[1,0,1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [3,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [2,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => [5,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => ([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => [4,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => [4,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => ([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => [4,2] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => ([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => [3,2,1] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => [4,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => [3,3] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => [4,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => [3,3] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,2,1] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [3,2,1] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,2,1] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => [3,2,1] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,1,1] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => [5,1] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => ([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => [4,2] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => [4,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => [4,2] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => [3,2,1] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => [4,2] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => [3,3] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => [4,2] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => [3,3] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => [3,2,1] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [3,2,1] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => [3,2,1] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => [3,2,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,1,1] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [4,1,1] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => [3,2,1] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => [4,1,1] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => [3,2,1] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => [3,2,1] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => [3,2,1] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => [3,2,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => [3,2,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,1,1] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => [3,1,1,1] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => [2,2,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => ([(1,5),(2,5),(3,5),(4,5)],6) => [2,1,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => [4,1,1] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => ([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => [3,2,1] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [3,2,1] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [3,2,1] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [2,2,2] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => [4,1,1] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => [3,2,1] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => [3,2,1] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => [3,2,1] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [2,2,2] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,2,1] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => [3,2,1] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [2,2,2] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,1,1] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => [4,1,1] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => [3,2,1] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => [3,2,1] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => [3,2,1] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [2,2,2] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => [3,2,1] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [2,2,2] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,1,1] => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => [3,1,1,1] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => [2,2,1,1] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => ([(1,5),(2,5),(3,4),(3,5)],6) => [2,2,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => ([(2,5),(3,5),(4,5)],6) => [2,1,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => [3,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => [2,2,1,1] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => [3,1,1,1] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => [2,2,1,1] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [2,2,1,1] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => [3,1,1,1] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => [2,2,1,1] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [2,2,1,1] => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(3,4),(3,5)],6) => [2,2,1,1] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => [3,1,1,1] => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => [2,2,1,1] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => ([(1,5),(2,3),(2,4),(2,5)],6) => [2,2,1,1] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => ([(2,5),(3,4),(3,5)],6) => [2,2,1,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => ([(3,5),(4,5)],6) => [2,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => [2,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4),(1,5)],6) => [2,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5)],6) => [2,1,1,1,1] => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => ([(3,4),(3,5)],6) => [2,1,1,1,1] => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => [1,1,1,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => [6,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [6,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [6,1] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => [5,1,1] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => [5,2] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => [6,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => [5,2] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => [5,1,1] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => [5,1,1] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => ([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7) => [5,1,1] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => [5,1,1] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => [4,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => [5,2] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => [5,2] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7) => [5,2] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => [4,2,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => [6,1] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => [5,2] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [5,2] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) => [5,2] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => ([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => [4,2,1] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => [5,1,1] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => ([(0,5),(1,3),(1,4),(3,6),(4,5),(5,6),(6,2)],7) => [5,1,1] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) => [4,2,1] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => [4,1,1,1] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => [5,1,1] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7) => [4,2,1] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => ([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => [5,1,1] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(4,6),(5,6),(6,3)],7) => [4,2,1] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => [4,2,1] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => [5,1,1] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) => [4,2,1] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => ([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) => [4,2,1] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => [4,1,1,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => [4,1,1,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => [4,1,1,1] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => [4,1,1,1] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => [4,1,1,1] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => [3,1,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => ([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => [5,2] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => [5,2] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => [5,2] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => [4,2,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) => [5,2] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => [4,3] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7) => [5,2] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => [4,3] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => ([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => [4,2,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [4,2,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [4,2,1] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => [4,2,1] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [3,2,1,1] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => [6,1] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => [5,2] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7) => [5,2] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) => [5,2] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7) => [4,2,1] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => [4,3] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7) => [5,2] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) => [4,3] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7) => [4,2,1] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => [4,2,1] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [4,2,1] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7) => [4,2,1] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [3,2,1,1] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => [5,1,1] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3),(5,3),(6,2)],7) => [4,2,1] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => [5,1,1] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(4,3),(5,4),(6,3)],7) => [4,2,1] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7) => [4,2,1] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => [4,2,1] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => ([(0,4),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7) => [4,2,1] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,6),(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7) => [4,2,1] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => [3,2,1,1] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => [4,1,1,1] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7) => [4,1,1,1] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7) => [4,1,1,1] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => [3,2,1,1] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => [3,1,1,1,1] => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => [5,1,1] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => ([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => [4,2,1] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [4,2,1] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [4,2,1] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,3),(5,3),(6,3)],7) => [3,2,2] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => [5,1,1] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => [4,2,1] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7) => [4,2,1] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [4,2,1] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [3,2,2] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [4,2,1] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [4,2,1] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [3,2,2] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => [5,1,1] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => [4,2,1] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => [4,2,1] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7) => [4,2,1] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [3,2,2] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => [4,2,1] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(4,6),(5,6)],7) => [4,2,1] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [3,2,2] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => ([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => ([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => [4,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => [4,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => [4,1,1,1] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => ([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => [4,1,1,1] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => ([(0,6),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [2,1,1,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => ([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => [6,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => ([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => [5,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) => [5,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => ([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7) => [5,2] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => [4,2,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => ([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) => [5,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => [4,3] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => [5,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => ([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => [4,3] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => ([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7) => [4,2,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => [4,2,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7) => [4,2,1] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7) => [4,2,1] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7) => [3,2,1,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) => [5,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => [4,3] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => [4,3] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => ([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => [4,3] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => [3,3,1] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7) => [5,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => [4,3] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7) => [4,3] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7) => [4,3] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => ([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => [3,3,1] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,2,1] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => ([(0,2),(0,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => [4,2,1] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => [3,3,1] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => [3,2,1,1] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [4,2,1] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,1] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => [4,2,1] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,1] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,1] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1)],7) => [4,2,1] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,1] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,1] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => ([(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) => [3,2,1,1] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => ([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => [6,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => ([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => [5,2] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7) => [5,2] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => ([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7) => [5,2] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => ([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7) => [4,2,1] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7) => [5,2] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => [4,3] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) => [5,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => ([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) => [4,3] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => ([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => [4,2,1] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => [4,2,1] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => ([(0,5),(0,6),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7) => [4,2,1] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) => [4,2,1] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => [3,2,1,1] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => ([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) => [5,2] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => [4,3] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => [4,3] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) => [4,3] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7) => [3,3,1] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => ([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7) => [5,2] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => [4,3] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7) => [4,3] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) => [4,3] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => [3,3,1] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => [4,2,1] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(0,6),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [4,2,1] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7) => [3,3,1] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7) => [3,2,1,1] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => ([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [4,2,1] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,2),(4,6),(5,2),(5,6)],7) => [3,3,1] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => [4,2,1] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,6),(4,6),(5,3),(5,6)],7) => [3,3,1] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => [3,3,1] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7) => [4,2,1] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => [3,3,1] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7) => [3,3,1] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => [3,2,1,1] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => ([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => [5,1,1] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7) => [4,2,1] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => [4,2,1] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => ([(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => [4,2,1] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => [3,2,2] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => ([(0,5),(2,6),(3,6),(4,1),(4,3),(5,2),(5,4)],7) => [5,1,1] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7) => [4,2,1] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(5,6)],7) => [4,2,1] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3)],7) => [4,2,1] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => ([(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7) => [3,2,2] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => [4,2,1] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => ([(0,2),(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(6,5)],7) => [4,2,1] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7) => [3,2,2] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7) => [3,2,1,1] => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => ([(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3),(5,4)],7) => [4,2,1] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => [3,3,1] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7) => [4,2,1] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7) => [3,3,1] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => [3,2,2] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,5)],7) => [4,2,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,6)],7) => [3,3,1] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => [3,2,2] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => [4,1,1,1] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => [4,1,1,1] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => [4,1,1,1] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(5,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => ([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(5,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [2,1,1,1,1,1] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => ([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7) => [5,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => ([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7) => [4,2,1] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => ([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7) => [4,2,1] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => ([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7) => [4,2,1] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => ([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7) => [3,2,2] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7) => [4,2,1] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => [3,3,1] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7) => [4,2,1] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => ([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => [3,3,1] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => [3,2,2] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => ([(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) => [3,2,2] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => ([(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) => [2,2,2,1] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => ([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7) => [5,1,1] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7) => [4,2,1] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7) => [4,2,1] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => ([(0,5),(0,6),(1,4),(4,5),(4,6),(6,2),(6,3)],7) => [4,2,1] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => [3,2,2] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => ([(0,4),(2,5),(2,6),(3,1),(3,5),(3,6),(4,2),(4,3)],7) => [4,2,1] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => [3,3,1] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,1),(3,6)],7) => [4,2,1] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4)],7) => [3,3,1] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7) => [3,2,2] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [4,2,1] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,2),(5,3),(6,2),(6,3)],7) => [3,3,1] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => [4,2,1] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(6,3),(6,4)],7) => [3,3,1] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => [3,2,2] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => [3,2,2] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => ([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7) => [5,1,1] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7) => [4,2,1] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7) => [4,2,1] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => ([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(6,2)],7) => [4,2,1] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => [3,2,2] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => ([(0,5),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4)],7) => [4,2,1] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7) => [3,3,1] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(2,6),(3,1),(3,5),(3,6)],7) => [4,2,1] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3)],7) => [3,3,1] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7) => [3,2,2] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(2,6),(3,4),(3,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => ([(0,5),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4)],7) => [4,2,1] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,3),(6,2),(6,3)],7) => [3,3,1] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,2),(4,6)],7) => [4,2,1] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(6,3)],7) => [3,3,1] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5)],7) => [3,2,2] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => [3,2,2] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7) => [3,2,2] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => [4,1,1,1] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(5,2),(6,2)],7) => [3,2,1,1] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => [4,1,1,1] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(6,3)],7) => [3,2,1,1] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => [3,2,1,1] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7) => [3,2,1,1] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6)],7) => [3,2,1,1] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7) => [3,2,1,1] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7) => [3,2,1,1] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,1,1,1] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => ([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => ([(2,6),(3,6),(4,6),(5,6)],7) => [2,1,1,1,1,1] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => [4,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => ([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7) => [4,1,1,1] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => ([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7) => [4,1,1,1] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(6,2),(6,3)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => ([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(4,5),(4,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => ([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7) => [4,1,1,1] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7) => [3,2,1,1] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3)],7) => [3,2,1,1] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => ([(0,2),(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4)],7) => [3,2,1,1] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7) => [3,2,1,1] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(4,5)],7) => [3,2,1,1] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,2,1] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => ([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => ([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => ([(2,6),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => ([(3,6),(4,6),(5,6)],7) => [2,1,1,1,1,1] => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => [3,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => [3,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => [3,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => [3,1,1,1,1] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => ([(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => ([(3,5),(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => [3,1,1,1,1] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => ([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => ([(2,6),(3,4),(3,5),(3,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => ([(3,6),(4,5),(4,6)],7) => [2,2,1,1,1] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => ([(4,6),(5,6)],7) => [2,1,1,1,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => [2,1,1,1,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => [2,1,1,1,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5),(2,6)],7) => [2,1,1,1,1,1] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => ([(3,4),(3,5),(3,6)],7) => [2,1,1,1,1,1] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => ([(4,5),(4,6)],7) => [2,1,1,1,1,1] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => [6,2] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => [6,2] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => [6,2] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8) => [6,2] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => [6,2] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8) => [5,3] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8) => [4,2,1,1] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [6,2] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8) => [4,1,1,1,1] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => 1