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------------------------------------------------------------------------
Map identifier: Mp00110

------------------------------------------------------------------------
Map name: Greene-Kleitman invariant

------------------------------------------------------------------------
Domain: Posets

------------------------------------------------------------------------
Codomain: Integer partitions

------------------------------------------------------------------------
Description: The Greene-Kleitman invariant of a poset.

This is the partition $(c_1 - c_0, c_2 - c_1, c_3 - c_2, \ldots)$, where $c_k$ is the maximum cardinality of a union of $k$ chains of the poset.   Equivalently, this is the conjugate of the partition $(a_1 - a_0, a_2 - a_1, a_3 - a_2, \ldots)$, where $a_k$ is the maximum cardinality of a union of $k$ antichains of the poset.

------------------------------------------------------------------------
References: [1]   Britz, T., Fomin, S. Finite posets and Ferrers shapes [[MathSciNet:1814900]]

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

def mapping(X):
 return X.greene_shape()


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

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

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Created: Jan 29, 2020 at 13:25 by FindStatCrew

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Last Updated: Jan 29, 2020 at 13:25 by Martin Rubey