***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 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. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000186 ----------------------------------------------------------------------------- Collection: Gelfand-Tsetlin patterns ----------------------------------------------------------------------------- Description: The sum of the first row in a Gelfand-Tsetlin pattern. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(GT): return sum(GT[0]) ----------------------------------------------------------------------------- Statistic values: [[1]] => 1 [[2]] => 2 [[3]] => 3 [[4]] => 4 [[1,0],[0]] => 1 [[1,0],[1]] => 1 [[2,0],[0]] => 2 [[2,0],[1]] => 2 [[2,0],[2]] => 2 [[1,1],[1]] => 2 [[3,0],[0]] => 3 [[3,0],[1]] => 3 [[3,0],[2]] => 3 [[3,0],[3]] => 3 [[2,1],[1]] => 3 [[2,1],[2]] => 3 [[4,0],[0]] => 4 [[4,0],[1]] => 4 [[4,0],[2]] => 4 [[4,0],[3]] => 4 [[4,0],[4]] => 4 [[3,1],[1]] => 4 [[3,1],[2]] => 4 [[3,1],[3]] => 4 [[2,2],[2]] => 4 [[4,1],[1]] => 5 [[4,1],[2]] => 5 [[4,1],[3]] => 5 [[4,1],[4]] => 5 [[3,2],[2]] => 5 [[3,2],[3]] => 5 [[4,2],[2]] => 6 [[4,2],[3]] => 6 [[4,2],[4]] => 6 [[3,3],[3]] => 6 [[4,3],[3]] => 7 [[4,3],[4]] => 7 [[4,4],[4]] => 8 [[1,0,0],[0,0],[0]] => 1 [[1,0,0],[1,0],[0]] => 1 [[1,0,0],[1,0],[1]] => 1 [[2,0,0],[0,0],[0]] => 2 [[2,0,0],[1,0],[0]] => 2 [[2,0,0],[1,0],[1]] => 2 [[2,0,0],[2,0],[0]] => 2 [[2,0,0],[2,0],[1]] => 2 [[2,0,0],[2,0],[2]] => 2 [[1,1,0],[1,0],[0]] => 2 [[1,1,0],[1,0],[1]] => 2 [[1,1,0],[1,1],[1]] => 2 [[3,0,0],[0,0],[0]] => 3 [[3,0,0],[1,0],[0]] => 3 [[3,0,0],[1,0],[1]] => 3 [[3,0,0],[2,0],[0]] => 3 [[3,0,0],[2,0],[1]] => 3 [[3,0,0],[2,0],[2]] => 3 [[3,0,0],[3,0],[0]] => 3 [[3,0,0],[3,0],[1]] => 3 [[3,0,0],[3,0],[2]] => 3 [[3,0,0],[3,0],[3]] => 3 [[2,1,0],[1,0],[0]] => 3 [[2,1,0],[1,0],[1]] => 3 [[2,1,0],[1,1],[1]] => 3 [[2,1,0],[2,0],[0]] => 3 [[2,1,0],[2,0],[1]] => 3 [[2,1,0],[2,0],[2]] => 3 [[2,1,0],[2,1],[1]] => 3 [[2,1,0],[2,1],[2]] => 3 [[1,1,1],[1,1],[1]] => 3 [[4,0,0],[0,0],[0]] => 4 [[4,0,0],[1,0],[0]] => 4 [[4,0,0],[1,0],[1]] => 4 [[4,0,0],[2,0],[0]] => 4 [[4,0,0],[2,0],[1]] => 4 [[4,0,0],[2,0],[2]] => 4 [[4,0,0],[3,0],[0]] => 4 [[4,0,0],[3,0],[1]] => 4 [[4,0,0],[3,0],[2]] => 4 [[4,0,0],[3,0],[3]] => 4 [[4,0,0],[4,0],[0]] => 4 [[4,0,0],[4,0],[1]] => 4 [[4,0,0],[4,0],[2]] => 4 [[4,0,0],[4,0],[3]] => 4 [[4,0,0],[4,0],[4]] => 4 [[3,1,0],[1,0],[0]] => 4 [[3,1,0],[1,0],[1]] => 4 [[3,1,0],[1,1],[1]] => 4 [[3,1,0],[2,0],[0]] => 4 [[3,1,0],[2,0],[1]] => 4 [[3,1,0],[2,0],[2]] => 4 [[3,1,0],[2,1],[1]] => 4 [[3,1,0],[2,1],[2]] => 4 [[3,1,0],[3,0],[0]] => 4 [[3,1,0],[3,0],[1]] => 4 [[3,1,0],[3,0],[2]] => 4 [[3,1,0],[3,0],[3]] => 4 [[3,1,0],[3,1],[1]] => 4 [[3,1,0],[3,1],[2]] => 4 [[3,1,0],[3,1],[3]] => 4 [[2,2,0],[2,0],[0]] => 4 [[2,2,0],[2,0],[1]] => 4 [[2,2,0],[2,0],[2]] => 4 [[2,2,0],[2,1],[1]] => 4 [[2,2,0],[2,1],[2]] => 4 [[2,2,0],[2,2],[2]] => 4 [[2,1,1],[1,1],[1]] => 4 [[2,1,1],[2,1],[1]] => 4 [[2,1,1],[2,1],[2]] => 4 [[4,1,0],[1,0],[0]] => 5 [[4,1,0],[1,0],[1]] => 5 [[4,1,0],[1,1],[1]] => 5 [[4,1,0],[2,0],[0]] => 5 [[4,1,0],[2,0],[1]] => 5 [[4,1,0],[2,0],[2]] => 5 [[4,1,0],[2,1],[1]] => 5 [[4,1,0],[2,1],[2]] => 5 [[4,1,0],[3,0],[0]] => 5 [[4,1,0],[3,0],[1]] => 5 [[4,1,0],[3,0],[2]] => 5 [[4,1,0],[3,0],[3]] => 5 [[4,1,0],[3,1],[1]] => 5 [[4,1,0],[3,1],[2]] => 5 [[4,1,0],[3,1],[3]] => 5 [[4,1,0],[4,0],[0]] => 5 [[4,1,0],[4,0],[1]] => 5 [[4,1,0],[4,0],[2]] => 5 [[4,1,0],[4,0],[3]] => 5 [[4,1,0],[4,0],[4]] => 5 [[4,1,0],[4,1],[1]] => 5 [[4,1,0],[4,1],[2]] => 5 [[4,1,0],[4,1],[3]] => 5 [[4,1,0],[4,1],[4]] => 5 [[3,2,0],[2,0],[0]] => 5 [[3,2,0],[2,0],[1]] => 5 [[3,2,0],[2,0],[2]] => 5 [[3,2,0],[2,1],[1]] => 5 [[3,2,0],[2,1],[2]] => 5 [[3,2,0],[2,2],[2]] => 5 [[3,2,0],[3,0],[0]] => 5 [[3,2,0],[3,0],[1]] => 5 [[3,2,0],[3,0],[2]] => 5 [[3,2,0],[3,0],[3]] => 5 [[3,2,0],[3,1],[1]] => 5 [[3,2,0],[3,1],[2]] => 5 [[3,2,0],[3,1],[3]] => 5 [[3,2,0],[3,2],[2]] => 5 [[3,2,0],[3,2],[3]] => 5 [[3,1,1],[1,1],[1]] => 5 [[3,1,1],[2,1],[1]] => 5 [[3,1,1],[2,1],[2]] => 5 [[3,1,1],[3,1],[1]] => 5 [[3,1,1],[3,1],[2]] => 5 [[3,1,1],[3,1],[3]] => 5 [[2,2,1],[2,1],[1]] => 5 [[2,2,1],[2,1],[2]] => 5 [[2,2,1],[2,2],[2]] => 5 [[4,2,0],[2,0],[0]] => 6 [[4,2,0],[2,0],[1]] => 6 [[4,2,0],[2,0],[2]] => 6 [[4,2,0],[2,1],[1]] => 6 [[4,2,0],[2,1],[2]] => 6 [[4,2,0],[2,2],[2]] => 6 [[4,2,0],[3,0],[0]] => 6 [[4,2,0],[3,0],[1]] => 6 [[4,2,0],[3,0],[2]] => 6 [[4,2,0],[3,0],[3]] => 6 [[4,2,0],[3,1],[1]] => 6 [[4,2,0],[3,1],[2]] => 6 [[4,2,0],[3,1],[3]] => 6 [[4,2,0],[3,2],[2]] => 6 [[4,2,0],[3,2],[3]] => 6 [[4,2,0],[4,0],[0]] => 6 [[4,2,0],[4,0],[1]] => 6 [[4,2,0],[4,0],[2]] => 6 [[4,2,0],[4,0],[3]] => 6 [[4,2,0],[4,0],[4]] => 6 [[4,2,0],[4,1],[1]] => 6 [[4,2,0],[4,1],[2]] => 6 [[4,2,0],[4,1],[3]] => 6 [[4,2,0],[4,1],[4]] => 6 [[4,2,0],[4,2],[2]] => 6 [[4,2,0],[4,2],[3]] => 6 [[4,2,0],[4,2],[4]] => 6 [[4,1,1],[1,1],[1]] => 6 [[4,1,1],[2,1],[1]] => 6 [[4,1,1],[2,1],[2]] => 6 [[4,1,1],[3,1],[1]] => 6 [[4,1,1],[3,1],[2]] => 6 [[4,1,1],[3,1],[3]] => 6 [[4,1,1],[4,1],[1]] => 6 [[4,1,1],[4,1],[2]] => 6 [[4,1,1],[4,1],[3]] => 6 [[4,1,1],[4,1],[4]] => 6 [[3,3,0],[3,0],[0]] => 6 [[3,3,0],[3,0],[1]] => 6 [[3,3,0],[3,0],[2]] => 6 [[3,3,0],[3,0],[3]] => 6 [[3,3,0],[3,1],[1]] => 6 [[3,3,0],[3,1],[2]] => 6 [[3,3,0],[3,1],[3]] => 6 [[3,3,0],[3,2],[2]] => 6 [[3,3,0],[3,2],[3]] => 6 [[3,3,0],[3,3],[3]] => 6 [[3,2,1],[2,1],[1]] => 6 [[3,2,1],[2,1],[2]] => 6 [[3,2,1],[2,2],[2]] => 6 [[3,2,1],[3,1],[1]] => 6 [[3,2,1],[3,1],[2]] => 6 [[3,2,1],[3,1],[3]] => 6 [[3,2,1],[3,2],[2]] => 6 [[3,2,1],[3,2],[3]] => 6 [[2,2,2],[2,2],[2]] => 6 [[4,3,0],[4,2],[4]] => 7 [[4,3,0],[4,1],[4]] => 7 [[4,3,0],[4,0],[4]] => 7 [[4,3,0],[4,2],[3]] => 7 [[4,3,0],[3,3],[3]] => 7 [[4,3,0],[4,1],[3]] => 7 [[4,3,0],[3,2],[3]] => 7 [[4,3,0],[4,0],[3]] => 7 [[4,3,0],[3,1],[3]] => 7 [[4,3,0],[3,0],[3]] => 7 [[4,3,0],[4,2],[2]] => 7 [[4,3,0],[4,1],[2]] => 7 [[4,3,0],[3,2],[2]] => 7 [[4,3,0],[4,0],[2]] => 7 [[4,3,0],[3,1],[2]] => 7 [[4,3,0],[3,0],[2]] => 7 [[4,3,0],[4,1],[1]] => 7 [[4,3,0],[4,0],[1]] => 7 [[4,3,0],[3,1],[1]] => 7 [[4,3,0],[3,0],[1]] => 7 [[4,3,0],[4,0],[0]] => 7 [[4,3,0],[3,0],[0]] => 7 [[4,2,1],[4,2],[4]] => 7 [[4,2,1],[4,1],[4]] => 7 [[4,2,1],[4,2],[3]] => 7 [[4,2,1],[4,1],[3]] => 7 [[4,2,1],[3,2],[3]] => 7 [[4,2,1],[3,1],[3]] => 7 [[4,2,1],[4,2],[2]] => 7 [[4,2,1],[4,1],[2]] => 7 [[4,2,1],[3,2],[2]] => 7 [[4,2,1],[3,1],[2]] => 7 [[4,2,1],[2,2],[2]] => 7 [[4,2,1],[2,1],[2]] => 7 [[4,2,1],[4,1],[1]] => 7 [[4,2,1],[3,1],[1]] => 7 [[4,2,1],[2,1],[1]] => 7 [[3,3,1],[3,3],[3]] => 7 [[3,3,1],[3,2],[3]] => 7 [[3,3,1],[3,1],[3]] => 7 [[3,3,1],[3,2],[2]] => 7 [[3,3,1],[3,1],[2]] => 7 [[3,3,1],[3,1],[1]] => 7 [[3,2,2],[3,2],[3]] => 7 [[3,2,2],[3,2],[2]] => 7 [[3,2,2],[2,2],[2]] => 7 [[1,0,0,0],[0,0,0],[0,0],[0]] => 1 [[1,0,0,0],[1,0,0],[0,0],[0]] => 1 [[1,0,0,0],[1,0,0],[1,0],[0]] => 1 [[1,0,0,0],[1,0,0],[1,0],[1]] => 1 [[2,0,0,0],[0,0,0],[0,0],[0]] => 2 [[2,0,0,0],[1,0,0],[0,0],[0]] => 2 [[2,0,0,0],[1,0,0],[1,0],[0]] => 2 [[2,0,0,0],[1,0,0],[1,0],[1]] => 2 [[2,0,0,0],[2,0,0],[0,0],[0]] => 2 [[2,0,0,0],[2,0,0],[1,0],[0]] => 2 [[2,0,0,0],[2,0,0],[1,0],[1]] => 2 [[2,0,0,0],[2,0,0],[2,0],[0]] => 2 [[2,0,0,0],[2,0,0],[2,0],[1]] => 2 [[2,0,0,0],[2,0,0],[2,0],[2]] => 2 [[1,1,0,0],[1,0,0],[0,0],[0]] => 2 [[1,1,0,0],[1,0,0],[1,0],[0]] => 2 [[1,1,0,0],[1,0,0],[1,0],[1]] => 2 [[1,1,0,0],[1,1,0],[1,0],[0]] => 2 [[1,1,0,0],[1,1,0],[1,0],[1]] => 2 [[1,1,0,0],[1,1,0],[1,1],[1]] => 2 [[3,0,0,0],[0,0,0],[0,0],[0]] => 3 [[3,0,0,0],[1,0,0],[0,0],[0]] => 3 [[3,0,0,0],[1,0,0],[1,0],[0]] => 3 [[3,0,0,0],[1,0,0],[1,0],[1]] => 3 [[3,0,0,0],[2,0,0],[0,0],[0]] => 3 [[3,0,0,0],[2,0,0],[1,0],[0]] => 3 [[3,0,0,0],[2,0,0],[1,0],[1]] => 3 [[3,0,0,0],[2,0,0],[2,0],[0]] => 3 [[3,0,0,0],[2,0,0],[2,0],[1]] => 3 [[3,0,0,0],[2,0,0],[2,0],[2]] => 3 [[3,0,0,0],[3,0,0],[0,0],[0]] => 3 [[3,0,0,0],[3,0,0],[1,0],[0]] => 3 [[3,0,0,0],[3,0,0],[1,0],[1]] => 3 [[3,0,0,0],[3,0,0],[2,0],[0]] => 3 [[3,0,0,0],[3,0,0],[2,0],[1]] => 3 [[3,0,0,0],[3,0,0],[2,0],[2]] => 3 [[3,0,0,0],[3,0,0],[3,0],[0]] => 3 [[3,0,0,0],[3,0,0],[3,0],[1]] => 3 [[3,0,0,0],[3,0,0],[3,0],[2]] => 3 [[3,0,0,0],[3,0,0],[3,0],[3]] => 3 [[2,1,0,0],[1,0,0],[0,0],[0]] => 3 [[2,1,0,0],[1,0,0],[1,0],[0]] => 3 [[2,1,0,0],[1,0,0],[1,0],[1]] => 3 [[2,1,0,0],[1,1,0],[1,0],[0]] => 3 [[2,1,0,0],[1,1,0],[1,0],[1]] => 3 [[2,1,0,0],[1,1,0],[1,1],[1]] => 3 [[2,1,0,0],[2,0,0],[0,0],[0]] => 3 [[2,1,0,0],[2,0,0],[1,0],[0]] => 3 [[2,1,0,0],[2,0,0],[1,0],[1]] => 3 [[2,1,0,0],[2,0,0],[2,0],[0]] => 3 [[2,1,0,0],[2,0,0],[2,0],[1]] => 3 [[2,1,0,0],[2,0,0],[2,0],[2]] => 3 [[2,1,0,0],[2,1,0],[1,0],[0]] => 3 [[2,1,0,0],[2,1,0],[1,0],[1]] => 3 [[2,1,0,0],[2,1,0],[1,1],[1]] => 3 [[2,1,0,0],[2,1,0],[2,0],[0]] => 3 [[2,1,0,0],[2,1,0],[2,0],[1]] => 3 [[2,1,0,0],[2,1,0],[2,0],[2]] => 3 [[2,1,0,0],[2,1,0],[2,1],[1]] => 3 [[2,1,0,0],[2,1,0],[2,1],[2]] => 3 [[1,1,1,0],[1,1,0],[1,0],[0]] => 3 [[1,1,1,0],[1,1,0],[1,0],[1]] => 3 [[1,1,1,0],[1,1,0],[1,1],[1]] => 3 [[1,1,1,0],[1,1,1],[1,1],[1]] => 3 [[4,0,0,0],[0,0,0],[0,0],[0]] => 4 [[4,0,0,0],[1,0,0],[0,0],[0]] => 4 [[4,0,0,0],[1,0,0],[1,0],[0]] => 4 [[4,0,0,0],[1,0,0],[1,0],[1]] => 4 [[4,0,0,0],[2,0,0],[0,0],[0]] => 4 [[4,0,0,0],[2,0,0],[1,0],[0]] => 4 [[4,0,0,0],[2,0,0],[1,0],[1]] => 4 [[4,0,0,0],[2,0,0],[2,0],[0]] => 4 [[4,0,0,0],[2,0,0],[2,0],[1]] => 4 [[4,0,0,0],[2,0,0],[2,0],[2]] => 4 [[4,0,0,0],[3,0,0],[0,0],[0]] => 4 [[4,0,0,0],[3,0,0],[1,0],[0]] => 4 [[4,0,0,0],[3,0,0],[1,0],[1]] => 4 [[4,0,0,0],[3,0,0],[2,0],[0]] => 4 [[4,0,0,0],[3,0,0],[2,0],[1]] => 4 [[4,0,0,0],[3,0,0],[2,0],[2]] => 4 [[4,0,0,0],[3,0,0],[3,0],[0]] => 4 [[4,0,0,0],[3,0,0],[3,0],[1]] => 4 [[4,0,0,0],[3,0,0],[3,0],[2]] => 4 [[4,0,0,0],[3,0,0],[3,0],[3]] => 4 [[4,0,0,0],[4,0,0],[0,0],[0]] => 4 [[4,0,0,0],[4,0,0],[1,0],[0]] => 4 [[4,0,0,0],[4,0,0],[1,0],[1]] => 4 [[4,0,0,0],[4,0,0],[2,0],[0]] => 4 [[4,0,0,0],[4,0,0],[2,0],[1]] => 4 [[4,0,0,0],[4,0,0],[2,0],[2]] => 4 [[4,0,0,0],[4,0,0],[3,0],[0]] => 4 [[4,0,0,0],[4,0,0],[3,0],[1]] => 4 [[4,0,0,0],[4,0,0],[3,0],[2]] => 4 [[4,0,0,0],[4,0,0],[3,0],[3]] => 4 [[4,0,0,0],[4,0,0],[4,0],[0]] => 4 [[4,0,0,0],[4,0,0],[4,0],[1]] => 4 [[4,0,0,0],[4,0,0],[4,0],[2]] => 4 [[4,0,0,0],[4,0,0],[4,0],[3]] => 4 [[4,0,0,0],[4,0,0],[4,0],[4]] => 4 [[3,1,0,0],[1,0,0],[0,0],[0]] => 4 [[3,1,0,0],[1,0,0],[1,0],[0]] => 4 [[3,1,0,0],[1,0,0],[1,0],[1]] => 4 [[3,1,0,0],[1,1,0],[1,0],[0]] => 4 [[3,1,0,0],[1,1,0],[1,0],[1]] => 4 [[3,1,0,0],[1,1,0],[1,1],[1]] => 4 [[3,1,0,0],[2,0,0],[0,0],[0]] => 4 [[3,1,0,0],[2,0,0],[1,0],[0]] => 4 [[3,1,0,0],[2,0,0],[1,0],[1]] => 4 [[3,1,0,0],[2,0,0],[2,0],[0]] => 4 [[3,1,0,0],[2,0,0],[2,0],[1]] => 4 [[3,1,0,0],[2,0,0],[2,0],[2]] => 4 [[3,1,0,0],[2,1,0],[1,0],[0]] => 4 [[3,1,0,0],[2,1,0],[1,0],[1]] => 4 [[3,1,0,0],[2,1,0],[1,1],[1]] => 4 [[3,1,0,0],[2,1,0],[2,0],[0]] => 4 [[3,1,0,0],[2,1,0],[2,0],[1]] => 4 [[3,1,0,0],[2,1,0],[2,0],[2]] => 4 [[3,1,0,0],[2,1,0],[2,1],[1]] => 4 [[3,1,0,0],[2,1,0],[2,1],[2]] => 4 [[3,1,0,0],[3,0,0],[0,0],[0]] => 4 [[3,1,0,0],[3,0,0],[1,0],[0]] => 4 [[3,1,0,0],[3,0,0],[1,0],[1]] => 4 [[3,1,0,0],[3,0,0],[2,0],[0]] => 4 [[3,1,0,0],[3,0,0],[2,0],[1]] => 4 [[3,1,0,0],[3,0,0],[2,0],[2]] => 4 [[3,1,0,0],[3,0,0],[3,0],[0]] => 4 [[3,1,0,0],[3,0,0],[3,0],[1]] => 4 [[3,1,0,0],[3,0,0],[3,0],[2]] => 4 [[3,1,0,0],[3,0,0],[3,0],[3]] => 4 [[3,1,0,0],[3,1,0],[1,0],[0]] => 4 [[3,1,0,0],[3,1,0],[1,0],[1]] => 4 [[3,1,0,0],[3,1,0],[1,1],[1]] => 4 [[3,1,0,0],[3,1,0],[2,0],[0]] => 4 [[3,1,0,0],[3,1,0],[2,0],[1]] => 4 [[3,1,0,0],[3,1,0],[2,0],[2]] => 4 [[3,1,0,0],[3,1,0],[2,1],[1]] => 4 [[3,1,0,0],[3,1,0],[2,1],[2]] => 4 [[3,1,0,0],[3,1,0],[3,0],[0]] => 4 [[3,1,0,0],[3,1,0],[3,0],[1]] => 4 [[3,1,0,0],[3,1,0],[3,0],[2]] => 4 [[3,1,0,0],[3,1,0],[3,0],[3]] => 4 [[3,1,0,0],[3,1,0],[3,1],[1]] => 4 [[3,1,0,0],[3,1,0],[3,1],[2]] => 4 [[3,1,0,0],[3,1,0],[3,1],[3]] => 4 [[2,2,0,0],[2,0,0],[0,0],[0]] => 4 [[2,2,0,0],[2,0,0],[1,0],[0]] => 4 [[2,2,0,0],[2,0,0],[1,0],[1]] => 4 [[2,2,0,0],[2,0,0],[2,0],[0]] => 4 [[2,2,0,0],[2,0,0],[2,0],[1]] => 4 [[2,2,0,0],[2,0,0],[2,0],[2]] => 4 [[2,2,0,0],[2,1,0],[1,0],[0]] => 4 [[2,2,0,0],[2,1,0],[1,0],[1]] => 4 [[2,2,0,0],[2,1,0],[1,1],[1]] => 4 [[2,2,0,0],[2,1,0],[2,0],[0]] => 4 [[2,2,0,0],[2,1,0],[2,0],[1]] => 4 [[2,2,0,0],[2,1,0],[2,0],[2]] => 4 [[2,2,0,0],[2,1,0],[2,1],[1]] => 4 [[2,2,0,0],[2,1,0],[2,1],[2]] => 4 [[2,2,0,0],[2,2,0],[2,0],[0]] => 4 [[2,2,0,0],[2,2,0],[2,0],[1]] => 4 [[2,2,0,0],[2,2,0],[2,0],[2]] => 4 [[2,2,0,0],[2,2,0],[2,1],[1]] => 4 [[2,2,0,0],[2,2,0],[2,1],[2]] => 4 [[2,2,0,0],[2,2,0],[2,2],[2]] => 4 [[2,1,1,0],[1,1,0],[1,0],[0]] => 4 [[2,1,1,0],[1,1,0],[1,0],[1]] => 4 [[2,1,1,0],[1,1,0],[1,1],[1]] => 4 [[2,1,1,0],[1,1,1],[1,1],[1]] => 4 [[2,1,1,0],[2,1,0],[1,0],[0]] => 4 [[2,1,1,0],[2,1,0],[1,0],[1]] => 4 [[2,1,1,0],[2,1,0],[1,1],[1]] => 4 [[2,1,1,0],[2,1,0],[2,0],[0]] => 4 [[2,1,1,0],[2,1,0],[2,0],[1]] => 4 [[2,1,1,0],[2,1,0],[2,0],[2]] => 4 [[2,1,1,0],[2,1,0],[2,1],[1]] => 4 [[2,1,1,0],[2,1,0],[2,1],[2]] => 4 [[2,1,1,0],[2,1,1],[1,1],[1]] => 4 [[2,1,1,0],[2,1,1],[2,1],[1]] => 4 [[2,1,1,0],[2,1,1],[2,1],[2]] => 4 [[1,1,1,1],[1,1,1],[1,1],[1]] => 4 [[4,1,0,0],[1,0,0],[0,0],[0]] => 5 [[4,1,0,0],[1,0,0],[1,0],[0]] => 5 [[4,1,0,0],[1,0,0],[1,0],[1]] => 5 [[4,1,0,0],[1,1,0],[1,0],[0]] => 5 [[4,1,0,0],[1,1,0],[1,0],[1]] => 5 [[4,1,0,0],[1,1,0],[1,1],[1]] => 5 [[4,1,0,0],[2,0,0],[0,0],[0]] => 5 [[4,1,0,0],[2,0,0],[1,0],[0]] => 5 [[4,1,0,0],[2,0,0],[1,0],[1]] => 5 [[4,1,0,0],[2,0,0],[2,0],[0]] => 5 [[4,1,0,0],[2,0,0],[2,0],[1]] => 5 [[4,1,0,0],[2,0,0],[2,0],[2]] => 5 [[4,1,0,0],[2,1,0],[1,0],[0]] => 5 [[4,1,0,0],[2,1,0],[1,0],[1]] => 5 [[4,1,0,0],[2,1,0],[1,1],[1]] => 5 [[4,1,0,0],[2,1,0],[2,0],[0]] => 5 [[4,1,0,0],[2,1,0],[2,0],[1]] => 5 [[4,1,0,0],[2,1,0],[2,0],[2]] => 5 [[4,1,0,0],[2,1,0],[2,1],[1]] => 5 [[4,1,0,0],[2,1,0],[2,1],[2]] => 5 [[4,1,0,0],[3,0,0],[0,0],[0]] => 5 [[4,1,0,0],[3,0,0],[1,0],[0]] => 5 [[4,1,0,0],[3,0,0],[1,0],[1]] => 5 [[4,1,0,0],[3,0,0],[2,0],[0]] => 5 [[4,1,0,0],[3,0,0],[2,0],[1]] => 5 [[4,1,0,0],[3,0,0],[2,0],[2]] => 5 [[4,1,0,0],[3,0,0],[3,0],[0]] => 5 [[4,1,0,0],[3,0,0],[3,0],[1]] => 5 [[4,1,0,0],[3,0,0],[3,0],[2]] => 5 [[4,1,0,0],[3,0,0],[3,0],[3]] => 5 [[4,1,0,0],[3,1,0],[1,0],[0]] => 5 [[4,1,0,0],[3,1,0],[1,0],[1]] => 5 [[4,1,0,0],[3,1,0],[1,1],[1]] => 5 [[4,1,0,0],[3,1,0],[2,0],[0]] => 5 [[4,1,0,0],[3,1,0],[2,0],[1]] => 5 [[4,1,0,0],[3,1,0],[2,0],[2]] => 5 [[4,1,0,0],[3,1,0],[2,1],[1]] => 5 [[4,1,0,0],[3,1,0],[2,1],[2]] => 5 [[4,1,0,0],[3,1,0],[3,0],[0]] => 5 [[4,1,0,0],[3,1,0],[3,0],[1]] => 5 [[4,1,0,0],[3,1,0],[3,0],[2]] => 5 [[4,1,0,0],[3,1,0],[3,0],[3]] => 5 [[4,1,0,0],[3,1,0],[3,1],[1]] => 5 [[4,1,0,0],[3,1,0],[3,1],[2]] => 5 [[4,1,0,0],[3,1,0],[3,1],[3]] => 5 [[4,1,0,0],[4,0,0],[0,0],[0]] => 5 [[4,1,0,0],[4,0,0],[1,0],[0]] => 5 [[4,1,0,0],[4,0,0],[1,0],[1]] => 5 [[4,1,0,0],[4,0,0],[2,0],[0]] => 5 [[4,1,0,0],[4,0,0],[2,0],[1]] => 5 [[4,1,0,0],[4,0,0],[2,0],[2]] => 5 [[4,1,0,0],[4,0,0],[3,0],[0]] => 5 [[4,1,0,0],[4,0,0],[3,0],[1]] => 5 [[4,1,0,0],[4,0,0],[3,0],[2]] => 5 [[4,1,0,0],[4,0,0],[3,0],[3]] => 5 [[4,1,0,0],[4,0,0],[4,0],[0]] => 5 [[4,1,0,0],[4,0,0],[4,0],[1]] => 5 [[4,1,0,0],[4,0,0],[4,0],[2]] => 5 [[4,1,0,0],[4,0,0],[4,0],[3]] => 5 [[4,1,0,0],[4,0,0],[4,0],[4]] => 5 [[4,1,0,0],[4,1,0],[1,0],[0]] => 5 [[4,1,0,0],[4,1,0],[1,0],[1]] => 5 [[4,1,0,0],[4,1,0],[1,1],[1]] => 5 [[4,1,0,0],[4,1,0],[2,0],[0]] => 5 [[4,1,0,0],[4,1,0],[2,0],[1]] => 5 [[4,1,0,0],[4,1,0],[2,0],[2]] => 5 [[4,1,0,0],[4,1,0],[2,1],[1]] => 5 [[4,1,0,0],[4,1,0],[2,1],[2]] => 5 [[4,1,0,0],[4,1,0],[3,0],[0]] => 5 [[4,1,0,0],[4,1,0],[3,0],[1]] => 5 [[4,1,0,0],[4,1,0],[3,0],[2]] => 5 [[4,1,0,0],[4,1,0],[3,0],[3]] => 5 [[4,1,0,0],[4,1,0],[3,1],[1]] => 5 [[4,1,0,0],[4,1,0],[3,1],[2]] => 5 [[4,1,0,0],[4,1,0],[3,1],[3]] => 5 [[4,1,0,0],[4,1,0],[4,0],[0]] => 5 [[4,1,0,0],[4,1,0],[4,0],[1]] => 5 [[4,1,0,0],[4,1,0],[4,0],[2]] => 5 [[4,1,0,0],[4,1,0],[4,0],[3]] => 5 [[4,1,0,0],[4,1,0],[4,0],[4]] => 5 [[4,1,0,0],[4,1,0],[4,1],[1]] => 5 [[4,1,0,0],[4,1,0],[4,1],[2]] => 5 [[4,1,0,0],[4,1,0],[4,1],[3]] => 5 [[4,1,0,0],[4,1,0],[4,1],[4]] => 5 [[3,2,0,0],[2,0,0],[0,0],[0]] => 5 [[3,2,0,0],[2,0,0],[1,0],[0]] => 5 [[3,2,0,0],[2,0,0],[1,0],[1]] => 5 [[3,2,0,0],[2,0,0],[2,0],[0]] => 5 [[3,2,0,0],[2,0,0],[2,0],[1]] => 5 [[3,2,0,0],[2,0,0],[2,0],[2]] => 5 [[3,2,0,0],[2,1,0],[1,0],[0]] => 5 [[3,2,0,0],[2,1,0],[1,0],[1]] => 5 [[3,2,0,0],[2,1,0],[1,1],[1]] => 5 [[3,2,0,0],[2,1,0],[2,0],[0]] => 5 [[3,2,0,0],[2,1,0],[2,0],[1]] => 5 [[3,2,0,0],[2,1,0],[2,0],[2]] => 5 [[3,2,0,0],[2,1,0],[2,1],[1]] => 5 [[3,2,0,0],[2,1,0],[2,1],[2]] => 5 [[3,2,0,0],[2,2,0],[2,0],[0]] => 5 [[3,2,0,0],[2,2,0],[2,0],[1]] => 5 [[3,2,0,0],[2,2,0],[2,0],[2]] => 5 [[3,2,0,0],[2,2,0],[2,1],[1]] => 5 [[3,2,0,0],[2,2,0],[2,1],[2]] => 5 [[3,2,0,0],[2,2,0],[2,2],[2]] => 5 [[3,2,0,0],[3,0,0],[0,0],[0]] => 5 [[3,2,0,0],[3,0,0],[1,0],[0]] => 5 [[3,2,0,0],[3,0,0],[1,0],[1]] => 5 [[3,2,0,0],[3,0,0],[2,0],[0]] => 5 [[3,2,0,0],[3,0,0],[2,0],[1]] => 5 [[3,2,0,0],[3,0,0],[2,0],[2]] => 5 [[3,2,0,0],[3,0,0],[3,0],[0]] => 5 [[3,2,0,0],[3,0,0],[3,0],[1]] => 5 [[3,2,0,0],[3,0,0],[3,0],[2]] => 5 [[3,2,0,0],[3,0,0],[3,0],[3]] => 5 [[3,2,0,0],[3,1,0],[1,0],[0]] => 5 [[3,2,0,0],[3,1,0],[1,0],[1]] => 5 [[3,2,0,0],[3,1,0],[1,1],[1]] => 5 [[3,2,0,0],[3,1,0],[2,0],[0]] => 5 [[3,2,0,0],[3,1,0],[2,0],[1]] => 5 [[3,2,0,0],[3,1,0],[2,0],[2]] => 5 [[3,2,0,0],[3,1,0],[2,1],[1]] => 5 [[3,2,0,0],[3,1,0],[2,1],[2]] => 5 [[3,2,0,0],[3,1,0],[3,0],[0]] => 5 [[3,2,0,0],[3,1,0],[3,0],[1]] => 5 [[3,2,0,0],[3,1,0],[3,0],[2]] => 5 [[3,2,0,0],[3,1,0],[3,0],[3]] => 5 [[3,2,0,0],[3,1,0],[3,1],[1]] => 5 [[3,2,0,0],[3,1,0],[3,1],[2]] => 5 [[3,2,0,0],[3,1,0],[3,1],[3]] => 5 [[3,2,0,0],[3,2,0],[2,0],[0]] => 5 [[3,2,0,0],[3,2,0],[2,0],[1]] => 5 [[3,2,0,0],[3,2,0],[2,0],[2]] => 5 [[3,2,0,0],[3,2,0],[2,1],[1]] => 5 [[3,2,0,0],[3,2,0],[2,1],[2]] => 5 [[3,2,0,0],[3,2,0],[2,2],[2]] => 5 [[3,2,0,0],[3,2,0],[3,0],[0]] => 5 [[3,2,0,0],[3,2,0],[3,0],[1]] => 5 [[3,2,0,0],[3,2,0],[3,0],[2]] => 5 [[3,2,0,0],[3,2,0],[3,0],[3]] => 5 [[3,2,0,0],[3,2,0],[3,1],[1]] => 5 [[3,2,0,0],[3,2,0],[3,1],[2]] => 5 [[3,2,0,0],[3,2,0],[3,1],[3]] => 5 [[3,2,0,0],[3,2,0],[3,2],[2]] => 5 [[3,2,0,0],[3,2,0],[3,2],[3]] => 5 [[3,1,1,0],[1,1,0],[1,0],[0]] => 5 [[3,1,1,0],[1,1,0],[1,0],[1]] => 5 [[3,1,1,0],[1,1,0],[1,1],[1]] => 5 [[3,1,1,0],[1,1,1],[1,1],[1]] => 5 [[3,1,1,0],[2,1,0],[1,0],[0]] => 5 [[3,1,1,0],[2,1,0],[1,0],[1]] => 5 [[3,1,1,0],[2,1,0],[1,1],[1]] => 5 [[3,1,1,0],[2,1,0],[2,0],[0]] => 5 [[3,1,1,0],[2,1,0],[2,0],[1]] => 5 [[3,1,1,0],[2,1,0],[2,0],[2]] => 5 [[3,1,1,0],[2,1,0],[2,1],[1]] => 5 [[3,1,1,0],[2,1,0],[2,1],[2]] => 5 [[3,1,1,0],[2,1,1],[1,1],[1]] => 5 [[3,1,1,0],[2,1,1],[2,1],[1]] => 5 [[3,1,1,0],[2,1,1],[2,1],[2]] => 5 [[3,1,1,0],[3,1,0],[1,0],[0]] => 5 [[3,1,1,0],[3,1,0],[1,0],[1]] => 5 [[3,1,1,0],[3,1,0],[1,1],[1]] => 5 [[3,1,1,0],[3,1,0],[2,0],[0]] => 5 [[3,1,1,0],[3,1,0],[2,0],[1]] => 5 [[3,1,1,0],[3,1,0],[2,0],[2]] => 5 [[3,1,1,0],[3,1,0],[2,1],[1]] => 5 [[3,1,1,0],[3,1,0],[2,1],[2]] => 5 [[3,1,1,0],[3,1,0],[3,0],[0]] => 5 [[3,1,1,0],[3,1,0],[3,0],[1]] => 5 [[3,1,1,0],[3,1,0],[3,0],[2]] => 5 [[3,1,1,0],[3,1,0],[3,0],[3]] => 5 [[3,1,1,0],[3,1,0],[3,1],[1]] => 5 [[3,1,1,0],[3,1,0],[3,1],[2]] => 5 [[3,1,1,0],[3,1,0],[3,1],[3]] => 5 [[3,1,1,0],[3,1,1],[1,1],[1]] => 5 [[3,1,1,0],[3,1,1],[2,1],[1]] => 5 [[3,1,1,0],[3,1,1],[2,1],[2]] => 5 [[3,1,1,0],[3,1,1],[3,1],[1]] => 5 [[3,1,1,0],[3,1,1],[3,1],[2]] => 5 [[3,1,1,0],[3,1,1],[3,1],[3]] => 5 [[2,2,1,0],[2,1,0],[1,0],[0]] => 5 [[2,2,1,0],[2,1,0],[1,0],[1]] => 5 [[2,2,1,0],[2,1,0],[1,1],[1]] => 5 [[2,2,1,0],[2,1,0],[2,0],[0]] => 5 [[2,2,1,0],[2,1,0],[2,0],[1]] => 5 [[2,2,1,0],[2,1,0],[2,0],[2]] => 5 [[2,2,1,0],[2,1,0],[2,1],[1]] => 5 [[2,2,1,0],[2,1,0],[2,1],[2]] => 5 [[2,2,1,0],[2,1,1],[1,1],[1]] => 5 [[2,2,1,0],[2,1,1],[2,1],[1]] => 5 [[2,2,1,0],[2,1,1],[2,1],[2]] => 5 [[2,2,1,0],[2,2,0],[2,0],[0]] => 5 [[2,2,1,0],[2,2,0],[2,0],[1]] => 5 [[2,2,1,0],[2,2,0],[2,0],[2]] => 5 [[2,2,1,0],[2,2,0],[2,1],[1]] => 5 [[2,2,1,0],[2,2,0],[2,1],[2]] => 5 [[2,2,1,0],[2,2,0],[2,2],[2]] => 5 [[2,2,1,0],[2,2,1],[2,1],[1]] => 5 [[2,2,1,0],[2,2,1],[2,1],[2]] => 5 [[2,2,1,0],[2,2,1],[2,2],[2]] => 5 [[2,1,1,1],[1,1,1],[1,1],[1]] => 5 [[2,1,1,1],[2,1,1],[1,1],[1]] => 5 [[2,1,1,1],[2,1,1],[2,1],[1]] => 5 [[2,1,1,1],[2,1,1],[2,1],[2]] => 5 [[4,1,1,0],[4,1,0],[4,1],[4]] => 6 [[4,1,1,0],[4,1,0],[4,0],[4]] => 6 [[4,1,1,0],[4,1,0],[4,1],[3]] => 6 [[4,1,1,0],[4,1,0],[4,0],[3]] => 6 [[4,1,1,0],[4,1,0],[3,1],[3]] => 6 [[4,1,1,0],[3,1,1],[3,1],[3]] => 6 [[4,1,1,0],[3,1,0],[3,1],[3]] => 6 [[4,1,1,0],[4,1,0],[3,0],[3]] => 6 [[4,1,1,0],[3,1,0],[3,0],[3]] => 6 [[4,1,1,0],[4,1,0],[4,1],[2]] => 6 [[4,1,1,0],[4,1,0],[4,0],[2]] => 6 [[4,1,1,0],[4,1,0],[3,1],[2]] => 6 [[4,1,1,0],[3,1,1],[3,1],[2]] => 6 [[4,1,1,0],[3,1,0],[3,1],[2]] => 6 [[4,1,1,0],[4,1,0],[3,0],[2]] => 6 [[4,1,1,0],[4,1,0],[2,1],[2]] => 6 [[4,1,1,0],[3,1,1],[2,1],[2]] => 6 [[4,1,1,0],[3,1,0],[3,0],[2]] => 6 [[4,1,1,0],[3,1,0],[2,1],[2]] => 6 [[4,1,1,0],[2,1,1],[2,1],[2]] => 6 [[4,1,1,0],[2,1,0],[2,1],[2]] => 6 [[4,1,1,0],[4,1,0],[2,0],[2]] => 6 [[4,1,1,0],[3,1,0],[2,0],[2]] => 6 [[4,1,1,0],[2,1,0],[2,0],[2]] => 6 [[4,1,1,0],[4,1,0],[4,1],[1]] => 6 [[4,1,1,0],[4,1,0],[4,0],[1]] => 6 [[4,1,1,0],[4,1,0],[3,1],[1]] => 6 [[4,1,1,0],[3,1,1],[3,1],[1]] => 6 [[4,1,1,0],[3,1,0],[3,1],[1]] => 6 [[4,1,1,0],[4,1,0],[3,0],[1]] => 6 [[4,1,1,0],[4,1,0],[2,1],[1]] => 6 [[4,1,1,0],[3,1,1],[2,1],[1]] => 6 [[4,1,1,0],[3,1,0],[3,0],[1]] => 6 [[4,1,1,0],[3,1,0],[2,1],[1]] => 6 [[4,1,1,0],[2,1,1],[2,1],[1]] => 6 [[4,1,1,0],[2,1,0],[2,1],[1]] => 6 [[4,1,1,0],[4,1,0],[2,0],[1]] => 6 [[4,1,1,0],[4,1,0],[1,1],[1]] => 6 [[4,1,1,0],[3,1,1],[1,1],[1]] => 6 [[4,1,1,0],[3,1,0],[2,0],[1]] => 6 [[4,1,1,0],[3,1,0],[1,1],[1]] => 6 [[4,1,1,0],[2,1,1],[1,1],[1]] => 6 [[4,1,1,0],[2,1,0],[2,0],[1]] => 6 [[4,1,1,0],[2,1,0],[1,1],[1]] => 6 [[4,1,1,0],[1,1,1],[1,1],[1]] => 6 [[4,1,1,0],[1,1,0],[1,1],[1]] => 6 [[4,1,1,0],[4,1,0],[1,0],[1]] => 6 [[4,1,1,0],[3,1,0],[1,0],[1]] => 6 [[4,1,1,0],[2,1,0],[1,0],[1]] => 6 [[4,1,1,0],[1,1,0],[1,0],[1]] => 6 [[4,1,1,0],[4,1,0],[4,0],[0]] => 6 [[4,1,1,0],[4,1,0],[3,0],[0]] => 6 [[4,1,1,0],[3,1,0],[3,0],[0]] => 6 [[4,1,1,0],[4,1,0],[2,0],[0]] => 6 [[4,1,1,0],[3,1,0],[2,0],[0]] => 6 [[4,1,1,0],[2,1,0],[2,0],[0]] => 6 [[4,1,1,0],[4,1,0],[1,0],[0]] => 6 [[4,1,1,0],[3,1,0],[1,0],[0]] => 6 [[4,1,1,0],[2,1,0],[1,0],[0]] => 6 [[4,1,1,0],[1,1,0],[1,0],[0]] => 6 [[3,3,0,0],[3,2,0],[3,2],[3]] => 6 [[3,3,0,0],[3,2,0],[3,1],[3]] => 6 [[3,3,0,0],[3,1,0],[3,1],[3]] => 6 [[3,3,0,0],[3,2,0],[3,0],[3]] => 6 [[3,3,0,0],[3,1,0],[3,0],[3]] => 6 [[3,3,0,0],[3,0,0],[3,0],[3]] => 6 [[3,3,0,0],[3,2,0],[3,2],[2]] => 6 [[3,3,0,0],[3,2,0],[3,1],[2]] => 6 [[3,3,0,0],[3,2,0],[2,2],[2]] => 6 [[3,3,0,0],[3,1,0],[3,1],[2]] => 6 [[3,3,0,0],[3,2,0],[3,0],[2]] => 6 [[3,3,0,0],[3,2,0],[2,1],[2]] => 6 [[3,3,0,0],[3,1,0],[3,0],[2]] => 6 [[3,3,0,0],[3,1,0],[2,1],[2]] => 6 [[3,3,0,0],[3,0,0],[3,0],[2]] => 6 [[3,3,0,0],[3,2,0],[2,0],[2]] => 6 [[3,3,0,0],[3,1,0],[2,0],[2]] => 6 [[3,3,0,0],[3,0,0],[2,0],[2]] => 6 [[3,3,0,0],[3,2,0],[3,1],[1]] => 6 [[3,3,0,0],[3,1,0],[3,1],[1]] => 6 [[3,3,0,0],[3,2,0],[3,0],[1]] => 6 [[3,3,0,0],[3,2,0],[2,1],[1]] => 6 [[3,3,0,0],[3,1,0],[3,0],[1]] => 6 [[3,3,0,0],[3,1,0],[2,1],[1]] => 6 [[3,3,0,0],[3,0,0],[3,0],[1]] => 6 [[3,3,0,0],[3,2,0],[2,0],[1]] => 6 [[3,3,0,0],[3,1,0],[2,0],[1]] => 6 [[3,3,0,0],[3,1,0],[1,1],[1]] => 6 [[3,3,0,0],[3,0,0],[2,0],[1]] => 6 [[3,3,0,0],[3,1,0],[1,0],[1]] => 6 [[3,3,0,0],[3,0,0],[1,0],[1]] => 6 [[3,3,0,0],[3,2,0],[3,0],[0]] => 6 [[3,3,0,0],[3,1,0],[3,0],[0]] => 6 [[3,3,0,0],[3,0,0],[3,0],[0]] => 6 [[3,3,0,0],[3,2,0],[2,0],[0]] => 6 [[3,3,0,0],[3,1,0],[2,0],[0]] => 6 [[3,3,0,0],[3,0,0],[2,0],[0]] => 6 [[3,3,0,0],[3,1,0],[1,0],[0]] => 6 [[3,3,0,0],[3,0,0],[1,0],[0]] => 6 [[3,3,0,0],[3,0,0],[0,0],[0]] => 6 [[3,2,1,0],[3,2,0],[3,2],[3]] => 6 [[3,2,1,0],[3,2,0],[3,1],[3]] => 6 [[3,2,1,0],[3,1,1],[3,1],[3]] => 6 [[3,2,1,0],[3,1,0],[3,1],[3]] => 6 [[3,2,1,0],[3,2,0],[3,0],[3]] => 6 [[3,2,1,0],[3,1,0],[3,0],[3]] => 6 [[3,2,1,0],[3,2,0],[3,2],[2]] => 6 [[3,2,1,0],[3,2,0],[3,1],[2]] => 6 [[3,2,1,0],[3,1,1],[3,1],[2]] => 6 [[3,2,1,0],[3,2,0],[2,2],[2]] => 6 [[3,2,1,0],[2,2,1],[2,2],[2]] => 6 [[3,2,1,0],[3,1,0],[3,1],[2]] => 6 [[3,2,1,0],[2,2,0],[2,2],[2]] => 6 [[3,2,1,0],[3,2,0],[3,0],[2]] => 6 [[3,2,1,0],[3,2,0],[2,1],[2]] => 6 [[3,2,1,0],[3,1,1],[2,1],[2]] => 6 [[3,2,1,0],[2,2,1],[2,1],[2]] => 6 [[3,2,1,0],[3,1,0],[3,0],[2]] => 6 [[3,2,1,0],[3,1,0],[2,1],[2]] => 6 [[3,2,1,0],[2,2,0],[2,1],[2]] => 6 [[3,2,1,0],[2,1,1],[2,1],[2]] => 6 [[3,2,1,0],[2,1,0],[2,1],[2]] => 6 [[3,2,1,0],[3,2,0],[2,0],[2]] => 6 [[3,2,1,0],[3,1,0],[2,0],[2]] => 6 [[3,2,1,0],[2,2,0],[2,0],[2]] => 6 [[3,2,1,0],[2,1,0],[2,0],[2]] => 6 [[3,2,1,0],[3,2,0],[3,1],[1]] => 6 [[3,2,1,0],[3,1,1],[3,1],[1]] => 6 [[3,2,1,0],[3,1,0],[3,1],[1]] => 6 [[3,2,1,0],[3,2,0],[3,0],[1]] => 6 [[3,2,1,0],[3,2,0],[2,1],[1]] => 6 [[3,2,1,0],[3,1,1],[2,1],[1]] => 6 [[3,2,1,0],[2,2,1],[2,1],[1]] => 6 [[3,2,1,0],[3,1,0],[3,0],[1]] => 6 [[3,2,1,0],[3,1,0],[2,1],[1]] => 6 [[3,2,1,0],[2,2,0],[2,1],[1]] => 6 [[3,2,1,0],[2,1,1],[2,1],[1]] => 6 [[3,2,1,0],[2,1,0],[2,1],[1]] => 6 [[3,2,1,0],[3,2,0],[2,0],[1]] => 6 [[3,2,1,0],[3,1,1],[1,1],[1]] => 6 [[3,2,1,0],[3,1,0],[2,0],[1]] => 6 [[3,2,1,0],[2,2,0],[2,0],[1]] => 6 [[3,2,1,0],[3,1,0],[1,1],[1]] => 6 [[3,2,1,0],[2,1,1],[1,1],[1]] => 6 [[3,2,1,0],[2,1,0],[2,0],[1]] => 6 [[3,2,1,0],[2,1,0],[1,1],[1]] => 6 [[3,2,1,0],[3,1,0],[1,0],[1]] => 6 [[3,2,1,0],[2,1,0],[1,0],[1]] => 6 [[3,2,1,0],[3,2,0],[3,0],[0]] => 6 [[3,2,1,0],[3,1,0],[3,0],[0]] => 6 [[3,2,1,0],[3,2,0],[2,0],[0]] => 6 [[3,2,1,0],[3,1,0],[2,0],[0]] => 6 [[3,2,1,0],[2,2,0],[2,0],[0]] => 6 [[3,2,1,0],[2,1,0],[2,0],[0]] => 6 [[3,2,1,0],[3,1,0],[1,0],[0]] => 6 [[3,2,1,0],[2,1,0],[1,0],[0]] => 6 [[3,1,1,1],[3,1,1],[3,1],[3]] => 6 [[3,1,1,1],[3,1,1],[3,1],[2]] => 6 [[3,1,1,1],[3,1,1],[2,1],[2]] => 6 [[3,1,1,1],[2,1,1],[2,1],[2]] => 6 [[3,1,1,1],[3,1,1],[3,1],[1]] => 6 [[3,1,1,1],[3,1,1],[2,1],[1]] => 6 [[3,1,1,1],[2,1,1],[2,1],[1]] => 6 [[3,1,1,1],[3,1,1],[1,1],[1]] => 6 [[3,1,1,1],[2,1,1],[1,1],[1]] => 6 [[3,1,1,1],[1,1,1],[1,1],[1]] => 6 [[2,2,2,0],[2,2,1],[2,2],[2]] => 6 [[2,2,2,0],[2,2,0],[2,2],[2]] => 6 [[2,2,2,0],[2,2,1],[2,1],[2]] => 6 [[2,2,2,0],[2,2,0],[2,1],[2]] => 6 [[2,2,2,0],[2,2,0],[2,0],[2]] => 6 [[2,2,2,0],[2,2,1],[2,1],[1]] => 6 [[2,2,2,0],[2,2,0],[2,1],[1]] => 6 [[2,2,2,0],[2,2,0],[2,0],[1]] => 6 [[2,2,2,0],[2,2,0],[2,0],[0]] => 6 [[2,2,1,1],[2,2,1],[2,2],[2]] => 6 [[2,2,1,1],[2,2,1],[2,1],[2]] => 6 [[2,2,1,1],[2,1,1],[2,1],[2]] => 6 [[2,2,1,1],[2,2,1],[2,1],[1]] => 6 [[2,2,1,1],[2,1,1],[2,1],[1]] => 6 [[2,2,1,1],[2,1,1],[1,1],[1]] => 6 [[0]] => 0 [[0,0],[0]] => 0 [[0,0,0],[0,0],[0]] => 0 [[3,3,2],[3,2],[2]] => 8 [[3,3,2],[3,2],[3]] => 8 [[3,3,2],[3,3],[3]] => 8 [[3,3,3],[3,3],[3]] => 9 [[4,2,2],[2,2],[2]] => 8 [[4,2,2],[3,2],[2]] => 8 [[4,2,2],[3,2],[3]] => 8 [[4,2,2],[4,2],[2]] => 8 [[4,2,2],[4,2],[3]] => 8 [[4,2,2],[4,2],[4]] => 8 [[4,3,0],[4,3],[3]] => 7 [[4,3,0],[4,3],[4]] => 7 [[4,3,1],[3,1],[1]] => 8 [[4,3,1],[3,1],[2]] => 8 [[4,3,1],[3,1],[3]] => 8 [[4,3,1],[3,2],[2]] => 8 [[4,3,1],[3,2],[3]] => 8 [[4,3,1],[3,3],[3]] => 8 [[4,3,1],[4,1],[1]] => 8 [[4,3,1],[4,1],[2]] => 8 [[4,3,1],[4,1],[3]] => 8 [[4,3,1],[4,1],[4]] => 8 [[4,3,1],[4,2],[2]] => 8 [[4,3,1],[4,2],[3]] => 8 [[4,3,1],[4,2],[4]] => 8 [[4,3,1],[4,3],[3]] => 8 [[4,3,1],[4,3],[4]] => 8 [[4,3,2],[3,2],[2]] => 9 [[4,3,2],[3,2],[3]] => 9 [[4,3,2],[3,3],[3]] => 9 [[4,3,2],[4,2],[2]] => 9 [[4,3,2],[4,2],[3]] => 9 [[4,3,2],[4,2],[4]] => 9 [[4,3,2],[4,3],[3]] => 9 [[4,3,2],[4,3],[4]] => 9 [[4,3,3],[3,3],[3]] => 10 [[4,3,3],[4,3],[3]] => 10 [[4,3,3],[4,3],[4]] => 10 [[4,4,0],[4,0],[0]] => 8 [[4,4,0],[4,0],[1]] => 8 [[4,4,0],[4,0],[2]] => 8 [[4,4,0],[4,0],[3]] => 8 [[4,4,0],[4,0],[4]] => 8 [[4,4,0],[4,1],[1]] => 8 [[4,4,0],[4,1],[2]] => 8 [[4,4,0],[4,1],[3]] => 8 [[4,4,0],[4,1],[4]] => 8 [[4,4,0],[4,2],[2]] => 8 [[4,4,0],[4,2],[3]] => 8 [[4,4,0],[4,2],[4]] => 8 [[4,4,0],[4,3],[3]] => 8 [[4,4,0],[4,3],[4]] => 8 [[4,4,0],[4,4],[4]] => 8 [[4,4,1],[4,1],[1]] => 9 [[4,4,1],[4,1],[2]] => 9 [[4,4,1],[4,1],[3]] => 9 [[4,4,1],[4,1],[4]] => 9 [[4,4,1],[4,2],[2]] => 9 [[4,4,1],[4,2],[3]] => 9 [[4,4,1],[4,2],[4]] => 9 [[4,4,1],[4,3],[3]] => 9 [[4,4,1],[4,3],[4]] => 9 [[4,4,1],[4,4],[4]] => 9 [[4,4,2],[4,2],[2]] => 10 [[4,4,2],[4,2],[3]] => 10 [[4,4,2],[4,2],[4]] => 10 [[4,4,2],[4,3],[3]] => 10 [[4,4,2],[4,3],[4]] => 10 [[4,4,2],[4,4],[4]] => 10 [[4,4,3],[4,3],[3]] => 11 [[4,4,3],[4,3],[4]] => 11 [[4,4,3],[4,4],[4]] => 11 [[4,4,4],[4,4],[4]] => 12 [[0,0,0,0],[0,0,0],[0,0],[0]] => 0 [[2,2,2,0],[2,2,2],[2,2],[2]] => 6 [[2,2,2,1],[2,2,1],[2,1],[1]] => 7 [[2,2,2,1],[2,2,1],[2,1],[2]] => 7 [[2,2,2,1],[2,2,1],[2,2],[2]] => 7 [[2,2,2,1],[2,2,2],[2,2],[2]] => 7 [[2,2,2,2],[2,2,2],[2,2],[2]] => 8 [[3,2,1,0],[3,2,1],[2,1],[1]] => 6 [[3,2,1,0],[3,2,1],[2,1],[2]] => 6 [[3,2,1,0],[3,2,1],[2,2],[2]] => 6 [[3,2,1,0],[3,2,1],[3,1],[1]] => 6 [[3,2,1,0],[3,2,1],[3,1],[2]] => 6 [[3,2,1,0],[3,2,1],[3,1],[3]] => 6 [[3,2,1,0],[3,2,1],[3,2],[2]] => 6 [[3,2,1,0],[3,2,1],[3,2],[3]] => 6 [[3,2,1,1],[2,1,1],[1,1],[1]] => 7 [[3,2,1,1],[2,1,1],[2,1],[1]] => 7 [[3,2,1,1],[2,1,1],[2,1],[2]] => 7 [[3,2,1,1],[2,2,1],[2,1],[1]] => 7 [[3,2,1,1],[2,2,1],[2,1],[2]] => 7 [[3,2,1,1],[2,2,1],[2,2],[2]] => 7 [[3,2,1,1],[3,1,1],[1,1],[1]] => 7 [[3,2,1,1],[3,1,1],[2,1],[1]] => 7 [[3,2,1,1],[3,1,1],[2,1],[2]] => 7 [[3,2,1,1],[3,1,1],[3,1],[1]] => 7 [[3,2,1,1],[3,1,1],[3,1],[2]] => 7 [[3,2,1,1],[3,1,1],[3,1],[3]] => 7 [[3,2,1,1],[3,2,1],[2,1],[1]] => 7 [[3,2,1,1],[3,2,1],[2,1],[2]] => 7 [[3,2,1,1],[3,2,1],[2,2],[2]] => 7 [[3,2,1,1],[3,2,1],[3,1],[1]] => 7 [[3,2,1,1],[3,2,1],[3,1],[2]] => 7 [[3,2,1,1],[3,2,1],[3,1],[3]] => 7 [[3,2,1,1],[3,2,1],[3,2],[2]] => 7 [[3,2,1,1],[3,2,1],[3,2],[3]] => 7 [[3,2,2,0],[2,2,0],[2,0],[0]] => 7 [[3,2,2,0],[2,2,0],[2,0],[1]] => 7 [[3,2,2,0],[2,2,0],[2,0],[2]] => 7 [[3,2,2,0],[2,2,0],[2,1],[1]] => 7 [[3,2,2,0],[2,2,0],[2,1],[2]] => 7 [[3,2,2,0],[2,2,0],[2,2],[2]] => 7 [[3,2,2,0],[2,2,1],[2,1],[1]] => 7 [[3,2,2,0],[2,2,1],[2,1],[2]] => 7 [[3,2,2,0],[2,2,1],[2,2],[2]] => 7 [[3,2,2,0],[2,2,2],[2,2],[2]] => 7 [[3,2,2,0],[3,2,0],[2,0],[0]] => 7 [[3,2,2,0],[3,2,0],[2,0],[1]] => 7 [[3,2,2,0],[3,2,0],[2,0],[2]] => 7 [[3,2,2,0],[3,2,0],[2,1],[1]] => 7 [[3,2,2,0],[3,2,0],[2,1],[2]] => 7 [[3,2,2,0],[3,2,0],[2,2],[2]] => 7 [[3,2,2,0],[3,2,0],[3,0],[0]] => 7 [[3,2,2,0],[3,2,0],[3,0],[1]] => 7 [[3,2,2,0],[3,2,0],[3,0],[2]] => 7 [[3,2,2,0],[3,2,0],[3,0],[3]] => 7 [[3,2,2,0],[3,2,0],[3,1],[1]] => 7 [[3,2,2,0],[3,2,0],[3,1],[2]] => 7 [[3,2,2,0],[3,2,0],[3,1],[3]] => 7 [[3,2,2,0],[3,2,0],[3,2],[2]] => 7 [[3,2,2,0],[3,2,0],[3,2],[3]] => 7 [[3,2,2,0],[3,2,1],[2,1],[1]] => 7 [[3,2,2,0],[3,2,1],[2,1],[2]] => 7 [[3,2,2,0],[3,2,1],[2,2],[2]] => 7 [[3,2,2,0],[3,2,1],[3,1],[1]] => 7 [[3,2,2,0],[3,2,1],[3,1],[2]] => 7 [[3,2,2,0],[3,2,1],[3,1],[3]] => 7 [[3,2,2,0],[3,2,1],[3,2],[2]] => 7 [[3,2,2,0],[3,2,1],[3,2],[3]] => 7 [[3,2,2,0],[3,2,2],[2,2],[2]] => 7 [[3,2,2,0],[3,2,2],[3,2],[2]] => 7 [[3,2,2,0],[3,2,2],[3,2],[3]] => 7 [[3,2,2,1],[2,2,1],[2,1],[1]] => 8 [[3,2,2,1],[2,2,1],[2,1],[2]] => 8 [[3,2,2,1],[2,2,1],[2,2],[2]] => 8 [[3,2,2,1],[2,2,2],[2,2],[2]] => 8 [[3,2,2,1],[3,2,1],[2,1],[1]] => 8 [[3,2,2,1],[3,2,1],[2,1],[2]] => 8 [[3,2,2,1],[3,2,1],[2,2],[2]] => 8 [[3,2,2,1],[3,2,1],[3,1],[1]] => 8 [[3,2,2,1],[3,2,1],[3,1],[2]] => 8 [[3,2,2,1],[3,2,1],[3,1],[3]] => 8 [[3,2,2,1],[3,2,1],[3,2],[2]] => 8 [[3,2,2,1],[3,2,1],[3,2],[3]] => 8 [[3,2,2,1],[3,2,2],[2,2],[2]] => 8 [[3,2,2,1],[3,2,2],[3,2],[2]] => 8 [[3,2,2,1],[3,2,2],[3,2],[3]] => 8 [[3,2,2,2],[2,2,2],[2,2],[2]] => 9 [[3,2,2,2],[3,2,2],[2,2],[2]] => 9 [[3,2,2,2],[3,2,2],[3,2],[2]] => 9 [[3,2,2,2],[3,2,2],[3,2],[3]] => 9 [[3,3,0,0],[3,3,0],[3,0],[0]] => 6 [[3,3,0,0],[3,3,0],[3,0],[1]] => 6 [[3,3,0,0],[3,3,0],[3,0],[2]] => 6 [[3,3,0,0],[3,3,0],[3,0],[3]] => 6 [[3,3,0,0],[3,3,0],[3,1],[1]] => 6 [[3,3,0,0],[3,3,0],[3,1],[2]] => 6 [[3,3,0,0],[3,3,0],[3,1],[3]] => 6 [[3,3,0,0],[3,3,0],[3,2],[2]] => 6 [[3,3,0,0],[3,3,0],[3,2],[3]] => 6 [[3,3,0,0],[3,3,0],[3,3],[3]] => 6 [[3,3,1,0],[3,1,0],[1,0],[0]] => 7 [[3,3,1,0],[3,1,0],[1,0],[1]] => 7 [[3,3,1,0],[3,1,0],[1,1],[1]] => 7 [[3,3,1,0],[3,1,0],[2,0],[0]] => 7 [[3,3,1,0],[3,1,0],[2,0],[1]] => 7 [[3,3,1,0],[3,1,0],[2,0],[2]] => 7 [[3,3,1,0],[3,1,0],[2,1],[1]] => 7 [[3,3,1,0],[3,1,0],[2,1],[2]] => 7 [[3,3,1,0],[3,1,0],[3,0],[0]] => 7 [[3,3,1,0],[3,1,0],[3,0],[1]] => 7 [[3,3,1,0],[3,1,0],[3,0],[2]] => 7 [[3,3,1,0],[3,1,0],[3,0],[3]] => 7 [[3,3,1,0],[3,1,0],[3,1],[1]] => 7 [[3,3,1,0],[3,1,0],[3,1],[2]] => 7 [[3,3,1,0],[3,1,0],[3,1],[3]] => 7 [[3,3,1,0],[3,1,1],[1,1],[1]] => 7 [[3,3,1,0],[3,1,1],[2,1],[1]] => 7 [[3,3,1,0],[3,1,1],[2,1],[2]] => 7 [[3,3,1,0],[3,1,1],[3,1],[1]] => 7 [[3,3,1,0],[3,1,1],[3,1],[2]] => 7 [[3,3,1,0],[3,1,1],[3,1],[3]] => 7 [[3,3,1,0],[3,2,0],[2,0],[0]] => 7 [[3,3,1,0],[3,2,0],[2,0],[1]] => 7 [[3,3,1,0],[3,2,0],[2,0],[2]] => 7 [[3,3,1,0],[3,2,0],[2,1],[1]] => 7 [[3,3,1,0],[3,2,0],[2,1],[2]] => 7 [[3,3,1,0],[3,2,0],[2,2],[2]] => 7 [[3,3,1,0],[3,2,0],[3,0],[0]] => 7 [[3,3,1,0],[3,2,0],[3,0],[1]] => 7 [[3,3,1,0],[3,2,0],[3,0],[2]] => 7 [[3,3,1,0],[3,2,0],[3,0],[3]] => 7 [[3,3,1,0],[3,2,0],[3,1],[1]] => 7 [[3,3,1,0],[3,2,0],[3,1],[2]] => 7 [[3,3,1,0],[3,2,0],[3,1],[3]] => 7 [[3,3,1,0],[3,2,0],[3,2],[2]] => 7 [[3,3,1,0],[3,2,0],[3,2],[3]] => 7 [[3,3,1,0],[3,2,1],[2,1],[1]] => 7 [[3,3,1,0],[3,2,1],[2,1],[2]] => 7 [[3,3,1,0],[3,2,1],[2,2],[2]] => 7 [[3,3,1,0],[3,2,1],[3,1],[1]] => 7 [[3,3,1,0],[3,2,1],[3,1],[2]] => 7 [[3,3,1,0],[3,2,1],[3,1],[3]] => 7 [[3,3,1,0],[3,2,1],[3,2],[2]] => 7 [[3,3,1,0],[3,2,1],[3,2],[3]] => 7 [[3,3,1,0],[3,3,0],[3,0],[0]] => 7 [[3,3,1,0],[3,3,0],[3,0],[1]] => 7 [[3,3,1,0],[3,3,0],[3,0],[2]] => 7 [[3,3,1,0],[3,3,0],[3,0],[3]] => 7 [[3,3,1,0],[3,3,0],[3,1],[1]] => 7 [[3,3,1,0],[3,3,0],[3,1],[2]] => 7 [[3,3,1,0],[3,3,0],[3,1],[3]] => 7 [[3,3,1,0],[3,3,0],[3,2],[2]] => 7 [[3,3,1,0],[3,3,0],[3,2],[3]] => 7 [[3,3,1,0],[3,3,0],[3,3],[3]] => 7 [[3,3,1,0],[3,3,1],[3,1],[1]] => 7 [[3,3,1,0],[3,3,1],[3,1],[2]] => 7 [[3,3,1,0],[3,3,1],[3,1],[3]] => 7 [[3,3,1,0],[3,3,1],[3,2],[2]] => 7 [[3,3,1,0],[3,3,1],[3,2],[3]] => 7 [[3,3,1,0],[3,3,1],[3,3],[3]] => 7 [[3,3,1,1],[3,1,1],[1,1],[1]] => 8 [[3,3,1,1],[3,1,1],[2,1],[1]] => 8 [[3,3,1,1],[3,1,1],[2,1],[2]] => 8 [[3,3,1,1],[3,1,1],[3,1],[1]] => 8 [[3,3,1,1],[3,1,1],[3,1],[2]] => 8 [[3,3,1,1],[3,1,1],[3,1],[3]] => 8 [[3,3,1,1],[3,2,1],[2,1],[1]] => 8 [[3,3,1,1],[3,2,1],[2,1],[2]] => 8 [[3,3,1,1],[3,2,1],[2,2],[2]] => 8 [[3,3,1,1],[3,2,1],[3,1],[1]] => 8 [[3,3,1,1],[3,2,1],[3,1],[2]] => 8 [[3,3,1,1],[3,2,1],[3,1],[3]] => 8 [[3,3,1,1],[3,2,1],[3,2],[2]] => 8 [[3,3,1,1],[3,2,1],[3,2],[3]] => 8 [[3,3,1,1],[3,3,1],[3,1],[1]] => 8 [[3,3,1,1],[3,3,1],[3,1],[2]] => 8 [[3,3,1,1],[3,3,1],[3,1],[3]] => 8 [[3,3,1,1],[3,3,1],[3,2],[2]] => 8 [[3,3,1,1],[3,3,1],[3,2],[3]] => 8 [[3,3,1,1],[3,3,1],[3,3],[3]] => 8 [[3,3,2,0],[3,2,0],[2,0],[0]] => 8 [[3,3,2,0],[3,2,0],[2,0],[1]] => 8 [[3,3,2,0],[3,2,0],[2,0],[2]] => 8 [[3,3,2,0],[3,2,0],[2,1],[1]] => 8 [[3,3,2,0],[3,2,0],[2,1],[2]] => 8 [[3,3,2,0],[3,2,0],[2,2],[2]] => 8 [[3,3,2,0],[3,2,0],[3,0],[0]] => 8 [[3,3,2,0],[3,2,0],[3,0],[1]] => 8 [[3,3,2,0],[3,2,0],[3,0],[2]] => 8 [[3,3,2,0],[3,2,0],[3,0],[3]] => 8 [[3,3,2,0],[3,2,0],[3,1],[1]] => 8 [[3,3,2,0],[3,2,0],[3,1],[2]] => 8 [[3,3,2,0],[3,2,0],[3,1],[3]] => 8 [[3,3,2,0],[3,2,0],[3,2],[2]] => 8 [[3,3,2,0],[3,2,0],[3,2],[3]] => 8 [[3,3,2,0],[3,2,1],[2,1],[1]] => 8 [[3,3,2,0],[3,2,1],[2,1],[2]] => 8 [[3,3,2,0],[3,2,1],[2,2],[2]] => 8 [[3,3,2,0],[3,2,1],[3,1],[1]] => 8 [[3,3,2,0],[3,2,1],[3,1],[2]] => 8 [[3,3,2,0],[3,2,1],[3,1],[3]] => 8 [[3,3,2,0],[3,2,1],[3,2],[2]] => 8 [[3,3,2,0],[3,2,1],[3,2],[3]] => 8 [[3,3,2,0],[3,2,2],[2,2],[2]] => 8 [[3,3,2,0],[3,2,2],[3,2],[2]] => 8 [[3,3,2,0],[3,2,2],[3,2],[3]] => 8 [[3,3,2,0],[3,3,0],[3,0],[0]] => 8 [[3,3,2,0],[3,3,0],[3,0],[1]] => 8 [[3,3,2,0],[3,3,0],[3,0],[2]] => 8 [[3,3,2,0],[3,3,0],[3,0],[3]] => 8 [[3,3,2,0],[3,3,0],[3,1],[1]] => 8 [[3,3,2,0],[3,3,0],[3,1],[2]] => 8 [[3,3,2,0],[3,3,0],[3,1],[3]] => 8 [[3,3,2,0],[3,3,0],[3,2],[2]] => 8 [[3,3,2,0],[3,3,0],[3,2],[3]] => 8 [[3,3,2,0],[3,3,0],[3,3],[3]] => 8 [[3,3,2,0],[3,3,1],[3,1],[1]] => 8 [[3,3,2,0],[3,3,1],[3,1],[2]] => 8 [[3,3,2,0],[3,3,1],[3,1],[3]] => 8 [[3,3,2,0],[3,3,1],[3,2],[2]] => 8 [[3,3,2,0],[3,3,1],[3,2],[3]] => 8 [[3,3,2,0],[3,3,1],[3,3],[3]] => 8 [[3,3,2,0],[3,3,2],[3,2],[2]] => 8 [[3,3,2,0],[3,3,2],[3,2],[3]] => 8 [[3,3,2,0],[3,3,2],[3,3],[3]] => 8 [[3,3,2,1],[3,2,1],[2,1],[1]] => 9 [[3,3,2,1],[3,2,1],[2,1],[2]] => 9 [[3,3,2,1],[3,2,1],[2,2],[2]] => 9 [[3,3,2,1],[3,2,1],[3,1],[1]] => 9 [[3,3,2,1],[3,2,1],[3,1],[2]] => 9 [[3,3,2,1],[3,2,1],[3,1],[3]] => 9 [[3,3,2,1],[3,2,1],[3,2],[2]] => 9 [[3,3,2,1],[3,2,1],[3,2],[3]] => 9 [[3,3,2,1],[3,2,2],[2,2],[2]] => 9 [[3,3,2,1],[3,2,2],[3,2],[2]] => 9 [[3,3,2,1],[3,2,2],[3,2],[3]] => 9 [[3,3,2,1],[3,3,1],[3,1],[1]] => 9 [[3,3,2,1],[3,3,1],[3,1],[2]] => 9 [[3,3,2,1],[3,3,1],[3,1],[3]] => 9 [[3,3,2,1],[3,3,1],[3,2],[2]] => 9 [[3,3,2,1],[3,3,1],[3,2],[3]] => 9 [[3,3,2,1],[3,3,1],[3,3],[3]] => 9 [[3,3,2,1],[3,3,2],[3,2],[2]] => 9 [[3,3,2,1],[3,3,2],[3,2],[3]] => 9 [[3,3,2,1],[3,3,2],[3,3],[3]] => 9 [[3,3,2,2],[3,2,2],[2,2],[2]] => 10 [[3,3,2,2],[3,2,2],[3,2],[2]] => 10 [[3,3,2,2],[3,2,2],[3,2],[3]] => 10 [[3,3,2,2],[3,3,2],[3,2],[2]] => 10 [[3,3,2,2],[3,3,2],[3,2],[3]] => 10 [[3,3,2,2],[3,3,2],[3,3],[3]] => 10 [[3,3,3,0],[3,3,0],[3,0],[0]] => 9 [[3,3,3,0],[3,3,0],[3,0],[1]] => 9 [[3,3,3,0],[3,3,0],[3,0],[2]] => 9 [[3,3,3,0],[3,3,0],[3,0],[3]] => 9 [[3,3,3,0],[3,3,0],[3,1],[1]] => 9 [[3,3,3,0],[3,3,0],[3,1],[2]] => 9 [[3,3,3,0],[3,3,0],[3,1],[3]] => 9 [[3,3,3,0],[3,3,0],[3,2],[2]] => 9 [[3,3,3,0],[3,3,0],[3,2],[3]] => 9 [[3,3,3,0],[3,3,0],[3,3],[3]] => 9 [[3,3,3,0],[3,3,1],[3,1],[1]] => 9 [[3,3,3,0],[3,3,1],[3,1],[2]] => 9 [[3,3,3,0],[3,3,1],[3,1],[3]] => 9 [[3,3,3,0],[3,3,1],[3,2],[2]] => 9 [[3,3,3,0],[3,3,1],[3,2],[3]] => 9 [[3,3,3,0],[3,3,1],[3,3],[3]] => 9 [[3,3,3,0],[3,3,2],[3,2],[2]] => 9 [[3,3,3,0],[3,3,2],[3,2],[3]] => 9 [[3,3,3,0],[3,3,2],[3,3],[3]] => 9 [[3,3,3,0],[3,3,3],[3,3],[3]] => 9 [[3,3,3,1],[3,3,1],[3,1],[1]] => 10 [[3,3,3,1],[3,3,1],[3,1],[2]] => 10 [[3,3,3,1],[3,3,1],[3,1],[3]] => 10 [[3,3,3,1],[3,3,1],[3,2],[2]] => 10 [[3,3,3,1],[3,3,1],[3,2],[3]] => 10 [[3,3,3,1],[3,3,1],[3,3],[3]] => 10 [[3,3,3,1],[3,3,2],[3,2],[2]] => 10 [[3,3,3,1],[3,3,2],[3,2],[3]] => 10 [[3,3,3,1],[3,3,2],[3,3],[3]] => 10 [[3,3,3,1],[3,3,3],[3,3],[3]] => 10 [[3,3,3,2],[3,3,2],[3,2],[2]] => 11 [[3,3,3,2],[3,3,2],[3,2],[3]] => 11 [[3,3,3,2],[3,3,2],[3,3],[3]] => 11 [[3,3,3,2],[3,3,3],[3,3],[3]] => 11 [[3,3,3,3],[3,3,3],[3,3],[3]] => 12 [[4,1,1,0],[4,1,1],[1,1],[1]] => 6 [[4,1,1,0],[4,1,1],[2,1],[1]] => 6 [[4,1,1,0],[4,1,1],[2,1],[2]] => 6 [[4,1,1,0],[4,1,1],[3,1],[1]] => 6 [[4,1,1,0],[4,1,1],[3,1],[2]] => 6 [[4,1,1,0],[4,1,1],[3,1],[3]] => 6 [[4,1,1,0],[4,1,1],[4,1],[1]] => 6 [[4,1,1,0],[4,1,1],[4,1],[2]] => 6 [[4,1,1,0],[4,1,1],[4,1],[3]] => 6 [[4,1,1,0],[4,1,1],[4,1],[4]] => 6 [[4,1,1,1],[1,1,1],[1,1],[1]] => 7 [[4,1,1,1],[2,1,1],[1,1],[1]] => 7 [[4,1,1,1],[2,1,1],[2,1],[1]] => 7 [[4,1,1,1],[2,1,1],[2,1],[2]] => 7 ----------------------------------------------------------------------------- Created: May 07, 2014 at 21:43 by Shahana Norton ----------------------------------------------------------------------------- Last Updated: May 20, 2016 at 22:11 by Martin Rubey