************************************************************************
*    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: Mp00192

------------------------------------------------------------------------
Map name: dominating sublattice

------------------------------------------------------------------------
Domain: Skew partitions

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

------------------------------------------------------------------------
Description: Return the sublattice of the dominance order induced by the support of the expansion of the skew Schur function into Schur functions.

Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.  

It is shown in [1] that the subposet of the dominance order whose elements are the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a lattice.

The example $\lambda = (5^2,4^2,1)$ and $\mu=(3,2)$ shows that this lattice is not a sublattice of the dominance order.

------------------------------------------------------------------------
References: [1]   Azenhas, O. The admissible interval for the invariant factors of a product of matrices [[MathSciNet:1712853]]

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

def mapping(la):
    support = SymmetricFunctions(QQ).s()(la).support()
    return LatticePoset((support, lambda mu, nu: mu.dominates(nu)))

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

[[1],[]]                        => ([],1)
[[2],[]]                        => ([],1)
[[1,1],[]]                      => ([],1)
[[2,1],[1]]                     => ([(0,1)],2)
[[3],[]]                        => ([],1)
[[2,1],[]]                      => ([],1)
[[3,1],[1]]                     => ([(0,1)],2)
[[2,2],[1]]                     => ([],1)
[[3,2],[2]]                     => ([(0,1)],2)
[[1,1,1],[]]                    => ([],1)
[[2,2,1],[1,1]]                 => ([(0,1)],2)
[[2,1,1],[1]]                   => ([(0,1)],2)
[[3,2,1],[2,1]]                 => ([(0,2),(2,1)],3)
[[4],[]]                        => ([],1)
[[3,1],[]]                      => ([],1)
[[4,1],[1]]                     => ([(0,1)],2)
[[2,2],[]]                      => ([],1)
[[3,2],[1]]                     => ([(0,1)],2)
[[4,2],[2]]                     => ([(0,2),(2,1)],3)
[[2,1,1],[]]                    => ([],1)
[[3,2,1],[1,1]]                 => ([(0,2),(2,1)],3)
[[3,1,1],[1]]                   => ([(0,1)],2)
[[4,2,1],[2,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[3,3],[2]]                     => ([],1)
[[4,3],[3]]                     => ([(0,1)],2)
[[2,2,1],[1]]                   => ([(0,1)],2)
[[3,3,1],[2,1]]                 => ([(0,2),(2,1)],3)
[[3,2,1],[2]]                   => ([(0,2),(2,1)],3)
[[4,3,1],[3,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[2,2,2],[1,1]]                 => ([],1)
[[3,3,2],[2,2]]                 => ([(0,1)],2)
[[3,2,2],[2,1]]                 => ([(0,2),(2,1)],3)
[[4,3,2],[3,2]]                 => ([(0,3),(2,1),(3,2)],4)
[[1,1,1,1],[]]                  => ([],1)
[[2,2,2,1],[1,1,1]]             => ([(0,1)],2)
[[2,2,1,1],[1,1]]               => ([(0,2),(2,1)],3)
[[3,3,2,1],[2,2,1]]             => ([(0,3),(2,1),(3,2)],4)
[[2,1,1,1],[1]]                 => ([(0,1)],2)
[[3,2,2,1],[2,1,1]]             => ([(0,3),(2,1),(3,2)],4)
[[3,2,1,1],[2,1]]               => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,1],[3,2,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5],[]]                        => ([],1)
[[4,1],[]]                      => ([],1)
[[5,1],[1]]                     => ([(0,1)],2)
[[3,2],[]]                      => ([],1)
[[4,2],[1]]                     => ([(0,1)],2)
[[5,2],[2]]                     => ([(0,2),(2,1)],3)
[[3,1,1],[]]                    => ([],1)
[[4,2,1],[1,1]]                 => ([(0,2),(2,1)],3)
[[4,1,1],[1]]                   => ([(0,1)],2)
[[5,2,1],[2,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[3,3],[1]]                     => ([],1)
[[4,3],[2]]                     => ([(0,1)],2)
[[5,3],[3]]                     => ([(0,2),(2,1)],3)
[[2,2,1],[]]                    => ([],1)
[[3,3,1],[1,1]]                 => ([(0,1)],2)
[[3,2,1],[1]]                   => ([(0,2),(2,1)],3)
[[4,3,1],[2,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[4,2,1],[2]]                   => ([(0,3),(2,1),(3,2)],4)
[[5,3,1],[3,1]]                 => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,2,2],[1,1]]                 => ([(0,1)],2)
[[4,3,2],[2,2]]                 => ([(0,3),(2,1),(3,2)],4)
[[4,2,2],[2,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[5,3,2],[3,2]]                 => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,1,1,1],[]]                  => ([],1)
[[3,2,2,1],[1,1,1]]             => ([(0,2),(2,1)],3)
[[3,2,1,1],[1,1]]               => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,1],[2,2,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,1,1,1],[1]]                 => ([(0,1)],2)
[[4,2,2,1],[2,1,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,2,1,1],[2,1]]               => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,3,2,1],[3,2,1]]             => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,4],[3]]                     => ([],1)
[[5,4],[4]]                     => ([(0,1)],2)
[[3,3,1],[2]]                   => ([(0,1)],2)
[[4,4,1],[3,1]]                 => ([(0,2),(2,1)],3)
[[4,3,1],[3]]                   => ([(0,2),(2,1)],3)
[[5,4,1],[4,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[2,2,2],[1]]                   => ([],1)
[[3,3,2],[2,1]]                 => ([(0,2),(2,1)],3)
[[4,4,2],[3,2]]                 => ([(0,3),(2,1),(3,2)],4)
[[3,2,2],[2]]                   => ([(0,1)],2)
[[4,3,2],[3,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[5,4,2],[4,2]]                 => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,1,1],[1]]                 => ([(0,1)],2)
[[3,3,2,1],[2,1,1]]             => ([(0,3),(2,1),(3,2)],4)
[[3,3,1,1],[2,1]]               => ([(0,3),(2,1),(3,2)],4)
[[4,4,2,1],[3,2,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,2,1,1],[2]]                 => ([(0,2),(2,1)],3)
[[4,3,2,1],[3,1,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,1,1],[3,1]]               => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,2,1],[4,2,1]]             => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,3,3],[2,2]]                 => ([],1)
[[4,4,3],[3,3]]                 => ([(0,1)],2)
[[4,3,3],[3,2]]                 => ([(0,2),(2,1)],3)
[[5,4,3],[4,3]]                 => ([(0,3),(2,1),(3,2)],4)
[[2,2,2,1],[1,1]]               => ([(0,1)],2)
[[3,3,3,1],[2,2,1]]             => ([(0,2),(2,1)],3)
[[3,3,2,1],[2,2]]               => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,1],[3,3,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,2,2,1],[2,1]]               => ([(0,3),(2,1),(3,2)],4)
[[4,3,3,1],[3,2,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,2,1],[3,2]]               => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,1],[4,3,1]]             => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,2],[1,1,1]]             => ([],1)
[[3,3,3,2],[2,2,2]]             => ([(0,1)],2)
[[3,3,2,2],[2,2,1]]             => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,2],[3,3,2]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,2,2,2],[2,1,1]]             => ([(0,2),(2,1)],3)
[[4,3,3,2],[3,2,2]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,2,2],[3,2,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,2],[4,3,2]]             => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,1,1],[]]                => ([],1)
[[2,2,2,2,1],[1,1,1,1]]         => ([(0,1)],2)
[[2,2,2,1,1],[1,1,1]]           => ([(0,2),(2,1)],3)
[[3,3,3,2,1],[2,2,2,1]]         => ([(0,3),(2,1),(3,2)],4)
[[2,2,1,1,1],[1,1]]             => ([(0,2),(2,1)],3)
[[3,3,2,2,1],[2,2,1,1]]         => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,2,1,1],[2,2,1]]           => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,2,1],[3,3,2,1]]         => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,1,1,1,1],[1]]               => ([(0,1)],2)
[[3,2,2,2,1],[2,1,1,1]]         => ([(0,3),(2,1),(3,2)],4)
[[3,2,2,1,1],[2,1,1]]           => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,2,1],[3,2,2,1]]         => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,2,1,1,1],[2,1]]             => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,2,1],[3,2,1,1]]         => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,3,2,1,1],[3,2,1]]           => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,3,2,1],[4,3,2,1]]         => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[6],[]]                        => ([],1)
[[5,1],[]]                      => ([],1)
[[6,1],[1]]                     => ([(0,1)],2)
[[4,2],[]]                      => ([],1)
[[5,2],[1]]                     => ([(0,1)],2)
[[6,2],[2]]                     => ([(0,2),(2,1)],3)
[[4,1,1],[]]                    => ([],1)
[[5,2,1],[1,1]]                 => ([(0,2),(2,1)],3)
[[5,1,1],[1]]                   => ([(0,1)],2)
[[6,2,1],[2,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[3,3],[]]                      => ([],1)
[[4,3],[1]]                     => ([(0,1)],2)
[[5,3],[2]]                     => ([(0,2),(2,1)],3)
[[6,3],[3]]                     => ([(0,3),(2,1),(3,2)],4)
[[3,2,1],[]]                    => ([],1)
[[4,3,1],[1,1]]                 => ([(0,2),(2,1)],3)
[[4,2,1],[1]]                   => ([(0,2),(2,1)],3)
[[5,3,1],[2,1]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,2,1],[2]]                   => ([(0,3),(2,1),(3,2)],4)
[[6,3,1],[3,1]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,2,2],[1,1]]                 => ([(0,1)],2)
[[5,3,2],[2,2]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,2,2],[2,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[6,3,2],[3,2]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[3,1,1,1],[]]                  => ([],1)
[[4,2,2,1],[1,1,1]]             => ([(0,2),(2,1)],3)
[[4,2,1,1],[1,1]]               => ([(0,3),(2,1),(3,2)],4)
[[5,3,2,1],[2,2,1]]             => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,1,1,1],[1]]                 => ([(0,1)],2)
[[5,2,2,1],[2,1,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,2,1,1],[2,1]]               => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,3,2,1],[3,2,1]]             => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4],[2]]                     => ([],1)
[[5,4],[3]]                     => ([(0,1)],2)
[[6,4],[4]]                     => ([(0,2),(2,1)],3)
[[3,3,1],[1]]                   => ([(0,1)],2)
[[4,4,1],[2,1]]                 => ([(0,2),(2,1)],3)
[[4,3,1],[2]]                   => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,4,1],[3,1]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,3,1],[3]]                   => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,4,1],[4,1]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[2,2,2],[]]                    => ([],1)
[[3,3,2],[1,1]]                 => ([(0,1)],2)
[[4,4,2],[2,2]]                 => ([(0,2),(2,1)],3)
[[3,2,2],[1]]                   => ([(0,1)],2)
[[4,3,2],[2,1]]                 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,4,2],[3,2]]                 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,2,2],[2]]                   => ([(0,2),(2,1)],3)
[[5,3,2],[3,1]]                 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,4,2],[4,2]]                 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[2,2,1,1],[]]                  => ([],1)
[[3,3,2,1],[1,1,1]]             => ([(0,2),(2,1)],3)
[[3,3,1,1],[1,1]]               => ([(0,2),(2,1)],3)
[[4,4,2,1],[2,2,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,2,1,1],[1]]                 => ([(0,2),(2,1)],3)
[[4,3,2,1],[2,1,1]]             => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[4,3,1,1],[2,1]]               => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[5,4,2,1],[3,2,1]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[4,2,1,1],[2]]                 => ([(0,3),(2,1),(3,2)],4)
[[5,3,2,1],[3,1,1]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[5,3,1,1],[3,1]]               => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[6,4,2,1],[4,2,1]]             => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)
[[4,3,3],[2,2]]                 => ([(0,1)],2)
[[5,4,3],[3,3]]                 => ([(0,3),(2,1),(3,2)],4)
[[5,3,3],[3,2]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,4,3],[4,3]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[3,2,2,1],[1,1]]               => ([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,3,1],[2,2,1]]             => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,3,2,1],[2,2]]               => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,4,3,1],[3,3,1]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[4,2,2,1],[2,1]]               => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[5,3,3,1],[3,2,1]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[5,3,2,1],[3,2]]               => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[6,4,3,1],[4,3,1]]             => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)
[[3,2,2,2],[1,1,1]]             => ([(0,1)],2)
[[4,3,3,2],[2,2,2]]             => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,2],[2,2,1]]             => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,4,3,2],[3,3,2]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[4,2,2,2],[2,1,1]]             => ([(0,3),(2,1),(3,2)],4)
[[5,3,3,2],[3,2,2]]             => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[5,3,2,2],[3,2,1]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[6,4,3,2],[4,3,2]]             => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)
[[2,1,1,1,1],[]]                => ([],1)
[[3,2,2,2,1],[1,1,1,1]]         => ([(0,2),(2,1)],3)
[[3,2,2,1,1],[1,1,1]]           => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,2,1],[2,2,2,1]]         => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,2,1,1,1],[1,1]]             => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,2,1],[2,2,1,1]]         => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[4,3,2,1,1],[2,2,1]]           => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,4,3,2,1],[3,3,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[3,1,1,1,1],[1]]               => ([(0,1)],2)
[[4,2,2,2,1],[2,1,1,1]]         => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,2,2,1,1],[2,1,1]]           => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[5,3,3,2,1],[3,2,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[4,2,1,1,1],[2,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,3,2,2,1],[3,2,1,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[5,3,2,1,1],[3,2,1]]           => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[6,4,3,2,1],[4,3,2,1]]         => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10)
[[5,5],[4]]                     => ([],1)
[[6,5],[5]]                     => ([(0,1)],2)
[[4,4,1],[3]]                   => ([(0,1)],2)
[[5,5,1],[4,1]]                 => ([(0,2),(2,1)],3)
[[5,4,1],[4]]                   => ([(0,2),(2,1)],3)
[[6,5,1],[5,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[3,3,2],[2]]                   => ([(0,1)],2)
[[4,4,2],[3,1]]                 => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,5,2],[4,2]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,3,2],[3]]                   => ([(0,2),(2,1)],3)
[[5,4,2],[4,1]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,5,2],[5,2]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[3,3,1,1],[2]]                 => ([(0,1)],2)
[[4,4,2,1],[3,1,1]]             => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,1,1],[3,1]]               => ([(0,3),(2,1),(3,2)],4)
[[5,5,2,1],[4,2,1]]             => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,1,1],[3]]                 => ([(0,2),(2,1)],3)
[[5,4,2,1],[4,1,1]]             => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,1,1],[4,1]]               => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,5,2,1],[5,2,1]]             => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,3,3],[2,1]]                 => ([],1)
[[4,4,3],[3,2]]                 => ([(0,2),(2,1)],3)
[[5,5,3],[4,3]]                 => ([(0,3),(2,1),(3,2)],4)
[[4,3,3],[3,1]]                 => ([(0,2),(2,1)],3)
[[5,4,3],[4,2]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,5,3],[5,3]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[2,2,2,1],[1]]                 => ([(0,1)],2)
[[3,3,3,1],[2,1,1]]             => ([(0,2),(2,1)],3)
[[3,3,2,1],[2,1]]               => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,4,3,1],[3,2,1]]             => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[4,4,2,1],[3,2]]               => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,5,3,1],[4,3,1]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[3,2,2,1],[2]]                 => ([(0,2),(2,1)],3)
[[4,3,3,1],[3,1,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,2,1],[3,1]]               => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,4,3,1],[4,2,1]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[5,4,2,1],[4,2]]               => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[6,5,3,1],[5,3,1]]             => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)
[[3,3,2,2],[2,1,1]]             => ([(0,1),(0,2),(1,3),(2,3)],4)
[[4,4,3,2],[3,2,2]]             => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,4,2,2],[3,2,1]]             => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,5,3,2],[4,3,2]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[4,3,2,2],[3,1,1]]             => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,4,3,2],[4,2,2]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[5,4,2,2],[4,2,1]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[6,5,3,2],[5,3,2]]             => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)
[[2,2,1,1,1],[1]]               => ([(0,1)],2)
[[3,3,2,2,1],[2,1,1,1]]         => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,2,1,1],[2,1,1]]           => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,4,3,2,1],[3,2,2,1]]         => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[3,3,1,1,1],[2,1]]             => ([(0,3),(2,1),(3,2)],4)
[[4,4,2,2,1],[3,2,1,1]]         => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[4,4,2,1,1],[3,2,1]]           => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,5,3,2,1],[4,3,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[3,2,1,1,1],[2]]               => ([(0,2),(2,1)],3)
[[4,3,2,2,1],[3,1,1,1]]         => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,2,1,1],[3,1,1]]           => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,4,3,2,1],[4,2,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[4,3,1,1,1],[3,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,2,2,1],[4,2,1,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[5,4,2,1,1],[4,2,1]]           => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[6,5,3,2,1],[5,3,2,1]]         => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10)
[[4,4,4],[3,3]]                 => ([],1)
[[5,5,4],[4,4]]                 => ([(0,1)],2)
[[5,4,4],[4,3]]                 => ([(0,2),(2,1)],3)
[[6,5,4],[5,4]]                 => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,1],[2,2]]               => ([(0,1)],2)
[[4,4,4,1],[3,3,1]]             => ([(0,2),(2,1)],3)
[[4,4,3,1],[3,3]]               => ([(0,3),(2,1),(3,2)],4)
[[5,5,4,1],[4,4,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,1],[3,2]]               => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,4,4,1],[4,3,1]]             => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,3,1],[4,3]]               => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,5,4,1],[5,4,1]]             => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[2,2,2,2],[1,1]]               => ([],1)
[[3,3,3,2],[2,2,1]]             => ([(0,2),(2,1)],3)
[[4,4,4,2],[3,3,2]]             => ([(0,3),(2,1),(3,2)],4)
[[3,3,2,2],[2,2]]               => ([(0,2),(2,1)],3)
[[4,4,3,2],[3,3,1]]             => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[5,5,4,2],[4,4,2]]             => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[3,2,2,2],[2,1]]               => ([(0,2),(2,1)],3)
[[4,3,3,2],[3,2,1]]             => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,4,4,2],[4,3,2]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[4,3,2,2],[3,2]]               => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,2],[4,3,1]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[6,5,4,2],[5,4,2]]             => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)
[[2,2,2,1,1],[1,1]]             => ([(0,2),(2,1)],3)
[[3,3,3,2,1],[2,2,1,1]]         => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,3,1,1],[2,2,1]]           => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,4,2,1],[3,3,2,1]]         => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,3,2,1,1],[2,2]]             => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,2,1],[3,3,1,1]]         => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[4,4,3,1,1],[3,3,1]]           => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[5,5,4,2,1],[4,4,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[3,2,2,1,1],[2,1]]             => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,2,1],[3,2,1,1]]         => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[4,3,3,1,1],[3,2,1]]           => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,4,4,2,1],[4,3,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[4,3,2,1,1],[3,2]]             => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,3,2,1],[4,3,1,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[5,4,3,1,1],[4,3,1]]           => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[6,5,4,2,1],[5,4,2,1]]         => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10)
[[3,3,3,3],[2,2,2]]             => ([],1)
[[4,4,4,3],[3,3,3]]             => ([(0,1)],2)
[[4,4,3,3],[3,3,2]]             => ([(0,3),(2,1),(3,2)],4)
[[5,5,4,3],[4,4,3]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,3],[3,2,2]]             => ([(0,2),(2,1)],3)
[[5,4,4,3],[4,3,3]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,3],[4,3,2]]             => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,5,4,3],[5,4,3]]             => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[2,2,2,2,1],[1,1,1]]           => ([(0,1)],2)
[[3,3,3,3,1],[2,2,2,1]]         => ([(0,2),(2,1)],3)
[[3,3,3,2,1],[2,2,2]]           => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,3,1],[3,3,3,1]]         => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,2,2,1],[2,2,1]]           => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,4,3,3,1],[3,3,2,1]]         => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[4,4,3,2,1],[3,3,2]]           => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,5,4,3,1],[4,4,3,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[3,2,2,2,1],[2,1,1]]           => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,3,1],[3,2,2,1]]         => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,3,2,1],[3,2,2]]           => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,4,4,3,1],[4,3,3,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[4,3,2,2,1],[3,2,1]]           => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,4,3,3,1],[4,3,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[5,4,3,2,1],[4,3,2]]           => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[6,5,4,3,1],[5,4,3,1]]         => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10)
[[2,2,2,2,2],[1,1,1,1]]         => ([],1)
[[3,3,3,3,2],[2,2,2,2]]         => ([(0,1)],2)
[[3,3,3,2,2],[2,2,2,1]]         => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,3,2],[3,3,3,2]]         => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,2,2,2],[2,2,1,1]]         => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,3,2],[3,3,2,2]]         => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4,3,2,2],[3,3,2,1]]         => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,5,4,3,2],[4,4,3,2]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[3,2,2,2,2],[2,1,1,1]]         => ([(0,2),(2,1)],3)
[[4,3,3,3,2],[3,2,2,2]]         => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,2,2],[3,2,2,1]]         => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,4,4,3,2],[4,3,3,2]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[4,3,2,2,2],[3,2,1,1]]         => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,3,3,2],[4,3,2,2]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[5,4,3,2,2],[4,3,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
[[6,5,4,3,2],[5,4,3,2]]         => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10)
[[1,1,1,1,1,1],[]]              => ([],1)
[[2,2,2,2,2,1],[1,1,1,1,1]]     => ([(0,1)],2)
[[2,2,2,2,1,1],[1,1,1,1]]       => ([(0,2),(2,1)],3)
[[3,3,3,3,2,1],[2,2,2,2,1]]     => ([(0,3),(2,1),(3,2)],4)
[[2,2,2,1,1,1],[1,1,1]]         => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,2,2,1],[2,2,2,1,1]]     => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[3,3,3,2,1,1],[2,2,2,1]]       => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[4,4,4,3,2,1],[3,3,3,2,1]]     => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[2,2,1,1,1,1],[1,1]]           => ([(0,2),(2,1)],3)
[[3,3,2,2,2,1],[2,2,1,1,1]]     => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[3,3,2,2,1,1],[2,2,1,1]]       => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[4,4,3,3,2,1],[3,3,2,2,1]]     => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)
[[3,3,2,1,1,1],[2,2,1]]         => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[4,4,3,2,2,1],[3,3,2,1,1]]     => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)
[[4,4,3,2,1,1],[3,3,2,1]]       => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)
[[5,5,4,3,2,1],[4,4,3,2,1]]     => ([(0,7),(1,9),(2,9),(4,8),(5,8),(6,3),(7,1),(7,2),(8,6),(9,4),(9,5)],10)
[[2,1,1,1,1,1],[1]]             => ([(0,1)],2)
[[3,2,2,2,2,1],[2,1,1,1,1]]     => ([(0,3),(2,1),(3,2)],4)
[[3,2,2,2,1,1],[2,1,1,1]]       => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[4,3,3,3,2,1],[3,2,2,2,1]]     => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[3,2,2,1,1,1],[2,1,1]]         => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[4,3,3,2,2,1],[3,2,2,1,1]]     => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)
[[4,3,3,2,1,1],[3,2,2,1]]       => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)
[[5,4,4,3,2,1],[4,3,3,2,1]]     => ([(0,7),(1,9),(2,9),(4,8),(5,8),(6,3),(7,1),(7,2),(8,6),(9,4),(9,5)],10)
[[3,2,1,1,1,1],[2,1]]           => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,2,2,1],[3,2,1,1,1]]     => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[4,3,2,2,1,1],[3,2,1,1]]       => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)
[[5,4,3,3,2,1],[4,3,2,2,1]]     => ([(0,7),(1,9),(2,9),(4,8),(5,8),(6,3),(7,1),(7,2),(8,6),(9,4),(9,5)],10)
[[4,3,2,1,1,1],[3,2,1]]         => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[5,4,3,2,2,1],[4,3,2,1,1]]     => ([(0,7),(1,9),(2,9),(4,8),(5,8),(6,3),(7,1),(7,2),(8,6),(9,4),(9,5)],10)
[[5,4,3,2,1,1],[4,3,2,1]]       => ([(0,7),(1,9),(2,9),(4,8),(5,8),(6,3),(7,1),(7,2),(8,6),(9,4),(9,5)],10)
[[6,5,4,3,2,1],[5,4,3,2,1]]     => ([(0,7),(1,10),(2,10),(4,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,6),(10,4),(10,5)],11)
[[7],[]]                        => ([],1)
[[6,1],[]]                      => ([],1)
[[7,1],[1]]                     => ([(0,1)],2)
[[5,2],[]]                      => ([],1)
[[6,2],[1]]                     => ([(0,1)],2)
[[7,2],[2]]                     => ([(0,2),(2,1)],3)
[[5,1,1],[]]                    => ([],1)
[[6,2,1],[1,1]]                 => ([(0,2),(2,1)],3)
[[6,1,1],[1]]                   => ([(0,1)],2)
[[7,2,1],[2,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[4,3],[]]                      => ([],1)
[[5,3],[1]]                     => ([(0,1)],2)
[[6,3],[2]]                     => ([(0,2),(2,1)],3)
[[7,3],[3]]                     => ([(0,3),(2,1),(3,2)],4)
[[4,2,1],[]]                    => ([],1)
[[5,3,1],[1,1]]                 => ([(0,2),(2,1)],3)
[[5,2,1],[1]]                   => ([(0,2),(2,1)],3)
[[6,3,1],[2,1]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,2,1],[2]]                   => ([(0,3),(2,1),(3,2)],4)
[[7,3,1],[3,1]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[5,2,2],[1,1]]                 => ([(0,1)],2)
[[6,3,2],[2,2]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,2,2],[2,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[7,3,2],[3,2]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,1,1,1],[]]                  => ([],1)
[[5,2,2,1],[1,1,1]]             => ([(0,2),(2,1)],3)
[[5,2,1,1],[1,1]]               => ([(0,3),(2,1),(3,2)],4)
[[6,3,2,1],[2,2,1]]             => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,1,1,1],[1]]                 => ([(0,1)],2)
[[6,2,2,1],[2,1,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,2,1,1],[2,1]]               => ([(0,4),(2,3),(3,1),(4,2)],5)
[[7,3,2,1],[3,2,1]]             => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4],[1]]                     => ([],1)
[[5,4],[2]]                     => ([(0,1)],2)
[[6,4],[3]]                     => ([(0,2),(2,1)],3)
[[7,4],[4]]                     => ([(0,3),(2,1),(3,2)],4)
[[3,3,1],[]]                    => ([],1)
[[4,4,1],[1,1]]                 => ([(0,1)],2)
[[4,3,1],[1]]                   => ([(0,2),(2,1)],3)
[[5,4,1],[2,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[5,3,1],[2]]                   => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[6,4,1],[3,1]]                 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,3,1],[3]]                   => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[7,4,1],[4,1]]                 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,2,2],[]]                    => ([],1)
[[4,3,2],[1,1]]                 => ([(0,2),(2,1)],3)
[[5,4,2],[2,2]]                 => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,2,2],[1]]                   => ([(0,1)],2)
[[5,3,2],[2,1]]                 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[6,4,2],[3,2]]                 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[5,2,2],[2]]                   => ([(0,2),(2,1)],3)
[[6,3,2],[3,1]]                 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[7,4,2],[4,2]]                 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
[[3,2,1,1],[]]                  => ([],1)
[[4,3,2,1],[1,1,1]]             => ([(0,3),(2,1),(3,2)],4)
[[4,3,1,1],[1,1]]               => ([(0,3),(2,1),(3,2)],4)
[[5,4,2,1],[2,2,1]]             => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,2,1,1],[1]]                 => ([(0,2),(2,1)],3)
[[5,3,2,1],[2,1,1]]             => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[5,3,1,1],[2,1]]               => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[6,4,2,1],[3,2,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[5,2,1,1],[2]]                 => ([(0,3),(2,1),(3,2)],4)
[[6,3,2,1],[3,1,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[6,3,1,1],[3,1]]               => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[7,4,2,1],[4,2,1]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[5,3,3],[2,2]]                 => ([(0,2),(2,1)],3)
[[6,4,3],[3,3]]                 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,3,3],[3,2]]                 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[7,4,3],[4,3]]                 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,2,2,1],[1,1]]               => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,3,3,1],[2,2,1]]             => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[5,3,2,1],[2,2]]               => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,4,3,1],[3,3,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[5,2,2,1],[2,1]]               => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[6,3,3,1],[3,2,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[6,3,2,1],[3,2]]               => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[7,4,3,1],[4,3,1]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[4,2,2,2],[1,1,1]]             => ([(0,1)],2)
[[5,3,3,2],[2,2,2]]             => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,3,2,2],[2,2,1]]             => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,4,3,2],[3,3,2]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[5,2,2,2],[2,1,1]]             => ([(0,3),(2,1),(3,2)],4)
[[6,3,3,2],[3,2,2]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[6,3,2,2],[3,2,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[7,4,3,2],[4,3,2]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,1,1,1,1],[]]                => ([],1)
[[4,2,2,2,1],[1,1,1,1]]         => ([(0,2),(2,1)],3)
[[4,2,2,1,1],[1,1,1]]           => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,3,3,2,1],[2,2,2,1]]         => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[4,2,1,1,1],[1,1]]             => ([(0,3),(2,1),(3,2)],4)
[[5,3,2,2,1],[2,2,1,1]]         => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[5,3,2,1,1],[2,2,1]]           => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,4,3,2,1],[3,3,2,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,1,1,1,1],[1]]               => ([(0,1)],2)
[[5,2,2,2,1],[2,1,1,1]]         => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,2,2,1,1],[2,1,1]]           => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[6,3,3,2,1],[3,2,2,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,2,1,1,1],[2,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,3,2,2,1],[3,2,1,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,3,2,1,1],[3,2,1]]           => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,4,3,2,1],[4,3,2,1]]         => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[5,5],[3]]                     => ([],1)
[[6,5],[4]]                     => ([(0,1)],2)
[[7,5],[5]]                     => ([(0,2),(2,1)],3)
[[4,4,1],[2]]                   => ([(0,1)],2)
[[5,5,1],[3,1]]                 => ([(0,2),(2,1)],3)
[[5,4,1],[3]]                   => ([(0,1),(0,2),(1,3),(2,3)],4)
[[6,5,1],[4,1]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,4,1],[4]]                   => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7,5,1],[5,1]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[3,3,2],[1]]                   => ([(0,1)],2)
[[4,4,2],[2,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[5,5,2],[3,2]]                 => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,2],[2]]                   => ([(0,3),(2,1),(3,2)],4)
[[5,4,2],[3,1]]                 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[6,5,2],[4,2]]                 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[5,3,2],[3]]                   => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,4,2],[4,1]]                 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[7,5,2],[5,2]]                 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
[[3,3,1,1],[1]]                 => ([(0,1)],2)
[[4,4,2,1],[2,1,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,1,1],[2,1]]               => ([(0,3),(2,1),(3,2)],4)
[[5,5,2,1],[3,2,1]]             => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,3,1,1],[2]]                 => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,4,2,1],[3,1,1]]             => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[5,4,1,1],[3,1]]               => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[6,5,2,1],[4,2,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[5,3,1,1],[3]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,4,2,1],[4,1,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[6,4,1,1],[4,1]]               => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[7,5,2,1],[5,2,1]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,3,3],[1,1]]                 => ([],1)
[[4,4,3],[2,2]]                 => ([(0,1)],2)
[[5,5,3],[3,3]]                 => ([(0,2),(2,1)],3)
[[4,3,3],[2,1]]                 => ([(0,2),(2,1)],3)
[[5,4,3],[3,2]]                 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[6,5,3],[4,3]]                 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[5,3,3],[3,1]]                 => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,4,3],[4,2]]                 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[7,5,3],[5,3]]                 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
[[2,2,2,1],[]]                  => ([],1)
[[3,3,3,1],[1,1,1]]             => ([(0,1)],2)
[[3,3,2,1],[1,1]]               => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,1],[2,2,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,2,1],[2,2]]               => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,5,3,1],[3,3,1]]             => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[3,2,2,1],[1]]                 => ([(0,2),(2,1)],3)
[[4,3,3,1],[2,1,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,2,1],[2,1]]               => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,4,3,1],[3,2,1]]             => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[5,4,2,1],[3,2]]               => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,5,3,1],[4,3,1]]             => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,2,2,1],[2]]                 => ([(0,3),(2,1),(3,2)],4)
[[5,3,3,1],[3,1,1]]             => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[5,3,2,1],[3,1]]               => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,4,3,1],[4,2,1]]             => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,4,2,1],[4,2]]               => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,5,3,1],[5,3,1]]             => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[3,3,2,2],[1,1,1]]             => ([(0,1)],2)
[[4,4,3,2],[2,2,2]]             => ([(0,3),(2,1),(3,2)],4)
[[4,4,2,2],[2,2,1]]             => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,5,3,2],[3,3,2]]             => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[4,3,2,2],[2,1,1]]             => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[5,4,3,2],[3,2,2]]             => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[5,4,2,2],[3,2,1]]             => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,5,3,2],[4,3,2]]             => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,3,2,2],[3,1,1]]             => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[6,4,3,2],[4,2,2]]             => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,4,2,2],[4,2,1]]             => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,5,3,2],[5,3,2]]             => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[2,2,1,1,1],[]]                => ([],1)
[[3,3,2,2,1],[1,1,1,1]]         => ([(0,2),(2,1)],3)
[[3,3,2,1,1],[1,1,1]]           => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,2,1],[2,2,2,1]]         => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,3,1,1,1],[1,1]]             => ([(0,2),(2,1)],3)
[[4,4,2,2,1],[2,2,1,1]]         => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[4,4,2,1,1],[2,2,1]]           => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[5,5,3,2,1],[3,3,2,1]]         => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[3,2,1,1,1],[1]]               => ([(0,2),(2,1)],3)
[[4,3,2,2,1],[2,1,1,1]]         => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[4,3,2,1,1],[2,1,1]]           => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,4,3,2,1],[3,2,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[4,3,1,1,1],[2,1]]             => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[5,4,2,2,1],[3,2,1,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,2,1,1],[3,2,1]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,3,2,1],[4,3,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,2,1,1,1],[2]]               => ([(0,3),(2,1),(3,2)],4)
[[5,3,2,2,1],[3,1,1,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,3,2,1,1],[3,1,1]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,4,3,2,1],[4,2,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,3,1,1,1],[3,1]]             => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[6,4,2,2,1],[4,2,1,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,4,2,1,1],[4,2,1]]           => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,5,3,2,1],[5,3,2,1]]         => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[5,4,4],[3,3]]                 => ([(0,1)],2)
[[6,5,4],[4,4]]                 => ([(0,3),(2,1),(3,2)],4)
[[6,4,4],[4,3]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7,5,4],[5,4]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,3,3,1],[2,2]]               => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[5,4,4,1],[3,3,1]]             => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[5,4,3,1],[3,3]]               => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,5,4,1],[4,4,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[5,3,3,1],[3,2]]               => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,4,4,1],[4,3,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[6,4,3,1],[4,3]]               => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[7,5,4,1],[5,4,1]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,2,2,2],[1,1]]               => ([(0,1)],2)
[[4,3,3,2],[2,2,1]]             => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[5,4,4,2],[3,3,2]]             => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[4,3,2,2],[2,2]]               => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,3,2],[3,3,1]]             => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,5,4,2],[4,4,2]]             => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,2,2,2],[2,1]]               => ([(0,3),(2,1),(3,2)],4)
[[5,3,3,2],[3,2,1]]             => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,4,4,2],[4,3,2]]             => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,3,2,2],[3,2]]               => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[6,4,3,2],[4,3,1]]             => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,5,4,2],[5,4,2]]             => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[3,2,2,1,1],[1,1]]             => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,3,3,2,1],[2,2,1,1]]         => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[4,3,3,1,1],[2,2,1]]           => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,4,4,2,1],[3,3,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[4,3,2,1,1],[2,2]]             => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,4,3,2,1],[3,3,1,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,3,1,1],[3,3,1]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,2,1],[4,4,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,2,2,1,1],[2,1]]             => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,3,3,2,1],[3,2,1,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,3,3,1,1],[3,2,1]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,4,4,2,1],[4,3,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,3,2,1,1],[3,2]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[6,4,3,2,1],[4,3,1,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,4,3,1,1],[4,3,1]]           => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,5,4,2,1],[5,4,2,1]]         => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[4,3,3,3],[2,2,2]]             => ([(0,1)],2)
[[5,4,4,3],[3,3,3]]             => ([(0,3),(2,1),(3,2)],4)
[[5,4,3,3],[3,3,2]]             => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,5,4,3],[4,4,3]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[5,3,3,3],[3,2,2]]             => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,4,4,3],[4,3,3]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[6,4,3,3],[4,3,2]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[7,5,4,3],[5,4,3]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,2,2,2,1],[1,1,1]]           => ([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,3,3,1],[2,2,2,1]]         => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,3,3,2,1],[2,2,2]]           => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,4,4,3,1],[3,3,3,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[4,3,2,2,1],[2,2,1]]           => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,4,3,3,1],[3,3,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,3,2,1],[3,3,2]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,3,1],[4,4,3,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,2,2,2,1],[2,1,1]]           => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,3,3,3,1],[3,2,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,3,3,2,1],[3,2,2]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,4,4,3,1],[4,3,3,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,3,2,2,1],[3,2,1]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,4,3,3,1],[4,3,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,4,3,2,1],[4,3,2]]           => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,5,4,3,1],[5,4,3,1]]         => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[3,2,2,2,2],[1,1,1,1]]         => ([(0,1)],2)
[[4,3,3,3,2],[2,2,2,2]]         => ([(0,3),(2,1),(3,2)],4)
[[4,3,3,2,2],[2,2,2,1]]         => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,4,4,3,2],[3,3,3,2]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[4,3,2,2,2],[2,2,1,1]]         => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,4,3,3,2],[3,3,2,2]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,3,2,2],[3,3,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,3,2],[4,4,3,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,2,2,2,2],[2,1,1,1]]         => ([(0,3),(2,1),(3,2)],4)
[[5,3,3,3,2],[3,2,2,2]]         => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[5,3,3,2,2],[3,2,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,4,4,3,2],[4,3,3,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,3,2,2,2],[3,2,1,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[6,4,3,3,2],[4,3,2,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,4,3,2,2],[4,3,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,5,4,3,2],[5,4,3,2]]         => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[2,1,1,1,1,1],[]]              => ([],1)
[[3,2,2,2,2,1],[1,1,1,1,1]]     => ([(0,2),(2,1)],3)
[[3,2,2,2,1,1],[1,1,1,1]]       => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,3,2,1],[2,2,2,2,1]]     => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,2,2,1,1,1],[1,1,1]]         => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,3,2,2,1],[2,2,2,1,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[4,3,3,2,1,1],[2,2,2,1]]       => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,4,3,2,1],[3,3,3,2,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[3,2,1,1,1,1],[1,1]]           => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,2,2,1],[2,2,1,1,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[4,3,2,2,1,1],[2,2,1,1]]       => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,3,3,2,1],[3,3,2,2,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,3,2,1,1,1],[2,2,1]]         => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,3,2,2,1],[3,3,2,1,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,3,2,1,1],[3,3,2,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,3,2,1],[4,4,3,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,1,1,1,1,1],[1]]             => ([(0,1)],2)
[[4,2,2,2,2,1],[2,1,1,1,1]]     => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,2,2,2,1,1],[2,1,1,1]]       => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,3,3,3,2,1],[3,2,2,2,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,2,2,1,1,1],[2,1,1]]         => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,3,3,2,2,1],[3,2,2,1,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,3,3,2,1,1],[3,2,2,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,4,4,3,2,1],[4,3,3,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,2,1,1,1,1],[2,1]]           => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,3,2,2,2,1],[3,2,1,1,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,3,2,2,1,1],[3,2,1,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,4,3,3,2,1],[4,3,2,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,3,2,1,1,1],[3,2,1]]         => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[6,4,3,2,2,1],[4,3,2,1,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,4,3,2,1,1],[4,3,2,1]]       => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,5,4,3,2,1],[5,4,3,2,1]]     => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[6,6],[5]]                     => ([],1)
[[7,6],[6]]                     => ([(0,1)],2)
[[5,5,1],[4]]                   => ([(0,1)],2)
[[6,6,1],[5,1]]                 => ([(0,2),(2,1)],3)
[[6,5,1],[5]]                   => ([(0,2),(2,1)],3)
[[7,6,1],[6,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[4,4,2],[3]]                   => ([(0,1)],2)
[[5,5,2],[4,1]]                 => ([(0,1),(0,2),(1,3),(2,3)],4)
[[6,6,2],[5,2]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,4,2],[4]]                   => ([(0,2),(2,1)],3)
[[6,5,2],[5,1]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7,6,2],[6,2]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,4,1,1],[3]]                 => ([(0,1)],2)
[[5,5,2,1],[4,1,1]]             => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,5,1,1],[4,1]]               => ([(0,3),(2,1),(3,2)],4)
[[6,6,2,1],[5,2,1]]             => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,1,1],[4]]                 => ([(0,2),(2,1)],3)
[[6,5,2,1],[5,1,1]]             => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,5,1,1],[5,1]]               => ([(0,4),(2,3),(3,1),(4,2)],5)
[[7,6,2,1],[6,2,1]]             => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,3,3],[2]]                   => ([],1)
[[4,4,3],[3,1]]                 => ([(0,2),(2,1)],3)
[[5,5,3],[4,2]]                 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[6,6,3],[5,3]]                 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,3],[3]]                   => ([(0,1)],2)
[[5,4,3],[4,1]]                 => ([(0,3),(2,1),(3,2)],4)
[[6,5,3],[5,2]]                 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[7,6,3],[6,3]]                 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,3,2,1],[2]]                 => ([(0,2),(2,1)],3)
[[4,4,3,1],[3,1,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,2,1],[3,1]]               => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[5,5,3,1],[4,2,1]]             => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[5,5,2,1],[4,2]]               => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,6,3,1],[5,3,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[4,3,2,1],[3]]                 => ([(0,3),(2,1),(3,2)],4)
[[5,4,3,1],[4,1,1]]             => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,2,1],[4,1]]               => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,5,3,1],[5,2,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[6,5,2,1],[5,2]]               => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[7,6,3,1],[6,3,1]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[4,4,2,2],[3,1,1]]             => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[5,5,3,2],[4,2,2]]             => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[5,5,2,2],[4,2,1]]             => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,6,3,2],[5,3,2]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[5,4,2,2],[4,1,1]]             => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[6,5,3,2],[5,2,2]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[6,5,2,2],[5,2,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[7,6,3,2],[6,3,2]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,3,1,1,1],[2]]               => ([(0,1)],2)
[[4,4,2,2,1],[3,1,1,1]]         => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[4,4,2,1,1],[3,1,1]]           => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,5,3,2,1],[4,2,2,1]]         => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[4,4,1,1,1],[3,1]]             => ([(0,3),(2,1),(3,2)],4)
[[5,5,2,2,1],[4,2,1,1]]         => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[5,5,2,1,1],[4,2,1]]           => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,6,3,2,1],[5,3,2,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,3,1,1,1],[3]]               => ([(0,2),(2,1)],3)
[[5,4,2,2,1],[4,1,1,1]]         => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,4,2,1,1],[4,1,1]]           => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,5,3,2,1],[5,2,2,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,4,1,1,1],[4,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,5,2,2,1],[5,2,1,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,5,2,1,1],[5,2,1]]           => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,6,3,2,1],[6,3,2,1]]         => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[4,4,4],[3,2]]                 => ([],1)
[[5,5,4],[4,3]]                 => ([(0,2),(2,1)],3)
[[6,6,4],[5,4]]                 => ([(0,3),(2,1),(3,2)],4)
[[5,4,4],[4,2]]                 => ([(0,2),(2,1)],3)
[[6,5,4],[5,3]]                 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7,6,4],[6,4]]                 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[3,3,3,1],[2,1]]               => ([(0,2),(2,1)],3)
[[4,4,4,1],[3,2,1]]             => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,1],[3,2]]               => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[5,5,4,1],[4,3,1]]             => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[5,5,3,1],[4,3]]               => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,6,4,1],[5,4,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[4,3,3,1],[3,1]]               => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,1],[4,2,1]]             => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,3,1],[4,2]]               => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,5,4,1],[5,3,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[6,5,3,1],[5,3]]               => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[7,6,4,1],[6,4,1]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[2,2,2,2],[1]]                 => ([],1)
[[3,3,3,2],[2,1,1]]             => ([(0,2),(2,1)],3)
[[4,4,4,2],[3,2,2]]             => ([(0,3),(2,1),(3,2)],4)
[[3,3,2,2],[2,1]]               => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,2],[3,2,1]]             => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,5,4,2],[4,3,2]]             => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[4,4,2,2],[3,2]]               => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,5,3,2],[4,3,1]]             => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,6,4,2],[5,4,2]]             => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[3,2,2,2],[2]]                 => ([(0,1)],2)
[[4,3,3,2],[3,1,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,2],[4,2,2]]             => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[4,3,2,2],[3,1]]               => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,2],[4,2,1]]             => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,5,4,2],[5,3,2]]             => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,4,2,2],[4,2]]               => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[6,5,3,2],[5,3,1]]             => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,6,4,2],[6,4,2]]             => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[2,2,2,1,1],[1]]               => ([(0,1)],2)
[[3,3,3,2,1],[2,1,1,1]]         => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,1,1],[2,1,1]]           => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,4,2,1],[3,2,2,1]]         => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,3,2,1,1],[2,1]]             => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,4,3,2,1],[3,2,1,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[4,4,3,1,1],[3,2,1]]           => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,5,4,2,1],[4,3,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[4,4,2,1,1],[3,2]]             => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,5,3,2,1],[4,3,1,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,5,3,1,1],[4,3,1]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,4,2,1],[5,4,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[3,2,2,1,1],[2]]               => ([(0,2),(2,1)],3)
[[4,3,3,2,1],[3,1,1,1]]         => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,3,3,1,1],[3,1,1]]           => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[5,4,4,2,1],[4,2,2,1]]         => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[4,3,2,1,1],[3,1]]             => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,4,3,2,1],[4,2,1,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,3,1,1],[4,2,1]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,2,1],[5,3,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,4,2,1,1],[4,2]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[6,5,3,2,1],[5,3,1,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,5,3,1,1],[5,3,1]]           => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,4,2,1],[6,4,2,1]]         => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[4,4,3,3],[3,2,2]]             => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,5,4,3],[4,3,3]]             => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[5,5,3,3],[4,3,2]]             => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,6,4,3],[5,4,3]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[5,4,3,3],[4,2,2]]             => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[6,5,4,3],[5,3,3]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[6,5,3,3],[5,3,2]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[7,6,4,3],[6,4,3]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,3,2,2,1],[2,1,1]]           => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,4,3,3,1],[3,2,2,1]]         => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[4,4,3,2,1],[3,2,2]]           => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,5,4,3,1],[4,3,3,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[4,4,2,2,1],[3,2,1]]           => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,5,3,3,1],[4,3,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,5,3,2,1],[4,3,2]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,4,3,1],[5,4,3,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,3,2,2,1],[3,1,1]]           => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,4,3,3,1],[4,2,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,4,3,2,1],[4,2,2]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,3,1],[5,3,3,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,4,2,2,1],[4,2,1]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,3,3,1],[5,3,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,5,3,2,1],[5,3,2]]           => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,4,3,1],[6,4,3,1]]         => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[3,3,2,2,2],[2,1,1,1]]         => ([(0,1),(0,2),(1,3),(2,3)],4)
[[4,4,3,3,2],[3,2,2,2]]         => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[4,4,3,2,2],[3,2,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,5,4,3,2],[4,3,3,2]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[4,4,2,2,2],[3,2,1,1]]         => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,5,3,3,2],[4,3,2,2]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,5,3,2,2],[4,3,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,4,3,2],[5,4,3,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,3,2,2,2],[3,1,1,1]]         => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,4,3,3,2],[4,2,2,2]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,4,3,2,2],[4,2,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,3,2],[5,3,3,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,4,2,2,2],[4,2,1,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[6,5,3,3,2],[5,3,2,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,5,3,2,2],[5,3,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,4,3,2],[6,4,3,2]]         => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[2,2,1,1,1,1],[1]]             => ([(0,1)],2)
[[3,3,2,2,2,1],[2,1,1,1,1]]     => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,2,2,1,1],[2,1,1,1]]       => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4,3,3,2,1],[3,2,2,2,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[3,3,2,1,1,1],[2,1,1]]         => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4,3,2,2,1],[3,2,2,1,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,4,3,2,1,1],[3,2,2,1]]       => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,3,2,1],[4,3,3,2,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[3,3,1,1,1,1],[2,1]]           => ([(0,3),(2,1),(3,2)],4)
[[4,4,2,2,2,1],[3,2,1,1,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[4,4,2,2,1,1],[3,2,1,1]]       => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,3,3,2,1],[4,3,2,2,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,4,2,1,1,1],[3,2,1]]         => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,5,3,2,2,1],[4,3,2,1,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,5,3,2,1,1],[4,3,2,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,6,4,3,2,1],[5,4,3,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,2,1,1,1,1],[2]]             => ([(0,2),(2,1)],3)
[[4,3,2,2,2,1],[3,1,1,1,1]]     => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,2,2,1,1],[3,1,1,1]]       => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,3,3,2,1],[4,2,2,2,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,3,2,1,1,1],[3,1,1]]         => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,3,2,2,1],[4,2,2,1,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,3,2,1,1],[4,2,2,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,3,2,1],[5,3,3,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,3,1,1,1,1],[3,1]]           => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,2,2,2,1],[4,2,1,1,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,2,2,1,1],[4,2,1,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,3,3,2,1],[5,3,2,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,4,2,1,1,1],[4,2,1]]         => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[6,5,3,2,2,1],[5,3,2,1,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,5,3,2,1,1],[5,3,2,1]]       => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,6,4,3,2,1],[6,4,3,2,1]]     => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[5,5,5],[4,4]]                 => ([],1)
[[6,6,5],[5,5]]                 => ([(0,1)],2)
[[6,5,5],[5,4]]                 => ([(0,2),(2,1)],3)
[[7,6,5],[6,5]]                 => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,1],[3,3]]               => ([(0,1)],2)
[[5,5,5,1],[4,4,1]]             => ([(0,2),(2,1)],3)
[[5,5,4,1],[4,4]]               => ([(0,3),(2,1),(3,2)],4)
[[6,6,5,1],[5,5,1]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,1],[4,3]]               => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[6,5,5,1],[5,4,1]]             => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,5,4,1],[5,4]]               => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[7,6,5,1],[6,5,1]]             => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,3,3,2],[2,2]]               => ([(0,1)],2)
[[4,4,4,2],[3,3,1]]             => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,5,5,2],[4,4,2]]             => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,4,3,2],[3,3]]               => ([(0,3),(2,1),(3,2)],4)
[[5,5,4,2],[4,4,1]]             => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[6,6,5,2],[5,5,2]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[4,3,3,2],[3,2]]               => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,2],[4,3,1]]             => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,5,5,2],[5,4,2]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[5,4,3,2],[4,3]]               => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[6,5,4,2],[5,4,1]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[7,6,5,2],[6,5,2]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,3,3,1,1],[2,2]]             => ([(0,2),(2,1)],3)
[[4,4,4,2,1],[3,3,1,1]]         => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[4,4,4,1,1],[3,3,1]]           => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,5,5,2,1],[4,4,2,1]]         => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[4,4,3,1,1],[3,3]]             => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,5,4,2,1],[4,4,1,1]]         => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[5,5,4,1,1],[4,4,1]]           => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[6,6,5,2,1],[5,5,2,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,3,3,1,1],[3,2]]             => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[5,4,4,2,1],[4,3,1,1]]         => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[5,4,4,1,1],[4,3,1]]           => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,5,5,2,1],[5,4,2,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,4,3,1,1],[4,3]]             => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[6,5,4,2,1],[5,4,1,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,5,4,1,1],[5,4,1]]           => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,6,5,2,1],[6,5,2,1]]         => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[3,3,3,3],[2,2,1]]             => ([],1)
[[4,4,4,3],[3,3,2]]             => ([(0,2),(2,1)],3)
[[5,5,5,3],[4,4,3]]             => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,3],[3,3,1]]             => ([(0,3),(2,1),(3,2)],4)
[[5,5,4,3],[4,4,2]]             => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[6,6,5,3],[5,5,3]]             => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[4,3,3,3],[3,2,1]]             => ([(0,3),(2,1),(3,2)],4)
[[5,4,4,3],[4,3,2]]             => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[[6,5,5,3],[5,4,3]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[5,4,3,3],[4,3,1]]             => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[6,5,4,3],[5,4,2]]             => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)
[[7,6,5,3],[6,5,3]]             => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[2,2,2,2,1],[1,1]]             => ([(0,1)],2)
[[3,3,3,3,1],[2,2,1,1]]         => ([(0,2),(2,1)],3)
[[3,3,3,2,1],[2,2,1]]           => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,4,4,3,1],[3,3,2,1]]         => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[4,4,4,2,1],[3,3,2]]           => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,5,5,3,1],[4,4,3,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[3,3,2,2,1],[2,2]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,3,1],[3,3,1,1]]         => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[4,4,3,2,1],[3,3,1]]           => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,5,4,3,1],[4,4,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,5,4,2,1],[4,4,2]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,5,3,1],[5,5,3,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[3,2,2,2,1],[2,1]]             => ([(0,3),(2,1),(3,2)],4)
[[4,3,3,3,1],[3,2,1,1]]         => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,3,3,2,1],[3,2,1]]           => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,4,4,3,1],[4,3,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,4,2,1],[4,3,2]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,5,3,1],[5,4,3,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,3,2,2,1],[3,2]]             => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,3,3,1],[4,3,1,1]]         => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[5,4,3,2,1],[4,3,1]]           => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,3,1],[5,4,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,5,4,2,1],[5,4,2]]           => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,5,3,1],[6,5,3,1]]         => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[3,3,3,2,2],[2,2,1,1]]         => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,4,4,3,2],[3,3,2,2]]         => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[4,4,4,2,2],[3,3,2,1]]         => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,5,5,3,2],[4,4,3,2]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[4,4,3,2,2],[3,3,1,1]]         => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,5,4,3,2],[4,4,2,2]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,5,4,2,2],[4,4,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,5,3,2],[5,5,3,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,3,3,2,2],[3,2,1,1]]         => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,4,4,3,2],[4,3,2,2]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,4,2,2],[4,3,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,5,3,2],[5,4,3,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,4,3,2,2],[4,3,1,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[6,5,4,3,2],[5,4,2,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,5,4,2,2],[5,4,2,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,5,3,2],[6,5,3,2]]         => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[2,2,2,1,1,1],[1,1]]           => ([(0,2),(2,1)],3)
[[3,3,3,2,2,1],[2,2,1,1,1]]     => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,3,3,2,1,1],[2,2,1,1]]       => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4,4,3,2,1],[3,3,2,2,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[3,3,3,1,1,1],[2,2,1]]         => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,4,4,2,2,1],[3,3,2,1,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[4,4,4,2,1,1],[3,3,2,1]]       => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,5,5,3,2,1],[4,4,3,2,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[3,3,2,1,1,1],[2,2]]           => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,2,2,1],[3,3,1,1,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[4,4,3,2,1,1],[3,3,1,1]]       => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,3,2,1],[4,4,2,2,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,4,3,1,1,1],[3,3,1]]         => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,5,4,2,2,1],[4,4,2,1,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,5,4,2,1,1],[4,4,2,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,6,5,3,2,1],[5,5,3,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,2,2,1,1,1],[2,1]]           => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,2,2,1],[3,2,1,1,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[4,3,3,2,1,1],[3,2,1,1]]       => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,4,3,2,1],[4,3,2,2,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,3,3,1,1,1],[3,2,1]]         => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,4,2,2,1],[4,3,2,1,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,4,2,1,1],[4,3,2,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,5,3,2,1],[5,4,3,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,3,2,1,1,1],[3,2]]           => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,3,2,2,1],[4,3,1,1,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,3,2,1,1],[4,3,1,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,3,2,1],[5,4,2,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,4,3,1,1,1],[4,3,1]]         => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[6,5,4,2,2,1],[5,4,2,1,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,5,4,2,1,1],[5,4,2,1]]       => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,6,5,3,2,1],[6,5,3,2,1]]     => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[4,4,4,4],[3,3,3]]             => ([],1)
[[5,5,5,4],[4,4,4]]             => ([(0,1)],2)
[[5,5,4,4],[4,4,3]]             => ([(0,3),(2,1),(3,2)],4)
[[6,6,5,4],[5,5,4]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,4],[4,3,3]]             => ([(0,2),(2,1)],3)
[[6,5,5,4],[5,4,4]]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,5,4,4],[5,4,3]]             => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[7,6,5,4],[6,5,4]]             => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,3,3,3,1],[2,2,2]]           => ([(0,1)],2)
[[4,4,4,4,1],[3,3,3,1]]         => ([(0,2),(2,1)],3)
[[4,4,4,3,1],[3,3,3]]           => ([(0,3),(2,1),(3,2)],4)
[[5,5,5,4,1],[4,4,4,1]]         => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,3,1],[3,3,2]]           => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,5,4,4,1],[4,4,3,1]]         => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[5,5,4,3,1],[4,4,3]]           => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,6,5,4,1],[5,5,4,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,3,3,3,1],[3,2,2]]           => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[5,4,4,4,1],[4,3,3,1]]         => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,4,4,3,1],[4,3,3]]           => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,5,5,4,1],[5,4,4,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,4,3,3,1],[4,3,2]]           => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,5,4,4,1],[5,4,3,1]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,5,4,3,1],[5,4,3]]           => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,6,5,4,1],[6,5,4,1]]         => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[2,2,2,2,2],[1,1,1]]           => ([],1)
[[3,3,3,3,2],[2,2,2,1]]         => ([(0,2),(2,1)],3)
[[4,4,4,4,2],[3,3,3,2]]         => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,2,2],[2,2,2]]           => ([(0,2),(2,1)],3)
[[4,4,4,3,2],[3,3,3,1]]         => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[5,5,5,4,2],[4,4,4,2]]         => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[3,3,2,2,2],[2,2,1]]           => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,3,2],[3,3,2,1]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[5,5,4,4,2],[4,4,3,2]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[4,4,3,2,2],[3,3,2]]           => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[5,5,4,3,2],[4,4,3,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,5,4,2],[5,5,4,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[3,2,2,2,2],[2,1,1]]           => ([(0,2),(2,1)],3)
[[4,3,3,3,2],[3,2,2,1]]         => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[5,4,4,4,2],[4,3,3,2]]         => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
[[4,3,3,2,2],[3,2,2]]           => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[5,4,4,3,2],[4,3,3,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,5,4,2],[5,4,4,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,3,2,2,2],[3,2,1]]           => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,3,3,2],[4,3,2,1]]         => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,4,2],[5,4,3,2]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,4,3,2,2],[4,3,2]]           => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[6,5,4,3,2],[5,4,3,1]]         => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,5,4,2],[6,5,4,2]]         => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[2,2,2,2,1,1],[1,1,1]]         => ([(0,2),(2,1)],3)
[[3,3,3,3,2,1],[2,2,2,1,1]]     => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,3,3,1,1],[2,2,2,1]]       => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,4,4,2,1],[3,3,3,2,1]]     => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,3,3,2,1,1],[2,2,2]]         => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,4,4,3,2,1],[3,3,3,1,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[4,4,4,3,1,1],[3,3,3,1]]       => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[5,5,5,4,2,1],[4,4,4,2,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[3,3,2,2,1,1],[2,2,1]]         => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4,3,3,2,1],[3,3,2,1,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,4,3,3,1,1],[3,3,2,1]]       => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,4,2,1],[4,4,3,2,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,4,3,2,1,1],[3,3,2]]         => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,5,4,3,2,1],[4,4,3,1,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,5,4,3,1,1],[4,4,3,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,6,5,4,2,1],[5,5,4,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,2,2,2,1,1],[2,1,1]]         => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,3,3,2,1],[3,2,2,1,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[4,3,3,3,1,1],[3,2,2,1]]       => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,4,4,2,1],[4,3,3,2,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,3,3,2,1,1],[3,2,2]]         => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,4,3,2,1],[4,3,3,1,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,4,3,1,1],[4,3,3,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,5,4,2,1],[5,4,4,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,3,2,2,1,1],[3,2,1]]         => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,3,3,2,1],[4,3,2,1,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,3,3,1,1],[4,3,2,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,4,2,1],[5,4,3,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,4,3,2,1,1],[4,3,2]]         => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[6,5,4,3,2,1],[5,4,3,1,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,5,4,3,1,1],[5,4,3,1]]       => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,6,5,4,2,1],[6,5,4,2,1]]     => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[3,3,3,3,3],[2,2,2,2]]         => ([],1)
[[4,4,4,4,3],[3,3,3,3]]         => ([(0,1)],2)
[[4,4,4,3,3],[3,3,3,2]]         => ([(0,3),(2,1),(3,2)],4)
[[5,5,5,4,3],[4,4,4,3]]         => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,3,3],[3,3,2,2]]         => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,5,4,4,3],[4,4,3,3]]         => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[5,5,4,3,3],[4,4,3,2]]         => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,6,5,4,3],[5,5,4,3]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,3,3,3,3],[3,2,2,2]]         => ([(0,2),(2,1)],3)
[[5,4,4,4,3],[4,3,3,3]]         => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,3,3],[4,3,3,2]]         => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)
[[6,5,5,4,3],[5,4,4,3]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,4,3,3,3],[4,3,2,2]]         => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[6,5,4,4,3],[5,4,3,3]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,5,4,3,3],[5,4,3,2]]         => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,6,5,4,3],[6,5,4,3]]         => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[2,2,2,2,2,1],[1,1,1,1]]       => ([(0,1)],2)
[[3,3,3,3,3,1],[2,2,2,2,1]]     => ([(0,2),(2,1)],3)
[[3,3,3,3,2,1],[2,2,2,2]]       => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,4,3,1],[3,3,3,3,1]]     => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,3,2,2,1],[2,2,2,1]]       => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4,4,3,3,1],[3,3,3,2,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[4,4,4,3,2,1],[3,3,3,2]]       => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,5,5,4,3,1],[4,4,4,3,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[3,3,2,2,2,1],[2,2,1,1]]       => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4,3,3,3,1],[3,3,2,2,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[4,4,3,3,2,1],[3,3,2,2]]       => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,4,3,1],[4,4,3,3,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,4,3,2,2,1],[3,3,2,1]]       => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,3,3,1],[4,4,3,2,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,5,4,3,2,1],[4,4,3,2]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,6,5,4,3,1],[5,5,4,3,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,2,2,2,2,1],[2,1,1,1]]       => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,3,3,1],[3,2,2,2,1]]     => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,3,3,2,1],[3,2,2,2]]       => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,4,4,3,1],[4,3,3,3,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,3,3,2,2,1],[3,2,2,1]]       => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,4,3,3,1],[4,3,3,2,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,4,3,2,1],[4,3,3,2]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,5,4,3,1],[5,4,4,3,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,3,2,2,2,1],[3,2,1,1]]       => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,3,3,3,1],[4,3,2,2,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,3,3,2,1],[4,3,2,2]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,4,3,1],[5,4,3,3,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,4,3,2,2,1],[4,3,2,1]]       => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,3,3,1],[5,4,3,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,5,4,3,2,1],[5,4,3,2]]       => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,6,5,4,3,1],[6,5,4,3,1]]     => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[2,2,2,2,2,2],[1,1,1,1,1]]     => ([],1)
[[3,3,3,3,3,2],[2,2,2,2,2]]     => ([(0,1)],2)
[[3,3,3,3,2,2],[2,2,2,2,1]]     => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,4,3,2],[3,3,3,3,2]]     => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,3,2,2,2],[2,2,2,1,1]]     => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,4,4,3,3,2],[3,3,3,2,2]]     => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[4,4,4,3,2,2],[3,3,3,2,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,5,5,4,3,2],[4,4,4,3,2]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[3,3,2,2,2,2],[2,2,1,1,1]]     => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,3,3,2],[3,3,2,2,2]]     => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[4,4,3,3,2,2],[3,3,2,2,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,4,3,2],[4,4,3,3,2]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,4,3,2,2,2],[3,3,2,1,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,5,4,3,3,2],[4,4,3,2,2]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,5,4,3,2,2],[4,4,3,2,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,6,5,4,3,2],[5,5,4,3,2]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,2,2,2,2,2],[2,1,1,1,1]]     => ([(0,2),(2,1)],3)
[[4,3,3,3,3,2],[3,2,2,2,2]]     => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,3,2,2],[3,2,2,2,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,4,4,3,2],[4,3,3,3,2]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,3,3,2,2,2],[3,2,2,1,1]]     => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)
[[5,4,4,3,3,2],[4,3,3,2,2]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,4,3,2,2],[4,3,3,2,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,5,4,3,2],[5,4,4,3,2]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,3,2,2,2,2],[3,2,1,1,1]]     => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,3,3,3,2],[4,3,2,2,2]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,3,3,2,2],[4,3,2,2,1]]     => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,4,3,2],[5,4,3,3,2]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,4,3,2,2,2],[4,3,2,1,1]]     => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[6,5,4,3,3,2],[5,4,3,2,2]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,5,4,3,2,2],[5,4,3,2,1]]     => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,6,5,4,3,2],[6,5,4,3,2]]     => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[1,1,1,1,1,1,1],[]]            => ([],1)
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => ([(0,1)],2)
[[2,2,2,2,2,1,1],[1,1,1,1,1]]   => ([(0,2),(2,1)],3)
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => ([(0,3),(2,1),(3,2)],4)
[[2,2,2,2,1,1,1],[1,1,1,1]]     => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[3,3,3,3,2,1,1],[2,2,2,2,1]]   => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[2,2,2,1,1,1,1],[1,1,1]]       => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[3,3,3,2,2,1,1],[2,2,2,1,1]]   => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[3,3,3,2,1,1,1],[2,2,2,1]]     => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)

-----------------------------------------------------------------------------
Created: Sep 27, 2020 at 14:56 by Martin Rubey

-----------------------------------------------------------------------------
Last Updated: Jun 08, 2022 at 17:02 by Martin Rubey