2
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)=>1
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>2
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)=>1
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)=>1
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>1
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)=>0
([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>0
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>0
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)=>1
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>1
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>3
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(1,5),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)=>0
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>0
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,3),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)=>1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>1
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,2),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)=>2
([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>3
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7)=>3
([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>1
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>3
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>4
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>0
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(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)=>1
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>3
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>4
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>4
([(0,1),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,4),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>1
([(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,6),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7)=>1
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7)=>1
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7)=>1
([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>1
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>1
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(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)=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)=>5
([(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)=>1
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(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)=>1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>1
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>1
([(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
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(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)=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(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)=>1
([(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)=>1
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)=>4
([(0,4),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(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
([(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)=>1
([(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)=>1
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(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)=>1
([(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)=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(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)=>1
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)=>0
([(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)=>1
([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>1
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(1,2),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,6),(1,2),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>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)=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>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)=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(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
([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The competition number of a graph.
The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x, v)$ and $(y, v)$ are arcs of $D$. For any graph, $G$ together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number $k(G)$ is the smallest number of such isolated vertices.
The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x, v)$ and $(y, v)$ are arcs of $D$. For any graph, $G$ together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number $k(G)$ is the smallest number of such isolated vertices.
References
[1] Kim, S.-R., Yeun Lee, J., Park, B., Sano, Y. The competition number of a graph and the dimension of its hole space arXiv:1103.1028
[2] Kim, S.-R., Roberts, F. S. Competition numbers of graphs with a small number of triangles MathSciNet:1475823
[3] Li, B.-J., Chang, G. J. Competition numbers of complete $r$-partite graphs MathSciNet:2954768
[2] Kim, S.-R., Roberts, F. S. Competition numbers of graphs with a small number of triangles MathSciNet:1475823
[3] Li, B.-J., Chang, G. J. Competition numbers of complete $r$-partite graphs MathSciNet:2954768
Code
N_vertices = 7 # 8 takes a long time (perhaps an hour)
def is_complete_tripartite(G):
"""
Return n1 <= n2 <= n3 or False.
"""
deg = G.degree()
degs = set(deg)
if len(degs) > 3:
return False
elif len(degs) == 3:
n1, n2, n3 = [deg.count(d) for d in degs]
if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])):
return tuple(sorted((n1, n2, n3)))
elif len(degs) == 2:
N1, N2 = [deg.count(d) for d in sorted(degs)]
n1 = N1
n2 = n3 = N2 // 2
if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])):
return tuple(sorted((n1, n2, n3)))
n1 = N2
n2 = n3 = N1 // 2
if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])):
return tuple(sorted((n1, n2, n3)))
elif len(degs) == 1:
n1 = n2 = n3 = G.num_verts() // 3
if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])):
return tuple(sorted((n1, n2, n3)))
return False
def competition_graph(D):
"""
Return the competition graph of a DAG.
"""
n = D.num_verts()
G = Graph(n)
for i in range(1,n):
for j in range(i):
if set(D.neighbors_out(i)).intersection(D.neighbors_out(j)):
G.add_edge(i,j)
return G.canonical_label().copy(immutable=True)
@cached_function
def competition_graphs(n):
"""
sage: [len(competition_graphs(n)) for n in range(8)]
[1, 1, 1, 2, 4, 10, 29, 116]
"""
return set(competition_graph(D) for D in digraphs(n, property = lambda g: g.is_directed_acyclic()))
def competition_number_naive(G, N):
"""
sage: [(G, competition_number_brute(G, N_vertices-G.num_verts())) for n in range(1, 6) for G in graphs(n)]
"""
n = G.num_verts()
H = G.copy()
if H.canonical_label().copy(immutable=True) in competition_graphs(H.num_verts()):
return 0
for i in range(1, N):
H.add_vertex()
if H.canonical_label().copy(immutable=True) in competition_graphs(H.num_verts()):
return i
def statistic(G):
"""special cases due to
* [1] Suh-Ryung Kim, Fred S. Roberts, "Competition numbers of graphs with a small number of triangles", DISCRETE APPLIED MATHEMATICS 153-162
* [2] Suh-Ryung Kim, Yoshio Sano, Discrete Applied Mathematics, Volume 156, Issue 18, 28 November 2008, The competition numbers of complete tripartite graphs
* [3] Li, Bo-Jr, and Gerard J. Chang. "Competition numbers of complete r-partite graphs." Discrete Applied Mathematics 160.15 (2012): 2271-2276.
"""
k = competition_number_naive(G, N_vertices-G.num_verts())
if k is not None:
return k
if G.is_chordal() and min(G.degree()) > 0:
# [2]
return 1
if not G.is_connected():
return
n = G.num_verts()
# [3], Theorem 5
N = is_complete_tripartite(G)
if N:
n1, n2, n3 = N
if n2 >= n3 + 2:
return n1*n2 - n + 2
elif n2 == n3 + 1 or n2 == n3 == 1:
return n1*n2 - n + 3
elif n2 == n3 >= 2:
return n1*n2 - n + 4
t = G.triangles_count()
if t == 0:
# [1]
return G.num_edges() - G.num_verts() + 2
if t == 1:
# [1]
if G.is_even_hole_free() and G.is_odd_hole_free():
return G.num_edges() - G.num_verts() + 1
return
Created
Oct 12, 2018 at 07:59 by Martin Rubey
Updated
Dec 29, 2018 at 22:55 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!