Values
([],1) => -1
([],2) => -2
([(0,1)],2) => -1
([],3) => -3
([(1,2)],3) => -2
([(0,1),(0,2)],3) => -1
([(0,2),(2,1)],3) => -1
([(0,2),(1,2)],3) => -1
([],4) => -4
([(2,3)],4) => -3
([(1,2),(1,3)],4) => -2
([(0,1),(0,2),(0,3)],4) => -1
([(0,2),(0,3),(3,1)],4) => -1
([(0,1),(0,2),(1,3),(2,3)],4) => -1
([(1,2),(2,3)],4) => -2
([(0,3),(3,1),(3,2)],4) => -1
([(1,3),(2,3)],4) => -2
([(0,3),(1,3),(3,2)],4) => -1
([(0,3),(1,3),(2,3)],4) => -1
([(0,3),(1,2)],4) => -2
([(0,3),(1,2),(1,3)],4) => -1
([(0,2),(0,3),(1,2),(1,3)],4) => 0
([(0,3),(2,1),(3,2)],4) => -1
([(0,3),(1,2),(2,3)],4) => -1
([],5) => -5
([(3,4)],5) => -4
([(2,3),(2,4)],5) => -3
([(1,2),(1,3),(1,4)],5) => -2
([(0,1),(0,2),(0,3),(0,4)],5) => -1
([(0,2),(0,3),(0,4),(4,1)],5) => -1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => -1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => -1
([(1,3),(1,4),(4,2)],5) => -2
([(0,3),(0,4),(4,1),(4,2)],5) => -1
([(1,2),(1,3),(2,4),(3,4)],5) => -2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => -1
([(0,3),(0,4),(3,2),(4,1)],5) => -1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => -1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => -1
([(2,3),(3,4)],5) => -3
([(1,4),(4,2),(4,3)],5) => -2
([(0,4),(4,1),(4,2),(4,3)],5) => -1
([(2,4),(3,4)],5) => -3
([(1,4),(2,4),(4,3)],5) => -2
([(0,4),(1,4),(4,2),(4,3)],5) => -1
([(1,4),(2,4),(3,4)],5) => -2
([(0,4),(1,4),(2,4),(4,3)],5) => -1
([(0,4),(1,4),(2,4),(3,4)],5) => -1
([(0,4),(1,4),(2,3)],5) => -2
([(0,4),(1,3),(2,3),(2,4)],5) => -1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 1
([(0,4),(1,4),(2,3),(4,2)],5) => -1
([(0,4),(1,3),(2,3),(3,4)],5) => -1
([(0,4),(1,4),(2,3),(2,4)],5) => -1
([(0,4),(1,4),(2,3),(3,4)],5) => -1
([(1,4),(2,3)],5) => -3
([(1,4),(2,3),(2,4)],5) => -2
([(0,4),(1,2),(1,4),(2,3)],5) => -1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => -1
([(1,3),(1,4),(2,3),(2,4)],5) => -1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 0
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => -1
([(0,4),(1,2),(1,4),(4,3)],5) => -1
([(0,4),(1,2),(1,3)],5) => -2
([(0,4),(1,2),(1,3),(1,4)],5) => -1
([(0,2),(0,4),(3,1),(4,3)],5) => -1
([(0,4),(1,2),(1,3),(3,4)],5) => -1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => -1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => -1
([(0,3),(0,4),(1,2),(1,4)],5) => -1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 0
([(0,3),(1,2),(1,4),(3,4)],5) => -1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 0
([(1,4),(3,2),(4,3)],5) => -2
([(0,3),(3,4),(4,1),(4,2)],5) => -1
([(1,4),(2,3),(3,4)],5) => -2
([(0,4),(1,2),(2,4),(4,3)],5) => -1
([(0,3),(1,4),(4,2)],5) => -2
([(0,4),(3,2),(4,1),(4,3)],5) => -1
([(0,4),(1,2),(2,3),(2,4)],5) => -1
([(0,4),(2,3),(3,1),(4,2)],5) => -1
([(0,3),(1,2),(2,4),(3,4)],5) => -1
([(0,4),(1,2),(2,3),(3,4)],5) => -1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => -1
([],6) => -6
([(4,5)],6) => -5
([(3,4),(3,5)],6) => -4
([(2,3),(2,4),(2,5)],6) => -3
([(1,2),(1,3),(1,4),(1,5)],6) => -2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => -1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => -1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => -1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => -1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => -1
([(1,3),(1,4),(1,5),(5,2)],6) => -2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => -1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => -2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => -2
>>> Load all 1200 entries. <<<([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => -1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => -1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => -1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => -1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => -1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => -1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => -1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => -1
([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => -1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => -1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => -1
([(2,3),(2,4),(4,5)],6) => -3
([(1,4),(1,5),(5,2),(5,3)],6) => -2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => -1
([(2,3),(2,4),(3,5),(4,5)],6) => -3
([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => -2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => -1
([(1,4),(1,5),(4,3),(5,2)],6) => -2
([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => -2
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => -2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => -1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => -1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => -1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => -1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => -1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => -1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => -1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => -1
([(3,4),(4,5)],6) => -4
([(2,3),(3,4),(3,5)],6) => -3
([(1,5),(5,2),(5,3),(5,4)],6) => -2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => -1
([(2,3),(3,5),(5,4)],6) => -3
([(1,4),(4,5),(5,2),(5,3)],6) => -2
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => -1
([(3,5),(4,5)],6) => -4
([(2,5),(3,5),(5,4)],6) => -3
([(1,5),(2,5),(5,3),(5,4)],6) => -2
([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => -1
([(2,5),(3,5),(4,5)],6) => -3
([(1,5),(2,5),(3,5),(5,4)],6) => -2
([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => -1
([(1,5),(2,5),(3,5),(4,5)],6) => -2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => -1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => -1
([(0,5),(1,5),(2,5),(3,4)],6) => -2
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => -1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => -1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => -1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => -1
([(1,5),(2,5),(3,4)],6) => -3
([(1,5),(2,4),(3,4),(3,5)],6) => -2
([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => -1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => -1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => -1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) => 0
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => -1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => -1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 0
([(1,5),(2,5),(3,4),(5,3)],6) => -2
([(1,5),(2,4),(3,4),(4,5)],6) => -2
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => -1
([(0,5),(1,5),(2,3),(5,4)],6) => -2
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => -1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6) => -1
([(1,5),(2,5),(3,4),(3,5)],6) => -2
([(0,5),(1,5),(2,3),(2,5),(5,4)],6) => -1
([(0,5),(1,5),(2,3),(2,5),(3,4)],6) => -1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => -1
([(0,5),(1,5),(2,3),(2,4)],6) => -2
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => -1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6) => -1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => -1
([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => -1
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => -1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => -1
([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => -1
([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => -1
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => -1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => -1
([(1,5),(2,5),(3,4),(4,5)],6) => -2
([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => -1
([(0,5),(1,5),(2,3),(3,4)],6) => -2
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => -1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => -1
([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => -1
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => -1
([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => -1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => -1
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => -1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => -1
([(0,5),(1,5),(2,4),(3,4)],6) => -2
([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => -1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => -1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => -1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => -1
([(2,5),(3,4)],6) => -4
([(2,5),(3,4),(3,5)],6) => -3
([(1,5),(2,3),(2,5),(3,4)],6) => -2
([(0,5),(1,4),(1,5),(4,2),(4,3)],6) => -1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => -1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => -1
([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => -2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => -1
([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => -1
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => -1
([(2,4),(2,5),(3,4),(3,5)],6) => -2
([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => -1
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 0
([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => -2
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => 0
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => -1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => -2
([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => -1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 0
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => -1
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => -1
([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => -1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 0
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 1
([(1,5),(2,3),(2,5),(5,4)],6) => -2
([(0,5),(1,2),(1,5),(5,3),(5,4)],6) => -1
([(1,5),(2,3),(2,4)],6) => -3
([(1,5),(2,3),(2,4),(2,5)],6) => -2
([(0,5),(1,3),(1,4),(1,5),(4,2)],6) => -1
([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => -1
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => -1
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => -1
([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => -1
([(0,5),(1,2),(1,3),(1,4)],6) => -2
([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => -1
([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => -1
([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => -1
([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => -1
([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => -1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => -1
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => -1
([(0,4),(1,2),(1,3),(1,5),(4,5)],6) => -1
([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) => 0
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 1
([(1,3),(1,5),(4,2),(5,4)],6) => -2
([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => -1
([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => -1
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => -1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => -1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => -1
([(1,5),(2,3),(2,4),(4,5)],6) => -2
([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => -1
([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => -2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => -1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => -2
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => -1
([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => -1
([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => -1
([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => -1
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => -1
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => -1
([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => -1
([(0,4),(1,3),(1,5),(5,2)],6) => -2
([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => -1
([(0,5),(1,3),(1,4),(4,2),(4,5)],6) => -1
([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => -1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => -1
([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => -2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => -1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => -1
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => -1
([(1,4),(1,5),(2,3),(2,5)],6) => -2
([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => -1
([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 0
([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) => -1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => -1
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => 0
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => -1
([(0,4),(0,5),(1,3),(1,5),(5,2)],6) => -1
([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => -1
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => 0
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => 0
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => -1
([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => -1
([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => -1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) => 0
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 0
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => 0
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => -1
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3)],6) => -2
([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => -1
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 0
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 1
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 1
([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) => 0
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 1
([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => -1
([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 0
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => -1
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => -1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => -1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => 0
([(1,4),(2,3),(2,5),(4,5)],6) => -2
([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => -1
([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => -1
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 0
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => -1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => -1
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => -1
([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,3),(1,4),(5,2)],6) => -2
([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => -1
([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => -1
([(0,4),(1,3),(1,5),(4,2),(4,5)],6) => -1
([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) => 0
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => 0
([(2,5),(3,4),(4,5)],6) => -3
([(1,5),(2,3),(3,5),(5,4)],6) => -2
([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => -1
([(1,3),(2,4),(4,5)],6) => -3
([(1,5),(4,3),(5,2),(5,4)],6) => -2
([(1,5),(2,3),(3,4),(3,5)],6) => -2
([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => -1
([(0,4),(1,5),(5,2),(5,3)],6) => -2
([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => -1
([(0,5),(1,4),(4,2),(4,3),(4,5)],6) => -1
([(1,5),(3,4),(4,2),(5,3)],6) => -2
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => -1
([(1,4),(2,3),(3,5),(4,5)],6) => -2
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => -1
([(0,5),(1,4),(4,2),(5,3)],6) => -2
([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => -1
([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => -1
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(1,5),(2,3),(3,4),(4,5)],6) => -2
([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => -2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => -1
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => -1
([(0,5),(1,4),(2,3)],6) => -3
([(0,5),(1,3),(2,4),(2,5)],6) => -2
([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => -1
([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => -1
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => -1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => -1
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => -1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => -1
([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => -1
([(0,5),(1,4),(2,3),(2,4),(4,5)],6) => -1
([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => -1
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => 1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 0
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 0
([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => -1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 0
([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => -1
([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 0
([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => -1
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 0
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => -1
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => -1
([(0,5),(1,4),(2,3),(2,5),(4,5)],6) => -1
([(0,5),(1,3),(4,2),(5,4)],6) => -2
([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => -1
([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => -1
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => -1
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => -1
([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => -1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => -1
([(0,5),(1,3),(2,4),(4,5)],6) => -2
([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => -1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => -1
([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => -1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => -1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => -1
([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => -1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => -1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => -1
([],7) => -7
([(5,6)],7) => -6
([(4,5),(4,6)],7) => -5
([(3,4),(3,5),(3,6)],7) => -4
([(2,3),(2,4),(2,5),(2,6)],7) => -3
([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => -2
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => -1
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => -1
([(1,3),(1,4),(1,5),(1,6),(6,2)],7) => -2
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => -1
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => -2
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => -2
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => -2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => -1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7) => -1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => -1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7) => -1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7) => -1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7) => -1
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => -1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7) => -1
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(2,4),(2,5),(2,6),(6,3)],7) => -3
([(1,4),(1,5),(1,6),(6,2),(6,3)],7) => -2
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => -1
([(2,3),(2,4),(2,5),(4,6),(5,6)],7) => -3
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => -3
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => -2
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => -1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => -2
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => -2
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -2
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -2
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => -1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => -1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7) => -1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => -1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7) => -1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => -2
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6),(6,2)],7) => -1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7) => -1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7) => -1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7) => -1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) => -2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => -1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7) => -1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7) => -1
([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => -2
([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7) => -1
([(1,4),(1,5),(1,6),(5,3),(6,2)],7) => -2
([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => -2
([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7) => -2
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1)],7) => -1
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7) => -1
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => -1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => -1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => -1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => -1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7) => -1
([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => -1
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7) => -1
([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7) => -1
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => -1
([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => -1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => -1
([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7) => -1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(4,6)],7) => -1
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7) => -1
([(0,1),(0,2),(0,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => -1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => -1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => -1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => -1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => -1
([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => -1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => -1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => -1
([(0,3),(0,4),(0,5),(3,6),(4,2),(4,6),(5,1),(5,6)],7) => -1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => -1
([(3,4),(3,5),(5,6)],7) => -4
([(2,5),(2,6),(6,3),(6,4)],7) => -3
([(1,5),(1,6),(6,2),(6,3),(6,4)],7) => -2
([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => -1
([(3,4),(3,5),(4,6),(5,6)],7) => -4
([(2,3),(2,4),(3,6),(4,6),(6,5)],7) => -3
([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7) => -2
([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7) => -1
([(2,5),(2,6),(5,4),(6,3)],7) => -3
([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => -3
([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => -3
([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7) => -2
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7) => -1
([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => -2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => -1
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => -1
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => -1
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => -1
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7) => -2
([(0,4),(0,5),(4,6),(5,1),(5,6),(6,2),(6,3)],7) => -1
([(1,5),(1,6),(5,4),(6,2),(6,3)],7) => -2
([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7) => -2
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,6),(6,3)],7) => -1
([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => -1
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7) => -1
([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7) => -2
([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7) => -2
([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => -2
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7) => -1
([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => -1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => -1
([(0,3),(0,4),(3,5),(3,6),(4,2),(4,5),(4,6),(6,1)],7) => -1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(0,4),(0,5),(4,2),(4,6),(5,1),(5,6),(6,3)],7) => -1
([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7) => -1
([(0,4),(0,5),(4,3),(4,6),(5,1),(5,2),(5,6)],7) => -1
([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7) => -1
([(0,3),(0,4),(3,2),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => -1
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7) => -1
([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => -1
([(2,3),(2,4),(3,5),(4,6),(5,6)],7) => -3
([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) => -2
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => -1
([(4,5),(5,6)],7) => -5
([(3,4),(4,5),(4,6)],7) => -4
([(2,6),(6,3),(6,4),(6,5)],7) => -3
([(1,6),(6,2),(6,3),(6,4),(6,5)],7) => -2
([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => -1
([(3,4),(4,6),(6,5)],7) => -4
([(2,5),(5,6),(6,3),(6,4)],7) => -3
([(1,5),(5,6),(6,2),(6,3),(6,4)],7) => -2
([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => -1
([(4,6),(5,6)],7) => -5
([(3,6),(4,6),(6,5)],7) => -4
([(2,6),(3,6),(6,4),(6,5)],7) => -3
([(1,6),(2,6),(6,3),(6,4),(6,5)],7) => -2
([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7) => -1
([(3,6),(4,6),(5,6)],7) => -4
([(2,6),(3,6),(4,6),(6,5)],7) => -3
([(1,6),(2,6),(3,6),(6,4),(6,5)],7) => -2
([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7) => -1
([(2,6),(3,6),(4,6),(5,6)],7) => -3
([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => -2
([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7) => -1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => -2
([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => -1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => -1
([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => -2
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => -1
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => -1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7) => -1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => -1
([(1,6),(2,6),(3,6),(4,5)],7) => -3
([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => -2
([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => -2
([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => -2
([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7) => -1
([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7) => -1
([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => -2
([(0,6),(1,6),(2,6),(3,4),(3,6),(6,5)],7) => -1
([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5)],7) => -1
([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
([(0,6),(1,6),(2,6),(3,4),(3,5)],7) => -2
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => -1
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,5)],7) => -1
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 0
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => -1
([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => -1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => -2
([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => -1
([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => -2
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => -1
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => -1
([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => -1
([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7) => -1
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => -1
([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => -1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => -1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => -1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => -2
([(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) => 0
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => -1
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => -1
([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => -1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => -1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => -1
([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => -1
([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => -1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => -1
([(2,6),(3,6),(4,5)],7) => -4
([(2,6),(3,5),(4,5),(4,6)],7) => -3
([(1,6),(2,5),(3,5),(3,6),(6,4)],7) => -2
([(0,6),(1,5),(2,5),(2,6),(6,3),(6,4)],7) => -1
([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => -2
([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => -1
([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7) => -1
([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => -1
([(0,6),(1,5),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => -1
([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -2
([(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => -1
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4)],7) => 0
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,4)],7) => -1
([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => -2
([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -2
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 0
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => -1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 1
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => -2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => -3
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7) => -1
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 2
([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => -1
([(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 0
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => -1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7) => 0
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => -1
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3),(6,5)],7) => -1
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 0
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,5),(6,3)],7) => -1
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 0
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(6,5)],7) => 0
([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 0
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(6,4)],7) => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 0
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 1
([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 0
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 0
([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => -2
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7) => -1
([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7) => -1
([(0,6),(1,4),(2,5),(3,4),(3,5),(5,6)],7) => -1
([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => -1
([(0,6),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6)],7) => -1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 0
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 1
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 1
([(0,6),(1,5),(1,6),(2,4),(3,4),(3,6),(4,5)],7) => 0
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 0
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 0
([(0,6),(1,5),(2,5),(2,6),(3,4),(4,6)],7) => -1
([(0,6),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 0
([(2,6),(3,6),(4,5),(6,4)],7) => -3
([(2,6),(3,5),(4,5),(5,6)],7) => -3
([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => -2
([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7) => -1
([(1,6),(2,6),(3,4),(6,5)],7) => -3
([(1,6),(2,6),(4,5),(6,3),(6,4)],7) => -2
([(1,6),(2,6),(3,5),(6,4),(6,5)],7) => -2
([(0,6),(1,5),(2,5),(5,3),(5,6),(6,4)],7) => -1
([(0,6),(1,6),(2,3),(6,4),(6,5)],7) => -2
([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7) => -1
([(0,6),(1,6),(2,5),(6,3),(6,4),(6,5)],7) => -1
([(2,6),(3,6),(4,5),(4,6)],7) => -3
([(1,6),(2,6),(3,4),(3,6),(6,5)],7) => -2
([(0,6),(1,6),(2,3),(2,6),(6,4),(6,5)],7) => -1
([(1,6),(2,6),(3,4),(3,6),(4,5)],7) => -2
([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -2
([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7) => -1
([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => -1
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5)],7) => -1
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,5)],7) => -1
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => -1
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7) => -1
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) => -1
([(0,6),(1,6),(2,3),(2,6),(3,4),(4,5),(6,5)],7) => -1
([(1,6),(2,6),(3,4),(3,5)],7) => -3
([(1,6),(2,6),(3,4),(3,5),(6,3)],7) => -2
([(1,5),(2,5),(3,4),(3,6),(5,6)],7) => -2
([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => 0
([(0,5),(1,5),(2,4),(2,6),(5,6),(6,3)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(6,5)],7) => -2
([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7) => -1
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,5)],7) => -1
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 0
([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => -2
([(0,6),(1,6),(2,3),(2,4),(2,6),(6,5)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => -1
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(2,5)],7) => -2
([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7) => -1
([(0,5),(1,5),(2,3),(2,4),(2,6),(5,6)],7) => -1
([(0,4),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7) => 0
([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 1
([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => -1
([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7) => -1
([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7) => -1
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,2),(5,1)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7) => -1
([(0,6),(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => -1
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7) => -1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => -1
([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => -1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => -1
([(1,6),(2,6),(3,4),(3,5),(5,6)],7) => -2
([(0,6),(1,6),(2,3),(2,4),(4,6),(6,5)],7) => -1
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => -2
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => -2
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => -1
([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7) => -1
([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 0
([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => -1
([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => -1
([(0,5),(1,5),(2,3),(2,4),(4,6),(5,6)],7) => -1
([(0,6),(1,3),(1,5),(4,6),(5,2),(5,4)],7) => -1
([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => -1
([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => -1
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => -1
([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7) => -1
([(0,4),(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3)],7) => -1
([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7) => -1
([(0,6),(1,3),(1,4),(2,6),(3,5),(3,6),(4,2),(4,5)],7) => -1
([(0,4),(0,5),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => -1
([(0,3),(0,4),(1,5),(2,5),(3,2),(3,6),(4,1),(4,6)],7) => -1
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => -1
([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7) => -1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => -1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6)],7) => -1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => -1
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => -1
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => -1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7) => -1
([(0,6),(1,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7) => -1
([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => -1
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => -1
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => -1
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => -2
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => -1
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(4,6)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7) => -1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => -1
([(0,6),(1,6),(2,3),(2,4),(4,5),(5,6)],7) => -1
([(0,6),(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7) => -1
([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => -1
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7) => -1
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => -1
([(2,6),(3,6),(4,5),(5,6)],7) => -3
([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => -2
([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7) => -1
([(1,6),(2,6),(3,4),(4,5)],7) => -3
([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => -2
([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => -2
([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => -1
([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => -2
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => -1
([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7) => -1
([(1,6),(2,6),(3,4),(4,5),(4,6)],7) => -2
([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7) => -1
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7) => -1
([(0,6),(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7) => -1
([(0,3),(1,6),(2,6),(3,4),(3,5)],7) => -2
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => -1
([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7) => -1
([(0,4),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7) => -1
([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => -1
([(0,3),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => -1
([(0,3),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => -1
([(0,6),(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => -1
([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => -1
([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => -1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => -1
([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => -2
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => -1
([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => -2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => -1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => -2
([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => -1
([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => -2
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => -1
([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => -1
([(0,6),(1,4),(3,6),(4,5),(5,2),(5,3)],7) => -1
([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => -1
([(0,3),(1,6),(2,6),(3,5),(5,4),(5,6)],7) => -1
([(1,6),(2,6),(3,5),(4,5)],7) => -3
([(1,6),(2,6),(3,5),(4,5),(4,6)],7) => -2
([(0,6),(1,6),(2,5),(3,5),(3,6),(5,4)],7) => -1
([(0,6),(1,6),(2,4),(3,4),(3,6),(4,5),(6,5)],7) => -1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 0
([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 0
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 0
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => -1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => -1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 1
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => -1
([(0,6),(1,6),(2,5),(3,5),(3,6),(6,4)],7) => -1
([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => -2
([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => -2
([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => -1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => -1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => -2
([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => -1
([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => -2
([(0,6),(1,5),(2,5),(4,6),(5,3),(5,4)],7) => -1
([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7) => -1
([(0,6),(1,6),(2,5),(3,5),(5,4),(5,6)],7) => -1
([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => -1
([(0,6),(1,6),(2,5),(3,4)],7) => -3
([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => -2
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(6,3),(6,5)],7) => -1
([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => -2
([(0,4),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => -1
([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => -1
([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(3,6)],7) => -2
([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(3,6),(6,5)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5)],7) => -1
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7) => -1
([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => -1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 0
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7) => -1
([(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 0
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 0
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 0
([(0,6),(1,6),(2,5),(3,4),(3,6),(5,6)],7) => -1
([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5)],7) => -1
([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 0
([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => -2
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7) => -1
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 0
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 1
([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7) => 0
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 0
([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7) => -1
([(0,4),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => -1
([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 0
([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7) => -1
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => -1
([(0,5),(1,5),(2,4),(2,6),(3,6),(5,3),(5,4)],7) => 0
([(0,6),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6)],7) => -1
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) => -1
([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7) => -1
([(0,5),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6)],7) => 1
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(4,6)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 2
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 5
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7) => 1
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3)],7) => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7) => 0
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => -1
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,6),(5,6)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 0
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 1
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(5,3)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7) => 0
([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => -1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 0
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => -1
([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => -1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => -1
([(0,6),(1,5),(2,3),(2,5),(4,6),(5,4)],7) => -1
([(0,6),(1,2),(1,6),(3,5),(4,5),(6,3),(6,4)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(3,5),(5,6)],7) => -1
([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => -2
([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => -1
([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => -2
([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => -1
([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => -1
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => -1
([(0,5),(1,5),(2,4),(3,6),(4,6),(5,3),(5,4)],7) => -1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6)],7) => -1
([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => -1
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => -1
([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => -1
([(3,6),(4,5)],7) => -5
([(3,6),(4,5),(4,6)],7) => -4
([(2,6),(3,4),(3,6),(4,5)],7) => -3
([(1,6),(2,3),(2,6),(3,4),(3,5)],7) => -2
([(0,6),(1,5),(1,6),(5,2),(5,3),(5,4)],7) => -1
([(0,6),(1,4),(1,6),(4,2),(4,3),(4,5),(6,5)],7) => -1
([(0,6),(1,3),(1,6),(3,2),(3,4),(3,5),(6,4),(6,5)],7) => -1
([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => -1
([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => -2
([(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => -2
([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) => -1
([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7) => -1
([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7) => -1
([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7) => -1
([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => -3
([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) => -2
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => -1
([(1,6),(2,3),(2,6),(3,5),(6,4)],7) => -2
([(1,5),(2,3),(2,5),(3,6),(5,4),(5,6)],7) => -2
([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7) => -1
([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7) => -1
([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => -2
([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => -2
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => -1
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) => -1
([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => -1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) => -1
([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7) => -1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) => -1
([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) => -1
([(3,5),(3,6),(4,5),(4,6)],7) => -3
([(2,5),(2,6),(3,5),(3,6),(6,4)],7) => -2
([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 0
([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => -3
([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => -2
([(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => -1
([(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => -2
([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => -3
([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => -2
([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => -3
([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => -2
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => -1
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 0
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => -1
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 0
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => -1
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 0
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3)],7) => 1
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 0
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => -1
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => 0
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 1
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(6,3)],7) => 0
([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => -2
([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => -2
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) => -1
([(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => -1
([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => -2
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => -2
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => -1
([(0,5),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 0
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,3),(5,6)],7) => -1
([(0,6),(1,4),(1,5),(2,4),(2,5),(5,6),(6,3)],7) => 0
([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,4),(6,3)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7) => -1
([(0,5),(1,4),(1,6),(2,4),(2,6),(6,3),(6,5)],7) => 0
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,6),(5,6)],7) => -2
([(0,4),(1,5),(1,6),(2,5),(2,6),(5,3),(6,3),(6,4)],7) => -1
([(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => -2
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(6,4)],7) => 0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 0
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 1
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3)],7) => 1
([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(5,4)],7) => 0
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(4,5),(6,5)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(5,3),(5,4)],7) => 1
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 0
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(5,4),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7) => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => -1
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => 0
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(6,5)],7) => 0
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5)],7) => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,6),(4,6),(5,6)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => -2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(5,6)],7) => 0
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7) => -1
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 1
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 0
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6)],7) => 0
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(4,5)],7) => 1
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 1
([(0,5),(0,6),(1,2),(1,4),(3,5),(3,6),(4,3)],7) => 0
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7) => -1
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => 0
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 1
([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => 0
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => -1
([(0,5),(0,6),(1,2),(1,4),(2,6),(3,5),(3,6),(4,3)],7) => 0
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,6),(4,1),(4,2)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,6)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1
([(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(6,4)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7) => 0
([(0,4),(0,6),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => -1
([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => -1
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(5,6)],7) => 0
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7) => -1
([(0,5),(0,6),(1,4),(3,5),(3,6),(4,2),(4,3)],7) => 0
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6)],7) => 0
([(0,4),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(4,5)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => 0
([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 0
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => -1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) => 1
([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 0
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => -1
([(2,6),(3,4),(3,6),(6,5)],7) => -3
([(1,6),(2,3),(2,6),(6,4),(6,5)],7) => -2
([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7) => -1
([(2,6),(3,4),(3,5)],7) => -4
([(2,6),(3,4),(3,5),(3,6)],7) => -3
([(1,6),(2,3),(2,4),(2,6),(4,5)],7) => -2
([(0,6),(1,4),(1,5),(1,6),(5,2),(5,3)],7) => -1
([(0,6),(1,3),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => -1
([(0,6),(1,2),(1,3),(1,6),(3,4),(3,5),(6,4),(6,5)],7) => -1
([(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => -2
([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7) => -1
([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7) => -1
([(0,6),(1,3),(1,4),(1,6),(4,5),(6,2),(6,5)],7) => -1
([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => -2
([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => -2
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) => -1
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,5),(6,2)],7) => -1
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,4),(5,6)],7) => -1
([(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(6,2)],7) => -1
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(5,4),(6,4)],7) => -1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7) => -1
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(4,5)],7) => -1
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(3,5),(6,4)],7) => -1
([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,5),(1,3),(1,4),(1,5),(3,6),(4,2),(4,6),(5,6)],7) => -1
([(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => -1
([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => -1
([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => -1
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => -1
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(6,4),(6,5)],7) => -1
([(1,6),(2,3),(2,4),(2,6),(6,5)],7) => -2
([(0,6),(1,2),(1,3),(1,6),(6,4),(6,5)],7) => -1
([(1,6),(2,3),(2,4),(2,5)],7) => -3
([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => -2
([(0,6),(1,3),(1,4),(1,5),(1,6),(5,2)],7) => -1
([(0,6),(1,2),(1,3),(1,4),(1,6),(4,5),(6,5)],7) => -1
([(0,6),(1,2),(1,3),(1,4),(1,6),(3,5),(4,5)],7) => -1
([(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => -1
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7) => -1
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => -1
([(0,6),(1,2),(1,3),(1,4),(1,6),(6,5)],7) => -1
([(0,6),(1,2),(1,3),(1,4),(1,5)],7) => -2
([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => -1
([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => -1
([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7) => -1
([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7) => -1
([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => -1
([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7) => -1
([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => -1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => -1
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => -1
([(0,5),(1,2),(1,3),(1,4),(1,6),(5,6)],7) => -1
([(0,4),(1,2),(1,3),(1,5),(1,6),(4,5),(4,6)],7) => 0
([(0,3),(1,2),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7) => 1
([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 2
([(1,3),(1,4),(1,6),(5,2),(6,5)],7) => -2
([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => -1
([(1,6),(2,3),(2,4),(2,5),(5,6)],7) => -2
([(0,6),(1,2),(1,3),(1,4),(4,6),(6,5)],7) => -1
([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => -2
([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7) => -1
([(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => -2
([(0,6),(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => -1
([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => -2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => -1
([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => -2
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => -1
([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => -1
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7) => -1
([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => -1
([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => -1
([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2)],7) => -1
([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7) => -1
([(0,3),(0,4),(0,5),(2,6),(4,6),(5,1),(5,2)],7) => -1
([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => -1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,1,3 1,1,4,9,1 1,1,4,12,38,5,2 1,1,4,13,54,181,47,13,3,1
$F_{1} = q^{-1}$
$F_{2} = q^{-2} + q^{-1}$
$F_{3} = q^{-3} + q^{-2} + 3\ q^{-1}$
$F_{4} = q^{-4} + q^{-3} + 4\ q^{-2} + 9\ q^{-1} + 1$
$F_{5} = q^{-5} + q^{-4} + 4\ q^{-3} + 12\ q^{-2} + 38\ q^{-1} + 5 + 2\ q$
$F_{6} = q^{-6} + q^{-5} + 4\ q^{-4} + 13\ q^{-3} + 54\ q^{-2} + 181\ q^{-1} + 47 + 13\ q + 3\ q^{2} + q^{3}$
Description
The trace of the Coxeter matrix of the incidence algebra of a poset.
Code
def statistic(P):
return P.coxeter_transformation().trace()
Created
Oct 07, 2020 at 22:14 by Martin Rubey
Updated
Oct 07, 2020 at 22:14 by Martin Rubey
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