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Statistic identifier: St001949

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Collection: Graphs

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Description: The rigidity index of a graph.

A base of a permutation group is a set $B$ such that the pointwise stabilizer of $B$ is trivial.  For example, a base of the symmetric group on $n$ letters must contain all but one letter.

This statistic yields the minimal size of a base for the automorphism group of a graph.

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References: [1]   [[wikipedia:Base_(group_theory)]]

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Code:
def minimal_base(G):
    """
    EXAMPLES::

        sage: n=7; [G for G in SymmetricGroup(n).conjugacy_classes_subgroups() if G.base() != minimal_base(G)]
        [Subgroup generated by [(2,4,5,7,3), (2,3)(4,7), (1,6)(2,7,3,4)] of (Symmetric group of order 7! as a permutation group)]

    """
    b = G.base()
    if G.degree() <= 1:
        m = 1
    else:
        m = ceil(log(G.cardinality())/log(G.degree()))
    for i in range(m, len(b)):
        for s in Subsets(G.domain(), i):
            nb = G.base(seed=s)
            if len(nb) < len(b):
                return nb
    return b

def statistic(G):
    return len(minimal_base(G.automorphism_group()))


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Statistic values:

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

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Created: Jul 05, 2024 at 11:14 by Martin Rubey

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Last Updated: Jul 05, 2024 at 11:14 by Martin Rubey