************************************************************************ * 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: Mp00180 ------------------------------------------------------------------------ Map name: to ribbon ------------------------------------------------------------------------ Domain: Integer compositions ------------------------------------------------------------------------ Codomain: Skew partitions ------------------------------------------------------------------------ Description: The ribbon shape corresponding to an integer composition. For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells. ------------------------------------------------------------------------ References: ------------------------------------------------------------------------ Code: def mapping(a): return a.to_skew_partition() ------------------------------------------------------------------------ Map images: [1] => [[1],[]] [1,1] => [[1,1],[]] [2] => [[2],[]] [1,1,1] => [[1,1,1],[]] [1,2] => [[2,1],[]] [2,1] => [[2,2],[1]] [3] => [[3],[]] [1,1,1,1] => [[1,1,1,1],[]] [1,1,2] => [[2,1,1],[]] [1,2,1] => [[2,2,1],[1]] [1,3] => [[3,1],[]] [2,1,1] => [[2,2,2],[1,1]] [2,2] => [[3,2],[1]] [3,1] => [[3,3],[2]] [4] => [[4],[]] [1,1,1,1,1] => [[1,1,1,1,1],[]] [1,1,1,2] => [[2,1,1,1],[]] [1,1,2,1] => [[2,2,1,1],[1]] [1,1,3] => [[3,1,1],[]] [1,2,1,1] => [[2,2,2,1],[1,1]] [1,2,2] => [[3,2,1],[1]] [1,3,1] => [[3,3,1],[2]] [1,4] => [[4,1],[]] [2,1,1,1] => [[2,2,2,2],[1,1,1]] [2,1,2] => [[3,2,2],[1,1]] [2,2,1] => [[3,3,2],[2,1]] [2,3] => [[4,2],[1]] [3,1,1] => [[3,3,3],[2,2]] [3,2] => [[4,3],[2]] [4,1] => [[4,4],[3]] [5] => [[5],[]] [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] [1,1,1,1,2] => [[2,1,1,1,1],[]] [1,1,1,2,1] => [[2,2,1,1,1],[1]] [1,1,1,3] => [[3,1,1,1],[]] [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] [1,1,2,2] => [[3,2,1,1],[1]] [1,1,3,1] => [[3,3,1,1],[2]] [1,1,4] => [[4,1,1],[]] [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] [1,2,1,2] => [[3,2,2,1],[1,1]] [1,2,2,1] => [[3,3,2,1],[2,1]] [1,2,3] => [[4,2,1],[1]] [1,3,1,1] => [[3,3,3,1],[2,2]] [1,3,2] => [[4,3,1],[2]] [1,4,1] => [[4,4,1],[3]] [1,5] => [[5,1],[]] [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] [2,1,1,2] => [[3,2,2,2],[1,1,1]] [2,1,2,1] => [[3,3,2,2],[2,1,1]] [2,1,3] => [[4,2,2],[1,1]] [2,2,1,1] => [[3,3,3,2],[2,2,1]] [2,2,2] => [[4,3,2],[2,1]] [2,3,1] => [[4,4,2],[3,1]] [2,4] => [[5,2],[1]] [3,1,1,1] => [[3,3,3,3],[2,2,2]] [3,1,2] => [[4,3,3],[2,2]] [3,2,1] => [[4,4,3],[3,2]] [3,3] => [[5,3],[2]] [4,1,1] => [[4,4,4],[3,3]] [4,2] => [[5,4],[3]] [5,1] => [[5,5],[4]] [6] => [[6],[]] [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] [1,1,1,1,1,2] => [[2,1,1,1,1,1],[]] [1,1,1,1,2,1] => [[2,2,1,1,1,1],[1]] [1,1,1,1,3] => [[3,1,1,1,1],[]] [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] [1,1,1,2,2] => [[3,2,1,1,1],[1]] [1,1,1,3,1] => [[3,3,1,1,1],[2]] [1,1,1,4] => [[4,1,1,1],[]] [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] [1,1,2,3] => [[4,2,1,1],[1]] [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] [1,1,3,2] => [[4,3,1,1],[2]] [1,1,4,1] => [[4,4,1,1],[3]] [1,1,5] => [[5,1,1],[]] [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] [1,2,1,3] => [[4,2,2,1],[1,1]] [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] [1,2,2,2] => [[4,3,2,1],[2,1]] [1,2,3,1] => [[4,4,2,1],[3,1]] [1,2,4] => [[5,2,1],[1]] [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] [1,3,1,2] => [[4,3,3,1],[2,2]] [1,3,2,1] => [[4,4,3,1],[3,2]] [1,3,3] => [[5,3,1],[2]] [1,4,1,1] => [[4,4,4,1],[3,3]] [1,4,2] => [[5,4,1],[3]] [1,5,1] => [[5,5,1],[4]] [1,6] => [[6,1],[]] [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] [2,1,1,3] => [[4,2,2,2],[1,1,1]] [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] [2,1,2,2] => [[4,3,2,2],[2,1,1]] [2,1,3,1] => [[4,4,2,2],[3,1,1]] [2,1,4] => [[5,2,2],[1,1]] [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] [2,2,1,2] => [[4,3,3,2],[2,2,1]] [2,2,2,1] => [[4,4,3,2],[3,2,1]] [2,2,3] => [[5,3,2],[2,1]] [2,3,1,1] => [[4,4,4,2],[3,3,1]] [2,3,2] => [[5,4,2],[3,1]] [2,4,1] => [[5,5,2],[4,1]] [2,5] => [[6,2],[1]] [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] [3,1,1,2] => [[4,3,3,3],[2,2,2]] [3,1,2,1] => [[4,4,3,3],[3,2,2]] [3,1,3] => [[5,3,3],[2,2]] [3,2,1,1] => [[4,4,4,3],[3,3,2]] [3,2,2] => [[5,4,3],[3,2]] [3,3,1] => [[5,5,3],[4,2]] [3,4] => [[6,3],[2]] [4,1,1,1] => [[4,4,4,4],[3,3,3]] [4,1,2] => [[5,4,4],[3,3]] [4,2,1] => [[5,5,4],[4,3]] [4,3] => [[6,4],[3]] [5,1,1] => [[5,5,5],[4,4]] [5,2] => [[6,5],[4]] [6,1] => [[6,6],[5]] [7] => [[7],[]] [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] [1,1,1,1,1,1,2] => [[2,1,1,1,1,1,1],[]] [1,1,1,1,1,2,1] => [[2,2,1,1,1,1,1],[1]] [1,1,1,1,1,3] => [[3,1,1,1,1,1],[]] [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] [1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]] [1,1,1,1,3,1] => [[3,3,1,1,1,1],[2]] [1,1,1,1,4] => [[4,1,1,1,1],[]] [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] [1,1,1,2,3] => [[4,2,1,1,1],[1]] [1,1,1,3,1,1] => [[3,3,3,1,1,1],[2,2]] [1,1,1,3,2] => [[4,3,1,1,1],[2]] [1,1,1,4,1] => [[4,4,1,1,1],[3]] [1,1,1,5] => [[5,1,1,1],[]] [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] [1,1,2,1,3] => [[4,2,2,1,1],[1,1]] [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] [1,1,2,2,2] => [[4,3,2,1,1],[2,1]] [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] [1,1,2,4] => [[5,2,1,1],[1]] [1,1,3,1,1,1] => [[3,3,3,3,1,1],[2,2,2]] [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] [1,1,3,3] => [[5,3,1,1],[2]] [1,1,4,1,1] => [[4,4,4,1,1],[3,3]] [1,1,4,2] => [[5,4,1,1],[3]] [1,1,5,1] => [[5,5,1,1],[4]] [1,1,6] => [[6,1,1],[]] [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] [1,2,1,1,3] => [[4,2,2,2,1],[1,1,1]] [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] [1,2,1,4] => [[5,2,2,1],[1,1]] [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] [1,2,2,3] => [[5,3,2,1],[2,1]] [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] [1,2,3,2] => [[5,4,2,1],[3,1]] [1,2,4,1] => [[5,5,2,1],[4,1]] [1,2,5] => [[6,2,1],[1]] [1,3,1,1,1,1] => [[3,3,3,3,3,1],[2,2,2,2]] [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] [1,3,1,3] => [[5,3,3,1],[2,2]] [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] [1,3,2,2] => [[5,4,3,1],[3,2]] [1,3,3,1] => [[5,5,3,1],[4,2]] [1,3,4] => [[6,3,1],[2]] [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] [1,4,1,2] => [[5,4,4,1],[3,3]] [1,4,2,1] => [[5,5,4,1],[4,3]] [1,4,3] => [[6,4,1],[3]] [1,5,1,1] => [[5,5,5,1],[4,4]] [1,5,2] => [[6,5,1],[4]] [1,6,1] => [[6,6,1],[5]] [1,7] => [[7,1],[]] [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] [2,1,1,1,3] => [[4,2,2,2,2],[1,1,1,1]] [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] [2,1,1,4] => [[5,2,2,2],[1,1,1]] [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] [2,1,2,3] => [[5,3,2,2],[2,1,1]] [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] [2,1,3,2] => [[5,4,2,2],[3,1,1]] [2,1,4,1] => [[5,5,2,2],[4,1,1]] [2,1,5] => [[6,2,2],[1,1]] [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] [2,2,1,3] => [[5,3,3,2],[2,2,1]] [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] [2,2,2,2] => [[5,4,3,2],[3,2,1]] [2,2,3,1] => [[5,5,3,2],[4,2,1]] [2,2,4] => [[6,3,2],[2,1]] [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] [2,3,1,2] => [[5,4,4,2],[3,3,1]] [2,3,2,1] => [[5,5,4,2],[4,3,1]] [2,3,3] => [[6,4,2],[3,1]] [2,4,1,1] => [[5,5,5,2],[4,4,1]] [2,4,2] => [[6,5,2],[4,1]] [2,5,1] => [[6,6,2],[5,1]] [2,6] => [[7,2],[1]] [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] [3,1,1,1,2] => [[4,3,3,3,3],[2,2,2,2]] [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] [3,1,1,3] => [[5,3,3,3],[2,2,2]] [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] [3,1,2,2] => [[5,4,3,3],[3,2,2]] [3,1,3,1] => [[5,5,3,3],[4,2,2]] [3,1,4] => [[6,3,3],[2,2]] [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] [3,2,1,2] => [[5,4,4,3],[3,3,2]] [3,2,2,1] => [[5,5,4,3],[4,3,2]] [3,2,3] => [[6,4,3],[3,2]] [3,3,1,1] => [[5,5,5,3],[4,4,2]] [3,3,2] => [[6,5,3],[4,2]] [3,4,1] => [[6,6,3],[5,2]] [3,5] => [[7,3],[2]] [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] [4,1,1,2] => [[5,4,4,4],[3,3,3]] [4,1,2,1] => [[5,5,4,4],[4,3,3]] [4,1,3] => [[6,4,4],[3,3]] [4,2,1,1] => [[5,5,5,4],[4,4,3]] [4,2,2] => [[6,5,4],[4,3]] [4,3,1] => [[6,6,4],[5,3]] [4,4] => [[7,4],[3]] [5,1,1,1] => [[5,5,5,5],[4,4,4]] [5,1,2] => [[6,5,5],[4,4]] [5,2,1] => [[6,6,5],[5,4]] [5,3] => [[7,5],[4]] [6,1,1] => [[6,6,6],[5,5]] [6,2] => [[7,6],[5]] [7,1] => [[7,7],[6]] [8] => [[8],[]] [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] [1,1,1,1,1,1,1,2] => [[2,1,1,1,1,1,1,1],[]] [1,1,1,1,1,1,2,1] => [[2,2,1,1,1,1,1,1],[1]] [1,1,1,1,1,1,3] => [[3,1,1,1,1,1,1],[]] [1,1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1,1],[1,1]] [1,1,1,1,1,2,2] => [[3,2,1,1,1,1,1],[1]] [1,1,1,1,1,3,1] => [[3,3,1,1,1,1,1],[2]] [1,1,1,1,1,4] => [[4,1,1,1,1,1],[]] [1,1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1,1],[1,1,1]] [1,1,1,1,2,1,2] => [[3,2,2,1,1,1,1],[1,1]] [1,1,1,1,2,2,1] => [[3,3,2,1,1,1,1],[2,1]] [1,1,1,1,2,3] => [[4,2,1,1,1,1],[1]] [1,1,1,1,3,1,1] => [[3,3,3,1,1,1,1],[2,2]] [1,1,1,1,3,2] => [[4,3,1,1,1,1],[2]] [1,1,1,1,4,1] => [[4,4,1,1,1,1],[3]] [1,1,1,1,5] => [[5,1,1,1,1],[]] [1,1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1,1],[1,1,1,1]] [1,1,1,2,1,1,2] => [[3,2,2,2,1,1,1],[1,1,1]] [1,1,1,2,1,2,1] => [[3,3,2,2,1,1,1],[2,1,1]] [1,1,1,2,1,3] => [[4,2,2,1,1,1],[1,1]] [1,1,1,2,2,1,1] => [[3,3,3,2,1,1,1],[2,2,1]] [1,1,1,2,2,2] => [[4,3,2,1,1,1],[2,1]] [1,1,1,2,3,1] => [[4,4,2,1,1,1],[3,1]] [1,1,1,2,4] => [[5,2,1,1,1],[1]] [1,1,1,3,1,1,1] => [[3,3,3,3,1,1,1],[2,2,2]] [1,1,1,3,1,2] => [[4,3,3,1,1,1],[2,2]] [1,1,1,3,2,1] => [[4,4,3,1,1,1],[3,2]] [1,1,1,3,3] => [[5,3,1,1,1],[2]] [1,1,1,4,1,1] => [[4,4,4,1,1,1],[3,3]] [1,1,1,4,2] => [[5,4,1,1,1],[3]] [1,1,1,5,1] => [[5,5,1,1,1],[4]] [1,1,1,6] => [[6,1,1,1],[]] [1,1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1,1],[1,1,1,1,1]] [1,1,2,1,1,1,2] => [[3,2,2,2,2,1,1],[1,1,1,1]] [1,1,2,1,1,2,1] => [[3,3,2,2,2,1,1],[2,1,1,1]] [1,1,2,1,1,3] => [[4,2,2,2,1,1],[1,1,1]] [1,1,2,1,2,1,1] => [[3,3,3,2,2,1,1],[2,2,1,1]] [1,1,2,1,2,2] => [[4,3,2,2,1,1],[2,1,1]] [1,1,2,1,3,1] => [[4,4,2,2,1,1],[3,1,1]] [1,1,2,1,4] => [[5,2,2,1,1],[1,1]] [1,1,2,2,1,1,1] => [[3,3,3,3,2,1,1],[2,2,2,1]] [1,1,2,2,1,2] => [[4,3,3,2,1,1],[2,2,1]] [1,1,2,2,2,1] => [[4,4,3,2,1,1],[3,2,1]] [1,1,2,2,3] => [[5,3,2,1,1],[2,1]] [1,1,2,3,1,1] => [[4,4,4,2,1,1],[3,3,1]] [1,1,2,3,2] => [[5,4,2,1,1],[3,1]] [1,1,2,4,1] => [[5,5,2,1,1],[4,1]] [1,1,2,5] => [[6,2,1,1],[1]] [1,1,3,1,1,1,1] => [[3,3,3,3,3,1,1],[2,2,2,2]] [1,1,3,1,1,2] => [[4,3,3,3,1,1],[2,2,2]] [1,1,3,1,2,1] => [[4,4,3,3,1,1],[3,2,2]] [1,1,3,1,3] => [[5,3,3,1,1],[2,2]] [1,1,3,2,1,1] => [[4,4,4,3,1,1],[3,3,2]] [1,1,3,2,2] => [[5,4,3,1,1],[3,2]] [1,1,3,3,1] => [[5,5,3,1,1],[4,2]] [1,1,3,4] => [[6,3,1,1],[2]] [1,1,4,1,1,1] => [[4,4,4,4,1,1],[3,3,3]] [1,1,4,1,2] => [[5,4,4,1,1],[3,3]] [1,1,4,2,1] => [[5,5,4,1,1],[4,3]] [1,1,4,3] => [[6,4,1,1],[3]] [1,1,5,1,1] => [[5,5,5,1,1],[4,4]] [1,1,5,2] => [[6,5,1,1],[4]] [1,1,6,1] => [[6,6,1,1],[5]] [1,1,7] => [[7,1,1],[]] [1,2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,1],[1,1,1,1,1,1]] [1,2,1,1,1,1,2] => [[3,2,2,2,2,2,1],[1,1,1,1,1]] [1,2,1,1,1,2,1] => [[3,3,2,2,2,2,1],[2,1,1,1,1]] [1,2,1,1,1,3] => [[4,2,2,2,2,1],[1,1,1,1]] [1,2,1,1,2,1,1] => [[3,3,3,2,2,2,1],[2,2,1,1,1]] [1,2,1,1,2,2] => [[4,3,2,2,2,1],[2,1,1,1]] [1,2,1,1,3,1] => [[4,4,2,2,2,1],[3,1,1,1]] [1,2,1,1,4] => [[5,2,2,2,1],[1,1,1]] [1,2,1,2,1,1,1] => [[3,3,3,3,2,2,1],[2,2,2,1,1]] [1,2,1,2,1,2] => [[4,3,3,2,2,1],[2,2,1,1]] [1,2,1,2,2,1] => [[4,4,3,2,2,1],[3,2,1,1]] [1,2,1,2,3] => [[5,3,2,2,1],[2,1,1]] [1,2,1,3,1,1] => [[4,4,4,2,2,1],[3,3,1,1]] [1,2,1,3,2] => [[5,4,2,2,1],[3,1,1]] [1,2,1,4,1] => [[5,5,2,2,1],[4,1,1]] [1,2,1,5] => [[6,2,2,1],[1,1]] [1,2,2,1,1,1,1] => [[3,3,3,3,3,2,1],[2,2,2,2,1]] [1,2,2,1,1,2] => [[4,3,3,3,2,1],[2,2,2,1]] [1,2,2,1,2,1] => [[4,4,3,3,2,1],[3,2,2,1]] [1,2,2,1,3] => [[5,3,3,2,1],[2,2,1]] [1,2,2,2,1,1] => [[4,4,4,3,2,1],[3,3,2,1]] [1,2,2,2,2] => [[5,4,3,2,1],[3,2,1]] [1,2,2,3,1] => [[5,5,3,2,1],[4,2,1]] [1,2,2,4] => [[6,3,2,1],[2,1]] [1,2,3,1,1,1] => [[4,4,4,4,2,1],[3,3,3,1]] [1,2,3,1,2] => [[5,4,4,2,1],[3,3,1]] [1,2,3,2,1] => [[5,5,4,2,1],[4,3,1]] [1,2,3,3] => [[6,4,2,1],[3,1]] [1,2,4,1,1] => [[5,5,5,2,1],[4,4,1]] [1,2,4,2] => [[6,5,2,1],[4,1]] [1,2,5,1] => [[6,6,2,1],[5,1]] [1,2,6] => [[7,2,1],[1]] [1,3,1,1,1,1,1] => [[3,3,3,3,3,3,1],[2,2,2,2,2]] [1,3,1,1,1,2] => [[4,3,3,3,3,1],[2,2,2,2]] [1,3,1,1,2,1] => [[4,4,3,3,3,1],[3,2,2,2]] [1,3,1,1,3] => [[5,3,3,3,1],[2,2,2]] [1,3,1,2,1,1] => [[4,4,4,3,3,1],[3,3,2,2]] [1,3,1,2,2] => [[5,4,3,3,1],[3,2,2]] [1,3,1,3,1] => [[5,5,3,3,1],[4,2,2]] [1,3,1,4] => [[6,3,3,1],[2,2]] [1,3,2,1,1,1] => [[4,4,4,4,3,1],[3,3,3,2]] [1,3,2,1,2] => [[5,4,4,3,1],[3,3,2]] [1,3,2,2,1] => [[5,5,4,3,1],[4,3,2]] [1,3,2,3] => [[6,4,3,1],[3,2]] [1,3,3,1,1] => [[5,5,5,3,1],[4,4,2]] [1,3,3,2] => [[6,5,3,1],[4,2]] [1,3,4,1] => [[6,6,3,1],[5,2]] [1,3,5] => [[7,3,1],[2]] [1,4,1,1,1,1] => [[4,4,4,4,4,1],[3,3,3,3]] [1,4,1,1,2] => [[5,4,4,4,1],[3,3,3]] [1,4,1,2,1] => [[5,5,4,4,1],[4,3,3]] [1,4,1,3] => [[6,4,4,1],[3,3]] [1,4,2,1,1] => [[5,5,5,4,1],[4,4,3]] [1,4,2,2] => [[6,5,4,1],[4,3]] [1,4,3,1] => [[6,6,4,1],[5,3]] [1,4,4] => [[7,4,1],[3]] [1,5,1,1,1] => [[5,5,5,5,1],[4,4,4]] [1,5,1,2] => [[6,5,5,1],[4,4]] [1,5,2,1] => [[6,6,5,1],[5,4]] [1,5,3] => [[7,5,1],[4]] [1,6,1,1] => [[6,6,6,1],[5,5]] [1,6,2] => [[7,6,1],[5]] [1,7,1] => [[7,7,1],[6]] [1,8] => [[8,1],[]] [2,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] [2,1,1,1,1,1,2] => [[3,2,2,2,2,2,2],[1,1,1,1,1,1]] [2,1,1,1,1,2,1] => [[3,3,2,2,2,2,2],[2,1,1,1,1,1]] [2,1,1,1,1,3] => [[4,2,2,2,2,2],[1,1,1,1,1]] [2,1,1,1,2,1,1] => [[3,3,3,2,2,2,2],[2,2,1,1,1,1]] [2,1,1,1,2,2] => [[4,3,2,2,2,2],[2,1,1,1,1]] [2,1,1,1,3,1] => [[4,4,2,2,2,2],[3,1,1,1,1]] [2,1,1,1,4] => [[5,2,2,2,2],[1,1,1,1]] [2,1,1,2,1,1,1] => [[3,3,3,3,2,2,2],[2,2,2,1,1,1]] [2,1,1,2,1,2] => [[4,3,3,2,2,2],[2,2,1,1,1]] [2,1,1,2,2,1] => [[4,4,3,2,2,2],[3,2,1,1,1]] [2,1,1,2,3] => [[5,3,2,2,2],[2,1,1,1]] [2,1,1,3,1,1] => [[4,4,4,2,2,2],[3,3,1,1,1]] [2,1,1,3,2] => [[5,4,2,2,2],[3,1,1,1]] [2,1,1,4,1] => [[5,5,2,2,2],[4,1,1,1]] [2,1,1,5] => [[6,2,2,2],[1,1,1]] [2,1,2,1,1,1,1] => [[3,3,3,3,3,2,2],[2,2,2,2,1,1]] [2,1,2,1,1,2] => [[4,3,3,3,2,2],[2,2,2,1,1]] [2,1,2,1,2,1] => [[4,4,3,3,2,2],[3,2,2,1,1]] [2,1,2,1,3] => [[5,3,3,2,2],[2,2,1,1]] [2,1,2,2,1,1] => [[4,4,4,3,2,2],[3,3,2,1,1]] [2,1,2,2,2] => [[5,4,3,2,2],[3,2,1,1]] [2,1,2,3,1] => [[5,5,3,2,2],[4,2,1,1]] [2,1,2,4] => [[6,3,2,2],[2,1,1]] [2,1,3,1,1,1] => [[4,4,4,4,2,2],[3,3,3,1,1]] [2,1,3,1,2] => [[5,4,4,2,2],[3,3,1,1]] [2,1,3,2,1] => [[5,5,4,2,2],[4,3,1,1]] [2,1,3,3] => [[6,4,2,2],[3,1,1]] [2,1,4,1,1] => [[5,5,5,2,2],[4,4,1,1]] [2,1,4,2] => [[6,5,2,2],[4,1,1]] [2,1,5,1] => [[6,6,2,2],[5,1,1]] [2,1,6] => [[7,2,2],[1,1]] [2,2,1,1,1,1,1] => [[3,3,3,3,3,3,2],[2,2,2,2,2,1]] [2,2,1,1,1,2] => [[4,3,3,3,3,2],[2,2,2,2,1]] [2,2,1,1,2,1] => [[4,4,3,3,3,2],[3,2,2,2,1]] [2,2,1,1,3] => [[5,3,3,3,2],[2,2,2,1]] [2,2,1,2,1,1] => [[4,4,4,3,3,2],[3,3,2,2,1]] [2,2,1,2,2] => [[5,4,3,3,2],[3,2,2,1]] [2,2,1,3,1] => [[5,5,3,3,2],[4,2,2,1]] [2,2,1,4] => [[6,3,3,2],[2,2,1]] [2,2,2,1,1,1] => [[4,4,4,4,3,2],[3,3,3,2,1]] [2,2,2,1,2] => [[5,4,4,3,2],[3,3,2,1]] [2,2,2,2,1] => [[5,5,4,3,2],[4,3,2,1]] [2,2,2,3] => [[6,4,3,2],[3,2,1]] [2,2,3,1,1] => [[5,5,5,3,2],[4,4,2,1]] [2,2,3,2] => [[6,5,3,2],[4,2,1]] [2,2,4,1] => [[6,6,3,2],[5,2,1]] [2,2,5] => [[7,3,2],[2,1]] [2,3,1,1,1,1] => [[4,4,4,4,4,2],[3,3,3,3,1]] [2,3,1,1,2] => [[5,4,4,4,2],[3,3,3,1]] [2,3,1,2,1] => [[5,5,4,4,2],[4,3,3,1]] [2,3,1,3] => [[6,4,4,2],[3,3,1]] [2,3,2,1,1] => [[5,5,5,4,2],[4,4,3,1]] [2,3,2,2] => [[6,5,4,2],[4,3,1]] [2,3,3,1] => [[6,6,4,2],[5,3,1]] [2,3,4] => [[7,4,2],[3,1]] [2,4,1,1,1] => [[5,5,5,5,2],[4,4,4,1]] [2,4,1,2] => [[6,5,5,2],[4,4,1]] [2,4,2,1] => [[6,6,5,2],[5,4,1]] [2,4,3] => [[7,5,2],[4,1]] [2,5,1,1] => [[6,6,6,2],[5,5,1]] [2,5,2] => [[7,6,2],[5,1]] [2,6,1] => [[7,7,2],[6,1]] [2,7] => [[8,2],[1]] [3,1,1,1,1,1,1] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] [3,1,1,1,1,2] => [[4,3,3,3,3,3],[2,2,2,2,2]] [3,1,1,1,2,1] => [[4,4,3,3,3,3],[3,2,2,2,2]] [3,1,1,1,3] => [[5,3,3,3,3],[2,2,2,2]] [3,1,1,2,1,1] => [[4,4,4,3,3,3],[3,3,2,2,2]] [3,1,1,2,2] => [[5,4,3,3,3],[3,2,2,2]] [3,1,1,3,1] => [[5,5,3,3,3],[4,2,2,2]] [3,1,1,4] => [[6,3,3,3],[2,2,2]] [3,1,2,1,1,1] => [[4,4,4,4,3,3],[3,3,3,2,2]] [3,1,2,1,2] => [[5,4,4,3,3],[3,3,2,2]] [3,1,2,2,1] => [[5,5,4,3,3],[4,3,2,2]] [3,1,2,3] => [[6,4,3,3],[3,2,2]] [3,1,3,1,1] => [[5,5,5,3,3],[4,4,2,2]] [3,1,3,2] => [[6,5,3,3],[4,2,2]] [3,1,4,1] => [[6,6,3,3],[5,2,2]] [3,1,5] => [[7,3,3],[2,2]] [3,2,1,1,1,1] => [[4,4,4,4,4,3],[3,3,3,3,2]] [3,2,1,1,2] => [[5,4,4,4,3],[3,3,3,2]] [3,2,1,2,1] => [[5,5,4,4,3],[4,3,3,2]] [3,2,1,3] => [[6,4,4,3],[3,3,2]] [3,2,2,1,1] => [[5,5,5,4,3],[4,4,3,2]] [3,2,2,2] => [[6,5,4,3],[4,3,2]] [3,2,3,1] => [[6,6,4,3],[5,3,2]] [3,2,4] => [[7,4,3],[3,2]] [3,3,1,1,1] => [[5,5,5,5,3],[4,4,4,2]] [3,3,1,2] => [[6,5,5,3],[4,4,2]] [3,3,2,1] => [[6,6,5,3],[5,4,2]] [3,3,3] => [[7,5,3],[4,2]] [3,4,1,1] => [[6,6,6,3],[5,5,2]] [3,4,2] => [[7,6,3],[5,2]] [3,5,1] => [[7,7,3],[6,2]] [3,6] => [[8,3],[2]] [4,1,1,1,1,1] => [[4,4,4,4,4,4],[3,3,3,3,3]] [4,1,1,1,2] => [[5,4,4,4,4],[3,3,3,3]] [4,1,1,2,1] => [[5,5,4,4,4],[4,3,3,3]] [4,1,1,3] => [[6,4,4,4],[3,3,3]] [4,1,2,1,1] => [[5,5,5,4,4],[4,4,3,3]] [4,1,2,2] => [[6,5,4,4],[4,3,3]] [4,1,3,1] => [[6,6,4,4],[5,3,3]] [4,1,4] => [[7,4,4],[3,3]] [4,2,1,1,1] => [[5,5,5,5,4],[4,4,4,3]] [4,2,1,2] => [[6,5,5,4],[4,4,3]] [4,2,2,1] => [[6,6,5,4],[5,4,3]] [4,2,3] => [[7,5,4],[4,3]] [4,3,1,1] => [[6,6,6,4],[5,5,3]] [4,3,2] => [[7,6,4],[5,3]] [4,4,1] => [[7,7,4],[6,3]] [4,5] => [[8,4],[3]] [5,1,1,1,1] => [[5,5,5,5,5],[4,4,4,4]] [5,1,1,2] => [[6,5,5,5],[4,4,4]] [5,1,2,1] => [[6,6,5,5],[5,4,4]] [5,1,3] => [[7,5,5],[4,4]] [5,2,1,1] => [[6,6,6,5],[5,5,4]] [5,2,2] => [[7,6,5],[5,4]] [5,3,1] => [[7,7,5],[6,4]] [5,4] => [[8,5],[4]] [6,1,1,1] => [[6,6,6,6],[5,5,5]] [6,1,2] => [[7,6,6],[5,5]] [6,2,1] => [[7,7,6],[6,5]] [6,3] => [[8,6],[5]] [7,1,1] => [[7,7,7],[6,6]] [7,2] => [[8,7],[6]] [8,1] => [[8,8],[7]] [9] => [[9],[]] [1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1],[]] [1,1,1,1,1,1,1,1,2] => [[2,1,1,1,1,1,1,1,1],[]] [1,1,1,1,1,1,1,2,1] => [[2,2,1,1,1,1,1,1,1],[1]] [1,1,1,1,1,1,1,3] => [[3,1,1,1,1,1,1,1],[]] [1,1,1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1,1,1],[1,1]] [1,1,1,1,1,1,2,2] => [[3,2,1,1,1,1,1,1],[1]] [1,1,1,1,1,1,3,1] => [[3,3,1,1,1,1,1,1],[2]] [1,1,1,1,1,1,4] => [[4,1,1,1,1,1,1],[]] [1,1,1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1,1,1],[1,1,1]] [1,1,1,1,1,2,1,2] => [[3,2,2,1,1,1,1,1],[1,1]] [1,1,1,1,1,2,2,1] => [[3,3,2,1,1,1,1,1],[2,1]] [1,1,1,1,1,2,3] => [[4,2,1,1,1,1,1],[1]] [1,1,1,1,1,3,1,1] => [[3,3,3,1,1,1,1,1],[2,2]] [1,1,1,1,1,3,2] => [[4,3,1,1,1,1,1],[2]] [1,1,1,1,1,4,1] => [[4,4,1,1,1,1,1],[3]] [1,1,1,1,1,5] => [[5,1,1,1,1,1],[]] [1,1,1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1,1,1],[1,1,1,1]] [1,1,1,1,2,1,1,2] => [[3,2,2,2,1,1,1,1],[1,1,1]] [1,1,1,1,2,1,2,1] => [[3,3,2,2,1,1,1,1],[2,1,1]] [1,1,1,1,2,1,3] => [[4,2,2,1,1,1,1],[1,1]] [1,1,1,1,2,2,1,1] => [[3,3,3,2,1,1,1,1],[2,2,1]] [1,1,1,1,2,2,2] => [[4,3,2,1,1,1,1],[2,1]] [1,1,1,1,2,3,1] => [[4,4,2,1,1,1,1],[3,1]] [1,1,1,1,2,4] => [[5,2,1,1,1,1],[1]] [1,1,1,1,3,1,1,1] => [[3,3,3,3,1,1,1,1],[2,2,2]] [1,1,1,1,3,1,2] => [[4,3,3,1,1,1,1],[2,2]] [1,1,1,1,3,2,1] => [[4,4,3,1,1,1,1],[3,2]] [1,1,1,1,3,3] => [[5,3,1,1,1,1],[2]] [1,1,1,1,4,1,1] => [[4,4,4,1,1,1,1],[3,3]] [1,1,1,1,4,2] => [[5,4,1,1,1,1],[3]] [1,1,1,1,5,1] => [[5,5,1,1,1,1],[4]] [1,1,1,1,6] => [[6,1,1,1,1],[]] [1,1,1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1,1,1],[1,1,1,1,1]] [1,1,1,2,1,1,1,2] => [[3,2,2,2,2,1,1,1],[1,1,1,1]] [1,1,1,2,1,1,2,1] => [[3,3,2,2,2,1,1,1],[2,1,1,1]] [1,1,1,2,1,1,3] => [[4,2,2,2,1,1,1],[1,1,1]] [1,1,1,2,1,2,1,1] => [[3,3,3,2,2,1,1,1],[2,2,1,1]] [1,1,1,2,1,2,2] => [[4,3,2,2,1,1,1],[2,1,1]] [1,1,1,2,1,3,1] => [[4,4,2,2,1,1,1],[3,1,1]] [1,1,1,2,1,4] => [[5,2,2,1,1,1],[1,1]] [1,1,1,2,2,1,1,1] => [[3,3,3,3,2,1,1,1],[2,2,2,1]] [1,1,1,2,2,1,2] => [[4,3,3,2,1,1,1],[2,2,1]] [1,1,1,2,2,2,1] => [[4,4,3,2,1,1,1],[3,2,1]] [1,1,1,2,2,3] => [[5,3,2,1,1,1],[2,1]] [1,1,1,2,3,1,1] => [[4,4,4,2,1,1,1],[3,3,1]] [1,1,1,2,3,2] => [[5,4,2,1,1,1],[3,1]] [1,1,1,2,4,1] => [[5,5,2,1,1,1],[4,1]] [1,1,1,2,5] => [[6,2,1,1,1],[1]] [1,1,1,3,1,1,1,1] => [[3,3,3,3,3,1,1,1],[2,2,2,2]] [1,1,1,3,1,1,2] => [[4,3,3,3,1,1,1],[2,2,2]] [1,1,1,3,1,2,1] => [[4,4,3,3,1,1,1],[3,2,2]] [1,1,1,3,1,3] => [[5,3,3,1,1,1],[2,2]] [1,1,1,3,2,1,1] => [[4,4,4,3,1,1,1],[3,3,2]] [1,1,1,3,2,2] => [[5,4,3,1,1,1],[3,2]] [1,1,1,3,3,1] => [[5,5,3,1,1,1],[4,2]] [1,1,1,3,4] => [[6,3,1,1,1],[2]] [1,1,1,4,1,1,1] => [[4,4,4,4,1,1,1],[3,3,3]] [1,1,1,4,1,2] => [[5,4,4,1,1,1],[3,3]] [1,1,1,4,2,1] => [[5,5,4,1,1,1],[4,3]] [1,1,1,4,3] => [[6,4,1,1,1],[3]] [1,1,1,5,1,1] => [[5,5,5,1,1,1],[4,4]] [1,1,1,5,2] => [[6,5,1,1,1],[4]] [1,1,1,6,1] => [[6,6,1,1,1],[5]] [1,1,1,7] => [[7,1,1,1],[]] [1,1,2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,1,1],[1,1,1,1,1,1]] [1,1,2,1,1,1,1,2] => [[3,2,2,2,2,2,1,1],[1,1,1,1,1]] [1,1,2,1,1,1,2,1] => [[3,3,2,2,2,2,1,1],[2,1,1,1,1]] [1,1,2,1,1,1,3] => [[4,2,2,2,2,1,1],[1,1,1,1]] [1,1,2,1,1,2,1,1] => [[3,3,3,2,2,2,1,1],[2,2,1,1,1]] [1,1,2,1,1,2,2] => [[4,3,2,2,2,1,1],[2,1,1,1]] [1,1,2,1,1,3,1] => [[4,4,2,2,2,1,1],[3,1,1,1]] [1,1,2,1,1,4] => [[5,2,2,2,1,1],[1,1,1]] [1,1,2,1,2,1,1,1] => [[3,3,3,3,2,2,1,1],[2,2,2,1,1]] [1,1,2,1,2,1,2] => [[4,3,3,2,2,1,1],[2,2,1,1]] [1,1,2,1,2,2,1] => [[4,4,3,2,2,1,1],[3,2,1,1]] [1,1,2,1,2,3] => [[5,3,2,2,1,1],[2,1,1]] [1,1,2,1,3,1,1] => [[4,4,4,2,2,1,1],[3,3,1,1]] [1,1,2,1,3,2] => [[5,4,2,2,1,1],[3,1,1]] [1,1,2,1,4,1] => [[5,5,2,2,1,1],[4,1,1]] [1,1,2,1,5] => [[6,2,2,1,1],[1,1]] [1,1,2,2,1,1,1,1] => [[3,3,3,3,3,2,1,1],[2,2,2,2,1]] [1,1,2,2,1,1,2] => [[4,3,3,3,2,1,1],[2,2,2,1]] [1,1,2,2,1,2,1] => [[4,4,3,3,2,1,1],[3,2,2,1]] [1,1,2,2,1,3] => [[5,3,3,2,1,1],[2,2,1]] [1,1,2,2,2,1,1] => [[4,4,4,3,2,1,1],[3,3,2,1]] [1,1,2,2,2,2] => [[5,4,3,2,1,1],[3,2,1]] [1,1,2,2,3,1] => [[5,5,3,2,1,1],[4,2,1]] [1,1,2,2,4] => [[6,3,2,1,1],[2,1]] [1,1,2,3,1,1,1] => [[4,4,4,4,2,1,1],[3,3,3,1]] [1,1,2,3,1,2] => [[5,4,4,2,1,1],[3,3,1]] [1,1,2,3,2,1] => [[5,5,4,2,1,1],[4,3,1]] [1,1,2,3,3] => [[6,4,2,1,1],[3,1]] [1,1,2,4,1,1] => [[5,5,5,2,1,1],[4,4,1]] [1,1,2,4,2] => [[6,5,2,1,1],[4,1]] [1,1,2,5,1] => [[6,6,2,1,1],[5,1]] [1,1,2,6] => [[7,2,1,1],[1]] [1,1,3,1,1,1,1,1] => [[3,3,3,3,3,3,1,1],[2,2,2,2,2]] [1,1,3,1,1,1,2] => [[4,3,3,3,3,1,1],[2,2,2,2]] [1,1,3,1,1,2,1] => [[4,4,3,3,3,1,1],[3,2,2,2]] [1,1,3,1,1,3] => [[5,3,3,3,1,1],[2,2,2]] [1,1,3,1,2,1,1] => [[4,4,4,3,3,1,1],[3,3,2,2]] [1,1,3,1,2,2] => [[5,4,3,3,1,1],[3,2,2]] [1,1,3,1,3,1] => [[5,5,3,3,1,1],[4,2,2]] [1,1,3,1,4] => [[6,3,3,1,1],[2,2]] [1,1,3,2,1,1,1] => [[4,4,4,4,3,1,1],[3,3,3,2]] [1,1,3,2,1,2] => [[5,4,4,3,1,1],[3,3,2]] [1,1,3,2,2,1] => [[5,5,4,3,1,1],[4,3,2]] [1,1,3,2,3] => [[6,4,3,1,1],[3,2]] [1,1,3,3,1,1] => [[5,5,5,3,1,1],[4,4,2]] [1,1,3,3,2] => [[6,5,3,1,1],[4,2]] [1,1,3,4,1] => [[6,6,3,1,1],[5,2]] [1,1,3,5] => [[7,3,1,1],[2]] [1,1,4,1,1,1,1] => [[4,4,4,4,4,1,1],[3,3,3,3]] [1,1,4,1,1,2] => [[5,4,4,4,1,1],[3,3,3]] [1,1,4,1,2,1] => [[5,5,4,4,1,1],[4,3,3]] [1,1,4,1,3] => [[6,4,4,1,1],[3,3]] [1,1,4,2,1,1] => [[5,5,5,4,1,1],[4,4,3]] [1,1,4,2,2] => [[6,5,4,1,1],[4,3]] [1,1,4,3,1] => [[6,6,4,1,1],[5,3]] [1,1,4,4] => [[7,4,1,1],[3]] [1,1,5,1,1,1] => [[5,5,5,5,1,1],[4,4,4]] [1,1,5,1,2] => [[6,5,5,1,1],[4,4]] [1,1,5,2,1] => [[6,6,5,1,1],[5,4]] [1,1,5,3] => [[7,5,1,1],[4]] [1,1,6,1,1] => [[6,6,6,1,1],[5,5]] [1,1,6,2] => [[7,6,1,1],[5]] [1,1,7,1] => [[7,7,1,1],[6]] [1,1,8] => [[8,1,1],[]] [1,2,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2,1],[1,1,1,1,1,1,1]] [1,2,1,1,1,1,1,2] => [[3,2,2,2,2,2,2,1],[1,1,1,1,1,1]] [1,2,1,1,1,1,2,1] => [[3,3,2,2,2,2,2,1],[2,1,1,1,1,1]] [1,2,1,1,1,1,3] => [[4,2,2,2,2,2,1],[1,1,1,1,1]] [1,2,1,1,1,2,1,1] => [[3,3,3,2,2,2,2,1],[2,2,1,1,1,1]] [1,2,1,1,1,2,2] => [[4,3,2,2,2,2,1],[2,1,1,1,1]] [1,2,1,1,1,3,1] => [[4,4,2,2,2,2,1],[3,1,1,1,1]] [1,2,1,1,1,4] => [[5,2,2,2,2,1],[1,1,1,1]] [1,2,1,1,2,1,1,1] => [[3,3,3,3,2,2,2,1],[2,2,2,1,1,1]] [1,2,1,1,2,1,2] => [[4,3,3,2,2,2,1],[2,2,1,1,1]] [1,2,1,1,2,2,1] => [[4,4,3,2,2,2,1],[3,2,1,1,1]] [1,2,1,1,2,3] => [[5,3,2,2,2,1],[2,1,1,1]] [1,2,1,1,3,1,1] => [[4,4,4,2,2,2,1],[3,3,1,1,1]] [1,2,1,1,3,2] => [[5,4,2,2,2,1],[3,1,1,1]] [1,2,1,1,4,1] => [[5,5,2,2,2,1],[4,1,1,1]] [1,2,1,1,5] => [[6,2,2,2,1],[1,1,1]] [1,2,1,2,1,1,1,1] => [[3,3,3,3,3,2,2,1],[2,2,2,2,1,1]] [1,2,1,2,1,1,2] => [[4,3,3,3,2,2,1],[2,2,2,1,1]] [1,2,1,2,1,2,1] => [[4,4,3,3,2,2,1],[3,2,2,1,1]] [1,2,1,2,1,3] => [[5,3,3,2,2,1],[2,2,1,1]] [1,2,1,2,2,1,1] => [[4,4,4,3,2,2,1],[3,3,2,1,1]] [1,2,1,2,2,2] => [[5,4,3,2,2,1],[3,2,1,1]] [1,2,1,2,3,1] => [[5,5,3,2,2,1],[4,2,1,1]] [1,2,1,2,4] => [[6,3,2,2,1],[2,1,1]] [1,2,1,3,1,1,1] => [[4,4,4,4,2,2,1],[3,3,3,1,1]] [1,2,1,3,1,2] => [[5,4,4,2,2,1],[3,3,1,1]] [1,2,1,3,2,1] => [[5,5,4,2,2,1],[4,3,1,1]] [1,2,1,3,3] => [[6,4,2,2,1],[3,1,1]] [1,2,1,4,1,1] => [[5,5,5,2,2,1],[4,4,1,1]] [1,2,1,4,2] => [[6,5,2,2,1],[4,1,1]] [1,2,1,5,1] => [[6,6,2,2,1],[5,1,1]] [1,2,1,6] => [[7,2,2,1],[1,1]] [1,2,2,1,1,1,1,1] => [[3,3,3,3,3,3,2,1],[2,2,2,2,2,1]] [1,2,2,1,1,1,2] => [[4,3,3,3,3,2,1],[2,2,2,2,1]] [1,2,2,1,1,2,1] => [[4,4,3,3,3,2,1],[3,2,2,2,1]] [1,2,2,1,1,3] => [[5,3,3,3,2,1],[2,2,2,1]] [1,2,2,1,2,1,1] => [[4,4,4,3,3,2,1],[3,3,2,2,1]] [1,2,2,1,2,2] => [[5,4,3,3,2,1],[3,2,2,1]] [1,2,2,1,3,1] => [[5,5,3,3,2,1],[4,2,2,1]] [1,2,2,1,4] => [[6,3,3,2,1],[2,2,1]] [1,2,2,2,1,1,1] => [[4,4,4,4,3,2,1],[3,3,3,2,1]] [1,2,2,2,1,2] => [[5,4,4,3,2,1],[3,3,2,1]] [1,2,2,2,2,1] => [[5,5,4,3,2,1],[4,3,2,1]] [1,2,2,2,3] => [[6,4,3,2,1],[3,2,1]] [1,2,2,3,1,1] => [[5,5,5,3,2,1],[4,4,2,1]] [1,2,2,3,2] => [[6,5,3,2,1],[4,2,1]] [1,2,2,4,1] => [[6,6,3,2,1],[5,2,1]] [1,2,2,5] => [[7,3,2,1],[2,1]] [1,2,3,1,1,1,1] => [[4,4,4,4,4,2,1],[3,3,3,3,1]] [1,2,3,1,1,2] => [[5,4,4,4,2,1],[3,3,3,1]] [1,2,3,1,2,1] => [[5,5,4,4,2,1],[4,3,3,1]] [1,2,3,1,3] => [[6,4,4,2,1],[3,3,1]] [1,2,3,2,1,1] => [[5,5,5,4,2,1],[4,4,3,1]] [1,2,3,2,2] => [[6,5,4,2,1],[4,3,1]] [1,2,3,3,1] => [[6,6,4,2,1],[5,3,1]] [1,2,3,4] => [[7,4,2,1],[3,1]] [1,2,4,1,1,1] => [[5,5,5,5,2,1],[4,4,4,1]] [1,2,4,1,2] => [[6,5,5,2,1],[4,4,1]] [1,2,4,2,1] => [[6,6,5,2,1],[5,4,1]] [1,2,4,3] => [[7,5,2,1],[4,1]] [1,2,5,1,1] => [[6,6,6,2,1],[5,5,1]] [1,2,5,2] => [[7,6,2,1],[5,1]] [1,2,6,1] => [[7,7,2,1],[6,1]] [1,2,7] => [[8,2,1],[1]] [1,3,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,1],[2,2,2,2,2,2]] [1,3,1,1,1,1,2] => [[4,3,3,3,3,3,1],[2,2,2,2,2]] [1,3,1,1,1,2,1] => [[4,4,3,3,3,3,1],[3,2,2,2,2]] [1,3,1,1,1,3] => [[5,3,3,3,3,1],[2,2,2,2]] [1,3,1,1,2,1,1] => [[4,4,4,3,3,3,1],[3,3,2,2,2]] [1,3,1,1,2,2] => [[5,4,3,3,3,1],[3,2,2,2]] [1,3,1,1,3,1] => [[5,5,3,3,3,1],[4,2,2,2]] [1,3,1,1,4] => [[6,3,3,3,1],[2,2,2]] [1,3,1,2,1,1,1] => [[4,4,4,4,3,3,1],[3,3,3,2,2]] [1,3,1,2,1,2] => [[5,4,4,3,3,1],[3,3,2,2]] [1,3,1,2,2,1] => [[5,5,4,3,3,1],[4,3,2,2]] [1,3,1,2,3] => [[6,4,3,3,1],[3,2,2]] [1,3,1,3,1,1] => [[5,5,5,3,3,1],[4,4,2,2]] [1,3,1,3,2] => [[6,5,3,3,1],[4,2,2]] [1,3,1,4,1] => [[6,6,3,3,1],[5,2,2]] [1,3,1,5] => [[7,3,3,1],[2,2]] [1,3,2,1,1,1,1] => [[4,4,4,4,4,3,1],[3,3,3,3,2]] [1,3,2,1,1,2] => [[5,4,4,4,3,1],[3,3,3,2]] [1,3,2,1,2,1] => [[5,5,4,4,3,1],[4,3,3,2]] [1,3,2,1,3] => [[6,4,4,3,1],[3,3,2]] [1,3,2,2,1,1] => [[5,5,5,4,3,1],[4,4,3,2]] [1,3,2,2,2] => [[6,5,4,3,1],[4,3,2]] [1,3,2,3,1] => [[6,6,4,3,1],[5,3,2]] [1,3,2,4] => [[7,4,3,1],[3,2]] [1,3,3,1,1,1] => [[5,5,5,5,3,1],[4,4,4,2]] [1,3,3,1,2] => [[6,5,5,3,1],[4,4,2]] [1,3,3,2,1] => [[6,6,5,3,1],[5,4,2]] [1,3,3,3] => [[7,5,3,1],[4,2]] [1,3,4,1,1] => [[6,6,6,3,1],[5,5,2]] [1,3,4,2] => [[7,6,3,1],[5,2]] [1,3,5,1] => [[7,7,3,1],[6,2]] [1,3,6] => [[8,3,1],[2]] [1,4,1,1,1,1,1] => [[4,4,4,4,4,4,1],[3,3,3,3,3]] [1,4,1,1,1,2] => [[5,4,4,4,4,1],[3,3,3,3]] [1,4,1,1,2,1] => [[5,5,4,4,4,1],[4,3,3,3]] [1,4,1,1,3] => [[6,4,4,4,1],[3,3,3]] [1,4,1,2,1,1] => [[5,5,5,4,4,1],[4,4,3,3]] [1,4,1,2,2] => [[6,5,4,4,1],[4,3,3]] [1,4,1,3,1] => [[6,6,4,4,1],[5,3,3]] [1,4,1,4] => [[7,4,4,1],[3,3]] [1,4,2,1,1,1] => [[5,5,5,5,4,1],[4,4,4,3]] [1,4,2,1,2] => [[6,5,5,4,1],[4,4,3]] [1,4,2,2,1] => [[6,6,5,4,1],[5,4,3]] [1,4,2,3] => [[7,5,4,1],[4,3]] [1,4,3,1,1] => [[6,6,6,4,1],[5,5,3]] [1,4,3,2] => [[7,6,4,1],[5,3]] [1,4,4,1] => [[7,7,4,1],[6,3]] [1,4,5] => [[8,4,1],[3]] [1,5,1,1,1,1] => [[5,5,5,5,5,1],[4,4,4,4]] [1,5,1,1,2] => [[6,5,5,5,1],[4,4,4]] [1,5,1,2,1] => [[6,6,5,5,1],[5,4,4]] [1,5,1,3] => [[7,5,5,1],[4,4]] [1,5,2,1,1] => [[6,6,6,5,1],[5,5,4]] [1,5,2,2] => [[7,6,5,1],[5,4]] [1,5,3,1] => [[7,7,5,1],[6,4]] [1,5,4] => [[8,5,1],[4]] [1,6,1,1,1] => [[6,6,6,6,1],[5,5,5]] [1,6,1,2] => [[7,6,6,1],[5,5]] [1,6,2,1] => [[7,7,6,1],[6,5]] [1,6,3] => [[8,6,1],[5]] [1,7,1,1] => [[7,7,7,1],[6,6]] [1,7,2] => [[8,7,1],[6]] [1,8,1] => [[8,8,1],[7]] [1,9] => [[9,1],[]] [2,1,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] [2,1,1,1,1,1,1,2] => [[3,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] [2,1,1,1,1,1,2,1] => [[3,3,2,2,2,2,2,2],[2,1,1,1,1,1,1]] [2,1,1,1,1,1,3] => [[4,2,2,2,2,2,2],[1,1,1,1,1,1]] [2,1,1,1,1,2,1,1] => [[3,3,3,2,2,2,2,2],[2,2,1,1,1,1,1]] [2,1,1,1,1,2,2] => [[4,3,2,2,2,2,2],[2,1,1,1,1,1]] [2,1,1,1,1,3,1] => [[4,4,2,2,2,2,2],[3,1,1,1,1,1]] [2,1,1,1,1,4] => [[5,2,2,2,2,2],[1,1,1,1,1]] [2,1,1,1,2,1,1,1] => [[3,3,3,3,2,2,2,2],[2,2,2,1,1,1,1]] [2,1,1,1,2,1,2] => [[4,3,3,2,2,2,2],[2,2,1,1,1,1]] [2,1,1,1,2,2,1] => [[4,4,3,2,2,2,2],[3,2,1,1,1,1]] [2,1,1,1,2,3] => [[5,3,2,2,2,2],[2,1,1,1,1]] [2,1,1,1,3,1,1] => [[4,4,4,2,2,2,2],[3,3,1,1,1,1]] [2,1,1,1,3,2] => [[5,4,2,2,2,2],[3,1,1,1,1]] [2,1,1,1,4,1] => [[5,5,2,2,2,2],[4,1,1,1,1]] [2,1,1,1,5] => [[6,2,2,2,2],[1,1,1,1]] [2,1,1,2,1,1,1,1] => [[3,3,3,3,3,2,2,2],[2,2,2,2,1,1,1]] [2,1,1,2,1,1,2] => [[4,3,3,3,2,2,2],[2,2,2,1,1,1]] [2,1,1,2,1,2,1] => [[4,4,3,3,2,2,2],[3,2,2,1,1,1]] [2,1,1,2,1,3] => [[5,3,3,2,2,2],[2,2,1,1,1]] [2,1,1,2,2,1,1] => [[4,4,4,3,2,2,2],[3,3,2,1,1,1]] [2,1,1,2,2,2] => [[5,4,3,2,2,2],[3,2,1,1,1]] [2,1,1,2,3,1] => [[5,5,3,2,2,2],[4,2,1,1,1]] [2,1,1,2,4] => [[6,3,2,2,2],[2,1,1,1]] [2,1,1,3,1,1,1] => [[4,4,4,4,2,2,2],[3,3,3,1,1,1]] [2,1,1,3,1,2] => [[5,4,4,2,2,2],[3,3,1,1,1]] [2,1,1,3,2,1] => [[5,5,4,2,2,2],[4,3,1,1,1]] [2,1,1,3,3] => [[6,4,2,2,2],[3,1,1,1]] [2,1,1,4,1,1] => [[5,5,5,2,2,2],[4,4,1,1,1]] [2,1,1,4,2] => [[6,5,2,2,2],[4,1,1,1]] [2,1,1,5,1] => [[6,6,2,2,2],[5,1,1,1]] [2,1,1,6] => [[7,2,2,2],[1,1,1]] [2,1,2,1,1,1,1,1] => [[3,3,3,3,3,3,2,2],[2,2,2,2,2,1,1]] [2,1,2,1,1,1,2] => [[4,3,3,3,3,2,2],[2,2,2,2,1,1]] [2,1,2,1,1,2,1] => [[4,4,3,3,3,2,2],[3,2,2,2,1,1]] [2,1,2,1,1,3] => [[5,3,3,3,2,2],[2,2,2,1,1]] [2,1,2,1,2,1,1] => [[4,4,4,3,3,2,2],[3,3,2,2,1,1]] [2,1,2,1,2,2] => [[5,4,3,3,2,2],[3,2,2,1,1]] [2,1,2,1,3,1] => [[5,5,3,3,2,2],[4,2,2,1,1]] [2,1,2,1,4] => [[6,3,3,2,2],[2,2,1,1]] [2,1,2,2,1,1,1] => [[4,4,4,4,3,2,2],[3,3,3,2,1,1]] [2,1,2,2,1,2] => [[5,4,4,3,2,2],[3,3,2,1,1]] [2,1,2,2,2,1] => [[5,5,4,3,2,2],[4,3,2,1,1]] [2,1,2,2,3] => [[6,4,3,2,2],[3,2,1,1]] [2,1,2,3,1,1] => [[5,5,5,3,2,2],[4,4,2,1,1]] [2,1,2,3,2] => [[6,5,3,2,2],[4,2,1,1]] [2,1,2,4,1] => [[6,6,3,2,2],[5,2,1,1]] [2,1,2,5] => [[7,3,2,2],[2,1,1]] [2,1,3,1,1,1,1] => [[4,4,4,4,4,2,2],[3,3,3,3,1,1]] [2,1,3,1,1,2] => [[5,4,4,4,2,2],[3,3,3,1,1]] [2,1,3,1,2,1] => [[5,5,4,4,2,2],[4,3,3,1,1]] [2,1,3,1,3] => [[6,4,4,2,2],[3,3,1,1]] [2,1,3,2,1,1] => [[5,5,5,4,2,2],[4,4,3,1,1]] [2,1,3,2,2] => [[6,5,4,2,2],[4,3,1,1]] [2,1,3,3,1] => [[6,6,4,2,2],[5,3,1,1]] [2,1,3,4] => [[7,4,2,2],[3,1,1]] [2,1,4,1,1,1] => [[5,5,5,5,2,2],[4,4,4,1,1]] [2,1,4,1,2] => [[6,5,5,2,2],[4,4,1,1]] [2,1,4,2,1] => [[6,6,5,2,2],[5,4,1,1]] [2,1,4,3] => [[7,5,2,2],[4,1,1]] [2,1,5,1,1] => [[6,6,6,2,2],[5,5,1,1]] [2,1,5,2] => [[7,6,2,2],[5,1,1]] [2,1,6,1] => [[7,7,2,2],[6,1,1]] [2,1,7] => [[8,2,2],[1,1]] [2,2,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,2],[2,2,2,2,2,2,1]] [2,2,1,1,1,1,2] => [[4,3,3,3,3,3,2],[2,2,2,2,2,1]] [2,2,1,1,1,2,1] => [[4,4,3,3,3,3,2],[3,2,2,2,2,1]] [2,2,1,1,1,3] => [[5,3,3,3,3,2],[2,2,2,2,1]] [2,2,1,1,2,1,1] => [[4,4,4,3,3,3,2],[3,3,2,2,2,1]] [2,2,1,1,2,2] => [[5,4,3,3,3,2],[3,2,2,2,1]] [2,2,1,1,3,1] => [[5,5,3,3,3,2],[4,2,2,2,1]] [2,2,1,1,4] => [[6,3,3,3,2],[2,2,2,1]] [2,2,1,2,1,1,1] => [[4,4,4,4,3,3,2],[3,3,3,2,2,1]] [2,2,1,2,1,2] => [[5,4,4,3,3,2],[3,3,2,2,1]] [2,2,1,2,2,1] => [[5,5,4,3,3,2],[4,3,2,2,1]] [2,2,1,2,3] => [[6,4,3,3,2],[3,2,2,1]] [2,2,1,3,1,1] => [[5,5,5,3,3,2],[4,4,2,2,1]] [2,2,1,3,2] => [[6,5,3,3,2],[4,2,2,1]] [2,2,1,4,1] => [[6,6,3,3,2],[5,2,2,1]] [2,2,1,5] => [[7,3,3,2],[2,2,1]] [2,2,2,1,1,1,1] => [[4,4,4,4,4,3,2],[3,3,3,3,2,1]] [2,2,2,1,1,2] => [[5,4,4,4,3,2],[3,3,3,2,1]] [2,2,2,1,2,1] => [[5,5,4,4,3,2],[4,3,3,2,1]] [2,2,2,1,3] => [[6,4,4,3,2],[3,3,2,1]] [2,2,2,2,1,1] => [[5,5,5,4,3,2],[4,4,3,2,1]] [2,2,2,2,2] => [[6,5,4,3,2],[4,3,2,1]] [2,2,2,3,1] => [[6,6,4,3,2],[5,3,2,1]] [2,2,2,4] => [[7,4,3,2],[3,2,1]] [2,2,3,1,1,1] => [[5,5,5,5,3,2],[4,4,4,2,1]] [2,2,3,1,2] => [[6,5,5,3,2],[4,4,2,1]] [2,2,3,2,1] => [[6,6,5,3,2],[5,4,2,1]] [2,2,3,3] => [[7,5,3,2],[4,2,1]] [2,2,4,1,1] => [[6,6,6,3,2],[5,5,2,1]] [2,2,4,2] => [[7,6,3,2],[5,2,1]] [2,2,5,1] => [[7,7,3,2],[6,2,1]] [2,2,6] => [[8,3,2],[2,1]] [2,3,1,1,1,1,1] => [[4,4,4,4,4,4,2],[3,3,3,3,3,1]] [2,3,1,1,1,2] => [[5,4,4,4,4,2],[3,3,3,3,1]] [2,3,1,1,2,1] => [[5,5,4,4,4,2],[4,3,3,3,1]] [2,3,1,1,3] => [[6,4,4,4,2],[3,3,3,1]] [2,3,1,2,1,1] => [[5,5,5,4,4,2],[4,4,3,3,1]] [2,3,1,2,2] => [[6,5,4,4,2],[4,3,3,1]] [2,3,1,3,1] => [[6,6,4,4,2],[5,3,3,1]] [2,3,1,4] => [[7,4,4,2],[3,3,1]] [2,3,2,1,1,1] => [[5,5,5,5,4,2],[4,4,4,3,1]] [2,3,2,1,2] => [[6,5,5,4,2],[4,4,3,1]] [2,3,2,2,1] => [[6,6,5,4,2],[5,4,3,1]] [2,3,2,3] => [[7,5,4,2],[4,3,1]] [2,3,3,1,1] => [[6,6,6,4,2],[5,5,3,1]] [2,3,3,2] => [[7,6,4,2],[5,3,1]] [2,3,4,1] => [[7,7,4,2],[6,3,1]] [2,3,5] => [[8,4,2],[3,1]] [2,4,1,1,1,1] => [[5,5,5,5,5,2],[4,4,4,4,1]] [2,4,1,1,2] => [[6,5,5,5,2],[4,4,4,1]] [2,4,1,2,1] => [[6,6,5,5,2],[5,4,4,1]] [2,4,1,3] => [[7,5,5,2],[4,4,1]] [2,4,2,1,1] => [[6,6,6,5,2],[5,5,4,1]] [2,4,2,2] => [[7,6,5,2],[5,4,1]] [2,4,3,1] => [[7,7,5,2],[6,4,1]] [2,4,4] => [[8,5,2],[4,1]] [2,5,1,1,1] => [[6,6,6,6,2],[5,5,5,1]] [2,5,1,2] => [[7,6,6,2],[5,5,1]] [2,5,2,1] => [[7,7,6,2],[6,5,1]] [2,5,3] => [[8,6,2],[5,1]] [2,6,1,1] => [[7,7,7,2],[6,6,1]] [2,6,2] => [[8,7,2],[6,1]] [2,7,1] => [[8,8,2],[7,1]] [2,8] => [[9,2],[1]] [3,1,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]] [3,1,1,1,1,1,2] => [[4,3,3,3,3,3,3],[2,2,2,2,2,2]] [3,1,1,1,1,2,1] => [[4,4,3,3,3,3,3],[3,2,2,2,2,2]] [3,1,1,1,1,3] => [[5,3,3,3,3,3],[2,2,2,2,2]] [3,1,1,1,2,1,1] => [[4,4,4,3,3,3,3],[3,3,2,2,2,2]] [3,1,1,1,2,2] => [[5,4,3,3,3,3],[3,2,2,2,2]] [3,1,1,1,3,1] => [[5,5,3,3,3,3],[4,2,2,2,2]] [3,1,1,1,4] => [[6,3,3,3,3],[2,2,2,2]] [3,1,1,2,1,1,1] => [[4,4,4,4,3,3,3],[3,3,3,2,2,2]] [3,1,1,2,1,2] => [[5,4,4,3,3,3],[3,3,2,2,2]] [3,1,1,2,2,1] => [[5,5,4,3,3,3],[4,3,2,2,2]] [3,1,1,2,3] => [[6,4,3,3,3],[3,2,2,2]] [3,1,1,3,1,1] => [[5,5,5,3,3,3],[4,4,2,2,2]] [3,1,1,3,2] => [[6,5,3,3,3],[4,2,2,2]] [3,1,1,4,1] => [[6,6,3,3,3],[5,2,2,2]] [3,1,1,5] => [[7,3,3,3],[2,2,2]] [3,1,2,1,1,1,1] => [[4,4,4,4,4,3,3],[3,3,3,3,2,2]] [3,1,2,1,1,2] => [[5,4,4,4,3,3],[3,3,3,2,2]] [3,1,2,1,2,1] => [[5,5,4,4,3,3],[4,3,3,2,2]] [3,1,2,1,3] => [[6,4,4,3,3],[3,3,2,2]] [3,1,2,2,1,1] => [[5,5,5,4,3,3],[4,4,3,2,2]] [3,1,2,2,2] => [[6,5,4,3,3],[4,3,2,2]] [3,1,2,3,1] => [[6,6,4,3,3],[5,3,2,2]] [3,1,2,4] => [[7,4,3,3],[3,2,2]] [3,1,3,1,1,1] => [[5,5,5,5,3,3],[4,4,4,2,2]] [3,1,3,1,2] => [[6,5,5,3,3],[4,4,2,2]] [3,1,3,2,1] => [[6,6,5,3,3],[5,4,2,2]] [3,1,3,3] => [[7,5,3,3],[4,2,2]] [3,1,4,1,1] => [[6,6,6,3,3],[5,5,2,2]] [3,1,4,2] => [[7,6,3,3],[5,2,2]] [3,1,5,1] => [[7,7,3,3],[6,2,2]] [3,1,6] => [[8,3,3],[2,2]] [3,2,1,1,1,1,1] => [[4,4,4,4,4,4,3],[3,3,3,3,3,2]] [3,2,1,1,1,2] => [[5,4,4,4,4,3],[3,3,3,3,2]] [3,2,1,1,2,1] => [[5,5,4,4,4,3],[4,3,3,3,2]] [3,2,1,1,3] => [[6,4,4,4,3],[3,3,3,2]] [3,2,1,2,1,1] => [[5,5,5,4,4,3],[4,4,3,3,2]] [3,2,1,2,2] => [[6,5,4,4,3],[4,3,3,2]] [3,2,1,3,1] => [[6,6,4,4,3],[5,3,3,2]] [3,2,1,4] => [[7,4,4,3],[3,3,2]] [3,2,2,1,1,1] => [[5,5,5,5,4,3],[4,4,4,3,2]] [3,2,2,1,2] => [[6,5,5,4,3],[4,4,3,2]] [3,2,2,2,1] => [[6,6,5,4,3],[5,4,3,2]] [3,2,2,3] => [[7,5,4,3],[4,3,2]] [3,2,3,1,1] => [[6,6,6,4,3],[5,5,3,2]] [3,2,3,2] => [[7,6,4,3],[5,3,2]] [3,2,4,1] => [[7,7,4,3],[6,3,2]] [3,2,5] => [[8,4,3],[3,2]] [3,3,1,1,1,1] => [[5,5,5,5,5,3],[4,4,4,4,2]] [3,3,1,1,2] => [[6,5,5,5,3],[4,4,4,2]] [3,3,1,2,1] => [[6,6,5,5,3],[5,4,4,2]] [3,3,1,3] => [[7,5,5,3],[4,4,2]] [3,3,2,1,1] => [[6,6,6,5,3],[5,5,4,2]] [3,3,2,2] => [[7,6,5,3],[5,4,2]] [3,3,3,1] => [[7,7,5,3],[6,4,2]] [3,3,4] => [[8,5,3],[4,2]] [3,4,1,1,1] => [[6,6,6,6,3],[5,5,5,2]] [3,4,1,2] => [[7,6,6,3],[5,5,2]] [3,4,2,1] => [[7,7,6,3],[6,5,2]] [3,4,3] => [[8,6,3],[5,2]] [3,5,1,1] => [[7,7,7,3],[6,6,2]] [3,5,2] => [[8,7,3],[6,2]] [3,6,1] => [[8,8,3],[7,2]] [3,7] => [[9,3],[2]] [4,1,1,1,1,1,1] => [[4,4,4,4,4,4,4],[3,3,3,3,3,3]] [4,1,1,1,1,2] => [[5,4,4,4,4,4],[3,3,3,3,3]] [4,1,1,1,2,1] => [[5,5,4,4,4,4],[4,3,3,3,3]] [4,1,1,1,3] => [[6,4,4,4,4],[3,3,3,3]] [4,1,1,2,1,1] => [[5,5,5,4,4,4],[4,4,3,3,3]] [4,1,1,2,2] => [[6,5,4,4,4],[4,3,3,3]] [4,1,1,3,1] => [[6,6,4,4,4],[5,3,3,3]] [4,1,1,4] => [[7,4,4,4],[3,3,3]] [4,1,2,1,1,1] => [[5,5,5,5,4,4],[4,4,4,3,3]] [4,1,2,1,2] => [[6,5,5,4,4],[4,4,3,3]] [4,1,2,2,1] => [[6,6,5,4,4],[5,4,3,3]] [4,1,2,3] => [[7,5,4,4],[4,3,3]] [4,1,3,1,1] => [[6,6,6,4,4],[5,5,3,3]] [4,1,3,2] => [[7,6,4,4],[5,3,3]] [4,1,4,1] => [[7,7,4,4],[6,3,3]] [4,1,5] => [[8,4,4],[3,3]] [4,2,1,1,1,1] => [[5,5,5,5,5,4],[4,4,4,4,3]] [4,2,1,1,2] => [[6,5,5,5,4],[4,4,4,3]] [4,2,1,2,1] => [[6,6,5,5,4],[5,4,4,3]] [4,2,1,3] => [[7,5,5,4],[4,4,3]] [4,2,2,1,1] => [[6,6,6,5,4],[5,5,4,3]] [4,2,2,2] => [[7,6,5,4],[5,4,3]] [4,2,3,1] => [[7,7,5,4],[6,4,3]] [4,2,4] => [[8,5,4],[4,3]] [4,3,1,1,1] => [[6,6,6,6,4],[5,5,5,3]] [4,3,1,2] => [[7,6,6,4],[5,5,3]] [4,3,2,1] => [[7,7,6,4],[6,5,3]] [4,3,3] => [[8,6,4],[5,3]] [4,4,1,1] => [[7,7,7,4],[6,6,3]] [4,4,2] => [[8,7,4],[6,3]] [4,5,1] => [[8,8,4],[7,3]] [4,6] => [[9,4],[3]] [5,1,1,1,1,1] => [[5,5,5,5,5,5],[4,4,4,4,4]] [5,1,1,1,2] => [[6,5,5,5,5],[4,4,4,4]] [5,1,1,2,1] => [[6,6,5,5,5],[5,4,4,4]] [5,1,1,3] => [[7,5,5,5],[4,4,4]] [5,1,2,1,1] => [[6,6,6,5,5],[5,5,4,4]] [5,1,2,2] => [[7,6,5,5],[5,4,4]] [5,1,3,1] => [[7,7,5,5],[6,4,4]] [5,1,4] => [[8,5,5],[4,4]] [5,2,1,1,1] => [[6,6,6,6,5],[5,5,5,4]] [5,2,1,2] => [[7,6,6,5],[5,5,4]] [5,2,2,1] => [[7,7,6,5],[6,5,4]] [5,2,3] => [[8,6,5],[5,4]] [5,3,1,1] => [[7,7,7,5],[6,6,4]] [5,3,2] => [[8,7,5],[6,4]] [5,4,1] => [[8,8,5],[7,4]] [5,5] => [[9,5],[4]] [6,1,1,1,1] => [[6,6,6,6,6],[5,5,5,5]] [6,1,1,2] => [[7,6,6,6],[5,5,5]] [6,1,2,1] => [[7,7,6,6],[6,5,5]] [6,1,3] => [[8,6,6],[5,5]] [6,2,1,1] => [[7,7,7,6],[6,6,5]] [6,2,2] => [[8,7,6],[6,5]] [6,3,1] => [[8,8,6],[7,5]] [6,4] => [[9,6],[5]] [7,1,1,1] => [[7,7,7,7],[6,6,6]] [7,1,2] => [[8,7,7],[6,6]] [7,2,1] => [[8,8,7],[7,6]] [7,3] => [[9,7],[6]] [8,1,1] => [[8,8,8],[7,7]] [8,2] => [[9,8],[7]] [9,1] => [[9,9],[8]] [10] => [[10],[]] [1,10] => [[10,1],[]] [1,8,1,1] => [[8,8,8,1],[7,7]] [1,7,2,1] => [[8,8,7,1],[7,6]] [1,6,3,1] => [[8,8,6,1],[7,5]] [1,5,4,1] => [[8,8,5,1],[7,4]] [1,4,5,1] => [[8,8,4,1],[7,3]] [1,3,6,1] => [[8,8,3,1],[7,2]] [1,2,7,1] => [[8,8,2,1],[7,1]] [1,1,8,1] => [[8,8,1,1],[7]] [10,1] => [[10,10],[9]] [1,1,1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1,1,1],[]] [1,1,1,1,1,1,1,1,2,2] => [[3,2,1,1,1,1,1,1,1,1],[1]] [1,1,1,1,1,1,2,2,1,1] => [[3,3,3,2,1,1,1,1,1,1],[2,2,1]] [1,1,1,1,1,1,2,1,1,2] => [[3,2,2,2,1,1,1,1,1,1],[1,1,1]] [1,1,1,1,1,1,3,3] => [[5,3,1,1,1,1,1,1],[2]] [1,1,1,1,2,2,1,1,1,1] => [[3,3,3,3,3,2,1,1,1,1],[2,2,2,2,1]] [1,1,1,1,2,2,2,2] => [[5,4,3,2,1,1,1,1],[3,2,1]] [1,1,1,1,2,1,1,2,1,1] => [[3,3,3,2,2,2,1,1,1,1],[2,2,1,1,1]] [1,1,1,1,2,1,1,1,1,2] => [[3,2,2,2,2,2,1,1,1,1],[1,1,1,1,1]] [1,1,1,1,2,1,2,3] => [[5,3,2,2,1,1,1,1],[2,1,1]] [1,1,1,1,3,3,1,1] => [[5,5,5,3,1,1,1,1],[4,4,2]] [1,1,1,1,3,2,1,2] => [[5,4,4,3,1,1,1,1],[3,3,2]] [1,1,1,1,3,1,1,3] => [[5,3,3,3,1,1,1,1],[2,2,2]] [1,1,1,1,4,4] => [[7,4,1,1,1,1],[3]] [1,1,2,2,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,2,1,1],[2,2,2,2,2,2,1]] [1,1,2,2,1,1,2,2] => [[5,4,3,3,3,2,1,1],[3,2,2,2,1]] [1,1,2,2,2,2,1,1] => [[5,5,5,4,3,2,1,1],[4,4,3,2,1]] [1,1,2,2,2,1,1,2] => [[5,4,4,4,3,2,1,1],[3,3,3,2,1]] [1,1,2,2,3,3] => [[7,5,3,2,1,1],[4,2,1]] [1,1,2,1,1,2,1,1,1,1] => [[3,3,3,3,3,2,2,2,1,1],[2,2,2,2,1,1,1]] [1,1,2,1,1,2,2,2] => [[5,4,3,2,2,2,1,1],[3,2,1,1,1]] [1,1,2,1,1,1,1,2,1,1] => [[3,3,3,2,2,2,2,2,1,1],[2,2,1,1,1,1,1]] [1,1,2,1,1,1,1,1,1,2] => [[3,2,2,2,2,2,2,2,1,1],[1,1,1,1,1,1,1]] [1,1,2,1,1,1,2,3] => [[5,3,2,2,2,2,1,1],[2,1,1,1,1]] [1,1,2,1,2,3,1,1] => [[5,5,5,3,2,2,1,1],[4,4,2,1,1]] [1,1,2,1,2,2,1,2] => [[5,4,4,3,2,2,1,1],[3,3,2,1,1]] [1,1,2,1,2,1,1,3] => [[5,3,3,3,2,2,1,1],[2,2,2,1,1]] [1,1,2,1,3,4] => [[7,4,2,2,1,1],[3,1,1]] [1,1,3,3,1,1,1,1] => [[5,5,5,5,5,3,1,1],[4,4,4,4,2]] [1,1,3,3,2,2] => [[7,6,5,3,1,1],[5,4,2]] [1,1,3,2,1,2,1,1] => [[5,5,5,4,4,3,1,1],[4,4,3,3,2]] [1,1,3,2,1,1,1,2] => [[5,4,4,4,4,3,1,1],[3,3,3,3,2]] [1,1,3,2,2,3] => [[7,5,4,3,1,1],[4,3,2]] [1,1,3,1,1,3,1,1] => [[5,5,5,3,3,3,1,1],[4,4,2,2,2]] [1,1,3,1,1,2,1,2] => [[5,4,4,3,3,3,1,1],[3,3,2,2,2]] [1,1,3,1,1,1,1,3] => [[5,3,3,3,3,3,1,1],[2,2,2,2,2]] [1,1,3,1,2,4] => [[7,4,3,3,1,1],[3,2,2]] [1,1,4,4,1,1] => [[7,7,7,4,1,1],[6,6,3]] [1,1,4,3,1,2] => [[7,6,6,4,1,1],[5,5,3]] [1,1,4,2,1,3] => [[7,5,5,4,1,1],[4,4,3]] [1,1,4,1,1,4] => [[7,4,4,4,1,1],[3,3,3]] [1,1,5,5] => [[9,5,1,1],[4]] [2,2,1,1,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,3,3,2],[2,2,2,2,2,2,2,2,1]] [2,2,1,1,1,1,2,2] => [[5,4,3,3,3,3,3,2],[3,2,2,2,2,2,1]] [2,2,1,1,2,2,1,1] => [[5,5,5,4,3,3,3,2],[4,4,3,2,2,2,1]] [2,2,1,1,2,1,1,2] => [[5,4,4,4,3,3,3,2],[3,3,3,2,2,2,1]] [2,2,1,1,3,3] => [[7,5,3,3,3,2],[4,2,2,2,1]] [2,2,2,2,1,1,1,1] => [[5,5,5,5,5,4,3,2],[4,4,4,4,3,2,1]] [2,2,2,2,2,2] => [[7,6,5,4,3,2],[5,4,3,2,1]] [2,2,2,1,1,2,1,1] => [[5,5,5,4,4,4,3,2],[4,4,3,3,3,2,1]] [2,2,2,1,1,1,1,2] => [[5,4,4,4,4,4,3,2],[3,3,3,3,3,2,1]] [2,2,2,1,2,3] => [[7,5,4,4,3,2],[4,3,3,2,1]] [2,2,3,3,1,1] => [[7,7,7,5,3,2],[6,6,4,2,1]] [2,2,3,2,1,2] => [[7,6,6,5,3,2],[5,5,4,2,1]] [2,2,3,1,1,3] => [[7,5,5,5,3,2],[4,4,4,2,1]] [2,2,4,4] => [[9,6,3,2],[5,2,1]] [2,1,1,2,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,2,2,2],[2,2,2,2,2,2,1,1,1]] [2,1,1,2,1,1,2,2] => [[5,4,3,3,3,2,2,2],[3,2,2,2,1,1,1]] [2,1,1,2,2,2,1,1] => [[5,5,5,4,3,2,2,2],[4,4,3,2,1,1,1]] [2,1,1,2,2,1,1,2] => [[5,4,4,4,3,2,2,2],[3,3,3,2,1,1,1]] [2,1,1,2,3,3] => [[7,5,3,2,2,2],[4,2,1,1,1]] [2,1,1,1,1,2,1,1,1,1] => [[3,3,3,3,3,2,2,2,2,2],[2,2,2,2,1,1,1,1,1]] [2,1,1,1,1,2,2,2] => [[5,4,3,2,2,2,2,2],[3,2,1,1,1,1,1]] [2,1,1,1,1,1,1,2,1,1] => [[3,3,3,2,2,2,2,2,2,2],[2,2,1,1,1,1,1,1,1]] [2,1,1,1,1,1,1,1,1,2] => [[3,2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1,1]] [2,1,1,1,1,1,2,3] => [[5,3,2,2,2,2,2,2],[2,1,1,1,1,1,1]] [2,1,1,1,2,3,1,1] => [[5,5,5,3,2,2,2,2],[4,4,2,1,1,1,1]] [2,1,1,1,2,2,1,2] => [[5,4,4,3,2,2,2,2],[3,3,2,1,1,1,1]] [2,1,1,1,2,1,1,3] => [[5,3,3,3,2,2,2,2],[2,2,2,1,1,1,1]] [2,1,1,1,3,4] => [[7,4,2,2,2,2],[3,1,1,1,1]] [2,1,2,3,1,1,1,1] => [[5,5,5,5,5,3,2,2],[4,4,4,4,2,1,1]] [2,1,2,3,2,2] => [[7,6,5,3,2,2],[5,4,2,1,1]] [2,1,2,2,1,2,1,1] => [[5,5,5,4,4,3,2,2],[4,4,3,3,2,1,1]] [2,1,2,2,1,1,1,2] => [[5,4,4,4,4,3,2,2],[3,3,3,3,2,1,1]] [2,1,2,2,2,3] => [[7,5,4,3,2,2],[4,3,2,1,1]] [2,1,2,1,1,3,1,1] => [[5,5,5,3,3,3,2,2],[4,4,2,2,2,1,1]] [2,1,2,1,1,2,1,2] => [[5,4,4,3,3,3,2,2],[3,3,2,2,2,1,1]] [2,1,2,1,1,1,1,3] => [[5,3,3,3,3,3,2,2],[2,2,2,2,2,1,1]] [2,1,2,1,2,4] => [[7,4,3,3,2,2],[3,2,2,1,1]] [2,1,3,4,1,1] => [[7,7,7,4,2,2],[6,6,3,1,1]] [2,1,3,3,1,2] => [[7,6,6,4,2,2],[5,5,3,1,1]] [2,1,3,2,1,3] => [[7,5,5,4,2,2],[4,4,3,1,1]] [2,1,3,1,1,4] => [[7,4,4,4,2,2],[3,3,3,1,1]] [2,1,4,5] => [[9,5,2,2],[4,1,1]] [3,3,1,1,1,1,1,1] => [[5,5,5,5,5,5,5,3],[4,4,4,4,4,4,2]] [3,3,1,1,2,2] => [[7,6,5,5,5,3],[5,4,4,4,2]] [3,3,2,2,1,1] => [[7,7,7,6,5,3],[6,6,5,4,2]] [3,3,2,1,1,2] => [[7,6,6,6,5,3],[5,5,5,4,2]] [3,3,3,3] => [[9,7,5,3],[6,4,2]] [3,2,1,2,1,1,1,1] => [[5,5,5,5,5,4,4,3],[4,4,4,4,3,3,2]] [3,2,1,2,2,2] => [[7,6,5,4,4,3],[5,4,3,3,2]] [3,2,1,1,1,2,1,1] => [[5,5,5,4,4,4,4,3],[4,4,3,3,3,3,2]] [3,2,1,1,1,1,1,2] => [[5,4,4,4,4,4,4,3],[3,3,3,3,3,3,2]] [3,2,1,1,2,3] => [[7,5,4,4,4,3],[4,3,3,3,2]] [3,2,2,3,1,1] => [[7,7,7,5,4,3],[6,6,4,3,2]] [3,2,2,2,1,2] => [[7,6,6,5,4,3],[5,5,4,3,2]] [3,2,2,1,1,3] => [[7,5,5,5,4,3],[4,4,4,3,2]] [3,2,3,4] => [[9,6,4,3],[5,3,2]] [3,1,1,3,1,1,1,1] => [[5,5,5,5,5,3,3,3],[4,4,4,4,2,2,2]] [3,1,1,3,2,2] => [[7,6,5,3,3,3],[5,4,2,2,2]] [3,1,1,2,1,2,1,1] => [[5,5,5,4,4,3,3,3],[4,4,3,3,2,2,2]] [3,1,1,2,1,1,1,2] => [[5,4,4,4,4,3,3,3],[3,3,3,3,2,2,2]] [3,1,1,2,2,3] => [[7,5,4,3,3,3],[4,3,2,2,2]] [3,1,1,1,1,3,1,1] => [[5,5,5,3,3,3,3,3],[4,4,2,2,2,2,2]] [3,1,1,1,1,2,1,2] => [[5,4,4,3,3,3,3,3],[3,3,2,2,2,2,2]] [3,1,1,1,1,1,1,3] => [[5,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]] [3,1,1,1,2,4] => [[7,4,3,3,3,3],[3,2,2,2,2]] [3,1,2,4,1,1] => [[7,7,7,4,3,3],[6,6,3,2,2]] [3,1,2,3,1,2] => [[7,6,6,4,3,3],[5,5,3,2,2]] [3,1,2,2,1,3] => [[7,5,5,4,3,3],[4,4,3,2,2]] [3,1,2,1,1,4] => [[7,4,4,4,3,3],[3,3,3,2,2]] [3,1,3,5] => [[9,5,3,3],[4,2,2]] [4,4,1,1,1,1] => [[7,7,7,7,7,4],[6,6,6,6,3]] [4,4,2,2] => [[9,8,7,4],[7,6,3]] [4,3,1,2,1,1] => [[7,7,7,6,6,4],[6,6,5,5,3]] [4,3,1,1,1,2] => [[7,6,6,6,6,4],[5,5,5,5,3]] [4,3,2,3] => [[9,7,6,4],[6,5,3]] [4,2,1,3,1,1] => [[7,7,7,5,5,4],[6,6,4,4,3]] [4,2,1,2,1,2] => [[7,6,6,5,5,4],[5,5,4,4,3]] [4,2,1,1,1,3] => [[7,5,5,5,5,4],[4,4,4,4,3]] [4,2,2,4] => [[9,6,5,4],[5,4,3]] [4,1,1,4,1,1] => [[7,7,7,4,4,4],[6,6,3,3,3]] [4,1,1,3,1,2] => [[7,6,6,4,4,4],[5,5,3,3,3]] [4,1,1,2,1,3] => [[7,5,5,4,4,4],[4,4,3,3,3]] [4,1,1,1,1,4] => [[7,4,4,4,4,4],[3,3,3,3,3]] [4,1,2,5] => [[9,5,4,4],[4,3,3]] [5,5,1,1] => [[9,9,9,5],[8,8,4]] [5,4,1,2] => [[9,8,8,5],[7,7,4]] [5,3,1,3] => [[9,7,7,5],[6,6,4]] [5,2,1,4] => [[9,6,6,5],[5,5,4]] [5,1,1,5] => [[9,5,5,5],[4,4,4]] [6,6] => [[11,6],[5]] [1,2,2,2,2,2,1] => [[6,6,5,4,3,2,1],[5,4,3,2,1]] [1,2,2,2,3,2] => [[7,6,4,3,2,1],[5,3,2,1]] [1,2,2,3,3,1] => [[7,7,5,3,2,1],[6,4,2,1]] [1,2,2,3,2,2] => [[7,6,5,3,2,1],[5,4,2,1]] [1,2,2,4,3] => [[8,6,3,2,1],[5,2,1]] [1,2,3,3,2,1] => [[7,7,6,4,2,1],[6,5,3,1]] [1,2,3,4,2] => [[8,7,4,2,1],[6,3,1]] [1,2,3,2,3,1] => [[7,7,5,4,2,1],[6,4,3,1]] [1,2,3,2,2,2] => [[7,6,5,4,2,1],[5,4,3,1]] [1,2,3,3,3] => [[8,6,4,2,1],[5,3,1]] [1,2,4,4,1] => [[8,8,5,2,1],[7,4,1]] [1,2,4,3,2] => [[8,7,5,2,1],[6,4,1]] [1,2,4,2,3] => [[8,6,5,2,1],[5,4,1]] [1,2,5,4] => [[9,6,2,1],[5,1]] [1,3,3,2,2,1] => [[7,7,6,5,3,1],[6,5,4,2]] [1,3,3,3,2] => [[8,7,5,3,1],[6,4,2]] [1,3,4,3,1] => [[8,8,6,3,1],[7,5,2]] [1,3,4,2,2] => [[8,7,6,3,1],[6,5,2]] [1,3,5,3] => [[9,7,3,1],[6,2]] [1,3,2,3,2,1] => [[7,7,6,4,3,1],[6,5,3,2]] [1,3,2,4,2] => [[8,7,4,3,1],[6,3,2]] [1,3,2,2,3,1] => [[7,7,5,4,3,1],[6,4,3,2]] [1,3,2,2,2,2] => [[7,6,5,4,3,1],[5,4,3,2]] [1,3,2,3,3] => [[8,6,4,3,1],[5,3,2]] [1,3,3,4,1] => [[8,8,5,3,1],[7,4,2]] [1,3,3,2,3] => [[8,6,5,3,1],[5,4,2]] [1,3,4,4] => [[9,6,3,1],[5,2]] [1,4,4,2,1] => [[8,8,7,4,1],[7,6,3]] [1,4,5,2] => [[9,8,4,1],[7,3]] [1,4,3,3,1] => [[8,8,6,4,1],[7,5,3]] [1,4,3,2,2] => [[8,7,6,4,1],[6,5,3]] [1,4,4,3] => [[9,7,4,1],[6,3]] [1,4,2,4,1] => [[8,8,5,4,1],[7,4,3]] [1,4,2,3,2] => [[8,7,5,4,1],[6,4,3]] [1,4,2,2,3] => [[8,6,5,4,1],[5,4,3]] ----------------------------------------------------------------------------- Created: Sep 22, 2020 at 11:07 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Sep 22, 2020 at 11:07 by Martin Rubey