***************************************************************************** * 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: St001658 ----------------------------------------------------------------------------- Collection: Skew partitions ----------------------------------------------------------------------------- Description: The total number of rook placements on a Ferrers board. ----------------------------------------------------------------------------- References: [1] [[wikipedia:Rook_polynomial]] ----------------------------------------------------------------------------- Code: def statistic(nu): import itertools rook_matrix = matrix([[0]*q + [1]*(p-q) + [0]*(nu[0][0]-p) for p, q in itertools.zip_longest(*nu, fillvalue=0)]) return sum(rook_matrix.rook_vector()) ----------------------------------------------------------------------------- Statistic values: [[1],[]] => 2 [[2],[]] => 3 [[1,1],[]] => 3 [[2,1],[1]] => 4 [[3],[]] => 4 [[2,1],[]] => 5 [[3,1],[1]] => 6 [[2,2],[1]] => 5 [[3,2],[2]] => 6 [[1,1,1],[]] => 4 [[2,2,1],[1,1]] => 6 [[2,1,1],[1]] => 6 [[3,2,1],[2,1]] => 8 [[4],[]] => 5 [[3,1],[]] => 7 [[4,1],[1]] => 8 [[2,2],[]] => 7 [[3,2],[1]] => 8 [[4,2],[2]] => 9 [[2,1,1],[]] => 7 [[3,2,1],[1,1]] => 10 [[3,1,1],[1]] => 9 [[4,2,1],[2,1]] => 12 [[3,3],[2]] => 7 [[4,3],[3]] => 8 [[2,2,1],[1]] => 8 [[3,3,1],[2,1]] => 10 [[3,2,1],[2]] => 10 [[4,3,1],[3,1]] => 12 [[2,2,2],[1,1]] => 7 [[3,3,2],[2,2]] => 9 [[3,2,2],[2,1]] => 10 [[4,3,2],[3,2]] => 12 [[1,1,1,1],[]] => 5 [[2,2,2,1],[1,1,1]] => 8 [[2,2,1,1],[1,1]] => 9 [[3,3,2,1],[2,2,1]] => 12 [[2,1,1,1],[1]] => 8 [[3,2,2,1],[2,1,1]] => 12 [[3,2,1,1],[2,1]] => 12 [[4,3,2,1],[3,2,1]] => 16 [[5],[]] => 6 [[4,1],[]] => 9 [[5,1],[1]] => 10 [[3,2],[]] => 10 [[4,2],[1]] => 11 [[5,2],[2]] => 12 [[3,1,1],[]] => 10 [[4,2,1],[1,1]] => 14 [[4,1,1],[1]] => 12 [[5,2,1],[2,1]] => 16 [[3,3],[1]] => 10 [[4,3],[2]] => 11 [[5,3],[3]] => 12 [[2,2,1],[]] => 10 [[3,3,1],[1,1]] => 14 [[3,2,1],[1]] => 13 [[4,3,1],[2,1]] => 16 [[4,2,1],[2]] => 15 [[5,3,1],[3,1]] => 18 [[3,2,2],[1,1]] => 12 [[4,3,2],[2,2]] => 15 [[4,2,2],[2,1]] => 15 [[5,3,2],[3,2]] => 18 [[2,1,1,1],[]] => 9 [[3,2,2,1],[1,1,1]] => 14 [[3,2,1,1],[1,1]] => 15 [[4,3,2,1],[2,2,1]] => 20 [[3,1,1,1],[1]] => 12 [[4,2,2,1],[2,1,1]] => 18 [[4,2,1,1],[2,1]] => 18 [[5,3,2,1],[3,2,1]] => 24 [[4,4],[3]] => 9 [[5,4],[4]] => 10 [[3,3,1],[2]] => 12 [[4,4,1],[3,1]] => 14 [[4,3,1],[3]] => 14 [[5,4,1],[4,1]] => 16 [[2,2,2],[1]] => 10 [[3,3,2],[2,1]] => 13 [[4,4,2],[3,2]] => 15 [[3,2,2],[2]] => 14 [[4,3,2],[3,1]] => 16 [[5,4,2],[4,2]] => 18 [[2,2,1,1],[1]] => 11 [[3,3,2,1],[2,1,1]] => 16 [[3,3,1,1],[2,1]] => 15 [[4,4,2,1],[3,2,1]] => 20 [[3,2,1,1],[2]] => 14 [[4,3,2,1],[3,1,1]] => 20 [[4,3,1,1],[3,1]] => 18 [[5,4,2,1],[4,2,1]] => 24 [[3,3,3],[2,2]] => 10 [[4,4,3],[3,3]] => 12 [[4,3,3],[3,2]] => 14 [[5,4,3],[4,3]] => 16 [[2,2,2,1],[1,1]] => 11 [[3,3,3,1],[2,2,1]] => 14 [[3,3,2,1],[2,2]] => 15 [[4,4,3,1],[3,3,1]] => 18 [[3,2,2,1],[2,1]] => 16 [[4,3,3,1],[3,2,1]] => 20 [[4,3,2,1],[3,2]] => 20 [[5,4,3,1],[4,3,1]] => 24 [[2,2,2,2],[1,1,1]] => 9 [[3,3,3,2],[2,2,2]] => 12 [[3,3,2,2],[2,2,1]] => 15 [[4,4,3,2],[3,3,2]] => 18 [[3,2,2,2],[2,1,1]] => 14 [[4,3,3,2],[3,2,2]] => 18 [[4,3,2,2],[3,2,1]] => 20 [[5,4,3,2],[4,3,2]] => 24 [[1,1,1,1,1],[]] => 6 [[2,2,2,2,1],[1,1,1,1]] => 10 [[2,2,2,1,1],[1,1,1]] => 12 [[3,3,3,2,1],[2,2,2,1]] => 16 [[2,2,1,1,1],[1,1]] => 12 [[3,3,2,2,1],[2,2,1,1]] => 18 [[3,3,2,1,1],[2,2,1]] => 18 [[4,4,3,2,1],[3,3,2,1]] => 24 [[2,1,1,1,1],[1]] => 10 [[3,2,2,2,1],[2,1,1,1]] => 16 [[3,2,2,1,1],[2,1,1]] => 18 [[4,3,3,2,1],[3,2,2,1]] => 24 [[3,2,1,1,1],[2,1]] => 16 [[4,3,2,2,1],[3,2,1,1]] => 24 [[4,3,2,1,1],[3,2,1]] => 24 [[5,4,3,2,1],[4,3,2,1]] => 32 [[6],[]] => 7 [[5,1],[]] => 11 [[6,1],[1]] => 12 [[4,2],[]] => 13 [[5,2],[1]] => 14 [[6,2],[2]] => 15 [[4,1,1],[]] => 13 [[5,2,1],[1,1]] => 18 [[5,1,1],[1]] => 15 [[6,2,1],[2,1]] => 20 [[3,3],[]] => 13 [[4,3],[1]] => 14 [[5,3],[2]] => 15 [[6,3],[3]] => 16 [[3,2,1],[]] => 15 [[4,3,1],[1,1]] => 20 [[4,2,1],[1]] => 18 [[5,3,1],[2,1]] => 22 [[5,2,1],[2]] => 20 [[6,3,1],[3,1]] => 24 [[4,2,2],[1,1]] => 17 [[5,3,2],[2,2]] => 21 [[5,2,2],[2,1]] => 20 [[6,3,2],[3,2]] => 24 [[3,1,1,1],[]] => 13 [[4,2,2,1],[1,1,1]] => 20 [[4,2,1,1],[1,1]] => 21 [[5,3,2,1],[2,2,1]] => 28 [[4,1,1,1],[1]] => 16 [[5,2,2,1],[2,1,1]] => 24 [[5,2,1,1],[2,1]] => 24 [[6,3,2,1],[3,2,1]] => 32 [[4,4],[2]] => 13 [[5,4],[3]] => 14 [[6,4],[4]] => 15 [[3,3,1],[1]] => 17 [[4,4,1],[2,1]] => 20 [[4,3,1],[2]] => 19 [[5,4,1],[3,1]] => 22 [[5,3,1],[3]] => 21 [[6,4,1],[4,1]] => 24 [[2,2,2],[]] => 13 [[3,3,2],[1,1]] => 17 [[4,4,2],[2,2]] => 21 [[3,2,2],[1]] => 17 [[4,3,2],[2,1]] => 21 [[5,4,2],[3,2]] => 24 [[4,2,2],[2]] => 21 [[5,3,2],[3,1]] => 24 [[6,4,2],[4,2]] => 27 [[2,2,1,1],[]] => 13 [[3,3,2,1],[1,1,1]] => 20 [[3,3,1,1],[1,1]] => 21 [[4,4,2,1],[2,2,1]] => 28 [[3,2,1,1],[1]] => 18 [[4,3,2,1],[2,1,1]] => 26 [[4,3,1,1],[2,1]] => 24 [[5,4,2,1],[3,2,1]] => 32 [[4,2,1,1],[2]] => 21 [[5,3,2,1],[3,1,1]] => 30 [[5,3,1,1],[3,1]] => 27 [[6,4,2,1],[4,2,1]] => 36 [[4,3,3],[2,2]] => 17 [[5,4,3],[3,3]] => 20 [[5,3,3],[3,2]] => 21 [[6,4,3],[4,3]] => 24 [[3,2,2,1],[1,1]] => 19 [[4,3,3,1],[2,2,1]] => 24 [[4,3,2,1],[2,2]] => 25 [[5,4,3,1],[3,3,1]] => 30 [[4,2,2,1],[2,1]] => 24 [[5,3,3,1],[3,2,1]] => 30 [[5,3,2,1],[3,2]] => 30 [[6,4,3,1],[4,3,1]] => 36 [[3,2,2,2],[1,1,1]] => 16 [[4,3,3,2],[2,2,2]] => 21 [[4,3,2,2],[2,2,1]] => 25 [[5,4,3,2],[3,3,2]] => 30 [[4,2,2,2],[2,1,1]] => 21 [[5,3,3,2],[3,2,2]] => 27 [[5,3,2,2],[3,2,1]] => 30 [[6,4,3,2],[4,3,2]] => 36 [[2,1,1,1,1],[]] => 11 [[3,2,2,2,1],[1,1,1,1]] => 18 [[3,2,2,1,1],[1,1,1]] => 21 [[4,3,3,2,1],[2,2,2,1]] => 28 [[3,2,1,1,1],[1,1]] => 20 [[4,3,2,2,1],[2,2,1,1]] => 30 [[4,3,2,1,1],[2,2,1]] => 30 [[5,4,3,2,1],[3,3,2,1]] => 40 [[3,1,1,1,1],[1]] => 15 [[4,2,2,2,1],[2,1,1,1]] => 24 [[4,2,2,1,1],[2,1,1]] => 27 [[5,3,3,2,1],[3,2,2,1]] => 36 [[4,2,1,1,1],[2,1]] => 24 [[5,3,2,2,1],[3,2,1,1]] => 36 [[5,3,2,1,1],[3,2,1]] => 36 [[6,4,3,2,1],[4,3,2,1]] => 48 [[5,5],[4]] => 11 [[6,5],[5]] => 12 [[4,4,1],[3]] => 16 [[5,5,1],[4,1]] => 18 [[5,4,1],[4]] => 18 [[6,5,1],[5,1]] => 20 [[3,3,2],[2]] => 17 [[4,4,2],[3,1]] => 19 [[5,5,2],[4,2]] => 21 [[4,3,2],[3]] => 20 [[5,4,2],[4,1]] => 22 [[6,5,2],[5,2]] => 24 [[3,3,1,1],[2]] => 17 [[4,4,2,1],[3,1,1]] => 24 [[4,4,1,1],[3,1]] => 21 [[5,5,2,1],[4,2,1]] => 28 [[4,3,1,1],[3]] => 20 [[5,4,2,1],[4,1,1]] => 28 [[5,4,1,1],[4,1]] => 24 [[6,5,2,1],[5,2,1]] => 32 [[3,3,3],[2,1]] => 15 [[4,4,3],[3,2]] => 18 [[5,5,3],[4,3]] => 20 [[4,3,3],[3,1]] => 20 [[5,4,3],[4,2]] => 22 [[6,5,3],[5,3]] => 24 [[2,2,2,1],[1]] => 14 [[3,3,3,1],[2,1,1]] => 20 [[3,3,2,1],[2,1]] => 21 [[4,4,3,1],[3,2,1]] => 26 [[4,4,2,1],[3,2]] => 25 [[5,5,3,1],[4,3,1]] => 30 [[3,2,2,1],[2]] => 20 [[4,3,3,1],[3,1,1]] => 28 [[4,3,2,1],[3,1]] => 26 [[5,4,3,1],[4,2,1]] => 32 [[5,4,2,1],[4,2]] => 30 [[6,5,3,1],[5,3,1]] => 36 [[3,3,2,2],[2,1,1]] => 19 [[4,4,3,2],[3,2,2]] => 24 [[4,4,2,2],[3,2,1]] => 25 [[5,5,3,2],[4,3,2]] => 30 [[4,3,2,2],[3,1,1]] => 24 [[5,4,3,2],[4,2,2]] => 30 [[5,4,2,2],[4,2,1]] => 30 [[6,5,3,2],[5,3,2]] => 36 [[2,2,1,1,1],[1]] => 14 [[3,3,2,2,1],[2,1,1,1]] => 22 [[3,3,2,1,1],[2,1,1]] => 24 [[4,4,3,2,1],[3,2,2,1]] => 32 [[3,3,1,1,1],[2,1]] => 20 [[4,4,2,2,1],[3,2,1,1]] => 30 [[4,4,2,1,1],[3,2,1]] => 30 [[5,5,3,2,1],[4,3,2,1]] => 40 [[3,2,1,1,1],[2]] => 18 [[4,3,2,2,1],[3,1,1,1]] => 28 [[4,3,2,1,1],[3,1,1]] => 30 [[5,4,3,2,1],[4,2,2,1]] => 40 [[4,3,1,1,1],[3,1]] => 24 [[5,4,2,2,1],[4,2,1,1]] => 36 [[5,4,2,1,1],[4,2,1]] => 36 [[6,5,3,2,1],[5,3,2,1]] => 48 [[4,4,4],[3,3]] => 13 [[5,5,4],[4,4]] => 15 [[5,4,4],[4,3]] => 18 [[6,5,4],[5,4]] => 20 [[3,3,3,1],[2,2]] => 17 [[4,4,4,1],[3,3,1]] => 20 [[4,4,3,1],[3,3]] => 21 [[5,5,4,1],[4,4,1]] => 24 [[4,3,3,1],[3,2]] => 24 [[5,4,4,1],[4,3,1]] => 28 [[5,4,3,1],[4,3]] => 28 [[6,5,4,1],[5,4,1]] => 32 [[2,2,2,2],[1,1]] => 13 [[3,3,3,2],[2,2,1]] => 18 [[4,4,4,2],[3,3,2]] => 21 [[3,3,2,2],[2,2]] => 21 [[4,4,3,2],[3,3,1]] => 24 [[5,5,4,2],[4,4,2]] => 27 [[3,2,2,2],[2,1]] => 20 [[4,3,3,2],[3,2,1]] => 26 [[5,4,4,2],[4,3,2]] => 30 [[4,3,2,2],[3,2]] => 28 [[5,4,3,2],[4,3,1]] => 32 [[6,5,4,2],[5,4,2]] => 36 [[2,2,2,1,1],[1,1]] => 15 [[3,3,3,2,1],[2,2,1,1]] => 22 [[3,3,3,1,1],[2,2,1]] => 21 [[4,4,4,2,1],[3,3,2,1]] => 28 [[3,3,2,1,1],[2,2]] => 21 [[4,4,3,2,1],[3,3,1,1]] => 30 [[4,4,3,1,1],[3,3,1]] => 27 [[5,5,4,2,1],[4,4,2,1]] => 36 [[3,2,2,1,1],[2,1]] => 22 [[4,3,3,2,1],[3,2,1,1]] => 32 [[4,3,3,1,1],[3,2,1]] => 30 [[5,4,4,2,1],[4,3,2,1]] => 40 [[4,3,2,1,1],[3,2]] => 28 [[5,4,3,2,1],[4,3,1,1]] => 40 [[5,4,3,1,1],[4,3,1]] => 36 [[6,5,4,2,1],[5,4,2,1]] => 48 [[3,3,3,3],[2,2,2]] => 13 [[4,4,4,3],[3,3,3]] => 16 [[4,4,3,3],[3,3,2]] => 21 [[5,5,4,3],[4,4,3]] => 24 [[4,3,3,3],[3,2,2]] => 20 [[5,4,4,3],[4,3,3]] => 24 [[5,4,3,3],[4,3,2]] => 28 [[6,5,4,3],[5,4,3]] => 32 [[2,2,2,2,1],[1,1,1]] => 14 [[3,3,3,3,1],[2,2,2,1]] => 18 [[3,3,3,2,1],[2,2,2]] => 20 [[4,4,4,3,1],[3,3,3,1]] => 24 [[3,3,2,2,1],[2,2,1]] => 24 [[4,4,3,3,1],[3,3,2,1]] => 30 [[4,4,3,2,1],[3,3,2]] => 30 [[5,5,4,3,1],[4,4,3,1]] => 36 [[3,2,2,2,1],[2,1,1]] => 22 [[4,3,3,3,1],[3,2,2,1]] => 28 [[4,3,3,2,1],[3,2,2]] => 30 [[5,4,4,3,1],[4,3,3,1]] => 36 [[4,3,2,2,1],[3,2,1]] => 32 [[5,4,3,3,1],[4,3,2,1]] => 40 [[5,4,3,2,1],[4,3,2]] => 40 [[6,5,4,3,1],[5,4,3,1]] => 48 [[2,2,2,2,2],[1,1,1,1]] => 11 [[3,3,3,3,2],[2,2,2,2]] => 15 [[3,3,3,2,2],[2,2,2,1]] => 20 [[4,4,4,3,2],[3,3,3,2]] => 24 [[3,3,2,2,2],[2,2,1,1]] => 21 [[4,4,3,3,2],[3,3,2,2]] => 27 [[4,4,3,2,2],[3,3,2,1]] => 30 [[5,5,4,3,2],[4,4,3,2]] => 36 [[3,2,2,2,2],[2,1,1,1]] => 18 [[4,3,3,3,2],[3,2,2,2]] => 24 [[4,3,3,2,2],[3,2,2,1]] => 30 [[5,4,4,3,2],[4,3,3,2]] => 36 [[4,3,2,2,2],[3,2,1,1]] => 28 [[5,4,3,3,2],[4,3,2,2]] => 36 [[5,4,3,2,2],[4,3,2,1]] => 40 [[6,5,4,3,2],[5,4,3,2]] => 48 [[1,1,1,1,1,1],[]] => 7 [[2,2,2,2,2,1],[1,1,1,1,1]] => 12 [[2,2,2,2,1,1],[1,1,1,1]] => 15 [[3,3,3,3,2,1],[2,2,2,2,1]] => 20 [[2,2,2,1,1,1],[1,1,1]] => 16 [[3,3,3,2,2,1],[2,2,2,1,1]] => 24 [[3,3,3,2,1,1],[2,2,2,1]] => 24 [[4,4,4,3,2,1],[3,3,3,2,1]] => 32 [[2,2,1,1,1,1],[1,1]] => 15 [[3,3,2,2,2,1],[2,2,1,1,1]] => 24 [[3,3,2,2,1,1],[2,2,1,1]] => 27 [[4,4,3,3,2,1],[3,3,2,2,1]] => 36 [[3,3,2,1,1,1],[2,2,1]] => 24 [[4,4,3,2,2,1],[3,3,2,1,1]] => 36 [[4,4,3,2,1,1],[3,3,2,1]] => 36 [[5,5,4,3,2,1],[4,4,3,2,1]] => 48 [[2,1,1,1,1,1],[1]] => 12 [[3,2,2,2,2,1],[2,1,1,1,1]] => 20 [[3,2,2,2,1,1],[2,1,1,1]] => 24 [[4,3,3,3,2,1],[3,2,2,2,1]] => 32 [[3,2,2,1,1,1],[2,1,1]] => 24 [[4,3,3,2,2,1],[3,2,2,1,1]] => 36 [[4,3,3,2,1,1],[3,2,2,1]] => 36 [[5,4,4,3,2,1],[4,3,3,2,1]] => 48 [[3,2,1,1,1,1],[2,1]] => 20 [[4,3,2,2,2,1],[3,2,1,1,1]] => 32 [[4,3,2,2,1,1],[3,2,1,1]] => 36 [[5,4,3,3,2,1],[4,3,2,2,1]] => 48 [[4,3,2,1,1,1],[3,2,1]] => 32 [[5,4,3,2,2,1],[4,3,2,1,1]] => 48 [[5,4,3,2,1,1],[4,3,2,1]] => 48 [[6,5,4,3,2,1],[5,4,3,2,1]] => 64 [[7],[]] => 8 [[6,1],[]] => 13 [[7,1],[1]] => 14 [[5,2],[]] => 16 [[6,2],[1]] => 17 [[7,2],[2]] => 18 [[5,1,1],[]] => 16 [[6,2,1],[1,1]] => 22 [[6,1,1],[1]] => 18 [[7,2,1],[2,1]] => 24 [[4,3],[]] => 17 [[5,3],[1]] => 18 [[6,3],[2]] => 19 [[7,3],[3]] => 20 [[4,2,1],[]] => 20 [[5,3,1],[1,1]] => 26 [[5,2,1],[1]] => 23 [[6,3,1],[2,1]] => 28 [[6,2,1],[2]] => 25 [[7,3,1],[3,1]] => 30 [[5,2,2],[1,1]] => 22 [[6,3,2],[2,2]] => 27 [[6,2,2],[2,1]] => 25 [[7,3,2],[3,2]] => 30 [[4,1,1,1],[]] => 17 [[5,2,2,1],[1,1,1]] => 26 [[5,2,1,1],[1,1]] => 27 [[6,3,2,1],[2,2,1]] => 36 [[5,1,1,1],[1]] => 20 [[6,2,2,1],[2,1,1]] => 30 [[6,2,1,1],[2,1]] => 30 [[7,3,2,1],[3,2,1]] => 40 [[4,4],[1]] => 17 [[5,4],[2]] => 18 [[6,4],[3]] => 19 [[7,4],[4]] => 20 [[3,3,1],[]] => 20 [[4,4,1],[1,1]] => 26 [[4,3,1],[1]] => 24 [[5,4,1],[2,1]] => 28 [[5,3,1],[2]] => 26 [[6,4,1],[3,1]] => 30 [[6,3,1],[3]] => 28 [[7,4,1],[4,1]] => 32 [[3,2,2],[]] => 20 [[4,3,2],[1,1]] => 25 [[5,4,2],[2,2]] => 30 [[4,2,2],[1]] => 24 [[5,3,2],[2,1]] => 29 [[6,4,2],[3,2]] => 33 [[5,2,2],[2]] => 28 [[6,3,2],[3,1]] => 32 [[7,4,2],[4,2]] => 36 [[3,2,1,1],[]] => 20 [[4,3,2,1],[1,1,1]] => 30 [[4,3,1,1],[1,1]] => 30 [[5,4,2,1],[2,2,1]] => 40 [[4,2,1,1],[1]] => 25 [[5,3,2,1],[2,1,1]] => 36 [[5,3,1,1],[2,1]] => 33 [[6,4,2,1],[3,2,1]] => 44 [[5,2,1,1],[2]] => 28 [[6,3,2,1],[3,1,1]] => 40 [[6,3,1,1],[3,1]] => 36 [[7,4,2,1],[4,2,1]] => 48 [[5,3,3],[2,2]] => 24 [[6,4,3],[3,3]] => 28 [[6,3,3],[3,2]] => 28 [[7,4,3],[4,3]] => 32 [[4,2,2,1],[1,1]] => 27 [[5,3,3,1],[2,2,1]] => 34 [[5,3,2,1],[2,2]] => 35 [[6,4,3,1],[3,3,1]] => 42 [[5,2,2,1],[2,1]] => 32 [[6,3,3,1],[3,2,1]] => 40 [[6,3,2,1],[3,2]] => 40 [[7,4,3,1],[4,3,1]] => 48 [[4,2,2,2],[1,1,1]] => 23 [[5,3,3,2],[2,2,2]] => 30 [[5,3,2,2],[2,2,1]] => 35 [[6,4,3,2],[3,3,2]] => 42 [[5,2,2,2],[2,1,1]] => 28 [[6,3,3,2],[3,2,2]] => 36 [[6,3,2,2],[3,2,1]] => 40 [[7,4,3,2],[4,3,2]] => 48 [[3,1,1,1,1],[]] => 16 [[4,2,2,2,1],[1,1,1,1]] => 26 [[4,2,2,1,1],[1,1,1]] => 30 [[5,3,3,2,1],[2,2,2,1]] => 40 [[4,2,1,1,1],[1,1]] => 28 [[5,3,2,2,1],[2,2,1,1]] => 42 [[5,3,2,1,1],[2,2,1]] => 42 [[6,4,3,2,1],[3,3,2,1]] => 56 [[4,1,1,1,1],[1]] => 20 [[5,2,2,2,1],[2,1,1,1]] => 32 [[5,2,2,1,1],[2,1,1]] => 36 [[6,3,3,2,1],[3,2,2,1]] => 48 [[5,2,1,1,1],[2,1]] => 32 [[6,3,2,2,1],[3,2,1,1]] => 48 [[6,3,2,1,1],[3,2,1]] => 48 [[7,4,3,2,1],[4,3,2,1]] => 64 [[5,5],[3]] => 16 [[6,5],[4]] => 17 [[7,5],[5]] => 18 [[4,4,1],[2]] => 23 [[5,5,1],[3,1]] => 26 [[5,4,1],[3]] => 25 [[6,5,1],[4,1]] => 28 [[6,4,1],[4]] => 27 [[7,5,1],[5,1]] => 30 [[3,3,2],[1]] => 22 [[4,4,2],[2,1]] => 27 [[5,5,2],[3,2]] => 30 [[4,3,2],[2]] => 27 [[5,4,2],[3,1]] => 30 [[6,5,2],[4,2]] => 33 [[5,3,2],[3]] => 30 [[6,4,2],[4,1]] => 33 [[7,5,2],[5,2]] => 36 [[3,3,1,1],[1]] => 24 [[4,4,2,1],[2,1,1]] => 34 [[4,4,1,1],[2,1]] => 30 [[5,5,2,1],[3,2,1]] => 40 [[4,3,1,1],[2]] => 27 [[5,4,2,1],[3,1,1]] => 38 [[5,4,1,1],[3,1]] => 33 [[6,5,2,1],[4,2,1]] => 44 [[5,3,1,1],[3]] => 30 [[6,4,2,1],[4,1,1]] => 42 [[6,4,1,1],[4,1]] => 36 [[7,5,2,1],[5,2,1]] => 48 [[3,3,3],[1,1]] => 20 [[4,4,3],[2,2]] => 24 [[5,5,3],[3,3]] => 28 [[4,3,3],[2,1]] => 25 [[5,4,3],[3,2]] => 29 [[6,5,3],[4,3]] => 32 [[5,3,3],[3,1]] => 30 [[6,4,3],[4,2]] => 33 [[7,5,3],[5,3]] => 36 [[2,2,2,1],[]] => 17 [[3,3,3,1],[1,1,1]] => 26 [[3,3,2,1],[1,1]] => 27 [[4,4,3,1],[2,2,1]] => 34 [[4,4,2,1],[2,2]] => 35 [[5,5,3,1],[3,3,1]] => 42 [[3,2,2,1],[1]] => 24 [[4,3,3,1],[2,1,1]] => 34 [[4,3,2,1],[2,1]] => 34 [[5,4,3,1],[3,2,1]] => 42 [[5,4,2,1],[3,2]] => 40 [[6,5,3,1],[4,3,1]] => 48 [[4,2,2,1],[2]] => 30 [[5,3,3,1],[3,1,1]] => 42 [[5,3,2,1],[3,1]] => 39 [[6,4,3,1],[4,2,1]] => 48 [[6,4,2,1],[4,2]] => 45 [[7,5,3,1],[5,3,1]] => 54 [[3,3,2,2],[1,1,1]] => 23 [[4,4,3,2],[2,2,2]] => 30 [[4,4,2,2],[2,2,1]] => 35 [[5,5,3,2],[3,3,2]] => 42 [[4,3,2,2],[2,1,1]] => 31 [[5,4,3,2],[3,2,2]] => 39 [[5,4,2,2],[3,2,1]] => 40 [[6,5,3,2],[4,3,2]] => 48 [[5,3,2,2],[3,1,1]] => 36 [[6,4,3,2],[4,2,2]] => 45 [[6,4,2,2],[4,2,1]] => 45 [[7,5,3,2],[5,3,2]] => 54 [[2,2,1,1,1],[]] => 16 [[3,3,2,2,1],[1,1,1,1]] => 26 [[3,3,2,1,1],[1,1,1]] => 30 [[4,4,3,2,1],[2,2,2,1]] => 40 [[3,3,1,1,1],[1,1]] => 28 [[4,4,2,2,1],[2,2,1,1]] => 42 [[4,4,2,1,1],[2,2,1]] => 42 [[5,5,3,2,1],[3,3,2,1]] => 56 [[3,2,1,1,1],[1]] => 23 [[4,3,2,2,1],[2,1,1,1]] => 36 [[4,3,2,1,1],[2,1,1]] => 39 [[5,4,3,2,1],[3,2,2,1]] => 52 [[4,3,1,1,1],[2,1]] => 32 [[5,4,2,2,1],[3,2,1,1]] => 48 [[5,4,2,1,1],[3,2,1]] => 48 [[6,5,3,2,1],[4,3,2,1]] => 64 [[4,2,1,1,1],[2]] => 27 [[5,3,2,2,1],[3,1,1,1]] => 42 [[5,3,2,1,1],[3,1,1]] => 45 [[6,4,3,2,1],[4,2,2,1]] => 60 [[5,3,1,1,1],[3,1]] => 36 [[6,4,2,2,1],[4,2,1,1]] => 54 [[6,4,2,1,1],[4,2,1]] => 54 [[7,5,3,2,1],[5,3,2,1]] => 72 [[5,4,4],[3,3]] => 22 [[6,5,4],[4,4]] => 25 [[6,4,4],[4,3]] => 27 [[7,5,4],[5,4]] => 30 [[4,3,3,1],[2,2]] => 29 [[5,4,4,1],[3,3,1]] => 34 [[5,4,3,1],[3,3]] => 35 [[6,5,4,1],[4,4,1]] => 40 [[5,3,3,1],[3,2]] => 36 [[6,4,4,1],[4,3,1]] => 42 [[6,4,3,1],[4,3]] => 42 [[7,5,4,1],[5,4,1]] => 48 [[3,2,2,2],[1,1]] => 23 [[4,3,3,2],[2,2,1]] => 31 [[5,4,4,2],[3,3,2]] => 36 [[4,3,2,2],[2,2]] => 35 [[5,4,3,2],[3,3,1]] => 40 [[6,5,4,2],[4,4,2]] => 45 [[4,2,2,2],[2,1]] => 30 [[5,3,3,2],[3,2,1]] => 39 [[6,4,4,2],[4,3,2]] => 45 [[5,3,2,2],[3,2]] => 42 [[6,4,3,2],[4,3,1]] => 48 [[7,5,4,2],[5,4,2]] => 54 [[3,2,2,1,1],[1,1]] => 26 [[4,3,3,2,1],[2,2,1,1]] => 38 [[4,3,3,1,1],[2,2,1]] => 36 [[5,4,4,2,1],[3,3,2,1]] => 48 [[4,3,2,1,1],[2,2]] => 35 [[5,4,3,2,1],[3,3,1,1]] => 50 [[5,4,3,1,1],[3,3,1]] => 45 [[6,5,4,2,1],[4,4,2,1]] => 60 [[4,2,2,1,1],[2,1]] => 33 [[5,3,3,2,1],[3,2,1,1]] => 48 [[5,3,3,1,1],[3,2,1]] => 45 [[6,4,4,2,1],[4,3,2,1]] => 60 [[5,3,2,1,1],[3,2]] => 42 [[6,4,3,2,1],[4,3,1,1]] => 60 [[6,4,3,1,1],[4,3,1]] => 54 [[7,5,4,2,1],[5,4,2,1]] => 72 [[4,3,3,3],[2,2,2]] => 23 [[5,4,4,3],[3,3,3]] => 28 [[5,4,3,3],[3,3,2]] => 35 [[6,5,4,3],[4,4,3]] => 40 [[5,3,3,3],[3,2,2]] => 30 [[6,4,4,3],[4,3,3]] => 36 [[6,4,3,3],[4,3,2]] => 42 [[7,5,4,3],[5,4,3]] => 48 [[3,2,2,2,1],[1,1,1]] => 25 [[4,3,3,3,1],[2,2,2,1]] => 32 [[4,3,3,2,1],[2,2,2]] => 35 [[5,4,4,3,1],[3,3,3,1]] => 42 [[4,3,2,2,1],[2,2,1]] => 40 [[5,4,3,3,1],[3,3,2,1]] => 50 [[5,4,3,2,1],[3,3,2]] => 50 [[6,5,4,3,1],[4,4,3,1]] => 60 [[4,2,2,2,1],[2,1,1]] => 33 [[5,3,3,3,1],[3,2,2,1]] => 42 [[5,3,3,2,1],[3,2,2]] => 45 [[6,4,4,3,1],[4,3,3,1]] => 54 [[5,3,2,2,1],[3,2,1]] => 48 [[6,4,3,3,1],[4,3,2,1]] => 60 [[6,4,3,2,1],[4,3,2]] => 60 [[7,5,4,3,1],[5,4,3,1]] => 72 [[3,2,2,2,2],[1,1,1,1]] => 20 [[4,3,3,3,2],[2,2,2,2]] => 27 [[4,3,3,2,2],[2,2,2,1]] => 35 [[5,4,4,3,2],[3,3,3,2]] => 42 [[4,3,2,2,2],[2,2,1,1]] => 35 [[5,4,3,3,2],[3,3,2,2]] => 45 [[5,4,3,2,2],[3,3,2,1]] => 50 [[6,5,4,3,2],[4,4,3,2]] => 60 [[4,2,2,2,2],[2,1,1,1]] => 27 [[5,3,3,3,2],[3,2,2,2]] => 36 [[5,3,3,2,2],[3,2,2,1]] => 45 [[6,4,4,3,2],[4,3,3,2]] => 54 [[5,3,2,2,2],[3,2,1,1]] => 42 [[6,4,3,3,2],[4,3,2,2]] => 54 [[6,4,3,2,2],[4,3,2,1]] => 60 [[7,5,4,3,2],[5,4,3,2]] => 72 [[2,1,1,1,1,1],[]] => 13 [[3,2,2,2,2,1],[1,1,1,1,1]] => 22 [[3,2,2,2,1,1],[1,1,1,1]] => 27 [[4,3,3,3,2,1],[2,2,2,2,1]] => 36 [[3,2,2,1,1,1],[1,1,1]] => 28 [[4,3,3,2,2,1],[2,2,2,1,1]] => 42 [[4,3,3,2,1,1],[2,2,2,1]] => 42 [[5,4,4,3,2,1],[3,3,3,2,1]] => 56 [[3,2,1,1,1,1],[1,1]] => 25 [[4,3,2,2,2,1],[2,2,1,1,1]] => 40 [[4,3,2,2,1,1],[2,2,1,1]] => 45 [[5,4,3,3,2,1],[3,3,2,2,1]] => 60 [[4,3,2,1,1,1],[2,2,1]] => 40 [[5,4,3,2,2,1],[3,3,2,1,1]] => 60 [[5,4,3,2,1,1],[3,3,2,1]] => 60 [[6,5,4,3,2,1],[4,4,3,2,1]] => 80 [[3,1,1,1,1,1],[1]] => 18 [[4,2,2,2,2,1],[2,1,1,1,1]] => 30 [[4,2,2,2,1,1],[2,1,1,1]] => 36 [[5,3,3,3,2,1],[3,2,2,2,1]] => 48 [[4,2,2,1,1,1],[2,1,1]] => 36 [[5,3,3,2,2,1],[3,2,2,1,1]] => 54 [[5,3,3,2,1,1],[3,2,2,1]] => 54 [[6,4,4,3,2,1],[4,3,3,2,1]] => 72 [[4,2,1,1,1,1],[2,1]] => 30 [[5,3,2,2,2,1],[3,2,1,1,1]] => 48 [[5,3,2,2,1,1],[3,2,1,1]] => 54 [[6,4,3,3,2,1],[4,3,2,2,1]] => 72 [[5,3,2,1,1,1],[3,2,1]] => 48 [[6,4,3,2,2,1],[4,3,2,1,1]] => 72 [[6,4,3,2,1,1],[4,3,2,1]] => 72 [[7,5,4,3,2,1],[5,4,3,2,1]] => 96 [[6,6],[5]] => 13 [[7,6],[6]] => 14 [[5,5,1],[4]] => 20 [[6,6,1],[5,1]] => 22 [[6,5,1],[5]] => 22 [[7,6,1],[6,1]] => 24 [[4,4,2],[3]] => 23 [[5,5,2],[4,1]] => 25 [[6,6,2],[5,2]] => 27 [[5,4,2],[4]] => 26 [[6,5,2],[5,1]] => 28 [[7,6,2],[6,2]] => 30 [[4,4,1,1],[3]] => 23 [[5,5,2,1],[4,1,1]] => 32 [[5,5,1,1],[4,1]] => 27 [[6,6,2,1],[5,2,1]] => 36 [[5,4,1,1],[4]] => 26 [[6,5,2,1],[5,1,1]] => 36 [[6,5,1,1],[5,1]] => 30 [[7,6,2,1],[6,2,1]] => 40 [[3,3,3],[2]] => 20 [[4,4,3],[3,1]] => 24 [[5,5,3],[4,2]] => 26 [[6,6,3],[5,3]] => 28 [[4,3,3],[3]] => 26 [[5,4,3],[4,1]] => 28 [[6,5,3],[5,2]] => 30 [[7,6,3],[6,3]] => 32 [[3,3,2,1],[2]] => 25 [[4,4,3,1],[3,1,1]] => 34 [[4,4,2,1],[3,1]] => 31 [[5,5,3,1],[4,2,1]] => 38 [[5,5,2,1],[4,2]] => 35 [[6,6,3,1],[5,3,1]] => 42 [[4,3,2,1],[3]] => 30 [[5,4,3,1],[4,1,1]] => 40 [[5,4,2,1],[4,1]] => 36 [[6,5,3,1],[5,2,1]] => 44 [[6,5,2,1],[5,2]] => 40 [[7,6,3,1],[6,3,1]] => 48 [[4,4,2,2],[3,1,1]] => 29 [[5,5,3,2],[4,2,2]] => 36 [[5,5,2,2],[4,2,1]] => 35 [[6,6,3,2],[5,3,2]] => 42 [[5,4,2,2],[4,1,1]] => 34 [[6,5,3,2],[5,2,2]] => 42 [[6,5,2,2],[5,2,1]] => 40 [[7,6,3,2],[6,3,2]] => 48 [[3,3,1,1,1],[2]] => 22 [[4,4,2,2,1],[3,1,1,1]] => 34 [[4,4,2,1,1],[3,1,1]] => 36 [[5,5,3,2,1],[4,2,2,1]] => 48 [[4,4,1,1,1],[3,1]] => 28 [[5,5,2,2,1],[4,2,1,1]] => 42 [[5,5,2,1,1],[4,2,1]] => 42 [[6,6,3,2,1],[5,3,2,1]] => 56 [[4,3,1,1,1],[3]] => 26 [[5,4,2,2,1],[4,1,1,1]] => 40 [[5,4,2,1,1],[4,1,1]] => 42 [[6,5,3,2,1],[5,2,2,1]] => 56 [[5,4,1,1,1],[4,1]] => 32 [[6,5,2,2,1],[5,2,1,1]] => 48 [[6,5,2,1,1],[5,2,1]] => 48 [[7,6,3,2,1],[6,3,2,1]] => 64 [[4,4,4],[3,2]] => 20 [[5,5,4],[4,3]] => 23 [[6,6,4],[5,4]] => 25 [[5,4,4],[4,2]] => 26 [[6,5,4],[5,3]] => 28 [[7,6,4],[6,4]] => 30 [[3,3,3,1],[2,1]] => 25 [[4,4,4,1],[3,2,1]] => 30 [[4,4,3,1],[3,2]] => 31 [[5,5,4,1],[4,3,1]] => 36 [[5,5,3,1],[4,3]] => 35 [[6,6,4,1],[5,4,1]] => 40 [[4,3,3,1],[3,1]] => 34 [[5,4,4,1],[4,2,1]] => 40 [[5,4,3,1],[4,2]] => 38 [[6,5,4,1],[5,3,1]] => 44 [[6,5,3,1],[5,3]] => 42 [[7,6,4,1],[6,4,1]] => 48 [[2,2,2,2],[1]] => 17 [[3,3,3,2],[2,1,1]] => 24 [[4,4,4,2],[3,2,2]] => 30 [[3,3,2,2],[2,1]] => 27 [[4,4,3,2],[3,2,1]] => 34 [[5,5,4,2],[4,3,2]] => 39 [[4,4,2,2],[3,2]] => 35 [[5,5,3,2],[4,3,1]] => 40 [[6,6,4,2],[5,4,2]] => 45 [[3,2,2,2],[2]] => 26 [[4,3,3,2],[3,1,1]] => 34 [[5,4,4,2],[4,2,2]] => 42 [[4,3,2,2],[3,1]] => 34 [[5,4,3,2],[4,2,1]] => 42 [[6,5,4,2],[5,3,2]] => 48 [[5,4,2,2],[4,2]] => 42 [[6,5,3,2],[5,3,1]] => 48 [[7,6,4,2],[6,4,2]] => 54 [[2,2,2,1,1],[1]] => 18 [[3,3,3,2,1],[2,1,1,1]] => 28 [[3,3,3,1,1],[2,1,1]] => 30 [[4,4,4,2,1],[3,2,2,1]] => 40 [[3,3,2,1,1],[2,1]] => 29 [[4,4,3,2,1],[3,2,1,1]] => 42 [[4,4,3,1,1],[3,2,1]] => 39 [[5,5,4,2,1],[4,3,2,1]] => 52 [[4,4,2,1,1],[3,2]] => 35 [[5,5,3,2,1],[4,3,1,1]] => 50 [[5,5,3,1,1],[4,3,1]] => 45 [[6,6,4,2,1],[5,4,2,1]] => 60 [[3,2,2,1,1],[2]] => 26 [[4,3,3,2,1],[3,1,1,1]] => 40 [[4,3,3,1,1],[3,1,1]] => 42 [[5,4,4,2,1],[4,2,2,1]] => 56 [[4,3,2,1,1],[3,1]] => 36 [[5,4,3,2,1],[4,2,1,1]] => 52 [[5,4,3,1,1],[4,2,1]] => 48 [[6,5,4,2,1],[5,3,2,1]] => 64 [[5,4,2,1,1],[4,2]] => 42 [[6,5,3,2,1],[5,3,1,1]] => 60 [[6,5,3,1,1],[5,3,1]] => 54 [[7,6,4,2,1],[6,4,2,1]] => 72 [[4,4,3,3],[3,2,2]] => 27 [[5,5,4,3],[4,3,3]] => 32 [[5,5,3,3],[4,3,2]] => 35 [[6,6,4,3],[5,4,3]] => 40 [[5,4,3,3],[4,2,2]] => 34 [[6,5,4,3],[5,3,3]] => 40 [[6,5,3,3],[5,3,2]] => 42 [[7,6,4,3],[6,4,3]] => 48 [[3,3,2,2,1],[2,1,1]] => 30 [[4,4,3,3,1],[3,2,2,1]] => 38 [[4,4,3,2,1],[3,2,2]] => 40 [[5,5,4,3,1],[4,3,3,1]] => 48 [[4,4,2,2,1],[3,2,1]] => 40 [[5,5,3,3,1],[4,3,2,1]] => 50 [[5,5,3,2,1],[4,3,2]] => 50 [[6,6,4,3,1],[5,4,3,1]] => 60 [[4,3,2,2,1],[3,1,1]] => 38 [[5,4,3,3,1],[4,2,2,1]] => 48 [[5,4,3,2,1],[4,2,2]] => 50 [[6,5,4,3,1],[5,3,3,1]] => 60 [[5,4,2,2,1],[4,2,1]] => 48 [[6,5,3,3,1],[5,3,2,1]] => 60 [[6,5,3,2,1],[5,3,2]] => 60 [[7,6,4,3,1],[6,4,3,1]] => 72 [[3,3,2,2,2],[2,1,1,1]] => 25 [[4,4,3,3,2],[3,2,2,2]] => 33 [[4,4,3,2,2],[3,2,2,1]] => 40 [[5,5,4,3,2],[4,3,3,2]] => 48 [[4,4,2,2,2],[3,2,1,1]] => 35 [[5,5,3,3,2],[4,3,2,2]] => 45 [[5,5,3,2,2],[4,3,2,1]] => 50 [[6,6,4,3,2],[5,4,3,2]] => 60 [[4,3,2,2,2],[3,1,1,1]] => 32 [[5,4,3,3,2],[4,2,2,2]] => 42 [[5,4,3,2,2],[4,2,2,1]] => 50 [[6,5,4,3,2],[5,3,3,2]] => 60 [[5,4,2,2,2],[4,2,1,1]] => 42 [[6,5,3,3,2],[5,3,2,2]] => 54 [[6,5,3,2,2],[5,3,2,1]] => 60 [[7,6,4,3,2],[6,4,3,2]] => 72 [[2,2,1,1,1,1],[1]] => 17 [[3,3,2,2,2,1],[2,1,1,1,1]] => 28 [[3,3,2,2,1,1],[2,1,1,1]] => 33 [[4,4,3,3,2,1],[3,2,2,2,1]] => 44 [[3,3,2,1,1,1],[2,1,1]] => 32 [[4,4,3,2,2,1],[3,2,2,1,1]] => 48 [[4,4,3,2,1,1],[3,2,2,1]] => 48 [[5,5,4,3,2,1],[4,3,3,2,1]] => 64 [[3,3,1,1,1,1],[2,1]] => 25 [[4,4,2,2,2,1],[3,2,1,1,1]] => 40 [[4,4,2,2,1,1],[3,2,1,1]] => 45 [[5,5,3,3,2,1],[4,3,2,2,1]] => 60 [[4,4,2,1,1,1],[3,2,1]] => 40 [[5,5,3,2,2,1],[4,3,2,1,1]] => 60 [[5,5,3,2,1,1],[4,3,2,1]] => 60 [[6,6,4,3,2,1],[5,4,3,2,1]] => 80 [[3,2,1,1,1,1],[2]] => 22 [[4,3,2,2,2,1],[3,1,1,1,1]] => 36 [[4,3,2,2,1,1],[3,1,1,1]] => 42 [[5,4,3,3,2,1],[4,2,2,2,1]] => 56 [[4,3,2,1,1,1],[3,1,1]] => 40 [[5,4,3,2,2,1],[4,2,2,1,1]] => 60 [[5,4,3,2,1,1],[4,2,2,1]] => 60 [[6,5,4,3,2,1],[5,3,3,2,1]] => 80 [[4,3,1,1,1,1],[3,1]] => 30 [[5,4,2,2,2,1],[4,2,1,1,1]] => 48 [[5,4,2,2,1,1],[4,2,1,1]] => 54 [[6,5,3,3,2,1],[5,3,2,2,1]] => 72 [[5,4,2,1,1,1],[4,2,1]] => 48 [[6,5,3,2,2,1],[5,3,2,1,1]] => 72 [[6,5,3,2,1,1],[5,3,2,1]] => 72 [[7,6,4,3,2,1],[6,4,3,2,1]] => 96 [[5,5,5],[4,4]] => 16 [[6,6,5],[5,5]] => 18 [[6,5,5],[5,4]] => 22 [[7,6,5],[6,5]] => 24 [[4,4,4,1],[3,3]] => 23 [[5,5,5,1],[4,4,1]] => 26 [[5,5,4,1],[4,4]] => 27 [[6,6,5,1],[5,5,1]] => 30 [[5,4,4,1],[4,3]] => 32 [[6,5,5,1],[5,4,1]] => 36 [[6,5,4,1],[5,4]] => 36 [[7,6,5,1],[6,5,1]] => 40 [[3,3,3,2],[2,2]] => 24 [[4,4,4,2],[3,3,1]] => 27 [[5,5,5,2],[4,4,2]] => 30 [[4,4,3,2],[3,3]] => 30 [[5,5,4,2],[4,4,1]] => 33 [[6,6,5,2],[5,5,2]] => 36 [[4,3,3,2],[3,2]] => 34 [[5,4,4,2],[4,3,1]] => 38 [[6,5,5,2],[5,4,2]] => 42 [[5,4,3,2],[4,3]] => 40 [[6,5,4,2],[5,4,1]] => 44 [[7,6,5,2],[6,5,2]] => 48 [[3,3,3,1,1],[2,2]] => 24 [[4,4,4,2,1],[3,3,1,1]] => 34 [[4,4,4,1,1],[3,3,1]] => 30 [[5,5,5,2,1],[4,4,2,1]] => 40 [[4,4,3,1,1],[3,3]] => 30 [[5,5,4,2,1],[4,4,1,1]] => 42 [[5,5,4,1,1],[4,4,1]] => 36 [[6,6,5,2,1],[5,5,2,1]] => 48 [[4,3,3,1,1],[3,2]] => 34 [[5,4,4,2,1],[4,3,1,1]] => 48 [[5,4,4,1,1],[4,3,1]] => 42 [[6,5,5,2,1],[5,4,2,1]] => 56 [[5,4,3,1,1],[4,3]] => 40 [[6,5,4,2,1],[5,4,1,1]] => 56 [[6,5,4,1,1],[5,4,1]] => 48 [[7,6,5,2,1],[6,5,2,1]] => 64 [[3,3,3,3],[2,2,1]] => 20 [[4,4,4,3],[3,3,2]] => 25 [[5,5,5,3],[4,4,3]] => 28 [[4,4,3,3],[3,3,1]] => 30 [[5,5,4,3],[4,4,2]] => 33 [[6,6,5,3],[5,5,3]] => 36 [[4,3,3,3],[3,2,1]] => 30 [[5,4,4,3],[4,3,2]] => 36 [[6,5,5,3],[5,4,3]] => 40 [[5,4,3,3],[4,3,1]] => 40 [[6,5,4,3],[5,4,2]] => 44 [[7,6,5,3],[6,5,3]] => 48 [[2,2,2,2,1],[1,1]] => 18 [[3,3,3,3,1],[2,2,1,1]] => 26 [[3,3,3,2,1],[2,2,1]] => 29 [[4,4,4,3,1],[3,3,2,1]] => 36 [[4,4,4,2,1],[3,3,2]] => 35 [[5,5,5,3,1],[4,4,3,1]] => 42 [[3,3,2,2,1],[2,2]] => 30 [[4,4,3,3,1],[3,3,1,1]] => 42 [[4,4,3,2,1],[3,3,1]] => 39 [[5,5,4,3,1],[4,4,2,1]] => 48 [[5,5,4,2,1],[4,4,2]] => 45 [[6,6,5,3,1],[5,5,3,1]] => 54 [[3,2,2,2,1],[2,1]] => 28 [[4,3,3,3,1],[3,2,1,1]] => 40 [[4,3,3,2,1],[3,2,1]] => 42 [[5,4,4,3,1],[4,3,2,1]] => 52 [[5,4,4,2,1],[4,3,2]] => 50 [[6,5,5,3,1],[5,4,3,1]] => 60 [[4,3,2,2,1],[3,2]] => 40 [[5,4,3,3,1],[4,3,1,1]] => 56 [[5,4,3,2,1],[4,3,1]] => 52 [[6,5,4,3,1],[5,4,2,1]] => 64 [[6,5,4,2,1],[5,4,2]] => 60 [[7,6,5,3,1],[6,5,3,1]] => 72 [[3,3,3,2,2],[2,2,1,1]] => 26 [[4,4,4,3,2],[3,3,2,2]] => 33 [[4,4,4,2,2],[3,3,2,1]] => 35 [[5,5,5,3,2],[4,4,3,2]] => 42 [[4,4,3,2,2],[3,3,1,1]] => 36 [[5,5,4,3,2],[4,4,2,2]] => 45 [[5,5,4,2,2],[4,4,2,1]] => 45 [[6,6,5,3,2],[5,5,3,2]] => 54 [[4,3,3,2,2],[3,2,1,1]] => 38 [[5,4,4,3,2],[4,3,2,2]] => 48 [[5,4,4,2,2],[4,3,2,1]] => 50 [[6,5,5,3,2],[5,4,3,2]] => 60 [[5,4,3,2,2],[4,3,1,1]] => 48 [[6,5,4,3,2],[5,4,2,2]] => 60 [[6,5,4,2,2],[5,4,2,1]] => 60 [[7,6,5,3,2],[6,5,3,2]] => 72 [[2,2,2,1,1,1],[1,1]] => 19 [[3,3,3,2,2,1],[2,2,1,1,1]] => 30 [[3,3,3,2,1,1],[2,2,1,1]] => 33 [[4,4,4,3,2,1],[3,3,2,2,1]] => 44 [[3,3,3,1,1,1],[2,2,1]] => 28 [[4,4,4,2,2,1],[3,3,2,1,1]] => 42 [[4,4,4,2,1,1],[3,3,2,1]] => 42 [[5,5,5,3,2,1],[4,4,3,2,1]] => 56 [[3,3,2,1,1,1],[2,2]] => 27 [[4,4,3,2,2,1],[3,3,1,1,1]] => 42 [[4,4,3,2,1,1],[3,3,1,1]] => 45 [[5,5,4,3,2,1],[4,4,2,2,1]] => 60 [[4,4,3,1,1,1],[3,3,1]] => 36 [[5,5,4,2,2,1],[4,4,2,1,1]] => 54 [[5,5,4,2,1,1],[4,4,2,1]] => 54 [[6,6,5,3,2,1],[5,5,3,2,1]] => 72 [[3,2,2,1,1,1],[2,1]] => 28 [[4,3,3,2,2,1],[3,2,1,1,1]] => 44 [[4,3,3,2,1,1],[3,2,1,1]] => 48 [[5,4,4,3,2,1],[4,3,2,2,1]] => 64 [[4,3,3,1,1,1],[3,2,1]] => 40 [[5,4,4,2,2,1],[4,3,2,1,1]] => 60 [[5,4,4,2,1,1],[4,3,2,1]] => 60 [[6,5,5,3,2,1],[5,4,3,2,1]] => 80 [[4,3,2,1,1,1],[3,2]] => 36 [[5,4,3,2,2,1],[4,3,1,1,1]] => 56 [[5,4,3,2,1,1],[4,3,1,1]] => 60 [[6,5,4,3,2,1],[5,4,2,2,1]] => 80 [[5,4,3,1,1,1],[4,3,1]] => 48 [[6,5,4,2,2,1],[5,4,2,1,1]] => 72 [[6,5,4,2,1,1],[5,4,2,1]] => 72 [[7,6,5,3,2,1],[6,5,3,2,1]] => 96 [[4,4,4,4],[3,3,3]] => 17 [[5,5,5,4],[4,4,4]] => 20 [[5,5,4,4],[4,4,3]] => 27 [[6,6,5,4],[5,5,4]] => 30 [[5,4,4,4],[4,3,3]] => 26 [[6,5,5,4],[5,4,4]] => 30 [[6,5,4,4],[5,4,3]] => 36 [[7,6,5,4],[6,5,4]] => 40 [[3,3,3,3,1],[2,2,2]] => 22 [[4,4,4,4,1],[3,3,3,1]] => 26 [[4,4,4,3,1],[3,3,3]] => 28 [[5,5,5,4,1],[4,4,4,1]] => 32 [[4,4,3,3,1],[3,3,2]] => 36 [[5,5,4,4,1],[4,4,3,1]] => 42 [[5,5,4,3,1],[4,4,3]] => 42 [[6,6,5,4,1],[5,5,4,1]] => 48 [[4,3,3,3,1],[3,2,2]] => 34 [[5,4,4,4,1],[4,3,3,1]] => 40 [[5,4,4,3,1],[4,3,3]] => 42 [[6,5,5,4,1],[5,4,4,1]] => 48 [[5,4,3,3,1],[4,3,2]] => 48 [[6,5,4,4,1],[5,4,3,1]] => 56 [[6,5,4,3,1],[5,4,3]] => 56 [[7,6,5,4,1],[6,5,4,1]] => 64 [[2,2,2,2,2],[1,1,1]] => 16 [[3,3,3,3,2],[2,2,2,1]] => 23 [[4,4,4,4,2],[3,3,3,2]] => 27 [[3,3,3,2,2],[2,2,2]] => 28 [[4,4,4,3,2],[3,3,3,1]] => 32 [[5,5,5,4,2],[4,4,4,2]] => 36 [[3,3,2,2,2],[2,2,1]] => 30 [[4,4,3,3,2],[3,3,2,1]] => 39 [[5,5,4,4,2],[4,4,3,2]] => 45 [[4,4,3,2,2],[3,3,2]] => 42 [[5,5,4,3,2],[4,4,3,1]] => 48 [[6,6,5,4,2],[5,5,4,2]] => 54 [[3,2,2,2,2],[2,1,1]] => 26 [[4,3,3,3,2],[3,2,2,1]] => 36 [[5,4,4,4,2],[4,3,3,2]] => 42 [[4,3,3,2,2],[3,2,2]] => 42 [[5,4,4,3,2],[4,3,3,1]] => 48 [[6,5,5,4,2],[5,4,4,2]] => 54 [[4,3,2,2,2],[3,2,1]] => 40 [[5,4,3,3,2],[4,3,2,1]] => 52 [[6,5,4,4,2],[5,4,3,2]] => 60 [[5,4,3,2,2],[4,3,2]] => 56 [[6,5,4,3,2],[5,4,3,1]] => 64 [[7,6,5,4,2],[6,5,4,2]] => 72 [[2,2,2,2,1,1],[1,1,1]] => 19 [[3,3,3,3,2,1],[2,2,2,1,1]] => 28 [[3,3,3,3,1,1],[2,2,2,1]] => 27 [[4,4,4,4,2,1],[3,3,3,2,1]] => 36 [[3,3,3,2,1,1],[2,2,2]] => 28 [[4,4,4,3,2,1],[3,3,3,1,1]] => 40 [[4,4,4,3,1,1],[3,3,3,1]] => 36 [[5,5,5,4,2,1],[4,4,4,2,1]] => 48 [[3,3,2,2,1,1],[2,2,1]] => 33 [[4,4,3,3,2,1],[3,3,2,1,1]] => 48 [[4,4,3,3,1,1],[3,3,2,1]] => 45 [[5,5,4,4,2,1],[4,4,3,2,1]] => 60 [[4,4,3,2,1,1],[3,3,2]] => 42 [[5,5,4,3,2,1],[4,4,3,1,1]] => 60 [[5,5,4,3,1,1],[4,4,3,1]] => 54 [[6,6,5,4,2,1],[5,5,4,2,1]] => 72 [[3,2,2,2,1,1],[2,1,1]] => 30 [[4,3,3,3,2,1],[3,2,2,1,1]] => 44 [[4,3,3,3,1,1],[3,2,2,1]] => 42 [[5,4,4,4,2,1],[4,3,3,2,1]] => 56 [[4,3,3,2,1,1],[3,2,2]] => 42 [[5,4,4,3,2,1],[4,3,3,1,1]] => 60 [[5,4,4,3,1,1],[4,3,3,1]] => 54 [[6,5,5,4,2,1],[5,4,4,2,1]] => 72 [[4,3,2,2,1,1],[3,2,1]] => 44 [[5,4,3,3,2,1],[4,3,2,1,1]] => 64 [[5,4,3,3,1,1],[4,3,2,1]] => 60 [[6,5,4,4,2,1],[5,4,3,2,1]] => 80 [[5,4,3,2,1,1],[4,3,2]] => 56 [[6,5,4,3,2,1],[5,4,3,1,1]] => 80 [[6,5,4,3,1,1],[5,4,3,1]] => 72 [[7,6,5,4,2,1],[6,5,4,2,1]] => 96 [[3,3,3,3,3],[2,2,2,2]] => 16 [[4,4,4,4,3],[3,3,3,3]] => 20 [[4,4,4,3,3],[3,3,3,2]] => 28 [[5,5,5,4,3],[4,4,4,3]] => 32 [[4,4,3,3,3],[3,3,2,2]] => 30 [[5,5,4,4,3],[4,4,3,3]] => 36 [[5,5,4,3,3],[4,4,3,2]] => 42 [[6,6,5,4,3],[5,5,4,3]] => 48 [[4,3,3,3,3],[3,2,2,2]] => 26 [[5,4,4,4,3],[4,3,3,3]] => 32 [[5,4,4,3,3],[4,3,3,2]] => 42 [[6,5,5,4,3],[5,4,4,3]] => 48 [[5,4,3,3,3],[4,3,2,2]] => 40 [[6,5,4,4,3],[5,4,3,3]] => 48 [[6,5,4,3,3],[5,4,3,2]] => 56 [[7,6,5,4,3],[6,5,4,3]] => 64 [[2,2,2,2,2,1],[1,1,1,1]] => 17 [[3,3,3,3,3,1],[2,2,2,2,1]] => 22 [[3,3,3,3,2,1],[2,2,2,2]] => 25 [[4,4,4,4,3,1],[3,3,3,3,1]] => 30 [[3,3,3,2,2,1],[2,2,2,1]] => 32 [[4,4,4,3,3,1],[3,3,3,2,1]] => 40 [[4,4,4,3,2,1],[3,3,3,2]] => 40 [[5,5,5,4,3,1],[4,4,4,3,1]] => 48 [[3,3,2,2,2,1],[2,2,1,1]] => 33 [[4,4,3,3,3,1],[3,3,2,2,1]] => 42 [[4,4,3,3,2,1],[3,3,2,2]] => 45 [[5,5,4,4,3,1],[4,4,3,3,1]] => 54 [[4,4,3,2,2,1],[3,3,2,1]] => 48 [[5,5,4,3,3,1],[4,4,3,2,1]] => 60 [[5,5,4,3,2,1],[4,4,3,2]] => 60 [[6,6,5,4,3,1],[5,5,4,3,1]] => 72 [[3,2,2,2,2,1],[2,1,1,1]] => 28 [[4,3,3,3,3,1],[3,2,2,2,1]] => 36 [[4,3,3,3,2,1],[3,2,2,2]] => 40 [[5,4,4,4,3,1],[4,3,3,3,1]] => 48 [[4,3,3,2,2,1],[3,2,2,1]] => 48 [[5,4,4,3,3,1],[4,3,3,2,1]] => 60 [[5,4,4,3,2,1],[4,3,3,2]] => 60 [[6,5,5,4,3,1],[5,4,4,3,1]] => 72 [[4,3,2,2,2,1],[3,2,1,1]] => 44 [[5,4,3,3,3,1],[4,3,2,2,1]] => 56 [[5,4,3,3,2,1],[4,3,2,2]] => 60 [[6,5,4,4,3,1],[5,4,3,3,1]] => 72 [[5,4,3,2,2,1],[4,3,2,1]] => 64 [[6,5,4,3,3,1],[5,4,3,2,1]] => 80 [[6,5,4,3,2,1],[5,4,3,2]] => 80 [[7,6,5,4,3,1],[6,5,4,3,1]] => 96 [[2,2,2,2,2,2],[1,1,1,1,1]] => 13 [[3,3,3,3,3,2],[2,2,2,2,2]] => 18 [[3,3,3,3,2,2],[2,2,2,2,1]] => 25 [[4,4,4,4,3,2],[3,3,3,3,2]] => 30 [[3,3,3,2,2,2],[2,2,2,1,1]] => 28 [[4,4,4,3,3,2],[3,3,3,2,2]] => 36 [[4,4,4,3,2,2],[3,3,3,2,1]] => 40 [[5,5,5,4,3,2],[4,4,4,3,2]] => 48 [[3,3,2,2,2,2],[2,2,1,1,1]] => 27 [[4,4,3,3,3,2],[3,3,2,2,2]] => 36 [[4,4,3,3,2,2],[3,3,2,2,1]] => 45 [[5,5,4,4,3,2],[4,4,3,3,2]] => 54 [[4,4,3,2,2,2],[3,3,2,1,1]] => 42 [[5,5,4,3,3,2],[4,4,3,2,2]] => 54 [[5,5,4,3,2,2],[4,4,3,2,1]] => 60 [[6,6,5,4,3,2],[5,5,4,3,2]] => 72 [[3,2,2,2,2,2],[2,1,1,1,1]] => 22 [[4,3,3,3,3,2],[3,2,2,2,2]] => 30 [[4,3,3,3,2,2],[3,2,2,2,1]] => 40 [[5,4,4,4,3,2],[4,3,3,3,2]] => 48 [[4,3,3,2,2,2],[3,2,2,1,1]] => 42 [[5,4,4,3,3,2],[4,3,3,2,2]] => 54 [[5,4,4,3,2,2],[4,3,3,2,1]] => 60 [[6,5,5,4,3,2],[5,4,4,3,2]] => 72 [[4,3,2,2,2,2],[3,2,1,1,1]] => 36 [[5,4,3,3,3,2],[4,3,2,2,2]] => 48 [[5,4,3,3,2,2],[4,3,2,2,1]] => 60 [[6,5,4,4,3,2],[5,4,3,3,2]] => 72 [[5,4,3,2,2,2],[4,3,2,1,1]] => 56 [[6,5,4,3,3,2],[5,4,3,2,2]] => 72 [[6,5,4,3,2,2],[5,4,3,2,1]] => 80 [[7,6,5,4,3,2],[6,5,4,3,2]] => 96 [[1,1,1,1,1,1,1],[]] => 8 [[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => 14 [[2,2,2,2,2,1,1],[1,1,1,1,1]] => 18 [[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => 24 [[2,2,2,2,1,1,1],[1,1,1,1]] => 20 [[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => 30 [[3,3,3,3,2,1,1],[2,2,2,2,1]] => 30 [[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => 40 [[2,2,2,1,1,1,1],[1,1,1]] => 20 [[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => 32 [[3,3,3,2,2,1,1],[2,2,2,1,1]] => 36 [[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => 48 [[3,3,3,2,1,1,1],[2,2,2,1]] => 32 [[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => 48 ----------------------------------------------------------------------------- Created: Dec 22, 2020 at 14:13 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Dec 22, 2020 at 14:13 by Martin Rubey