************************************************************************ * 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: Mp00186 ------------------------------------------------------------------------ Map name: dominating partition ------------------------------------------------------------------------ Domain: Skew partitions ------------------------------------------------------------------------ Codomain: Integer partitions ------------------------------------------------------------------------ Description: The dominating partition in the Schur expansion. 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 partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a sublattice of the dominance order and that its top element is the conjugate of the partition formed by sorting the column lengths of $\lambda / \mu$ into decreasing order. This map returns the largest partition $\nu$ in dominance order for which $c^\lambda_{\mu, \nu}$ is positive. For example, $$s_{331/2} = s_{311} + s_{32},$$ and the partition $32$ dominates $311$. ------------------------------------------------------------------------ References: [1] Azenhas, O. The admissible interval for the invariant factors of a product of matrices [[MathSciNet:1712853]] ------------------------------------------------------------------------ Code: def mapping(la): return Partition(sorted(la.column_lengths(), reverse=True)).conjugate() ------------------------------------------------------------------------ Map images: [[1],[]] => [1] [[2],[]] => [2] [[1,1],[]] => [1,1] [[2,1],[1]] => [2] [[3],[]] => [3] [[2,1],[]] => [2,1] [[3,1],[1]] => [3] [[2,2],[1]] => [2,1] [[3,2],[2]] => [3] [[1,1,1],[]] => [1,1,1] [[2,2,1],[1,1]] => [2,1] [[2,1,1],[1]] => [2,1] [[3,2,1],[2,1]] => [3] [[4],[]] => [4] [[3,1],[]] => [3,1] [[4,1],[1]] => [4] [[2,2],[]] => [2,2] [[3,2],[1]] => [3,1] [[4,2],[2]] => [4] [[2,1,1],[]] => [2,1,1] [[3,2,1],[1,1]] => [3,1] [[3,1,1],[1]] => [3,1] [[4,2,1],[2,1]] => [4] [[3,3],[2]] => [3,1] [[4,3],[3]] => [4] [[2,2,1],[1]] => [2,2] [[3,3,1],[2,1]] => [3,1] [[3,2,1],[2]] => [3,1] [[4,3,1],[3,1]] => [4] [[2,2,2],[1,1]] => [2,1,1] [[3,3,2],[2,2]] => [3,1] [[3,2,2],[2,1]] => [3,1] [[4,3,2],[3,2]] => [4] [[1,1,1,1],[]] => [1,1,1,1] [[2,2,2,1],[1,1,1]] => [2,1,1] [[2,2,1,1],[1,1]] => [2,2] [[3,3,2,1],[2,2,1]] => [3,1] [[2,1,1,1],[1]] => [2,1,1] [[3,2,2,1],[2,1,1]] => [3,1] [[3,2,1,1],[2,1]] => [3,1] [[4,3,2,1],[3,2,1]] => [4] [[5],[]] => [5] [[4,1],[]] => [4,1] [[5,1],[1]] => [5] [[3,2],[]] => [3,2] [[4,2],[1]] => [4,1] [[5,2],[2]] => [5] [[3,1,1],[]] => [3,1,1] [[4,2,1],[1,1]] => [4,1] [[4,1,1],[1]] => [4,1] [[5,2,1],[2,1]] => [5] [[3,3],[1]] => [3,2] [[4,3],[2]] => [4,1] [[5,3],[3]] => [5] [[2,2,1],[]] => [2,2,1] [[3,3,1],[1,1]] => [3,2] [[3,2,1],[1]] => [3,2] [[4,3,1],[2,1]] => [4,1] [[4,2,1],[2]] => [4,1] [[5,3,1],[3,1]] => [5] [[3,2,2],[1,1]] => [3,1,1] [[4,3,2],[2,2]] => [4,1] [[4,2,2],[2,1]] => [4,1] [[5,3,2],[3,2]] => [5] [[2,1,1,1],[]] => [2,1,1,1] [[3,2,2,1],[1,1,1]] => [3,1,1] [[3,2,1,1],[1,1]] => [3,2] [[4,3,2,1],[2,2,1]] => [4,1] [[3,1,1,1],[1]] => [3,1,1] [[4,2,2,1],[2,1,1]] => [4,1] [[4,2,1,1],[2,1]] => [4,1] [[5,3,2,1],[3,2,1]] => [5] [[4,4],[3]] => [4,1] [[5,4],[4]] => [5] [[3,3,1],[2]] => [3,2] [[4,4,1],[3,1]] => [4,1] [[4,3,1],[3]] => [4,1] [[5,4,1],[4,1]] => [5] [[2,2,2],[1]] => [2,2,1] [[3,3,2],[2,1]] => [3,2] [[4,4,2],[3,2]] => [4,1] [[3,2,2],[2]] => [3,2] [[4,3,2],[3,1]] => [4,1] [[5,4,2],[4,2]] => [5] [[2,2,1,1],[1]] => [2,2,1] [[3,3,2,1],[2,1,1]] => [3,2] [[3,3,1,1],[2,1]] => [3,2] [[4,4,2,1],[3,2,1]] => [4,1] [[3,2,1,1],[2]] => [3,1,1] [[4,3,2,1],[3,1,1]] => [4,1] [[4,3,1,1],[3,1]] => [4,1] [[5,4,2,1],[4,2,1]] => [5] [[3,3,3],[2,2]] => [3,1,1] [[4,4,3],[3,3]] => [4,1] [[4,3,3],[3,2]] => [4,1] [[5,4,3],[4,3]] => [5] [[2,2,2,1],[1,1]] => [2,2,1] [[3,3,3,1],[2,2,1]] => [3,1,1] [[3,3,2,1],[2,2]] => [3,2] [[4,4,3,1],[3,3,1]] => [4,1] [[3,2,2,1],[2,1]] => [3,2] [[4,3,3,1],[3,2,1]] => [4,1] [[4,3,2,1],[3,2]] => [4,1] [[5,4,3,1],[4,3,1]] => [5] [[2,2,2,2],[1,1,1]] => [2,1,1,1] [[3,3,3,2],[2,2,2]] => [3,1,1] [[3,3,2,2],[2,2,1]] => [3,2] [[4,4,3,2],[3,3,2]] => [4,1] [[3,2,2,2],[2,1,1]] => [3,1,1] [[4,3,3,2],[3,2,2]] => [4,1] [[4,3,2,2],[3,2,1]] => [4,1] [[5,4,3,2],[4,3,2]] => [5] [[1,1,1,1,1],[]] => [1,1,1,1,1] [[2,2,2,2,1],[1,1,1,1]] => [2,1,1,1] [[2,2,2,1,1],[1,1,1]] => [2,2,1] [[3,3,3,2,1],[2,2,2,1]] => [3,1,1] [[2,2,1,1,1],[1,1]] => [2,2,1] [[3,3,2,2,1],[2,2,1,1]] => [3,2] [[3,3,2,1,1],[2,2,1]] => [3,2] [[4,4,3,2,1],[3,3,2,1]] => [4,1] [[2,1,1,1,1],[1]] => [2,1,1,1] [[3,2,2,2,1],[2,1,1,1]] => [3,1,1] [[3,2,2,1,1],[2,1,1]] => [3,2] [[4,3,3,2,1],[3,2,2,1]] => [4,1] [[3,2,1,1,1],[2,1]] => [3,1,1] [[4,3,2,2,1],[3,2,1,1]] => [4,1] [[4,3,2,1,1],[3,2,1]] => [4,1] [[5,4,3,2,1],[4,3,2,1]] => [5] [[6],[]] => [6] [[5,1],[]] => [5,1] [[6,1],[1]] => [6] [[4,2],[]] => [4,2] [[5,2],[1]] => [5,1] [[6,2],[2]] => [6] [[4,1,1],[]] => [4,1,1] [[5,2,1],[1,1]] => [5,1] [[5,1,1],[1]] => [5,1] [[6,2,1],[2,1]] => [6] [[3,3],[]] => [3,3] [[4,3],[1]] => [4,2] [[5,3],[2]] => [5,1] [[6,3],[3]] => [6] [[3,2,1],[]] => [3,2,1] [[4,3,1],[1,1]] => [4,2] [[4,2,1],[1]] => [4,2] [[5,3,1],[2,1]] => [5,1] [[5,2,1],[2]] => [5,1] [[6,3,1],[3,1]] => [6] [[4,2,2],[1,1]] => [4,1,1] [[5,3,2],[2,2]] => [5,1] [[5,2,2],[2,1]] => [5,1] [[6,3,2],[3,2]] => [6] [[3,1,1,1],[]] => [3,1,1,1] [[4,2,2,1],[1,1,1]] => [4,1,1] [[4,2,1,1],[1,1]] => [4,2] [[5,3,2,1],[2,2,1]] => [5,1] [[4,1,1,1],[1]] => [4,1,1] [[5,2,2,1],[2,1,1]] => [5,1] [[5,2,1,1],[2,1]] => [5,1] [[6,3,2,1],[3,2,1]] => [6] [[4,4],[2]] => [4,2] [[5,4],[3]] => [5,1] [[6,4],[4]] => [6] [[3,3,1],[1]] => [3,3] [[4,4,1],[2,1]] => [4,2] [[4,3,1],[2]] => [4,2] [[5,4,1],[3,1]] => [5,1] [[5,3,1],[3]] => [5,1] [[6,4,1],[4,1]] => [6] [[2,2,2],[]] => [2,2,2] [[3,3,2],[1,1]] => [3,2,1] [[4,4,2],[2,2]] => [4,2] [[3,2,2],[1]] => [3,2,1] [[4,3,2],[2,1]] => [4,2] [[5,4,2],[3,2]] => [5,1] [[4,2,2],[2]] => [4,2] [[5,3,2],[3,1]] => [5,1] [[6,4,2],[4,2]] => [6] [[2,2,1,1],[]] => [2,2,1,1] [[3,3,2,1],[1,1,1]] => [3,2,1] [[3,3,1,1],[1,1]] => [3,3] [[4,4,2,1],[2,2,1]] => [4,2] [[3,2,1,1],[1]] => [3,2,1] [[4,3,2,1],[2,1,1]] => [4,2] [[4,3,1,1],[2,1]] => [4,2] [[5,4,2,1],[3,2,1]] => [5,1] [[4,2,1,1],[2]] => [4,1,1] [[5,3,2,1],[3,1,1]] => [5,1] [[5,3,1,1],[3,1]] => [5,1] [[6,4,2,1],[4,2,1]] => [6] [[4,3,3],[2,2]] => [4,1,1] [[5,4,3],[3,3]] => [5,1] [[5,3,3],[3,2]] => [5,1] [[6,4,3],[4,3]] => [6] [[3,2,2,1],[1,1]] => [3,2,1] [[4,3,3,1],[2,2,1]] => [4,1,1] [[4,3,2,1],[2,2]] => [4,2] [[5,4,3,1],[3,3,1]] => [5,1] [[4,2,2,1],[2,1]] => [4,2] [[5,3,3,1],[3,2,1]] => [5,1] [[5,3,2,1],[3,2]] => [5,1] [[6,4,3,1],[4,3,1]] => [6] [[3,2,2,2],[1,1,1]] => [3,1,1,1] [[4,3,3,2],[2,2,2]] => [4,1,1] [[4,3,2,2],[2,2,1]] => [4,2] [[5,4,3,2],[3,3,2]] => [5,1] [[4,2,2,2],[2,1,1]] => [4,1,1] [[5,3,3,2],[3,2,2]] => [5,1] [[5,3,2,2],[3,2,1]] => [5,1] [[6,4,3,2],[4,3,2]] => [6] [[2,1,1,1,1],[]] => [2,1,1,1,1] [[3,2,2,2,1],[1,1,1,1]] => [3,1,1,1] [[3,2,2,1,1],[1,1,1]] => [3,2,1] [[4,3,3,2,1],[2,2,2,1]] => [4,1,1] [[3,2,1,1,1],[1,1]] => [3,2,1] [[4,3,2,2,1],[2,2,1,1]] => [4,2] [[4,3,2,1,1],[2,2,1]] => [4,2] [[5,4,3,2,1],[3,3,2,1]] => [5,1] [[3,1,1,1,1],[1]] => [3,1,1,1] [[4,2,2,2,1],[2,1,1,1]] => [4,1,1] [[4,2,2,1,1],[2,1,1]] => [4,2] [[5,3,3,2,1],[3,2,2,1]] => [5,1] [[4,2,1,1,1],[2,1]] => [4,1,1] [[5,3,2,2,1],[3,2,1,1]] => [5,1] [[5,3,2,1,1],[3,2,1]] => [5,1] [[6,4,3,2,1],[4,3,2,1]] => [6] [[5,5],[4]] => [5,1] [[6,5],[5]] => [6] [[4,4,1],[3]] => [4,2] [[5,5,1],[4,1]] => [5,1] [[5,4,1],[4]] => [5,1] [[6,5,1],[5,1]] => [6] [[3,3,2],[2]] => [3,3] [[4,4,2],[3,1]] => [4,2] [[5,5,2],[4,2]] => [5,1] [[4,3,2],[3]] => [4,2] [[5,4,2],[4,1]] => [5,1] [[6,5,2],[5,2]] => [6] [[3,3,1,1],[2]] => [3,2,1] [[4,4,2,1],[3,1,1]] => [4,2] [[4,4,1,1],[3,1]] => [4,2] [[5,5,2,1],[4,2,1]] => [5,1] [[4,3,1,1],[3]] => [4,1,1] [[5,4,2,1],[4,1,1]] => [5,1] [[5,4,1,1],[4,1]] => [5,1] [[6,5,2,1],[5,2,1]] => [6] [[3,3,3],[2,1]] => [3,2,1] [[4,4,3],[3,2]] => [4,2] [[5,5,3],[4,3]] => [5,1] [[4,3,3],[3,1]] => [4,2] [[5,4,3],[4,2]] => [5,1] [[6,5,3],[5,3]] => [6] [[2,2,2,1],[1]] => [2,2,2] [[3,3,3,1],[2,1,1]] => [3,2,1] [[3,3,2,1],[2,1]] => [3,3] [[4,4,3,1],[3,2,1]] => [4,2] [[4,4,2,1],[3,2]] => [4,2] [[5,5,3,1],[4,3,1]] => [5,1] [[3,2,2,1],[2]] => [3,2,1] [[4,3,3,1],[3,1,1]] => [4,2] [[4,3,2,1],[3,1]] => [4,2] [[5,4,3,1],[4,2,1]] => [5,1] [[5,4,2,1],[4,2]] => [5,1] [[6,5,3,1],[5,3,1]] => [6] [[3,3,2,2],[2,1,1]] => [3,2,1] [[4,4,3,2],[3,2,2]] => [4,2] [[4,4,2,2],[3,2,1]] => [4,2] [[5,5,3,2],[4,3,2]] => [5,1] [[4,3,2,2],[3,1,1]] => [4,1,1] [[5,4,3,2],[4,2,2]] => [5,1] [[5,4,2,2],[4,2,1]] => [5,1] [[6,5,3,2],[5,3,2]] => [6] [[2,2,1,1,1],[1]] => [2,2,1,1] [[3,3,2,2,1],[2,1,1,1]] => [3,2,1] [[3,3,2,1,1],[2,1,1]] => [3,3] [[4,4,3,2,1],[3,2,2,1]] => [4,2] [[3,3,1,1,1],[2,1]] => [3,2,1] [[4,4,2,2,1],[3,2,1,1]] => [4,2] [[4,4,2,1,1],[3,2,1]] => [4,2] [[5,5,3,2,1],[4,3,2,1]] => [5,1] [[3,2,1,1,1],[2]] => [3,1,1,1] [[4,3,2,2,1],[3,1,1,1]] => [4,1,1] [[4,3,2,1,1],[3,1,1]] => [4,2] [[5,4,3,2,1],[4,2,2,1]] => [5,1] [[4,3,1,1,1],[3,1]] => [4,1,1] [[5,4,2,2,1],[4,2,1,1]] => [5,1] [[5,4,2,1,1],[4,2,1]] => [5,1] [[6,5,3,2,1],[5,3,2,1]] => [6] [[4,4,4],[3,3]] => [4,1,1] [[5,5,4],[4,4]] => [5,1] [[5,4,4],[4,3]] => [5,1] [[6,5,4],[5,4]] => [6] [[3,3,3,1],[2,2]] => [3,2,1] [[4,4,4,1],[3,3,1]] => [4,1,1] [[4,4,3,1],[3,3]] => [4,2] [[5,5,4,1],[4,4,1]] => [5,1] [[4,3,3,1],[3,2]] => [4,2] [[5,4,4,1],[4,3,1]] => [5,1] [[5,4,3,1],[4,3]] => [5,1] [[6,5,4,1],[5,4,1]] => [6] [[2,2,2,2],[1,1]] => [2,2,1,1] [[3,3,3,2],[2,2,1]] => [3,2,1] [[4,4,4,2],[3,3,2]] => [4,1,1] [[3,3,2,2],[2,2]] => [3,3] [[4,4,3,2],[3,3,1]] => [4,2] [[5,5,4,2],[4,4,2]] => [5,1] [[3,2,2,2],[2,1]] => [3,2,1] [[4,3,3,2],[3,2,1]] => [4,2] [[5,4,4,2],[4,3,2]] => [5,1] [[4,3,2,2],[3,2]] => [4,2] [[5,4,3,2],[4,3,1]] => [5,1] [[6,5,4,2],[5,4,2]] => [6] [[2,2,2,1,1],[1,1]] => [2,2,2] [[3,3,3,2,1],[2,2,1,1]] => [3,2,1] [[3,3,3,1,1],[2,2,1]] => [3,2,1] [[4,4,4,2,1],[3,3,2,1]] => [4,1,1] [[3,3,2,1,1],[2,2]] => [3,2,1] [[4,4,3,2,1],[3,3,1,1]] => [4,2] [[4,4,3,1,1],[3,3,1]] => [4,2] [[5,5,4,2,1],[4,4,2,1]] => [5,1] [[3,2,2,1,1],[2,1]] => [3,2,1] [[4,3,3,2,1],[3,2,1,1]] => [4,2] [[4,3,3,1,1],[3,2,1]] => [4,2] [[5,4,4,2,1],[4,3,2,1]] => [5,1] [[4,3,2,1,1],[3,2]] => [4,1,1] [[5,4,3,2,1],[4,3,1,1]] => [5,1] [[5,4,3,1,1],[4,3,1]] => [5,1] [[6,5,4,2,1],[5,4,2,1]] => [6] [[3,3,3,3],[2,2,2]] => [3,1,1,1] [[4,4,4,3],[3,3,3]] => [4,1,1] [[4,4,3,3],[3,3,2]] => [4,2] [[5,5,4,3],[4,4,3]] => [5,1] [[4,3,3,3],[3,2,2]] => [4,1,1] [[5,4,4,3],[4,3,3]] => [5,1] [[5,4,3,3],[4,3,2]] => [5,1] [[6,5,4,3],[5,4,3]] => [6] [[2,2,2,2,1],[1,1,1]] => [2,2,1,1] [[3,3,3,3,1],[2,2,2,1]] => [3,1,1,1] [[3,3,3,2,1],[2,2,2]] => [3,2,1] [[4,4,4,3,1],[3,3,3,1]] => [4,1,1] [[3,3,2,2,1],[2,2,1]] => [3,3] [[4,4,3,3,1],[3,3,2,1]] => [4,2] [[4,4,3,2,1],[3,3,2]] => [4,2] [[5,5,4,3,1],[4,4,3,1]] => [5,1] [[3,2,2,2,1],[2,1,1]] => [3,2,1] [[4,3,3,3,1],[3,2,2,1]] => [4,1,1] [[4,3,3,2,1],[3,2,2]] => [4,2] [[5,4,4,3,1],[4,3,3,1]] => [5,1] [[4,3,2,2,1],[3,2,1]] => [4,2] [[5,4,3,3,1],[4,3,2,1]] => [5,1] [[5,4,3,2,1],[4,3,2]] => [5,1] [[6,5,4,3,1],[5,4,3,1]] => [6] [[2,2,2,2,2],[1,1,1,1]] => [2,1,1,1,1] [[3,3,3,3,2],[2,2,2,2]] => [3,1,1,1] [[3,3,3,2,2],[2,2,2,1]] => [3,2,1] [[4,4,4,3,2],[3,3,3,2]] => [4,1,1] [[3,3,2,2,2],[2,2,1,1]] => [3,2,1] [[4,4,3,3,2],[3,3,2,2]] => [4,2] [[4,4,3,2,2],[3,3,2,1]] => [4,2] [[5,5,4,3,2],[4,4,3,2]] => [5,1] [[3,2,2,2,2],[2,1,1,1]] => [3,1,1,1] [[4,3,3,3,2],[3,2,2,2]] => [4,1,1] [[4,3,3,2,2],[3,2,2,1]] => [4,2] [[5,4,4,3,2],[4,3,3,2]] => [5,1] [[4,3,2,2,2],[3,2,1,1]] => [4,1,1] [[5,4,3,3,2],[4,3,2,2]] => [5,1] [[5,4,3,2,2],[4,3,2,1]] => [5,1] [[6,5,4,3,2],[5,4,3,2]] => [6] [[1,1,1,1,1,1],[]] => [1,1,1,1,1,1] [[2,2,2,2,2,1],[1,1,1,1,1]] => [2,1,1,1,1] [[2,2,2,2,1,1],[1,1,1,1]] => [2,2,1,1] [[3,3,3,3,2,1],[2,2,2,2,1]] => [3,1,1,1] [[2,2,2,1,1,1],[1,1,1]] => [2,2,2] [[3,3,3,2,2,1],[2,2,2,1,1]] => [3,2,1] [[3,3,3,2,1,1],[2,2,2,1]] => [3,2,1] [[4,4,4,3,2,1],[3,3,3,2,1]] => [4,1,1] [[2,2,1,1,1,1],[1,1]] => [2,2,1,1] [[3,3,2,2,2,1],[2,2,1,1,1]] => [3,2,1] [[3,3,2,2,1,1],[2,2,1,1]] => [3,3] [[4,4,3,3,2,1],[3,3,2,2,1]] => [4,2] [[3,3,2,1,1,1],[2,2,1]] => [3,2,1] [[4,4,3,2,2,1],[3,3,2,1,1]] => [4,2] [[4,4,3,2,1,1],[3,3,2,1]] => [4,2] [[5,5,4,3,2,1],[4,4,3,2,1]] => [5,1] [[2,1,1,1,1,1],[1]] => [2,1,1,1,1] [[3,2,2,2,2,1],[2,1,1,1,1]] => [3,1,1,1] [[3,2,2,2,1,1],[2,1,1,1]] => [3,2,1] [[4,3,3,3,2,1],[3,2,2,2,1]] => [4,1,1] [[3,2,2,1,1,1],[2,1,1]] => [3,2,1] [[4,3,3,2,2,1],[3,2,2,1,1]] => [4,2] [[4,3,3,2,1,1],[3,2,2,1]] => [4,2] [[5,4,4,3,2,1],[4,3,3,2,1]] => [5,1] [[3,2,1,1,1,1],[2,1]] => [3,1,1,1] [[4,3,2,2,2,1],[3,2,1,1,1]] => [4,1,1] [[4,3,2,2,1,1],[3,2,1,1]] => [4,2] [[5,4,3,3,2,1],[4,3,2,2,1]] => [5,1] [[4,3,2,1,1,1],[3,2,1]] => [4,1,1] [[5,4,3,2,2,1],[4,3,2,1,1]] => [5,1] [[5,4,3,2,1,1],[4,3,2,1]] => [5,1] [[6,5,4,3,2,1],[5,4,3,2,1]] => [6] [[7],[]] => [7] [[6,1],[]] => [6,1] [[7,1],[1]] => [7] [[5,2],[]] => [5,2] [[6,2],[1]] => [6,1] [[7,2],[2]] => [7] [[5,1,1],[]] => [5,1,1] [[6,2,1],[1,1]] => [6,1] [[6,1,1],[1]] => [6,1] [[7,2,1],[2,1]] => [7] [[4,3],[]] => [4,3] [[5,3],[1]] => [5,2] [[6,3],[2]] => [6,1] [[7,3],[3]] => [7] [[4,2,1],[]] => [4,2,1] [[5,3,1],[1,1]] => [5,2] [[5,2,1],[1]] => [5,2] [[6,3,1],[2,1]] => [6,1] [[6,2,1],[2]] => [6,1] [[7,3,1],[3,1]] => [7] [[5,2,2],[1,1]] => [5,1,1] [[6,3,2],[2,2]] => [6,1] [[6,2,2],[2,1]] => [6,1] [[7,3,2],[3,2]] => [7] [[4,1,1,1],[]] => [4,1,1,1] [[5,2,2,1],[1,1,1]] => [5,1,1] [[5,2,1,1],[1,1]] => [5,2] [[6,3,2,1],[2,2,1]] => [6,1] [[5,1,1,1],[1]] => [5,1,1] [[6,2,2,1],[2,1,1]] => [6,1] [[6,2,1,1],[2,1]] => [6,1] [[7,3,2,1],[3,2,1]] => [7] [[4,4],[1]] => [4,3] [[5,4],[2]] => [5,2] [[6,4],[3]] => [6,1] [[7,4],[4]] => [7] [[3,3,1],[]] => [3,3,1] [[4,4,1],[1,1]] => [4,3] [[4,3,1],[1]] => [4,3] [[5,4,1],[2,1]] => [5,2] [[5,3,1],[2]] => [5,2] [[6,4,1],[3,1]] => [6,1] [[6,3,1],[3]] => [6,1] [[7,4,1],[4,1]] => [7] [[3,2,2],[]] => [3,2,2] [[4,3,2],[1,1]] => [4,2,1] [[5,4,2],[2,2]] => [5,2] [[4,2,2],[1]] => [4,2,1] [[5,3,2],[2,1]] => [5,2] [[6,4,2],[3,2]] => [6,1] [[5,2,2],[2]] => [5,2] [[6,3,2],[3,1]] => [6,1] [[7,4,2],[4,2]] => [7] [[3,2,1,1],[]] => [3,2,1,1] [[4,3,2,1],[1,1,1]] => [4,2,1] [[4,3,1,1],[1,1]] => [4,3] [[5,4,2,1],[2,2,1]] => [5,2] [[4,2,1,1],[1]] => [4,2,1] [[5,3,2,1],[2,1,1]] => [5,2] [[5,3,1,1],[2,1]] => [5,2] [[6,4,2,1],[3,2,1]] => [6,1] [[5,2,1,1],[2]] => [5,1,1] [[6,3,2,1],[3,1,1]] => [6,1] [[6,3,1,1],[3,1]] => [6,1] [[7,4,2,1],[4,2,1]] => [7] [[5,3,3],[2,2]] => [5,1,1] [[6,4,3],[3,3]] => [6,1] [[6,3,3],[3,2]] => [6,1] [[7,4,3],[4,3]] => [7] [[4,2,2,1],[1,1]] => [4,2,1] [[5,3,3,1],[2,2,1]] => [5,1,1] [[5,3,2,1],[2,2]] => [5,2] [[6,4,3,1],[3,3,1]] => [6,1] [[5,2,2,1],[2,1]] => [5,2] [[6,3,3,1],[3,2,1]] => [6,1] [[6,3,2,1],[3,2]] => [6,1] [[7,4,3,1],[4,3,1]] => [7] [[4,2,2,2],[1,1,1]] => [4,1,1,1] [[5,3,3,2],[2,2,2]] => [5,1,1] [[5,3,2,2],[2,2,1]] => [5,2] [[6,4,3,2],[3,3,2]] => [6,1] [[5,2,2,2],[2,1,1]] => [5,1,1] [[6,3,3,2],[3,2,2]] => [6,1] [[6,3,2,2],[3,2,1]] => [6,1] [[7,4,3,2],[4,3,2]] => [7] [[3,1,1,1,1],[]] => [3,1,1,1,1] [[4,2,2,2,1],[1,1,1,1]] => [4,1,1,1] [[4,2,2,1,1],[1,1,1]] => [4,2,1] [[5,3,3,2,1],[2,2,2,1]] => [5,1,1] [[4,2,1,1,1],[1,1]] => [4,2,1] [[5,3,2,2,1],[2,2,1,1]] => [5,2] [[5,3,2,1,1],[2,2,1]] => [5,2] [[6,4,3,2,1],[3,3,2,1]] => [6,1] [[4,1,1,1,1],[1]] => [4,1,1,1] [[5,2,2,2,1],[2,1,1,1]] => [5,1,1] [[5,2,2,1,1],[2,1,1]] => [5,2] [[6,3,3,2,1],[3,2,2,1]] => [6,1] [[5,2,1,1,1],[2,1]] => [5,1,1] [[6,3,2,2,1],[3,2,1,1]] => [6,1] [[6,3,2,1,1],[3,2,1]] => [6,1] [[7,4,3,2,1],[4,3,2,1]] => [7] [[5,5],[3]] => [5,2] [[6,5],[4]] => [6,1] [[7,5],[5]] => [7] [[4,4,1],[2]] => [4,3] [[5,5,1],[3,1]] => [5,2] [[5,4,1],[3]] => [5,2] [[6,5,1],[4,1]] => [6,1] [[6,4,1],[4]] => [6,1] [[7,5,1],[5,1]] => [7] [[3,3,2],[1]] => [3,3,1] [[4,4,2],[2,1]] => [4,3] [[5,5,2],[3,2]] => [5,2] [[4,3,2],[2]] => [4,3] [[5,4,2],[3,1]] => [5,2] [[6,5,2],[4,2]] => [6,1] [[5,3,2],[3]] => [5,2] [[6,4,2],[4,1]] => [6,1] [[7,5,2],[5,2]] => [7] [[3,3,1,1],[1]] => [3,3,1] [[4,4,2,1],[2,1,1]] => [4,3] [[4,4,1,1],[2,1]] => [4,3] [[5,5,2,1],[3,2,1]] => [5,2] [[4,3,1,1],[2]] => [4,2,1] [[5,4,2,1],[3,1,1]] => [5,2] [[5,4,1,1],[3,1]] => [5,2] [[6,5,2,1],[4,2,1]] => [6,1] [[5,3,1,1],[3]] => [5,1,1] [[6,4,2,1],[4,1,1]] => [6,1] [[6,4,1,1],[4,1]] => [6,1] [[7,5,2,1],[5,2,1]] => [7] [[3,3,3],[1,1]] => [3,2,2] [[4,4,3],[2,2]] => [4,2,1] [[5,5,3],[3,3]] => [5,2] [[4,3,3],[2,1]] => [4,2,1] [[5,4,3],[3,2]] => [5,2] [[6,5,3],[4,3]] => [6,1] [[5,3,3],[3,1]] => [5,2] [[6,4,3],[4,2]] => [6,1] [[7,5,3],[5,3]] => [7] [[2,2,2,1],[]] => [2,2,2,1] [[3,3,3,1],[1,1,1]] => [3,2,2] [[3,3,2,1],[1,1]] => [3,3,1] [[4,4,3,1],[2,2,1]] => [4,2,1] [[4,4,2,1],[2,2]] => [4,3] [[5,5,3,1],[3,3,1]] => [5,2] [[3,2,2,1],[1]] => [3,2,2] [[4,3,3,1],[2,1,1]] => [4,2,1] [[4,3,2,1],[2,1]] => [4,3] [[5,4,3,1],[3,2,1]] => [5,2] [[5,4,2,1],[3,2]] => [5,2] [[6,5,3,1],[4,3,1]] => [6,1] [[4,2,2,1],[2]] => [4,2,1] [[5,3,3,1],[3,1,1]] => [5,2] [[5,3,2,1],[3,1]] => [5,2] [[6,4,3,1],[4,2,1]] => [6,1] [[6,4,2,1],[4,2]] => [6,1] [[7,5,3,1],[5,3,1]] => [7] [[3,3,2,2],[1,1,1]] => [3,2,1,1] [[4,4,3,2],[2,2,2]] => [4,2,1] [[4,4,2,2],[2,2,1]] => [4,3] [[5,5,3,2],[3,3,2]] => [5,2] [[4,3,2,2],[2,1,1]] => [4,2,1] [[5,4,3,2],[3,2,2]] => [5,2] [[5,4,2,2],[3,2,1]] => [5,2] [[6,5,3,2],[4,3,2]] => [6,1] [[5,3,2,2],[3,1,1]] => [5,1,1] [[6,4,3,2],[4,2,2]] => [6,1] [[6,4,2,2],[4,2,1]] => [6,1] [[7,5,3,2],[5,3,2]] => [7] [[2,2,1,1,1],[]] => [2,2,1,1,1] [[3,3,2,2,1],[1,1,1,1]] => [3,2,1,1] [[3,3,2,1,1],[1,1,1]] => [3,3,1] [[4,4,3,2,1],[2,2,2,1]] => [4,2,1] [[3,3,1,1,1],[1,1]] => [3,3,1] [[4,4,2,2,1],[2,2,1,1]] => [4,3] [[4,4,2,1,1],[2,2,1]] => [4,3] [[5,5,3,2,1],[3,3,2,1]] => [5,2] [[3,2,1,1,1],[1]] => [3,2,1,1] [[4,3,2,2,1],[2,1,1,1]] => [4,2,1] [[4,3,2,1,1],[2,1,1]] => [4,3] [[5,4,3,2,1],[3,2,2,1]] => [5,2] [[4,3,1,1,1],[2,1]] => [4,2,1] [[5,4,2,2,1],[3,2,1,1]] => [5,2] [[5,4,2,1,1],[3,2,1]] => [5,2] [[6,5,3,2,1],[4,3,2,1]] => [6,1] [[4,2,1,1,1],[2]] => [4,1,1,1] [[5,3,2,2,1],[3,1,1,1]] => [5,1,1] [[5,3,2,1,1],[3,1,1]] => [5,2] [[6,4,3,2,1],[4,2,2,1]] => [6,1] [[5,3,1,1,1],[3,1]] => [5,1,1] [[6,4,2,2,1],[4,2,1,1]] => [6,1] [[6,4,2,1,1],[4,2,1]] => [6,1] [[7,5,3,2,1],[5,3,2,1]] => [7] [[5,4,4],[3,3]] => [5,1,1] [[6,5,4],[4,4]] => [6,1] [[6,4,4],[4,3]] => [6,1] [[7,5,4],[5,4]] => [7] [[4,3,3,1],[2,2]] => [4,2,1] [[5,4,4,1],[3,3,1]] => [5,1,1] [[5,4,3,1],[3,3]] => [5,2] [[6,5,4,1],[4,4,1]] => [6,1] [[5,3,3,1],[3,2]] => [5,2] [[6,4,4,1],[4,3,1]] => [6,1] [[6,4,3,1],[4,3]] => [6,1] [[7,5,4,1],[5,4,1]] => [7] [[3,2,2,2],[1,1]] => [3,2,1,1] [[4,3,3,2],[2,2,1]] => [4,2,1] [[5,4,4,2],[3,3,2]] => [5,1,1] [[4,3,2,2],[2,2]] => [4,3] [[5,4,3,2],[3,3,1]] => [5,2] [[6,5,4,2],[4,4,2]] => [6,1] [[4,2,2,2],[2,1]] => [4,2,1] [[5,3,3,2],[3,2,1]] => [5,2] [[6,4,4,2],[4,3,2]] => [6,1] [[5,3,2,2],[3,2]] => [5,2] [[6,4,3,2],[4,3,1]] => [6,1] [[7,5,4,2],[5,4,2]] => [7] [[3,2,2,1,1],[1,1]] => [3,2,2] [[4,3,3,2,1],[2,2,1,1]] => [4,2,1] [[4,3,3,1,1],[2,2,1]] => [4,2,1] [[5,4,4,2,1],[3,3,2,1]] => [5,1,1] [[4,3,2,1,1],[2,2]] => [4,2,1] [[5,4,3,2,1],[3,3,1,1]] => [5,2] [[5,4,3,1,1],[3,3,1]] => [5,2] [[6,5,4,2,1],[4,4,2,1]] => [6,1] [[4,2,2,1,1],[2,1]] => [4,2,1] [[5,3,3,2,1],[3,2,1,1]] => [5,2] [[5,3,3,1,1],[3,2,1]] => [5,2] [[6,4,4,2,1],[4,3,2,1]] => [6,1] [[5,3,2,1,1],[3,2]] => [5,1,1] [[6,4,3,2,1],[4,3,1,1]] => [6,1] [[6,4,3,1,1],[4,3,1]] => [6,1] [[7,5,4,2,1],[5,4,2,1]] => [7] [[4,3,3,3],[2,2,2]] => [4,1,1,1] [[5,4,4,3],[3,3,3]] => [5,1,1] [[5,4,3,3],[3,3,2]] => [5,2] [[6,5,4,3],[4,4,3]] => [6,1] [[5,3,3,3],[3,2,2]] => [5,1,1] [[6,4,4,3],[4,3,3]] => [6,1] [[6,4,3,3],[4,3,2]] => [6,1] [[7,5,4,3],[5,4,3]] => [7] [[3,2,2,2,1],[1,1,1]] => [3,2,1,1] [[4,3,3,3,1],[2,2,2,1]] => [4,1,1,1] [[4,3,3,2,1],[2,2,2]] => [4,2,1] [[5,4,4,3,1],[3,3,3,1]] => [5,1,1] [[4,3,2,2,1],[2,2,1]] => [4,3] [[5,4,3,3,1],[3,3,2,1]] => [5,2] [[5,4,3,2,1],[3,3,2]] => [5,2] [[6,5,4,3,1],[4,4,3,1]] => [6,1] [[4,2,2,2,1],[2,1,1]] => [4,2,1] [[5,3,3,3,1],[3,2,2,1]] => [5,1,1] [[5,3,3,2,1],[3,2,2]] => [5,2] [[6,4,4,3,1],[4,3,3,1]] => [6,1] [[5,3,2,2,1],[3,2,1]] => [5,2] [[6,4,3,3,1],[4,3,2,1]] => [6,1] [[6,4,3,2,1],[4,3,2]] => [6,1] [[7,5,4,3,1],[5,4,3,1]] => [7] [[3,2,2,2,2],[1,1,1,1]] => [3,1,1,1,1] [[4,3,3,3,2],[2,2,2,2]] => [4,1,1,1] [[4,3,3,2,2],[2,2,2,1]] => [4,2,1] [[5,4,4,3,2],[3,3,3,2]] => [5,1,1] [[4,3,2,2,2],[2,2,1,1]] => [4,2,1] [[5,4,3,3,2],[3,3,2,2]] => [5,2] [[5,4,3,2,2],[3,3,2,1]] => [5,2] [[6,5,4,3,2],[4,4,3,2]] => [6,1] [[4,2,2,2,2],[2,1,1,1]] => [4,1,1,1] [[5,3,3,3,2],[3,2,2,2]] => [5,1,1] [[5,3,3,2,2],[3,2,2,1]] => [5,2] [[6,4,4,3,2],[4,3,3,2]] => [6,1] [[5,3,2,2,2],[3,2,1,1]] => [5,1,1] [[6,4,3,3,2],[4,3,2,2]] => [6,1] [[6,4,3,2,2],[4,3,2,1]] => [6,1] [[7,5,4,3,2],[5,4,3,2]] => [7] [[2,1,1,1,1,1],[]] => [2,1,1,1,1,1] [[3,2,2,2,2,1],[1,1,1,1,1]] => [3,1,1,1,1] [[3,2,2,2,1,1],[1,1,1,1]] => [3,2,1,1] [[4,3,3,3,2,1],[2,2,2,2,1]] => [4,1,1,1] [[3,2,2,1,1,1],[1,1,1]] => [3,2,2] [[4,3,3,2,2,1],[2,2,2,1,1]] => [4,2,1] [[4,3,3,2,1,1],[2,2,2,1]] => [4,2,1] [[5,4,4,3,2,1],[3,3,3,2,1]] => [5,1,1] [[3,2,1,1,1,1],[1,1]] => [3,2,1,1] [[4,3,2,2,2,1],[2,2,1,1,1]] => [4,2,1] [[4,3,2,2,1,1],[2,2,1,1]] => [4,3] [[5,4,3,3,2,1],[3,3,2,2,1]] => [5,2] [[4,3,2,1,1,1],[2,2,1]] => [4,2,1] [[5,4,3,2,2,1],[3,3,2,1,1]] => [5,2] [[5,4,3,2,1,1],[3,3,2,1]] => [5,2] [[6,5,4,3,2,1],[4,4,3,2,1]] => [6,1] [[3,1,1,1,1,1],[1]] => [3,1,1,1,1] [[4,2,2,2,2,1],[2,1,1,1,1]] => [4,1,1,1] [[4,2,2,2,1,1],[2,1,1,1]] => [4,2,1] [[5,3,3,3,2,1],[3,2,2,2,1]] => [5,1,1] [[4,2,2,1,1,1],[2,1,1]] => [4,2,1] [[5,3,3,2,2,1],[3,2,2,1,1]] => [5,2] [[5,3,3,2,1,1],[3,2,2,1]] => [5,2] [[6,4,4,3,2,1],[4,3,3,2,1]] => [6,1] [[4,2,1,1,1,1],[2,1]] => [4,1,1,1] [[5,3,2,2,2,1],[3,2,1,1,1]] => [5,1,1] [[5,3,2,2,1,1],[3,2,1,1]] => [5,2] [[6,4,3,3,2,1],[4,3,2,2,1]] => [6,1] [[5,3,2,1,1,1],[3,2,1]] => [5,1,1] [[6,4,3,2,2,1],[4,3,2,1,1]] => [6,1] [[6,4,3,2,1,1],[4,3,2,1]] => [6,1] [[7,5,4,3,2,1],[5,4,3,2,1]] => [7] [[6,6],[5]] => [6,1] [[7,6],[6]] => [7] [[5,5,1],[4]] => [5,2] [[6,6,1],[5,1]] => [6,1] [[6,5,1],[5]] => [6,1] [[7,6,1],[6,1]] => [7] [[4,4,2],[3]] => [4,3] [[5,5,2],[4,1]] => [5,2] [[6,6,2],[5,2]] => [6,1] [[5,4,2],[4]] => [5,2] [[6,5,2],[5,1]] => [6,1] [[7,6,2],[6,2]] => [7] [[4,4,1,1],[3]] => [4,2,1] [[5,5,2,1],[4,1,1]] => [5,2] [[5,5,1,1],[4,1]] => [5,2] [[6,6,2,1],[5,2,1]] => [6,1] [[5,4,1,1],[4]] => [5,1,1] [[6,5,2,1],[5,1,1]] => [6,1] [[6,5,1,1],[5,1]] => [6,1] [[7,6,2,1],[6,2,1]] => [7] [[3,3,3],[2]] => [3,3,1] [[4,4,3],[3,1]] => [4,3] [[5,5,3],[4,2]] => [5,2] [[6,6,3],[5,3]] => [6,1] [[4,3,3],[3]] => [4,3] [[5,4,3],[4,1]] => [5,2] [[6,5,3],[5,2]] => [6,1] [[7,6,3],[6,3]] => [7] [[3,3,2,1],[2]] => [3,3,1] [[4,4,3,1],[3,1,1]] => [4,3] [[4,4,2,1],[3,1]] => [4,3] [[5,5,3,1],[4,2,1]] => [5,2] [[5,5,2,1],[4,2]] => [5,2] [[6,6,3,1],[5,3,1]] => [6,1] [[4,3,2,1],[3]] => [4,2,1] [[5,4,3,1],[4,1,1]] => [5,2] [[5,4,2,1],[4,1]] => [5,2] [[6,5,3,1],[5,2,1]] => [6,1] [[6,5,2,1],[5,2]] => [6,1] [[7,6,3,1],[6,3,1]] => [7] [[4,4,2,2],[3,1,1]] => [4,2,1] [[5,5,3,2],[4,2,2]] => [5,2] [[5,5,2,2],[4,2,1]] => [5,2] [[6,6,3,2],[5,3,2]] => [6,1] [[5,4,2,2],[4,1,1]] => [5,1,1] [[6,5,3,2],[5,2,2]] => [6,1] [[6,5,2,2],[5,2,1]] => [6,1] [[7,6,3,2],[6,3,2]] => [7] [[3,3,1,1,1],[2]] => [3,2,1,1] [[4,4,2,2,1],[3,1,1,1]] => [4,2,1] [[4,4,2,1,1],[3,1,1]] => [4,3] [[5,5,3,2,1],[4,2,2,1]] => [5,2] [[4,4,1,1,1],[3,1]] => [4,2,1] [[5,5,2,2,1],[4,2,1,1]] => [5,2] [[5,5,2,1,1],[4,2,1]] => [5,2] [[6,6,3,2,1],[5,3,2,1]] => [6,1] [[4,3,1,1,1],[3]] => [4,1,1,1] [[5,4,2,2,1],[4,1,1,1]] => [5,1,1] [[5,4,2,1,1],[4,1,1]] => [5,2] [[6,5,3,2,1],[5,2,2,1]] => [6,1] [[5,4,1,1,1],[4,1]] => [5,1,1] [[6,5,2,2,1],[5,2,1,1]] => [6,1] [[6,5,2,1,1],[5,2,1]] => [6,1] [[7,6,3,2,1],[6,3,2,1]] => [7] [[4,4,4],[3,2]] => [4,2,1] [[5,5,4],[4,3]] => [5,2] [[6,6,4],[5,4]] => [6,1] [[5,4,4],[4,2]] => [5,2] [[6,5,4],[5,3]] => [6,1] [[7,6,4],[6,4]] => [7] [[3,3,3,1],[2,1]] => [3,3,1] [[4,4,4,1],[3,2,1]] => [4,2,1] [[4,4,3,1],[3,2]] => [4,3] [[5,5,4,1],[4,3,1]] => [5,2] [[5,5,3,1],[4,3]] => [5,2] [[6,6,4,1],[5,4,1]] => [6,1] [[4,3,3,1],[3,1]] => [4,3] [[5,4,4,1],[4,2,1]] => [5,2] [[5,4,3,1],[4,2]] => [5,2] [[6,5,4,1],[5,3,1]] => [6,1] [[6,5,3,1],[5,3]] => [6,1] [[7,6,4,1],[6,4,1]] => [7] [[2,2,2,2],[1]] => [2,2,2,1] [[3,3,3,2],[2,1,1]] => [3,2,2] [[4,4,4,2],[3,2,2]] => [4,2,1] [[3,3,2,2],[2,1]] => [3,3,1] [[4,4,3,2],[3,2,1]] => [4,3] [[5,5,4,2],[4,3,2]] => [5,2] [[4,4,2,2],[3,2]] => [4,3] [[5,5,3,2],[4,3,1]] => [5,2] [[6,6,4,2],[5,4,2]] => [6,1] [[3,2,2,2],[2]] => [3,2,2] [[4,3,3,2],[3,1,1]] => [4,2,1] [[5,4,4,2],[4,2,2]] => [5,2] [[4,3,2,2],[3,1]] => [4,2,1] [[5,4,3,2],[4,2,1]] => [5,2] [[6,5,4,2],[5,3,2]] => [6,1] [[5,4,2,2],[4,2]] => [5,2] [[6,5,3,2],[5,3,1]] => [6,1] [[7,6,4,2],[6,4,2]] => [7] [[2,2,2,1,1],[1]] => [2,2,2,1] [[3,3,3,2,1],[2,1,1,1]] => [3,2,2] [[3,3,3,1,1],[2,1,1]] => [3,3,1] [[4,4,4,2,1],[3,2,2,1]] => [4,2,1] [[3,3,2,1,1],[2,1]] => [3,3,1] [[4,4,3,2,1],[3,2,1,1]] => [4,3] [[4,4,3,1,1],[3,2,1]] => [4,3] [[5,5,4,2,1],[4,3,2,1]] => [5,2] [[4,4,2,1,1],[3,2]] => [4,2,1] [[5,5,3,2,1],[4,3,1,1]] => [5,2] [[5,5,3,1,1],[4,3,1]] => [5,2] [[6,6,4,2,1],[5,4,2,1]] => [6,1] [[3,2,2,1,1],[2]] => [3,2,1,1] [[4,3,3,2,1],[3,1,1,1]] => [4,2,1] [[4,3,3,1,1],[3,1,1]] => [4,3] [[5,4,4,2,1],[4,2,2,1]] => [5,2] [[4,3,2,1,1],[3,1]] => [4,2,1] [[5,4,3,2,1],[4,2,1,1]] => [5,2] [[5,4,3,1,1],[4,2,1]] => [5,2] [[6,5,4,2,1],[5,3,2,1]] => [6,1] [[5,4,2,1,1],[4,2]] => [5,1,1] [[6,5,3,2,1],[5,3,1,1]] => [6,1] [[6,5,3,1,1],[5,3,1]] => [6,1] [[7,6,4,2,1],[6,4,2,1]] => [7] [[4,4,3,3],[3,2,2]] => [4,2,1] [[5,5,4,3],[4,3,3]] => [5,2] [[5,5,3,3],[4,3,2]] => [5,2] [[6,6,4,3],[5,4,3]] => [6,1] [[5,4,3,3],[4,2,2]] => [5,1,1] [[6,5,4,3],[5,3,3]] => [6,1] [[6,5,3,3],[5,3,2]] => [6,1] [[7,6,4,3],[6,4,3]] => [7] [[3,3,2,2,1],[2,1,1]] => [3,3,1] [[4,4,3,3,1],[3,2,2,1]] => [4,2,1] [[4,4,3,2,1],[3,2,2]] => [4,3] [[5,5,4,3,1],[4,3,3,1]] => [5,2] [[4,4,2,2,1],[3,2,1]] => [4,3] [[5,5,3,3,1],[4,3,2,1]] => [5,2] [[5,5,3,2,1],[4,3,2]] => [5,2] [[6,6,4,3,1],[5,4,3,1]] => [6,1] [[4,3,2,2,1],[3,1,1]] => [4,2,1] [[5,4,3,3,1],[4,2,2,1]] => [5,1,1] [[5,4,3,2,1],[4,2,2]] => [5,2] [[6,5,4,3,1],[5,3,3,1]] => [6,1] [[5,4,2,2,1],[4,2,1]] => [5,2] [[6,5,3,3,1],[5,3,2,1]] => [6,1] [[6,5,3,2,1],[5,3,2]] => [6,1] [[7,6,4,3,1],[6,4,3,1]] => [7] [[3,3,2,2,2],[2,1,1,1]] => [3,2,1,1] [[4,4,3,3,2],[3,2,2,2]] => [4,2,1] [[4,4,3,2,2],[3,2,2,1]] => [4,3] [[5,5,4,3,2],[4,3,3,2]] => [5,2] [[4,4,2,2,2],[3,2,1,1]] => [4,2,1] [[5,5,3,3,2],[4,3,2,2]] => [5,2] [[5,5,3,2,2],[4,3,2,1]] => [5,2] [[6,6,4,3,2],[5,4,3,2]] => [6,1] [[4,3,2,2,2],[3,1,1,1]] => [4,1,1,1] [[5,4,3,3,2],[4,2,2,2]] => [5,1,1] [[5,4,3,2,2],[4,2,2,1]] => [5,2] [[6,5,4,3,2],[5,3,3,2]] => [6,1] [[5,4,2,2,2],[4,2,1,1]] => [5,1,1] [[6,5,3,3,2],[5,3,2,2]] => [6,1] [[6,5,3,2,2],[5,3,2,1]] => [6,1] [[7,6,4,3,2],[6,4,3,2]] => [7] [[2,2,1,1,1,1],[1]] => [2,2,1,1,1] [[3,3,2,2,2,1],[2,1,1,1,1]] => [3,2,1,1] [[3,3,2,2,1,1],[2,1,1,1]] => [3,3,1] [[4,4,3,3,2,1],[3,2,2,2,1]] => [4,2,1] [[3,3,2,1,1,1],[2,1,1]] => [3,3,1] [[4,4,3,2,2,1],[3,2,2,1,1]] => [4,3] [[4,4,3,2,1,1],[3,2,2,1]] => [4,3] [[5,5,4,3,2,1],[4,3,3,2,1]] => [5,2] [[3,3,1,1,1,1],[2,1]] => [3,2,1,1] [[4,4,2,2,2,1],[3,2,1,1,1]] => [4,2,1] [[4,4,2,2,1,1],[3,2,1,1]] => [4,3] [[5,5,3,3,2,1],[4,3,2,2,1]] => [5,2] [[4,4,2,1,1,1],[3,2,1]] => [4,2,1] [[5,5,3,2,2,1],[4,3,2,1,1]] => [5,2] [[5,5,3,2,1,1],[4,3,2,1]] => [5,2] [[6,6,4,3,2,1],[5,4,3,2,1]] => [6,1] [[3,2,1,1,1,1],[2]] => [3,1,1,1,1] [[4,3,2,2,2,1],[3,1,1,1,1]] => [4,1,1,1] [[4,3,2,2,1,1],[3,1,1,1]] => [4,2,1] [[5,4,3,3,2,1],[4,2,2,2,1]] => [5,1,1] [[4,3,2,1,1,1],[3,1,1]] => [4,2,1] [[5,4,3,2,2,1],[4,2,2,1,1]] => [5,2] [[5,4,3,2,1,1],[4,2,2,1]] => [5,2] [[6,5,4,3,2,1],[5,3,3,2,1]] => [6,1] [[4,3,1,1,1,1],[3,1]] => [4,1,1,1] [[5,4,2,2,2,1],[4,2,1,1,1]] => [5,1,1] [[5,4,2,2,1,1],[4,2,1,1]] => [5,2] [[6,5,3,3,2,1],[5,3,2,2,1]] => [6,1] [[5,4,2,1,1,1],[4,2,1]] => [5,1,1] [[6,5,3,2,2,1],[5,3,2,1,1]] => [6,1] [[6,5,3,2,1,1],[5,3,2,1]] => [6,1] [[7,6,4,3,2,1],[6,4,3,2,1]] => [7] [[5,5,5],[4,4]] => [5,1,1] [[6,6,5],[5,5]] => [6,1] [[6,5,5],[5,4]] => [6,1] [[7,6,5],[6,5]] => [7] [[4,4,4,1],[3,3]] => [4,2,1] [[5,5,5,1],[4,4,1]] => [5,1,1] [[5,5,4,1],[4,4]] => [5,2] [[6,6,5,1],[5,5,1]] => [6,1] [[5,4,4,1],[4,3]] => [5,2] [[6,5,5,1],[5,4,1]] => [6,1] [[6,5,4,1],[5,4]] => [6,1] [[7,6,5,1],[6,5,1]] => [7] [[3,3,3,2],[2,2]] => [3,3,1] [[4,4,4,2],[3,3,1]] => [4,2,1] [[5,5,5,2],[4,4,2]] => [5,1,1] [[4,4,3,2],[3,3]] => [4,3] [[5,5,4,2],[4,4,1]] => [5,2] [[6,6,5,2],[5,5,2]] => [6,1] [[4,3,3,2],[3,2]] => [4,3] [[5,4,4,2],[4,3,1]] => [5,2] [[6,5,5,2],[5,4,2]] => [6,1] [[5,4,3,2],[4,3]] => [5,2] [[6,5,4,2],[5,4,1]] => [6,1] [[7,6,5,2],[6,5,2]] => [7] [[3,3,3,1,1],[2,2]] => [3,2,2] [[4,4,4,2,1],[3,3,1,1]] => [4,2,1] [[4,4,4,1,1],[3,3,1]] => [4,2,1] [[5,5,5,2,1],[4,4,2,1]] => [5,1,1] [[4,4,3,1,1],[3,3]] => [4,2,1] [[5,5,4,2,1],[4,4,1,1]] => [5,2] [[5,5,4,1,1],[4,4,1]] => [5,2] [[6,6,5,2,1],[5,5,2,1]] => [6,1] [[4,3,3,1,1],[3,2]] => [4,2,1] [[5,4,4,2,1],[4,3,1,1]] => [5,2] [[5,4,4,1,1],[4,3,1]] => [5,2] [[6,5,5,2,1],[5,4,2,1]] => [6,1] [[5,4,3,1,1],[4,3]] => [5,1,1] [[6,5,4,2,1],[5,4,1,1]] => [6,1] [[6,5,4,1,1],[5,4,1]] => [6,1] [[7,6,5,2,1],[6,5,2,1]] => [7] [[3,3,3,3],[2,2,1]] => [3,2,1,1] [[4,4,4,3],[3,3,2]] => [4,2,1] [[5,5,5,3],[4,4,3]] => [5,1,1] [[4,4,3,3],[3,3,1]] => [4,3] [[5,5,4,3],[4,4,2]] => [5,2] [[6,6,5,3],[5,5,3]] => [6,1] [[4,3,3,3],[3,2,1]] => [4,2,1] [[5,4,4,3],[4,3,2]] => [5,2] [[6,5,5,3],[5,4,3]] => [6,1] [[5,4,3,3],[4,3,1]] => [5,2] [[6,5,4,3],[5,4,2]] => [6,1] [[7,6,5,3],[6,5,3]] => [7] [[2,2,2,2,1],[1,1]] => [2,2,2,1] [[3,3,3,3,1],[2,2,1,1]] => [3,2,1,1] [[3,3,3,2,1],[2,2,1]] => [3,3,1] [[4,4,4,3,1],[3,3,2,1]] => [4,2,1] [[4,4,4,2,1],[3,3,2]] => [4,2,1] [[5,5,5,3,1],[4,4,3,1]] => [5,1,1] [[3,3,2,2,1],[2,2]] => [3,3,1] [[4,4,3,3,1],[3,3,1,1]] => [4,3] [[4,4,3,2,1],[3,3,1]] => [4,3] [[5,5,4,3,1],[4,4,2,1]] => [5,2] [[5,5,4,2,1],[4,4,2]] => [5,2] [[6,6,5,3,1],[5,5,3,1]] => [6,1] [[3,2,2,2,1],[2,1]] => [3,2,2] [[4,3,3,3,1],[3,2,1,1]] => [4,2,1] [[4,3,3,2,1],[3,2,1]] => [4,3] [[5,4,4,3,1],[4,3,2,1]] => [5,2] [[5,4,4,2,1],[4,3,2]] => [5,2] [[6,5,5,3,1],[5,4,3,1]] => [6,1] [[4,3,2,2,1],[3,2]] => [4,2,1] [[5,4,3,3,1],[4,3,1,1]] => [5,2] [[5,4,3,2,1],[4,3,1]] => [5,2] [[6,5,4,3,1],[5,4,2,1]] => [6,1] [[6,5,4,2,1],[5,4,2]] => [6,1] [[7,6,5,3,1],[6,5,3,1]] => [7] [[3,3,3,2,2],[2,2,1,1]] => [3,2,2] [[4,4,4,3,2],[3,3,2,2]] => [4,2,1] [[4,4,4,2,2],[3,3,2,1]] => [4,2,1] [[5,5,5,3,2],[4,4,3,2]] => [5,1,1] [[4,4,3,2,2],[3,3,1,1]] => [4,2,1] [[5,5,4,3,2],[4,4,2,2]] => [5,2] [[5,5,4,2,2],[4,4,2,1]] => [5,2] [[6,6,5,3,2],[5,5,3,2]] => [6,1] [[4,3,3,2,2],[3,2,1,1]] => [4,2,1] [[5,4,4,3,2],[4,3,2,2]] => [5,2] [[5,4,4,2,2],[4,3,2,1]] => [5,2] [[6,5,5,3,2],[5,4,3,2]] => [6,1] [[5,4,3,2,2],[4,3,1,1]] => [5,1,1] [[6,5,4,3,2],[5,4,2,2]] => [6,1] [[6,5,4,2,2],[5,4,2,1]] => [6,1] [[7,6,5,3,2],[6,5,3,2]] => [7] [[2,2,2,1,1,1],[1,1]] => [2,2,2,1] [[3,3,3,2,2,1],[2,2,1,1,1]] => [3,2,2] [[3,3,3,2,1,1],[2,2,1,1]] => [3,3,1] [[4,4,4,3,2,1],[3,3,2,2,1]] => [4,2,1] [[3,3,3,1,1,1],[2,2,1]] => [3,2,2] [[4,4,4,2,2,1],[3,3,2,1,1]] => [4,2,1] [[4,4,4,2,1,1],[3,3,2,1]] => [4,2,1] [[5,5,5,3,2,1],[4,4,3,2,1]] => [5,1,1] [[3,3,2,1,1,1],[2,2]] => [3,2,1,1] [[4,4,3,2,2,1],[3,3,1,1,1]] => [4,2,1] [[4,4,3,2,1,1],[3,3,1,1]] => [4,3] [[5,5,4,3,2,1],[4,4,2,2,1]] => [5,2] [[4,4,3,1,1,1],[3,3,1]] => [4,2,1] [[5,5,4,2,2,1],[4,4,2,1,1]] => [5,2] [[5,5,4,2,1,1],[4,4,2,1]] => [5,2] [[6,6,5,3,2,1],[5,5,3,2,1]] => [6,1] [[3,2,2,1,1,1],[2,1]] => [3,2,1,1] [[4,3,3,2,2,1],[3,2,1,1,1]] => [4,2,1] [[4,3,3,2,1,1],[3,2,1,1]] => [4,3] [[5,4,4,3,2,1],[4,3,2,2,1]] => [5,2] [[4,3,3,1,1,1],[3,2,1]] => [4,2,1] [[5,4,4,2,2,1],[4,3,2,1,1]] => [5,2] [[5,4,4,2,1,1],[4,3,2,1]] => [5,2] [[6,5,5,3,2,1],[5,4,3,2,1]] => [6,1] [[4,3,2,1,1,1],[3,2]] => [4,1,1,1] [[5,4,3,2,2,1],[4,3,1,1,1]] => [5,1,1] [[5,4,3,2,1,1],[4,3,1,1]] => [5,2] [[6,5,4,3,2,1],[5,4,2,2,1]] => [6,1] [[5,4,3,1,1,1],[4,3,1]] => [5,1,1] [[6,5,4,2,2,1],[5,4,2,1,1]] => [6,1] [[6,5,4,2,1,1],[5,4,2,1]] => [6,1] [[7,6,5,3,2,1],[6,5,3,2,1]] => [7] [[4,4,4,4],[3,3,3]] => [4,1,1,1] [[5,5,5,4],[4,4,4]] => [5,1,1] [[5,5,4,4],[4,4,3]] => [5,2] [[6,6,5,4],[5,5,4]] => [6,1] [[5,4,4,4],[4,3,3]] => [5,1,1] [[6,5,5,4],[5,4,4]] => [6,1] [[6,5,4,4],[5,4,3]] => [6,1] [[7,6,5,4],[6,5,4]] => [7] [[3,3,3,3,1],[2,2,2]] => [3,2,1,1] [[4,4,4,4,1],[3,3,3,1]] => [4,1,1,1] [[4,4,4,3,1],[3,3,3]] => [4,2,1] [[5,5,5,4,1],[4,4,4,1]] => [5,1,1] [[4,4,3,3,1],[3,3,2]] => [4,3] [[5,5,4,4,1],[4,4,3,1]] => [5,2] [[5,5,4,3,1],[4,4,3]] => [5,2] [[6,6,5,4,1],[5,5,4,1]] => [6,1] [[4,3,3,3,1],[3,2,2]] => [4,2,1] [[5,4,4,4,1],[4,3,3,1]] => [5,1,1] [[5,4,4,3,1],[4,3,3]] => [5,2] [[6,5,5,4,1],[5,4,4,1]] => [6,1] [[5,4,3,3,1],[4,3,2]] => [5,2] [[6,5,4,4,1],[5,4,3,1]] => [6,1] [[6,5,4,3,1],[5,4,3]] => [6,1] [[7,6,5,4,1],[6,5,4,1]] => [7] [[2,2,2,2,2],[1,1,1]] => [2,2,1,1,1] [[3,3,3,3,2],[2,2,2,1]] => [3,2,1,1] [[4,4,4,4,2],[3,3,3,2]] => [4,1,1,1] [[3,3,3,2,2],[2,2,2]] => [3,3,1] [[4,4,4,3,2],[3,3,3,1]] => [4,2,1] [[5,5,5,4,2],[4,4,4,2]] => [5,1,1] [[3,3,2,2,2],[2,2,1]] => [3,3,1] [[4,4,3,3,2],[3,3,2,1]] => [4,3] [[5,5,4,4,2],[4,4,3,2]] => [5,2] [[4,4,3,2,2],[3,3,2]] => [4,3] [[5,5,4,3,2],[4,4,3,1]] => [5,2] [[6,6,5,4,2],[5,5,4,2]] => [6,1] [[3,2,2,2,2],[2,1,1]] => [3,2,1,1] [[4,3,3,3,2],[3,2,2,1]] => [4,2,1] [[5,4,4,4,2],[4,3,3,2]] => [5,1,1] [[4,3,3,2,2],[3,2,2]] => [4,3] [[5,4,4,3,2],[4,3,3,1]] => [5,2] [[6,5,5,4,2],[5,4,4,2]] => [6,1] [[4,3,2,2,2],[3,2,1]] => [4,2,1] [[5,4,3,3,2],[4,3,2,1]] => [5,2] [[6,5,4,4,2],[5,4,3,2]] => [6,1] [[5,4,3,2,2],[4,3,2]] => [5,2] [[6,5,4,3,2],[5,4,3,1]] => [6,1] [[7,6,5,4,2],[6,5,4,2]] => [7] [[2,2,2,2,1,1],[1,1,1]] => [2,2,2,1] [[3,3,3,3,2,1],[2,2,2,1,1]] => [3,2,1,1] [[3,3,3,3,1,1],[2,2,2,1]] => [3,2,1,1] [[4,4,4,4,2,1],[3,3,3,2,1]] => [4,1,1,1] [[3,3,3,2,1,1],[2,2,2]] => [3,2,2] [[4,4,4,3,2,1],[3,3,3,1,1]] => [4,2,1] [[4,4,4,3,1,1],[3,3,3,1]] => [4,2,1] [[5,5,5,4,2,1],[4,4,4,2,1]] => [5,1,1] [[3,3,2,2,1,1],[2,2,1]] => [3,3,1] [[4,4,3,3,2,1],[3,3,2,1,1]] => [4,3] [[4,4,3,3,1,1],[3,3,2,1]] => [4,3] [[5,5,4,4,2,1],[4,4,3,2,1]] => [5,2] [[4,4,3,2,1,1],[3,3,2]] => [4,2,1] [[5,5,4,3,2,1],[4,4,3,1,1]] => [5,2] [[5,5,4,3,1,1],[4,4,3,1]] => [5,2] [[6,6,5,4,2,1],[5,5,4,2,1]] => [6,1] [[3,2,2,2,1,1],[2,1,1]] => [3,2,2] [[4,3,3,3,2,1],[3,2,2,1,1]] => [4,2,1] [[4,3,3,3,1,1],[3,2,2,1]] => [4,2,1] [[5,4,4,4,2,1],[4,3,3,2,1]] => [5,1,1] [[4,3,3,2,1,1],[3,2,2]] => [4,2,1] [[5,4,4,3,2,1],[4,3,3,1,1]] => [5,2] [[5,4,4,3,1,1],[4,3,3,1]] => [5,2] [[6,5,5,4,2,1],[5,4,4,2,1]] => [6,1] [[4,3,2,2,1,1],[3,2,1]] => [4,2,1] [[5,4,3,3,2,1],[4,3,2,1,1]] => [5,2] [[5,4,3,3,1,1],[4,3,2,1]] => [5,2] [[6,5,4,4,2,1],[5,4,3,2,1]] => [6,1] [[5,4,3,2,1,1],[4,3,2]] => [5,1,1] [[6,5,4,3,2,1],[5,4,3,1,1]] => [6,1] [[6,5,4,3,1,1],[5,4,3,1]] => [6,1] [[7,6,5,4,2,1],[6,5,4,2,1]] => [7] [[3,3,3,3,3],[2,2,2,2]] => [3,1,1,1,1] [[4,4,4,4,3],[3,3,3,3]] => [4,1,1,1] [[4,4,4,3,3],[3,3,3,2]] => [4,2,1] [[5,5,5,4,3],[4,4,4,3]] => [5,1,1] [[4,4,3,3,3],[3,3,2,2]] => [4,2,1] [[5,5,4,4,3],[4,4,3,3]] => [5,2] [[5,5,4,3,3],[4,4,3,2]] => [5,2] [[6,6,5,4,3],[5,5,4,3]] => [6,1] [[4,3,3,3,3],[3,2,2,2]] => [4,1,1,1] [[5,4,4,4,3],[4,3,3,3]] => [5,1,1] [[5,4,4,3,3],[4,3,3,2]] => [5,2] [[6,5,5,4,3],[5,4,4,3]] => [6,1] [[5,4,3,3,3],[4,3,2,2]] => [5,1,1] [[6,5,4,4,3],[5,4,3,3]] => [6,1] [[6,5,4,3,3],[5,4,3,2]] => [6,1] [[7,6,5,4,3],[6,5,4,3]] => [7] [[2,2,2,2,2,1],[1,1,1,1]] => [2,2,1,1,1] [[3,3,3,3,3,1],[2,2,2,2,1]] => [3,1,1,1,1] [[3,3,3,3,2,1],[2,2,2,2]] => [3,2,1,1] [[4,4,4,4,3,1],[3,3,3,3,1]] => [4,1,1,1] [[3,3,3,2,2,1],[2,2,2,1]] => [3,3,1] [[4,4,4,3,3,1],[3,3,3,2,1]] => [4,2,1] [[4,4,4,3,2,1],[3,3,3,2]] => [4,2,1] [[5,5,5,4,3,1],[4,4,4,3,1]] => [5,1,1] [[3,3,2,2,2,1],[2,2,1,1]] => [3,3,1] [[4,4,3,3,3,1],[3,3,2,2,1]] => [4,2,1] [[4,4,3,3,2,1],[3,3,2,2]] => [4,3] [[5,5,4,4,3,1],[4,4,3,3,1]] => [5,2] [[4,4,3,2,2,1],[3,3,2,1]] => [4,3] [[5,5,4,3,3,1],[4,4,3,2,1]] => [5,2] [[5,5,4,3,2,1],[4,4,3,2]] => [5,2] [[6,6,5,4,3,1],[5,5,4,3,1]] => [6,1] [[3,2,2,2,2,1],[2,1,1,1]] => [3,2,1,1] [[4,3,3,3,3,1],[3,2,2,2,1]] => [4,1,1,1] [[4,3,3,3,2,1],[3,2,2,2]] => [4,2,1] [[5,4,4,4,3,1],[4,3,3,3,1]] => [5,1,1] [[4,3,3,2,2,1],[3,2,2,1]] => [4,3] [[5,4,4,3,3,1],[4,3,3,2,1]] => [5,2] [[5,4,4,3,2,1],[4,3,3,2]] => [5,2] [[6,5,5,4,3,1],[5,4,4,3,1]] => [6,1] [[4,3,2,2,2,1],[3,2,1,1]] => [4,2,1] [[5,4,3,3,3,1],[4,3,2,2,1]] => [5,1,1] [[5,4,3,3,2,1],[4,3,2,2]] => [5,2] [[6,5,4,4,3,1],[5,4,3,3,1]] => [6,1] [[5,4,3,2,2,1],[4,3,2,1]] => [5,2] [[6,5,4,3,3,1],[5,4,3,2,1]] => [6,1] [[6,5,4,3,2,1],[5,4,3,2]] => [6,1] [[7,6,5,4,3,1],[6,5,4,3,1]] => [7] [[2,2,2,2,2,2],[1,1,1,1,1]] => [2,1,1,1,1,1] [[3,3,3,3,3,2],[2,2,2,2,2]] => [3,1,1,1,1] [[3,3,3,3,2,2],[2,2,2,2,1]] => [3,2,1,1] [[4,4,4,4,3,2],[3,3,3,3,2]] => [4,1,1,1] [[3,3,3,2,2,2],[2,2,2,1,1]] => [3,2,2] [[4,4,4,3,3,2],[3,3,3,2,2]] => [4,2,1] [[4,4,4,3,2,2],[3,3,3,2,1]] => [4,2,1] [[5,5,5,4,3,2],[4,4,4,3,2]] => [5,1,1] [[3,3,2,2,2,2],[2,2,1,1,1]] => [3,2,1,1] [[4,4,3,3,3,2],[3,3,2,2,2]] => [4,2,1] [[4,4,3,3,2,2],[3,3,2,2,1]] => [4,3] [[5,5,4,4,3,2],[4,4,3,3,2]] => [5,2] [[4,4,3,2,2,2],[3,3,2,1,1]] => [4,2,1] [[5,5,4,3,3,2],[4,4,3,2,2]] => [5,2] [[5,5,4,3,2,2],[4,4,3,2,1]] => [5,2] [[6,6,5,4,3,2],[5,5,4,3,2]] => [6,1] [[3,2,2,2,2,2],[2,1,1,1,1]] => [3,1,1,1,1] [[4,3,3,3,3,2],[3,2,2,2,2]] => [4,1,1,1] [[4,3,3,3,2,2],[3,2,2,2,1]] => [4,2,1] [[5,4,4,4,3,2],[4,3,3,3,2]] => [5,1,1] [[4,3,3,2,2,2],[3,2,2,1,1]] => [4,2,1] [[5,4,4,3,3,2],[4,3,3,2,2]] => [5,2] [[5,4,4,3,2,2],[4,3,3,2,1]] => [5,2] [[6,5,5,4,3,2],[5,4,4,3,2]] => [6,1] [[4,3,2,2,2,2],[3,2,1,1,1]] => [4,1,1,1] [[5,4,3,3,3,2],[4,3,2,2,2]] => [5,1,1] [[5,4,3,3,2,2],[4,3,2,2,1]] => [5,2] [[6,5,4,4,3,2],[5,4,3,3,2]] => [6,1] [[5,4,3,2,2,2],[4,3,2,1,1]] => [5,1,1] [[6,5,4,3,3,2],[5,4,3,2,2]] => [6,1] [[6,5,4,3,2,2],[5,4,3,2,1]] => [6,1] [[7,6,5,4,3,2],[6,5,4,3,2]] => [7] [[1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1] [[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [2,1,1,1,1,1] [[2,2,2,2,2,1,1],[1,1,1,1,1]] => [2,2,1,1,1] [[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [3,1,1,1,1] [[2,2,2,2,1,1,1],[1,1,1,1]] => [2,2,2,1] [[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [3,2,1,1] [[3,3,3,3,2,1,1],[2,2,2,2,1]] => [3,2,1,1] [[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [4,1,1,1] [[2,2,2,1,1,1,1],[1,1,1]] => [2,2,2,1] [[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [3,2,2] [[3,3,3,2,2,1,1],[2,2,2,1,1]] => [3,3,1] [[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [4,2,1] [[3,3,3,2,1,1,1],[2,2,2,1]] => [3,2,2] [[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [4,2,1] ----------------------------------------------------------------------------- Created: Sep 27, 2020 at 14:56 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Sep 08, 2023 at 21:38 by Martin Rubey