***************************************************************************** * 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: St000173 ----------------------------------------------------------------------------- Collection: Semistandard tableaux ----------------------------------------------------------------------------- Description: The segment statistic of a semistandard tableau. Let ''T'' be a tableau. A ''k''-segment of ''T'' (in the ''i''th row) is defined to be a maximal consecutive sequence of ''k''-boxes in the ith row. Note that the possible ''i''-boxes in the ''i''th row are not considered to be ''i''-segments. Then seg(''T'') is the total number of ''k''-segments in ''T'' as ''k'' varies over all possible values. ----------------------------------------------------------------------------- References: [1] Salisbury, B. The flush statistic on semistandard Young tableaux [[arXiv:1401.1185]] ----------------------------------------------------------------------------- Code: def statistic(x): return x.seg() ----------------------------------------------------------------------------- Statistic values: [[1]] => 0 [[2]] => 1 [[3]] => 1 [[4]] => 1 [[1,1]] => 0 [[1,2]] => 1 [[2,2]] => 1 [[1],[2]] => 0 [[1,3]] => 1 [[2,3]] => 2 [[3,3]] => 1 [[1],[3]] => 1 [[2],[3]] => 2 [[1,4]] => 1 [[2,4]] => 2 [[3,4]] => 2 [[4,4]] => 1 [[1],[4]] => 1 [[2],[4]] => 2 [[3],[4]] => 2 [[1,1,1]] => 0 [[1,1,2]] => 1 [[1,2,2]] => 1 [[2,2,2]] => 1 [[1,1],[2]] => 0 [[1,2],[2]] => 1 [[1,1,3]] => 1 [[1,2,3]] => 2 [[1,3,3]] => 1 [[2,2,3]] => 2 [[2,3,3]] => 2 [[3,3,3]] => 1 [[1,1],[3]] => 1 [[1,2],[3]] => 2 [[1,3],[2]] => 1 [[1,3],[3]] => 2 [[2,2],[3]] => 2 [[2,3],[3]] => 3 [[1],[2],[3]] => 0 [[1,1,4]] => 1 [[1,2,4]] => 2 [[1,3,4]] => 2 [[1,4,4]] => 1 [[2,2,4]] => 2 [[2,3,4]] => 3 [[2,4,4]] => 2 [[3,3,4]] => 2 [[3,4,4]] => 2 [[4,4,4]] => 1 [[1,1],[4]] => 1 [[1,2],[4]] => 2 [[1,4],[2]] => 1 [[1,3],[4]] => 2 [[1,4],[3]] => 2 [[1,4],[4]] => 2 [[2,2],[4]] => 2 [[2,3],[4]] => 3 [[2,4],[3]] => 3 [[2,4],[4]] => 3 [[3,3],[4]] => 2 [[3,4],[4]] => 3 [[1],[2],[4]] => 1 [[1],[3],[4]] => 2 [[2],[3],[4]] => 3 [[1,1,1,1]] => 0 [[1,1,1,2]] => 1 [[1,1,2,2]] => 1 [[1,2,2,2]] => 1 [[2,2,2,2]] => 1 [[1,1,1],[2]] => 0 [[1,1,2],[2]] => 1 [[1,2,2],[2]] => 1 [[1,1],[2,2]] => 0 [[1,1,1,3]] => 1 [[1,1,2,3]] => 2 [[1,1,3,3]] => 1 [[1,2,2,3]] => 2 [[1,2,3,3]] => 2 [[1,3,3,3]] => 1 [[2,2,2,3]] => 2 [[2,2,3,3]] => 2 [[2,3,3,3]] => 2 [[3,3,3,3]] => 1 [[1,1,1],[3]] => 1 [[1,1,2],[3]] => 2 [[1,1,3],[2]] => 1 [[1,1,3],[3]] => 2 [[1,2,2],[3]] => 2 [[1,2,3],[2]] => 2 [[1,2,3],[3]] => 3 [[1,3,3],[2]] => 1 [[1,3,3],[3]] => 2 [[2,2,2],[3]] => 2 [[2,2,3],[3]] => 3 [[2,3,3],[3]] => 3 [[1,1],[2,3]] => 1 [[1,1],[3,3]] => 1 [[1,2],[2,3]] => 2 [[1,2],[3,3]] => 2 [[2,2],[3,3]] => 2 [[1,1],[2],[3]] => 0 [[1,2],[2],[3]] => 1 [[1,3],[2],[3]] => 1 [[1,1,1,4]] => 1 [[1,1,2,4]] => 2 [[1,1,3,4]] => 2 [[1,1,4,4]] => 1 [[1,2,2,4]] => 2 [[1,2,3,4]] => 3 [[1,2,4,4]] => 2 [[1,3,3,4]] => 2 [[1,3,4,4]] => 2 [[1,4,4,4]] => 1 [[2,2,2,4]] => 2 [[2,2,3,4]] => 3 [[2,2,4,4]] => 2 [[2,3,3,4]] => 3 [[2,3,4,4]] => 3 [[2,4,4,4]] => 2 [[3,3,3,4]] => 2 [[3,3,4,4]] => 2 [[3,4,4,4]] => 2 [[4,4,4,4]] => 1 [[1,1,1],[4]] => 1 [[1,1,2],[4]] => 2 [[1,1,4],[2]] => 1 [[1,1,3],[4]] => 2 [[1,1,4],[3]] => 2 [[1,1,4],[4]] => 2 [[1,2,2],[4]] => 2 [[1,2,4],[2]] => 2 [[1,2,3],[4]] => 3 [[1,2,4],[3]] => 3 [[1,3,4],[2]] => 2 [[1,2,4],[4]] => 3 [[1,4,4],[2]] => 1 [[1,3,3],[4]] => 2 [[1,3,4],[3]] => 3 [[1,3,4],[4]] => 3 [[1,4,4],[3]] => 2 [[1,4,4],[4]] => 2 [[2,2,2],[4]] => 2 [[2,2,3],[4]] => 3 [[2,2,4],[3]] => 3 [[2,2,4],[4]] => 3 [[2,3,3],[4]] => 3 [[2,3,4],[3]] => 4 [[2,3,4],[4]] => 4 [[2,4,4],[3]] => 3 [[2,4,4],[4]] => 3 [[3,3,3],[4]] => 2 [[3,3,4],[4]] => 3 [[3,4,4],[4]] => 3 [[1,1],[2,4]] => 1 [[1,1],[3,4]] => 2 [[1,1],[4,4]] => 1 [[1,2],[2,4]] => 2 [[1,2],[3,4]] => 3 [[1,3],[2,4]] => 2 [[1,2],[4,4]] => 2 [[1,3],[3,4]] => 3 [[1,3],[4,4]] => 2 [[2,2],[3,4]] => 3 [[2,2],[4,4]] => 2 [[2,3],[3,4]] => 4 [[2,3],[4,4]] => 3 [[3,3],[4,4]] => 2 [[1,1],[2],[4]] => 1 [[1,1],[3],[4]] => 2 [[1,2],[2],[4]] => 2 [[1,2],[3],[4]] => 3 [[1,3],[2],[4]] => 2 [[1,4],[2],[3]] => 1 [[1,4],[2],[4]] => 2 [[1,3],[3],[4]] => 3 [[1,4],[3],[4]] => 3 [[2,2],[3],[4]] => 3 [[2,3],[3],[4]] => 4 [[2,4],[3],[4]] => 4 [[1],[2],[3],[4]] => 0 [[1,1,1,1,1]] => 0 [[1,1,1,1,2]] => 1 [[1,1,1,2,2]] => 1 [[1,1,2,2,2]] => 1 [[1,2,2,2,2]] => 1 [[2,2,2,2,2]] => 1 [[1,1,1,1],[2]] => 0 [[1,1,1,2],[2]] => 1 [[1,1,2,2],[2]] => 1 [[1,2,2,2],[2]] => 1 [[1,1,1],[2,2]] => 0 [[1,1,2],[2,2]] => 1 [[1,1,1,1,3]] => 1 [[1,1,1,2,3]] => 2 [[1,1,1,3,3]] => 1 [[1,1,2,2,3]] => 2 [[1,1,2,3,3]] => 2 [[1,1,3,3,3]] => 1 [[1,2,2,2,3]] => 2 [[1,2,2,3,3]] => 2 [[1,2,3,3,3]] => 2 [[1,3,3,3,3]] => 1 [[2,2,2,2,3]] => 2 [[2,2,2,3,3]] => 2 [[2,2,3,3,3]] => 2 [[2,3,3,3,3]] => 2 [[3,3,3,3,3]] => 1 [[1,1,1,1],[3]] => 1 [[1,1,1,2],[3]] => 2 [[1,1,1,3],[2]] => 1 [[1,1,1,3],[3]] => 2 [[1,1,2,2],[3]] => 2 [[1,1,2,3],[2]] => 2 [[1,1,2,3],[3]] => 3 [[1,1,3,3],[2]] => 1 [[1,1,3,3],[3]] => 2 [[1,2,2,2],[3]] => 2 [[1,2,2,3],[2]] => 2 [[1,2,2,3],[3]] => 3 [[1,2,3,3],[2]] => 2 [[1,2,3,3],[3]] => 3 [[1,3,3,3],[2]] => 1 [[1,3,3,3],[3]] => 2 [[2,2,2,2],[3]] => 2 [[2,2,2,3],[3]] => 3 [[2,2,3,3],[3]] => 3 [[2,3,3,3],[3]] => 3 [[1,1,1],[2,3]] => 1 [[1,1,1],[3,3]] => 1 [[1,1,2],[2,3]] => 2 [[1,1,3],[2,2]] => 1 [[1,1,2],[3,3]] => 2 [[1,1,3],[2,3]] => 2 [[1,1,3],[3,3]] => 2 [[1,2,2],[2,3]] => 2 [[1,2,2],[3,3]] => 2 [[1,2,3],[2,3]] => 3 [[1,2,3],[3,3]] => 3 [[2,2,2],[3,3]] => 2 [[2,2,3],[3,3]] => 3 [[1,1,1],[2],[3]] => 0 [[1,1,2],[2],[3]] => 1 [[1,1,3],[2],[3]] => 1 [[1,2,2],[2],[3]] => 1 [[1,2,3],[2],[3]] => 2 [[1,3,3],[2],[3]] => 1 [[1,1],[2,2],[3]] => 0 [[1,1],[2,3],[3]] => 1 [[1,2],[2,3],[3]] => 2 [[1,1,1,1,4]] => 1 [[1,1,1,2,4]] => 2 [[1,1,1,3,4]] => 2 [[1,1,1,4,4]] => 1 [[1,1,2,2,4]] => 2 [[1,1,2,3,4]] => 3 [[1,1,2,4,4]] => 2 [[1,1,3,3,4]] => 2 [[1,1,3,4,4]] => 2 [[1,1,4,4,4]] => 1 [[1,2,2,2,4]] => 2 [[1,2,2,3,4]] => 3 [[1,2,2,4,4]] => 2 [[1,2,3,3,4]] => 3 [[1,2,3,4,4]] => 3 [[1,2,4,4,4]] => 2 [[1,3,3,3,4]] => 2 [[1,3,3,4,4]] => 2 [[1,3,4,4,4]] => 2 [[1,4,4,4,4]] => 1 [[2,2,2,2,4]] => 2 [[2,2,2,3,4]] => 3 [[2,2,2,4,4]] => 2 [[2,2,3,3,4]] => 3 [[2,2,3,4,4]] => 3 [[2,2,4,4,4]] => 2 [[2,3,3,3,4]] => 3 [[2,3,3,4,4]] => 3 [[2,3,4,4,4]] => 3 [[2,4,4,4,4]] => 2 [[3,3,3,3,4]] => 2 [[3,3,3,4,4]] => 2 [[3,3,4,4,4]] => 2 [[3,4,4,4,4]] => 2 [[4,4,4,4,4]] => 1 [[1,1,1,1],[4]] => 1 [[1,1,1,2],[4]] => 2 [[1,1,1,4],[2]] => 1 [[1,1,1,3],[4]] => 2 [[1,1,1,4],[3]] => 2 [[1,1,1,4],[4]] => 2 [[1,1,2,2],[4]] => 2 [[1,1,2,4],[2]] => 2 [[1,1,2,3],[4]] => 3 [[1,1,2,4],[3]] => 3 [[1,1,3,4],[2]] => 2 [[1,1,2,4],[4]] => 3 [[1,1,4,4],[2]] => 1 [[1,1,3,3],[4]] => 2 [[1,1,3,4],[3]] => 3 [[1,1,3,4],[4]] => 3 [[1,1,4,4],[3]] => 2 [[1,1,4,4],[4]] => 2 [[1,2,2,2],[4]] => 2 [[1,2,2,4],[2]] => 2 [[1,2,2,3],[4]] => 3 [[1,2,2,4],[3]] => 3 [[1,2,3,4],[2]] => 3 [[1,2,2,4],[4]] => 3 [[1,2,4,4],[2]] => 2 [[1,2,3,3],[4]] => 3 [[1,2,3,4],[3]] => 4 [[1,3,3,4],[2]] => 2 [[1,2,3,4],[4]] => 4 [[1,2,4,4],[3]] => 3 [[1,3,4,4],[2]] => 2 [[1,2,4,4],[4]] => 3 [[1,4,4,4],[2]] => 1 [[1,3,3,3],[4]] => 2 [[1,3,3,4],[3]] => 3 [[1,3,3,4],[4]] => 3 [[1,3,4,4],[3]] => 3 [[1,3,4,4],[4]] => 3 [[1,4,4,4],[3]] => 2 [[1,4,4,4],[4]] => 2 [[2,2,2,2],[4]] => 2 [[2,2,2,3],[4]] => 3 [[2,2,2,4],[3]] => 3 [[2,2,2,4],[4]] => 3 [[2,2,3,3],[4]] => 3 [[2,2,3,4],[3]] => 4 [[2,2,3,4],[4]] => 4 [[2,2,4,4],[3]] => 3 [[2,2,4,4],[4]] => 3 [[2,3,3,3],[4]] => 3 [[2,3,3,4],[3]] => 4 [[2,3,3,4],[4]] => 4 [[2,3,4,4],[3]] => 4 [[2,3,4,4],[4]] => 4 [[2,4,4,4],[3]] => 3 [[2,4,4,4],[4]] => 3 [[3,3,3,3],[4]] => 2 [[3,3,3,4],[4]] => 3 [[3,3,4,4],[4]] => 3 [[3,4,4,4],[4]] => 3 [[1,1,1],[2,4]] => 1 [[1,1,1],[3,4]] => 2 [[1,1,1],[4,4]] => 1 [[1,1,2],[2,4]] => 2 [[1,1,4],[2,2]] => 1 [[1,1,2],[3,4]] => 3 [[1,1,3],[2,4]] => 2 [[1,1,4],[2,3]] => 2 [[1,1,2],[4,4]] => 2 [[1,1,4],[2,4]] => 2 [[1,1,3],[3,4]] => 3 [[1,1,4],[3,3]] => 2 [[1,1,3],[4,4]] => 2 [[1,1,4],[3,4]] => 3 [[1,1,4],[4,4]] => 2 [[1,2,2],[2,4]] => 2 [[1,2,2],[3,4]] => 3 [[1,2,3],[2,4]] => 3 [[1,2,4],[2,3]] => 3 [[1,2,2],[4,4]] => 2 [[1,2,4],[2,4]] => 3 [[1,2,3],[3,4]] => 4 [[1,2,4],[3,3]] => 3 [[1,3,3],[2,4]] => 2 [[1,2,3],[4,4]] => 3 [[1,2,4],[3,4]] => 4 [[1,3,4],[2,4]] => 3 [[1,2,4],[4,4]] => 3 [[1,3,3],[3,4]] => 3 [[1,3,3],[4,4]] => 2 [[1,3,4],[3,4]] => 4 [[1,3,4],[4,4]] => 3 [[2,2,2],[3,4]] => 3 [[2,2,2],[4,4]] => 2 [[2,2,3],[3,4]] => 4 [[2,2,4],[3,3]] => 3 [[2,2,3],[4,4]] => 3 [[2,2,4],[3,4]] => 4 [[2,2,4],[4,4]] => 3 [[2,3,3],[3,4]] => 4 [[2,3,3],[4,4]] => 3 [[2,3,4],[3,4]] => 5 [[2,3,4],[4,4]] => 4 [[3,3,3],[4,4]] => 2 [[3,3,4],[4,4]] => 3 [[1,1,1],[2],[4]] => 1 [[1,1,1],[3],[4]] => 2 [[1,1,2],[2],[4]] => 2 [[1,1,2],[3],[4]] => 3 [[1,1,3],[2],[4]] => 2 [[1,1,4],[2],[3]] => 1 [[1,1,4],[2],[4]] => 2 [[1,1,3],[3],[4]] => 3 [[1,1,4],[3],[4]] => 3 [[1,2,2],[2],[4]] => 2 [[1,2,2],[3],[4]] => 3 [[1,2,3],[2],[4]] => 3 [[1,2,4],[2],[3]] => 2 [[1,2,4],[2],[4]] => 3 [[1,2,3],[3],[4]] => 4 [[1,3,3],[2],[4]] => 2 [[1,3,4],[2],[3]] => 2 [[1,2,4],[3],[4]] => 4 [[1,3,4],[2],[4]] => 3 [[1,4,4],[2],[3]] => 1 [[1,4,4],[2],[4]] => 2 [[1,3,3],[3],[4]] => 3 [[1,3,4],[3],[4]] => 4 [[1,4,4],[3],[4]] => 3 [[2,2,2],[3],[4]] => 3 [[2,2,3],[3],[4]] => 4 [[2,2,4],[3],[4]] => 4 [[2,3,3],[3],[4]] => 4 [[2,3,4],[3],[4]] => 5 [[2,4,4],[3],[4]] => 4 [[1,1],[2,2],[4]] => 1 [[1,1],[2,3],[4]] => 2 [[1,1],[2,4],[3]] => 1 [[1,1],[2,4],[4]] => 2 [[1,1],[3,3],[4]] => 2 [[1,1],[3,4],[4]] => 3 [[1,2],[2,3],[4]] => 3 [[1,2],[2,4],[3]] => 2 [[1,2],[2,4],[4]] => 3 [[1,2],[3,3],[4]] => 3 [[1,3],[2,4],[3]] => 2 [[1,2],[3,4],[4]] => 4 [[1,3],[2,4],[4]] => 3 [[1,3],[3,4],[4]] => 4 [[2,2],[3,3],[4]] => 3 [[2,2],[3,4],[4]] => 4 [[2,3],[3,4],[4]] => 5 [[1,1],[2],[3],[4]] => 0 [[1,2],[2],[3],[4]] => 1 [[1,3],[2],[3],[4]] => 1 [[1,4],[2],[3],[4]] => 1 [[1,1,1,1,1,1]] => 0 [[1,1,1,1,1,2]] => 1 [[1,1,1,1,2,2]] => 1 [[1,1,1,2,2,2]] => 1 [[1,1,2,2,2,2]] => 1 [[1,2,2,2,2,2]] => 1 [[2,2,2,2,2,2]] => 1 [[1,1,1,1,1],[2]] => 0 [[1,1,1,1,2],[2]] => 1 [[1,1,1,2,2],[2]] => 1 [[1,1,2,2,2],[2]] => 1 [[1,2,2,2,2],[2]] => 1 [[1,1,1,1],[2,2]] => 0 [[1,1,1,2],[2,2]] => 1 [[1,1,2,2],[2,2]] => 1 [[1,1,1],[2,2,2]] => 0 [[1,1,1,1,1,3]] => 1 [[1,1,1,1,2,3]] => 2 [[1,1,1,1,3,3]] => 1 [[1,1,1,2,2,3]] => 2 [[1,1,1,2,3,3]] => 2 [[1,1,1,3,3,3]] => 1 [[1,1,2,2,2,3]] => 2 [[1,1,2,2,3,3]] => 2 [[1,1,2,3,3,3]] => 2 [[1,1,3,3,3,3]] => 1 [[1,2,2,2,2,3]] => 2 [[1,2,2,2,3,3]] => 2 [[1,2,2,3,3,3]] => 2 [[1,2,3,3,3,3]] => 2 [[1,3,3,3,3,3]] => 1 [[2,2,2,2,2,3]] => 2 [[2,2,2,2,3,3]] => 2 [[2,2,2,3,3,3]] => 2 [[2,2,3,3,3,3]] => 2 [[2,3,3,3,3,3]] => 2 [[3,3,3,3,3,3]] => 1 [[1,1,1,1,1],[3]] => 1 [[1,1,1,1,2],[3]] => 2 [[1,1,1,1,3],[2]] => 1 [[1,1,1,1,3],[3]] => 2 [[1,1,1,2,2],[3]] => 2 [[1,1,1,2,3],[2]] => 2 [[1,1,1,2,3],[3]] => 3 [[1,1,1,3,3],[2]] => 1 [[1,1,1,3,3],[3]] => 2 [[1,1,2,2,2],[3]] => 2 [[1,1,2,2,3],[2]] => 2 [[1,1,2,2,3],[3]] => 3 [[1,1,2,3,3],[2]] => 2 [[1,1,2,3,3],[3]] => 3 [[1,1,3,3,3],[2]] => 1 [[1,1,3,3,3],[3]] => 2 [[1,2,2,2,2],[3]] => 2 [[1,2,2,2,3],[2]] => 2 [[1,2,2,2,3],[3]] => 3 [[1,2,2,3,3],[2]] => 2 [[1,2,2,3,3],[3]] => 3 [[1,2,3,3,3],[2]] => 2 [[1,2,3,3,3],[3]] => 3 [[1,3,3,3,3],[2]] => 1 [[1,3,3,3,3],[3]] => 2 [[2,2,2,2,2],[3]] => 2 [[2,2,2,2,3],[3]] => 3 [[2,2,2,3,3],[3]] => 3 [[2,2,3,3,3],[3]] => 3 [[2,3,3,3,3],[3]] => 3 [[1,1,1,1],[2,3]] => 1 [[1,1,1,1],[3,3]] => 1 [[1,1,1,2],[2,3]] => 2 [[1,1,1,3],[2,2]] => 1 [[1,1,1,2],[3,3]] => 2 [[1,1,1,3],[2,3]] => 2 [[1,1,1,3],[3,3]] => 2 [[1,1,2,2],[2,3]] => 2 [[1,1,2,3],[2,2]] => 2 [[1,1,2,2],[3,3]] => 2 [[1,1,2,3],[2,3]] => 3 [[1,1,3,3],[2,2]] => 1 [[1,1,2,3],[3,3]] => 3 [[1,1,3,3],[2,3]] => 2 [[1,1,3,3],[3,3]] => 2 [[1,2,2,2],[2,3]] => 2 [[1,2,2,2],[3,3]] => 2 [[1,2,2,3],[2,3]] => 3 [[1,2,2,3],[3,3]] => 3 [[1,2,3,3],[2,3]] => 3 [[1,2,3,3],[3,3]] => 3 [[2,2,2,2],[3,3]] => 2 [[2,2,2,3],[3,3]] => 3 [[2,2,3,3],[3,3]] => 3 [[1,1,1,1],[2],[3]] => 0 [[1,1,1,2],[2],[3]] => 1 [[1,1,1,3],[2],[3]] => 1 [[1,1,2,2],[2],[3]] => 1 [[1,1,2,3],[2],[3]] => 2 [[1,1,3,3],[2],[3]] => 1 [[1,2,2,2],[2],[3]] => 1 [[1,2,2,3],[2],[3]] => 2 [[1,2,3,3],[2],[3]] => 2 [[1,3,3,3],[2],[3]] => 1 [[1,1,1],[2,2,3]] => 1 [[1,1,1],[2,3,3]] => 1 [[1,1,1],[3,3,3]] => 1 [[1,1,2],[2,2,3]] => 2 [[1,1,2],[2,3,3]] => 2 [[1,1,2],[3,3,3]] => 2 [[1,2,2],[2,3,3]] => 2 [[1,2,2],[3,3,3]] => 2 [[2,2,2],[3,3,3]] => 2 [[1,1,1],[2,2],[3]] => 0 [[1,1,1],[2,3],[3]] => 1 [[1,1,2],[2,2],[3]] => 1 [[1,1,2],[2,3],[3]] => 2 [[1,1,3],[2,2],[3]] => 1 [[1,1,3],[2,3],[3]] => 2 [[1,2,2],[2,3],[3]] => 2 [[1,2,3],[2,3],[3]] => 3 [[1,1],[2,2],[3,3]] => 0 [[1,1,1,1,1,4]] => 1 [[1,1,1,1,2,4]] => 2 [[1,1,1,1,3,4]] => 2 [[1,1,1,1,4,4]] => 1 [[1,1,1,2,2,4]] => 2 [[1,1,1,2,3,4]] => 3 [[1,1,1,2,4,4]] => 2 [[1,1,1,3,3,4]] => 2 [[1,1,1,3,4,4]] => 2 [[1,1,1,4,4,4]] => 1 [[1,1,2,2,2,4]] => 2 [[1,1,2,2,3,4]] => 3 [[1,1,2,2,4,4]] => 2 [[1,1,2,3,3,4]] => 3 [[1,1,2,3,4,4]] => 3 [[1,1,2,4,4,4]] => 2 [[1,1,3,3,3,4]] => 2 [[1,1,3,3,4,4]] => 2 [[1,1,3,4,4,4]] => 2 [[1,1,4,4,4,4]] => 1 [[1,2,2,2,2,4]] => 2 [[1,2,2,2,3,4]] => 3 [[1,2,2,2,4,4]] => 2 [[1,2,2,3,3,4]] => 3 [[1,2,2,3,4,4]] => 3 [[1,2,2,4,4,4]] => 2 [[1,2,3,3,3,4]] => 3 [[1,2,3,3,4,4]] => 3 [[1,2,3,4,4,4]] => 3 [[1,2,4,4,4,4]] => 2 [[1,3,3,3,3,4]] => 2 [[1,3,3,3,4,4]] => 2 [[1,3,3,4,4,4]] => 2 [[1,3,4,4,4,4]] => 2 [[1,4,4,4,4,4]] => 1 [[2,2,2,2,2,4]] => 2 [[2,2,2,2,3,4]] => 3 [[2,2,2,2,4,4]] => 2 [[2,2,2,3,3,4]] => 3 [[2,2,2,3,4,4]] => 3 [[2,2,2,4,4,4]] => 2 [[2,2,3,3,3,4]] => 3 [[2,2,3,3,4,4]] => 3 [[2,2,3,4,4,4]] => 3 [[2,2,4,4,4,4]] => 2 [[2,3,3,3,3,4]] => 3 [[2,3,3,3,4,4]] => 3 [[2,3,3,4,4,4]] => 3 [[2,3,4,4,4,4]] => 3 [[2,4,4,4,4,4]] => 2 [[3,3,3,3,3,4]] => 2 [[3,3,3,3,4,4]] => 2 [[3,3,3,4,4,4]] => 2 [[3,3,4,4,4,4]] => 2 [[3,4,4,4,4,4]] => 2 [[4,4,4,4,4,4]] => 1 [[1,1,1,1,1],[4]] => 1 [[1,1,1,1,2],[4]] => 2 [[1,1,1,1,4],[2]] => 1 [[1,1,1,1,3],[4]] => 2 [[1,1,1,1,4],[3]] => 2 [[1,1,1,1,4],[4]] => 2 [[1,1,1,2,2],[4]] => 2 [[1,1,1,2,4],[2]] => 2 [[1,1,1,2,3],[4]] => 3 [[1,1,1,2,4],[3]] => 3 [[1,1,1,3,4],[2]] => 2 [[1,1,1,2,4],[4]] => 3 [[1,1,1,4,4],[2]] => 1 [[1,1,1,3,3],[4]] => 2 [[1,1,1,3,4],[3]] => 3 [[1,1,1,3,4],[4]] => 3 [[1,1,1,4,4],[3]] => 2 [[1,1,1,4,4],[4]] => 2 [[1,1,2,2,2],[4]] => 2 [[1,1,2,2,4],[2]] => 2 [[1,1,2,2,3],[4]] => 3 [[1,1,2,2,4],[3]] => 3 [[1,1,2,3,4],[2]] => 3 [[1,1,2,2,4],[4]] => 3 [[1,1,2,4,4],[2]] => 2 [[1,1,2,3,3],[4]] => 3 [[1,1,2,3,4],[3]] => 4 [[1,1,3,3,4],[2]] => 2 [[1,1,2,3,4],[4]] => 4 [[1,1,2,4,4],[3]] => 3 [[1,1,3,4,4],[2]] => 2 [[1,1,2,4,4],[4]] => 3 [[1,1,4,4,4],[2]] => 1 [[1,1,3,3,3],[4]] => 2 [[1,1,3,3,4],[3]] => 3 [[1,1,3,3,4],[4]] => 3 [[1,1,3,4,4],[3]] => 3 [[1,1,3,4,4],[4]] => 3 [[1,1,4,4,4],[3]] => 2 [[1,1,4,4,4],[4]] => 2 [[1,2,2,2,2],[4]] => 2 [[1,2,2,2,4],[2]] => 2 [[1,2,2,2,3],[4]] => 3 [[1,2,2,2,4],[3]] => 3 [[1,2,2,3,4],[2]] => 3 [[1,2,2,2,4],[4]] => 3 [[1,2,2,4,4],[2]] => 2 [[1,2,2,3,3],[4]] => 3 [[1,2,2,3,4],[3]] => 4 [[1,2,3,3,4],[2]] => 3 [[1,2,2,3,4],[4]] => 4 [[1,2,2,4,4],[3]] => 3 [[1,2,3,4,4],[2]] => 3 [[1,2,2,4,4],[4]] => 3 [[1,2,4,4,4],[2]] => 2 [[1,2,3,3,3],[4]] => 3 [[1,2,3,3,4],[3]] => 4 [[1,3,3,3,4],[2]] => 2 [[1,2,3,3,4],[4]] => 4 [[1,2,3,4,4],[3]] => 4 [[1,3,3,4,4],[2]] => 2 [[1,2,3,4,4],[4]] => 4 [[1,2,4,4,4],[3]] => 3 [[1,3,4,4,4],[2]] => 2 [[1,2,4,4,4],[4]] => 3 [[1,4,4,4,4],[2]] => 1 [[1,3,3,3,3],[4]] => 2 [[1,3,3,3,4],[3]] => 3 [[1,3,3,3,4],[4]] => 3 [[1,3,3,4,4],[3]] => 3 [[1,3,3,4,4],[4]] => 3 [[1,3,4,4,4],[3]] => 3 [[1,3,4,4,4],[4]] => 3 [[1,4,4,4,4],[3]] => 2 [[1,4,4,4,4],[4]] => 2 [[2,2,2,2,2],[4]] => 2 [[2,2,2,2,3],[4]] => 3 [[2,2,2,2,4],[3]] => 3 [[2,2,2,2,4],[4]] => 3 [[2,2,2,3,3],[4]] => 3 [[2,2,2,3,4],[3]] => 4 [[2,2,2,3,4],[4]] => 4 [[2,2,2,4,4],[3]] => 3 [[2,2,2,4,4],[4]] => 3 [[2,2,3,3,3],[4]] => 3 [[2,2,3,3,4],[3]] => 4 [[2,2,3,3,4],[4]] => 4 [[2,2,3,4,4],[3]] => 4 [[2,2,3,4,4],[4]] => 4 [[2,2,4,4,4],[3]] => 3 [[2,2,4,4,4],[4]] => 3 [[2,3,3,3,3],[4]] => 3 [[2,3,3,3,4],[3]] => 4 [[2,3,3,3,4],[4]] => 4 [[2,3,3,4,4],[3]] => 4 [[2,3,3,4,4],[4]] => 4 [[2,3,4,4,4],[3]] => 4 [[2,3,4,4,4],[4]] => 4 [[2,4,4,4,4],[3]] => 3 [[2,4,4,4,4],[4]] => 3 [[3,3,3,3,3],[4]] => 2 [[3,3,3,3,4],[4]] => 3 [[3,3,3,4,4],[4]] => 3 [[3,3,4,4,4],[4]] => 3 [[3,4,4,4,4],[4]] => 3 [[1,1,1,1],[2,4]] => 1 [[1,1,1,1],[3,4]] => 2 [[1,1,1,1],[4,4]] => 1 [[1,1,1,2],[2,4]] => 2 [[1,1,1,4],[2,2]] => 1 [[1,1,1,2],[3,4]] => 3 [[1,1,1,3],[2,4]] => 2 [[1,1,1,4],[2,3]] => 2 [[1,1,1,2],[4,4]] => 2 [[1,1,1,4],[2,4]] => 2 [[1,1,1,3],[3,4]] => 3 [[1,1,1,4],[3,3]] => 2 [[1,1,1,3],[4,4]] => 2 [[1,1,1,4],[3,4]] => 3 [[1,1,1,4],[4,4]] => 2 [[1,1,2,2],[2,4]] => 2 [[1,1,2,4],[2,2]] => 2 [[1,1,2,2],[3,4]] => 3 [[1,1,2,3],[2,4]] => 3 [[1,1,2,4],[2,3]] => 3 [[1,1,3,4],[2,2]] => 2 [[1,1,2,2],[4,4]] => 2 [[1,1,2,4],[2,4]] => 3 [[1,1,4,4],[2,2]] => 1 [[1,1,2,3],[3,4]] => 4 [[1,1,2,4],[3,3]] => 3 [[1,1,3,3],[2,4]] => 2 [[1,1,3,4],[2,3]] => 3 [[1,1,2,3],[4,4]] => 3 [[1,1,2,4],[3,4]] => 4 [[1,1,3,4],[2,4]] => 3 [[1,1,4,4],[2,3]] => 2 [[1,1,2,4],[4,4]] => 3 [[1,1,4,4],[2,4]] => 2 [[1,1,3,3],[3,4]] => 3 [[1,1,3,4],[3,3]] => 3 [[1,1,3,3],[4,4]] => 2 [[1,1,3,4],[3,4]] => 4 [[1,1,4,4],[3,3]] => 2 [[1,1,3,4],[4,4]] => 3 [[1,1,4,4],[3,4]] => 3 [[1,1,4,4],[4,4]] => 2 [[1,2,2,2],[2,4]] => 2 [[1,2,2,2],[3,4]] => 3 [[1,2,2,3],[2,4]] => 3 [[1,2,2,4],[2,3]] => 3 [[1,2,2,2],[4,4]] => 2 [[1,2,2,4],[2,4]] => 3 [[1,2,2,3],[3,4]] => 4 [[1,2,2,4],[3,3]] => 3 [[1,2,3,3],[2,4]] => 3 [[1,2,3,4],[2,3]] => 4 [[1,2,2,3],[4,4]] => 3 [[1,2,2,4],[3,4]] => 4 [[1,2,3,4],[2,4]] => 4 [[1,2,4,4],[2,3]] => 3 [[1,2,2,4],[4,4]] => 3 [[1,2,4,4],[2,4]] => 3 [[1,2,3,3],[3,4]] => 4 [[1,2,3,4],[3,3]] => 4 [[1,3,3,3],[2,4]] => 2 [[1,2,3,3],[4,4]] => 3 [[1,2,3,4],[3,4]] => 5 [[1,2,4,4],[3,3]] => 3 [[1,3,3,4],[2,4]] => 3 [[1,2,3,4],[4,4]] => 4 [[1,2,4,4],[3,4]] => 4 [[1,3,4,4],[2,4]] => 3 [[1,2,4,4],[4,4]] => 3 [[1,3,3,3],[3,4]] => 3 [[1,3,3,3],[4,4]] => 2 [[1,3,3,4],[3,4]] => 4 [[1,3,3,4],[4,4]] => 3 [[1,3,4,4],[3,4]] => 4 [[1,3,4,4],[4,4]] => 3 [[2,2,2,2],[3,4]] => 3 [[2,2,2,2],[4,4]] => 2 [[2,2,2,3],[3,4]] => 4 [[2,2,2,4],[3,3]] => 3 [[2,2,2,3],[4,4]] => 3 [[2,2,2,4],[3,4]] => 4 [[2,2,2,4],[4,4]] => 3 [[2,2,3,3],[3,4]] => 4 [[2,2,3,4],[3,3]] => 4 [[2,2,3,3],[4,4]] => 3 [[2,2,3,4],[3,4]] => 5 [[2,2,4,4],[3,3]] => 3 [[2,2,3,4],[4,4]] => 4 [[2,2,4,4],[3,4]] => 4 [[2,2,4,4],[4,4]] => 3 [[2,3,3,3],[3,4]] => 4 [[2,3,3,3],[4,4]] => 3 [[2,3,3,4],[3,4]] => 5 [[2,3,3,4],[4,4]] => 4 [[2,3,4,4],[3,4]] => 5 [[2,3,4,4],[4,4]] => 4 [[3,3,3,3],[4,4]] => 2 [[3,3,3,4],[4,4]] => 3 [[3,3,4,4],[4,4]] => 3 [[1,1,1,1],[2],[4]] => 1 [[1,1,1,1],[3],[4]] => 2 [[1,1,1,2],[2],[4]] => 2 [[1,1,1,2],[3],[4]] => 3 [[1,1,1,3],[2],[4]] => 2 [[1,1,1,4],[2],[3]] => 1 [[1,1,1,4],[2],[4]] => 2 [[1,1,1,3],[3],[4]] => 3 [[1,1,1,4],[3],[4]] => 3 [[1,1,2,2],[2],[4]] => 2 [[1,1,2,2],[3],[4]] => 3 [[1,1,2,3],[2],[4]] => 3 [[1,1,2,4],[2],[3]] => 2 [[1,1,2,4],[2],[4]] => 3 [[1,1,2,3],[3],[4]] => 4 [[1,1,3,3],[2],[4]] => 2 [[1,1,3,4],[2],[3]] => 2 [[1,1,2,4],[3],[4]] => 4 [[1,1,3,4],[2],[4]] => 3 [[1,1,4,4],[2],[3]] => 1 [[1,1,4,4],[2],[4]] => 2 [[1,1,3,3],[3],[4]] => 3 [[1,1,3,4],[3],[4]] => 4 [[1,1,4,4],[3],[4]] => 3 [[1,2,2,2],[2],[4]] => 2 [[1,2,2,2],[3],[4]] => 3 [[1,2,2,3],[2],[4]] => 3 [[1,2,2,4],[2],[3]] => 2 [[1,2,2,4],[2],[4]] => 3 [[1,2,2,3],[3],[4]] => 4 [[1,2,3,3],[2],[4]] => 3 [[1,2,3,4],[2],[3]] => 3 [[1,2,2,4],[3],[4]] => 4 [[1,2,3,4],[2],[4]] => 4 [[1,2,4,4],[2],[3]] => 2 [[1,2,4,4],[2],[4]] => 3 [[1,2,3,3],[3],[4]] => 4 [[1,3,3,3],[2],[4]] => 2 [[1,3,3,4],[2],[3]] => 2 [[1,2,3,4],[3],[4]] => 5 [[1,3,3,4],[2],[4]] => 3 [[1,3,4,4],[2],[3]] => 2 [[1,2,4,4],[3],[4]] => 4 [[1,3,4,4],[2],[4]] => 3 [[1,4,4,4],[2],[3]] => 1 [[1,4,4,4],[2],[4]] => 2 [[1,3,3,3],[3],[4]] => 3 [[1,3,3,4],[3],[4]] => 4 [[1,3,4,4],[3],[4]] => 4 [[1,4,4,4],[3],[4]] => 3 [[2,2,2,2],[3],[4]] => 3 [[2,2,2,3],[3],[4]] => 4 [[2,2,2,4],[3],[4]] => 4 [[2,2,3,3],[3],[4]] => 4 [[2,2,3,4],[3],[4]] => 5 [[2,2,4,4],[3],[4]] => 4 [[2,3,3,3],[3],[4]] => 4 [[2,3,3,4],[3],[4]] => 5 [[2,3,4,4],[3],[4]] => 5 [[2,4,4,4],[3],[4]] => 4 [[1,1,1],[2,2,4]] => 1 [[1,1,1],[2,3,4]] => 2 [[1,1,1],[2,4,4]] => 1 [[1,1,1],[3,3,4]] => 2 [[1,1,1],[3,4,4]] => 2 [[1,1,1],[4,4,4]] => 1 [[1,1,2],[2,2,4]] => 2 [[1,1,2],[2,3,4]] => 3 [[1,1,3],[2,2,4]] => 2 [[1,1,2],[2,4,4]] => 2 [[1,1,2],[3,3,4]] => 3 [[1,1,3],[2,3,4]] => 3 [[1,1,2],[3,4,4]] => 3 [[1,1,3],[2,4,4]] => 2 [[1,1,2],[4,4,4]] => 2 [[1,1,3],[3,3,4]] => 3 [[1,1,3],[3,4,4]] => 3 [[1,1,3],[4,4,4]] => 2 [[1,2,2],[2,3,4]] => 3 [[1,2,2],[2,4,4]] => 2 [[1,2,2],[3,3,4]] => 3 [[1,2,3],[2,3,4]] => 4 [[1,2,2],[3,4,4]] => 3 [[1,2,3],[2,4,4]] => 3 [[1,2,2],[4,4,4]] => 2 [[1,2,3],[3,3,4]] => 4 [[1,2,3],[3,4,4]] => 4 [[1,3,3],[2,4,4]] => 2 [[1,2,3],[4,4,4]] => 3 [[1,3,3],[3,4,4]] => 3 [[1,3,3],[4,4,4]] => 2 [[2,2,2],[3,3,4]] => 3 [[2,2,2],[3,4,4]] => 3 [[2,2,2],[4,4,4]] => 2 [[2,2,3],[3,3,4]] => 4 [[2,2,3],[3,4,4]] => 4 [[2,2,3],[4,4,4]] => 3 [[2,3,3],[3,4,4]] => 4 [[2,3,3],[4,4,4]] => 3 [[3,3,3],[4,4,4]] => 2 [[1,1,1],[2,2],[4]] => 1 [[1,1,1],[2,3],[4]] => 2 [[1,1,1],[2,4],[3]] => 1 [[1,1,1],[2,4],[4]] => 2 [[1,1,1],[3,3],[4]] => 2 [[1,1,1],[3,4],[4]] => 3 [[1,1,2],[2,2],[4]] => 2 [[1,1,2],[2,3],[4]] => 3 [[1,1,2],[2,4],[3]] => 2 [[1,1,3],[2,2],[4]] => 2 [[1,1,4],[2,2],[3]] => 1 [[1,1,2],[2,4],[4]] => 3 [[1,1,4],[2,2],[4]] => 2 [[1,1,2],[3,3],[4]] => 3 [[1,1,3],[2,3],[4]] => 3 [[1,1,3],[2,4],[3]] => 2 [[1,1,4],[2,3],[3]] => 2 [[1,1,2],[3,4],[4]] => 4 [[1,1,3],[2,4],[4]] => 3 [[1,1,4],[2,3],[4]] => 3 [[1,1,4],[2,4],[3]] => 2 [[1,1,4],[2,4],[4]] => 3 [[1,1,3],[3,3],[4]] => 3 [[1,1,3],[3,4],[4]] => 4 [[1,1,4],[3,3],[4]] => 3 [[1,1,4],[3,4],[4]] => 4 [[1,2,2],[2,3],[4]] => 3 [[1,2,2],[2,4],[3]] => 2 [[1,2,2],[2,4],[4]] => 3 [[1,2,2],[3,3],[4]] => 3 [[1,2,3],[2,3],[4]] => 4 [[1,2,3],[2,4],[3]] => 3 [[1,2,4],[2,3],[3]] => 3 [[1,2,2],[3,4],[4]] => 4 [[1,2,3],[2,4],[4]] => 4 [[1,2,4],[2,3],[4]] => 4 [[1,2,4],[2,4],[3]] => 3 [[1,2,4],[2,4],[4]] => 4 [[1,2,3],[3,3],[4]] => 4 [[1,3,3],[2,4],[3]] => 2 [[1,2,3],[3,4],[4]] => 5 [[1,2,4],[3,3],[4]] => 4 [[1,3,3],[2,4],[4]] => 3 [[1,3,4],[2,4],[3]] => 3 [[1,2,4],[3,4],[4]] => 5 [[1,3,4],[2,4],[4]] => 4 [[1,3,3],[3,4],[4]] => 4 [[1,3,4],[3,4],[4]] => 5 [[2,2,2],[3,3],[4]] => 3 [[2,2,2],[3,4],[4]] => 4 [[2,2,3],[3,3],[4]] => 4 [[2,2,3],[3,4],[4]] => 5 [[2,2,4],[3,3],[4]] => 4 [[2,2,4],[3,4],[4]] => 5 [[2,3,3],[3,4],[4]] => 5 [[2,3,4],[3,4],[4]] => 6 [[1,1,1],[2],[3],[4]] => 0 [[1,1,2],[2],[3],[4]] => 1 [[1,1,3],[2],[3],[4]] => 1 [[1,1,4],[2],[3],[4]] => 1 [[1,2,2],[2],[3],[4]] => 1 [[1,2,3],[2],[3],[4]] => 2 [[1,2,4],[2],[3],[4]] => 2 [[1,3,3],[2],[3],[4]] => 1 [[1,3,4],[2],[3],[4]] => 2 [[1,4,4],[2],[3],[4]] => 1 [[1,1],[2,2],[3,4]] => 1 [[1,1],[2,2],[4,4]] => 1 [[1,1],[2,3],[3,4]] => 2 [[1,1],[2,3],[4,4]] => 2 [[1,1],[3,3],[4,4]] => 2 [[1,2],[2,3],[3,4]] => 3 [[1,2],[2,3],[4,4]] => 3 [[1,2],[3,3],[4,4]] => 3 [[2,2],[3,3],[4,4]] => 3 [[1,1],[2,2],[3],[4]] => 0 [[1,1],[2,3],[3],[4]] => 1 [[1,1],[2,4],[3],[4]] => 1 [[1,2],[2,3],[3],[4]] => 2 [[1,2],[2,4],[3],[4]] => 2 [[1,3],[2,4],[3],[4]] => 2 [[1,1,1,1,1,1,1]] => 0 [[1,1,1,1,1,1,2]] => 1 [[1,1,1,1,1,2,2]] => 1 [[1,1,1,1,2,2,2]] => 1 [[1,1,1,2,2,2,2]] => 1 [[1,1,2,2,2,2,2]] => 1 [[1,2,2,2,2,2,2]] => 1 [[2,2,2,2,2,2,2]] => 1 [[1,1,1,1,1,1],[2]] => 0 [[1,1,1,1,1,2],[2]] => 1 [[1,1,1,1,2,2],[2]] => 1 [[1,1,1,2,2,2],[2]] => 1 [[1,1,2,2,2,2],[2]] => 1 [[1,1,1,1,1,1,3]] => 1 [[1,1,1,1,1,2,3]] => 2 [[1,1,1,1,1,3,3]] => 1 [[1,1,1,1,2,2,3]] => 2 [[1,1,1,1,2,3,3]] => 2 [[1,1,1,1,3,3,3]] => 1 [[1,1,1,2,2,2,3]] => 2 [[1,1,1,2,2,3,3]] => 2 [[1,1,1,2,3,3,3]] => 2 [[1,1,1,3,3,3,3]] => 1 [[1,1,2,2,2,2,3]] => 2 [[1,1,2,2,2,3,3]] => 2 [[1,1,2,2,3,3,3]] => 2 [[1,1,2,3,3,3,3]] => 2 [[1,1,3,3,3,3,3]] => 1 [[1,2,2,2,2,2,3]] => 2 [[1,2,2,2,2,3,3]] => 2 [[1,2,2,2,3,3,3]] => 2 [[1,2,2,3,3,3,3]] => 2 [[1,2,3,3,3,3,3]] => 2 [[1,3,3,3,3,3,3]] => 1 [[2,2,2,2,2,2,3]] => 2 [[2,2,2,2,2,3,3]] => 2 [[2,2,2,2,3,3,3]] => 2 [[2,2,2,3,3,3,3]] => 2 [[2,2,3,3,3,3,3]] => 2 [[2,3,3,3,3,3,3]] => 2 [[3,3,3,3,3,3,3]] => 1 [[1,1,1,1,1,1],[3]] => 1 [[1,1,1,1,1,2],[3]] => 2 [[1,1,1,1,1,3],[2]] => 1 [[1,1,1,1,1,3],[3]] => 2 [[1,1,1,1,2,2],[3]] => 2 [[1,1,1,1,2,3],[2]] => 2 [[1,1,1,1,2,3],[3]] => 3 [[1,1,1,1,3,3],[2]] => 1 [[1,1,1,1,3,3],[3]] => 2 [[1,1,1,2,2,2],[3]] => 2 [[1,1,1,2,2,3],[2]] => 2 [[1,1,1,2,2,3],[3]] => 3 [[1,1,1,2,3,3],[2]] => 2 [[1,1,1,2,3,3],[3]] => 3 [[1,1,1,3,3,3],[2]] => 1 [[1,1,1,3,3,3],[3]] => 2 [[1,1,2,2,2,2],[3]] => 2 [[1,1,2,2,2,3],[2]] => 2 [[1,1,2,2,2,3],[3]] => 3 [[1,1,2,2,3,3],[2]] => 2 [[1,1,2,2,3,3],[3]] => 3 [[1,1,2,3,3,3],[2]] => 2 [[1,1,1,1,1,1,4]] => 1 [[1,1,1,1,1,2,4]] => 2 [[1,1,1,1,1,3,4]] => 2 [[1,1,1,1,1,4,4]] => 1 [[1,1,1,1,2,2,4]] => 2 [[1,1,1,1,2,3,4]] => 3 [[1,1,1,1,2,4,4]] => 2 [[1,1,1,1,3,3,4]] => 2 [[1,1,1,1,3,4,4]] => 2 [[1,1,1,1,4,4,4]] => 1 [[1,1,1,2,2,2,4]] => 2 [[1,1,1,2,2,3,4]] => 3 [[1,1,1,2,2,4,4]] => 2 [[1,1,1,2,3,3,4]] => 3 [[1,1,1,2,3,4,4]] => 3 [[1,1,1,2,4,4,4]] => 2 [[1,1,1,3,3,3,4]] => 2 [[1,1,1,3,3,4,4]] => 2 [[1,1,1,3,4,4,4]] => 2 [[1,1,1,4,4,4,4]] => 1 [[1,1,2,2,2,2,4]] => 2 [[1,1,2,2,2,3,4]] => 3 [[1,1,2,2,2,4,4]] => 2 [[1,1,2,2,3,3,4]] => 3 [[1,1,2,2,3,4,4]] => 3 [[1,1,2,2,4,4,4]] => 2 [[1,1,2,3,3,3,4]] => 3 [[1,1,2,3,3,4,4]] => 3 [[1,1,2,3,4,4,4]] => 3 [[1,1,2,4,4,4,4]] => 2 [[1,1,3,3,3,3,4]] => 2 [[1,1,3,3,3,4,4]] => 2 [[1,1,3,3,4,4,4]] => 2 [[1,1,3,4,4,4,4]] => 2 [[1,1,4,4,4,4,4]] => 1 [[1,2,2,2,2,2,4]] => 2 [[1,2,2,2,2,3,4]] => 3 [[1,2,2,2,2,4,4]] => 2 [[1,2,2,2,3,3,4]] => 3 [[1,2,2,2,3,4,4]] => 3 [[1,2,2,2,4,4,4]] => 2 [[1,2,2,3,3,3,4]] => 3 [[1,2,2,3,3,4,4]] => 3 [[1,2,2,3,4,4,4]] => 3 [[1,2,2,4,4,4,4]] => 2 [[1,2,3,3,3,3,4]] => 3 [[1,2,3,3,3,4,4]] => 3 [[1,2,3,3,4,4,4]] => 3 [[1,2,3,4,4,4,4]] => 3 [[1,2,4,4,4,4,4]] => 2 [[1,3,3,3,3,3,4]] => 2 [[1,3,3,3,3,4,4]] => 2 [[1,3,3,3,4,4,4]] => 2 [[1,3,3,4,4,4,4]] => 2 [[1,3,4,4,4,4,4]] => 2 [[1,4,4,4,4,4,4]] => 1 [[2,2,2,2,2,2,4]] => 2 [[2,2,2,2,2,3,4]] => 3 [[2,2,2,2,2,4,4]] => 2 [[2,2,2,2,3,3,4]] => 3 [[2,2,2,2,3,4,4]] => 3 [[2,2,2,2,4,4,4]] => 2 [[2,2,2,3,3,3,4]] => 3 [[2,2,2,3,3,4,4]] => 3 [[2,2,2,3,4,4,4]] => 3 [[2,2,2,4,4,4,4]] => 2 [[2,2,3,3,3,3,4]] => 3 [[2,2,3,3,3,4,4]] => 3 [[2,2,3,3,4,4,4]] => 3 [[2,2,3,4,4,4,4]] => 3 [[2,2,4,4,4,4,4]] => 2 [[2,3,3,3,3,3,4]] => 3 [[2,3,3,3,3,4,4]] => 3 [[2,3,3,3,4,4,4]] => 3 [[2,3,3,4,4,4,4]] => 3 [[2,3,4,4,4,4,4]] => 3 [[2,4,4,4,4,4,4]] => 2 [[3,3,3,3,3,3,4]] => 2 [[3,3,3,3,3,4,4]] => 2 [[3,3,3,3,4,4,4]] => 2 [[3,3,3,4,4,4,4]] => 2 [[3,3,4,4,4,4,4]] => 2 [[3,4,4,4,4,4,4]] => 2 [[4,4,4,4,4,4,4]] => 1 [[1,1,1,1,1,1],[4]] => 1 [[1,1,1,1,1,2],[4]] => 2 [[1,1,1,1,1,4],[2]] => 1 [[1,1,1,1,1,3],[4]] => 2 [[1,1,1,1,1,4],[3]] => 2 [[1,1,1,1,1,4],[4]] => 2 [[1,1,1,1,2,2],[4]] => 2 [[1,1,1,1,2,4],[2]] => 2 [[1,1,1,1,2,3],[4]] => 3 [[1,1,1,1,2,4],[3]] => 3 [[1,1,1,1,3,4],[2]] => 2 [[1,1,1,1,2,4],[4]] => 3 [[1,1,1,1,4,4],[2]] => 1 [[1,1,1,1,3,3],[4]] => 2 [[1,1,1,1,3,4],[3]] => 3 [[1,1,1,1,3,4],[4]] => 3 [[1,1,1,1,4,4],[3]] => 2 [[1,1,1,1,4,4],[4]] => 2 [[1,1,1,2,2,2],[4]] => 2 [[1,1,1,2,2,4],[2]] => 2 [[1,1,1,2,2,3],[4]] => 3 [[1,1,1,2,2,4],[3]] => 3 [[1,1,1,2,3,4],[2]] => 3 [[1,1,1,2,2,4],[4]] => 3 [[1,1,1,2,4,4],[2]] => 2 [[1,1,1,2,3,3],[4]] => 3 [[1,1,1,2,3,4],[3]] => 4 [[1,1,1,3,3,4],[2]] => 2 [[1,1,1,2,3,4],[4]] => 4 [[1,1,1,2,4,4],[3]] => 3 [[1,1,1,3,4,4],[2]] => 2 [[1,1,1,2,4,4],[4]] => 3 [[1,1,1,4,4,4],[2]] => 1 [[1,1,1,3,3,3],[4]] => 2 [[1,1,1,3,3,4],[3]] => 3 [[1,1,1,3,3,4],[4]] => 3 [[1,1,1,3,4,4],[3]] => 3 [[1,1,1,3,4,4],[4]] => 3 [[1,1,1,4,4,4],[3]] => 2 [[1,1,1,4,4,4],[4]] => 2 [[1,1,2,2,2,2],[4]] => 2 [[1,1,2,2,2,4],[2]] => 2 [[1,1,2,2,2,3],[4]] => 3 [[1,1,2,2,2,4],[3]] => 3 [[1,1,2,2,3,4],[2]] => 3 [[1,1,2,2,2,4],[4]] => 3 [[1,1,2,2,4,4],[2]] => 2 [[1,1,2,2,3,3],[4]] => 3 [[1,1,2,2,3,4],[3]] => 4 [[1,1,2,3,3,4],[2]] => 3 [[1,1,2,2,3,4],[4]] => 4 [[1,1,2,2,4,4],[3]] => 3 [[1,1,2,3,4,4],[2]] => 3 ----------------------------------------------------------------------------- Created: Jan 13, 2014 at 21:21 by Ben Salisbury ----------------------------------------------------------------------------- Last Updated: Oct 19, 2015 at 16:36 by Christian Stump