***************************************************************************** * 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: St000103 ----------------------------------------------------------------------------- Collection: Semistandard tableaux ----------------------------------------------------------------------------- Description: The sum of the entries of a semistandard tableau. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(s): return sum(s.entries()) ----------------------------------------------------------------------------- Statistic values: [[1]] => 1 [[1,1]] => 2 [[1,2]] => 3 [[2,2]] => 4 [[1],[2]] => 3 [[1,1,1]] => 3 [[1,1,2]] => 4 [[1,2,2]] => 5 [[2,2,2]] => 6 [[1,1],[2]] => 4 [[1,2],[2]] => 5 [[1,1,3]] => 5 [[1,2,3]] => 6 [[1,3,3]] => 7 [[2,2,3]] => 7 [[2,3,3]] => 8 [[3,3,3]] => 9 [[1,1],[3]] => 5 [[1,2],[3]] => 6 [[1,3],[2]] => 6 [[1,3],[3]] => 7 [[2,2],[3]] => 7 [[2,3],[3]] => 8 [[1],[2],[3]] => 6 [[1,1,1,1]] => 4 [[1,1,1,2]] => 5 [[1,1,2,2]] => 6 [[1,2,2,2]] => 7 [[2,2,2,2]] => 8 [[1,1,1],[2]] => 5 [[1,1,2],[2]] => 6 [[1,2,2],[2]] => 7 [[1,1],[2,2]] => 6 [[1,1,1,3]] => 6 [[1,1,2,3]] => 7 [[1,1,3,3]] => 8 [[1,2,2,3]] => 8 [[1,2,3,3]] => 9 [[1,3,3,3]] => 10 [[2,2,2,3]] => 9 [[2,2,3,3]] => 10 [[2,3,3,3]] => 11 [[3,3,3,3]] => 12 [[1,1,1],[3]] => 6 [[1,1,2],[3]] => 7 [[1,1,3],[2]] => 7 [[1,1,3],[3]] => 8 [[1,2,2],[3]] => 8 [[1,2,3],[2]] => 8 [[1,2,3],[3]] => 9 [[1,3,3],[2]] => 9 [[1,3,3],[3]] => 10 [[2,2,2],[3]] => 9 [[2,2,3],[3]] => 10 [[2,3,3],[3]] => 11 [[1,1],[2,3]] => 7 [[1,1],[3,3]] => 8 [[1,2],[2,3]] => 8 [[1,2],[3,3]] => 9 [[2,2],[3,3]] => 10 [[1,1],[2],[3]] => 7 [[1,2],[2],[3]] => 8 [[1,3],[2],[3]] => 9 [[1,1,1,4]] => 7 [[1,1,2,4]] => 8 [[1,1,3,4]] => 9 [[1,1,4,4]] => 10 [[1,2,2,4]] => 9 [[1,2,3,4]] => 10 [[1,2,4,4]] => 11 [[1,3,3,4]] => 11 [[1,3,4,4]] => 12 [[1,4,4,4]] => 13 [[2,2,2,4]] => 10 [[2,2,3,4]] => 11 [[2,2,4,4]] => 12 [[2,3,3,4]] => 12 [[2,3,4,4]] => 13 [[2,4,4,4]] => 14 [[3,3,3,4]] => 13 [[3,3,4,4]] => 14 [[3,4,4,4]] => 15 [[4,4,4,4]] => 16 [[1,1,1],[4]] => 7 [[1,1,2],[4]] => 8 [[1,1,4],[2]] => 8 [[1,1,3],[4]] => 9 [[1,1,4],[3]] => 9 [[1,1,4],[4]] => 10 [[1,2,2],[4]] => 9 [[1,2,4],[2]] => 9 [[1,2,3],[4]] => 10 [[1,2,4],[3]] => 10 [[1,3,4],[2]] => 10 [[1,2,4],[4]] => 11 [[1,4,4],[2]] => 11 [[1,3,3],[4]] => 11 [[1,3,4],[3]] => 11 [[1,3,4],[4]] => 12 [[1,4,4],[3]] => 12 [[1,4,4],[4]] => 13 [[2,2,2],[4]] => 10 [[2,2,3],[4]] => 11 [[2,2,4],[3]] => 11 [[2,2,4],[4]] => 12 [[2,3,3],[4]] => 12 [[2,3,4],[3]] => 12 [[2,3,4],[4]] => 13 [[2,4,4],[3]] => 13 [[2,4,4],[4]] => 14 [[3,3,3],[4]] => 13 [[3,3,4],[4]] => 14 [[3,4,4],[4]] => 15 [[1,1],[2,4]] => 8 [[1,1],[3,4]] => 9 [[1,1],[4,4]] => 10 [[1,2],[2,4]] => 9 [[1,2],[3,4]] => 10 [[1,3],[2,4]] => 10 [[1,2],[4,4]] => 11 [[1,3],[3,4]] => 11 [[1,3],[4,4]] => 12 [[2,2],[3,4]] => 11 [[2,2],[4,4]] => 12 [[2,3],[3,4]] => 12 [[2,3],[4,4]] => 13 [[3,3],[4,4]] => 14 [[1,1],[2],[4]] => 8 [[1,1],[3],[4]] => 9 [[1,2],[2],[4]] => 9 [[1,2],[3],[4]] => 10 [[1,3],[2],[4]] => 10 [[1,4],[2],[3]] => 10 [[1,4],[2],[4]] => 11 [[1,3],[3],[4]] => 11 [[1,4],[3],[4]] => 12 [[2,2],[3],[4]] => 11 [[2,3],[3],[4]] => 12 [[2,4],[3],[4]] => 13 [[1],[2],[3],[4]] => 10 [[1,1,1,1,1]] => 5 [[1,1,1,1,2]] => 6 [[1,1,1,2,2]] => 7 [[1,1,2,2,2]] => 8 [[1,2,2,2,2]] => 9 [[2,2,2,2,2]] => 10 [[1,1,1,1],[2]] => 6 [[1,1,1,2],[2]] => 7 [[1,1,2,2],[2]] => 8 [[1,2,2,2],[2]] => 9 [[1,1,1],[2,2]] => 7 [[1,1,2],[2,2]] => 8 [[1,1,1,1,3]] => 7 [[1,1,1,2,3]] => 8 [[1,1,1,3,3]] => 9 [[1,1,2,2,3]] => 9 [[1,1,2,3,3]] => 10 [[1,1,3,3,3]] => 11 [[1,2,2,2,3]] => 10 [[1,2,2,3,3]] => 11 [[1,2,3,3,3]] => 12 [[1,3,3,3,3]] => 13 [[2,2,2,2,3]] => 11 [[2,2,2,3,3]] => 12 [[2,2,3,3,3]] => 13 [[2,3,3,3,3]] => 14 [[3,3,3,3,3]] => 15 [[1,1,1,1],[3]] => 7 [[1,1,1,2],[3]] => 8 [[1,1,1,3],[2]] => 8 [[1,1,1,3],[3]] => 9 [[1,1,2,2],[3]] => 9 [[1,1,2,3],[2]] => 9 [[1,1,2,3],[3]] => 10 [[1,1,3,3],[2]] => 10 [[1,1,3,3],[3]] => 11 [[1,2,2,2],[3]] => 10 [[1,2,2,3],[2]] => 10 [[1,2,2,3],[3]] => 11 [[1,2,3,3],[2]] => 11 [[1,2,3,3],[3]] => 12 [[1,3,3,3],[2]] => 12 [[1,3,3,3],[3]] => 13 [[2,2,2,2],[3]] => 11 [[2,2,2,3],[3]] => 12 [[2,2,3,3],[3]] => 13 [[2,3,3,3],[3]] => 14 [[1,1,1],[2,3]] => 8 [[1,1,1],[3,3]] => 9 [[1,1,2],[2,3]] => 9 [[1,1,3],[2,2]] => 9 [[1,1,2],[3,3]] => 10 [[1,1,3],[2,3]] => 10 [[1,1,3],[3,3]] => 11 [[1,2,2],[2,3]] => 10 [[1,2,2],[3,3]] => 11 [[1,2,3],[2,3]] => 11 [[1,2,3],[3,3]] => 12 [[2,2,2],[3,3]] => 12 [[2,2,3],[3,3]] => 13 [[1,1,1],[2],[3]] => 8 [[1,1,2],[2],[3]] => 9 [[1,1,3],[2],[3]] => 10 [[1,2,2],[2],[3]] => 10 [[1,2,3],[2],[3]] => 11 [[1,3,3],[2],[3]] => 12 [[1,1],[2,2],[3]] => 9 [[1,1],[2,3],[3]] => 10 [[1,2],[2,3],[3]] => 11 [[1,1,1,1,4]] => 8 [[1,1,1,2,4]] => 9 [[1,1,1,3,4]] => 10 [[1,1,1,4,4]] => 11 [[1,1,2,2,4]] => 10 [[1,1,2,3,4]] => 11 [[1,1,2,4,4]] => 12 [[1,1,3,3,4]] => 12 [[1,1,3,4,4]] => 13 [[1,1,4,4,4]] => 14 [[1,2,2,2,4]] => 11 [[1,2,2,3,4]] => 12 [[1,2,2,4,4]] => 13 [[1,2,3,3,4]] => 13 [[1,2,3,4,4]] => 14 [[1,2,4,4,4]] => 15 [[1,3,3,3,4]] => 14 [[1,3,3,4,4]] => 15 [[1,3,4,4,4]] => 16 [[1,4,4,4,4]] => 17 [[2,2,2,2,4]] => 12 [[2,2,2,3,4]] => 13 [[2,2,2,4,4]] => 14 [[2,2,3,3,4]] => 14 [[2,2,3,4,4]] => 15 [[2,2,4,4,4]] => 16 [[2,3,3,3,4]] => 15 [[2,3,3,4,4]] => 16 [[2,3,4,4,4]] => 17 [[2,4,4,4,4]] => 18 [[3,3,3,3,4]] => 16 [[3,3,3,4,4]] => 17 [[3,3,4,4,4]] => 18 [[3,4,4,4,4]] => 19 [[4,4,4,4,4]] => 20 [[1,1,1,1],[4]] => 8 [[1,1,1,2],[4]] => 9 [[1,1,1,4],[2]] => 9 [[1,1,1,3],[4]] => 10 [[1,1,1,4],[3]] => 10 [[1,1,1,4],[4]] => 11 [[1,1,2,2],[4]] => 10 [[1,1,2,4],[2]] => 10 [[1,1,2,3],[4]] => 11 [[1,1,2,4],[3]] => 11 [[1,1,3,4],[2]] => 11 [[1,1,2,4],[4]] => 12 [[1,1,4,4],[2]] => 12 [[1,1,3,3],[4]] => 12 [[1,1,3,4],[3]] => 12 [[1,1,3,4],[4]] => 13 [[1,1,4,4],[3]] => 13 [[1,1,4,4],[4]] => 14 [[1,2,2,2],[4]] => 11 [[1,2,2,4],[2]] => 11 [[1,2,2,3],[4]] => 12 [[1,2,2,4],[3]] => 12 [[1,2,3,4],[2]] => 12 [[1,2,2,4],[4]] => 13 [[1,2,4,4],[2]] => 13 [[1,2,3,3],[4]] => 13 [[1,2,3,4],[3]] => 13 [[1,3,3,4],[2]] => 13 [[1,2,3,4],[4]] => 14 [[1,2,4,4],[3]] => 14 [[1,3,4,4],[2]] => 14 [[1,2,4,4],[4]] => 15 [[1,4,4,4],[2]] => 15 [[1,3,3,3],[4]] => 14 [[1,3,3,4],[3]] => 14 [[1,3,3,4],[4]] => 15 [[1,3,4,4],[3]] => 15 [[1,3,4,4],[4]] => 16 [[1,4,4,4],[3]] => 16 [[1,4,4,4],[4]] => 17 [[2,2,2,2],[4]] => 12 [[2,2,2,3],[4]] => 13 [[2,2,2,4],[3]] => 13 [[2,2,2,4],[4]] => 14 [[2,2,3,3],[4]] => 14 [[2,2,3,4],[3]] => 14 [[2,2,3,4],[4]] => 15 [[2,2,4,4],[3]] => 15 [[2,2,4,4],[4]] => 16 [[2,3,3,3],[4]] => 15 [[2,3,3,4],[3]] => 15 [[2,3,3,4],[4]] => 16 [[2,3,4,4],[3]] => 16 [[2,3,4,4],[4]] => 17 [[2,4,4,4],[3]] => 17 [[2,4,4,4],[4]] => 18 [[3,3,3,3],[4]] => 16 [[3,3,3,4],[4]] => 17 [[3,3,4,4],[4]] => 18 [[3,4,4,4],[4]] => 19 [[1,1,1],[2,4]] => 9 [[1,1,1],[3,4]] => 10 [[1,1,1],[4,4]] => 11 [[1,1,2],[2,4]] => 10 [[1,1,4],[2,2]] => 10 [[1,1,2],[3,4]] => 11 [[1,1,3],[2,4]] => 11 [[1,1,4],[2,3]] => 11 [[1,1,2],[4,4]] => 12 [[1,1,4],[2,4]] => 12 [[1,1,3],[3,4]] => 12 [[1,1,4],[3,3]] => 12 [[1,1,3],[4,4]] => 13 [[1,1,4],[3,4]] => 13 [[1,1,4],[4,4]] => 14 [[1,2,2],[2,4]] => 11 [[1,2,2],[3,4]] => 12 [[1,2,3],[2,4]] => 12 [[1,2,4],[2,3]] => 12 [[1,2,2],[4,4]] => 13 [[1,2,4],[2,4]] => 13 [[1,2,3],[3,4]] => 13 [[1,2,4],[3,3]] => 13 [[1,3,3],[2,4]] => 13 [[1,2,3],[4,4]] => 14 [[1,2,4],[3,4]] => 14 [[1,3,4],[2,4]] => 14 [[1,2,4],[4,4]] => 15 [[1,3,3],[3,4]] => 14 [[1,3,3],[4,4]] => 15 [[1,3,4],[3,4]] => 15 [[1,3,4],[4,4]] => 16 [[2,2,2],[3,4]] => 13 [[2,2,2],[4,4]] => 14 [[2,2,3],[3,4]] => 14 [[2,2,4],[3,3]] => 14 [[2,2,3],[4,4]] => 15 [[2,2,4],[3,4]] => 15 [[2,2,4],[4,4]] => 16 [[2,3,3],[3,4]] => 15 [[2,3,3],[4,4]] => 16 [[2,3,4],[3,4]] => 16 [[2,3,4],[4,4]] => 17 [[3,3,3],[4,4]] => 17 [[3,3,4],[4,4]] => 18 [[1,1,1],[2],[4]] => 9 [[1,1,1],[3],[4]] => 10 [[1,1,2],[2],[4]] => 10 [[1,1,2],[3],[4]] => 11 [[1,1,3],[2],[4]] => 11 [[1,1,4],[2],[3]] => 11 [[1,1,4],[2],[4]] => 12 [[1,1,3],[3],[4]] => 12 [[1,1,4],[3],[4]] => 13 [[1,2,2],[2],[4]] => 11 [[1,2,2],[3],[4]] => 12 [[1,2,3],[2],[4]] => 12 [[1,2,4],[2],[3]] => 12 [[1,2,4],[2],[4]] => 13 [[1,2,3],[3],[4]] => 13 [[1,3,3],[2],[4]] => 13 [[1,3,4],[2],[3]] => 13 [[1,2,4],[3],[4]] => 14 [[1,3,4],[2],[4]] => 14 [[1,4,4],[2],[3]] => 14 [[1,4,4],[2],[4]] => 15 [[1,3,3],[3],[4]] => 14 [[1,3,4],[3],[4]] => 15 [[1,4,4],[3],[4]] => 16 [[2,2,2],[3],[4]] => 13 [[2,2,3],[3],[4]] => 14 [[2,2,4],[3],[4]] => 15 [[2,3,3],[3],[4]] => 15 [[2,3,4],[3],[4]] => 16 [[2,4,4],[3],[4]] => 17 [[1,1],[2,2],[4]] => 10 [[1,1],[2,3],[4]] => 11 [[1,1],[2,4],[3]] => 11 [[1,1],[2,4],[4]] => 12 [[1,1],[3,3],[4]] => 12 [[1,1],[3,4],[4]] => 13 [[1,2],[2,3],[4]] => 12 [[1,2],[2,4],[3]] => 12 [[1,2],[2,4],[4]] => 13 [[1,2],[3,3],[4]] => 13 [[1,3],[2,4],[3]] => 13 [[1,2],[3,4],[4]] => 14 [[1,3],[2,4],[4]] => 14 [[1,3],[3,4],[4]] => 15 [[2,2],[3,3],[4]] => 14 [[2,2],[3,4],[4]] => 15 [[2,3],[3,4],[4]] => 16 [[1,1],[2],[3],[4]] => 11 [[1,2],[2],[3],[4]] => 12 [[1,3],[2],[3],[4]] => 13 [[1,4],[2],[3],[4]] => 14 [[1,1,1,1,5]] => 9 [[1,1,1,2,5]] => 10 [[1,1,1,3,5]] => 11 [[1,1,1,4,5]] => 12 [[1,1,1,5,5]] => 13 [[1,1,2,2,5]] => 11 [[1,1,2,3,5]] => 12 [[1,1,2,4,5]] => 13 [[1,1,2,5,5]] => 14 [[1,1,3,3,5]] => 13 [[1,1,3,4,5]] => 14 [[1,1,3,5,5]] => 15 [[1,1,4,4,5]] => 15 [[1,1,4,5,5]] => 16 [[1,1,5,5,5]] => 17 [[1,2,2,2,5]] => 12 [[1,2,2,3,5]] => 13 [[1,2,2,4,5]] => 14 [[1,2,2,5,5]] => 15 [[1,2,3,3,5]] => 14 [[1,2,3,4,5]] => 15 [[1,2,3,5,5]] => 16 [[1,2,4,4,5]] => 16 [[1,2,4,5,5]] => 17 [[1,2,5,5,5]] => 18 [[1,3,3,3,5]] => 15 [[1,3,3,4,5]] => 16 [[1,3,3,5,5]] => 17 [[1,3,4,4,5]] => 17 [[1,3,4,5,5]] => 18 [[1,3,5,5,5]] => 19 [[1,4,4,4,5]] => 18 [[1,4,4,5,5]] => 19 [[1,4,5,5,5]] => 20 [[1,5,5,5,5]] => 21 [[2,2,2,2,5]] => 13 [[2,2,2,3,5]] => 14 [[2,2,2,4,5]] => 15 [[2,2,2,5,5]] => 16 [[2,2,3,3,5]] => 15 [[2,2,3,4,5]] => 16 [[2,2,3,5,5]] => 17 [[2,2,4,4,5]] => 17 [[2,2,4,5,5]] => 18 [[2,2,5,5,5]] => 19 [[2,3,3,3,5]] => 16 [[2,3,3,4,5]] => 17 [[2,3,3,5,5]] => 18 [[2,3,4,4,5]] => 18 [[2,3,4,5,5]] => 19 [[2,3,5,5,5]] => 20 [[2,4,4,4,5]] => 19 [[2,4,4,5,5]] => 20 [[2,4,5,5,5]] => 21 [[2,5,5,5,5]] => 22 [[3,3,3,3,5]] => 17 [[3,3,3,4,5]] => 18 [[3,3,3,5,5]] => 19 [[3,3,4,4,5]] => 19 [[3,3,4,5,5]] => 20 [[3,3,5,5,5]] => 21 [[3,4,4,4,5]] => 20 [[3,4,4,5,5]] => 21 [[3,4,5,5,5]] => 22 [[3,5,5,5,5]] => 23 [[4,4,4,4,5]] => 21 [[4,4,4,5,5]] => 22 [[4,4,5,5,5]] => 23 [[4,5,5,5,5]] => 24 [[5,5,5,5,5]] => 25 [[1,1,1,1],[5]] => 9 [[1,1,1,2],[5]] => 10 [[1,1,1,5],[2]] => 10 [[1,1,1,3],[5]] => 11 [[1,1,1,5],[3]] => 11 [[1,1,1,4],[5]] => 12 [[1,1,1,5],[4]] => 12 [[1,1,1,5],[5]] => 13 [[1,1,2,2],[5]] => 11 [[1,1,2,5],[2]] => 11 [[1,1,2,3],[5]] => 12 [[1,1,2,5],[3]] => 12 [[1,1,3,5],[2]] => 12 [[1,1,2,4],[5]] => 13 [[1,1,2,5],[4]] => 13 [[1,1,4,5],[2]] => 13 [[1,1,2,5],[5]] => 14 [[1,1,5,5],[2]] => 14 [[1,1,3,3],[5]] => 13 [[1,1,3,5],[3]] => 13 [[1,1,3,4],[5]] => 14 [[1,1,3,5],[4]] => 14 [[1,1,4,5],[3]] => 14 [[1,1,3,5],[5]] => 15 [[1,1,5,5],[3]] => 15 [[1,1,4,4],[5]] => 15 [[1,1,4,5],[4]] => 15 [[1,1,4,5],[5]] => 16 [[1,1,5,5],[4]] => 16 [[1,1,5,5],[5]] => 17 [[1,2,2,2],[5]] => 12 [[1,2,2,5],[2]] => 12 [[1,2,2,3],[5]] => 13 [[1,2,2,5],[3]] => 13 [[1,2,3,5],[2]] => 13 [[1,2,2,4],[5]] => 14 [[1,2,2,5],[4]] => 14 [[1,2,4,5],[2]] => 14 [[1,2,2,5],[5]] => 15 [[1,2,5,5],[2]] => 15 [[1,2,3,3],[5]] => 14 [[1,2,3,5],[3]] => 14 [[1,3,3,5],[2]] => 14 [[1,2,3,4],[5]] => 15 [[1,2,3,5],[4]] => 15 [[1,2,4,5],[3]] => 15 [[1,3,4,5],[2]] => 15 [[1,2,3,5],[5]] => 16 [[1,2,5,5],[3]] => 16 [[1,3,5,5],[2]] => 16 [[1,2,4,4],[5]] => 16 [[1,2,4,5],[4]] => 16 [[1,4,4,5],[2]] => 16 [[1,2,4,5],[5]] => 17 [[1,2,5,5],[4]] => 17 [[1,4,5,5],[2]] => 17 [[1,2,5,5],[5]] => 18 [[1,5,5,5],[2]] => 18 [[1,3,3,3],[5]] => 15 [[1,3,3,5],[3]] => 15 [[1,3,3,4],[5]] => 16 [[1,3,3,5],[4]] => 16 [[1,3,4,5],[3]] => 16 [[1,3,3,5],[5]] => 17 [[1,3,5,5],[3]] => 17 [[1,3,4,4],[5]] => 17 [[1,3,4,5],[4]] => 17 [[1,4,4,5],[3]] => 17 [[1,3,4,5],[5]] => 18 [[1,3,5,5],[4]] => 18 [[1,4,5,5],[3]] => 18 [[1,3,5,5],[5]] => 19 [[1,5,5,5],[3]] => 19 [[1,4,4,4],[5]] => 18 [[1,4,4,5],[4]] => 18 [[1,4,4,5],[5]] => 19 [[1,4,5,5],[4]] => 19 [[1,4,5,5],[5]] => 20 [[1,5,5,5],[4]] => 20 [[1,5,5,5],[5]] => 21 [[2,2,2,2],[5]] => 13 [[2,2,2,3],[5]] => 14 [[2,2,2,5],[3]] => 14 [[2,2,2,4],[5]] => 15 [[2,2,2,5],[4]] => 15 [[2,2,2,5],[5]] => 16 [[2,2,3,3],[5]] => 15 [[2,2,3,5],[3]] => 15 [[2,2,3,4],[5]] => 16 [[2,2,3,5],[4]] => 16 [[2,2,4,5],[3]] => 16 [[2,2,3,5],[5]] => 17 [[2,2,5,5],[3]] => 17 [[2,2,4,4],[5]] => 17 [[2,2,4,5],[4]] => 17 [[2,2,4,5],[5]] => 18 [[2,2,5,5],[4]] => 18 [[2,2,5,5],[5]] => 19 [[2,3,3,3],[5]] => 16 [[2,3,3,5],[3]] => 16 [[2,3,3,4],[5]] => 17 [[2,3,3,5],[4]] => 17 [[2,3,4,5],[3]] => 17 [[2,3,3,5],[5]] => 18 [[2,3,5,5],[3]] => 18 [[2,3,4,4],[5]] => 18 [[2,3,4,5],[4]] => 18 [[2,4,4,5],[3]] => 18 [[2,3,4,5],[5]] => 19 [[2,3,5,5],[4]] => 19 [[2,4,5,5],[3]] => 19 [[2,3,5,5],[5]] => 20 [[2,5,5,5],[3]] => 20 [[2,4,4,4],[5]] => 19 [[2,4,4,5],[4]] => 19 [[2,4,4,5],[5]] => 20 [[2,4,5,5],[4]] => 20 [[2,4,5,5],[5]] => 21 [[2,5,5,5],[4]] => 21 [[2,5,5,5],[5]] => 22 [[3,3,3,3],[5]] => 17 [[3,3,3,4],[5]] => 18 [[3,3,3,5],[4]] => 18 [[3,3,3,5],[5]] => 19 [[3,3,4,4],[5]] => 19 [[3,3,4,5],[4]] => 19 [[3,3,4,5],[5]] => 20 [[3,3,5,5],[4]] => 20 [[3,3,5,5],[5]] => 21 [[3,4,4,4],[5]] => 20 [[3,4,4,5],[4]] => 20 [[3,4,4,5],[5]] => 21 [[3,4,5,5],[4]] => 21 [[3,4,5,5],[5]] => 22 [[3,5,5,5],[4]] => 22 [[3,5,5,5],[5]] => 23 [[4,4,4,4],[5]] => 21 [[4,4,4,5],[5]] => 22 [[4,4,5,5],[5]] => 23 [[4,5,5,5],[5]] => 24 [[1,1,1],[2,5]] => 10 [[1,1,1],[3,5]] => 11 [[1,1,1],[4,5]] => 12 [[1,1,1],[5,5]] => 13 [[1,1,2],[2,5]] => 11 [[1,1,5],[2,2]] => 11 [[1,1,2],[3,5]] => 12 [[1,1,3],[2,5]] => 12 [[1,1,5],[2,3]] => 12 [[1,1,2],[4,5]] => 13 [[1,1,4],[2,5]] => 13 [[1,1,5],[2,4]] => 13 [[1,1,2],[5,5]] => 14 [[1,1,5],[2,5]] => 14 [[1,1,3],[3,5]] => 13 [[1,1,5],[3,3]] => 13 [[1,1,3],[4,5]] => 14 [[1,1,4],[3,5]] => 14 [[1,1,5],[3,4]] => 14 [[1,1,3],[5,5]] => 15 [[1,1,5],[3,5]] => 15 [[1,1,4],[4,5]] => 15 [[1,1,5],[4,4]] => 15 [[1,1,4],[5,5]] => 16 [[1,1,5],[4,5]] => 16 [[1,1,5],[5,5]] => 17 [[1,2,2],[2,5]] => 12 [[1,2,2],[3,5]] => 13 [[1,2,3],[2,5]] => 13 [[1,2,5],[2,3]] => 13 [[1,2,2],[4,5]] => 14 [[1,2,4],[2,5]] => 14 [[1,2,5],[2,4]] => 14 [[1,2,2],[5,5]] => 15 [[1,2,5],[2,5]] => 15 [[1,2,3],[3,5]] => 14 [[1,2,5],[3,3]] => 14 [[1,3,3],[2,5]] => 14 [[1,2,3],[4,5]] => 15 [[1,2,4],[3,5]] => 15 [[1,2,5],[3,4]] => 15 [[1,3,4],[2,5]] => 15 [[1,3,5],[2,4]] => 15 [[1,2,3],[5,5]] => 16 [[1,2,5],[3,5]] => 16 [[1,3,5],[2,5]] => 16 [[1,2,4],[4,5]] => 16 [[1,2,5],[4,4]] => 16 [[1,4,4],[2,5]] => 16 [[1,2,4],[5,5]] => 17 [[1,2,5],[4,5]] => 17 [[1,4,5],[2,5]] => 17 [[1,2,5],[5,5]] => 18 [[1,3,3],[3,5]] => 15 [[1,3,3],[4,5]] => 16 [[1,3,4],[3,5]] => 16 [[1,3,5],[3,4]] => 16 [[1,3,3],[5,5]] => 17 [[1,3,5],[3,5]] => 17 [[1,3,4],[4,5]] => 17 [[1,3,5],[4,4]] => 17 [[1,4,4],[3,5]] => 17 [[1,3,4],[5,5]] => 18 [[1,3,5],[4,5]] => 18 [[1,4,5],[3,5]] => 18 [[1,3,5],[5,5]] => 19 [[1,4,4],[4,5]] => 18 [[1,4,4],[5,5]] => 19 [[1,4,5],[4,5]] => 19 [[1,4,5],[5,5]] => 20 [[2,2,2],[3,5]] => 14 [[2,2,2],[4,5]] => 15 [[2,2,2],[5,5]] => 16 [[2,2,3],[3,5]] => 15 [[2,2,5],[3,3]] => 15 [[2,2,3],[4,5]] => 16 [[2,2,4],[3,5]] => 16 [[2,2,5],[3,4]] => 16 [[2,2,3],[5,5]] => 17 [[2,2,5],[3,5]] => 17 [[2,2,4],[4,5]] => 17 [[2,2,5],[4,4]] => 17 [[2,2,4],[5,5]] => 18 [[2,2,5],[4,5]] => 18 [[2,2,5],[5,5]] => 19 [[2,3,3],[3,5]] => 16 [[2,3,3],[4,5]] => 17 [[2,3,4],[3,5]] => 17 [[2,3,5],[3,4]] => 17 [[2,3,3],[5,5]] => 18 [[2,3,5],[3,5]] => 18 [[2,3,4],[4,5]] => 18 [[2,3,5],[4,4]] => 18 [[2,4,4],[3,5]] => 18 [[2,3,4],[5,5]] => 19 [[2,3,5],[4,5]] => 19 [[2,4,5],[3,5]] => 19 [[2,3,5],[5,5]] => 20 [[2,4,4],[4,5]] => 19 [[2,4,4],[5,5]] => 20 [[2,4,5],[4,5]] => 20 [[2,4,5],[5,5]] => 21 [[3,3,3],[4,5]] => 18 [[3,3,3],[5,5]] => 19 [[3,3,4],[4,5]] => 19 [[3,3,5],[4,4]] => 19 [[3,3,4],[5,5]] => 20 [[3,3,5],[4,5]] => 20 [[3,3,5],[5,5]] => 21 [[3,4,4],[4,5]] => 20 [[3,4,4],[5,5]] => 21 [[3,4,5],[4,5]] => 21 [[3,4,5],[5,5]] => 22 [[4,4,4],[5,5]] => 22 [[4,4,5],[5,5]] => 23 [[1,1,1],[2],[5]] => 10 [[1,1,1],[3],[5]] => 11 [[1,1,1],[4],[5]] => 12 [[1,1,2],[2],[5]] => 11 [[1,1,2],[3],[5]] => 12 [[1,1,3],[2],[5]] => 12 [[1,1,5],[2],[3]] => 12 [[1,1,2],[4],[5]] => 13 [[1,1,4],[2],[5]] => 13 [[1,1,5],[2],[4]] => 13 [[1,1,5],[2],[5]] => 14 [[1,1,3],[3],[5]] => 13 [[1,1,3],[4],[5]] => 14 [[1,1,4],[3],[5]] => 14 [[1,1,5],[3],[4]] => 14 [[1,1,5],[3],[5]] => 15 [[1,1,4],[4],[5]] => 15 [[1,1,5],[4],[5]] => 16 [[1,2,2],[2],[5]] => 12 [[1,2,2],[3],[5]] => 13 [[1,2,3],[2],[5]] => 13 [[1,2,5],[2],[3]] => 13 [[1,2,2],[4],[5]] => 14 [[1,2,4],[2],[5]] => 14 [[1,2,5],[2],[4]] => 14 [[1,2,5],[2],[5]] => 15 [[1,2,3],[3],[5]] => 14 [[1,3,3],[2],[5]] => 14 [[1,3,5],[2],[3]] => 14 [[1,2,3],[4],[5]] => 15 [[1,2,4],[3],[5]] => 15 [[1,2,5],[3],[4]] => 15 [[1,3,4],[2],[5]] => 15 [[1,3,5],[2],[4]] => 15 [[1,4,5],[2],[3]] => 15 [[1,2,5],[3],[5]] => 16 [[1,3,5],[2],[5]] => 16 [[1,5,5],[2],[3]] => 16 [[1,2,4],[4],[5]] => 16 [[1,4,4],[2],[5]] => 16 [[1,4,5],[2],[4]] => 16 [[1,2,5],[4],[5]] => 17 [[1,4,5],[2],[5]] => 17 [[1,5,5],[2],[4]] => 17 [[1,5,5],[2],[5]] => 18 [[1,3,3],[3],[5]] => 15 [[1,3,3],[4],[5]] => 16 [[1,3,4],[3],[5]] => 16 [[1,3,5],[3],[4]] => 16 [[1,3,5],[3],[5]] => 17 [[1,3,4],[4],[5]] => 17 [[1,4,4],[3],[5]] => 17 [[1,4,5],[3],[4]] => 17 [[1,3,5],[4],[5]] => 18 [[1,4,5],[3],[5]] => 18 [[1,5,5],[3],[4]] => 18 [[1,5,5],[3],[5]] => 19 [[1,4,4],[4],[5]] => 18 [[1,4,5],[4],[5]] => 19 [[1,5,5],[4],[5]] => 20 [[2,2,2],[3],[5]] => 14 [[2,2,2],[4],[5]] => 15 [[2,2,3],[3],[5]] => 15 [[2,2,3],[4],[5]] => 16 [[2,2,4],[3],[5]] => 16 [[2,2,5],[3],[4]] => 16 [[2,2,5],[3],[5]] => 17 [[2,2,4],[4],[5]] => 17 [[2,2,5],[4],[5]] => 18 [[2,3,3],[3],[5]] => 16 [[2,3,3],[4],[5]] => 17 [[2,3,4],[3],[5]] => 17 [[2,3,5],[3],[4]] => 17 [[2,3,5],[3],[5]] => 18 [[2,3,4],[4],[5]] => 18 [[2,4,4],[3],[5]] => 18 [[2,4,5],[3],[4]] => 18 [[2,3,5],[4],[5]] => 19 [[2,4,5],[3],[5]] => 19 [[2,5,5],[3],[4]] => 19 [[2,5,5],[3],[5]] => 20 [[2,4,4],[4],[5]] => 19 [[2,4,5],[4],[5]] => 20 [[2,5,5],[4],[5]] => 21 [[3,3,3],[4],[5]] => 18 [[3,3,4],[4],[5]] => 19 [[3,3,5],[4],[5]] => 20 [[3,4,4],[4],[5]] => 20 [[3,4,5],[4],[5]] => 21 [[3,5,5],[4],[5]] => 22 [[1,1],[2,2],[5]] => 11 [[1,1],[2,3],[5]] => 12 [[1,1],[2,5],[3]] => 12 [[1,1],[2,4],[5]] => 13 [[1,1],[2,5],[4]] => 13 [[1,1],[2,5],[5]] => 14 [[1,1],[3,3],[5]] => 13 [[1,1],[3,4],[5]] => 14 [[1,1],[3,5],[4]] => 14 [[1,1],[3,5],[5]] => 15 [[1,1],[4,4],[5]] => 15 [[1,1],[4,5],[5]] => 16 [[1,2],[2,3],[5]] => 13 [[1,2],[2,5],[3]] => 13 [[1,2],[2,4],[5]] => 14 [[1,2],[2,5],[4]] => 14 [[1,2],[2,5],[5]] => 15 [[1,2],[3,3],[5]] => 14 [[1,3],[2,5],[3]] => 14 [[1,2],[3,4],[5]] => 15 [[1,2],[3,5],[4]] => 15 [[1,3],[2,4],[5]] => 15 [[1,3],[2,5],[4]] => 15 [[1,4],[2,5],[3]] => 15 [[1,2],[3,5],[5]] => 16 [[1,3],[2,5],[5]] => 16 [[1,2],[4,4],[5]] => 16 [[1,4],[2,5],[4]] => 16 [[1,2],[4,5],[5]] => 17 [[1,4],[2,5],[5]] => 17 [[1,3],[3,4],[5]] => 16 [[1,3],[3,5],[4]] => 16 [[1,3],[3,5],[5]] => 17 [[1,3],[4,4],[5]] => 17 [[1,4],[3,5],[4]] => 17 [[1,3],[4,5],[5]] => 18 [[1,4],[3,5],[5]] => 18 [[1,4],[4,5],[5]] => 19 [[2,2],[3,3],[5]] => 15 [[2,2],[3,4],[5]] => 16 [[2,2],[3,5],[4]] => 16 [[2,2],[3,5],[5]] => 17 [[2,2],[4,4],[5]] => 17 [[2,2],[4,5],[5]] => 18 [[2,3],[3,4],[5]] => 17 [[2,3],[3,5],[4]] => 17 [[2,3],[3,5],[5]] => 18 [[2,3],[4,4],[5]] => 18 [[2,4],[3,5],[4]] => 18 [[2,3],[4,5],[5]] => 19 [[2,4],[3,5],[5]] => 19 [[2,4],[4,5],[5]] => 20 [[3,3],[4,4],[5]] => 19 [[3,3],[4,5],[5]] => 20 [[3,4],[4,5],[5]] => 21 [[1,1],[2],[3],[5]] => 12 [[1,1],[2],[4],[5]] => 13 [[1,1],[3],[4],[5]] => 14 [[1,2],[2],[3],[5]] => 13 [[1,2],[2],[4],[5]] => 14 [[1,3],[2],[3],[5]] => 14 [[1,2],[3],[4],[5]] => 15 [[1,3],[2],[4],[5]] => 15 [[1,4],[2],[3],[5]] => 15 [[1,5],[2],[3],[4]] => 15 [[1,5],[2],[3],[5]] => 16 [[1,4],[2],[4],[5]] => 16 [[1,5],[2],[4],[5]] => 17 [[1,3],[3],[4],[5]] => 16 [[1,4],[3],[4],[5]] => 17 [[1,5],[3],[4],[5]] => 18 [[2,2],[3],[4],[5]] => 16 [[2,3],[3],[4],[5]] => 17 [[2,4],[3],[4],[5]] => 18 [[2,5],[3],[4],[5]] => 19 [[1],[2],[3],[4],[5]] => 15 ----------------------------------------------------------------------------- Created: Jun 14, 2013 at 00:58 by Jessica Striker ----------------------------------------------------------------------------- Last Updated: Oct 19, 2015 at 16:36 by Christian Stump