***************************************************************************** * 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: St001595 ----------------------------------------------------------------------------- Collection: Skew partitions ----------------------------------------------------------------------------- Description: The number of standard Young tableaux of the skew partition. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(la): return StandardTableaux(la).cardinality() ----------------------------------------------------------------------------- Statistic values: [[1],[]] => 1 [[2],[]] => 1 [[1,1],[]] => 1 [[2,1],[1]] => 2 [[3],[]] => 1 [[2,1],[]] => 2 [[3,1],[1]] => 3 [[2,2],[1]] => 2 [[3,2],[2]] => 3 [[1,1,1],[]] => 1 [[2,2,1],[1,1]] => 3 [[2,1,1],[1]] => 3 [[3,2,1],[2,1]] => 6 [[4],[]] => 1 [[3,1],[]] => 3 [[4,1],[1]] => 4 [[2,2],[]] => 2 [[3,2],[1]] => 5 [[4,2],[2]] => 6 [[2,1,1],[]] => 3 [[3,2,1],[1,1]] => 8 [[3,1,1],[1]] => 6 [[4,2,1],[2,1]] => 12 [[3,3],[2]] => 3 [[4,3],[3]] => 4 [[2,2,1],[1]] => 5 [[3,3,1],[2,1]] => 8 [[3,2,1],[2]] => 8 [[4,3,1],[3,1]] => 12 [[2,2,2],[1,1]] => 3 [[3,3,2],[2,2]] => 6 [[3,2,2],[2,1]] => 8 [[4,3,2],[3,2]] => 12 [[1,1,1,1],[]] => 1 [[2,2,2,1],[1,1,1]] => 4 [[2,2,1,1],[1,1]] => 6 [[3,3,2,1],[2,2,1]] => 12 [[2,1,1,1],[1]] => 4 [[3,2,2,1],[2,1,1]] => 12 [[3,2,1,1],[2,1]] => 12 [[4,3,2,1],[3,2,1]] => 24 [[5],[]] => 1 [[4,1],[]] => 4 [[5,1],[1]] => 5 [[3,2],[]] => 5 [[4,2],[1]] => 9 [[5,2],[2]] => 10 [[3,1,1],[]] => 6 [[4,2,1],[1,1]] => 15 [[4,1,1],[1]] => 10 [[5,2,1],[2,1]] => 20 [[3,3],[1]] => 5 [[4,3],[2]] => 9 [[5,3],[3]] => 10 [[2,2,1],[]] => 5 [[3,3,1],[1,1]] => 10 [[3,2,1],[1]] => 16 [[4,3,1],[2,1]] => 25 [[4,2,1],[2]] => 20 [[5,3,1],[3,1]] => 30 [[3,2,2],[1,1]] => 11 [[4,3,2],[2,2]] => 20 [[4,2,2],[2,1]] => 20 [[5,3,2],[3,2]] => 30 [[2,1,1,1],[]] => 4 [[3,2,2,1],[1,1,1]] => 15 [[3,2,1,1],[1,1]] => 20 [[4,3,2,1],[2,2,1]] => 40 [[3,1,1,1],[1]] => 10 [[4,2,2,1],[2,1,1]] => 30 [[4,2,1,1],[2,1]] => 30 [[5,3,2,1],[3,2,1]] => 60 [[4,4],[3]] => 4 [[5,4],[4]] => 5 [[3,3,1],[2]] => 11 [[4,4,1],[3,1]] => 15 [[4,3,1],[3]] => 15 [[5,4,1],[4,1]] => 20 [[2,2,2],[1]] => 5 [[3,3,2],[2,1]] => 16 [[4,4,2],[3,2]] => 20 [[3,2,2],[2]] => 10 [[4,3,2],[3,1]] => 25 [[5,4,2],[4,2]] => 30 [[2,2,1,1],[1]] => 9 [[3,3,2,1],[2,1,1]] => 25 [[3,3,1,1],[2,1]] => 20 [[4,4,2,1],[3,2,1]] => 40 [[3,2,1,1],[2]] => 15 [[4,3,2,1],[3,1,1]] => 40 [[4,3,1,1],[3,1]] => 30 [[5,4,2,1],[4,2,1]] => 60 [[3,3,3],[2,2]] => 6 [[4,4,3],[3,3]] => 10 [[4,3,3],[3,2]] => 15 [[5,4,3],[4,3]] => 20 [[2,2,2,1],[1,1]] => 9 [[3,3,3,1],[2,2,1]] => 15 [[3,3,2,1],[2,2]] => 20 [[4,4,3,1],[3,3,1]] => 30 [[3,2,2,1],[2,1]] => 25 [[4,3,3,1],[3,2,1]] => 40 [[4,3,2,1],[3,2]] => 40 [[5,4,3,1],[4,3,1]] => 60 [[2,2,2,2],[1,1,1]] => 4 [[3,3,3,2],[2,2,2]] => 10 [[3,3,2,2],[2,2,1]] => 20 [[4,4,3,2],[3,3,2]] => 30 [[3,2,2,2],[2,1,1]] => 15 [[4,3,3,2],[3,2,2]] => 30 [[4,3,2,2],[3,2,1]] => 40 [[5,4,3,2],[4,3,2]] => 60 [[1,1,1,1,1],[]] => 1 [[2,2,2,2,1],[1,1,1,1]] => 5 [[2,2,2,1,1],[1,1,1]] => 10 [[3,3,3,2,1],[2,2,2,1]] => 20 [[2,2,1,1,1],[1,1]] => 10 [[3,3,2,2,1],[2,2,1,1]] => 30 [[3,3,2,1,1],[2,2,1]] => 30 [[4,4,3,2,1],[3,3,2,1]] => 60 [[2,1,1,1,1],[1]] => 5 [[3,2,2,2,1],[2,1,1,1]] => 20 [[3,2,2,1,1],[2,1,1]] => 30 [[4,3,3,2,1],[3,2,2,1]] => 60 [[3,2,1,1,1],[2,1]] => 20 [[4,3,2,2,1],[3,2,1,1]] => 60 [[4,3,2,1,1],[3,2,1]] => 60 [[5,4,3,2,1],[4,3,2,1]] => 120 [[6],[]] => 1 [[5,1],[]] => 5 [[6,1],[1]] => 6 [[4,2],[]] => 9 [[5,2],[1]] => 14 [[6,2],[2]] => 15 [[4,1,1],[]] => 10 [[5,2,1],[1,1]] => 24 [[5,1,1],[1]] => 15 [[6,2,1],[2,1]] => 30 [[3,3],[]] => 5 [[4,3],[1]] => 14 [[5,3],[2]] => 19 [[6,3],[3]] => 20 [[3,2,1],[]] => 16 [[4,3,1],[1,1]] => 30 [[4,2,1],[1]] => 35 [[5,3,1],[2,1]] => 54 [[5,2,1],[2]] => 40 [[6,3,1],[3,1]] => 60 [[4,2,2],[1,1]] => 26 [[5,3,2],[2,2]] => 45 [[5,2,2],[2,1]] => 40 [[6,3,2],[3,2]] => 60 [[3,1,1,1],[]] => 10 [[4,2,2,1],[1,1,1]] => 36 [[4,2,1,1],[1,1]] => 45 [[5,3,2,1],[2,2,1]] => 90 [[4,1,1,1],[1]] => 20 [[5,2,2,1],[2,1,1]] => 60 [[5,2,1,1],[2,1]] => 60 [[6,3,2,1],[3,2,1]] => 120 [[4,4],[2]] => 9 [[5,4],[3]] => 14 [[6,4],[4]] => 15 [[3,3,1],[1]] => 21 [[4,4,1],[2,1]] => 30 [[4,3,1],[2]] => 40 [[5,4,1],[3,1]] => 54 [[5,3,1],[3]] => 45 [[6,4,1],[4,1]] => 60 [[2,2,2],[]] => 5 [[3,3,2],[1,1]] => 21 [[4,4,2],[2,2]] => 30 [[3,2,2],[1]] => 21 [[4,3,2],[2,1]] => 61 [[5,4,2],[3,2]] => 75 [[4,2,2],[2]] => 30 [[5,3,2],[3,1]] => 75 [[6,4,2],[4,2]] => 90 [[2,2,1,1],[]] => 9 [[3,3,2,1],[1,1,1]] => 30 [[3,3,1,1],[1,1]] => 30 [[4,4,2,1],[2,2,1]] => 60 [[3,2,1,1],[1]] => 35 [[4,3,2,1],[2,1,1]] => 96 [[4,3,1,1],[2,1]] => 75 [[5,4,2,1],[3,2,1]] => 150 [[4,2,1,1],[2]] => 45 [[5,3,2,1],[3,1,1]] => 120 [[5,3,1,1],[3,1]] => 90 [[6,4,2,1],[4,2,1]] => 180 [[4,3,3],[2,2]] => 26 [[5,4,3],[3,3]] => 40 [[5,3,3],[3,2]] => 45 [[6,4,3],[4,3]] => 60 [[3,2,2,1],[1,1]] => 40 [[4,3,3,1],[2,2,1]] => 66 [[4,3,2,1],[2,2]] => 80 [[5,4,3,1],[3,3,1]] => 120 [[4,2,2,1],[2,1]] => 75 [[5,3,3,1],[3,2,1]] => 120 [[5,3,2,1],[3,2]] => 120 [[6,4,3,1],[4,3,1]] => 180 [[3,2,2,2],[1,1,1]] => 19 [[4,3,3,2],[2,2,2]] => 45 [[4,3,2,2],[2,2,1]] => 80 [[5,4,3,2],[3,3,2]] => 120 [[4,2,2,2],[2,1,1]] => 45 [[5,3,3,2],[3,2,2]] => 90 [[5,3,2,2],[3,2,1]] => 120 [[6,4,3,2],[4,3,2]] => 180 [[2,1,1,1,1],[]] => 5 [[3,2,2,2,1],[1,1,1,1]] => 24 [[3,2,2,1,1],[1,1,1]] => 45 [[4,3,3,2,1],[2,2,2,1]] => 90 [[3,2,1,1,1],[1,1]] => 40 [[4,3,2,2,1],[2,2,1,1]] => 120 [[4,3,2,1,1],[2,2,1]] => 120 [[5,4,3,2,1],[3,3,2,1]] => 240 [[3,1,1,1,1],[1]] => 15 [[4,2,2,2,1],[2,1,1,1]] => 60 [[4,2,2,1,1],[2,1,1]] => 90 [[5,3,3,2,1],[3,2,2,1]] => 180 [[4,2,1,1,1],[2,1]] => 60 [[5,3,2,2,1],[3,2,1,1]] => 180 [[5,3,2,1,1],[3,2,1]] => 180 [[6,4,3,2,1],[4,3,2,1]] => 360 [[5,5],[4]] => 5 [[6,5],[5]] => 6 [[4,4,1],[3]] => 19 [[5,5,1],[4,1]] => 24 [[5,4,1],[4]] => 24 [[6,5,1],[5,1]] => 30 [[3,3,2],[2]] => 21 [[4,4,2],[3,1]] => 40 [[5,5,2],[4,2]] => 45 [[4,3,2],[3]] => 30 [[5,4,2],[4,1]] => 54 [[6,5,2],[5,2]] => 60 [[3,3,1,1],[2]] => 26 [[4,4,2,1],[3,1,1]] => 66 [[4,4,1,1],[3,1]] => 45 [[5,5,2,1],[4,2,1]] => 90 [[4,3,1,1],[3]] => 36 [[5,4,2,1],[4,1,1]] => 90 [[5,4,1,1],[4,1]] => 60 [[6,5,2,1],[5,2,1]] => 120 [[3,3,3],[2,1]] => 16 [[4,4,3],[3,2]] => 35 [[5,5,3],[4,3]] => 40 [[4,3,3],[3,1]] => 30 [[5,4,3],[4,2]] => 54 [[6,5,3],[5,3]] => 60 [[2,2,2,1],[1]] => 14 [[3,3,3,1],[2,1,1]] => 30 [[3,3,2,1],[2,1]] => 61 [[4,4,3,1],[3,2,1]] => 96 [[4,4,2,1],[3,2]] => 80 [[5,5,3,1],[4,3,1]] => 120 [[3,2,2,1],[2]] => 30 [[4,3,3,1],[3,1,1]] => 60 [[4,3,2,1],[3,1]] => 96 [[5,4,3,1],[4,2,1]] => 150 [[5,4,2,1],[4,2]] => 120 [[6,5,3,1],[5,3,1]] => 180 [[3,3,2,2],[2,1,1]] => 40 [[4,4,3,2],[3,2,2]] => 75 [[4,4,2,2],[3,2,1]] => 80 [[5,5,3,2],[4,3,2]] => 120 [[4,3,2,2],[3,1,1]] => 66 [[5,4,3,2],[4,2,2]] => 120 [[5,4,2,2],[4,2,1]] => 120 [[6,5,3,2],[5,3,2]] => 180 [[2,2,1,1,1],[1]] => 14 [[3,3,2,2,1],[2,1,1,1]] => 54 [[3,3,2,1,1],[2,1,1]] => 75 [[4,4,3,2,1],[3,2,2,1]] => 150 [[3,3,1,1,1],[2,1]] => 40 [[4,4,2,2,1],[3,2,1,1]] => 120 [[4,4,2,1,1],[3,2,1]] => 120 [[5,5,3,2,1],[4,3,2,1]] => 240 [[3,2,1,1,1],[2]] => 24 [[4,3,2,2,1],[3,1,1,1]] => 90 [[4,3,2,1,1],[3,1,1]] => 120 [[5,4,3,2,1],[4,2,2,1]] => 240 [[4,3,1,1,1],[3,1]] => 60 [[5,4,2,2,1],[4,2,1,1]] => 180 [[5,4,2,1,1],[4,2,1]] => 180 [[6,5,3,2,1],[5,3,2,1]] => 360 [[4,4,4],[3,3]] => 10 [[5,5,4],[4,4]] => 15 [[5,4,4],[4,3]] => 24 [[6,5,4],[5,4]] => 30 [[3,3,3,1],[2,2]] => 26 [[4,4,4,1],[3,3,1]] => 36 [[4,4,3,1],[3,3]] => 45 [[5,5,4,1],[4,4,1]] => 60 [[4,3,3,1],[3,2]] => 66 [[5,4,4,1],[4,3,1]] => 90 [[5,4,3,1],[4,3]] => 90 [[6,5,4,1],[5,4,1]] => 120 [[2,2,2,2],[1,1]] => 9 [[3,3,3,2],[2,2,1]] => 35 [[4,4,4,2],[3,3,2]] => 45 [[3,3,2,2],[2,2]] => 30 [[4,4,3,2],[3,3,1]] => 75 [[5,5,4,2],[4,4,2]] => 90 [[3,2,2,2],[2,1]] => 30 [[4,3,3,2],[3,2,1]] => 96 [[5,4,4,2],[4,3,2]] => 120 [[4,3,2,2],[3,2]] => 60 [[5,4,3,2],[4,3,1]] => 150 [[6,5,4,2],[5,4,2]] => 180 [[2,2,2,1,1],[1,1]] => 19 [[3,3,3,2,1],[2,2,1,1]] => 54 [[3,3,3,1,1],[2,2,1]] => 45 [[4,4,4,2,1],[3,3,2,1]] => 90 [[3,3,2,1,1],[2,2]] => 45 [[4,4,3,2,1],[3,3,1,1]] => 120 [[4,4,3,1,1],[3,3,1]] => 90 [[5,5,4,2,1],[4,4,2,1]] => 180 [[3,2,2,1,1],[2,1]] => 54 [[4,3,3,2,1],[3,2,1,1]] => 150 [[4,3,3,1,1],[3,2,1]] => 120 [[5,4,4,2,1],[4,3,2,1]] => 240 [[4,3,2,1,1],[3,2]] => 90 [[5,4,3,2,1],[4,3,1,1]] => 240 [[5,4,3,1,1],[4,3,1]] => 180 [[6,5,4,2,1],[5,4,2,1]] => 360 [[3,3,3,3],[2,2,2]] => 10 [[4,4,4,3],[3,3,3]] => 20 [[4,4,3,3],[3,3,2]] => 45 [[5,5,4,3],[4,4,3]] => 60 [[4,3,3,3],[3,2,2]] => 36 [[5,4,4,3],[4,3,3]] => 60 [[5,4,3,3],[4,3,2]] => 90 [[6,5,4,3],[5,4,3]] => 120 [[2,2,2,2,1],[1,1,1]] => 14 [[3,3,3,3,1],[2,2,2,1]] => 24 [[3,3,3,2,1],[2,2,2]] => 40 [[4,4,4,3,1],[3,3,3,1]] => 60 [[3,3,2,2,1],[2,2,1]] => 75 [[4,4,3,3,1],[3,3,2,1]] => 120 [[4,4,3,2,1],[3,3,2]] => 120 [[5,5,4,3,1],[4,4,3,1]] => 180 [[3,2,2,2,1],[2,1,1]] => 54 [[4,3,3,3,1],[3,2,2,1]] => 90 [[4,3,3,2,1],[3,2,2]] => 120 [[5,4,4,3,1],[4,3,3,1]] => 180 [[4,3,2,2,1],[3,2,1]] => 150 [[5,4,3,3,1],[4,3,2,1]] => 240 [[5,4,3,2,1],[4,3,2]] => 240 [[6,5,4,3,1],[5,4,3,1]] => 360 [[2,2,2,2,2],[1,1,1,1]] => 5 [[3,3,3,3,2],[2,2,2,2]] => 15 [[3,3,3,2,2],[2,2,2,1]] => 40 [[4,4,4,3,2],[3,3,3,2]] => 60 [[3,3,2,2,2],[2,2,1,1]] => 45 [[4,4,3,3,2],[3,3,2,2]] => 90 [[4,4,3,2,2],[3,3,2,1]] => 120 [[5,5,4,3,2],[4,4,3,2]] => 180 [[3,2,2,2,2],[2,1,1,1]] => 24 [[4,3,3,3,2],[3,2,2,2]] => 60 [[4,3,3,2,2],[3,2,2,1]] => 120 [[5,4,4,3,2],[4,3,3,2]] => 180 [[4,3,2,2,2],[3,2,1,1]] => 90 [[5,4,3,3,2],[4,3,2,2]] => 180 [[5,4,3,2,2],[4,3,2,1]] => 240 [[6,5,4,3,2],[5,4,3,2]] => 360 [[1,1,1,1,1,1],[]] => 1 [[2,2,2,2,2,1],[1,1,1,1,1]] => 6 [[2,2,2,2,1,1],[1,1,1,1]] => 15 [[3,3,3,3,2,1],[2,2,2,2,1]] => 30 [[2,2,2,1,1,1],[1,1,1]] => 20 [[3,3,3,2,2,1],[2,2,2,1,1]] => 60 [[3,3,3,2,1,1],[2,2,2,1]] => 60 [[4,4,4,3,2,1],[3,3,3,2,1]] => 120 [[2,2,1,1,1,1],[1,1]] => 15 [[3,3,2,2,2,1],[2,2,1,1,1]] => 60 [[3,3,2,2,1,1],[2,2,1,1]] => 90 [[4,4,3,3,2,1],[3,3,2,2,1]] => 180 [[3,3,2,1,1,1],[2,2,1]] => 60 [[4,4,3,2,2,1],[3,3,2,1,1]] => 180 [[4,4,3,2,1,1],[3,3,2,1]] => 180 [[5,5,4,3,2,1],[4,4,3,2,1]] => 360 [[2,1,1,1,1,1],[1]] => 6 [[3,2,2,2,2,1],[2,1,1,1,1]] => 30 [[3,2,2,2,1,1],[2,1,1,1]] => 60 [[4,3,3,3,2,1],[3,2,2,2,1]] => 120 [[3,2,2,1,1,1],[2,1,1]] => 60 [[4,3,3,2,2,1],[3,2,2,1,1]] => 180 [[4,3,3,2,1,1],[3,2,2,1]] => 180 [[5,4,4,3,2,1],[4,3,3,2,1]] => 360 [[3,2,1,1,1,1],[2,1]] => 30 [[4,3,2,2,2,1],[3,2,1,1,1]] => 120 [[4,3,2,2,1,1],[3,2,1,1]] => 180 [[5,4,3,3,2,1],[4,3,2,2,1]] => 360 [[4,3,2,1,1,1],[3,2,1]] => 120 [[5,4,3,2,2,1],[4,3,2,1,1]] => 360 [[5,4,3,2,1,1],[4,3,2,1]] => 360 [[6,5,4,3,2,1],[5,4,3,2,1]] => 720 [[7],[]] => 1 [[6,1],[]] => 6 [[7,1],[1]] => 7 [[5,2],[]] => 14 [[6,2],[1]] => 20 [[7,2],[2]] => 21 [[5,1,1],[]] => 15 [[6,2,1],[1,1]] => 35 [[6,1,1],[1]] => 21 [[7,2,1],[2,1]] => 42 [[4,3],[]] => 14 [[5,3],[1]] => 28 [[6,3],[2]] => 34 [[7,3],[3]] => 35 [[4,2,1],[]] => 35 [[5,3,1],[1,1]] => 63 [[5,2,1],[1]] => 64 [[6,3,1],[2,1]] => 98 [[6,2,1],[2]] => 70 [[7,3,1],[3,1]] => 105 [[5,2,2],[1,1]] => 50 [[6,3,2],[2,2]] => 84 [[6,2,2],[2,1]] => 70 [[7,3,2],[3,2]] => 105 [[4,1,1,1],[]] => 20 [[5,2,2,1],[1,1,1]] => 70 [[5,2,1,1],[1,1]] => 84 [[6,3,2,1],[2,2,1]] => 168 [[5,1,1,1],[1]] => 35 [[6,2,2,1],[2,1,1]] => 105 [[6,2,1,1],[2,1]] => 105 [[7,3,2,1],[3,2,1]] => 210 [[4,4],[1]] => 14 [[5,4],[2]] => 28 [[6,4],[3]] => 34 [[7,4],[4]] => 35 [[3,3,1],[]] => 21 [[4,4,1],[1,1]] => 35 [[4,3,1],[1]] => 70 [[5,4,1],[2,1]] => 98 [[5,3,1],[2]] => 99 [[6,4,1],[3,1]] => 133 [[6,3,1],[3]] => 105 [[7,4,1],[4,1]] => 140 [[3,2,2],[]] => 21 [[4,3,2],[1,1]] => 77 [[5,4,2],[2,2]] => 105 [[4,2,2],[1]] => 56 [[5,3,2],[2,1]] => 155 [[6,4,2],[3,2]] => 189 [[5,2,2],[2]] => 70 [[6,3,2],[3,1]] => 175 [[7,4,2],[4,2]] => 210 [[3,2,1,1],[]] => 35 [[4,3,2,1],[1,1,1]] => 112 [[4,3,1,1],[1,1]] => 105 [[5,4,2,1],[2,2,1]] => 210 [[4,2,1,1],[1]] => 90 [[5,3,2,1],[2,1,1]] => 245 [[5,3,1,1],[2,1]] => 189 [[6,4,2,1],[3,2,1]] => 378 [[5,2,1,1],[2]] => 105 [[6,3,2,1],[3,1,1]] => 280 [[6,3,1,1],[3,1]] => 210 [[7,4,2,1],[4,2,1]] => 420 [[5,3,3],[2,2]] => 71 [[6,4,3],[3,3]] => 105 [[6,3,3],[3,2]] => 105 [[7,4,3],[4,3]] => 140 [[4,2,2,1],[1,1]] => 111 [[5,3,3,1],[2,2,1]] => 182 [[5,3,2,1],[2,2]] => 210 [[6,4,3,1],[3,3,1]] => 315 [[5,2,2,1],[2,1]] => 175 [[6,3,3,1],[3,2,1]] => 280 [[6,3,2,1],[3,2]] => 280 [[7,4,3,1],[4,3,1]] => 420 [[4,2,2,2],[1,1,1]] => 55 [[5,3,3,2],[2,2,2]] => 126 [[5,3,2,2],[2,2,1]] => 210 [[6,4,3,2],[3,3,2]] => 315 [[5,2,2,2],[2,1,1]] => 105 [[6,3,3,2],[3,2,2]] => 210 [[6,3,2,2],[3,2,1]] => 280 [[7,4,3,2],[4,3,2]] => 420 [[3,1,1,1,1],[]] => 15 [[4,2,2,2,1],[1,1,1,1]] => 70 [[4,2,2,1,1],[1,1,1]] => 126 [[5,3,3,2,1],[2,2,2,1]] => 252 [[4,2,1,1,1],[1,1]] => 105 [[5,3,2,2,1],[2,2,1,1]] => 315 [[5,3,2,1,1],[2,2,1]] => 315 [[6,4,3,2,1],[3,3,2,1]] => 630 [[4,1,1,1,1],[1]] => 35 [[5,2,2,2,1],[2,1,1,1]] => 140 [[5,2,2,1,1],[2,1,1]] => 210 [[6,3,3,2,1],[3,2,2,1]] => 420 [[5,2,1,1,1],[2,1]] => 140 [[6,3,2,2,1],[3,2,1,1]] => 420 [[6,3,2,1,1],[3,2,1]] => 420 [[7,4,3,2,1],[4,3,2,1]] => 840 [[5,5],[3]] => 14 [[6,5],[4]] => 20 [[7,5],[5]] => 21 [[4,4,1],[2]] => 49 [[5,5,1],[3,1]] => 63 [[5,4,1],[3]] => 78 [[6,5,1],[4,1]] => 98 [[6,4,1],[4]] => 84 [[7,5,1],[5,1]] => 105 [[3,3,2],[1]] => 42 [[4,4,2],[2,1]] => 91 [[5,5,2],[3,2]] => 105 [[4,3,2],[2]] => 91 [[5,4,2],[3,1]] => 169 [[6,5,2],[4,2]] => 189 [[5,3,2],[3]] => 105 [[6,4,2],[4,1]] => 189 [[7,5,2],[5,2]] => 210 [[3,3,1,1],[1]] => 56 [[4,4,2,1],[2,1,1]] => 147 [[4,4,1,1],[2,1]] => 105 [[5,5,2,1],[3,2,1]] => 210 [[4,3,1,1],[2]] => 111 [[5,4,2,1],[3,1,1]] => 280 [[5,4,1,1],[3,1]] => 189 [[6,5,2,1],[4,2,1]] => 378 [[5,3,1,1],[3]] => 126 [[6,4,2,1],[4,1,1]] => 315 [[6,4,1,1],[4,1]] => 210 [[7,5,2,1],[5,2,1]] => 420 [[3,3,3],[1,1]] => 21 [[4,4,3],[2,2]] => 56 [[5,5,3],[3,3]] => 70 [[4,3,3],[2,1]] => 77 [[5,4,3],[3,2]] => 155 [[6,5,3],[4,3]] => 175 [[5,3,3],[3,1]] => 105 [[6,4,3],[4,2]] => 189 [[7,5,3],[5,3]] => 210 [[2,2,2,1],[]] => 14 [[3,3,3,1],[1,1,1]] => 35 [[3,3,2,1],[1,1]] => 91 [[4,4,3,1],[2,2,1]] => 147 [[4,4,2,1],[2,2]] => 140 [[5,5,3,1],[3,3,1]] => 210 [[3,2,2,1],[1]] => 70 [[4,3,3,1],[2,1,1]] => 147 [[4,3,2,1],[2,1]] => 272 [[5,4,3,1],[3,2,1]] => 427 [[5,4,2,1],[3,2]] => 350 [[6,5,3,1],[4,3,1]] => 525 [[4,2,2,1],[2]] => 105 [[5,3,3,1],[3,1,1]] => 210 [[5,3,2,1],[3,1]] => 336 [[6,4,3,1],[4,2,1]] => 525 [[6,4,2,1],[4,2]] => 420 [[7,5,3,1],[5,3,1]] => 630 [[3,3,2,2],[1,1,1]] => 49 [[4,4,3,2],[2,2,2]] => 105 [[4,4,2,2],[2,2,1]] => 140 [[5,5,3,2],[3,3,2]] => 210 [[4,3,2,2],[2,1,1]] => 181 [[5,4,3,2],[3,2,2]] => 336 [[5,4,2,2],[3,2,1]] => 350 [[6,5,3,2],[4,3,2]] => 525 [[5,3,2,2],[3,1,1]] => 231 [[6,4,3,2],[4,2,2]] => 420 [[6,4,2,2],[4,2,1]] => 420 [[7,5,3,2],[5,3,2]] => 630 [[2,2,1,1,1],[]] => 14 [[3,3,2,2,1],[1,1,1,1]] => 63 [[3,3,2,1,1],[1,1,1]] => 105 [[4,4,3,2,1],[2,2,2,1]] => 210 [[3,3,1,1,1],[1,1]] => 70 [[4,4,2,2,1],[2,2,1,1]] => 210 [[4,4,2,1,1],[2,2,1]] => 210 [[5,5,3,2,1],[3,3,2,1]] => 420 [[3,2,1,1,1],[1]] => 64 [[4,3,2,2,1],[2,1,1,1]] => 245 [[4,3,2,1,1],[2,1,1]] => 336 [[5,4,3,2,1],[3,2,2,1]] => 672 [[4,3,1,1,1],[2,1]] => 175 [[5,4,2,2,1],[3,2,1,1]] => 525 [[5,4,2,1,1],[3,2,1]] => 525 [[6,5,3,2,1],[4,3,2,1]] => 1050 [[4,2,1,1,1],[2]] => 84 [[5,3,2,2,1],[3,1,1,1]] => 315 [[5,3,2,1,1],[3,1,1]] => 420 [[6,4,3,2,1],[4,2,2,1]] => 840 [[5,3,1,1,1],[3,1]] => 210 [[6,4,2,2,1],[4,2,1,1]] => 630 [[6,4,2,1,1],[4,2,1]] => 630 [[7,5,3,2,1],[5,3,2,1]] => 1260 [[5,4,4],[3,3]] => 50 [[6,5,4],[4,4]] => 70 [[6,4,4],[4,3]] => 84 [[7,5,4],[5,4]] => 105 [[4,3,3,1],[2,2]] => 132 [[5,4,4,1],[3,3,1]] => 182 [[5,4,3,1],[3,3]] => 210 [[6,5,4,1],[4,4,1]] => 280 [[5,3,3,1],[3,2]] => 231 [[6,4,4,1],[4,3,1]] => 315 [[6,4,3,1],[4,3]] => 315 [[7,5,4,1],[5,4,1]] => 420 [[3,2,2,2],[1,1]] => 49 [[4,3,3,2],[2,2,1]] => 181 [[5,4,4,2],[3,3,2]] => 231 [[4,3,2,2],[2,2]] => 140 [[5,4,3,2],[3,3,1]] => 350 [[6,5,4,2],[4,4,2]] => 420 [[4,2,2,2],[2,1]] => 105 [[5,3,3,2],[3,2,1]] => 336 [[6,4,4,2],[4,3,2]] => 420 [[5,3,2,2],[3,2]] => 210 [[6,4,3,2],[4,3,1]] => 525 [[7,5,4,2],[5,4,2]] => 630 [[3,2,2,1,1],[1,1]] => 99 [[4,3,3,2,1],[2,2,1,1]] => 280 [[4,3,3,1,1],[2,2,1]] => 231 [[5,4,4,2,1],[3,3,2,1]] => 462 [[4,3,2,1,1],[2,2]] => 210 [[5,4,3,2,1],[3,3,1,1]] => 560 [[5,4,3,1,1],[3,3,1]] => 420 [[6,5,4,2,1],[4,4,2,1]] => 840 [[4,2,2,1,1],[2,1]] => 189 [[5,3,3,2,1],[3,2,1,1]] => 525 [[5,3,3,1,1],[3,2,1]] => 420 [[6,4,4,2,1],[4,3,2,1]] => 840 [[5,3,2,1,1],[3,2]] => 315 [[6,4,3,2,1],[4,3,1,1]] => 840 [[6,4,3,1,1],[4,3,1]] => 630 [[7,5,4,2,1],[5,4,2,1]] => 1260 [[4,3,3,3],[2,2,2]] => 55 [[5,4,4,3],[3,3,3]] => 105 [[5,4,3,3],[3,3,2]] => 210 [[6,5,4,3],[4,4,3]] => 280 [[5,3,3,3],[3,2,2]] => 126 [[6,4,4,3],[4,3,3]] => 210 [[6,4,3,3],[4,3,2]] => 315 [[7,5,4,3],[5,4,3]] => 420 [[3,2,2,2,1],[1,1,1]] => 78 [[4,3,3,3,1],[2,2,2,1]] => 133 [[4,3,3,2,1],[2,2,2]] => 210 [[5,4,4,3,1],[3,3,3,1]] => 315 [[4,3,2,2,1],[2,2,1]] => 350 [[5,4,3,3,1],[3,3,2,1]] => 560 [[5,4,3,2,1],[3,3,2]] => 560 [[6,5,4,3,1],[4,4,3,1]] => 840 [[4,2,2,2,1],[2,1,1]] => 189 [[5,3,3,3,1],[3,2,2,1]] => 315 [[5,3,3,2,1],[3,2,2]] => 420 [[6,4,4,3,1],[4,3,3,1]] => 630 [[5,3,2,2,1],[3,2,1]] => 525 [[6,4,3,3,1],[4,3,2,1]] => 840 [[6,4,3,2,1],[4,3,2]] => 840 [[7,5,4,3,1],[5,4,3,1]] => 1260 [[3,2,2,2,2],[1,1,1,1]] => 29 [[4,3,3,3,2],[2,2,2,2]] => 84 [[4,3,3,2,2],[2,2,2,1]] => 210 [[5,4,4,3,2],[3,3,3,2]] => 315 [[4,3,2,2,2],[2,2,1,1]] => 210 [[5,4,3,3,2],[3,3,2,2]] => 420 [[5,4,3,2,2],[3,3,2,1]] => 560 [[6,5,4,3,2],[4,4,3,2]] => 840 [[4,2,2,2,2],[2,1,1,1]] => 84 [[5,3,3,3,2],[3,2,2,2]] => 210 [[5,3,3,2,2],[3,2,2,1]] => 420 [[6,4,4,3,2],[4,3,3,2]] => 630 [[5,3,2,2,2],[3,2,1,1]] => 315 [[6,4,3,3,2],[4,3,2,2]] => 630 [[6,4,3,2,2],[4,3,2,1]] => 840 [[7,5,4,3,2],[5,4,3,2]] => 1260 [[2,1,1,1,1,1],[]] => 6 [[3,2,2,2,2,1],[1,1,1,1,1]] => 35 [[3,2,2,2,1,1],[1,1,1,1]] => 84 [[4,3,3,3,2,1],[2,2,2,2,1]] => 168 [[3,2,2,1,1,1],[1,1,1]] => 105 [[4,3,3,2,2,1],[2,2,2,1,1]] => 315 [[4,3,3,2,1,1],[2,2,2,1]] => 315 [[5,4,4,3,2,1],[3,3,3,2,1]] => 630 [[3,2,1,1,1,1],[1,1]] => 70 [[4,3,2,2,2,1],[2,2,1,1,1]] => 280 [[4,3,2,2,1,1],[2,2,1,1]] => 420 [[5,4,3,3,2,1],[3,3,2,2,1]] => 840 [[4,3,2,1,1,1],[2,2,1]] => 280 [[5,4,3,2,2,1],[3,3,2,1,1]] => 840 [[5,4,3,2,1,1],[3,3,2,1]] => 840 [[6,5,4,3,2,1],[4,4,3,2,1]] => 1680 [[3,1,1,1,1,1],[1]] => 21 [[4,2,2,2,2,1],[2,1,1,1,1]] => 105 [[4,2,2,2,1,1],[2,1,1,1]] => 210 [[5,3,3,3,2,1],[3,2,2,2,1]] => 420 [[4,2,2,1,1,1],[2,1,1]] => 210 [[5,3,3,2,2,1],[3,2,2,1,1]] => 630 [[5,3,3,2,1,1],[3,2,2,1]] => 630 [[6,4,4,3,2,1],[4,3,3,2,1]] => 1260 [[4,2,1,1,1,1],[2,1]] => 105 [[5,3,2,2,2,1],[3,2,1,1,1]] => 420 [[5,3,2,2,1,1],[3,2,1,1]] => 630 [[6,4,3,3,2,1],[4,3,2,2,1]] => 1260 [[5,3,2,1,1,1],[3,2,1]] => 420 [[6,4,3,2,2,1],[4,3,2,1,1]] => 1260 [[6,4,3,2,1,1],[4,3,2,1]] => 1260 [[7,5,4,3,2,1],[5,4,3,2,1]] => 2520 [[6,6],[5]] => 6 [[7,6],[6]] => 7 [[5,5,1],[4]] => 29 [[6,6,1],[5,1]] => 35 [[6,5,1],[5]] => 35 [[7,6,1],[6,1]] => 42 [[4,4,2],[3]] => 49 [[5,5,2],[4,1]] => 78 [[6,6,2],[5,2]] => 84 [[5,4,2],[4]] => 63 [[6,5,2],[5,1]] => 98 [[7,6,2],[6,2]] => 105 [[4,4,1,1],[3]] => 55 [[5,5,2,1],[4,1,1]] => 133 [[5,5,1,1],[4,1]] => 84 [[6,6,2,1],[5,2,1]] => 168 [[5,4,1,1],[4]] => 70 [[6,5,2,1],[5,1,1]] => 168 [[6,5,1,1],[5,1]] => 105 [[7,6,2,1],[6,2,1]] => 210 [[3,3,3],[2]] => 21 [[4,4,3],[3,1]] => 70 [[5,5,3],[4,2]] => 99 [[6,6,3],[5,3]] => 105 [[4,3,3],[3]] => 35 [[5,4,3],[4,1]] => 98 [[6,5,3],[5,2]] => 133 [[7,6,3],[6,3]] => 140 [[3,3,2,1],[2]] => 77 [[4,4,3,1],[3,1,1]] => 147 [[4,4,2,1],[3,1]] => 181 [[5,5,3,1],[4,2,1]] => 280 [[5,5,2,1],[4,2]] => 210 [[6,6,3,1],[5,3,1]] => 315 [[4,3,2,1],[3]] => 112 [[5,4,3,1],[4,1,1]] => 210 [[5,4,2,1],[4,1]] => 245 [[6,5,3,1],[5,2,1]] => 378 [[6,5,2,1],[5,2]] => 280 [[7,6,3,1],[6,3,1]] => 420 [[4,4,2,2],[3,1,1]] => 132 [[5,5,3,2],[4,2,2]] => 231 [[5,5,2,2],[4,2,1]] => 210 [[6,6,3,2],[5,3,2]] => 315 [[5,4,2,2],[4,1,1]] => 182 [[6,5,3,2],[5,2,2]] => 315 [[6,5,2,2],[5,2,1]] => 280 [[7,6,3,2],[6,3,2]] => 420 [[3,3,1,1,1],[2]] => 50 [[4,4,2,2,1],[3,1,1,1]] => 182 [[4,4,2,1,1],[3,1,1]] => 231 [[5,5,3,2,1],[4,2,2,1]] => 462 [[4,4,1,1,1],[3,1]] => 105 [[5,5,2,2,1],[4,2,1,1]] => 315 [[5,5,2,1,1],[4,2,1]] => 315 [[6,6,3,2,1],[5,3,2,1]] => 630 [[4,3,1,1,1],[3]] => 70 [[5,4,2,2,1],[4,1,1,1]] => 252 [[5,4,2,1,1],[4,1,1]] => 315 [[6,5,3,2,1],[5,2,2,1]] => 630 [[5,4,1,1,1],[4,1]] => 140 [[6,5,2,2,1],[5,2,1,1]] => 420 [[6,5,2,1,1],[5,2,1]] => 420 [[7,6,3,2,1],[6,3,2,1]] => 840 [[4,4,4],[3,2]] => 35 [[5,5,4],[4,3]] => 64 [[6,6,4],[5,4]] => 70 [[5,4,4],[4,2]] => 63 [[6,5,4],[5,3]] => 98 [[7,6,4],[6,4]] => 105 [[3,3,3,1],[2,1]] => 77 [[4,4,4,1],[3,2,1]] => 112 [[4,4,3,1],[3,2]] => 181 [[5,5,4,1],[4,3,1]] => 245 [[5,5,3,1],[4,3]] => 210 [[6,6,4,1],[5,4,1]] => 280 [[4,3,3,1],[3,1]] => 147 [[5,4,4,1],[4,2,1]] => 210 [[5,4,3,1],[4,2]] => 280 [[6,5,4,1],[5,3,1]] => 378 [[6,5,3,1],[5,3]] => 315 [[7,6,4,1],[6,4,1]] => 420 [[2,2,2,2],[1]] => 14 [[3,3,3,2],[2,1,1]] => 70 [[4,4,4,2],[3,2,2]] => 105 [[3,3,2,2],[2,1]] => 91 [[4,4,3,2],[3,2,1]] => 272 [[5,5,4,2],[4,3,2]] => 336 [[4,4,2,2],[3,2]] => 140 [[5,5,3,2],[4,3,1]] => 350 [[6,6,4,2],[5,4,2]] => 420 [[3,2,2,2],[2]] => 35 [[4,3,3,2],[3,1,1]] => 147 [[5,4,4,2],[4,2,2]] => 210 [[4,3,2,2],[3,1]] => 147 [[5,4,3,2],[4,2,1]] => 427 [[6,5,4,2],[5,3,2]] => 525 [[5,4,2,2],[4,2]] => 210 [[6,5,3,2],[5,3,1]] => 525 [[7,6,4,2],[6,4,2]] => 630 [[2,2,2,1,1],[1]] => 28 [[3,3,3,2,1],[2,1,1,1]] => 98 [[3,3,3,1,1],[2,1,1]] => 105 [[4,4,4,2,1],[3,2,2,1]] => 210 [[3,3,2,1,1],[2,1]] => 155 [[4,4,3,2,1],[3,2,1,1]] => 427 [[4,4,3,1,1],[3,2,1]] => 336 [[5,5,4,2,1],[4,3,2,1]] => 672 [[4,4,2,1,1],[3,2]] => 210 [[5,5,3,2,1],[4,3,1,1]] => 560 [[5,5,3,1,1],[4,3,1]] => 420 [[6,6,4,2,1],[5,4,2,1]] => 840 [[3,2,2,1,1],[2]] => 63 [[4,3,3,2,1],[3,1,1,1]] => 210 [[4,3,3,1,1],[3,1,1]] => 210 [[5,4,4,2,1],[4,2,2,1]] => 420 [[4,3,2,1,1],[3,1]] => 245 [[5,4,3,2,1],[4,2,1,1]] => 672 [[5,4,3,1,1],[4,2,1]] => 525 [[6,5,4,2,1],[5,3,2,1]] => 1050 [[5,4,2,1,1],[4,2]] => 315 [[6,5,3,2,1],[5,3,1,1]] => 840 [[6,5,3,1,1],[5,3,1]] => 630 [[7,6,4,2,1],[6,4,2,1]] => 1260 [[4,4,3,3],[3,2,2]] => 111 [[5,5,4,3],[4,3,3]] => 175 [[5,5,3,3],[4,3,2]] => 210 [[6,6,4,3],[5,4,3]] => 280 [[5,4,3,3],[4,2,2]] => 182 [[6,5,4,3],[5,3,3]] => 280 [[6,5,3,3],[5,3,2]] => 315 [[7,6,4,3],[6,4,3]] => 420 [[3,3,2,2,1],[2,1,1]] => 169 [[4,4,3,3,1],[3,2,2,1]] => 280 [[4,4,3,2,1],[3,2,2]] => 350 [[5,5,4,3,1],[4,3,3,1]] => 525 [[4,4,2,2,1],[3,2,1]] => 350 [[5,5,3,3,1],[4,3,2,1]] => 560 [[5,5,3,2,1],[4,3,2]] => 560 [[6,6,4,3,1],[5,4,3,1]] => 840 [[4,3,2,2,1],[3,1,1]] => 280 [[5,4,3,3,1],[4,2,2,1]] => 462 [[5,4,3,2,1],[4,2,2]] => 560 [[6,5,4,3,1],[5,3,3,1]] => 840 [[5,4,2,2,1],[4,2,1]] => 525 [[6,5,3,3,1],[5,3,2,1]] => 840 [[6,5,3,2,1],[5,3,2]] => 840 [[7,6,4,3,1],[6,4,3,1]] => 1260 [[3,3,2,2,2],[2,1,1,1]] => 78 [[4,4,3,3,2],[3,2,2,2]] => 189 [[4,4,3,2,2],[3,2,2,1]] => 350 [[5,5,4,3,2],[4,3,3,2]] => 525 [[4,4,2,2,2],[3,2,1,1]] => 210 [[5,5,3,3,2],[4,3,2,2]] => 420 [[5,5,3,2,2],[4,3,2,1]] => 560 [[6,6,4,3,2],[5,4,3,2]] => 840 [[4,3,2,2,2],[3,1,1,1]] => 133 [[5,4,3,3,2],[4,2,2,2]] => 315 [[5,4,3,2,2],[4,2,2,1]] => 560 [[6,5,4,3,2],[5,3,3,2]] => 840 [[5,4,2,2,2],[4,2,1,1]] => 315 [[6,5,3,3,2],[5,3,2,2]] => 630 [[6,5,3,2,2],[5,3,2,1]] => 840 [[7,6,4,3,2],[6,4,3,2]] => 1260 [[2,2,1,1,1,1],[1]] => 20 [[3,3,2,2,2,1],[2,1,1,1,1]] => 98 [[3,3,2,2,1,1],[2,1,1,1]] => 189 [[4,4,3,3,2,1],[3,2,2,2,1]] => 378 [[3,3,2,1,1,1],[2,1,1]] => 175 [[4,4,3,2,2,1],[3,2,2,1,1]] => 525 [[4,4,3,2,1,1],[3,2,2,1]] => 525 [[5,5,4,3,2,1],[4,3,3,2,1]] => 1050 [[3,3,1,1,1,1],[2,1]] => 70 [[4,4,2,2,2,1],[3,2,1,1,1]] => 280 [[4,4,2,2,1,1],[3,2,1,1]] => 420 [[5,5,3,3,2,1],[4,3,2,2,1]] => 840 [[4,4,2,1,1,1],[3,2,1]] => 280 [[5,5,3,2,2,1],[4,3,2,1,1]] => 840 [[5,5,3,2,1,1],[4,3,2,1]] => 840 [[6,6,4,3,2,1],[5,4,3,2,1]] => 1680 [[3,2,1,1,1,1],[2]] => 35 [[4,3,2,2,2,1],[3,1,1,1,1]] => 168 [[4,3,2,2,1,1],[3,1,1,1]] => 315 [[5,4,3,3,2,1],[4,2,2,2,1]] => 630 [[4,3,2,1,1,1],[3,1,1]] => 280 [[5,4,3,2,2,1],[4,2,2,1,1]] => 840 [[5,4,3,2,1,1],[4,2,2,1]] => 840 [[6,5,4,3,2,1],[5,3,3,2,1]] => 1680 [[4,3,1,1,1,1],[3,1]] => 105 [[5,4,2,2,2,1],[4,2,1,1,1]] => 420 [[5,4,2,2,1,1],[4,2,1,1]] => 630 [[6,5,3,3,2,1],[5,3,2,2,1]] => 1260 [[5,4,2,1,1,1],[4,2,1]] => 420 [[6,5,3,2,2,1],[5,3,2,1,1]] => 1260 [[6,5,3,2,1,1],[5,3,2,1]] => 1260 [[7,6,4,3,2,1],[6,4,3,2,1]] => 2520 [[5,5,5],[4,4]] => 15 [[6,6,5],[5,5]] => 21 [[6,5,5],[5,4]] => 35 [[7,6,5],[6,5]] => 42 [[4,4,4,1],[3,3]] => 55 [[5,5,5,1],[4,4,1]] => 70 [[5,5,4,1],[4,4]] => 84 [[6,6,5,1],[5,5,1]] => 105 [[5,4,4,1],[4,3]] => 133 [[6,5,5,1],[5,4,1]] => 168 [[6,5,4,1],[5,4]] => 168 [[7,6,5,1],[6,5,1]] => 210 [[3,3,3,2],[2,2]] => 56 [[4,4,4,2],[3,3,1]] => 111 [[5,5,5,2],[4,4,2]] => 126 [[4,4,3,2],[3,3]] => 105 [[5,5,4,2],[4,4,1]] => 189 [[6,6,5,2],[5,5,2]] => 210 [[4,3,3,2],[3,2]] => 147 [[5,4,4,2],[4,3,1]] => 280 [[6,5,5,2],[5,4,2]] => 315 [[5,4,3,2],[4,3]] => 210 [[6,5,4,2],[5,4,1]] => 378 [[7,6,5,2],[6,5,2]] => 420 [[3,3,3,1,1],[2,2]] => 71 [[4,4,4,2,1],[3,3,1,1]] => 182 [[4,4,4,1,1],[3,3,1]] => 126 [[5,5,5,2,1],[4,4,2,1]] => 252 [[4,4,3,1,1],[3,3]] => 126 [[5,5,4,2,1],[4,4,1,1]] => 315 [[5,5,4,1,1],[4,4,1]] => 210 [[6,6,5,2,1],[5,5,2,1]] => 420 [[4,3,3,1,1],[3,2]] => 182 [[5,4,4,2,1],[4,3,1,1]] => 462 [[5,4,4,1,1],[4,3,1]] => 315 [[6,5,5,2,1],[5,4,2,1]] => 630 [[5,4,3,1,1],[4,3]] => 252 [[6,5,4,2,1],[5,4,1,1]] => 630 [[6,5,4,1,1],[5,4,1]] => 420 [[7,6,5,2,1],[6,5,2,1]] => 840 [[3,3,3,3],[2,2,1]] => 35 [[4,4,4,3],[3,3,2]] => 90 [[5,5,5,3],[4,4,3]] => 105 [[4,4,3,3],[3,3,1]] => 105 [[5,5,4,3],[4,4,2]] => 189 [[6,6,5,3],[5,5,3]] => 210 [[4,3,3,3],[3,2,1]] => 112 [[5,4,4,3],[4,3,2]] => 245 [[6,5,5,3],[5,4,3]] => 280 [[5,4,3,3],[4,3,1]] => 210 [[6,5,4,3],[5,4,2]] => 378 [[7,6,5,3],[6,5,3]] => 420 [[2,2,2,2,1],[1,1]] => 28 [[3,3,3,3,1],[2,2,1,1]] => 63 [[3,3,3,2,1],[2,2,1]] => 155 [[4,4,4,3,1],[3,3,2,1]] => 245 [[4,4,4,2,1],[3,3,2]] => 210 [[5,5,5,3,1],[4,4,3,1]] => 315 [[3,3,2,2,1],[2,2]] => 105 [[4,4,3,3,1],[3,3,1,1]] => 210 [[4,4,3,2,1],[3,3,1]] => 336 [[5,5,4,3,1],[4,4,2,1]] => 525 [[5,5,4,2,1],[4,4,2]] => 420 [[6,6,5,3,1],[5,5,3,1]] => 630 [[3,2,2,2,1],[2,1]] => 98 [[4,3,3,3,1],[3,2,1,1]] => 210 [[4,3,3,2,1],[3,2,1]] => 427 [[5,4,4,3,1],[4,3,2,1]] => 672 [[5,4,4,2,1],[4,3,2]] => 560 [[6,5,5,3,1],[5,4,3,1]] => 840 [[4,3,2,2,1],[3,2]] => 210 [[5,4,3,3,1],[4,3,1,1]] => 420 [[5,4,3,2,1],[4,3,1]] => 672 [[6,5,4,3,1],[5,4,2,1]] => 1050 [[6,5,4,2,1],[5,4,2]] => 840 [[7,6,5,3,1],[6,5,3,1]] => 1260 [[3,3,3,2,2],[2,2,1,1]] => 99 [[4,4,4,3,2],[3,3,2,2]] => 189 [[4,4,4,2,2],[3,3,2,1]] => 210 [[5,5,5,3,2],[4,4,3,2]] => 315 [[4,4,3,2,2],[3,3,1,1]] => 231 [[5,5,4,3,2],[4,4,2,2]] => 420 [[5,5,4,2,2],[4,4,2,1]] => 420 [[6,6,5,3,2],[5,5,3,2]] => 630 [[4,3,3,2,2],[3,2,1,1]] => 280 [[5,4,4,3,2],[4,3,2,2]] => 525 [[5,4,4,2,2],[4,3,2,1]] => 560 [[6,5,5,3,2],[5,4,3,2]] => 840 [[5,4,3,2,2],[4,3,1,1]] => 462 [[6,5,4,3,2],[5,4,2,2]] => 840 [[6,5,4,2,2],[5,4,2,1]] => 840 [[7,6,5,3,2],[6,5,3,2]] => 1260 [[2,2,2,1,1,1],[1,1]] => 34 [[3,3,3,2,2,1],[2,2,1,1,1]] => 133 [[3,3,3,2,1,1],[2,2,1,1]] => 189 [[4,4,4,3,2,1],[3,3,2,2,1]] => 378 [[3,3,3,1,1,1],[2,2,1]] => 105 [[4,4,4,2,2,1],[3,3,2,1,1]] => 315 [[4,4,4,2,1,1],[3,3,2,1]] => 315 [[5,5,5,3,2,1],[4,4,3,2,1]] => 630 [[3,3,2,1,1,1],[2,2]] => 84 [[4,4,3,2,2,1],[3,3,1,1,1]] => 315 [[4,4,3,2,1,1],[3,3,1,1]] => 420 [[5,5,4,3,2,1],[4,4,2,2,1]] => 840 [[4,4,3,1,1,1],[3,3,1]] => 210 [[5,5,4,2,2,1],[4,4,2,1,1]] => 630 [[5,5,4,2,1,1],[4,4,2,1]] => 630 [[6,6,5,3,2,1],[5,5,3,2,1]] => 1260 [[3,2,2,1,1,1],[2,1]] => 98 [[4,3,3,2,2,1],[3,2,1,1,1]] => 378 [[4,3,3,2,1,1],[3,2,1,1]] => 525 [[5,4,4,3,2,1],[4,3,2,2,1]] => 1050 [[4,3,3,1,1,1],[3,2,1]] => 280 [[5,4,4,2,2,1],[4,3,2,1,1]] => 840 [[5,4,4,2,1,1],[4,3,2,1]] => 840 [[6,5,5,3,2,1],[5,4,3,2,1]] => 1680 [[4,3,2,1,1,1],[3,2]] => 168 [[5,4,3,2,2,1],[4,3,1,1,1]] => 630 [[5,4,3,2,1,1],[4,3,1,1]] => 840 [[6,5,4,3,2,1],[5,4,2,2,1]] => 1680 [[5,4,3,1,1,1],[4,3,1]] => 420 [[6,5,4,2,2,1],[5,4,2,1,1]] => 1260 [[6,5,4,2,1,1],[5,4,2,1]] => 1260 [[7,6,5,3,2,1],[6,5,3,2,1]] => 2520 [[4,4,4,4],[3,3,3]] => 20 [[5,5,5,4],[4,4,4]] => 35 [[5,5,4,4],[4,4,3]] => 84 [[6,6,5,4],[5,5,4]] => 105 [[5,4,4,4],[4,3,3]] => 70 [[6,5,5,4],[5,4,4]] => 105 [[6,5,4,4],[5,4,3]] => 168 [[7,6,5,4],[6,5,4]] => 210 [[3,3,3,3,1],[2,2,2]] => 50 [[4,4,4,4,1],[3,3,3,1]] => 70 [[4,4,4,3,1],[3,3,3]] => 105 [[5,5,5,4,1],[4,4,4,1]] => 140 [[4,4,3,3,1],[3,3,2]] => 231 [[5,5,4,4,1],[4,4,3,1]] => 315 [[5,5,4,3,1],[4,4,3]] => 315 [[6,6,5,4,1],[5,5,4,1]] => 420 [[4,3,3,3,1],[3,2,2]] => 182 [[5,4,4,4,1],[4,3,3,1]] => 252 [[5,4,4,3,1],[4,3,3]] => 315 [[6,5,5,4,1],[5,4,4,1]] => 420 [[5,4,3,3,1],[4,3,2]] => 462 [[6,5,4,4,1],[5,4,3,1]] => 630 [[6,5,4,3,1],[5,4,3]] => 630 [[7,6,5,4,1],[6,5,4,1]] => 840 [[2,2,2,2,2],[1,1,1]] => 14 [[3,3,3,3,2],[2,2,2,1]] => 64 [[4,4,4,4,2],[3,3,3,2]] => 84 [[3,3,3,2,2],[2,2,2]] => 70 [[4,4,4,3,2],[3,3,3,1]] => 175 [[5,5,5,4,2],[4,4,4,2]] => 210 [[3,3,2,2,2],[2,2,1]] => 105 [[4,4,3,3,2],[3,3,2,1]] => 336 [[5,5,4,4,2],[4,4,3,2]] => 420 [[4,4,3,2,2],[3,3,2]] => 210 [[5,5,4,3,2],[4,4,3,1]] => 525 [[6,6,5,4,2],[5,5,4,2]] => 630 [[3,2,2,2,2],[2,1,1]] => 63 [[4,3,3,3,2],[3,2,2,1]] => 245 [[5,4,4,4,2],[4,3,3,2]] => 315 [[4,3,3,2,2],[3,2,2]] => 210 [[5,4,4,3,2],[4,3,3,1]] => 525 [[6,5,5,4,2],[5,4,4,2]] => 630 [[4,3,2,2,2],[3,2,1]] => 210 [[5,4,3,3,2],[4,3,2,1]] => 672 [[6,5,4,4,2],[5,4,3,2]] => 840 [[5,4,3,2,2],[4,3,2]] => 420 [[6,5,4,3,2],[5,4,3,1]] => 1050 [[7,6,5,4,2],[6,5,4,2]] => 1260 [[2,2,2,2,1,1],[1,1,1]] => 34 [[3,3,3,3,2,1],[2,2,2,1,1]] => 98 [[3,3,3,3,1,1],[2,2,2,1]] => 84 [[4,4,4,4,2,1],[3,3,3,2,1]] => 168 [[3,3,3,2,1,1],[2,2,2]] => 105 [[4,4,4,3,2,1],[3,3,3,1,1]] => 280 [[4,4,4,3,1,1],[3,3,3,1]] => 210 [[5,5,5,4,2,1],[4,4,4,2,1]] => 420 [[3,3,2,2,1,1],[2,2,1]] => 189 [[4,4,3,3,2,1],[3,3,2,1,1]] => 525 [[4,4,3,3,1,1],[3,3,2,1]] => 420 [[5,5,4,4,2,1],[4,4,3,2,1]] => 840 [[4,4,3,2,1,1],[3,3,2]] => 315 [[5,5,4,3,2,1],[4,4,3,1,1]] => 840 [[5,5,4,3,1,1],[4,4,3,1]] => 630 [[6,6,5,4,2,1],[5,5,4,2,1]] => 1260 [[3,2,2,2,1,1],[2,1,1]] => 133 [[4,3,3,3,2,1],[3,2,2,1,1]] => 378 [[4,3,3,3,1,1],[3,2,2,1]] => 315 [[5,4,4,4,2,1],[4,3,3,2,1]] => 630 [[4,3,3,2,1,1],[3,2,2]] => 315 [[5,4,4,3,2,1],[4,3,3,1,1]] => 840 [[5,4,4,3,1,1],[4,3,3,1]] => 630 [[6,5,5,4,2,1],[5,4,4,2,1]] => 1260 [[4,3,2,2,1,1],[3,2,1]] => 378 [[5,4,3,3,2,1],[4,3,2,1,1]] => 1050 [[5,4,3,3,1,1],[4,3,2,1]] => 840 [[6,5,4,4,2,1],[5,4,3,2,1]] => 1680 [[5,4,3,2,1,1],[4,3,2]] => 630 [[6,5,4,3,2,1],[5,4,3,1,1]] => 1680 [[6,5,4,3,1,1],[5,4,3,1]] => 1260 [[7,6,5,4,2,1],[6,5,4,2,1]] => 2520 [[3,3,3,3,3],[2,2,2,2]] => 15 [[4,4,4,4,3],[3,3,3,3]] => 35 [[4,4,4,3,3],[3,3,3,2]] => 105 [[5,5,5,4,3],[4,4,4,3]] => 140 [[4,4,3,3,3],[3,3,2,2]] => 126 [[5,5,4,4,3],[4,4,3,3]] => 210 [[5,5,4,3,3],[4,4,3,2]] => 315 [[6,6,5,4,3],[5,5,4,3]] => 420 [[4,3,3,3,3],[3,2,2,2]] => 70 [[5,4,4,4,3],[4,3,3,3]] => 140 [[5,4,4,3,3],[4,3,3,2]] => 315 [[6,5,5,4,3],[5,4,4,3]] => 420 [[5,4,3,3,3],[4,3,2,2]] => 252 [[6,5,4,4,3],[5,4,3,3]] => 420 [[6,5,4,3,3],[5,4,3,2]] => 630 [[7,6,5,4,3],[6,5,4,3]] => 840 [[2,2,2,2,2,1],[1,1,1,1]] => 20 [[3,3,3,3,3,1],[2,2,2,2,1]] => 35 [[3,3,3,3,2,1],[2,2,2,2]] => 70 [[4,4,4,4,3,1],[3,3,3,3,1]] => 105 [[3,3,3,2,2,1],[2,2,2,1]] => 175 [[4,4,4,3,3,1],[3,3,3,2,1]] => 280 [[4,4,4,3,2,1],[3,3,3,2]] => 280 [[5,5,5,4,3,1],[4,4,4,3,1]] => 420 [[3,3,2,2,2,1],[2,2,1,1]] => 189 [[4,4,3,3,3,1],[3,3,2,2,1]] => 315 [[4,4,3,3,2,1],[3,3,2,2]] => 420 [[5,5,4,4,3,1],[4,4,3,3,1]] => 630 [[4,4,3,2,2,1],[3,3,2,1]] => 525 [[5,5,4,3,3,1],[4,4,3,2,1]] => 840 [[5,5,4,3,2,1],[4,4,3,2]] => 840 [[6,6,5,4,3,1],[5,5,4,3,1]] => 1260 [[3,2,2,2,2,1],[2,1,1,1]] => 98 [[4,3,3,3,3,1],[3,2,2,2,1]] => 168 [[4,3,3,3,2,1],[3,2,2,2]] => 280 [[5,4,4,4,3,1],[4,3,3,3,1]] => 420 [[4,3,3,2,2,1],[3,2,2,1]] => 525 [[5,4,4,3,3,1],[4,3,3,2,1]] => 840 [[5,4,4,3,2,1],[4,3,3,2]] => 840 [[6,5,5,4,3,1],[5,4,4,3,1]] => 1260 [[4,3,2,2,2,1],[3,2,1,1]] => 378 [[5,4,3,3,3,1],[4,3,2,2,1]] => 630 [[5,4,3,3,2,1],[4,3,2,2]] => 840 [[6,5,4,4,3,1],[5,4,3,3,1]] => 1260 [[5,4,3,2,2,1],[4,3,2,1]] => 1050 [[6,5,4,3,3,1],[5,4,3,2,1]] => 1680 [[6,5,4,3,2,1],[5,4,3,2]] => 1680 [[7,6,5,4,3,1],[6,5,4,3,1]] => 2520 [[2,2,2,2,2,2],[1,1,1,1,1]] => 6 [[3,3,3,3,3,2],[2,2,2,2,2]] => 21 [[3,3,3,3,2,2],[2,2,2,2,1]] => 70 [[4,4,4,4,3,2],[3,3,3,3,2]] => 105 [[3,3,3,2,2,2],[2,2,2,1,1]] => 105 [[4,4,4,3,3,2],[3,3,3,2,2]] => 210 [[4,4,4,3,2,2],[3,3,3,2,1]] => 280 [[5,5,5,4,3,2],[4,4,4,3,2]] => 420 [[3,3,2,2,2,2],[2,2,1,1,1]] => 84 [[4,4,3,3,3,2],[3,3,2,2,2]] => 210 [[4,4,3,3,2,2],[3,3,2,2,1]] => 420 [[5,5,4,4,3,2],[4,4,3,3,2]] => 630 [[4,4,3,2,2,2],[3,3,2,1,1]] => 315 [[5,5,4,3,3,2],[4,4,3,2,2]] => 630 [[5,5,4,3,2,2],[4,4,3,2,1]] => 840 [[6,6,5,4,3,2],[5,5,4,3,2]] => 1260 [[3,2,2,2,2,2],[2,1,1,1,1]] => 35 [[4,3,3,3,3,2],[3,2,2,2,2]] => 105 [[4,3,3,3,2,2],[3,2,2,2,1]] => 280 [[5,4,4,4,3,2],[4,3,3,3,2]] => 420 [[4,3,3,2,2,2],[3,2,2,1,1]] => 315 [[5,4,4,3,3,2],[4,3,3,2,2]] => 630 [[5,4,4,3,2,2],[4,3,3,2,1]] => 840 [[6,5,5,4,3,2],[5,4,4,3,2]] => 1260 [[4,3,2,2,2,2],[3,2,1,1,1]] => 168 [[5,4,3,3,3,2],[4,3,2,2,2]] => 420 [[5,4,3,3,2,2],[4,3,2,2,1]] => 840 [[6,5,4,4,3,2],[5,4,3,3,2]] => 1260 [[5,4,3,2,2,2],[4,3,2,1,1]] => 630 [[6,5,4,3,3,2],[5,4,3,2,2]] => 1260 [[6,5,4,3,2,2],[5,4,3,2,1]] => 1680 [[7,6,5,4,3,2],[6,5,4,3,2]] => 2520 [[1,1,1,1,1,1,1],[]] => 1 [[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => 7 [[2,2,2,2,2,1,1],[1,1,1,1,1]] => 21 [[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => 42 [[2,2,2,2,1,1,1],[1,1,1,1]] => 35 [[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => 105 [[3,3,3,3,2,1,1],[2,2,2,2,1]] => 105 [[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => 210 [[2,2,2,1,1,1,1],[1,1,1]] => 35 [[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => 140 [[3,3,3,2,2,1,1],[2,2,2,1,1]] => 210 [[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => 420 [[3,3,3,2,1,1,1],[2,2,2,1]] => 140 [[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => 420 ----------------------------------------------------------------------------- Created: Sep 22, 2020 at 09:47 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Sep 22, 2020 at 09:47 by Martin Rubey