************************************************************************ * 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: Mp00189 ------------------------------------------------------------------------ Map name: rotate ------------------------------------------------------------------------ Domain: Skew partitions ------------------------------------------------------------------------ Codomain: Skew partitions ------------------------------------------------------------------------ Description: The rotation of a skew partition. This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition $\lambda/\mu$, its rotation $(\lambda/\mu)^\natural$ is the skew partition with cells $\{(a-i, b-j)| (i, j) \in \lambda/\mu\}$, where $b$ and $a$ are the first part and the number of parts of $\lambda$ respectively. ------------------------------------------------------------------------ References: ------------------------------------------------------------------------ Code: def mapping(a): if a: la = a.outer() n = len(la) width = la[0] nu = [width - p for p in reversed(la)] ka = [x + y for x, y in zip(nu, reversed(a.row_lengths()))] return SkewPartition([ka, nu]) return a ------------------------------------------------------------------------ Map images: [[1],[]] => [[1],[]] [[2],[]] => [[2],[]] [[1,1],[]] => [[1,1],[]] [[2,1],[1]] => [[2,1],[1]] [[3],[]] => [[3],[]] [[2,1],[]] => [[2,2],[1]] [[3,1],[1]] => [[3,2],[2]] [[2,2],[1]] => [[2,1],[]] [[3,2],[2]] => [[3,1],[1]] [[1,1,1],[]] => [[1,1,1],[]] [[2,2,1],[1,1]] => [[2,1,1],[1]] [[2,1,1],[1]] => [[2,2,1],[1,1]] [[3,2,1],[2,1]] => [[3,2,1],[2,1]] [[4],[]] => [[4],[]] [[3,1],[]] => [[3,3],[2]] [[4,1],[1]] => [[4,3],[3]] [[2,2],[]] => [[2,2],[]] [[3,2],[1]] => [[3,2],[1]] [[4,2],[2]] => [[4,2],[2]] [[2,1,1],[]] => [[2,2,2],[1,1]] [[3,2,1],[1,1]] => [[3,2,2],[2,1]] [[3,1,1],[1]] => [[3,3,2],[2,2]] [[4,2,1],[2,1]] => [[4,3,2],[3,2]] [[3,3],[2]] => [[3,1],[]] [[4,3],[3]] => [[4,1],[1]] [[2,2,1],[1]] => [[2,2,1],[1]] [[3,3,1],[2,1]] => [[3,2,1],[2]] [[3,2,1],[2]] => [[3,3,1],[2,1]] [[4,3,1],[3,1]] => [[4,3,1],[3,1]] [[2,2,2],[1,1]] => [[2,1,1],[]] [[3,3,2],[2,2]] => [[3,1,1],[1]] [[3,2,2],[2,1]] => [[3,2,1],[1,1]] [[4,3,2],[3,2]] => [[4,2,1],[2,1]] [[1,1,1,1],[]] => [[1,1,1,1],[]] [[2,2,2,1],[1,1,1]] => [[2,1,1,1],[1]] [[2,2,1,1],[1,1]] => [[2,2,1,1],[1,1]] [[3,3,2,1],[2,2,1]] => [[3,2,1,1],[2,1]] [[2,1,1,1],[1]] => [[2,2,2,1],[1,1,1]] [[3,2,2,1],[2,1,1]] => [[3,2,2,1],[2,1,1]] [[3,2,1,1],[2,1]] => [[3,3,2,1],[2,2,1]] [[4,3,2,1],[3,2,1]] => [[4,3,2,1],[3,2,1]] [[5],[]] => [[5],[]] [[4,1],[]] => [[4,4],[3]] [[5,1],[1]] => [[5,4],[4]] [[3,2],[]] => [[3,3],[1]] [[4,2],[1]] => [[4,3],[2]] [[5,2],[2]] => [[5,3],[3]] [[3,1,1],[]] => [[3,3,3],[2,2]] [[4,2,1],[1,1]] => [[4,3,3],[3,2]] [[4,1,1],[1]] => [[4,4,3],[3,3]] [[5,2,1],[2,1]] => [[5,4,3],[4,3]] [[3,3],[1]] => [[3,2],[]] [[4,3],[2]] => [[4,2],[1]] [[5,3],[3]] => [[5,2],[2]] [[2,2,1],[]] => [[2,2,2],[1]] [[3,3,1],[1,1]] => [[3,2,2],[2]] [[3,2,1],[1]] => [[3,3,2],[2,1]] [[4,3,1],[2,1]] => [[4,3,2],[3,1]] [[4,2,1],[2]] => [[4,4,2],[3,2]] [[5,3,1],[3,1]] => [[5,4,2],[4,2]] [[3,2,2],[1,1]] => [[3,2,2],[1,1]] [[4,3,2],[2,2]] => [[4,2,2],[2,1]] [[4,2,2],[2,1]] => [[4,3,2],[2,2]] [[5,3,2],[3,2]] => [[5,3,2],[3,2]] [[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] [[3,2,2,1],[1,1,1]] => [[3,2,2,2],[2,1,1]] [[3,2,1,1],[1,1]] => [[3,3,2,2],[2,2,1]] [[4,3,2,1],[2,2,1]] => [[4,3,2,2],[3,2,1]] [[3,1,1,1],[1]] => [[3,3,3,2],[2,2,2]] [[4,2,2,1],[2,1,1]] => [[4,3,3,2],[3,2,2]] [[4,2,1,1],[2,1]] => [[4,4,3,2],[3,3,2]] [[5,3,2,1],[3,2,1]] => [[5,4,3,2],[4,3,2]] [[4,4],[3]] => [[4,1],[]] [[5,4],[4]] => [[5,1],[1]] [[3,3,1],[2]] => [[3,3,1],[2]] [[4,4,1],[3,1]] => [[4,3,1],[3]] [[4,3,1],[3]] => [[4,4,1],[3,1]] [[5,4,1],[4,1]] => [[5,4,1],[4,1]] [[2,2,2],[1]] => [[2,2,1],[]] [[3,3,2],[2,1]] => [[3,2,1],[1]] [[4,4,2],[3,2]] => [[4,2,1],[2]] [[3,2,2],[2]] => [[3,3,1],[1,1]] [[4,3,2],[3,1]] => [[4,3,1],[2,1]] [[5,4,2],[4,2]] => [[5,3,1],[3,1]] [[2,2,1,1],[1]] => [[2,2,2,1],[1,1]] [[3,3,2,1],[2,1,1]] => [[3,2,2,1],[2,1]] [[3,3,1,1],[2,1]] => [[3,3,2,1],[2,2]] [[4,4,2,1],[3,2,1]] => [[4,3,2,1],[3,2]] [[3,2,1,1],[2]] => [[3,3,3,1],[2,2,1]] [[4,3,2,1],[3,1,1]] => [[4,3,3,1],[3,2,1]] [[4,3,1,1],[3,1]] => [[4,4,3,1],[3,3,1]] [[5,4,2,1],[4,2,1]] => [[5,4,3,1],[4,3,1]] [[3,3,3],[2,2]] => [[3,1,1],[]] [[4,4,3],[3,3]] => [[4,1,1],[1]] [[4,3,3],[3,2]] => [[4,2,1],[1,1]] [[5,4,3],[4,3]] => [[5,2,1],[2,1]] [[2,2,2,1],[1,1]] => [[2,2,1,1],[1]] [[3,3,3,1],[2,2,1]] => [[3,2,1,1],[2]] [[3,3,2,1],[2,2]] => [[3,3,1,1],[2,1]] [[4,4,3,1],[3,3,1]] => [[4,3,1,1],[3,1]] [[3,2,2,1],[2,1]] => [[3,3,2,1],[2,1,1]] [[4,3,3,1],[3,2,1]] => [[4,3,2,1],[3,1,1]] [[4,3,2,1],[3,2]] => [[4,4,2,1],[3,2,1]] [[5,4,3,1],[4,3,1]] => [[5,4,2,1],[4,2,1]] [[2,2,2,2],[1,1,1]] => [[2,1,1,1],[]] [[3,3,3,2],[2,2,2]] => [[3,1,1,1],[1]] [[3,3,2,2],[2,2,1]] => [[3,2,1,1],[1,1]] [[4,4,3,2],[3,3,2]] => [[4,2,1,1],[2,1]] [[3,2,2,2],[2,1,1]] => [[3,2,2,1],[1,1,1]] [[4,3,3,2],[3,2,2]] => [[4,2,2,1],[2,1,1]] [[4,3,2,2],[3,2,1]] => [[4,3,2,1],[2,2,1]] [[5,4,3,2],[4,3,2]] => [[5,3,2,1],[3,2,1]] [[1,1,1,1,1],[]] => [[1,1,1,1,1],[]] [[2,2,2,2,1],[1,1,1,1]] => [[2,1,1,1,1],[1]] [[2,2,2,1,1],[1,1,1]] => [[2,2,1,1,1],[1,1]] [[3,3,3,2,1],[2,2,2,1]] => [[3,2,1,1,1],[2,1]] [[2,2,1,1,1],[1,1]] => [[2,2,2,1,1],[1,1,1]] [[3,3,2,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1,1]] [[3,3,2,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2,1]] [[4,4,3,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2,1]] [[2,1,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1,1]] [[3,2,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1,1]] [[3,2,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1,1]] [[4,3,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1,1]] [[3,2,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2,1]] [[4,3,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2,1]] [[4,3,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2,1]] [[5,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2,1]] [[6],[]] => [[6],[]] [[5,1],[]] => [[5,5],[4]] [[6,1],[1]] => [[6,5],[5]] [[4,2],[]] => [[4,4],[2]] [[5,2],[1]] => [[5,4],[3]] [[6,2],[2]] => [[6,4],[4]] [[4,1,1],[]] => [[4,4,4],[3,3]] [[5,2,1],[1,1]] => [[5,4,4],[4,3]] [[5,1,1],[1]] => [[5,5,4],[4,4]] [[6,2,1],[2,1]] => [[6,5,4],[5,4]] [[3,3],[]] => [[3,3],[]] [[4,3],[1]] => [[4,3],[1]] [[5,3],[2]] => [[5,3],[2]] [[6,3],[3]] => [[6,3],[3]] [[3,2,1],[]] => [[3,3,3],[2,1]] [[4,3,1],[1,1]] => [[4,3,3],[3,1]] [[4,2,1],[1]] => [[4,4,3],[3,2]] [[5,3,1],[2,1]] => [[5,4,3],[4,2]] [[5,2,1],[2]] => [[5,5,3],[4,3]] [[6,3,1],[3,1]] => [[6,5,3],[5,3]] [[4,2,2],[1,1]] => [[4,3,3],[2,2]] [[5,3,2],[2,2]] => [[5,3,3],[3,2]] [[5,2,2],[2,1]] => [[5,4,3],[3,3]] [[6,3,2],[3,2]] => [[6,4,3],[4,3]] [[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]] [[4,2,2,1],[1,1,1]] => [[4,3,3,3],[3,2,2]] [[4,2,1,1],[1,1]] => [[4,4,3,3],[3,3,2]] [[5,3,2,1],[2,2,1]] => [[5,4,3,3],[4,3,2]] [[4,1,1,1],[1]] => [[4,4,4,3],[3,3,3]] [[5,2,2,1],[2,1,1]] => [[5,4,4,3],[4,3,3]] [[5,2,1,1],[2,1]] => [[5,5,4,3],[4,4,3]] [[6,3,2,1],[3,2,1]] => [[6,5,4,3],[5,4,3]] [[4,4],[2]] => [[4,2],[]] [[5,4],[3]] => [[5,2],[1]] [[6,4],[4]] => [[6,2],[2]] [[3,3,1],[1]] => [[3,3,2],[2]] [[4,4,1],[2,1]] => [[4,3,2],[3]] [[4,3,1],[2]] => [[4,4,2],[3,1]] [[5,4,1],[3,1]] => [[5,4,2],[4,1]] [[5,3,1],[3]] => [[5,5,2],[4,2]] [[6,4,1],[4,1]] => [[6,5,2],[5,2]] [[2,2,2],[]] => [[2,2,2],[]] [[3,3,2],[1,1]] => [[3,2,2],[1]] [[4,4,2],[2,2]] => [[4,2,2],[2]] [[3,2,2],[1]] => [[3,3,2],[1,1]] [[4,3,2],[2,1]] => [[4,3,2],[2,1]] [[5,4,2],[3,2]] => [[5,3,2],[3,1]] [[4,2,2],[2]] => [[4,4,2],[2,2]] [[5,3,2],[3,1]] => [[5,4,2],[3,2]] [[6,4,2],[4,2]] => [[6,4,2],[4,2]] [[2,2,1,1],[]] => [[2,2,2,2],[1,1]] [[3,3,2,1],[1,1,1]] => [[3,2,2,2],[2,1]] [[3,3,1,1],[1,1]] => [[3,3,2,2],[2,2]] [[4,4,2,1],[2,2,1]] => [[4,3,2,2],[3,2]] [[3,2,1,1],[1]] => [[3,3,3,2],[2,2,1]] [[4,3,2,1],[2,1,1]] => [[4,3,3,2],[3,2,1]] [[4,3,1,1],[2,1]] => [[4,4,3,2],[3,3,1]] [[5,4,2,1],[3,2,1]] => [[5,4,3,2],[4,3,1]] [[4,2,1,1],[2]] => [[4,4,4,2],[3,3,2]] [[5,3,2,1],[3,1,1]] => [[5,4,4,2],[4,3,2]] [[5,3,1,1],[3,1]] => [[5,5,4,2],[4,4,2]] [[6,4,2,1],[4,2,1]] => [[6,5,4,2],[5,4,2]] [[4,3,3],[2,2]] => [[4,2,2],[1,1]] [[5,4,3],[3,3]] => [[5,2,2],[2,1]] [[5,3,3],[3,2]] => [[5,3,2],[2,2]] [[6,4,3],[4,3]] => [[6,3,2],[3,2]] [[3,2,2,1],[1,1]] => [[3,3,2,2],[2,1,1]] [[4,3,3,1],[2,2,1]] => [[4,3,2,2],[3,1,1]] [[4,3,2,1],[2,2]] => [[4,4,2,2],[3,2,1]] [[5,4,3,1],[3,3,1]] => [[5,4,2,2],[4,2,1]] [[4,2,2,1],[2,1]] => [[4,4,3,2],[3,2,2]] [[5,3,3,1],[3,2,1]] => [[5,4,3,2],[4,2,2]] [[5,3,2,1],[3,2]] => [[5,5,3,2],[4,3,2]] [[6,4,3,1],[4,3,1]] => [[6,5,3,2],[5,3,2]] [[3,2,2,2],[1,1,1]] => [[3,2,2,2],[1,1,1]] [[4,3,3,2],[2,2,2]] => [[4,2,2,2],[2,1,1]] [[4,3,2,2],[2,2,1]] => [[4,3,2,2],[2,2,1]] [[5,4,3,2],[3,3,2]] => [[5,3,2,2],[3,2,1]] [[4,2,2,2],[2,1,1]] => [[4,3,3,2],[2,2,2]] [[5,3,3,2],[3,2,2]] => [[5,3,3,2],[3,2,2]] [[5,3,2,2],[3,2,1]] => [[5,4,3,2],[3,3,2]] [[6,4,3,2],[4,3,2]] => [[6,4,3,2],[4,3,2]] [[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]] [[3,2,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1,1]] [[3,2,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1,1]] [[4,3,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1,1]] [[3,2,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2,1]] [[4,3,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2,1]] [[4,3,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2,1]] [[5,4,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2,1]] [[3,1,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,2]] [[4,2,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,2]] [[4,2,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,2]] [[5,3,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,2]] [[4,2,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,2]] [[5,3,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,2]] [[5,3,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,2]] [[6,4,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,2]] [[5,5],[4]] => [[5,1],[]] [[6,5],[5]] => [[6,1],[1]] [[4,4,1],[3]] => [[4,4,1],[3]] [[5,5,1],[4,1]] => [[5,4,1],[4]] [[5,4,1],[4]] => [[5,5,1],[4,1]] [[6,5,1],[5,1]] => [[6,5,1],[5,1]] [[3,3,2],[2]] => [[3,3,1],[1]] [[4,4,2],[3,1]] => [[4,3,1],[2]] [[5,5,2],[4,2]] => [[5,3,1],[3]] [[4,3,2],[3]] => [[4,4,1],[2,1]] [[5,4,2],[4,1]] => [[5,4,1],[3,1]] [[6,5,2],[5,2]] => [[6,4,1],[4,1]] [[3,3,1,1],[2]] => [[3,3,3,1],[2,2]] [[4,4,2,1],[3,1,1]] => [[4,3,3,1],[3,2]] [[4,4,1,1],[3,1]] => [[4,4,3,1],[3,3]] [[5,5,2,1],[4,2,1]] => [[5,4,3,1],[4,3]] [[4,3,1,1],[3]] => [[4,4,4,1],[3,3,1]] [[5,4,2,1],[4,1,1]] => [[5,4,4,1],[4,3,1]] [[5,4,1,1],[4,1]] => [[5,5,4,1],[4,4,1]] [[6,5,2,1],[5,2,1]] => [[6,5,4,1],[5,4,1]] [[3,3,3],[2,1]] => [[3,2,1],[]] [[4,4,3],[3,2]] => [[4,2,1],[1]] [[5,5,3],[4,3]] => [[5,2,1],[2]] [[4,3,3],[3,1]] => [[4,3,1],[1,1]] [[5,4,3],[4,2]] => [[5,3,1],[2,1]] [[6,5,3],[5,3]] => [[6,3,1],[3,1]] [[2,2,2,1],[1]] => [[2,2,2,1],[1]] [[3,3,3,1],[2,1,1]] => [[3,2,2,1],[2]] [[3,3,2,1],[2,1]] => [[3,3,2,1],[2,1]] [[4,4,3,1],[3,2,1]] => [[4,3,2,1],[3,1]] [[4,4,2,1],[3,2]] => [[4,4,2,1],[3,2]] [[5,5,3,1],[4,3,1]] => [[5,4,2,1],[4,2]] [[3,2,2,1],[2]] => [[3,3,3,1],[2,1,1]] [[4,3,3,1],[3,1,1]] => [[4,3,3,1],[3,1,1]] [[4,3,2,1],[3,1]] => [[4,4,3,1],[3,2,1]] [[5,4,3,1],[4,2,1]] => [[5,4,3,1],[4,2,1]] [[5,4,2,1],[4,2]] => [[5,5,3,1],[4,3,1]] [[6,5,3,1],[5,3,1]] => [[6,5,3,1],[5,3,1]] [[3,3,2,2],[2,1,1]] => [[3,2,2,1],[1,1]] [[4,4,3,2],[3,2,2]] => [[4,2,2,1],[2,1]] [[4,4,2,2],[3,2,1]] => [[4,3,2,1],[2,2]] [[5,5,3,2],[4,3,2]] => [[5,3,2,1],[3,2]] [[4,3,2,2],[3,1,1]] => [[4,3,3,1],[2,2,1]] [[5,4,3,2],[4,2,2]] => [[5,3,3,1],[3,2,1]] [[5,4,2,2],[4,2,1]] => [[5,4,3,1],[3,3,1]] [[6,5,3,2],[5,3,2]] => [[6,4,3,1],[4,3,1]] [[2,2,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1]] [[3,3,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1]] [[3,3,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1]] [[4,4,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1]] [[3,3,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2]] [[4,4,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2]] [[4,4,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2]] [[5,5,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2]] [[3,2,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2,1]] [[4,3,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2,1]] [[4,3,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2,1]] [[5,4,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2,1]] [[4,3,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3,1]] [[5,4,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3,1]] [[5,4,2,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,3,1]] [[6,5,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3,1]] [[4,4,4],[3,3]] => [[4,1,1],[]] [[5,5,4],[4,4]] => [[5,1,1],[1]] [[5,4,4],[4,3]] => [[5,2,1],[1,1]] [[6,5,4],[5,4]] => [[6,2,1],[2,1]] [[3,3,3,1],[2,2]] => [[3,3,1,1],[2]] [[4,4,4,1],[3,3,1]] => [[4,3,1,1],[3]] [[4,4,3,1],[3,3]] => [[4,4,1,1],[3,1]] [[5,5,4,1],[4,4,1]] => [[5,4,1,1],[4,1]] [[4,3,3,1],[3,2]] => [[4,4,2,1],[3,1,1]] [[5,4,4,1],[4,3,1]] => [[5,4,2,1],[4,1,1]] [[5,4,3,1],[4,3]] => [[5,5,2,1],[4,2,1]] [[6,5,4,1],[5,4,1]] => [[6,5,2,1],[5,2,1]] [[2,2,2,2],[1,1]] => [[2,2,1,1],[]] [[3,3,3,2],[2,2,1]] => [[3,2,1,1],[1]] [[4,4,4,2],[3,3,2]] => [[4,2,1,1],[2]] [[3,3,2,2],[2,2]] => [[3,3,1,1],[1,1]] [[4,4,3,2],[3,3,1]] => [[4,3,1,1],[2,1]] [[5,5,4,2],[4,4,2]] => [[5,3,1,1],[3,1]] [[3,2,2,2],[2,1]] => [[3,3,2,1],[1,1,1]] [[4,3,3,2],[3,2,1]] => [[4,3,2,1],[2,1,1]] [[5,4,4,2],[4,3,2]] => [[5,3,2,1],[3,1,1]] [[4,3,2,2],[3,2]] => [[4,4,2,1],[2,2,1]] [[5,4,3,2],[4,3,1]] => [[5,4,2,1],[3,2,1]] [[6,5,4,2],[5,4,2]] => [[6,4,2,1],[4,2,1]] [[2,2,2,1,1],[1,1]] => [[2,2,2,1,1],[1,1]] [[3,3,3,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1]] [[3,3,3,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2]] [[4,4,4,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2]] [[3,3,2,1,1],[2,2]] => [[3,3,3,1,1],[2,2,1]] [[4,4,3,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2,1]] [[4,4,3,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3,1]] [[5,5,4,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3,1]] [[3,2,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1,1]] [[4,3,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1,1]] [[4,3,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1,1]] [[5,4,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1,1]] [[4,3,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2,1]] [[5,4,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2,1]] [[5,4,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2,1]] [[6,5,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2,1]] [[3,3,3,3],[2,2,2]] => [[3,1,1,1],[]] [[4,4,4,3],[3,3,3]] => [[4,1,1,1],[1]] [[4,4,3,3],[3,3,2]] => [[4,2,1,1],[1,1]] [[5,5,4,3],[4,4,3]] => [[5,2,1,1],[2,1]] [[4,3,3,3],[3,2,2]] => [[4,2,2,1],[1,1,1]] [[5,4,4,3],[4,3,3]] => [[5,2,2,1],[2,1,1]] [[5,4,3,3],[4,3,2]] => [[5,3,2,1],[2,2,1]] [[6,5,4,3],[5,4,3]] => [[6,3,2,1],[3,2,1]] [[2,2,2,2,1],[1,1,1]] => [[2,2,1,1,1],[1]] [[3,3,3,3,1],[2,2,2,1]] => [[3,2,1,1,1],[2]] [[3,3,3,2,1],[2,2,2]] => [[3,3,1,1,1],[2,1]] [[4,4,4,3,1],[3,3,3,1]] => [[4,3,1,1,1],[3,1]] [[3,3,2,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1,1]] [[4,4,3,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1,1]] [[4,4,3,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2,1]] [[5,5,4,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2,1]] [[3,2,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1,1]] [[4,3,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1,1]] [[4,3,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1,1]] [[5,4,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1,1]] [[4,3,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2,1]] [[5,4,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2,1]] [[5,4,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2,1]] [[6,5,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2,1]] [[2,2,2,2,2],[1,1,1,1]] => [[2,1,1,1,1],[]] [[3,3,3,3,2],[2,2,2,2]] => [[3,1,1,1,1],[1]] [[3,3,3,2,2],[2,2,2,1]] => [[3,2,1,1,1],[1,1]] [[4,4,4,3,2],[3,3,3,2]] => [[4,2,1,1,1],[2,1]] [[3,3,2,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1,1]] [[4,4,3,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1,1]] [[4,4,3,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2,1]] [[5,5,4,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2,1]] [[3,2,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1,1]] [[4,3,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1,1]] [[4,3,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1,1]] [[5,4,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1,1]] [[4,3,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2,1]] [[5,4,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2,1]] [[5,4,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2,1]] [[6,5,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2,1]] [[1,1,1,1,1,1],[]] => [[1,1,1,1,1,1],[]] [[2,2,2,2,2,1],[1,1,1,1,1]] => [[2,1,1,1,1,1],[1]] [[2,2,2,2,1,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1,1]] [[3,3,3,3,2,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2,1]] [[2,2,2,1,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1,1]] [[3,3,3,2,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1,1]] [[3,3,3,2,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2,1]] [[4,4,4,3,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2,1]] [[2,2,1,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1,1]] [[3,3,2,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1,1]] [[3,3,2,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1,1]] [[4,4,3,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1,1]] [[3,3,2,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2,1]] [[4,4,3,2,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,2,1]] [[4,4,3,2,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,2,1]] [[5,5,4,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2,1]] [[2,1,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1,1]] [[3,2,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1,1]] [[3,2,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1,1]] [[4,3,3,3,2,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,2,1,1,1]] [[3,2,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1,1]] [[4,3,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1,1]] [[4,3,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1,1]] [[5,4,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1,1]] [[3,2,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2,1]] [[4,3,2,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,2,1]] [[4,3,2,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,2,1]] [[5,4,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2,1]] [[4,3,2,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,2,1]] [[5,4,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2,1]] [[5,4,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2,1]] [[6,5,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2,1]] [[7],[]] => [[7],[]] [[6,1],[]] => [[6,6],[5]] [[7,1],[1]] => [[7,6],[6]] [[5,2],[]] => [[5,5],[3]] [[6,2],[1]] => [[6,5],[4]] [[7,2],[2]] => [[7,5],[5]] [[5,1,1],[]] => [[5,5,5],[4,4]] [[6,2,1],[1,1]] => [[6,5,5],[5,4]] [[6,1,1],[1]] => [[6,6,5],[5,5]] [[7,2,1],[2,1]] => [[7,6,5],[6,5]] [[4,3],[]] => [[4,4],[1]] [[5,3],[1]] => [[5,4],[2]] [[6,3],[2]] => [[6,4],[3]] [[7,3],[3]] => [[7,4],[4]] [[4,2,1],[]] => [[4,4,4],[3,2]] [[5,3,1],[1,1]] => [[5,4,4],[4,2]] [[5,2,1],[1]] => [[5,5,4],[4,3]] [[6,3,1],[2,1]] => [[6,5,4],[5,3]] [[6,2,1],[2]] => [[6,6,4],[5,4]] [[7,3,1],[3,1]] => [[7,6,4],[6,4]] [[5,2,2],[1,1]] => [[5,4,4],[3,3]] [[6,3,2],[2,2]] => [[6,4,4],[4,3]] [[6,2,2],[2,1]] => [[6,5,4],[4,4]] [[7,3,2],[3,2]] => [[7,5,4],[5,4]] [[4,1,1,1],[]] => [[4,4,4,4],[3,3,3]] [[5,2,2,1],[1,1,1]] => [[5,4,4,4],[4,3,3]] [[5,2,1,1],[1,1]] => [[5,5,4,4],[4,4,3]] [[6,3,2,1],[2,2,1]] => [[6,5,4,4],[5,4,3]] [[5,1,1,1],[1]] => [[5,5,5,4],[4,4,4]] [[6,2,2,1],[2,1,1]] => [[6,5,5,4],[5,4,4]] [[6,2,1,1],[2,1]] => [[6,6,5,4],[5,5,4]] [[7,3,2,1],[3,2,1]] => [[7,6,5,4],[6,5,4]] [[4,4],[1]] => [[4,3],[]] [[5,4],[2]] => [[5,3],[1]] [[6,4],[3]] => [[6,3],[2]] [[7,4],[4]] => [[7,3],[3]] [[3,3,1],[]] => [[3,3,3],[2]] [[4,4,1],[1,1]] => [[4,3,3],[3]] [[4,3,1],[1]] => [[4,4,3],[3,1]] [[5,4,1],[2,1]] => [[5,4,3],[4,1]] [[5,3,1],[2]] => [[5,5,3],[4,2]] [[6,4,1],[3,1]] => [[6,5,3],[5,2]] [[6,3,1],[3]] => [[6,6,3],[5,3]] [[7,4,1],[4,1]] => [[7,6,3],[6,3]] [[3,2,2],[]] => [[3,3,3],[1,1]] [[4,3,2],[1,1]] => [[4,3,3],[2,1]] [[5,4,2],[2,2]] => [[5,3,3],[3,1]] [[4,2,2],[1]] => [[4,4,3],[2,2]] [[5,3,2],[2,1]] => [[5,4,3],[3,2]] [[6,4,2],[3,2]] => [[6,4,3],[4,2]] [[5,2,2],[2]] => [[5,5,3],[3,3]] [[6,3,2],[3,1]] => [[6,5,3],[4,3]] [[7,4,2],[4,2]] => [[7,5,3],[5,3]] [[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] [[4,3,2,1],[1,1,1]] => [[4,3,3,3],[3,2,1]] [[4,3,1,1],[1,1]] => [[4,4,3,3],[3,3,1]] [[5,4,2,1],[2,2,1]] => [[5,4,3,3],[4,3,1]] [[4,2,1,1],[1]] => [[4,4,4,3],[3,3,2]] [[5,3,2,1],[2,1,1]] => [[5,4,4,3],[4,3,2]] [[5,3,1,1],[2,1]] => [[5,5,4,3],[4,4,2]] [[6,4,2,1],[3,2,1]] => [[6,5,4,3],[5,4,2]] [[5,2,1,1],[2]] => [[5,5,5,3],[4,4,3]] [[6,3,2,1],[3,1,1]] => [[6,5,5,3],[5,4,3]] [[6,3,1,1],[3,1]] => [[6,6,5,3],[5,5,3]] [[7,4,2,1],[4,2,1]] => [[7,6,5,3],[6,5,3]] [[5,3,3],[2,2]] => [[5,3,3],[2,2]] [[6,4,3],[3,3]] => [[6,3,3],[3,2]] [[6,3,3],[3,2]] => [[6,4,3],[3,3]] [[7,4,3],[4,3]] => [[7,4,3],[4,3]] [[4,2,2,1],[1,1]] => [[4,4,3,3],[3,2,2]] [[5,3,3,1],[2,2,1]] => [[5,4,3,3],[4,2,2]] [[5,3,2,1],[2,2]] => [[5,5,3,3],[4,3,2]] [[6,4,3,1],[3,3,1]] => [[6,5,3,3],[5,3,2]] [[5,2,2,1],[2,1]] => [[5,5,4,3],[4,3,3]] [[6,3,3,1],[3,2,1]] => [[6,5,4,3],[5,3,3]] [[6,3,2,1],[3,2]] => [[6,6,4,3],[5,4,3]] [[7,4,3,1],[4,3,1]] => [[7,6,4,3],[6,4,3]] [[4,2,2,2],[1,1,1]] => [[4,3,3,3],[2,2,2]] [[5,3,3,2],[2,2,2]] => [[5,3,3,3],[3,2,2]] [[5,3,2,2],[2,2,1]] => [[5,4,3,3],[3,3,2]] [[6,4,3,2],[3,3,2]] => [[6,4,3,3],[4,3,2]] [[5,2,2,2],[2,1,1]] => [[5,4,4,3],[3,3,3]] [[6,3,3,2],[3,2,2]] => [[6,4,4,3],[4,3,3]] [[6,3,2,2],[3,2,1]] => [[6,5,4,3],[4,4,3]] [[7,4,3,2],[4,3,2]] => [[7,5,4,3],[5,4,3]] [[3,1,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,2]] [[4,2,2,2,1],[1,1,1,1]] => [[4,3,3,3,3],[3,2,2,2]] [[4,2,2,1,1],[1,1,1]] => [[4,4,3,3,3],[3,3,2,2]] [[5,3,3,2,1],[2,2,2,1]] => [[5,4,3,3,3],[4,3,2,2]] [[4,2,1,1,1],[1,1]] => [[4,4,4,3,3],[3,3,3,2]] [[5,3,2,2,1],[2,2,1,1]] => [[5,4,4,3,3],[4,3,3,2]] [[5,3,2,1,1],[2,2,1]] => [[5,5,4,3,3],[4,4,3,2]] [[6,4,3,2,1],[3,3,2,1]] => [[6,5,4,3,3],[5,4,3,2]] [[4,1,1,1,1],[1]] => [[4,4,4,4,3],[3,3,3,3]] [[5,2,2,2,1],[2,1,1,1]] => [[5,4,4,4,3],[4,3,3,3]] [[5,2,2,1,1],[2,1,1]] => [[5,5,4,4,3],[4,4,3,3]] [[6,3,3,2,1],[3,2,2,1]] => [[6,5,4,4,3],[5,4,3,3]] [[5,2,1,1,1],[2,1]] => [[5,5,5,4,3],[4,4,4,3]] [[6,3,2,2,1],[3,2,1,1]] => [[6,5,5,4,3],[5,4,4,3]] [[6,3,2,1,1],[3,2,1]] => [[6,6,5,4,3],[5,5,4,3]] [[7,4,3,2,1],[4,3,2,1]] => [[7,6,5,4,3],[6,5,4,3]] [[5,5],[3]] => [[5,2],[]] [[6,5],[4]] => [[6,2],[1]] [[7,5],[5]] => [[7,2],[2]] [[4,4,1],[2]] => [[4,4,2],[3]] [[5,5,1],[3,1]] => [[5,4,2],[4]] [[5,4,1],[3]] => [[5,5,2],[4,1]] [[6,5,1],[4,1]] => [[6,5,2],[5,1]] [[6,4,1],[4]] => [[6,6,2],[5,2]] [[7,5,1],[5,1]] => [[7,6,2],[6,2]] [[3,3,2],[1]] => [[3,3,2],[1]] [[4,4,2],[2,1]] => [[4,3,2],[2]] [[5,5,2],[3,2]] => [[5,3,2],[3]] [[4,3,2],[2]] => [[4,4,2],[2,1]] [[5,4,2],[3,1]] => [[5,4,2],[3,1]] [[6,5,2],[4,2]] => [[6,4,2],[4,1]] [[5,3,2],[3]] => [[5,5,2],[3,2]] [[6,4,2],[4,1]] => [[6,5,2],[4,2]] [[7,5,2],[5,2]] => [[7,5,2],[5,2]] [[3,3,1,1],[1]] => [[3,3,3,2],[2,2]] [[4,4,2,1],[2,1,1]] => [[4,3,3,2],[3,2]] [[4,4,1,1],[2,1]] => [[4,4,3,2],[3,3]] [[5,5,2,1],[3,2,1]] => [[5,4,3,2],[4,3]] [[4,3,1,1],[2]] => [[4,4,4,2],[3,3,1]] [[5,4,2,1],[3,1,1]] => [[5,4,4,2],[4,3,1]] [[5,4,1,1],[3,1]] => [[5,5,4,2],[4,4,1]] [[6,5,2,1],[4,2,1]] => [[6,5,4,2],[5,4,1]] [[5,3,1,1],[3]] => [[5,5,5,2],[4,4,2]] [[6,4,2,1],[4,1,1]] => [[6,5,5,2],[5,4,2]] [[6,4,1,1],[4,1]] => [[6,6,5,2],[5,5,2]] [[7,5,2,1],[5,2,1]] => [[7,6,5,2],[6,5,2]] [[3,3,3],[1,1]] => [[3,2,2],[]] [[4,4,3],[2,2]] => [[4,2,2],[1]] [[5,5,3],[3,3]] => [[5,2,2],[2]] [[4,3,3],[2,1]] => [[4,3,2],[1,1]] [[5,4,3],[3,2]] => [[5,3,2],[2,1]] [[6,5,3],[4,3]] => [[6,3,2],[3,1]] [[5,3,3],[3,1]] => [[5,4,2],[2,2]] [[6,4,3],[4,2]] => [[6,4,2],[3,2]] [[7,5,3],[5,3]] => [[7,4,2],[4,2]] [[2,2,2,1],[]] => [[2,2,2,2],[1]] [[3,3,3,1],[1,1,1]] => [[3,2,2,2],[2]] [[3,3,2,1],[1,1]] => [[3,3,2,2],[2,1]] [[4,4,3,1],[2,2,1]] => [[4,3,2,2],[3,1]] [[4,4,2,1],[2,2]] => [[4,4,2,2],[3,2]] [[5,5,3,1],[3,3,1]] => [[5,4,2,2],[4,2]] [[3,2,2,1],[1]] => [[3,3,3,2],[2,1,1]] [[4,3,3,1],[2,1,1]] => [[4,3,3,2],[3,1,1]] [[4,3,2,1],[2,1]] => [[4,4,3,2],[3,2,1]] [[5,4,3,1],[3,2,1]] => [[5,4,3,2],[4,2,1]] [[5,4,2,1],[3,2]] => [[5,5,3,2],[4,3,1]] [[6,5,3,1],[4,3,1]] => [[6,5,3,2],[5,3,1]] [[4,2,2,1],[2]] => [[4,4,4,2],[3,2,2]] [[5,3,3,1],[3,1,1]] => [[5,4,4,2],[4,2,2]] [[5,3,2,1],[3,1]] => [[5,5,4,2],[4,3,2]] [[6,4,3,1],[4,2,1]] => [[6,5,4,2],[5,3,2]] [[6,4,2,1],[4,2]] => [[6,6,4,2],[5,4,2]] [[7,5,3,1],[5,3,1]] => [[7,6,4,2],[6,4,2]] [[3,3,2,2],[1,1,1]] => [[3,2,2,2],[1,1]] [[4,4,3,2],[2,2,2]] => [[4,2,2,2],[2,1]] [[4,4,2,2],[2,2,1]] => [[4,3,2,2],[2,2]] [[5,5,3,2],[3,3,2]] => [[5,3,2,2],[3,2]] [[4,3,2,2],[2,1,1]] => [[4,3,3,2],[2,2,1]] [[5,4,3,2],[3,2,2]] => [[5,3,3,2],[3,2,1]] [[5,4,2,2],[3,2,1]] => [[5,4,3,2],[3,3,1]] [[6,5,3,2],[4,3,2]] => [[6,4,3,2],[4,3,1]] [[5,3,2,2],[3,1,1]] => [[5,4,4,2],[3,3,2]] [[6,4,3,2],[4,2,2]] => [[6,4,4,2],[4,3,2]] [[6,4,2,2],[4,2,1]] => [[6,5,4,2],[4,4,2]] [[7,5,3,2],[5,3,2]] => [[7,5,4,2],[5,4,2]] [[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]] [[3,3,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1]] [[3,3,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1]] [[4,4,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1]] [[3,3,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2]] [[4,4,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2]] [[4,4,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2]] [[5,5,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2]] [[3,2,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,1]] [[4,3,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,1]] [[4,3,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,1]] [[5,4,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,1]] [[4,3,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,1]] [[5,4,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,1]] [[5,4,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,1]] [[6,5,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,1]] [[4,2,1,1,1],[2]] => [[4,4,4,4,2],[3,3,3,2]] [[5,3,2,2,1],[3,1,1,1]] => [[5,4,4,4,2],[4,3,3,2]] [[5,3,2,1,1],[3,1,1]] => [[5,5,4,4,2],[4,4,3,2]] [[6,4,3,2,1],[4,2,2,1]] => [[6,5,4,4,2],[5,4,3,2]] [[5,3,1,1,1],[3,1]] => [[5,5,5,4,2],[4,4,4,2]] [[6,4,2,2,1],[4,2,1,1]] => [[6,5,5,4,2],[5,4,4,2]] [[6,4,2,1,1],[4,2,1]] => [[6,6,5,4,2],[5,5,4,2]] [[7,5,3,2,1],[5,3,2,1]] => [[7,6,5,4,2],[6,5,4,2]] [[5,4,4],[3,3]] => [[5,2,2],[1,1]] [[6,5,4],[4,4]] => [[6,2,2],[2,1]] [[6,4,4],[4,3]] => [[6,3,2],[2,2]] [[7,5,4],[5,4]] => [[7,3,2],[3,2]] [[4,3,3,1],[2,2]] => [[4,4,2,2],[3,1,1]] [[5,4,4,1],[3,3,1]] => [[5,4,2,2],[4,1,1]] [[5,4,3,1],[3,3]] => [[5,5,2,2],[4,2,1]] [[6,5,4,1],[4,4,1]] => [[6,5,2,2],[5,2,1]] [[5,3,3,1],[3,2]] => [[5,5,3,2],[4,2,2]] [[6,4,4,1],[4,3,1]] => [[6,5,3,2],[5,2,2]] [[6,4,3,1],[4,3]] => [[6,6,3,2],[5,3,2]] [[7,5,4,1],[5,4,1]] => [[7,6,3,2],[6,3,2]] [[3,2,2,2],[1,1]] => [[3,3,2,2],[1,1,1]] [[4,3,3,2],[2,2,1]] => [[4,3,2,2],[2,1,1]] [[5,4,4,2],[3,3,2]] => [[5,3,2,2],[3,1,1]] [[4,3,2,2],[2,2]] => [[4,4,2,2],[2,2,1]] [[5,4,3,2],[3,3,1]] => [[5,4,2,2],[3,2,1]] [[6,5,4,2],[4,4,2]] => [[6,4,2,2],[4,2,1]] [[4,2,2,2],[2,1]] => [[4,4,3,2],[2,2,2]] [[5,3,3,2],[3,2,1]] => [[5,4,3,2],[3,2,2]] [[6,4,4,2],[4,3,2]] => [[6,4,3,2],[4,2,2]] [[5,3,2,2],[3,2]] => [[5,5,3,2],[3,3,2]] [[6,4,3,2],[4,3,1]] => [[6,5,3,2],[4,3,2]] [[7,5,4,2],[5,4,2]] => [[7,5,3,2],[5,3,2]] [[3,2,2,1,1],[1,1]] => [[3,3,3,2,2],[2,2,1,1]] [[4,3,3,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,1,1]] [[4,3,3,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,1,1]] [[5,4,4,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,1,1]] [[4,3,2,1,1],[2,2]] => [[4,4,4,2,2],[3,3,2,1]] [[5,4,3,2,1],[3,3,1,1]] => [[5,4,4,2,2],[4,3,2,1]] [[5,4,3,1,1],[3,3,1]] => [[5,5,4,2,2],[4,4,2,1]] [[6,5,4,2,1],[4,4,2,1]] => [[6,5,4,2,2],[5,4,2,1]] [[4,2,2,1,1],[2,1]] => [[4,4,4,3,2],[3,3,2,2]] [[5,3,3,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,2,2]] [[5,3,3,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,2,2]] [[6,4,4,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,2,2]] [[5,3,2,1,1],[3,2]] => [[5,5,5,3,2],[4,4,3,2]] [[6,4,3,2,1],[4,3,1,1]] => [[6,5,5,3,2],[5,4,3,2]] [[6,4,3,1,1],[4,3,1]] => [[6,6,5,3,2],[5,5,3,2]] [[7,5,4,2,1],[5,4,2,1]] => [[7,6,5,3,2],[6,5,3,2]] [[4,3,3,3],[2,2,2]] => [[4,2,2,2],[1,1,1]] [[5,4,4,3],[3,3,3]] => [[5,2,2,2],[2,1,1]] [[5,4,3,3],[3,3,2]] => [[5,3,2,2],[2,2,1]] [[6,5,4,3],[4,4,3]] => [[6,3,2,2],[3,2,1]] [[5,3,3,3],[3,2,2]] => [[5,3,3,2],[2,2,2]] [[6,4,4,3],[4,3,3]] => [[6,3,3,2],[3,2,2]] [[6,4,3,3],[4,3,2]] => [[6,4,3,2],[3,3,2]] [[7,5,4,3],[5,4,3]] => [[7,4,3,2],[4,3,2]] [[3,2,2,2,1],[1,1,1]] => [[3,3,2,2,2],[2,1,1,1]] [[4,3,3,3,1],[2,2,2,1]] => [[4,3,2,2,2],[3,1,1,1]] [[4,3,3,2,1],[2,2,2]] => [[4,4,2,2,2],[3,2,1,1]] [[5,4,4,3,1],[3,3,3,1]] => [[5,4,2,2,2],[4,2,1,1]] [[4,3,2,2,1],[2,2,1]] => [[4,4,3,2,2],[3,2,2,1]] [[5,4,3,3,1],[3,3,2,1]] => [[5,4,3,2,2],[4,2,2,1]] [[5,4,3,2,1],[3,3,2]] => [[5,5,3,2,2],[4,3,2,1]] [[6,5,4,3,1],[4,4,3,1]] => [[6,5,3,2,2],[5,3,2,1]] [[4,2,2,2,1],[2,1,1]] => [[4,4,3,3,2],[3,2,2,2]] [[5,3,3,3,1],[3,2,2,1]] => [[5,4,3,3,2],[4,2,2,2]] [[5,3,3,2,1],[3,2,2]] => [[5,5,3,3,2],[4,3,2,2]] [[6,4,4,3,1],[4,3,3,1]] => [[6,5,3,3,2],[5,3,2,2]] [[5,3,2,2,1],[3,2,1]] => [[5,5,4,3,2],[4,3,3,2]] [[6,4,3,3,1],[4,3,2,1]] => [[6,5,4,3,2],[5,3,3,2]] [[6,4,3,2,1],[4,3,2]] => [[6,6,4,3,2],[5,4,3,2]] [[7,5,4,3,1],[5,4,3,1]] => [[7,6,4,3,2],[6,4,3,2]] [[3,2,2,2,2],[1,1,1,1]] => [[3,2,2,2,2],[1,1,1,1]] [[4,3,3,3,2],[2,2,2,2]] => [[4,2,2,2,2],[2,1,1,1]] [[4,3,3,2,2],[2,2,2,1]] => [[4,3,2,2,2],[2,2,1,1]] [[5,4,4,3,2],[3,3,3,2]] => [[5,3,2,2,2],[3,2,1,1]] [[4,3,2,2,2],[2,2,1,1]] => [[4,3,3,2,2],[2,2,2,1]] [[5,4,3,3,2],[3,3,2,2]] => [[5,3,3,2,2],[3,2,2,1]] [[5,4,3,2,2],[3,3,2,1]] => [[5,4,3,2,2],[3,3,2,1]] [[6,5,4,3,2],[4,4,3,2]] => [[6,4,3,2,2],[4,3,2,1]] [[4,2,2,2,2],[2,1,1,1]] => [[4,3,3,3,2],[2,2,2,2]] [[5,3,3,3,2],[3,2,2,2]] => [[5,3,3,3,2],[3,2,2,2]] [[5,3,3,2,2],[3,2,2,1]] => [[5,4,3,3,2],[3,3,2,2]] [[6,4,4,3,2],[4,3,3,2]] => [[6,4,3,3,2],[4,3,2,2]] [[5,3,2,2,2],[3,2,1,1]] => [[5,4,4,3,2],[3,3,3,2]] [[6,4,3,3,2],[4,3,2,2]] => [[6,4,4,3,2],[4,3,3,2]] [[6,4,3,2,2],[4,3,2,1]] => [[6,5,4,3,2],[4,4,3,2]] [[7,5,4,3,2],[5,4,3,2]] => [[7,5,4,3,2],[5,4,3,2]] [[2,1,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1,1]] [[3,2,2,2,2,1],[1,1,1,1,1]] => [[3,2,2,2,2,2],[2,1,1,1,1]] [[3,2,2,2,1,1],[1,1,1,1]] => [[3,3,2,2,2,2],[2,2,1,1,1]] [[4,3,3,3,2,1],[2,2,2,2,1]] => [[4,3,2,2,2,2],[3,2,1,1,1]] [[3,2,2,1,1,1],[1,1,1]] => [[3,3,3,2,2,2],[2,2,2,1,1]] [[4,3,3,2,2,1],[2,2,2,1,1]] => [[4,3,3,2,2,2],[3,2,2,1,1]] [[4,3,3,2,1,1],[2,2,2,1]] => [[4,4,3,2,2,2],[3,3,2,1,1]] [[5,4,4,3,2,1],[3,3,3,2,1]] => [[5,4,3,2,2,2],[4,3,2,1,1]] [[3,2,1,1,1,1],[1,1]] => [[3,3,3,3,2,2],[2,2,2,2,1]] [[4,3,2,2,2,1],[2,2,1,1,1]] => [[4,3,3,3,2,2],[3,2,2,2,1]] [[4,3,2,2,1,1],[2,2,1,1]] => [[4,4,3,3,2,2],[3,3,2,2,1]] [[5,4,3,3,2,1],[3,3,2,2,1]] => [[5,4,3,3,2,2],[4,3,2,2,1]] [[4,3,2,1,1,1],[2,2,1]] => [[4,4,4,3,2,2],[3,3,3,2,1]] [[5,4,3,2,2,1],[3,3,2,1,1]] => [[5,4,4,3,2,2],[4,3,3,2,1]] [[5,4,3,2,1,1],[3,3,2,1]] => [[5,5,4,3,2,2],[4,4,3,2,1]] [[6,5,4,3,2,1],[4,4,3,2,1]] => [[6,5,4,3,2,2],[5,4,3,2,1]] [[3,1,1,1,1,1],[1]] => [[3,3,3,3,3,2],[2,2,2,2,2]] [[4,2,2,2,2,1],[2,1,1,1,1]] => [[4,3,3,3,3,2],[3,2,2,2,2]] [[4,2,2,2,1,1],[2,1,1,1]] => [[4,4,3,3,3,2],[3,3,2,2,2]] [[5,3,3,3,2,1],[3,2,2,2,1]] => [[5,4,3,3,3,2],[4,3,2,2,2]] [[4,2,2,1,1,1],[2,1,1]] => [[4,4,4,3,3,2],[3,3,3,2,2]] [[5,3,3,2,2,1],[3,2,2,1,1]] => [[5,4,4,3,3,2],[4,3,3,2,2]] [[5,3,3,2,1,1],[3,2,2,1]] => [[5,5,4,3,3,2],[4,4,3,2,2]] [[6,4,4,3,2,1],[4,3,3,2,1]] => [[6,5,4,3,3,2],[5,4,3,2,2]] [[4,2,1,1,1,1],[2,1]] => [[4,4,4,4,3,2],[3,3,3,3,2]] [[5,3,2,2,2,1],[3,2,1,1,1]] => [[5,4,4,4,3,2],[4,3,3,3,2]] [[5,3,2,2,1,1],[3,2,1,1]] => [[5,5,4,4,3,2],[4,4,3,3,2]] [[6,4,3,3,2,1],[4,3,2,2,1]] => [[6,5,4,4,3,2],[5,4,3,3,2]] [[5,3,2,1,1,1],[3,2,1]] => [[5,5,5,4,3,2],[4,4,4,3,2]] [[6,4,3,2,2,1],[4,3,2,1,1]] => [[6,5,5,4,3,2],[5,4,4,3,2]] [[6,4,3,2,1,1],[4,3,2,1]] => [[6,6,5,4,3,2],[5,5,4,3,2]] [[7,5,4,3,2,1],[5,4,3,2,1]] => [[7,6,5,4,3,2],[6,5,4,3,2]] [[6,6],[5]] => [[6,1],[]] [[7,6],[6]] => [[7,1],[1]] [[5,5,1],[4]] => [[5,5,1],[4]] [[6,6,1],[5,1]] => [[6,5,1],[5]] [[6,5,1],[5]] => [[6,6,1],[5,1]] [[7,6,1],[6,1]] => [[7,6,1],[6,1]] [[4,4,2],[3]] => [[4,4,1],[2]] [[5,5,2],[4,1]] => [[5,4,1],[3]] [[6,6,2],[5,2]] => [[6,4,1],[4]] [[5,4,2],[4]] => [[5,5,1],[3,1]] [[6,5,2],[5,1]] => [[6,5,1],[4,1]] [[7,6,2],[6,2]] => [[7,5,1],[5,1]] [[4,4,1,1],[3]] => [[4,4,4,1],[3,3]] [[5,5,2,1],[4,1,1]] => [[5,4,4,1],[4,3]] [[5,5,1,1],[4,1]] => [[5,5,4,1],[4,4]] [[6,6,2,1],[5,2,1]] => [[6,5,4,1],[5,4]] [[5,4,1,1],[4]] => [[5,5,5,1],[4,4,1]] [[6,5,2,1],[5,1,1]] => [[6,5,5,1],[5,4,1]] [[6,5,1,1],[5,1]] => [[6,6,5,1],[5,5,1]] [[7,6,2,1],[6,2,1]] => [[7,6,5,1],[6,5,1]] [[3,3,3],[2]] => [[3,3,1],[]] [[4,4,3],[3,1]] => [[4,3,1],[1]] [[5,5,3],[4,2]] => [[5,3,1],[2]] [[6,6,3],[5,3]] => [[6,3,1],[3]] [[4,3,3],[3]] => [[4,4,1],[1,1]] [[5,4,3],[4,1]] => [[5,4,1],[2,1]] [[6,5,3],[5,2]] => [[6,4,1],[3,1]] [[7,6,3],[6,3]] => [[7,4,1],[4,1]] [[3,3,2,1],[2]] => [[3,3,3,1],[2,1]] [[4,4,3,1],[3,1,1]] => [[4,3,3,1],[3,1]] [[4,4,2,1],[3,1]] => [[4,4,3,1],[3,2]] [[5,5,3,1],[4,2,1]] => [[5,4,3,1],[4,2]] [[5,5,2,1],[4,2]] => [[5,5,3,1],[4,3]] [[6,6,3,1],[5,3,1]] => [[6,5,3,1],[5,3]] [[4,3,2,1],[3]] => [[4,4,4,1],[3,2,1]] [[5,4,3,1],[4,1,1]] => [[5,4,4,1],[4,2,1]] [[5,4,2,1],[4,1]] => [[5,5,4,1],[4,3,1]] [[6,5,3,1],[5,2,1]] => [[6,5,4,1],[5,3,1]] [[6,5,2,1],[5,2]] => [[6,6,4,1],[5,4,1]] [[7,6,3,1],[6,3,1]] => [[7,6,4,1],[6,4,1]] [[4,4,2,2],[3,1,1]] => [[4,3,3,1],[2,2]] [[5,5,3,2],[4,2,2]] => [[5,3,3,1],[3,2]] [[5,5,2,2],[4,2,1]] => [[5,4,3,1],[3,3]] [[6,6,3,2],[5,3,2]] => [[6,4,3,1],[4,3]] [[5,4,2,2],[4,1,1]] => [[5,4,4,1],[3,3,1]] [[6,5,3,2],[5,2,2]] => [[6,4,4,1],[4,3,1]] [[6,5,2,2],[5,2,1]] => [[6,5,4,1],[4,4,1]] [[7,6,3,2],[6,3,2]] => [[7,5,4,1],[5,4,1]] [[3,3,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2]] [[4,4,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2]] [[4,4,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2]] [[5,5,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2]] [[4,4,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3]] [[5,5,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3]] [[5,5,2,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,3]] [[6,6,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3]] [[4,3,1,1,1],[3]] => [[4,4,4,4,1],[3,3,3,1]] [[5,4,2,2,1],[4,1,1,1]] => [[5,4,4,4,1],[4,3,3,1]] [[5,4,2,1,1],[4,1,1]] => [[5,5,4,4,1],[4,4,3,1]] [[6,5,3,2,1],[5,2,2,1]] => [[6,5,4,4,1],[5,4,3,1]] [[5,4,1,1,1],[4,1]] => [[5,5,5,4,1],[4,4,4,1]] [[6,5,2,2,1],[5,2,1,1]] => [[6,5,5,4,1],[5,4,4,1]] [[6,5,2,1,1],[5,2,1]] => [[6,6,5,4,1],[5,5,4,1]] [[7,6,3,2,1],[6,3,2,1]] => [[7,6,5,4,1],[6,5,4,1]] [[4,4,4],[3,2]] => [[4,2,1],[]] [[5,5,4],[4,3]] => [[5,2,1],[1]] [[6,6,4],[5,4]] => [[6,2,1],[2]] [[5,4,4],[4,2]] => [[5,3,1],[1,1]] [[6,5,4],[5,3]] => [[6,3,1],[2,1]] [[7,6,4],[6,4]] => [[7,3,1],[3,1]] [[3,3,3,1],[2,1]] => [[3,3,2,1],[2]] [[4,4,4,1],[3,2,1]] => [[4,3,2,1],[3]] [[4,4,3,1],[3,2]] => [[4,4,2,1],[3,1]] [[5,5,4,1],[4,3,1]] => [[5,4,2,1],[4,1]] [[5,5,3,1],[4,3]] => [[5,5,2,1],[4,2]] [[6,6,4,1],[5,4,1]] => [[6,5,2,1],[5,2]] [[4,3,3,1],[3,1]] => [[4,4,3,1],[3,1,1]] [[5,4,4,1],[4,2,1]] => [[5,4,3,1],[4,1,1]] [[5,4,3,1],[4,2]] => [[5,5,3,1],[4,2,1]] [[6,5,4,1],[5,3,1]] => [[6,5,3,1],[5,2,1]] [[6,5,3,1],[5,3]] => [[6,6,3,1],[5,3,1]] [[7,6,4,1],[6,4,1]] => [[7,6,3,1],[6,3,1]] [[2,2,2,2],[1]] => [[2,2,2,1],[]] [[3,3,3,2],[2,1,1]] => [[3,2,2,1],[1]] [[4,4,4,2],[3,2,2]] => [[4,2,2,1],[2]] [[3,3,2,2],[2,1]] => [[3,3,2,1],[1,1]] [[4,4,3,2],[3,2,1]] => [[4,3,2,1],[2,1]] [[5,5,4,2],[4,3,2]] => [[5,3,2,1],[3,1]] [[4,4,2,2],[3,2]] => [[4,4,2,1],[2,2]] [[5,5,3,2],[4,3,1]] => [[5,4,2,1],[3,2]] [[6,6,4,2],[5,4,2]] => [[6,4,2,1],[4,2]] [[3,2,2,2],[2]] => [[3,3,3,1],[1,1,1]] [[4,3,3,2],[3,1,1]] => [[4,3,3,1],[2,1,1]] [[5,4,4,2],[4,2,2]] => [[5,3,3,1],[3,1,1]] [[4,3,2,2],[3,1]] => [[4,4,3,1],[2,2,1]] [[5,4,3,2],[4,2,1]] => [[5,4,3,1],[3,2,1]] [[6,5,4,2],[5,3,2]] => [[6,4,3,1],[4,2,1]] [[5,4,2,2],[4,2]] => [[5,5,3,1],[3,3,1]] [[6,5,3,2],[5,3,1]] => [[6,5,3,1],[4,3,1]] [[7,6,4,2],[6,4,2]] => [[7,5,3,1],[5,3,1]] [[2,2,2,1,1],[1]] => [[2,2,2,2,1],[1,1]] [[3,3,3,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1]] [[3,3,3,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2]] [[4,4,4,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2]] [[3,3,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1]] [[4,4,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1]] [[4,4,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1]] [[5,5,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1]] [[4,4,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2]] [[5,5,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2]] [[5,5,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2]] [[6,6,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2]] [[3,2,2,1,1],[2]] => [[3,3,3,3,1],[2,2,1,1]] [[4,3,3,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,1,1]] [[4,3,3,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,1,1]] [[5,4,4,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,1,1]] [[4,3,2,1,1],[3,1]] => [[4,4,4,3,1],[3,3,2,1]] [[5,4,3,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,2,1]] [[5,4,3,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,2,1]] [[6,5,4,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,2,1]] [[5,4,2,1,1],[4,2]] => [[5,5,5,3,1],[4,4,3,1]] [[6,5,3,2,1],[5,3,1,1]] => [[6,5,5,3,1],[5,4,3,1]] [[6,5,3,1,1],[5,3,1]] => [[6,6,5,3,1],[5,5,3,1]] [[7,6,4,2,1],[6,4,2,1]] => [[7,6,5,3,1],[6,5,3,1]] [[4,4,3,3],[3,2,2]] => [[4,2,2,1],[1,1]] [[5,5,4,3],[4,3,3]] => [[5,2,2,1],[2,1]] [[5,5,3,3],[4,3,2]] => [[5,3,2,1],[2,2]] [[6,6,4,3],[5,4,3]] => [[6,3,2,1],[3,2]] [[5,4,3,3],[4,2,2]] => [[5,3,3,1],[2,2,1]] [[6,5,4,3],[5,3,3]] => [[6,3,3,1],[3,2,1]] [[6,5,3,3],[5,3,2]] => [[6,4,3,1],[3,3,1]] [[7,6,4,3],[6,4,3]] => [[7,4,3,1],[4,3,1]] [[3,3,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1]] [[4,4,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1]] [[4,4,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1]] [[5,5,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1]] [[4,4,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2]] [[5,5,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2]] [[5,5,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2]] [[6,6,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2]] [[4,3,2,2,1],[3,1,1]] => [[4,4,3,3,1],[3,2,2,1]] [[5,4,3,3,1],[4,2,2,1]] => [[5,4,3,3,1],[4,2,2,1]] [[5,4,3,2,1],[4,2,2]] => [[5,5,3,3,1],[4,3,2,1]] [[6,5,4,3,1],[5,3,3,1]] => [[6,5,3,3,1],[5,3,2,1]] [[5,4,2,2,1],[4,2,1]] => [[5,5,4,3,1],[4,3,3,1]] [[6,5,3,3,1],[5,3,2,1]] => [[6,5,4,3,1],[5,3,3,1]] [[6,5,3,2,1],[5,3,2]] => [[6,6,4,3,1],[5,4,3,1]] [[7,6,4,3,1],[6,4,3,1]] => [[7,6,4,3,1],[6,4,3,1]] [[3,3,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1]] [[4,4,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1]] [[4,4,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1]] [[5,5,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1]] [[4,4,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2]] [[5,5,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2]] [[5,5,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2]] [[6,6,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2]] [[4,3,2,2,2],[3,1,1,1]] => [[4,3,3,3,1],[2,2,2,1]] [[5,4,3,3,2],[4,2,2,2]] => [[5,3,3,3,1],[3,2,2,1]] [[5,4,3,2,2],[4,2,2,1]] => [[5,4,3,3,1],[3,3,2,1]] [[6,5,4,3,2],[5,3,3,2]] => [[6,4,3,3,1],[4,3,2,1]] [[5,4,2,2,2],[4,2,1,1]] => [[5,4,4,3,1],[3,3,3,1]] [[6,5,3,3,2],[5,3,2,2]] => [[6,4,4,3,1],[4,3,3,1]] [[6,5,3,2,2],[5,3,2,1]] => [[6,5,4,3,1],[4,4,3,1]] [[7,6,4,3,2],[6,4,3,2]] => [[7,5,4,3,1],[5,4,3,1]] [[2,2,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1]] [[3,3,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1]] [[3,3,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1]] [[4,4,3,3,2,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,2,1,1]] [[3,3,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1]] [[4,4,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1]] [[4,4,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1]] [[5,5,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1]] [[3,3,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2]] [[4,4,2,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,2]] [[4,4,2,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,2]] [[5,5,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2]] [[4,4,2,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,2]] [[5,5,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2]] [[5,5,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2]] [[6,6,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2]] [[3,2,1,1,1,1],[2]] => [[3,3,3,3,3,1],[2,2,2,2,1]] [[4,3,2,2,2,1],[3,1,1,1,1]] => [[4,3,3,3,3,1],[3,2,2,2,1]] [[4,3,2,2,1,1],[3,1,1,1]] => [[4,4,3,3,3,1],[3,3,2,2,1]] [[5,4,3,3,2,1],[4,2,2,2,1]] => [[5,4,3,3,3,1],[4,3,2,2,1]] [[4,3,2,1,1,1],[3,1,1]] => [[4,4,4,3,3,1],[3,3,3,2,1]] [[5,4,3,2,2,1],[4,2,2,1,1]] => [[5,4,4,3,3,1],[4,3,3,2,1]] [[5,4,3,2,1,1],[4,2,2,1]] => [[5,5,4,3,3,1],[4,4,3,2,1]] [[6,5,4,3,2,1],[5,3,3,2,1]] => [[6,5,4,3,3,1],[5,4,3,2,1]] [[4,3,1,1,1,1],[3,1]] => [[4,4,4,4,3,1],[3,3,3,3,1]] [[5,4,2,2,2,1],[4,2,1,1,1]] => [[5,4,4,4,3,1],[4,3,3,3,1]] [[5,4,2,2,1,1],[4,2,1,1]] => [[5,5,4,4,3,1],[4,4,3,3,1]] [[6,5,3,3,2,1],[5,3,2,2,1]] => [[6,5,4,4,3,1],[5,4,3,3,1]] [[5,4,2,1,1,1],[4,2,1]] => [[5,5,5,4,3,1],[4,4,4,3,1]] [[6,5,3,2,2,1],[5,3,2,1,1]] => [[6,5,5,4,3,1],[5,4,4,3,1]] [[6,5,3,2,1,1],[5,3,2,1]] => [[6,6,5,4,3,1],[5,5,4,3,1]] [[7,6,4,3,2,1],[6,4,3,2,1]] => [[7,6,5,4,3,1],[6,5,4,3,1]] [[5,5,5],[4,4]] => [[5,1,1],[]] [[6,6,5],[5,5]] => [[6,1,1],[1]] [[6,5,5],[5,4]] => [[6,2,1],[1,1]] [[7,6,5],[6,5]] => [[7,2,1],[2,1]] [[4,4,4,1],[3,3]] => [[4,4,1,1],[3]] [[5,5,5,1],[4,4,1]] => [[5,4,1,1],[4]] [[5,5,4,1],[4,4]] => [[5,5,1,1],[4,1]] [[6,6,5,1],[5,5,1]] => [[6,5,1,1],[5,1]] [[5,4,4,1],[4,3]] => [[5,5,2,1],[4,1,1]] [[6,5,5,1],[5,4,1]] => [[6,5,2,1],[5,1,1]] [[6,5,4,1],[5,4]] => [[6,6,2,1],[5,2,1]] [[7,6,5,1],[6,5,1]] => [[7,6,2,1],[6,2,1]] [[3,3,3,2],[2,2]] => [[3,3,1,1],[1]] [[4,4,4,2],[3,3,1]] => [[4,3,1,1],[2]] [[5,5,5,2],[4,4,2]] => [[5,3,1,1],[3]] [[4,4,3,2],[3,3]] => [[4,4,1,1],[2,1]] [[5,5,4,2],[4,4,1]] => [[5,4,1,1],[3,1]] [[6,6,5,2],[5,5,2]] => [[6,4,1,1],[4,1]] [[4,3,3,2],[3,2]] => [[4,4,2,1],[2,1,1]] [[5,4,4,2],[4,3,1]] => [[5,4,2,1],[3,1,1]] [[6,5,5,2],[5,4,2]] => [[6,4,2,1],[4,1,1]] [[5,4,3,2],[4,3]] => [[5,5,2,1],[3,2,1]] [[6,5,4,2],[5,4,1]] => [[6,5,2,1],[4,2,1]] [[7,6,5,2],[6,5,2]] => [[7,5,2,1],[5,2,1]] [[3,3,3,1,1],[2,2]] => [[3,3,3,1,1],[2,2]] [[4,4,4,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2]] [[4,4,4,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3]] [[5,5,5,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3]] [[4,4,3,1,1],[3,3]] => [[4,4,4,1,1],[3,3,1]] [[5,5,4,2,1],[4,4,1,1]] => [[5,4,4,1,1],[4,3,1]] [[5,5,4,1,1],[4,4,1]] => [[5,5,4,1,1],[4,4,1]] [[6,6,5,2,1],[5,5,2,1]] => [[6,5,4,1,1],[5,4,1]] [[4,3,3,1,1],[3,2]] => [[4,4,4,2,1],[3,3,1,1]] [[5,4,4,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,1,1]] [[5,4,4,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,1,1]] [[6,5,5,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,1,1]] [[5,4,3,1,1],[4,3]] => [[5,5,5,2,1],[4,4,2,1]] [[6,5,4,2,1],[5,4,1,1]] => [[6,5,5,2,1],[5,4,2,1]] [[6,5,4,1,1],[5,4,1]] => [[6,6,5,2,1],[5,5,2,1]] [[7,6,5,2,1],[6,5,2,1]] => [[7,6,5,2,1],[6,5,2,1]] [[3,3,3,3],[2,2,1]] => [[3,2,1,1],[]] [[4,4,4,3],[3,3,2]] => [[4,2,1,1],[1]] [[5,5,5,3],[4,4,3]] => [[5,2,1,1],[2]] [[4,4,3,3],[3,3,1]] => [[4,3,1,1],[1,1]] [[5,5,4,3],[4,4,2]] => [[5,3,1,1],[2,1]] [[6,6,5,3],[5,5,3]] => [[6,3,1,1],[3,1]] [[4,3,3,3],[3,2,1]] => [[4,3,2,1],[1,1,1]] [[5,4,4,3],[4,3,2]] => [[5,3,2,1],[2,1,1]] [[6,5,5,3],[5,4,3]] => [[6,3,2,1],[3,1,1]] [[5,4,3,3],[4,3,1]] => [[5,4,2,1],[2,2,1]] [[6,5,4,3],[5,4,2]] => [[6,4,2,1],[3,2,1]] [[7,6,5,3],[6,5,3]] => [[7,4,2,1],[4,2,1]] [[2,2,2,2,1],[1,1]] => [[2,2,2,1,1],[1]] [[3,3,3,3,1],[2,2,1,1]] => [[3,2,2,1,1],[2]] [[3,3,3,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1]] [[4,4,4,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1]] [[4,4,4,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2]] [[5,5,5,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2]] [[3,3,2,2,1],[2,2]] => [[3,3,3,1,1],[2,1,1]] [[4,4,3,3,1],[3,3,1,1]] => [[4,3,3,1,1],[3,1,1]] [[4,4,3,2,1],[3,3,1]] => [[4,4,3,1,1],[3,2,1]] [[5,5,4,3,1],[4,4,2,1]] => [[5,4,3,1,1],[4,2,1]] [[5,5,4,2,1],[4,4,2]] => [[5,5,3,1,1],[4,3,1]] [[6,6,5,3,1],[5,5,3,1]] => [[6,5,3,1,1],[5,3,1]] [[3,2,2,2,1],[2,1]] => [[3,3,3,2,1],[2,1,1,1]] [[4,3,3,3,1],[3,2,1,1]] => [[4,3,3,2,1],[3,1,1,1]] [[4,3,3,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,1,1]] [[5,4,4,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,1,1]] [[5,4,4,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,1,1]] [[6,5,5,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,1,1]] [[4,3,2,2,1],[3,2]] => [[4,4,4,2,1],[3,2,2,1]] [[5,4,3,3,1],[4,3,1,1]] => [[5,4,4,2,1],[4,2,2,1]] [[5,4,3,2,1],[4,3,1]] => [[5,5,4,2,1],[4,3,2,1]] [[6,5,4,3,1],[5,4,2,1]] => [[6,5,4,2,1],[5,3,2,1]] [[6,5,4,2,1],[5,4,2]] => [[6,6,4,2,1],[5,4,2,1]] [[7,6,5,3,1],[6,5,3,1]] => [[7,6,4,2,1],[6,4,2,1]] [[3,3,3,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1]] [[4,4,4,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1]] [[4,4,4,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2]] [[5,5,5,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2]] [[4,4,3,2,2],[3,3,1,1]] => [[4,3,3,1,1],[2,2,1]] [[5,5,4,3,2],[4,4,2,2]] => [[5,3,3,1,1],[3,2,1]] [[5,5,4,2,2],[4,4,2,1]] => [[5,4,3,1,1],[3,3,1]] [[6,6,5,3,2],[5,5,3,2]] => [[6,4,3,1,1],[4,3,1]] [[4,3,3,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,1,1]] [[5,4,4,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,1,1]] [[5,4,4,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,1,1]] [[6,5,5,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,1,1]] [[5,4,3,2,2],[4,3,1,1]] => [[5,4,4,2,1],[3,3,2,1]] [[6,5,4,3,2],[5,4,2,2]] => [[6,4,4,2,1],[4,3,2,1]] [[6,5,4,2,2],[5,4,2,1]] => [[6,5,4,2,1],[4,4,2,1]] [[7,6,5,3,2],[6,5,3,2]] => [[7,5,4,2,1],[5,4,2,1]] [[2,2,2,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1]] [[3,3,3,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1]] [[3,3,3,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1]] [[4,4,4,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1]] [[3,3,3,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2]] [[4,4,4,2,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,2]] [[4,4,4,2,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,2]] [[5,5,5,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2]] [[3,3,2,1,1,1],[2,2]] => [[3,3,3,3,1,1],[2,2,2,1]] [[4,4,3,2,2,1],[3,3,1,1,1]] => [[4,3,3,3,1,1],[3,2,2,1]] [[4,4,3,2,1,1],[3,3,1,1]] => [[4,4,3,3,1,1],[3,3,2,1]] [[5,5,4,3,2,1],[4,4,2,2,1]] => [[5,4,3,3,1,1],[4,3,2,1]] [[4,4,3,1,1,1],[3,3,1]] => [[4,4,4,3,1,1],[3,3,3,1]] [[5,5,4,2,2,1],[4,4,2,1,1]] => [[5,4,4,3,1,1],[4,3,3,1]] [[5,5,4,2,1,1],[4,4,2,1]] => [[5,5,4,3,1,1],[4,4,3,1]] [[6,6,5,3,2,1],[5,5,3,2,1]] => [[6,5,4,3,1,1],[5,4,3,1]] [[3,2,2,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,1,1]] [[4,3,3,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,1,1]] [[4,3,3,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,1,1]] [[5,4,4,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,1,1]] [[4,3,3,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,1,1]] [[5,4,4,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,1,1]] [[5,4,4,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,1,1]] [[6,5,5,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,1,1]] [[4,3,2,1,1,1],[3,2]] => [[4,4,4,4,2,1],[3,3,3,2,1]] [[5,4,3,2,2,1],[4,3,1,1,1]] => [[5,4,4,4,2,1],[4,3,3,2,1]] [[5,4,3,2,1,1],[4,3,1,1]] => [[5,5,4,4,2,1],[4,4,3,2,1]] [[6,5,4,3,2,1],[5,4,2,2,1]] => [[6,5,4,4,2,1],[5,4,3,2,1]] [[5,4,3,1,1,1],[4,3,1]] => [[5,5,5,4,2,1],[4,4,4,2,1]] [[6,5,4,2,2,1],[5,4,2,1,1]] => [[6,5,5,4,2,1],[5,4,4,2,1]] [[6,5,4,2,1,1],[5,4,2,1]] => [[6,6,5,4,2,1],[5,5,4,2,1]] [[7,6,5,3,2,1],[6,5,3,2,1]] => [[7,6,5,4,2,1],[6,5,4,2,1]] [[4,4,4,4],[3,3,3]] => [[4,1,1,1],[]] [[5,5,5,4],[4,4,4]] => [[5,1,1,1],[1]] [[5,5,4,4],[4,4,3]] => [[5,2,1,1],[1,1]] [[6,6,5,4],[5,5,4]] => [[6,2,1,1],[2,1]] [[5,4,4,4],[4,3,3]] => [[5,2,2,1],[1,1,1]] [[6,5,5,4],[5,4,4]] => [[6,2,2,1],[2,1,1]] [[6,5,4,4],[5,4,3]] => [[6,3,2,1],[2,2,1]] [[7,6,5,4],[6,5,4]] => [[7,3,2,1],[3,2,1]] [[3,3,3,3,1],[2,2,2]] => [[3,3,1,1,1],[2]] [[4,4,4,4,1],[3,3,3,1]] => [[4,3,1,1,1],[3]] [[4,4,4,3,1],[3,3,3]] => [[4,4,1,1,1],[3,1]] [[5,5,5,4,1],[4,4,4,1]] => [[5,4,1,1,1],[4,1]] [[4,4,3,3,1],[3,3,2]] => [[4,4,2,1,1],[3,1,1]] [[5,5,4,4,1],[4,4,3,1]] => [[5,4,2,1,1],[4,1,1]] [[5,5,4,3,1],[4,4,3]] => [[5,5,2,1,1],[4,2,1]] [[6,6,5,4,1],[5,5,4,1]] => [[6,5,2,1,1],[5,2,1]] [[4,3,3,3,1],[3,2,2]] => [[4,4,2,2,1],[3,1,1,1]] [[5,4,4,4,1],[4,3,3,1]] => [[5,4,2,2,1],[4,1,1,1]] [[5,4,4,3,1],[4,3,3]] => [[5,5,2,2,1],[4,2,1,1]] [[6,5,5,4,1],[5,4,4,1]] => [[6,5,2,2,1],[5,2,1,1]] [[5,4,3,3,1],[4,3,2]] => [[5,5,3,2,1],[4,2,2,1]] [[6,5,4,4,1],[5,4,3,1]] => [[6,5,3,2,1],[5,2,2,1]] [[6,5,4,3,1],[5,4,3]] => [[6,6,3,2,1],[5,3,2,1]] [[7,6,5,4,1],[6,5,4,1]] => [[7,6,3,2,1],[6,3,2,1]] [[2,2,2,2,2],[1,1,1]] => [[2,2,1,1,1],[]] [[3,3,3,3,2],[2,2,2,1]] => [[3,2,1,1,1],[1]] [[4,4,4,4,2],[3,3,3,2]] => [[4,2,1,1,1],[2]] [[3,3,3,2,2],[2,2,2]] => [[3,3,1,1,1],[1,1]] [[4,4,4,3,2],[3,3,3,1]] => [[4,3,1,1,1],[2,1]] [[5,5,5,4,2],[4,4,4,2]] => [[5,3,1,1,1],[3,1]] [[3,3,2,2,2],[2,2,1]] => [[3,3,2,1,1],[1,1,1]] [[4,4,3,3,2],[3,3,2,1]] => [[4,3,2,1,1],[2,1,1]] [[5,5,4,4,2],[4,4,3,2]] => [[5,3,2,1,1],[3,1,1]] [[4,4,3,2,2],[3,3,2]] => [[4,4,2,1,1],[2,2,1]] [[5,5,4,3,2],[4,4,3,1]] => [[5,4,2,1,1],[3,2,1]] [[6,6,5,4,2],[5,5,4,2]] => [[6,4,2,1,1],[4,2,1]] [[3,2,2,2,2],[2,1,1]] => [[3,3,2,2,1],[1,1,1,1]] [[4,3,3,3,2],[3,2,2,1]] => [[4,3,2,2,1],[2,1,1,1]] [[5,4,4,4,2],[4,3,3,2]] => [[5,3,2,2,1],[3,1,1,1]] [[4,3,3,2,2],[3,2,2]] => [[4,4,2,2,1],[2,2,1,1]] [[5,4,4,3,2],[4,3,3,1]] => [[5,4,2,2,1],[3,2,1,1]] [[6,5,5,4,2],[5,4,4,2]] => [[6,4,2,2,1],[4,2,1,1]] [[4,3,2,2,2],[3,2,1]] => [[4,4,3,2,1],[2,2,2,1]] [[5,4,3,3,2],[4,3,2,1]] => [[5,4,3,2,1],[3,2,2,1]] [[6,5,4,4,2],[5,4,3,2]] => [[6,4,3,2,1],[4,2,2,1]] [[5,4,3,2,2],[4,3,2]] => [[5,5,3,2,1],[3,3,2,1]] [[6,5,4,3,2],[5,4,3,1]] => [[6,5,3,2,1],[4,3,2,1]] [[7,6,5,4,2],[6,5,4,2]] => [[7,5,3,2,1],[5,3,2,1]] [[2,2,2,2,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1]] [[3,3,3,3,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1]] [[3,3,3,3,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2]] [[4,4,4,4,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2]] [[3,3,3,2,1,1],[2,2,2]] => [[3,3,3,1,1,1],[2,2,1]] [[4,4,4,3,2,1],[3,3,3,1,1]] => [[4,3,3,1,1,1],[3,2,1]] [[4,4,4,3,1,1],[3,3,3,1]] => [[4,4,3,1,1,1],[3,3,1]] [[5,5,5,4,2,1],[4,4,4,2,1]] => [[5,4,3,1,1,1],[4,3,1]] [[3,3,2,2,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,1,1]] [[4,4,3,3,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,1,1]] [[4,4,3,3,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,1,1]] [[5,5,4,4,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,1,1]] [[4,4,3,2,1,1],[3,3,2]] => [[4,4,4,2,1,1],[3,3,2,1]] [[5,5,4,3,2,1],[4,4,3,1,1]] => [[5,4,4,2,1,1],[4,3,2,1]] [[5,5,4,3,1,1],[4,4,3,1]] => [[5,5,4,2,1,1],[4,4,2,1]] [[6,6,5,4,2,1],[5,5,4,2,1]] => [[6,5,4,2,1,1],[5,4,2,1]] [[3,2,2,2,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,1,1,1]] [[4,3,3,3,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,1,1,1]] [[4,3,3,3,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,1,1,1]] [[5,4,4,4,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,1,1,1]] [[4,3,3,2,1,1],[3,2,2]] => [[4,4,4,2,2,1],[3,3,2,1,1]] [[5,4,4,3,2,1],[4,3,3,1,1]] => [[5,4,4,2,2,1],[4,3,2,1,1]] [[5,4,4,3,1,1],[4,3,3,1]] => [[5,5,4,2,2,1],[4,4,2,1,1]] [[6,5,5,4,2,1],[5,4,4,2,1]] => [[6,5,4,2,2,1],[5,4,2,1,1]] [[4,3,2,2,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,2,2,1]] [[5,4,3,3,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,2,2,1]] [[5,4,3,3,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,2,2,1]] [[6,5,4,4,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,2,2,1]] [[5,4,3,2,1,1],[4,3,2]] => [[5,5,5,3,2,1],[4,4,3,2,1]] [[6,5,4,3,2,1],[5,4,3,1,1]] => [[6,5,5,3,2,1],[5,4,3,2,1]] [[6,5,4,3,1,1],[5,4,3,1]] => [[6,6,5,3,2,1],[5,5,3,2,1]] [[7,6,5,4,2,1],[6,5,4,2,1]] => [[7,6,5,3,2,1],[6,5,3,2,1]] [[3,3,3,3,3],[2,2,2,2]] => [[3,1,1,1,1],[]] [[4,4,4,4,3],[3,3,3,3]] => [[4,1,1,1,1],[1]] [[4,4,4,3,3],[3,3,3,2]] => [[4,2,1,1,1],[1,1]] [[5,5,5,4,3],[4,4,4,3]] => [[5,2,1,1,1],[2,1]] [[4,4,3,3,3],[3,3,2,2]] => [[4,2,2,1,1],[1,1,1]] [[5,5,4,4,3],[4,4,3,3]] => [[5,2,2,1,1],[2,1,1]] [[5,5,4,3,3],[4,4,3,2]] => [[5,3,2,1,1],[2,2,1]] [[6,6,5,4,3],[5,5,4,3]] => [[6,3,2,1,1],[3,2,1]] [[4,3,3,3,3],[3,2,2,2]] => [[4,2,2,2,1],[1,1,1,1]] [[5,4,4,4,3],[4,3,3,3]] => [[5,2,2,2,1],[2,1,1,1]] [[5,4,4,3,3],[4,3,3,2]] => [[5,3,2,2,1],[2,2,1,1]] [[6,5,5,4,3],[5,4,4,3]] => [[6,3,2,2,1],[3,2,1,1]] [[5,4,3,3,3],[4,3,2,2]] => [[5,3,3,2,1],[2,2,2,1]] [[6,5,4,4,3],[5,4,3,3]] => [[6,3,3,2,1],[3,2,2,1]] [[6,5,4,3,3],[5,4,3,2]] => [[6,4,3,2,1],[3,3,2,1]] [[7,6,5,4,3],[6,5,4,3]] => [[7,4,3,2,1],[4,3,2,1]] [[2,2,2,2,2,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1]] [[3,3,3,3,3,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2]] [[3,3,3,3,2,1],[2,2,2,2]] => [[3,3,1,1,1,1],[2,1]] [[4,4,4,4,3,1],[3,3,3,3,1]] => [[4,3,1,1,1,1],[3,1]] [[3,3,3,2,2,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,1,1]] [[4,4,4,3,3,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,1,1]] [[4,4,4,3,2,1],[3,3,3,2]] => [[4,4,2,1,1,1],[3,2,1]] [[5,5,5,4,3,1],[4,4,4,3,1]] => [[5,4,2,1,1,1],[4,2,1]] [[3,3,2,2,2,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,1,1,1]] [[4,4,3,3,3,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,1,1,1]] [[4,4,3,3,2,1],[3,3,2,2]] => [[4,4,2,2,1,1],[3,2,1,1]] [[5,5,4,4,3,1],[4,4,3,3,1]] => [[5,4,2,2,1,1],[4,2,1,1]] [[4,4,3,2,2,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,2,2,1]] [[5,5,4,3,3,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,2,2,1]] [[5,5,4,3,2,1],[4,4,3,2]] => [[5,5,3,2,1,1],[4,3,2,1]] [[6,6,5,4,3,1],[5,5,4,3,1]] => [[6,5,3,2,1,1],[5,3,2,1]] [[3,2,2,2,2,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,1,1,1,1]] [[4,3,3,3,3,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,1,1,1,1]] [[4,3,3,3,2,1],[3,2,2,2]] => [[4,4,2,2,2,1],[3,2,1,1,1]] [[5,4,4,4,3,1],[4,3,3,3,1]] => [[5,4,2,2,2,1],[4,2,1,1,1]] [[4,3,3,2,2,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,2,2,1,1]] [[5,4,4,3,3,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,2,2,1,1]] [[5,4,4,3,2,1],[4,3,3,2]] => [[5,5,3,2,2,1],[4,3,2,1,1]] [[6,5,5,4,3,1],[5,4,4,3,1]] => [[6,5,3,2,2,1],[5,3,2,1,1]] [[4,3,2,2,2,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,2,2,2,1]] [[5,4,3,3,3,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,2,2,2,1]] [[5,4,3,3,2,1],[4,3,2,2]] => [[5,5,3,3,2,1],[4,3,2,2,1]] [[6,5,4,4,3,1],[5,4,3,3,1]] => [[6,5,3,3,2,1],[5,3,2,2,1]] [[5,4,3,2,2,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,3,3,2,1]] [[6,5,4,3,3,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,3,3,2,1]] [[6,5,4,3,2,1],[5,4,3,2]] => [[6,6,4,3,2,1],[5,4,3,2,1]] [[7,6,5,4,3,1],[6,5,4,3,1]] => [[7,6,4,3,2,1],[6,4,3,2,1]] [[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]] => [[3,1,1,1,1,1],[1]] [[3,3,3,3,2,2],[2,2,2,2,1]] => [[3,2,1,1,1,1],[1,1]] [[4,4,4,4,3,2],[3,3,3,3,2]] => [[4,2,1,1,1,1],[2,1]] [[3,3,3,2,2,2],[2,2,2,1,1]] => [[3,2,2,1,1,1],[1,1,1]] [[4,4,4,3,3,2],[3,3,3,2,2]] => [[4,2,2,1,1,1],[2,1,1]] [[4,4,4,3,2,2],[3,3,3,2,1]] => [[4,3,2,1,1,1],[2,2,1]] [[5,5,5,4,3,2],[4,4,4,3,2]] => [[5,3,2,1,1,1],[3,2,1]] [[3,3,2,2,2,2],[2,2,1,1,1]] => [[3,2,2,2,1,1],[1,1,1,1]] [[4,4,3,3,3,2],[3,3,2,2,2]] => [[4,2,2,2,1,1],[2,1,1,1]] [[4,4,3,3,2,2],[3,3,2,2,1]] => [[4,3,2,2,1,1],[2,2,1,1]] [[5,5,4,4,3,2],[4,4,3,3,2]] => [[5,3,2,2,1,1],[3,2,1,1]] [[4,4,3,2,2,2],[3,3,2,1,1]] => [[4,3,3,2,1,1],[2,2,2,1]] [[5,5,4,3,3,2],[4,4,3,2,2]] => [[5,3,3,2,1,1],[3,2,2,1]] [[5,5,4,3,2,2],[4,4,3,2,1]] => [[5,4,3,2,1,1],[3,3,2,1]] [[6,6,5,4,3,2],[5,5,4,3,2]] => [[6,4,3,2,1,1],[4,3,2,1]] [[3,2,2,2,2,2],[2,1,1,1,1]] => [[3,2,2,2,2,1],[1,1,1,1,1]] [[4,3,3,3,3,2],[3,2,2,2,2]] => [[4,2,2,2,2,1],[2,1,1,1,1]] [[4,3,3,3,2,2],[3,2,2,2,1]] => [[4,3,2,2,2,1],[2,2,1,1,1]] [[5,4,4,4,3,2],[4,3,3,3,2]] => [[5,3,2,2,2,1],[3,2,1,1,1]] [[4,3,3,2,2,2],[3,2,2,1,1]] => [[4,3,3,2,2,1],[2,2,2,1,1]] [[5,4,4,3,3,2],[4,3,3,2,2]] => [[5,3,3,2,2,1],[3,2,2,1,1]] [[5,4,4,3,2,2],[4,3,3,2,1]] => [[5,4,3,2,2,1],[3,3,2,1,1]] [[6,5,5,4,3,2],[5,4,4,3,2]] => [[6,4,3,2,2,1],[4,3,2,1,1]] [[4,3,2,2,2,2],[3,2,1,1,1]] => [[4,3,3,3,2,1],[2,2,2,2,1]] [[5,4,3,3,3,2],[4,3,2,2,2]] => [[5,3,3,3,2,1],[3,2,2,2,1]] [[5,4,3,3,2,2],[4,3,2,2,1]] => [[5,4,3,3,2,1],[3,3,2,2,1]] [[6,5,4,4,3,2],[5,4,3,3,2]] => [[6,4,3,3,2,1],[4,3,2,2,1]] [[5,4,3,2,2,2],[4,3,2,1,1]] => [[5,4,4,3,2,1],[3,3,3,2,1]] [[6,5,4,3,3,2],[5,4,3,2,2]] => [[6,4,4,3,2,1],[4,3,3,2,1]] [[6,5,4,3,2,2],[5,4,3,2,1]] => [[6,5,4,3,2,1],[4,4,3,2,1]] [[7,6,5,4,3,2],[6,5,4,3,2]] => [[7,5,4,3,2,1],[5,4,3,2,1]] [[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]] => [[2,1,1,1,1,1,1],[1]] [[2,2,2,2,2,1,1],[1,1,1,1,1]] => [[2,2,1,1,1,1,1],[1,1]] [[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [[3,2,1,1,1,1,1],[2,1]] [[2,2,2,2,1,1,1],[1,1,1,1]] => [[2,2,2,1,1,1,1],[1,1,1]] [[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [[3,2,2,1,1,1,1],[2,1,1]] [[3,3,3,3,2,1,1],[2,2,2,2,1]] => [[3,3,2,1,1,1,1],[2,2,1]] [[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [[4,3,2,1,1,1,1],[3,2,1]] [[2,2,2,1,1,1,1],[1,1,1]] => [[2,2,2,2,1,1,1],[1,1,1,1]] [[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [[3,2,2,2,1,1,1],[2,1,1,1]] [[3,3,3,2,2,1,1],[2,2,2,1,1]] => [[3,3,2,2,1,1,1],[2,2,1,1]] [[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [[4,3,2,2,1,1,1],[3,2,1,1]] [[3,3,3,2,1,1,1],[2,2,2,1]] => [[3,3,3,2,1,1,1],[2,2,2,1]] [[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [[4,3,3,2,1,1,1],[3,2,2,1]] ----------------------------------------------------------------------------- Created: Sep 26, 2020 at 18:34 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Sep 26, 2020 at 18:34 by Martin Rubey