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------------------------------------------------------------------------
Map identifier: Mp00203

------------------------------------------------------------------------
Map name: cone

------------------------------------------------------------------------
Domain: Graphs

------------------------------------------------------------------------
Codomain: Graphs

------------------------------------------------------------------------
Description: The cone of a graph.

The cone of a graph is obtained by joining a new vertex to all the vertices of the graph. The added vertex is called a '''universal vertex''' or a '''dominating vertex'''.

------------------------------------------------------------------------
References: [1]   [[wikipedia:Universal_vertex]]
[2]   [[wikipedia:Threshold_graph]]

------------------------------------------------------------------------
Code:

def mapping(G):#
    H = G.relabel(inplace=False, immutable=False)
    V = H.vertices()
    n = max(V, default=0) + 1
    H.add_vertex(n)
    H.add_edges([(v, n) for v in V])
    return H.copy(immutable=True)

------------------------------------------------------------------------
Map images:

([],1)                                                                                                            => ([(0,1)],2)
([],2)                                                                                                            => ([(0,2),(1,2)],3)
([(0,1)],2)                                                                                                       => ([(0,1),(0,2),(1,2)],3)
([],3)                                                                                                            => ([(0,3),(1,3),(2,3)],4)
([(1,2)],3)                                                                                                       => ([(0,3),(1,2),(1,3),(2,3)],4)
([(0,2),(1,2)],3)                                                                                                 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([(0,1),(0,2),(1,2)],3)                                                                                           => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
([],4)                                                                                                            => ([(0,4),(1,4),(2,4),(3,4)],5)
([(2,3)],4)                                                                                                       => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
([(1,3),(2,3)],4)                                                                                                 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(1,3),(2,3)],4)                                                                                           => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(1,2)],4)                                                                                                 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
([(0,3),(1,2),(2,3)],4)                                                                                           => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
([(1,2),(1,3),(2,3)],4)                                                                                           => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,3),(1,2),(1,3),(2,3)],4)                                                                                     => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,2),(0,3),(1,2),(1,3)],4)                                                                                     => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)                                                                               => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)                                                                         => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
([],5)                                                                                                            => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
([(3,4)],5)                                                                                                       => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
([(2,4),(3,4)],5)                                                                                                 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(1,4),(2,4),(3,4)],5)                                                                                           => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(1,4),(2,4),(3,4)],5)                                                                                     => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(1,4),(2,3)],5)                                                                                                 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
([(1,4),(2,3),(3,4)],5)                                                                                           => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
([(0,1),(2,4),(3,4)],5)                                                                                           => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(2,3),(2,4),(3,4)],5)                                                                                           => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(1,4),(2,3),(3,4)],5)                                                                                     => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
([(1,4),(2,3),(2,4),(3,4)],5)                                                                                     => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)                                                                               => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(1,3),(1,4),(2,3),(2,4)],5)                                                                                     => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)                                                                               => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                                               => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)                                                                               => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                                         => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)                                                                         => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                                   => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(1,3),(2,3),(2,4)],5)                                                                                     => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,1),(2,3),(2,4),(3,4)],5)                                                                                     => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)                                                                               => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)                                                                         => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)                                                                               => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)                                                                         => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)                                                                   => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)                                                                         => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                                         => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                                   => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                             => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)                                                                   => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)                                                             => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                       => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
([],6)                                                                                                            => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
([(4,5)],6)                                                                                                       => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
([(3,5),(4,5)],6)                                                                                                 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(2,5),(3,5),(4,5)],6)                                                                                           => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,5),(2,5),(3,5),(4,5)],6)                                                                                     => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)                                                                               => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(2,5),(3,4)],6)                                                                                                 => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
([(2,5),(3,4),(4,5)],6)                                                                                           => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
([(1,2),(3,5),(4,5)],6)                                                                                           => ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(3,4),(3,5),(4,5)],6)                                                                                           => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,5),(2,5),(3,4),(4,5)],6)                                                                                     => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(2,5),(3,5),(4,5)],6)                                                                                     => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(2,5),(3,4),(3,5),(4,5)],6)                                                                                     => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)                                                                               => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)                                                                               => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)                                                                         => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(2,4),(2,5),(3,4),(3,5)],6)                                                                                     => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(1,5),(2,4),(3,4)],6)                                                                                     => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)                                                                               => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)                                                                               => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                                               => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)                                                                               => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)                                                                               => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)                                                                         => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                                         => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)                                                                         => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                                                         => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)                                                                         => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                                                   => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                             => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                                             => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(2,3)],6)                                                                                           => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
([(1,5),(2,4),(3,4),(3,5)],6)                                                                                     => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,1),(2,5),(3,4),(4,5)],6)                                                                                     => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
([(1,2),(3,4),(3,5),(4,5)],6)                                                                                     => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)                                                                               => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)                                                                               => ([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)                                                                               => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)                                                                         => ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)                                                                         => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)                                                                   => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)                                                                               => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)                                                                         => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)                                                                         => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)                                                                         => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                                                         => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)                                                                         => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)                                                             => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)                                                                               => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)                                                                               => ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)                                                                               => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)                                                                         => ([(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)                                                                         => ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)                                                                         => ([(0,4),(0,6),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                                         => ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)                                                                         => ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)                                                                   => ([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)                                                                   => ([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                             => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                                         => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                             => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)                                                                   => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)                                                             => ([(0,3),(0,5),(0,6),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                             => ([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                                             => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                             => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                                             => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                             => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                             => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                                       => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)                                                                   => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                                                   => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                                             => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                                             => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                                       => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)                                                                         => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)                                                                   => ([(0,3),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,1),(0,2),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                                                   => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)                                                                   => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                             => ([(0,1),(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                                             => ([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)                                                             => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                                       => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)                                                             => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)                                                             => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                                       => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,4),(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                                       => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)                                                       => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => ([(0,1),(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                                 => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                           => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)                                                                         => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)                                                                   => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                                   => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                                             => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                             => ([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)                                                             => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)                                                       => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,3),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => ([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                                 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)                                                             => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                                             => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)                                                       => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)                                                 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)                                                       => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => ([(0,1),(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                                 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => ([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                                 => ([(0,2),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                           => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                           => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => ([(0,1),(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                     => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                     => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                         => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                   => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
([],7)                                                                                                            => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
([(5,6)],7)                                                                                                       => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(4,6),(5,6)],7)                                                                                                 => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(3,6),(4,6),(5,6)],7)                                                                                           => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,6),(3,6),(4,6),(5,6)],7)                                                                                     => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)                                                                               => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)                                                                         => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(3,6),(4,5)],7)                                                                                                 => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(3,6),(4,5),(5,6)],7)                                                                                           => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(2,3),(4,6),(5,6)],7)                                                                                           => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(4,5),(4,6),(5,6)],7)                                                                                           => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,6),(3,6),(4,5),(5,6)],7)                                                                                     => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(3,6),(4,6),(5,6)],7)                                                                                     => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(3,6),(4,5),(4,6),(5,6)],7)                                                                                     => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)                                                                               => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)                                                                               => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                                               => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)                                                                         => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(3,5),(3,6),(4,5),(4,6)],7)                                                                                     => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,6),(2,6),(3,5),(4,5)],7)                                                                                     => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                                                               => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)                                                                               => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)                                                                               => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                               => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                                               => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)                                                                               => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)                                                                         => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)                                                                         => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                                         => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                                                         => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)                                                                         => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,5),(3,4)],7)                                                                                           => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
([(2,6),(3,5),(4,5),(4,6)],7)                                                                                     => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,2),(3,6),(4,5),(5,6)],7)                                                                                     => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,2),(4,6),(5,6)],7)                                                                                     => ([(0,3),(0,7),(1,2),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,3),(4,5),(4,6),(5,6)],7)                                                                                     => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)                                                                               => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)                                                                               => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)                                                                               => ([(0,7),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)                                                                               => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)                                                                         => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)                                                                               => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)                                                                         => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)                                                                               => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)                                                                               => ([(0,7),(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)                                                                               => ([(0,6),(0,7),(1,5),(1,7),(2,4),(2,7),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)                                                                               => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)                                                                         => ([(0,6),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                                         => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)                                                                         => ([(0,7),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,6),(0,7),(1,3),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,5),(1,7),(2,3),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)                                                                         => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)                                                                   => ([(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,5),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                                             => ([(0,4),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)                                                                         => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,6),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                                             => ([(0,7),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                                             => ([(0,6),(0,7),(1,4),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,5),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                                       => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)                                                                   => ([(0,6),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)                                                             => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                                             => ([(0,6),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                             => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                             => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)                                                                         => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)                                                                   => ([(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,2),(1,3),(1,7),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,2),(1,3),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,4),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)                                                             => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,2),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,2),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,4),(1,7),(2,3),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,2),(1,3),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                             => ([(0,7),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,4),(1,7),(2,3),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)                                                                         => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,7),(5,7),(6,7)],8)
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)                                                                   => ([(0,5),(0,7),(1,2),(1,3),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)                                                                   => ([(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)                                                                   => ([(0,4),(0,7),(1,4),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)                                                             => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7)                                                             => ([(0,4),(0,7),(1,4),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,5),(0,7),(1,2),(1,3),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                                             => ([(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                                             => ([(0,5),(0,7),(1,4),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,2),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)                                                       => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,1),(0,2),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5)],7)                                                             => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)                                                             => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)                                                       => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)                                                       => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(1,4),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(5,6)],7)                                                       => ([(0,4),(0,6),(0,7),(1,4),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,3),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)                                                       => ([(0,3),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,2),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,3),(0,6),(0,7),(1,3),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)                                                 => ([(0,3),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                 => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)                                                       => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,3),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)                                                       => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                                       => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,4),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                                                       => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)                                                 => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,3),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                 => ([(0,4),(0,5),(0,7),(1,4),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)                                           => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)                                           => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                                     => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                                     => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)                               => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                               => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)                                                                               => ([(0,1),(0,7),(1,7),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)                                                                               => ([(0,3),(0,7),(1,2),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)                                                                         => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)                                                                         => ([(0,1),(0,7),(1,7),(2,3),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)                                                                   => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                                   => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)                                                             => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)                                                       => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)                                                                         => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)                                                                         => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)                                                                         => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,4),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)                                                                   => ([(0,4),(0,7),(1,3),(1,7),(2,5),(2,6),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,1),(0,7),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7)                                                                   => ([(0,5),(0,7),(1,2),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,4),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)                                                                   => ([(0,5),(0,7),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,6),(5,6)],7)                                                             => ([(0,4),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7)                                                             => ([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                                             => ([(0,4),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)                                                             => ([(0,1),(0,5),(0,7),(1,4),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,4),(0,7),(1,3),(1,7),(2,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)                                                                         => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,3),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,1),(0,7),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)                                                                   => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,6),(0,7),(1,2),(1,3),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                                   => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)                                                             => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,7),(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)                                                             => ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,3),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                                       => ([(0,1),(0,6),(0,7),(1,4),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,4),(0,7),(1,3),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,3),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,4),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)                                                       => ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,4),(0,6),(0,7),(1,3),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)                                                             => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)                                                       => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,6),(0,7),(1,2),(1,5),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,4),(0,7),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)                                                             => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)                                                       => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)                                                                   => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,7),(2,3),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)                                                             => ([(0,6),(0,7),(1,2),(1,4),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,4),(1,5),(2,4),(2,6),(3,5),(4,6),(5,6)],7)                                                             => ([(0,3),(0,7),(1,4),(1,5),(1,7),(2,4),(2,6),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,1),(0,3),(0,7),(1,2),(1,7),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7)                                                             => ([(0,3),(0,4),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,6),(0,7),(1,2),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,2),(1,3),(1,7),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,2),(1,5),(2,4),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,3),(0,7),(1,2),(1,5),(1,7),(2,4),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)                                                             => ([(0,6),(0,7),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,6),(1,2),(1,6),(2,4),(3,4),(3,5),(4,5),(5,6)],7)                                                             => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,6),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,2),(1,4),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(1,6),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,2),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,2),(1,6),(2,4),(3,5),(4,5),(4,6),(5,6)],7)                                                       => ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,3),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,3),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,3),(1,4),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,1),(0,5),(0,7),(1,4),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,3),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,4),(0,6),(0,7),(1,3),(1,6),(1,7),(2,3),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                                 => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)                                                             => ([(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)                                                             => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                       => ([(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                 => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)                                                 => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,5),(2,3),(2,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,3),(1,5),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5)],7)                                                 => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)                                                       => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,3),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7)                                                       => ([(0,4),(0,6),(0,7),(1,3),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7)                                                       => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,4),(0,5),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)                                                 => ([(0,4),(0,5),(0,7),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6)],7)                                                 => ([(0,4),(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,5),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,7),(2,3),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,4),(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(5,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                               => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7)                                                             => ([(0,3),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,6),(4,6),(5,6)],7)                                                             => ([(0,3),(0,4),(0,7),(1,2),(1,5),(1,7),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                             => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(1,4),(1,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,2),(0,7),(1,4),(1,5),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,1),(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                                 => ([(0,1),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                                                       => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,3),(0,4),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(5,6)],7)                                                       => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7)                                                       => ([(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)                                                 => ([(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)                                                 => ([(0,5),(0,7),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)                                                 => ([(0,3),(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                                 => ([(0,1),(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,4),(0,7),(1,2),(1,3),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,3),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,3),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,2),(0,3),(0,7),(1,4),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,4),(0,7),(1,2),(1,3),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,3),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                                       => ([(0,3),(0,4),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)                                                       => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7)                                                       => ([(0,4),(0,6),(0,7),(1,3),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6)],7)                                                       => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)                                                 => ([(0,1),(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)                                                 => ([(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,5),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(5,6)],7)                                                 => ([(0,4),(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,7),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,2),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,4),(0,7),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,5),(2,3),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,2),(1,5),(1,7),(2,3),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,3),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,4),(0,7),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                                 => ([(0,4),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,3),(1,5),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,3),(0,6),(0,7),(1,3),(1,5),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,3),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,5),(0,7),(1,4),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,4),(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,6),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,5),(0,7),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)                                                 => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,4),(0,6),(0,7),(1,3),(1,5),(1,7),(2,3),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                                 => ([(0,4),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                 => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,3),(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,3),(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,3),(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,3),(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,2),(1,3),(1,5),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)                                     => ([(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,6),(0,7),(1,2),(1,3),(1,5),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,5),(0,7),(1,2),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)                                           => ([(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                                     => ([(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                               => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)                                                                   => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,3),(0,7),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,2),(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7)                                                             => ([(0,6),(0,7),(1,2),(1,4),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                             => ([(0,1),(0,2),(0,7),(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7)                                                             => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,2),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,2),(0,7),(1,2),(1,6),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                                       => ([(0,1),(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                       => ([(0,5),(0,7),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,1),(0,2),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,3),(0,6),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                 => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                               => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,4),(0,5),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                     => ([(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)                                                 => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)                                           => ([(0,3),(0,4),(0,5),(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,4),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,3),(0,4),(1,2),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,3),(0,4),(0,7),(1,2),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                     => ([(0,3),(0,5),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,4),(0,5),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                               => ([(0,1),(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)                                     => ([(0,1),(0,4),(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(0,6),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                               => ([(0,3),(0,4),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,2),(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                               => ([(0,3),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(0,6),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,3),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                               => ([(0,4),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,4),(0,5),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                               => ([(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                               => ([(0,4),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,1),(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)                                           => ([(0,4),(0,5),(0,7),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,7),(1,3),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,3),(1,5),(2,4),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,6),(0,7),(1,3),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,6),(2,3),(2,4),(2,5),(3,4),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,3),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,4),(0,5),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                                           => ([(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,3),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)                                     => ([(0,3),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,5),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,4),(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                               => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,6),(0,7),(1,2),(1,5),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                           => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)                               => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                               => ([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                               => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                         => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                   => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)             => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                               => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                               => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                         => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)                                                       => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
([(0,2),(0,6),(1,2),(1,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                                       => ([(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5)],7)                                                       => ([(0,4),(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)                                                 => ([(0,4),(0,5),(0,7),(1,3),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                                 => ([(0,1),(0,5),(0,7),(1,4),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                 => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                           => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                     => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,2),(1,3),(1,5),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,4),(0,7),(1,2),(1,3),(1,5),(1,7),(2,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                           => ([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,2),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,2),(1,5),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,2),(0,4),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,3),(0,5),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,7),(1,2),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,5),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,6),(0,7),(1,2),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                     => ([(0,3),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,6),(3,5),(4,5),(4,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7)                                                 => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)                                           => ([(0,1),(0,4),(0,5),(0,7),(1,3),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,4),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,2),(1,3),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(0,6),(1,2),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,4),(0,6),(0,7),(1,2),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,3),(1,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,2),(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,3),(0,5),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,2),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,4),(0,6),(0,7),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,4),(1,3),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,2),(0,4),(0,7),(1,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,6),(1,3),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,2),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,2),(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,1),(0,5),(0,6),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,4),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,4),(0,6),(0,7),(1,3),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,4),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                               => ([(0,3),(0,4),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,4),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,3),(0,4),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,1),(0,2),(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                               => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,2),(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                     => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,1),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,2),(0,6),(1,2),(1,4),(1,5),(2,3),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,2),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)                                     => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                               => ([(0,1),(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,5),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                               => ([(0,2),(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,1),(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                   => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,3),(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,2),(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)             => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                         => ([(0,4),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                         => ([(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)             => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,3),(0,5),(0,7),(1,2),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,2),(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,2),(0,5),(1,4),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,1),(0,2),(0,5),(0,7),(1,4),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)                                     => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)                                     => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,1),(0,2),(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,2),(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,4),(0,6),(0,7),(1,3),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                               => ([(0,4),(0,5),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,3),(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)                         => ([(0,3),(0,4),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,4),(0,5),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,2),(0,4),(0,5),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)             => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)                   => ([(0,3),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                   => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                   => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                   => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)             => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)       => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                               => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                               => ([(0,1),(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)                         => ([(0,3),(0,4),(0,5),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)                   => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                         => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
([(0,2),(0,3),(0,4),(0,6),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,2),(0,3),(0,4),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,1),(0,2),(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)             => ([(0,1),(0,2),(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)             => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)       => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7)                                                       => ([(0,4),(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                                       => ([(0,1),(0,2),(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                                 => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                                 => ([(0,1),(0,5),(0,7),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,6),(0,7),(1,3),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,4),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,3),(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,4),(0,5),(0,7),(1,2),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,2),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,2),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(5,6)],7)                                                 => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,4),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)                                           => ([(0,3),(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,3),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,3),(0,5),(0,7),(1,2),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                           => ([(0,1),(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,3),(0,6),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,3),(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,2),(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                               => ([(0,1),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,1),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                         => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)                                     => ([(0,3),(0,4),(0,5),(0,7),(1,2),(1,4),(1,5),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,2),(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)                                     => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,4),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,3),(0,4),(1,2),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,3),(0,4),(0,7),(1,2),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,2),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                                     => ([(0,1),(0,3),(0,5),(0,7),(1,2),(1,4),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,2),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,1),(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)                                     => ([(0,1),(0,4),(0,5),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,2),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                               => ([(0,1),(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                               => ([(0,1),(0,4),(0,6),(0,7),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)                         => ([(0,1),(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)                               => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                               => ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)                         => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,2),(0,3),(0,4),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,4),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)                         => ([(0,4),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,3),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,2),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,1),(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,2),(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)                         => ([(0,1),(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                         => ([(0,1),(0,4),(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,1),(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)             => ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,1),(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)                   => ([(0,1),(0,2),(0,3),(0,4),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)                   => ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)             => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

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Created: Dec 25, 2020 at 20:32 by Martin Rubey

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Last Updated: Dec 05, 2022 at 23:05 by Harry Richman