************************************************************************ * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2013 The FindStatCrew * * * * 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