************************************************************************
*    www.FindStat.org - The Combinatorial Statistic Finder             *
*                                                                      *
*    Copyright (C) 2013 The FindStatCrew <info@findstat.org>           *
*                                                                      *
*    This information is distributed in the hope that it will be       *
*    useful, but WITHOUT ANY WARRANTY; without even the implied        *
*    warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  *
************************************************************************

------------------------------------------------------------------------
Map identifier: Mp00205

------------------------------------------------------------------------
Map name: maximal antichains

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

------------------------------------------------------------------------
Codomain: Lattices

------------------------------------------------------------------------
Description: The lattice of maximal antichains in a poset.

An antichain $A$ in a poset is maximal if there is no antichain of larger cardinality which contains all elements of $A$.

The set of maximal antichains can be ordered by setting $A \leq B \Leftrightarrow \mathop{\downarrow} A  \subseteq \mathop{\downarrow}B$, where $\mathop{\downarrow}A$ is the order ideal generated by $A$.

------------------------------------------------------------------------
References: [1]   Reuter, K. The jump number and the lattice of maximal antichains [[MathSciNet:1108021]]

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

def mapping(P):
    A = [tuple(sorted(X)) for X in P.maximal_antichains()]
    if len(A) > 20:
        raise ValueError("Poset has too many maximal antichains for this map")   
    return LatticePoset([A, lambda X, Y: all(any(P.le(x, y) for y in Y) for x in X)])

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

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

-----------------------------------------------------------------------------
Created: Jan 26, 2021 at 20:20 by Martin Rubey

-----------------------------------------------------------------------------
Last Updated: Jan 28, 2021 at 17:46 by Christian Stump