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------------------------------------------------------------------------
Map identifier: Mp00152

------------------------------------------------------------------------
Map name: Laplacian multiplicities

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

------------------------------------------------------------------------
Codomain: Integer compositions

------------------------------------------------------------------------
Description: The composition of multiplicities of the Laplacian eigenvalues.

Let $\lambda_1 > \lambda_2 > \dots$ be the eigenvalues of the Laplacian matrix of a graph on $n$ vertices.  Then this map returns the composition $a_1,\dots,a_k$ of $n$ where $a_i$ is the multiplicity of $\lambda_i$.

------------------------------------------------------------------------
References: [1]   Rubey, M. Multiplicities of the Laplacian eigenvalues of a graph [[MathOverflow:370748]]

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

def mapping(G):
    if G.num_verts() > 30:
        raise ValueError("Graph too big for this map")
    s = G.spectrum(laplacian=True)
    c = []
    i, o = 0, None
    for v in s:
        if v != o:
            c.append(i)
            i, o = 0, v
        i += 1
    c.append(i)
    return Composition(c[1:])

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

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

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Created: Sep 03, 2020 at 21:03 by Martin Rubey

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Last Updated: Sep 03, 2020 at 21:03 by Martin Rubey