Values
([],2) => 4
([(0,1)],2) => 2
([],3) => 5
([(1,2)],3) => 5
([(0,1),(0,2)],3) => 4
([(0,2),(2,1)],3) => 3
([(0,2),(1,2)],3) => 4
([],4) => 6
([(2,3)],4) => 6
([(1,2),(1,3)],4) => 6
([(0,1),(0,2),(0,3)],4) => 5
([(0,2),(0,3),(3,1)],4) => 5
([(0,1),(0,2),(1,3),(2,3)],4) => 4
([(1,2),(2,3)],4) => 6
([(0,3),(3,1),(3,2)],4) => 5
([(1,3),(2,3)],4) => 6
([(0,3),(1,3),(3,2)],4) => 5
([(0,3),(1,3),(2,3)],4) => 5
([(0,3),(1,2)],4) => 6
([(0,3),(1,2),(1,3)],4) => 6
([(0,2),(0,3),(1,2),(1,3)],4) => 7
([(0,3),(2,1),(3,2)],4) => 4
([(0,3),(1,2),(2,3)],4) => 5
([],5) => 7
([(3,4)],5) => 7
([(2,3),(2,4)],5) => 7
([(1,2),(1,3),(1,4)],5) => 7
([(0,1),(0,2),(0,3),(0,4)],5) => 6
([(0,2),(0,3),(0,4),(4,1)],5) => 6
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 6
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 5
([(1,3),(1,4),(4,2)],5) => 7
([(0,3),(0,4),(4,1),(4,2)],5) => 6
([(1,2),(1,3),(2,4),(3,4)],5) => 7
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 5
([(0,3),(0,4),(3,2),(4,1)],5) => 6
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 6
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 7
([(2,3),(3,4)],5) => 7
([(1,4),(4,2),(4,3)],5) => 7
([(0,4),(4,1),(4,2),(4,3)],5) => 6
([(2,4),(3,4)],5) => 7
([(1,4),(2,4),(4,3)],5) => 7
([(0,4),(1,4),(4,2),(4,3)],5) => 7
([(1,4),(2,4),(3,4)],5) => 7
([(0,4),(1,4),(2,4),(4,3)],5) => 6
([(0,4),(1,4),(2,4),(3,4)],5) => 6
([(0,4),(1,4),(2,3)],5) => 7
([(0,4),(1,3),(2,3),(2,4)],5) => 7
([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 8
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 8
([(0,4),(1,4),(2,3),(4,2)],5) => 6
([(0,4),(1,3),(2,3),(3,4)],5) => 6
([(0,4),(1,4),(2,3),(2,4)],5) => 7
([(0,4),(1,4),(2,3),(3,4)],5) => 6
([(1,4),(2,3)],5) => 7
([(1,4),(2,3),(2,4)],5) => 7
([(0,4),(1,2),(1,4),(2,3)],5) => 7
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 6
([(1,3),(1,4),(2,3),(2,4)],5) => 8
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 8
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 7
([(0,4),(1,2),(1,4),(4,3)],5) => 7
([(0,4),(1,2),(1,3)],5) => 7
([(0,4),(1,2),(1,3),(1,4)],5) => 7
([(0,2),(0,4),(3,1),(4,3)],5) => 6
([(0,4),(1,2),(1,3),(3,4)],5) => 7
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 5
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 6
([(0,3),(0,4),(1,2),(1,4)],5) => 7
([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 8
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 8
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 8
([(0,3),(1,2),(1,4),(3,4)],5) => 7
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 8
([(1,4),(3,2),(4,3)],5) => 7
([(0,3),(3,4),(4,1),(4,2)],5) => 6
([(1,4),(2,3),(3,4)],5) => 7
([(0,4),(1,2),(2,4),(4,3)],5) => 6
([(0,3),(1,4),(4,2)],5) => 7
([(0,4),(3,2),(4,1),(4,3)],5) => 6
([(0,4),(1,2),(2,3),(2,4)],5) => 7
([(0,4),(2,3),(3,1),(4,2)],5) => 5
([(0,3),(1,2),(2,4),(3,4)],5) => 6
([(0,4),(1,2),(2,3),(3,4)],5) => 6
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 5
([],6) => 8
([(4,5)],6) => 8
([(3,4),(3,5)],6) => 8
([(2,3),(2,4),(2,5)],6) => 8
([(1,2),(1,3),(1,4),(1,5)],6) => 8
([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 7
([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 7
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 7
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 7
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 6
([(1,3),(1,4),(1,5),(5,2)],6) => 8
([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 7
([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 8
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 8
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 6
>>> Load all 1200 entries. <<<([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => 7
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => 7
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 8
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 8
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => 7
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => 7
([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 7
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => 7
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 8
([(2,3),(2,4),(4,5)],6) => 8
([(1,4),(1,5),(5,2),(5,3)],6) => 8
([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 7
([(2,3),(2,4),(3,5),(4,5)],6) => 8
([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 8
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 7
([(1,4),(1,5),(4,3),(5,2)],6) => 8
([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 8
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 9
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 8
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 7
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => 7
([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 7
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => 7
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 7
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => 8
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 8
([(3,4),(4,5)],6) => 8
([(2,3),(3,4),(3,5)],6) => 8
([(1,5),(5,2),(5,3),(5,4)],6) => 8
([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 7
([(2,3),(3,5),(5,4)],6) => 8
([(1,4),(4,5),(5,2),(5,3)],6) => 8
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 7
([(3,5),(4,5)],6) => 8
([(2,5),(3,5),(5,4)],6) => 8
([(1,5),(2,5),(5,3),(5,4)],6) => 8
([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 8
([(2,5),(3,5),(4,5)],6) => 8
([(1,5),(2,5),(3,5),(5,4)],6) => 8
([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 8
([(1,5),(2,5),(3,5),(4,5)],6) => 8
([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 7
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 7
([(0,5),(1,5),(2,5),(3,4)],6) => 8
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 7
([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 7
([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 8
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 7
([(1,5),(2,5),(3,4)],6) => 8
([(1,5),(2,4),(3,4),(3,5)],6) => 8
([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => 8
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 7
([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 9
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) => 9
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 8
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 8
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 9
([(1,5),(2,5),(3,4),(5,3)],6) => 8
([(1,5),(2,4),(3,4),(4,5)],6) => 8
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 7
([(0,5),(1,5),(2,3),(5,4)],6) => 8
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 8
([(0,5),(1,5),(2,4),(5,3),(5,4)],6) => 8
([(1,5),(2,5),(3,4),(3,5)],6) => 8
([(0,5),(1,5),(2,3),(2,5),(5,4)],6) => 8
([(0,5),(1,5),(2,3),(2,5),(3,4)],6) => 8
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 7
([(0,5),(1,5),(2,3),(2,4)],6) => 8
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 8
([(0,4),(1,4),(2,3),(2,5),(4,5)],6) => 8
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 9
([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 8
([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => 8
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => 7
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 6
([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 8
([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 7
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 6
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 7
([(1,5),(2,5),(3,4),(4,5)],6) => 8
([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 7
([(0,5),(1,5),(2,3),(3,4)],6) => 8
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 7
([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 7
([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => 8
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 7
([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => 8
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 7
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 7
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 6
([(0,5),(1,5),(2,4),(3,4)],6) => 8
([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 8
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 9
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 9
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 9
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 7
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 7
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 7
([(2,5),(3,4)],6) => 8
([(2,5),(3,4),(3,5)],6) => 8
([(1,5),(2,3),(2,5),(3,4)],6) => 8
([(0,5),(1,4),(1,5),(4,2),(4,3)],6) => 8
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 8
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => 9
([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 8
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 7
([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 8
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => 8
([(2,4),(2,5),(3,4),(3,5)],6) => 9
([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 9
([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 10
([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 8
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 8
([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 9
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 8
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 9
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 10
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 9
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 9
([(1,5),(2,3),(2,5),(5,4)],6) => 8
([(0,5),(1,2),(1,5),(5,3),(5,4)],6) => 8
([(1,5),(2,3),(2,4)],6) => 8
([(1,5),(2,3),(2,4),(2,5)],6) => 8
([(0,5),(1,3),(1,4),(1,5),(4,2)],6) => 8
([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 8
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 8
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 7
([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => 8
([(0,5),(1,2),(1,3),(1,4)],6) => 8
([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 8
([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 7
([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 8
([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => 7
([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 8
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 6
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 7
([(0,4),(1,2),(1,3),(1,5),(4,5)],6) => 8
([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) => 9
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 9
([(1,3),(1,5),(4,2),(5,4)],6) => 8
([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 7
([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 7
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 7
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => 7
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => 8
([(1,5),(2,3),(2,4),(4,5)],6) => 8
([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => 8
([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 8
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 6
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 8
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 7
([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => 8
([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 8
([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 9
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => 7
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => 7
([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 8
([(0,4),(1,3),(1,5),(5,2)],6) => 8
([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 7
([(0,5),(1,3),(1,4),(4,2),(4,5)],6) => 8
([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => 8
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 6
([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 8
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 7
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 6
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 7
([(1,4),(1,5),(2,3),(2,5)],6) => 8
([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 9
([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 9
([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) => 9
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 9
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 9
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 9
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 8
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => 9
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 9
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 8
([(0,4),(0,5),(1,3),(1,5),(5,2)],6) => 8
([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 9
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => 9
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => 9
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 8
([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => 8
([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => 8
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) => 9
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 10
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => 9
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => 7
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => 9
([(0,4),(0,5),(1,2),(1,3)],6) => 8
([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => 8
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 9
([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 9
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 9
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 9
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 9
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 9
([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 9
([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) => 9
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 10
([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => 8
([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 9
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 8
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => 7
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => 8
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 9
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 9
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 9
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => 9
([(1,4),(2,3),(2,5),(4,5)],6) => 8
([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 8
([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 9
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 9
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 8
([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 8
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 7
([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => 9
([(0,5),(1,3),(1,4),(5,2)],6) => 8
([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 7
([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 7
([(0,4),(1,3),(1,5),(4,2),(4,5)],6) => 8
([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) => 9
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => 9
([(2,5),(3,4),(4,5)],6) => 8
([(1,5),(2,3),(3,5),(5,4)],6) => 8
([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 8
([(1,3),(2,4),(4,5)],6) => 8
([(1,5),(4,3),(5,2),(5,4)],6) => 8
([(1,5),(2,3),(3,4),(3,5)],6) => 8
([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => 8
([(0,4),(1,5),(5,2),(5,3)],6) => 8
([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 7
([(0,5),(1,4),(4,2),(4,3),(4,5)],6) => 8
([(1,5),(3,4),(4,2),(5,3)],6) => 8
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 7
([(1,4),(2,3),(3,5),(4,5)],6) => 8
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 7
([(0,5),(1,4),(4,2),(5,3)],6) => 8
([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 7
([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 8
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => 9
([(1,5),(2,3),(3,4),(4,5)],6) => 8
([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 8
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 6
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 7
([(0,5),(1,4),(2,3)],6) => 8
([(0,5),(1,3),(2,4),(2,5)],6) => 8
([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => 8
([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 8
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 7
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 8
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 7
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 7
([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 8
([(0,5),(1,4),(2,3),(2,4),(4,5)],6) => 8
([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 8
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 9
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 9
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => 8
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => 10
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 10
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 9
([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 9
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 9
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 9
([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 8
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 9
([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 8
([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 9
([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 8
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 9
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 8
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => 7
([(0,5),(1,4),(2,3),(2,5),(4,5)],6) => 8
([(0,5),(1,3),(4,2),(5,4)],6) => 8
([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 7
([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => 8
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => 7
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 7
([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => 8
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
([(0,5),(1,3),(2,4),(4,5)],6) => 8
([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => 8
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 7
([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 7
([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 7
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 6
([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 7
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 6
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 7
([],7) => 9
([(5,6)],7) => 9
([(4,5),(4,6)],7) => 9
([(3,4),(3,5),(3,6)],7) => 9
([(2,3),(2,4),(2,5),(2,6)],7) => 9
([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 9
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => 8
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 8
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7) => 8
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7) => 8
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7) => 8
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 7
([(1,3),(1,4),(1,5),(1,6),(6,2)],7) => 9
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => 8
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 9
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 9
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 9
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 7
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7) => 8
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7) => 8
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 7
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7) => 8
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7) => 8
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7) => 8
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 9
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 9
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7) => 8
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7) => 8
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 8
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 9
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 9
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 9
([(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) => 9
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 7
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7) => 8
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7) => 8
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => 8
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7) => 8
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7) => 9
([(2,4),(2,5),(2,6),(6,3)],7) => 9
([(1,4),(1,5),(1,6),(6,2),(6,3)],7) => 9
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => 8
([(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 9
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 9
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 9
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => 8
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => 9
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => 9
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 9
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 8
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7) => 9
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 8
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 9
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7) => 8
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 7
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => 9
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6),(6,2)],7) => 8
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7) => 8
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7) => 8
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7) => 8
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 9
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) => 9
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 7
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7) => 8
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7) => 8
([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => 9
([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7) => 8
([(1,4),(1,5),(1,6),(5,3),(6,2)],7) => 9
([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => 9
([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1)],7) => 9
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7) => 9
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 9
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 10
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 9
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 8
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 9
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 9
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7) => 8
([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => 8
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7) => 8
([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7) => 8
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 9
([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 9
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => 8
([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7) => 8
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(4,6)],7) => 8
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7) => 8
([(0,1),(0,2),(0,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 9
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 9
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 8
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(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) => 9
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 9
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 9
([(0,3),(0,4),(0,5),(3,6),(4,2),(4,6),(5,1),(5,6)],7) => 8
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => 8
([(3,4),(3,5),(5,6)],7) => 9
([(2,5),(2,6),(6,3),(6,4)],7) => 9
([(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 9
([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => 8
([(3,4),(3,5),(4,6),(5,6)],7) => 9
([(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 9
([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7) => 9
([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7) => 8
([(2,5),(2,6),(5,4),(6,3)],7) => 9
([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 9
([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7) => 10
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7) => 9
([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 10
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => 8
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => 9
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => 9
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 10
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7) => 9
([(0,4),(0,5),(4,6),(5,1),(5,6),(6,2),(6,3)],7) => 8
([(1,5),(1,6),(5,4),(6,2),(6,3)],7) => 9
([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7) => 9
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,6),(6,3)],7) => 8
([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => 8
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7) => 8
([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7) => 9
([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7) => 10
([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7) => 9
([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 9
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 8
([(0,3),(0,4),(3,5),(3,6),(4,2),(4,5),(4,6),(6,1)],7) => 9
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7) => 9
([(0,4),(0,5),(4,2),(4,6),(5,1),(5,6),(6,3)],7) => 8
([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7) => 8
([(0,4),(0,5),(4,3),(4,6),(5,1),(5,2),(5,6)],7) => 8
([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7) => 9
([(0,3),(0,4),(3,2),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 9
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7) => 9
([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 9
([(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 9
([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) => 9
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => 8
([(4,5),(5,6)],7) => 9
([(3,4),(4,5),(4,6)],7) => 9
([(2,6),(6,3),(6,4),(6,5)],7) => 9
([(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 9
([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => 8
([(3,4),(4,6),(6,5)],7) => 9
([(2,5),(5,6),(6,3),(6,4)],7) => 9
([(1,5),(5,6),(6,2),(6,3),(6,4)],7) => 9
([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => 8
([(4,6),(5,6)],7) => 9
([(3,6),(4,6),(6,5)],7) => 9
([(2,6),(3,6),(6,4),(6,5)],7) => 9
([(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 9
([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 9
([(3,6),(4,6),(5,6)],7) => 9
([(2,6),(3,6),(4,6),(6,5)],7) => 9
([(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 9
([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 9
([(2,6),(3,6),(4,6),(5,6)],7) => 9
([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 9
([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 9
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 9
([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 8
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 8
([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 9
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 8
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 8
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 9
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 8
([(1,6),(2,6),(3,6),(4,5)],7) => 9
([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 9
([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 9
([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 9
([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 9
([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7) => 9
([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 9
([(0,6),(1,6),(2,6),(3,4),(3,6),(6,5)],7) => 9
([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5)],7) => 9
([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 8
([(0,6),(1,6),(2,6),(3,4),(3,5)],7) => 9
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 9
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,5)],7) => 9
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 10
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 9
([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 9
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 8
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 9
([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 8
([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 9
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 8
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 8
([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 8
([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7) => 9
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 8
([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 8
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 7
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 8
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 9
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 9
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 8
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 8
([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 8
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 9
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 8
([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 8
([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 8
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 8
([(2,6),(3,6),(4,5)],7) => 9
([(2,6),(3,5),(4,5),(4,6)],7) => 9
([(1,6),(2,5),(3,5),(3,6),(6,4)],7) => 9
([(0,6),(1,5),(2,5),(2,6),(6,3),(6,4)],7) => 9
([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 9
([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 8
([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7) => 9
([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 9
([(0,6),(1,5),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 10
([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,4)],7) => 10
([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 11
([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 10
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 10
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 10
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7) => 9
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 10
([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7) => 10
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => 9
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3),(6,5)],7) => 9
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 10
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,5),(6,3)],7) => 9
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 9
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 10
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(6,5)],7) => 10
([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(6,4)],7) => 11
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 10
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 11
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 10
([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 10
([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => 9
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7) => 9
([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7) => 9
([(0,6),(1,4),(2,5),(3,4),(3,5),(5,6)],7) => 9
([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 8
([(0,6),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 8
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6)],7) => 9
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 9
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 11
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 11
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 11
([(0,6),(1,5),(1,6),(2,4),(3,4),(3,6),(4,5)],7) => 10
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 10
([(0,6),(1,5),(2,5),(2,6),(3,4),(4,6)],7) => 9
([(0,6),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 10
([(2,6),(3,6),(4,5),(6,4)],7) => 9
([(2,6),(3,5),(4,5),(5,6)],7) => 9
([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 9
([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7) => 9
([(1,6),(2,6),(3,4),(6,5)],7) => 9
([(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 9
([(1,6),(2,6),(3,5),(6,4),(6,5)],7) => 9
([(0,6),(1,5),(2,5),(5,3),(5,6),(6,4)],7) => 9
([(0,6),(1,6),(2,3),(6,4),(6,5)],7) => 9
([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7) => 9
([(0,6),(1,6),(2,5),(6,3),(6,4),(6,5)],7) => 9
([(2,6),(3,6),(4,5),(4,6)],7) => 9
([(1,6),(2,6),(3,4),(3,6),(6,5)],7) => 9
([(0,6),(1,6),(2,3),(2,6),(6,4),(6,5)],7) => 9
([(1,6),(2,6),(3,4),(3,6),(4,5)],7) => 9
([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 9
([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7) => 9
([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 9
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5)],7) => 9
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,5)],7) => 9
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 10
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 9
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) => 8
([(0,6),(1,6),(2,3),(2,6),(3,4),(4,5),(6,5)],7) => 8
([(1,6),(2,6),(3,4),(3,5)],7) => 9
([(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 9
([(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 9
([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => 10
([(0,5),(1,5),(2,4),(2,6),(5,6),(6,3)],7) => 9
([(0,6),(1,6),(2,3),(2,4),(6,5)],7) => 9
([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7) => 9
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,5)],7) => 9
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 10
([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 9
([(0,6),(1,6),(2,3),(2,4),(2,6),(6,5)],7) => 9
([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5)],7) => 9
([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => 9
([(0,6),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 9
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 8
([(0,6),(1,6),(2,3),(2,4),(2,5)],7) => 9
([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7) => 9
([(0,5),(1,5),(2,3),(2,4),(2,6),(5,6)],7) => 9
([(0,4),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7) => 10
([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 10
([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 9
([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7) => 9
([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7) => 8
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,2),(5,1)],7) => 8
([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7) => 9
([(0,6),(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => 9
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7) => 8
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => 7
([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 9
([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 8
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 7
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 8
([(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 9
([(0,6),(1,6),(2,3),(2,4),(4,6),(6,5)],7) => 9
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 9
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 8
([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => 9
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => 9
([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7) => 9
([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 10
([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => 8
([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => 9
([(0,5),(1,5),(2,3),(2,4),(4,6),(5,6)],7) => 9
([(0,6),(1,3),(1,5),(4,6),(5,2),(5,4)],7) => 9
([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 8
([(0,6),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 9
([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => 9
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => 8
([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7) => 9
([(0,4),(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3)],7) => 8
([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7) => 9
([(0,6),(1,3),(1,4),(2,6),(3,5),(3,6),(4,2),(4,5)],7) => 10
([(0,4),(0,5),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 8
([(0,3),(0,4),(1,5),(2,5),(3,2),(3,6),(4,1),(4,6)],7) => 9
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => 7
([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7) => 8
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 7
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6)],7) => 8
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => 7
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => 9
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => 8
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 7
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6)],7) => 9
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7) => 8
([(0,6),(1,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7) => 9
([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 8
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 9
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 8
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 8
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 7
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => 9
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => 8
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 8
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(4,6)],7) => 9
([(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7) => 8
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 7
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 8
([(0,6),(1,6),(2,3),(2,4),(4,5),(5,6)],7) => 9
([(0,6),(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7) => 9
([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 8
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7) => 8
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 7
([(2,6),(3,6),(4,5),(5,6)],7) => 9
([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 9
([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7) => 9
([(1,6),(2,6),(3,4),(4,5)],7) => 9
([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 9
([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 9
([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 8
([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 9
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => 9
([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7) => 9
([(1,6),(2,6),(3,4),(4,5),(4,6)],7) => 9
([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7) => 9
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7) => 9
([(0,6),(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7) => 8
([(0,3),(1,6),(2,6),(3,4),(3,5)],7) => 9
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => 9
([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7) => 9
([(0,4),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7) => 9
([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 8
([(0,3),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 9
([(0,3),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 9
([(0,6),(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 9
([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 8
([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 8
([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 8
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 7
([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 9
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 8
([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 9
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 7
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 9
([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 8
([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 9
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 8
([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 8
([(0,6),(1,4),(3,6),(4,5),(5,2),(5,3)],7) => 9
([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 8
([(0,3),(1,6),(2,6),(3,5),(5,4),(5,6)],7) => 9
([(1,6),(2,6),(3,5),(4,5)],7) => 9
([(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 9
([(0,6),(1,6),(2,5),(3,5),(3,6),(5,4)],7) => 9
([(0,6),(1,6),(2,4),(3,4),(3,6),(4,5),(6,5)],7) => 8
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 10
([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 9
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 10
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 10
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 9
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 9
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 10
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 9
([(0,6),(1,6),(2,5),(3,5),(3,6),(6,4)],7) => 9
([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 9
([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 9
([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 8
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => 8
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 9
([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 8
([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 9
([(0,6),(1,5),(2,5),(4,6),(5,3),(5,4)],7) => 9
([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7) => 9
([(0,6),(1,6),(2,5),(3,5),(5,4),(5,6)],7) => 9
([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 8
([(0,6),(1,6),(2,5),(3,4)],7) => 9
([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 9
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => 9
([(0,6),(1,6),(2,5),(3,4),(6,3),(6,5)],7) => 9
([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 9
([(0,4),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => 9
([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 8
([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 8
([(0,6),(1,6),(2,5),(3,4),(3,6)],7) => 9
([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7) => 9
([(0,6),(1,6),(2,5),(3,4),(3,6),(6,5)],7) => 9
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5)],7) => 9
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7) => 8
([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 8
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 9
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 10
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7) => 9
([(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 10
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 10
([(0,6),(1,6),(2,5),(3,4),(3,6),(5,6)],7) => 9
([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5)],7) => 9
([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 10
([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 9
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7) => 9
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7) => 10
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 10
([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7) => 9
([(0,4),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 9
([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 10
([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7) => 9
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => 9
([(0,5),(1,5),(2,4),(2,6),(3,6),(5,3),(5,4)],7) => 10
([(0,6),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 9
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6)],7) => 9
([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 9
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) => 8
([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7) => 8
([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 8
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7) => 10
([(0,5),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6)],7) => 10
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 11
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 11
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 12
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 11
([(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) => 10
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7) => 11
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3)],7) => 11
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7) => 10
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => 10
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,6),(5,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 10
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 10
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(5,3)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7) => 10
([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 10
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 10
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 9
([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 9
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 9
([(0,6),(1,5),(2,3),(2,5),(4,6),(5,4)],7) => 9
([(0,6),(1,2),(1,6),(3,5),(4,5),(6,3),(6,4)],7) => 9
([(0,6),(1,6),(2,5),(3,4),(3,5),(5,6)],7) => 9
([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 9
([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 8
([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 8
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 8
([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 9
([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 8
([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 8
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => 8
([(0,5),(1,5),(2,4),(3,6),(4,6),(5,3),(5,4)],7) => 8
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 8
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6)],7) => 9
([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 8
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 8
([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 8
([(3,6),(4,5)],7) => 9
([(3,6),(4,5),(4,6)],7) => 9
([(2,6),(3,4),(3,6),(4,5)],7) => 9
([(1,6),(2,3),(2,6),(3,4),(3,5)],7) => 9
([(0,6),(1,5),(1,6),(5,2),(5,3),(5,4)],7) => 9
([(0,6),(1,4),(1,6),(4,2),(4,3),(4,5),(6,5)],7) => 9
([(0,6),(1,3),(1,6),(3,2),(3,4),(3,5),(6,4),(6,5)],7) => 10
([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 10
([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => 9
([(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) => 9
([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7) => 9
([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7) => 9
([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7) => 10
([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 9
([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) => 9
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => 9
([(1,6),(2,3),(2,6),(3,5),(6,4)],7) => 9
([(1,5),(2,3),(2,5),(3,6),(5,4),(5,6)],7) => 9
([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7) => 9
([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7) => 9
([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 9
([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 9
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => 8
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) => 9
([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => 9
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) => 9
([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7) => 9
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) => 9
([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) => 10
([(3,5),(3,6),(4,5),(4,6)],7) => 10
([(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 10
([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 10
([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 10
([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 10
([(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 10
([(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 10
([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => 11
([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 10
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 10
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 10
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 10
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 10
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 9
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3)],7) => 10
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 10
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 9
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => 10
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 10
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(6,3)],7) => 10
([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) => 10
([(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 10
([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 10
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 10
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 9
([(0,5),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 10
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,3),(5,6)],7) => 10
([(0,6),(1,4),(1,5),(2,4),(2,5),(5,6),(6,3)],7) => 10
([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,4),(6,3)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7) => 10
([(0,5),(1,4),(1,6),(2,4),(2,6),(6,3),(6,5)],7) => 10
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,6),(5,6)],7) => 10
([(0,4),(1,5),(1,6),(2,5),(2,6),(5,3),(6,3),(6,4)],7) => 10
([(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 11
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(6,4)],7) => 10
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 11
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 11
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3)],7) => 11
([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(5,4)],7) => 10
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(4,5),(6,5)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(5,3),(5,4)],7) => 11
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 12
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(5,4),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7) => 10
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 9
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => 10
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(6,5)],7) => 10
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5)],7) => 11
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,6),(4,6),(5,6)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => 11
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(5,6)],7) => 10
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 11
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7) => 10
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 11
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 11
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6)],7) => 10
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(4,5)],7) => 11
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 10
([(0,5),(0,6),(1,2),(1,4),(3,5),(3,6),(4,3)],7) => 10
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7) => 9
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => 10
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 10
([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => 10
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => 9
([(0,5),(0,6),(1,2),(1,4),(2,6),(3,5),(3,6),(4,3)],7) => 10
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,6),(4,1),(4,2)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(6,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7) => 10
([(0,4),(0,6),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => 9
([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => 9
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(5,6)],7) => 10
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7) => 9
([(0,5),(0,6),(1,4),(3,5),(3,6),(4,2),(4,3)],7) => 10
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6)],7) => 10
([(0,4),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(4,5)],7) => 11
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => 10
([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 10
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 9
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) => 10
([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 10
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 9
([(2,6),(3,4),(3,6),(6,5)],7) => 9
([(1,6),(2,3),(2,6),(6,4),(6,5)],7) => 9
([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7) => 9
([(2,6),(3,4),(3,5)],7) => 9
([(2,6),(3,4),(3,5),(3,6)],7) => 9
([(1,6),(2,3),(2,4),(2,6),(4,5)],7) => 9
([(0,6),(1,4),(1,5),(1,6),(5,2),(5,3)],7) => 9
([(0,6),(1,3),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => 9
([(0,6),(1,2),(1,3),(1,6),(3,4),(3,5),(6,4),(6,5)],7) => 10
([(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 9
([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7) => 9
([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7) => 9
([(0,6),(1,3),(1,4),(1,6),(4,5),(6,2),(6,5)],7) => 9
([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 9
([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 9
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) => 8
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,5),(6,2)],7) => 9
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,4),(5,6)],7) => 9
([(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(6,2)],7) => 9
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(5,4),(6,4)],7) => 8
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7) => 9
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(4,5)],7) => 9
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(3,5),(6,4)],7) => 9
([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,5),(1,3),(1,4),(1,5),(3,6),(4,2),(4,6),(5,6)],7) => 9
([(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 10
([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 10
([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => 9
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(6,4),(6,5)],7) => 9
([(1,6),(2,3),(2,4),(2,6),(6,5)],7) => 9
([(0,6),(1,2),(1,3),(1,6),(6,4),(6,5)],7) => 9
([(1,6),(2,3),(2,4),(2,5)],7) => 9
([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 9
([(0,6),(1,3),(1,4),(1,5),(1,6),(5,2)],7) => 9
([(0,6),(1,2),(1,3),(1,4),(1,6),(4,5),(6,5)],7) => 9
([(0,6),(1,2),(1,3),(1,4),(1,6),(3,5),(4,5)],7) => 9
([(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 9
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7) => 9
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 8
([(0,6),(1,2),(1,3),(1,4),(1,6),(6,5)],7) => 9
([(0,6),(1,2),(1,3),(1,4),(1,5)],7) => 9
([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 9
([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => 8
([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7) => 9
([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7) => 8
([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 9
([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7) => 8
([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 9
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 7
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 8
([(0,5),(1,2),(1,3),(1,4),(1,6),(5,6)],7) => 9
([(0,4),(1,2),(1,3),(1,5),(1,6),(4,5),(4,6)],7) => 10
([(0,3),(1,2),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7) => 10
([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 10
([(1,3),(1,4),(1,6),(5,2),(6,5)],7) => 9
([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => 8
([(1,6),(2,3),(2,4),(2,5),(5,6)],7) => 9
([(0,6),(1,2),(1,3),(1,4),(4,6),(6,5)],7) => 9
([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => 9
([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7) => 8
([(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 9
([(0,6),(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => 9
([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 9
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 7
([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 9
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 8
([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => 9
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7) => 8
([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 8
([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => 9
([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2)],7) => 9
([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7) => 9
([(0,3),(0,4),(0,5),(2,6),(4,6),(5,1),(5,2)],7) => 8
([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => 9
([(0,3),(0,4),(0,5),(2,6),(3,6),(4,1),(5,2)],7) => 8
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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:
1,0,1 1,2,2 2,6,7,1 5,20,30,8 15,77,149,71,6
$F_{2} = q^{2} + q^{4}$
$F_{3} = q^{3} + 2\ q^{4} + 2\ q^{5}$
$F_{4} = 2\ q^{4} + 6\ q^{5} + 7\ q^{6} + q^{7}$
$F_{5} = 5\ q^{5} + 20\ q^{6} + 30\ q^{7} + 8\ q^{8}$
$F_{6} = 15\ q^{6} + 77\ q^{7} + 149\ q^{8} + 71\ q^{9} + 6\ q^{10}$
Description
The number of cuts of a poset.
A cut is a subset $A$ of the poset such that the set of lower bounds of the set of upper bounds of $A$ is exactly $A$.
A cut is a subset $A$ of the poset such that the set of lower bounds of the set of upper bounds of $A$ is exactly $A$.
Code
def statistic(P):
return len(P.cuts())
Created
Nov 24, 2016 at 22:56 by Martin Rubey
Updated
Nov 24, 2016 at 22:56 by Martin Rubey
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