***************************************************************************** * 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: St000077 ----------------------------------------------------------------------------- Collection: Gelfand-Tsetlin patterns ----------------------------------------------------------------------------- Description: The number of boxed and circled entries. An entry $a_{i,j}$ is boxed and circled if $a_{i-1,j-i} = a_{i,j} = a_{i-1,j}$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(g): boxed = g.boxed_entries() return sum(1 for x in g.circled_entries() if x in boxed) ----------------------------------------------------------------------------- Statistic values: [[1]] => 0 [[2]] => 0 [[3]] => 0 [[1,0],[0]] => 0 [[1,0],[1]] => 0 [[2,0],[0]] => 0 [[2,0],[1]] => 0 [[2,0],[2]] => 0 [[1,1],[1]] => 1 [[3,0],[0]] => 0 [[3,0],[1]] => 0 [[3,0],[2]] => 0 [[3,0],[3]] => 0 [[2,1],[1]] => 0 [[2,1],[2]] => 0 [[3,1],[1]] => 0 [[3,1],[2]] => 0 [[3,1],[3]] => 0 [[2,2],[2]] => 1 [[3,2],[2]] => 0 [[3,2],[3]] => 0 [[3,3],[3]] => 1 [[1,0,0],[0,0],[0]] => 2 [[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]] => 1 [[2,0,0],[1,0],[1]] => 1 [[2,0,0],[2,0],[0]] => 1 [[2,0,0],[2,0],[1]] => 1 [[2,0,0],[2,0],[2]] => 1 [[1,1,0],[1,0],[0]] => 1 [[1,1,0],[1,0],[1]] => 1 [[1,1,0],[1,1],[1]] => 2 [[3,0,0],[0,0],[0]] => 2 [[3,0,0],[1,0],[0]] => 1 [[3,0,0],[1,0],[1]] => 1 [[3,0,0],[2,0],[0]] => 1 [[3,0,0],[2,0],[1]] => 1 [[3,0,0],[2,0],[2]] => 1 [[3,0,0],[3,0],[0]] => 1 [[3,0,0],[3,0],[1]] => 1 [[3,0,0],[3,0],[2]] => 1 [[3,0,0],[3,0],[3]] => 1 [[2,1,0],[1,0],[0]] => 0 [[2,1,0],[1,0],[1]] => 0 [[2,1,0],[1,1],[1]] => 1 [[2,1,0],[2,0],[0]] => 0 [[2,1,0],[2,0],[1]] => 0 [[2,1,0],[2,0],[2]] => 0 [[2,1,0],[2,1],[1]] => 0 [[2,1,0],[2,1],[2]] => 0 [[1,1,1],[1,1],[1]] => 3 [[3,1,0],[1,0],[0]] => 0 [[3,1,0],[1,0],[1]] => 0 [[3,1,0],[1,1],[1]] => 1 [[3,1,0],[2,0],[0]] => 0 [[3,1,0],[2,0],[1]] => 0 [[3,1,0],[2,0],[2]] => 0 [[3,1,0],[2,1],[1]] => 0 [[3,1,0],[2,1],[2]] => 0 [[3,1,0],[3,0],[0]] => 0 [[3,1,0],[3,0],[1]] => 0 [[3,1,0],[3,0],[2]] => 0 [[3,1,0],[3,0],[3]] => 0 [[3,1,0],[3,1],[1]] => 0 [[3,1,0],[3,1],[2]] => 0 [[3,1,0],[3,1],[3]] => 0 [[2,2,0],[2,0],[0]] => 1 [[2,2,0],[2,0],[1]] => 1 [[2,2,0],[2,0],[2]] => 1 [[2,2,0],[2,1],[1]] => 1 [[2,2,0],[2,1],[2]] => 1 [[2,2,0],[2,2],[2]] => 2 [[2,1,1],[1,1],[1]] => 2 [[2,1,1],[2,1],[1]] => 1 [[2,1,1],[2,1],[2]] => 1 [[3,2,0],[2,0],[0]] => 0 [[3,2,0],[2,0],[1]] => 0 [[3,2,0],[2,0],[2]] => 0 [[3,2,0],[2,1],[1]] => 0 [[3,2,0],[2,1],[2]] => 0 [[3,2,0],[2,2],[2]] => 1 [[3,2,0],[3,0],[0]] => 0 [[3,2,0],[3,0],[1]] => 0 [[3,2,0],[3,0],[2]] => 0 [[3,2,0],[3,0],[3]] => 0 [[3,2,0],[3,1],[1]] => 0 [[3,2,0],[3,1],[2]] => 0 [[3,2,0],[3,1],[3]] => 0 [[3,2,0],[3,2],[2]] => 0 [[3,2,0],[3,2],[3]] => 0 [[3,1,1],[1,1],[1]] => 2 [[3,1,1],[2,1],[1]] => 1 [[3,1,1],[2,1],[2]] => 1 [[3,1,1],[3,1],[1]] => 1 [[3,1,1],[3,1],[2]] => 1 [[3,1,1],[3,1],[3]] => 1 [[2,2,1],[2,1],[1]] => 1 [[2,2,1],[2,1],[2]] => 1 [[2,2,1],[2,2],[2]] => 2 [[3,3,0],[3,0],[0]] => 1 [[3,3,0],[3,0],[1]] => 1 [[3,3,0],[3,0],[2]] => 1 [[3,3,0],[3,0],[3]] => 1 [[3,3,0],[3,1],[1]] => 1 [[3,3,0],[3,1],[2]] => 1 [[3,3,0],[3,1],[3]] => 1 [[3,3,0],[3,2],[2]] => 1 [[3,3,0],[3,2],[3]] => 1 [[3,3,0],[3,3],[3]] => 2 [[3,2,1],[2,1],[1]] => 0 [[3,2,1],[2,1],[2]] => 0 [[3,2,1],[2,2],[2]] => 1 [[3,2,1],[3,1],[1]] => 0 [[3,2,1],[3,1],[2]] => 0 [[3,2,1],[3,1],[3]] => 0 [[3,2,1],[3,2],[2]] => 0 [[3,2,1],[3,2],[3]] => 0 [[2,2,2],[2,2],[2]] => 3 [[3,3,1],[3,3],[3]] => 2 [[3,3,1],[3,2],[3]] => 1 [[3,3,1],[3,1],[3]] => 1 [[3,3,1],[3,2],[2]] => 1 [[3,3,1],[3,1],[2]] => 1 [[3,3,1],[3,1],[1]] => 1 [[3,2,2],[3,2],[3]] => 1 [[3,2,2],[3,2],[2]] => 1 [[3,2,2],[2,2],[2]] => 2 [[1,0,0,0],[0,0,0],[0,0],[0]] => 5 [[1,0,0,0],[1,0,0],[0,0],[0]] => 4 [[1,0,0,0],[1,0,0],[1,0],[0]] => 3 [[1,0,0,0],[1,0,0],[1,0],[1]] => 3 [[2,0,0,0],[0,0,0],[0,0],[0]] => 5 [[2,0,0,0],[1,0,0],[0,0],[0]] => 4 [[2,0,0,0],[1,0,0],[1,0],[0]] => 3 [[2,0,0,0],[1,0,0],[1,0],[1]] => 3 [[2,0,0,0],[2,0,0],[0,0],[0]] => 4 [[2,0,0,0],[2,0,0],[1,0],[0]] => 3 [[2,0,0,0],[2,0,0],[1,0],[1]] => 3 [[2,0,0,0],[2,0,0],[2,0],[0]] => 3 [[2,0,0,0],[2,0,0],[2,0],[1]] => 3 [[2,0,0,0],[2,0,0],[2,0],[2]] => 3 [[1,1,0,0],[1,0,0],[0,0],[0]] => 4 [[1,1,0,0],[1,0,0],[1,0],[0]] => 3 [[1,1,0,0],[1,0,0],[1,0],[1]] => 3 [[1,1,0,0],[1,1,0],[1,0],[0]] => 3 [[1,1,0,0],[1,1,0],[1,0],[1]] => 3 [[1,1,0,0],[1,1,0],[1,1],[1]] => 4 [[3,0,0,0],[0,0,0],[0,0],[0]] => 5 [[3,0,0,0],[1,0,0],[0,0],[0]] => 4 [[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]] => 4 [[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]] => 4 [[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]] => 2 [[2,1,0,0],[1,0,0],[1,0],[1]] => 2 [[2,1,0,0],[1,1,0],[1,0],[0]] => 2 [[2,1,0,0],[1,1,0],[1,0],[1]] => 2 [[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]] => 2 [[2,1,0,0],[2,0,0],[1,0],[1]] => 2 [[2,1,0,0],[2,0,0],[2,0],[0]] => 2 [[2,1,0,0],[2,0,0],[2,0],[1]] => 2 [[2,1,0,0],[2,0,0],[2,0],[2]] => 2 [[2,1,0,0],[2,1,0],[1,0],[0]] => 1 [[2,1,0,0],[2,1,0],[1,0],[1]] => 1 [[2,1,0,0],[2,1,0],[1,1],[1]] => 2 [[2,1,0,0],[2,1,0],[2,0],[0]] => 1 [[2,1,0,0],[2,1,0],[2,0],[1]] => 1 [[2,1,0,0],[2,1,0],[2,0],[2]] => 1 [[2,1,0,0],[2,1,0],[2,1],[1]] => 1 [[2,1,0,0],[2,1,0],[2,1],[2]] => 1 [[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]] => 4 [[1,1,1,0],[1,1,1],[1,1],[1]] => 5 [[3,1,0,0],[1,0,0],[0,0],[0]] => 3 [[3,1,0,0],[1,0,0],[1,0],[0]] => 2 [[3,1,0,0],[1,0,0],[1,0],[1]] => 2 [[3,1,0,0],[1,1,0],[1,0],[0]] => 2 [[3,1,0,0],[1,1,0],[1,0],[1]] => 2 [[3,1,0,0],[1,1,0],[1,1],[1]] => 3 [[3,1,0,0],[2,0,0],[0,0],[0]] => 3 [[3,1,0,0],[2,0,0],[1,0],[0]] => 2 [[3,1,0,0],[2,0,0],[1,0],[1]] => 2 [[3,1,0,0],[2,0,0],[2,0],[0]] => 2 [[3,1,0,0],[2,0,0],[2,0],[1]] => 2 [[3,1,0,0],[2,0,0],[2,0],[2]] => 2 [[3,1,0,0],[2,1,0],[1,0],[0]] => 1 [[3,1,0,0],[2,1,0],[1,0],[1]] => 1 [[3,1,0,0],[2,1,0],[1,1],[1]] => 2 [[3,1,0,0],[2,1,0],[2,0],[0]] => 1 [[3,1,0,0],[2,1,0],[2,0],[1]] => 1 [[3,1,0,0],[2,1,0],[2,0],[2]] => 1 [[3,1,0,0],[2,1,0],[2,1],[1]] => 1 [[3,1,0,0],[2,1,0],[2,1],[2]] => 1 [[3,1,0,0],[3,0,0],[0,0],[0]] => 3 [[3,1,0,0],[3,0,0],[1,0],[0]] => 2 [[3,1,0,0],[3,0,0],[1,0],[1]] => 2 [[3,1,0,0],[3,0,0],[2,0],[0]] => 2 [[3,1,0,0],[3,0,0],[2,0],[1]] => 2 [[3,1,0,0],[3,0,0],[2,0],[2]] => 2 [[3,1,0,0],[3,0,0],[3,0],[0]] => 2 [[3,1,0,0],[3,0,0],[3,0],[1]] => 2 [[3,1,0,0],[3,0,0],[3,0],[2]] => 2 [[3,1,0,0],[3,0,0],[3,0],[3]] => 2 [[3,1,0,0],[3,1,0],[1,0],[0]] => 1 [[3,1,0,0],[3,1,0],[1,0],[1]] => 1 [[3,1,0,0],[3,1,0],[1,1],[1]] => 2 [[3,1,0,0],[3,1,0],[2,0],[0]] => 1 [[3,1,0,0],[3,1,0],[2,0],[1]] => 1 [[3,1,0,0],[3,1,0],[2,0],[2]] => 1 [[3,1,0,0],[3,1,0],[2,1],[1]] => 1 [[3,1,0,0],[3,1,0],[2,1],[2]] => 1 [[3,1,0,0],[3,1,0],[3,0],[0]] => 1 [[3,1,0,0],[3,1,0],[3,0],[1]] => 1 [[3,1,0,0],[3,1,0],[3,0],[2]] => 1 [[3,1,0,0],[3,1,0],[3,0],[3]] => 1 [[3,1,0,0],[3,1,0],[3,1],[1]] => 1 [[3,1,0,0],[3,1,0],[3,1],[2]] => 1 [[3,1,0,0],[3,1,0],[3,1],[3]] => 1 [[2,2,0,0],[2,0,0],[0,0],[0]] => 4 [[2,2,0,0],[2,0,0],[1,0],[0]] => 3 [[2,2,0,0],[2,0,0],[1,0],[1]] => 3 [[2,2,0,0],[2,0,0],[2,0],[0]] => 3 [[2,2,0,0],[2,0,0],[2,0],[1]] => 3 [[2,2,0,0],[2,0,0],[2,0],[2]] => 3 [[2,2,0,0],[2,1,0],[1,0],[0]] => 2 [[2,2,0,0],[2,1,0],[1,0],[1]] => 2 [[2,2,0,0],[2,1,0],[1,1],[1]] => 3 [[2,2,0,0],[2,1,0],[2,0],[0]] => 2 [[2,2,0,0],[2,1,0],[2,0],[1]] => 2 [[2,2,0,0],[2,1,0],[2,0],[2]] => 2 [[2,2,0,0],[2,1,0],[2,1],[1]] => 2 [[2,2,0,0],[2,1,0],[2,1],[2]] => 2 [[2,2,0,0],[2,2,0],[2,0],[0]] => 3 [[2,2,0,0],[2,2,0],[2,0],[1]] => 3 [[2,2,0,0],[2,2,0],[2,0],[2]] => 3 [[2,2,0,0],[2,2,0],[2,1],[1]] => 3 [[2,2,0,0],[2,2,0],[2,1],[2]] => 3 [[2,2,0,0],[2,2,0],[2,2],[2]] => 4 [[2,1,1,0],[1,1,0],[1,0],[0]] => 2 [[2,1,1,0],[1,1,0],[1,0],[1]] => 2 [[2,1,1,0],[1,1,0],[1,1],[1]] => 3 [[2,1,1,0],[1,1,1],[1,1],[1]] => 4 [[2,1,1,0],[2,1,0],[1,0],[0]] => 1 [[2,1,1,0],[2,1,0],[1,0],[1]] => 1 [[2,1,1,0],[2,1,0],[1,1],[1]] => 2 [[2,1,1,0],[2,1,0],[2,0],[0]] => 1 [[2,1,1,0],[2,1,0],[2,0],[1]] => 1 [[2,1,1,0],[2,1,0],[2,0],[2]] => 1 [[2,1,1,0],[2,1,0],[2,1],[1]] => 1 [[2,1,1,0],[2,1,0],[2,1],[2]] => 1 [[2,1,1,0],[2,1,1],[1,1],[1]] => 3 [[2,1,1,0],[2,1,1],[2,1],[1]] => 2 [[2,1,1,0],[2,1,1],[2,1],[2]] => 2 [[1,1,1,1],[1,1,1],[1,1],[1]] => 6 [[3,2,0,0],[2,0,0],[0,0],[0]] => 3 [[3,2,0,0],[2,0,0],[1,0],[0]] => 2 [[3,2,0,0],[2,0,0],[1,0],[1]] => 2 [[3,2,0,0],[2,0,0],[2,0],[0]] => 2 [[3,2,0,0],[2,0,0],[2,0],[1]] => 2 [[3,2,0,0],[2,0,0],[2,0],[2]] => 2 [[3,2,0,0],[2,1,0],[1,0],[0]] => 1 [[3,2,0,0],[2,1,0],[1,0],[1]] => 1 [[3,2,0,0],[2,1,0],[1,1],[1]] => 2 [[3,2,0,0],[2,1,0],[2,0],[0]] => 1 [[3,2,0,0],[2,1,0],[2,0],[1]] => 1 [[3,2,0,0],[2,1,0],[2,0],[2]] => 1 [[3,2,0,0],[2,1,0],[2,1],[1]] => 1 [[3,2,0,0],[2,1,0],[2,1],[2]] => 1 [[3,2,0,0],[2,2,0],[2,0],[0]] => 2 [[3,2,0,0],[2,2,0],[2,0],[1]] => 2 [[3,2,0,0],[2,2,0],[2,0],[2]] => 2 [[3,2,0,0],[2,2,0],[2,1],[1]] => 2 [[3,2,0,0],[2,2,0],[2,1],[2]] => 2 [[3,2,0,0],[2,2,0],[2,2],[2]] => 3 [[3,2,0,0],[3,0,0],[0,0],[0]] => 3 [[3,2,0,0],[3,0,0],[1,0],[0]] => 2 [[3,2,0,0],[3,0,0],[1,0],[1]] => 2 [[3,2,0,0],[3,0,0],[2,0],[0]] => 2 [[3,2,0,0],[3,0,0],[2,0],[1]] => 2 [[3,2,0,0],[3,0,0],[2,0],[2]] => 2 [[3,2,0,0],[3,0,0],[3,0],[0]] => 2 [[3,2,0,0],[3,0,0],[3,0],[1]] => 2 [[3,2,0,0],[3,0,0],[3,0],[2]] => 2 [[3,2,0,0],[3,0,0],[3,0],[3]] => 2 [[3,2,0,0],[3,1,0],[1,0],[0]] => 1 [[3,2,0,0],[3,1,0],[1,0],[1]] => 1 [[3,2,0,0],[3,1,0],[1,1],[1]] => 2 [[3,2,0,0],[3,1,0],[2,0],[0]] => 1 [[3,2,0,0],[3,1,0],[2,0],[1]] => 1 [[3,2,0,0],[3,1,0],[2,0],[2]] => 1 [[3,2,0,0],[3,1,0],[2,1],[1]] => 1 [[3,2,0,0],[3,1,0],[2,1],[2]] => 1 [[3,2,0,0],[3,1,0],[3,0],[0]] => 1 [[3,2,0,0],[3,1,0],[3,0],[1]] => 1 [[3,2,0,0],[3,1,0],[3,0],[2]] => 1 [[3,2,0,0],[3,1,0],[3,0],[3]] => 1 [[3,2,0,0],[3,1,0],[3,1],[1]] => 1 [[3,2,0,0],[3,1,0],[3,1],[2]] => 1 [[3,2,0,0],[3,1,0],[3,1],[3]] => 1 [[3,2,0,0],[3,2,0],[2,0],[0]] => 1 [[3,2,0,0],[3,2,0],[2,0],[1]] => 1 [[3,2,0,0],[3,2,0],[2,0],[2]] => 1 [[3,2,0,0],[3,2,0],[2,1],[1]] => 1 [[3,2,0,0],[3,2,0],[2,1],[2]] => 1 [[3,2,0,0],[3,2,0],[2,2],[2]] => 2 [[3,2,0,0],[3,2,0],[3,0],[0]] => 1 [[3,2,0,0],[3,2,0],[3,0],[1]] => 1 [[3,2,0,0],[3,2,0],[3,0],[2]] => 1 [[3,2,0,0],[3,2,0],[3,0],[3]] => 1 [[3,2,0,0],[3,2,0],[3,1],[1]] => 1 [[3,2,0,0],[3,2,0],[3,1],[2]] => 1 [[3,2,0,0],[3,2,0],[3,1],[3]] => 1 [[3,2,0,0],[3,2,0],[3,2],[2]] => 1 [[3,2,0,0],[3,2,0],[3,2],[3]] => 1 [[3,1,1,0],[1,1,0],[1,0],[0]] => 2 [[3,1,1,0],[1,1,0],[1,0],[1]] => 2 [[3,1,1,0],[1,1,0],[1,1],[1]] => 3 [[3,1,1,0],[1,1,1],[1,1],[1]] => 4 [[3,1,1,0],[2,1,0],[1,0],[0]] => 1 [[3,1,1,0],[2,1,0],[1,0],[1]] => 1 [[3,1,1,0],[2,1,0],[1,1],[1]] => 2 [[3,1,1,0],[2,1,0],[2,0],[0]] => 1 [[3,1,1,0],[2,1,0],[2,0],[1]] => 1 [[3,1,1,0],[2,1,0],[2,0],[2]] => 1 [[3,1,1,0],[2,1,0],[2,1],[1]] => 1 [[3,1,1,0],[2,1,0],[2,1],[2]] => 1 [[3,1,1,0],[2,1,1],[1,1],[1]] => 3 [[3,1,1,0],[2,1,1],[2,1],[1]] => 2 [[3,1,1,0],[2,1,1],[2,1],[2]] => 2 [[3,1,1,0],[3,1,0],[1,0],[0]] => 1 [[3,1,1,0],[3,1,0],[1,0],[1]] => 1 [[3,1,1,0],[3,1,0],[1,1],[1]] => 2 [[3,1,1,0],[3,1,0],[2,0],[0]] => 1 [[3,1,1,0],[3,1,0],[2,0],[1]] => 1 [[3,1,1,0],[3,1,0],[2,0],[2]] => 1 [[3,1,1,0],[3,1,0],[2,1],[1]] => 1 [[3,1,1,0],[3,1,0],[2,1],[2]] => 1 [[3,1,1,0],[3,1,0],[3,0],[0]] => 1 [[3,1,1,0],[3,1,0],[3,0],[1]] => 1 [[3,1,1,0],[3,1,0],[3,0],[2]] => 1 [[3,1,1,0],[3,1,0],[3,0],[3]] => 1 [[3,1,1,0],[3,1,0],[3,1],[1]] => 1 [[3,1,1,0],[3,1,0],[3,1],[2]] => 1 [[3,1,1,0],[3,1,0],[3,1],[3]] => 1 [[3,1,1,0],[3,1,1],[1,1],[1]] => 3 [[3,1,1,0],[3,1,1],[2,1],[1]] => 2 [[3,1,1,0],[3,1,1],[2,1],[2]] => 2 [[3,1,1,0],[3,1,1],[3,1],[1]] => 2 [[3,1,1,0],[3,1,1],[3,1],[2]] => 2 [[3,1,1,0],[3,1,1],[3,1],[3]] => 2 [[2,2,1,0],[2,1,0],[1,0],[0]] => 1 [[2,2,1,0],[2,1,0],[1,0],[1]] => 1 [[2,2,1,0],[2,1,0],[1,1],[1]] => 2 [[2,2,1,0],[2,1,0],[2,0],[0]] => 1 [[2,2,1,0],[2,1,0],[2,0],[1]] => 1 [[2,2,1,0],[2,1,0],[2,0],[2]] => 1 [[2,2,1,0],[2,1,0],[2,1],[1]] => 1 [[2,2,1,0],[2,1,0],[2,1],[2]] => 1 [[2,2,1,0],[2,1,1],[1,1],[1]] => 3 [[2,2,1,0],[2,1,1],[2,1],[1]] => 2 [[2,2,1,0],[2,1,1],[2,1],[2]] => 2 [[2,2,1,0],[2,2,0],[2,0],[0]] => 2 [[2,2,1,0],[2,2,0],[2,0],[1]] => 2 [[2,2,1,0],[2,2,0],[2,0],[2]] => 2 [[2,2,1,0],[2,2,0],[2,1],[1]] => 2 [[2,2,1,0],[2,2,0],[2,1],[2]] => 2 [[2,2,1,0],[2,2,0],[2,2],[2]] => 3 [[2,2,1,0],[2,2,1],[2,1],[1]] => 2 [[2,2,1,0],[2,2,1],[2,1],[2]] => 2 [[2,2,1,0],[2,2,1],[2,2],[2]] => 3 [[2,1,1,1],[1,1,1],[1,1],[1]] => 5 [[2,1,1,1],[2,1,1],[1,1],[1]] => 4 [[2,1,1,1],[2,1,1],[2,1],[1]] => 3 [[2,1,1,1],[2,1,1],[2,1],[2]] => 3 [[3,3,0,0],[3,2,0],[3,2],[3]] => 2 [[3,3,0,0],[3,2,0],[3,1],[3]] => 2 [[3,3,0,0],[3,1,0],[3,1],[3]] => 2 [[3,3,0,0],[3,2,0],[3,0],[3]] => 2 [[3,3,0,0],[3,1,0],[3,0],[3]] => 2 [[3,3,0,0],[3,0,0],[3,0],[3]] => 3 [[3,3,0,0],[3,2,0],[3,2],[2]] => 2 [[3,3,0,0],[3,2,0],[3,1],[2]] => 2 [[3,3,0,0],[3,2,0],[2,2],[2]] => 3 [[3,3,0,0],[3,1,0],[3,1],[2]] => 2 [[3,3,0,0],[3,2,0],[3,0],[2]] => 2 [[3,3,0,0],[3,2,0],[2,1],[2]] => 2 [[3,3,0,0],[3,1,0],[3,0],[2]] => 2 [[3,3,0,0],[3,1,0],[2,1],[2]] => 2 [[3,3,0,0],[3,0,0],[3,0],[2]] => 3 [[3,3,0,0],[3,2,0],[2,0],[2]] => 2 [[3,3,0,0],[3,1,0],[2,0],[2]] => 2 [[3,3,0,0],[3,0,0],[2,0],[2]] => 3 [[3,3,0,0],[3,2,0],[3,1],[1]] => 2 [[3,3,0,0],[3,1,0],[3,1],[1]] => 2 [[3,3,0,0],[3,2,0],[3,0],[1]] => 2 [[3,3,0,0],[3,2,0],[2,1],[1]] => 2 [[3,3,0,0],[3,1,0],[3,0],[1]] => 2 [[3,3,0,0],[3,1,0],[2,1],[1]] => 2 [[3,3,0,0],[3,0,0],[3,0],[1]] => 3 [[3,3,0,0],[3,2,0],[2,0],[1]] => 2 [[3,3,0,0],[3,1,0],[2,0],[1]] => 2 [[3,3,0,0],[3,1,0],[1,1],[1]] => 3 [[3,3,0,0],[3,0,0],[2,0],[1]] => 3 [[3,3,0,0],[3,1,0],[1,0],[1]] => 2 [[3,3,0,0],[3,0,0],[1,0],[1]] => 3 [[3,3,0,0],[3,2,0],[3,0],[0]] => 2 [[3,3,0,0],[3,1,0],[3,0],[0]] => 2 [[3,3,0,0],[3,0,0],[3,0],[0]] => 3 [[3,3,0,0],[3,2,0],[2,0],[0]] => 2 [[3,3,0,0],[3,1,0],[2,0],[0]] => 2 [[3,3,0,0],[3,0,0],[2,0],[0]] => 3 [[3,3,0,0],[3,1,0],[1,0],[0]] => 2 [[3,3,0,0],[3,0,0],[1,0],[0]] => 3 [[3,3,0,0],[3,0,0],[0,0],[0]] => 4 [[3,2,1,0],[3,2,0],[3,2],[3]] => 0 [[3,2,1,0],[3,2,0],[3,1],[3]] => 0 [[3,2,1,0],[3,1,1],[3,1],[3]] => 1 [[3,2,1,0],[3,1,0],[3,1],[3]] => 0 [[3,2,1,0],[3,2,0],[3,0],[3]] => 0 [[3,2,1,0],[3,1,0],[3,0],[3]] => 0 [[3,2,1,0],[3,2,0],[3,2],[2]] => 0 [[3,2,1,0],[3,2,0],[3,1],[2]] => 0 [[3,2,1,0],[3,1,1],[3,1],[2]] => 1 [[3,2,1,0],[3,2,0],[2,2],[2]] => 1 [[3,2,1,0],[2,2,1],[2,2],[2]] => 2 [[3,2,1,0],[3,1,0],[3,1],[2]] => 0 [[3,2,1,0],[2,2,0],[2,2],[2]] => 2 [[3,2,1,0],[3,2,0],[3,0],[2]] => 0 [[3,2,1,0],[3,2,0],[2,1],[2]] => 0 [[3,2,1,0],[3,1,1],[2,1],[2]] => 1 [[3,2,1,0],[2,2,1],[2,1],[2]] => 1 [[3,2,1,0],[3,1,0],[3,0],[2]] => 0 [[3,2,1,0],[3,1,0],[2,1],[2]] => 0 [[3,2,1,0],[2,2,0],[2,1],[2]] => 1 [[3,2,1,0],[2,1,1],[2,1],[2]] => 1 [[3,2,1,0],[2,1,0],[2,1],[2]] => 0 [[3,2,1,0],[3,2,0],[2,0],[2]] => 0 [[3,2,1,0],[3,1,0],[2,0],[2]] => 0 [[3,2,1,0],[2,2,0],[2,0],[2]] => 1 [[3,2,1,0],[2,1,0],[2,0],[2]] => 0 [[3,2,1,0],[3,2,0],[3,1],[1]] => 0 [[3,2,1,0],[3,1,1],[3,1],[1]] => 1 [[3,2,1,0],[3,1,0],[3,1],[1]] => 0 [[3,2,1,0],[3,2,0],[3,0],[1]] => 0 [[3,2,1,0],[3,2,0],[2,1],[1]] => 0 [[3,2,1,0],[3,1,1],[2,1],[1]] => 1 [[3,2,1,0],[2,2,1],[2,1],[1]] => 1 [[3,2,1,0],[3,1,0],[3,0],[1]] => 0 [[3,2,1,0],[3,1,0],[2,1],[1]] => 0 [[3,2,1,0],[2,2,0],[2,1],[1]] => 1 [[3,2,1,0],[2,1,1],[2,1],[1]] => 1 [[3,2,1,0],[2,1,0],[2,1],[1]] => 0 [[3,2,1,0],[3,2,0],[2,0],[1]] => 0 [[3,2,1,0],[3,1,1],[1,1],[1]] => 2 [[3,2,1,0],[3,1,0],[2,0],[1]] => 0 [[3,2,1,0],[2,2,0],[2,0],[1]] => 1 [[3,2,1,0],[3,1,0],[1,1],[1]] => 1 [[3,2,1,0],[2,1,1],[1,1],[1]] => 2 [[3,2,1,0],[2,1,0],[2,0],[1]] => 0 [[3,2,1,0],[2,1,0],[1,1],[1]] => 1 [[3,2,1,0],[3,1,0],[1,0],[1]] => 0 [[3,2,1,0],[2,1,0],[1,0],[1]] => 0 [[3,2,1,0],[3,2,0],[3,0],[0]] => 0 [[3,2,1,0],[3,1,0],[3,0],[0]] => 0 [[3,2,1,0],[3,2,0],[2,0],[0]] => 0 [[3,2,1,0],[3,1,0],[2,0],[0]] => 0 [[3,2,1,0],[2,2,0],[2,0],[0]] => 1 [[3,2,1,0],[2,1,0],[2,0],[0]] => 0 [[3,2,1,0],[3,1,0],[1,0],[0]] => 0 [[3,2,1,0],[2,1,0],[1,0],[0]] => 0 [[3,1,1,1],[3,1,1],[3,1],[3]] => 3 [[3,1,1,1],[3,1,1],[3,1],[2]] => 3 [[3,1,1,1],[3,1,1],[2,1],[2]] => 3 [[3,1,1,1],[2,1,1],[2,1],[2]] => 3 [[3,1,1,1],[3,1,1],[3,1],[1]] => 3 [[3,1,1,1],[3,1,1],[2,1],[1]] => 3 [[3,1,1,1],[2,1,1],[2,1],[1]] => 3 [[3,1,1,1],[3,1,1],[1,1],[1]] => 4 [[3,1,1,1],[2,1,1],[1,1],[1]] => 4 [[3,1,1,1],[1,1,1],[1,1],[1]] => 5 [[2,2,2,0],[2,2,1],[2,2],[2]] => 4 [[2,2,2,0],[2,2,0],[2,2],[2]] => 4 [[2,2,2,0],[2,2,1],[2,1],[2]] => 3 [[2,2,2,0],[2,2,0],[2,1],[2]] => 3 [[2,2,2,0],[2,2,0],[2,0],[2]] => 3 [[2,2,2,0],[2,2,1],[2,1],[1]] => 3 [[2,2,2,0],[2,2,0],[2,1],[1]] => 3 [[2,2,2,0],[2,2,0],[2,0],[1]] => 3 [[2,2,2,0],[2,2,0],[2,0],[0]] => 3 [[2,2,1,1],[2,2,1],[2,2],[2]] => 4 [[2,2,1,1],[2,2,1],[2,1],[2]] => 3 [[2,2,1,1],[2,1,1],[2,1],[2]] => 3 [[2,2,1,1],[2,2,1],[2,1],[1]] => 3 [[2,2,1,1],[2,1,1],[2,1],[1]] => 3 [[2,2,1,1],[2,1,1],[1,1],[1]] => 4 [] => 0 [[0]] => 0 [[0,0],[0]] => 1 [[0,0,0],[0,0],[0]] => 3 [[3,3,2],[3,2],[2]] => 1 [[3,3,2],[3,2],[3]] => 1 [[3,3,2],[3,3],[3]] => 2 [[3,3,3],[3,3],[3]] => 3 [[0,0,0,0],[0,0,0],[0,0],[0]] => 6 [[2,2,2,0],[2,2,2],[2,2],[2]] => 5 [[2,2,2,1],[2,2,1],[2,1],[1]] => 3 [[2,2,2,1],[2,2,1],[2,1],[2]] => 3 [[2,2,2,1],[2,2,1],[2,2],[2]] => 4 [[2,2,2,1],[2,2,2],[2,2],[2]] => 5 [[2,2,2,2],[2,2,2],[2,2],[2]] => 6 [[3,2,1,0],[3,2,1],[2,1],[1]] => 0 [[3,2,1,0],[3,2,1],[2,1],[2]] => 0 [[3,2,1,0],[3,2,1],[2,2],[2]] => 1 [[3,2,1,0],[3,2,1],[3,1],[1]] => 0 [[3,2,1,0],[3,2,1],[3,1],[2]] => 0 [[3,2,1,0],[3,2,1],[3,1],[3]] => 0 [[3,2,1,0],[3,2,1],[3,2],[2]] => 0 [[3,2,1,0],[3,2,1],[3,2],[3]] => 0 [[3,2,1,1],[2,1,1],[1,1],[1]] => 3 [[3,2,1,1],[2,1,1],[2,1],[1]] => 2 [[3,2,1,1],[2,1,1],[2,1],[2]] => 2 [[3,2,1,1],[2,2,1],[2,1],[1]] => 2 [[3,2,1,1],[2,2,1],[2,1],[2]] => 2 [[3,2,1,1],[2,2,1],[2,2],[2]] => 3 [[3,2,1,1],[3,1,1],[1,1],[1]] => 3 [[3,2,1,1],[3,1,1],[2,1],[1]] => 2 [[3,2,1,1],[3,1,1],[2,1],[2]] => 2 [[3,2,1,1],[3,1,1],[3,1],[1]] => 2 [[3,2,1,1],[3,1,1],[3,1],[2]] => 2 [[3,2,1,1],[3,1,1],[3,1],[3]] => 2 [[3,2,1,1],[3,2,1],[2,1],[1]] => 1 [[3,2,1,1],[3,2,1],[2,1],[2]] => 1 [[3,2,1,1],[3,2,1],[2,2],[2]] => 2 [[3,2,1,1],[3,2,1],[3,1],[1]] => 1 [[3,2,1,1],[3,2,1],[3,1],[2]] => 1 [[3,2,1,1],[3,2,1],[3,1],[3]] => 1 [[3,2,1,1],[3,2,1],[3,2],[2]] => 1 [[3,2,1,1],[3,2,1],[3,2],[3]] => 1 [[3,2,2,0],[2,2,0],[2,0],[0]] => 2 [[3,2,2,0],[2,2,0],[2,0],[1]] => 2 [[3,2,2,0],[2,2,0],[2,0],[2]] => 2 [[3,2,2,0],[2,2,0],[2,1],[1]] => 2 [[3,2,2,0],[2,2,0],[2,1],[2]] => 2 [[3,2,2,0],[2,2,0],[2,2],[2]] => 3 [[3,2,2,0],[2,2,1],[2,1],[1]] => 2 [[3,2,2,0],[2,2,1],[2,1],[2]] => 2 [[3,2,2,0],[2,2,1],[2,2],[2]] => 3 [[3,2,2,0],[2,2,2],[2,2],[2]] => 4 [[3,2,2,0],[3,2,0],[2,0],[0]] => 1 [[3,2,2,0],[3,2,0],[2,0],[1]] => 1 [[3,2,2,0],[3,2,0],[2,0],[2]] => 1 [[3,2,2,0],[3,2,0],[2,1],[1]] => 1 [[3,2,2,0],[3,2,0],[2,1],[2]] => 1 [[3,2,2,0],[3,2,0],[2,2],[2]] => 2 [[3,2,2,0],[3,2,0],[3,0],[0]] => 1 [[3,2,2,0],[3,2,0],[3,0],[1]] => 1 [[3,2,2,0],[3,2,0],[3,0],[2]] => 1 [[3,2,2,0],[3,2,0],[3,0],[3]] => 1 [[3,2,2,0],[3,2,0],[3,1],[1]] => 1 [[3,2,2,0],[3,2,0],[3,1],[2]] => 1 [[3,2,2,0],[3,2,0],[3,1],[3]] => 1 [[3,2,2,0],[3,2,0],[3,2],[2]] => 1 [[3,2,2,0],[3,2,0],[3,2],[3]] => 1 [[3,2,2,0],[3,2,1],[2,1],[1]] => 1 [[3,2,2,0],[3,2,1],[2,1],[2]] => 1 [[3,2,2,0],[3,2,1],[2,2],[2]] => 2 [[3,2,2,0],[3,2,1],[3,1],[1]] => 1 [[3,2,2,0],[3,2,1],[3,1],[2]] => 1 [[3,2,2,0],[3,2,1],[3,1],[3]] => 1 [[3,2,2,0],[3,2,1],[3,2],[2]] => 1 [[3,2,2,0],[3,2,1],[3,2],[3]] => 1 [[3,2,2,0],[3,2,2],[2,2],[2]] => 3 [[3,2,2,0],[3,2,2],[3,2],[2]] => 2 [[3,2,2,0],[3,2,2],[3,2],[3]] => 2 [[3,2,2,1],[2,2,1],[2,1],[1]] => 2 [[3,2,2,1],[2,2,1],[2,1],[2]] => 2 [[3,2,2,1],[2,2,1],[2,2],[2]] => 3 [[3,2,2,1],[2,2,2],[2,2],[2]] => 4 [[3,2,2,1],[3,2,1],[2,1],[1]] => 1 [[3,2,2,1],[3,2,1],[2,1],[2]] => 1 [[3,2,2,1],[3,2,1],[2,2],[2]] => 2 [[3,2,2,1],[3,2,1],[3,1],[1]] => 1 [[3,2,2,1],[3,2,1],[3,1],[2]] => 1 [[3,2,2,1],[3,2,1],[3,1],[3]] => 1 [[3,2,2,1],[3,2,1],[3,2],[2]] => 1 [[3,2,2,1],[3,2,1],[3,2],[3]] => 1 [[3,2,2,1],[3,2,2],[2,2],[2]] => 3 [[3,2,2,1],[3,2,2],[3,2],[2]] => 2 [[3,2,2,1],[3,2,2],[3,2],[3]] => 2 [[3,2,2,2],[2,2,2],[2,2],[2]] => 5 [[3,2,2,2],[3,2,2],[2,2],[2]] => 4 [[3,2,2,2],[3,2,2],[3,2],[2]] => 3 [[3,2,2,2],[3,2,2],[3,2],[3]] => 3 [[3,3,0,0],[3,3,0],[3,0],[0]] => 3 [[3,3,0,0],[3,3,0],[3,0],[1]] => 3 [[3,3,0,0],[3,3,0],[3,0],[2]] => 3 [[3,3,0,0],[3,3,0],[3,0],[3]] => 3 [[3,3,0,0],[3,3,0],[3,1],[1]] => 3 [[3,3,0,0],[3,3,0],[3,1],[2]] => 3 [[3,3,0,0],[3,3,0],[3,1],[3]] => 3 [[3,3,0,0],[3,3,0],[3,2],[2]] => 3 [[3,3,0,0],[3,3,0],[3,2],[3]] => 3 [[3,3,0,0],[3,3,0],[3,3],[3]] => 4 [[3,3,1,0],[3,1,0],[1,0],[0]] => 1 [[3,3,1,0],[3,1,0],[1,0],[1]] => 1 [[3,3,1,0],[3,1,0],[1,1],[1]] => 2 [[3,3,1,0],[3,1,0],[2,0],[0]] => 1 [[3,3,1,0],[3,1,0],[2,0],[1]] => 1 [[3,3,1,0],[3,1,0],[2,0],[2]] => 1 [[3,3,1,0],[3,1,0],[2,1],[1]] => 1 [[3,3,1,0],[3,1,0],[2,1],[2]] => 1 [[3,3,1,0],[3,1,0],[3,0],[0]] => 1 [[3,3,1,0],[3,1,0],[3,0],[1]] => 1 [[3,3,1,0],[3,1,0],[3,0],[2]] => 1 [[3,3,1,0],[3,1,0],[3,0],[3]] => 1 [[3,3,1,0],[3,1,0],[3,1],[1]] => 1 [[3,3,1,0],[3,1,0],[3,1],[2]] => 1 [[3,3,1,0],[3,1,0],[3,1],[3]] => 1 [[3,3,1,0],[3,1,1],[1,1],[1]] => 3 [[3,3,1,0],[3,1,1],[2,1],[1]] => 2 [[3,3,1,0],[3,1,1],[2,1],[2]] => 2 [[3,3,1,0],[3,1,1],[3,1],[1]] => 2 [[3,3,1,0],[3,1,1],[3,1],[2]] => 2 [[3,3,1,0],[3,1,1],[3,1],[3]] => 2 [[3,3,1,0],[3,2,0],[2,0],[0]] => 1 [[3,3,1,0],[3,2,0],[2,0],[1]] => 1 [[3,3,1,0],[3,2,0],[2,0],[2]] => 1 [[3,3,1,0],[3,2,0],[2,1],[1]] => 1 [[3,3,1,0],[3,2,0],[2,1],[2]] => 1 [[3,3,1,0],[3,2,0],[2,2],[2]] => 2 [[3,3,1,0],[3,2,0],[3,0],[0]] => 1 [[3,3,1,0],[3,2,0],[3,0],[1]] => 1 [[3,3,1,0],[3,2,0],[3,0],[2]] => 1 [[3,3,1,0],[3,2,0],[3,0],[3]] => 1 [[3,3,1,0],[3,2,0],[3,1],[1]] => 1 [[3,3,1,0],[3,2,0],[3,1],[2]] => 1 [[3,3,1,0],[3,2,0],[3,1],[3]] => 1 [[3,3,1,0],[3,2,0],[3,2],[2]] => 1 [[3,3,1,0],[3,2,0],[3,2],[3]] => 1 [[3,3,1,0],[3,2,1],[2,1],[1]] => 1 [[3,3,1,0],[3,2,1],[2,1],[2]] => 1 [[3,3,1,0],[3,2,1],[2,2],[2]] => 2 [[3,3,1,0],[3,2,1],[3,1],[1]] => 1 [[3,3,1,0],[3,2,1],[3,1],[2]] => 1 [[3,3,1,0],[3,2,1],[3,1],[3]] => 1 [[3,3,1,0],[3,2,1],[3,2],[2]] => 1 [[3,3,1,0],[3,2,1],[3,2],[3]] => 1 [[3,3,1,0],[3,3,0],[3,0],[0]] => 2 [[3,3,1,0],[3,3,0],[3,0],[1]] => 2 [[3,3,1,0],[3,3,0],[3,0],[2]] => 2 [[3,3,1,0],[3,3,0],[3,0],[3]] => 2 [[3,3,1,0],[3,3,0],[3,1],[1]] => 2 [[3,3,1,0],[3,3,0],[3,1],[2]] => 2 [[3,3,1,0],[3,3,0],[3,1],[3]] => 2 [[3,3,1,0],[3,3,0],[3,2],[2]] => 2 [[3,3,1,0],[3,3,0],[3,2],[3]] => 2 [[3,3,1,0],[3,3,0],[3,3],[3]] => 3 [[3,3,1,0],[3,3,1],[3,1],[1]] => 2 [[3,3,1,0],[3,3,1],[3,1],[2]] => 2 [[3,3,1,0],[3,3,1],[3,1],[3]] => 2 [[3,3,1,0],[3,3,1],[3,2],[2]] => 2 [[3,3,1,0],[3,3,1],[3,2],[3]] => 2 [[3,3,1,0],[3,3,1],[3,3],[3]] => 3 [[3,3,1,1],[3,1,1],[1,1],[1]] => 4 [[3,3,1,1],[3,1,1],[2,1],[1]] => 3 [[3,3,1,1],[3,1,1],[2,1],[2]] => 3 [[3,3,1,1],[3,1,1],[3,1],[1]] => 3 [[3,3,1,1],[3,1,1],[3,1],[2]] => 3 [[3,3,1,1],[3,1,1],[3,1],[3]] => 3 [[3,3,1,1],[3,2,1],[2,1],[1]] => 2 [[3,3,1,1],[3,2,1],[2,1],[2]] => 2 [[3,3,1,1],[3,2,1],[2,2],[2]] => 3 [[3,3,1,1],[3,2,1],[3,1],[1]] => 2 [[3,3,1,1],[3,2,1],[3,1],[2]] => 2 [[3,3,1,1],[3,2,1],[3,1],[3]] => 2 [[3,3,1,1],[3,2,1],[3,2],[2]] => 2 [[3,3,1,1],[3,2,1],[3,2],[3]] => 2 [[3,3,1,1],[3,3,1],[3,1],[1]] => 3 [[3,3,1,1],[3,3,1],[3,1],[2]] => 3 [[3,3,1,1],[3,3,1],[3,1],[3]] => 3 [[3,3,1,1],[3,3,1],[3,2],[2]] => 3 [[3,3,1,1],[3,3,1],[3,2],[3]] => 3 [[3,3,1,1],[3,3,1],[3,3],[3]] => 4 [[3,3,2,0],[3,2,0],[2,0],[0]] => 1 [[3,3,2,0],[3,2,0],[2,0],[1]] => 1 [[3,3,2,0],[3,2,0],[2,0],[2]] => 1 [[3,3,2,0],[3,2,0],[2,1],[1]] => 1 [[3,3,2,0],[3,2,0],[2,1],[2]] => 1 [[3,3,2,0],[3,2,0],[2,2],[2]] => 2 [[3,3,2,0],[3,2,0],[3,0],[0]] => 1 [[3,3,2,0],[3,2,0],[3,0],[1]] => 1 [[3,3,2,0],[3,2,0],[3,0],[2]] => 1 [[3,3,2,0],[3,2,0],[3,0],[3]] => 1 [[3,3,2,0],[3,2,0],[3,1],[1]] => 1 [[3,3,2,0],[3,2,0],[3,1],[2]] => 1 [[3,3,2,0],[3,2,0],[3,1],[3]] => 1 [[3,3,2,0],[3,2,0],[3,2],[2]] => 1 [[3,3,2,0],[3,2,0],[3,2],[3]] => 1 [[3,3,2,0],[3,2,1],[2,1],[1]] => 1 [[3,3,2,0],[3,2,1],[2,1],[2]] => 1 [[3,3,2,0],[3,2,1],[2,2],[2]] => 2 [[3,3,2,0],[3,2,1],[3,1],[1]] => 1 [[3,3,2,0],[3,2,1],[3,1],[2]] => 1 [[3,3,2,0],[3,2,1],[3,1],[3]] => 1 [[3,3,2,0],[3,2,1],[3,2],[2]] => 1 [[3,3,2,0],[3,2,1],[3,2],[3]] => 1 [[3,3,2,0],[3,2,2],[2,2],[2]] => 3 [[3,3,2,0],[3,2,2],[3,2],[2]] => 2 [[3,3,2,0],[3,2,2],[3,2],[3]] => 2 [[3,3,2,0],[3,3,0],[3,0],[0]] => 2 [[3,3,2,0],[3,3,0],[3,0],[1]] => 2 [[3,3,2,0],[3,3,0],[3,0],[2]] => 2 [[3,3,2,0],[3,3,0],[3,0],[3]] => 2 [[3,3,2,0],[3,3,0],[3,1],[1]] => 2 [[3,3,2,0],[3,3,0],[3,1],[2]] => 2 [[3,3,2,0],[3,3,0],[3,1],[3]] => 2 [[3,3,2,0],[3,3,0],[3,2],[2]] => 2 [[3,3,2,0],[3,3,0],[3,2],[3]] => 2 [[3,3,2,0],[3,3,0],[3,3],[3]] => 3 [[3,3,2,0],[3,3,1],[3,1],[1]] => 2 [[3,3,2,0],[3,3,1],[3,1],[2]] => 2 [[3,3,2,0],[3,3,1],[3,1],[3]] => 2 [[3,3,2,0],[3,3,1],[3,2],[2]] => 2 [[3,3,2,0],[3,3,1],[3,2],[3]] => 2 [[3,3,2,0],[3,3,1],[3,3],[3]] => 3 [[3,3,2,0],[3,3,2],[3,2],[2]] => 2 [[3,3,2,0],[3,3,2],[3,2],[3]] => 2 [[3,3,2,0],[3,3,2],[3,3],[3]] => 3 [[3,3,2,1],[3,2,1],[2,1],[1]] => 1 [[3,3,2,1],[3,2,1],[2,1],[2]] => 1 [[3,3,2,1],[3,2,1],[2,2],[2]] => 2 [[3,3,2,1],[3,2,1],[3,1],[1]] => 1 [[3,3,2,1],[3,2,1],[3,1],[2]] => 1 [[3,3,2,1],[3,2,1],[3,1],[3]] => 1 [[3,3,2,1],[3,2,1],[3,2],[2]] => 1 [[3,3,2,1],[3,2,1],[3,2],[3]] => 1 [[3,3,2,1],[3,2,2],[2,2],[2]] => 3 [[3,3,2,1],[3,2,2],[3,2],[2]] => 2 [[3,3,2,1],[3,2,2],[3,2],[3]] => 2 [[3,3,2,1],[3,3,1],[3,1],[1]] => 2 [[3,3,2,1],[3,3,1],[3,1],[2]] => 2 [[3,3,2,1],[3,3,1],[3,1],[3]] => 2 [[3,3,2,1],[3,3,1],[3,2],[2]] => 2 [[3,3,2,1],[3,3,1],[3,2],[3]] => 2 [[3,3,2,1],[3,3,1],[3,3],[3]] => 3 [[3,3,2,1],[3,3,2],[3,2],[2]] => 2 [[3,3,2,1],[3,3,2],[3,2],[3]] => 2 [[3,3,2,1],[3,3,2],[3,3],[3]] => 3 [[3,3,2,2],[3,2,2],[2,2],[2]] => 4 [[3,3,2,2],[3,2,2],[3,2],[2]] => 3 [[3,3,2,2],[3,2,2],[3,2],[3]] => 3 [[3,3,2,2],[3,3,2],[3,2],[2]] => 3 [[3,3,2,2],[3,3,2],[3,2],[3]] => 3 [[3,3,2,2],[3,3,2],[3,3],[3]] => 4 [[3,3,3,0],[3,3,0],[3,0],[0]] => 3 [[3,3,3,0],[3,3,0],[3,0],[1]] => 3 [[3,3,3,0],[3,3,0],[3,0],[2]] => 3 [[3,3,3,0],[3,3,0],[3,0],[3]] => 3 [[3,3,3,0],[3,3,0],[3,1],[1]] => 3 [[3,3,3,0],[3,3,0],[3,1],[2]] => 3 [[3,3,3,0],[3,3,0],[3,1],[3]] => 3 [[3,3,3,0],[3,3,0],[3,2],[2]] => 3 [[3,3,3,0],[3,3,0],[3,2],[3]] => 3 [[3,3,3,0],[3,3,0],[3,3],[3]] => 4 [[3,3,3,0],[3,3,1],[3,1],[1]] => 3 [[3,3,3,0],[3,3,1],[3,1],[2]] => 3 [[3,3,3,0],[3,3,1],[3,1],[3]] => 3 [[3,3,3,0],[3,3,1],[3,2],[2]] => 3 [[3,3,3,0],[3,3,1],[3,2],[3]] => 3 [[3,3,3,0],[3,3,1],[3,3],[3]] => 4 [[3,3,3,0],[3,3,2],[3,2],[2]] => 3 [[3,3,3,0],[3,3,2],[3,2],[3]] => 3 [[3,3,3,0],[3,3,2],[3,3],[3]] => 4 [[3,3,3,0],[3,3,3],[3,3],[3]] => 5 [[3,3,3,1],[3,3,1],[3,1],[1]] => 3 [[3,3,3,1],[3,3,1],[3,1],[2]] => 3 [[3,3,3,1],[3,3,1],[3,1],[3]] => 3 [[3,3,3,1],[3,3,1],[3,2],[2]] => 3 [[3,3,3,1],[3,3,1],[3,2],[3]] => 3 [[3,3,3,1],[3,3,1],[3,3],[3]] => 4 [[3,3,3,1],[3,3,2],[3,2],[2]] => 3 [[3,3,3,1],[3,3,2],[3,2],[3]] => 3 [[3,3,3,1],[3,3,2],[3,3],[3]] => 4 [[3,3,3,1],[3,3,3],[3,3],[3]] => 5 [[3,3,3,2],[3,3,2],[3,2],[2]] => 3 [[3,3,3,2],[3,3,2],[3,2],[3]] => 3 [[3,3,3,2],[3,3,2],[3,3],[3]] => 4 [[3,3,3,2],[3,3,3],[3,3],[3]] => 5 [[3,3,3,3],[3,3,3],[3,3],[3]] => 6 ----------------------------------------------------------------------------- Created: Jun 11, 2013 at 18:28 by Travis Scrimshaw ----------------------------------------------------------------------------- Last Updated: Apr 01, 2015 at 21:33 by Martin Rubey