***************************************************************************** * 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: St001785 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. Given a partition $\lambda\vdash n$, let $\alpha(\lambda)$ be the partition given by the lengths of the antidiagonals of the Ferrers diagram of $\lambda$. Then, the value of the statistic on $\mu$ is the number of times $\mu$ appears in the multiset $\{\{\alpha(\lambda)\mid \lambda\vdash n\}\}$. ----------------------------------------------------------------------------- References: [1] Amdeberhan, T. Agreement between two sets of data on partitions [[MathOverflow:420033]] ----------------------------------------------------------------------------- Code: def alpha(la): la = Partition(la) if not la: return la result = [0]*(2*max(len(la), la[0])-1) for i, j in la.cells(): result[i+j] += 1 return Partition(sorted(result, reverse=True)) @cached_function def frequencies(l): return {d: l.count(d) for d in set(l)} def statistic(la): F = frequencies(tuple(alpha(mu) for mu in Partitions(la.size()))) return F.get(la, 0) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 0 [1,1] => 2 [3] => 0 [2,1] => 1 [1,1,1] => 2 [4] => 0 [3,1] => 0 [2,2] => 0 [2,1,1] => 3 [1,1,1,1] => 2 [5] => 0 [4,1] => 0 [3,2] => 0 [3,1,1] => 0 [2,2,1] => 3 [2,1,1,1] => 2 [1,1,1,1,1] => 2 [6] => 0 [5,1] => 0 [4,2] => 0 [4,1,1] => 0 [3,3] => 0 [3,2,1] => 1 [3,1,1,1] => 0 [2,2,2] => 0 [2,2,1,1] => 6 [2,1,1,1,1] => 2 [1,1,1,1,1,1] => 2 [7] => 0 [6,1] => 0 [5,2] => 0 [5,1,1] => 0 [4,3] => 0 [4,2,1] => 0 [4,1,1,1] => 0 [3,3,1] => 0 [3,2,2] => 0 [3,2,1,1] => 4 [3,1,1,1,1] => 0 [2,2,2,1] => 3 [2,2,1,1,1] => 4 [2,1,1,1,1,1] => 2 [1,1,1,1,1,1,1] => 2 [8] => 0 [7,1] => 0 [6,2] => 0 [6,1,1] => 0 [5,3] => 0 [5,2,1] => 0 [5,1,1,1] => 0 [4,4] => 0 [4,3,1] => 0 [4,2,2] => 0 [4,2,1,1] => 0 [4,1,1,1,1] => 0 [3,3,2] => 0 [3,3,1,1] => 0 [3,2,2,1] => 6 [3,2,1,1,1] => 2 [3,1,1,1,1,1] => 0 [2,2,2,2] => 0 [2,2,2,1,1] => 6 [2,2,1,1,1,1] => 4 [2,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1] => 2 [9] => 0 [8,1] => 0 [7,2] => 0 [7,1,1] => 0 [6,3] => 0 [6,2,1] => 0 [6,1,1,1] => 0 [5,4] => 0 [5,3,1] => 0 [5,2,2] => 0 [5,2,1,1] => 0 [5,1,1,1,1] => 0 [4,4,1] => 0 [4,3,2] => 0 [4,3,1,1] => 0 [4,2,2,1] => 0 [4,2,1,1,1] => 0 [4,1,1,1,1,1] => 0 [3,3,3] => 0 [3,3,2,1] => 4 [3,3,1,1,1] => 0 [3,2,2,2] => 0 [3,2,2,1,1] => 9 [3,2,1,1,1,1] => 2 [3,1,1,1,1,1,1] => 0 [2,2,2,2,1] => 3 [2,2,2,1,1,1] => 4 [2,2,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1] => 2 [10] => 0 [9,1] => 0 [8,2] => 0 [8,1,1] => 0 [7,3] => 0 [7,2,1] => 0 [7,1,1,1] => 0 [6,4] => 0 [6,3,1] => 0 [6,2,2] => 0 [6,2,1,1] => 0 [6,1,1,1,1] => 0 [5,5] => 0 [5,4,1] => 0 [5,3,2] => 0 [5,3,1,1] => 0 [5,2,2,1] => 0 [5,2,1,1,1] => 0 [5,1,1,1,1,1] => 0 [4,4,2] => 0 [4,4,1,1] => 0 [4,3,3] => 0 [4,3,2,1] => 1 [4,3,1,1,1] => 0 [4,2,2,2] => 0 [4,2,2,1,1] => 0 [4,2,1,1,1,1] => 0 [4,1,1,1,1,1,1] => 0 [3,3,3,1] => 0 [3,3,2,2] => 0 [3,3,2,1,1] => 12 [3,3,1,1,1,1] => 0 [3,2,2,2,1] => 3 [3,2,2,1,1,1] => 6 [3,2,1,1,1,1,1] => 2 [3,1,1,1,1,1,1,1] => 0 [2,2,2,2,2] => 0 [2,2,2,2,1,1] => 6 [2,2,2,1,1,1,1] => 4 [2,2,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1] => 2 [11] => 0 [10,1] => 0 [9,2] => 0 [9,1,1] => 0 [8,3] => 0 [8,2,1] => 0 [8,1,1,1] => 0 [7,4] => 0 [7,3,1] => 0 [7,2,2] => 0 [7,2,1,1] => 0 [7,1,1,1,1] => 0 [6,5] => 0 [6,4,1] => 0 [6,3,2] => 0 [6,3,1,1] => 0 [6,2,2,1] => 0 [6,2,1,1,1] => 0 [6,1,1,1,1,1] => 0 [5,5,1] => 0 [5,4,2] => 0 [5,4,1,1] => 0 [5,3,3] => 0 [5,3,2,1] => 0 [5,3,1,1,1] => 0 [5,2,2,2] => 0 [5,2,2,1,1] => 0 [5,2,1,1,1,1] => 0 [5,1,1,1,1,1,1] => 0 [4,4,3] => 0 [4,4,2,1] => 0 [4,4,1,1,1] => 0 [4,3,3,1] => 0 [4,3,2,2] => 0 [4,3,2,1,1] => 5 [4,3,1,1,1,1] => 0 [4,2,2,2,1] => 0 [4,2,2,1,1,1] => 0 [4,2,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1] => 0 [3,3,3,2] => 0 [3,3,3,1,1] => 0 [3,3,2,2,1] => 12 [3,3,2,1,1,1] => 6 [3,3,1,1,1,1,1] => 0 [3,2,2,2,2] => 0 [3,2,2,2,1,1] => 6 [3,2,2,1,1,1,1] => 6 [3,2,1,1,1,1,1,1] => 2 [3,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,1] => 3 [2,2,2,2,1,1,1] => 4 [2,2,2,1,1,1,1,1] => 4 [2,2,1,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1] => 2 [12] => 0 [11,1] => 0 [10,2] => 0 [10,1,1] => 0 [9,3] => 0 [9,2,1] => 0 [9,1,1,1] => 0 [8,4] => 0 [8,3,1] => 0 [8,2,2] => 0 [8,2,1,1] => 0 [8,1,1,1,1] => 0 [7,5] => 0 [7,4,1] => 0 [7,3,2] => 0 [7,3,1,1] => 0 [7,2,2,1] => 0 [7,2,1,1,1] => 0 [7,1,1,1,1,1] => 0 [6,6] => 0 [6,5,1] => 0 [6,4,2] => 0 [6,4,1,1] => 0 [6,3,3] => 0 [6,3,2,1] => 0 [6,3,1,1,1] => 0 [6,2,2,2] => 0 [6,2,2,1,1] => 0 [6,2,1,1,1,1] => 0 [6,1,1,1,1,1,1] => 0 [5,5,2] => 0 [5,5,1,1] => 0 [5,4,3] => 0 [5,4,2,1] => 0 [5,4,1,1,1] => 0 [5,3,3,1] => 0 [5,3,2,2] => 0 [5,3,2,1,1] => 0 [5,3,1,1,1,1] => 0 [5,2,2,2,1] => 0 [5,2,2,1,1,1] => 0 [5,2,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1] => 0 [4,4,4] => 0 [4,4,3,1] => 0 [4,4,2,2] => 0 [4,4,2,1,1] => 0 [4,4,1,1,1,1] => 0 [4,3,3,2] => 0 [4,3,3,1,1] => 0 [4,3,2,2,1] => 10 [4,3,2,1,1,1] => 2 [4,3,1,1,1,1,1] => 0 [4,2,2,2,2] => 0 [4,2,2,2,1,1] => 0 [4,2,2,1,1,1,1] => 0 [4,2,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1] => 0 [3,3,3,3] => 0 [3,3,3,2,1] => 4 [3,3,3,1,1,1] => 0 [3,3,2,2,2] => 0 [3,3,2,2,1,1] => 18 [3,3,2,1,1,1,1] => 6 [3,3,1,1,1,1,1,1] => 0 [3,2,2,2,2,1] => 3 [3,2,2,2,1,1,1] => 4 [3,2,2,1,1,1,1,1] => 6 [3,2,1,1,1,1,1,1,1] => 2 [3,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2] => 0 [2,2,2,2,2,1,1] => 6 [2,2,2,2,1,1,1,1] => 4 [2,2,2,1,1,1,1,1,1] => 4 [2,2,1,1,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1,1] => 2 [13] => 0 [12,1] => 0 [11,2] => 0 [11,1,1] => 0 [10,3] => 0 [10,2,1] => 0 [10,1,1,1] => 0 [9,4] => 0 [9,3,1] => 0 [9,2,2] => 0 [9,2,1,1] => 0 [9,1,1,1,1] => 0 [8,5] => 0 [8,4,1] => 0 [8,3,2] => 0 [8,3,1,1] => 0 [8,2,2,1] => 0 [8,2,1,1,1] => 0 [8,1,1,1,1,1] => 0 [7,6] => 0 [7,5,1] => 0 [7,4,2] => 0 [7,4,1,1] => 0 [7,3,3] => 0 [7,3,2,1] => 0 [7,3,1,1,1] => 0 [7,2,2,2] => 0 [7,2,2,1,1] => 0 [7,2,1,1,1,1] => 0 [7,1,1,1,1,1,1] => 0 [6,6,1] => 0 [6,5,2] => 0 [6,5,1,1] => 0 [6,4,3] => 0 [6,4,2,1] => 0 [6,4,1,1,1] => 0 [6,3,3,1] => 0 [6,3,2,2] => 0 [6,3,2,1,1] => 0 [6,3,1,1,1,1] => 0 [6,2,2,2,1] => 0 [6,2,2,1,1,1] => 0 [6,2,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1] => 0 [5,5,3] => 0 [5,5,2,1] => 0 [5,5,1,1,1] => 0 [5,4,4] => 0 [5,4,3,1] => 0 [5,4,2,2] => 0 [5,4,2,1,1] => 0 [5,4,1,1,1,1] => 0 [5,3,3,2] => 0 [5,3,3,1,1] => 0 [5,3,2,2,1] => 0 [5,3,2,1,1,1] => 0 [5,3,1,1,1,1,1] => 0 [5,2,2,2,2] => 0 [5,2,2,2,1,1] => 0 [5,2,2,1,1,1,1] => 0 [5,2,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1] => 0 [4,4,4,1] => 0 [4,4,3,2] => 0 [4,4,3,1,1] => 0 [4,4,2,2,1] => 0 [4,4,2,1,1,1] => 0 [4,4,1,1,1,1,1] => 0 [4,3,3,3] => 0 [4,3,3,2,1] => 10 [4,3,3,1,1,1] => 0 [4,3,2,2,2] => 0 [4,3,2,2,1,1] => 12 [4,3,2,1,1,1,1] => 2 [4,3,1,1,1,1,1,1] => 0 [4,2,2,2,2,1] => 0 [4,2,2,2,1,1,1] => 0 [4,2,2,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,1] => 0 [3,3,3,2,2] => 0 [3,3,3,2,1,1] => 12 [3,3,3,1,1,1,1] => 0 [3,3,2,2,2,1] => 6 [3,3,2,2,1,1,1] => 12 [3,3,2,1,1,1,1,1] => 6 [3,3,1,1,1,1,1,1,1] => 0 [3,2,2,2,2,2] => 0 [3,2,2,2,2,1,1] => 6 [3,2,2,2,1,1,1,1] => 4 [3,2,2,1,1,1,1,1,1] => 6 [3,2,1,1,1,1,1,1,1,1] => 2 [3,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2,1] => 3 [2,2,2,2,2,1,1,1] => 4 [2,2,2,2,1,1,1,1,1] => 4 [2,2,2,1,1,1,1,1,1,1] => 4 [2,2,1,1,1,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [14] => 0 [13,1] => 0 [12,2] => 0 [12,1,1] => 0 [11,3] => 0 [11,2,1] => 0 [11,1,1,1] => 0 [10,4] => 0 [10,3,1] => 0 [10,2,2] => 0 [10,2,1,1] => 0 [10,1,1,1,1] => 0 [9,5] => 0 [9,4,1] => 0 [9,3,2] => 0 [9,3,1,1] => 0 [9,2,2,1] => 0 [9,2,1,1,1] => 0 [9,1,1,1,1,1] => 0 [8,6] => 0 [8,5,1] => 0 [8,4,2] => 0 [8,4,1,1] => 0 [8,3,3] => 0 [8,3,2,1] => 0 [8,3,1,1,1] => 0 [8,2,2,2] => 0 [8,2,2,1,1] => 0 [8,2,1,1,1,1] => 0 [8,1,1,1,1,1,1] => 0 [7,7] => 0 [7,6,1] => 0 [7,5,2] => 0 [7,5,1,1] => 0 [7,4,3] => 0 [7,4,2,1] => 0 [7,4,1,1,1] => 0 [7,3,3,1] => 0 [7,3,2,2] => 0 [7,3,2,1,1] => 0 [7,3,1,1,1,1] => 0 [7,2,2,2,1] => 0 [7,2,2,1,1,1] => 0 [7,2,1,1,1,1,1] => 0 [7,1,1,1,1,1,1,1] => 0 [6,6,2] => 0 [6,6,1,1] => 0 [6,5,3] => 0 [6,5,2,1] => 0 [6,5,1,1,1] => 0 [6,4,4] => 0 [6,4,3,1] => 0 [6,4,2,2] => 0 [6,4,2,1,1] => 0 [6,4,1,1,1,1] => 0 [6,3,3,2] => 0 [6,3,3,1,1] => 0 [6,3,2,2,1] => 0 [6,3,2,1,1,1] => 0 [6,3,1,1,1,1,1] => 0 [6,2,2,2,2] => 0 [6,2,2,2,1,1] => 0 [6,2,2,1,1,1,1] => 0 [6,2,1,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1,1] => 0 [5,5,4] => 0 [5,5,3,1] => 0 [5,5,2,2] => 0 [5,5,2,1,1] => 0 [5,5,1,1,1,1] => 0 [5,4,4,1] => 0 [5,4,3,2] => 0 [5,4,3,1,1] => 0 [5,4,2,2,1] => 0 [5,4,2,1,1,1] => 0 [5,4,1,1,1,1,1] => 0 [5,3,3,3] => 0 [5,3,3,2,1] => 0 [5,3,3,1,1,1] => 0 [5,3,2,2,2] => 0 [5,3,2,2,1,1] => 0 [5,3,2,1,1,1,1] => 0 [5,3,1,1,1,1,1,1] => 0 [5,2,2,2,2,1] => 0 [5,2,2,2,1,1,1] => 0 [5,2,2,1,1,1,1,1] => 0 [5,2,1,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1,1] => 0 [4,4,4,2] => 0 [4,4,4,1,1] => 0 [4,4,3,3] => 0 [4,4,3,2,1] => 5 [4,4,3,1,1,1] => 0 [4,4,2,2,2] => 0 [4,4,2,2,1,1] => 0 [4,4,2,1,1,1,1] => 0 [4,4,1,1,1,1,1,1] => 0 [4,3,3,3,1] => 0 [4,3,3,2,2] => 0 [4,3,3,2,1,1] => 24 [4,3,3,1,1,1,1] => 0 [4,3,2,2,2,1] => 3 [4,3,2,2,1,1,1] => 8 [4,3,2,1,1,1,1,1] => 2 [4,3,1,1,1,1,1,1,1] => 0 [4,2,2,2,2,2] => 0 [4,2,2,2,2,1,1] => 0 [4,2,2,2,1,1,1,1] => 0 [4,2,2,1,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,2] => 0 [3,3,3,3,1,1] => 0 [3,3,3,2,2,1] => 12 [3,3,3,2,1,1,1] => 6 [3,3,3,1,1,1,1,1] => 0 [3,3,2,2,2,2] => 0 [3,3,2,2,2,1,1] => 12 [3,3,2,2,1,1,1,1] => 12 [3,3,2,1,1,1,1,1,1] => 6 [3,3,1,1,1,1,1,1,1,1] => 0 [3,2,2,2,2,2,1] => 3 [3,2,2,2,2,1,1,1] => 4 [3,2,2,2,1,1,1,1,1] => 4 [3,2,2,1,1,1,1,1,1,1] => 6 [3,2,1,1,1,1,1,1,1,1,1] => 2 [3,1,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2,2] => 0 [2,2,2,2,2,2,1,1] => 6 [2,2,2,2,2,1,1,1,1] => 4 [2,2,2,2,1,1,1,1,1,1] => 4 [2,2,2,1,1,1,1,1,1,1,1] => 4 [2,2,1,1,1,1,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [15] => 0 [14,1] => 0 [13,2] => 0 [13,1,1] => 0 [12,3] => 0 [12,2,1] => 0 [12,1,1,1] => 0 [11,4] => 0 [11,3,1] => 0 [11,2,2] => 0 [11,2,1,1] => 0 [11,1,1,1,1] => 0 [10,5] => 0 [10,4,1] => 0 [10,3,2] => 0 [10,3,1,1] => 0 [10,2,2,1] => 0 [10,2,1,1,1] => 0 [10,1,1,1,1,1] => 0 [9,6] => 0 [9,5,1] => 0 [9,4,2] => 0 [9,4,1,1] => 0 [9,3,3] => 0 [9,3,2,1] => 0 [9,3,1,1,1] => 0 [9,2,2,2] => 0 [9,2,2,1,1] => 0 [9,2,1,1,1,1] => 0 [9,1,1,1,1,1,1] => 0 [8,7] => 0 [8,6,1] => 0 [8,5,2] => 0 [8,5,1,1] => 0 [8,4,3] => 0 [8,4,2,1] => 0 [8,4,1,1,1] => 0 [8,3,3,1] => 0 [8,3,2,2] => 0 [8,3,2,1,1] => 0 [8,3,1,1,1,1] => 0 [8,2,2,2,1] => 0 [8,2,2,1,1,1] => 0 [8,2,1,1,1,1,1] => 0 [8,1,1,1,1,1,1,1] => 0 [7,7,1] => 0 [7,6,2] => 0 [7,6,1,1] => 0 [7,5,3] => 0 [7,5,2,1] => 0 [7,5,1,1,1] => 0 [7,4,4] => 0 [7,4,3,1] => 0 [7,4,2,2] => 0 [7,4,2,1,1] => 0 [7,4,1,1,1,1] => 0 [7,3,3,2] => 0 [7,3,3,1,1] => 0 [7,3,2,2,1] => 0 [7,3,2,1,1,1] => 0 [7,3,1,1,1,1,1] => 0 [7,2,2,2,2] => 0 [7,2,2,2,1,1] => 0 [7,2,2,1,1,1,1] => 0 [7,2,1,1,1,1,1,1] => 0 [7,1,1,1,1,1,1,1,1] => 0 [6,6,3] => 0 [6,6,2,1] => 0 [6,6,1,1,1] => 0 [6,5,4] => 0 [6,5,3,1] => 0 [6,5,2,2] => 0 [6,5,2,1,1] => 0 [6,5,1,1,1,1] => 0 [6,4,4,1] => 0 [6,4,3,2] => 0 [6,4,3,1,1] => 0 [6,4,2,2,1] => 0 [6,4,2,1,1,1] => 0 [6,4,1,1,1,1,1] => 0 [6,3,3,3] => 0 [6,3,3,2,1] => 0 [6,3,3,1,1,1] => 0 [6,3,2,2,2] => 0 [6,3,2,2,1,1] => 0 [6,3,2,1,1,1,1] => 0 [6,3,1,1,1,1,1,1] => 0 [6,2,2,2,2,1] => 0 [6,2,2,2,1,1,1] => 0 [6,2,2,1,1,1,1,1] => 0 [6,2,1,1,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1,1,1] => 0 [5,5,5] => 0 [5,5,4,1] => 0 [5,5,3,2] => 0 [5,5,3,1,1] => 0 [5,5,2,2,1] => 0 [5,5,2,1,1,1] => 0 [5,5,1,1,1,1,1] => 0 [5,4,4,2] => 0 [5,4,4,1,1] => 0 [5,4,3,3] => 0 [5,4,3,2,1] => 1 [5,4,3,1,1,1] => 0 [5,4,2,2,2] => 0 [5,4,2,2,1,1] => 0 [5,4,2,1,1,1,1] => 0 [5,4,1,1,1,1,1,1] => 0 [5,3,3,3,1] => 0 [5,3,3,2,2] => 0 [5,3,3,2,1,1] => 0 [5,3,3,1,1,1,1] => 0 [5,3,2,2,2,1] => 0 [5,3,2,2,1,1,1] => 0 [5,3,2,1,1,1,1,1] => 0 [5,3,1,1,1,1,1,1,1] => 0 [5,2,2,2,2,2] => 0 [5,2,2,2,2,1,1] => 0 [5,2,2,2,1,1,1,1] => 0 [5,2,2,1,1,1,1,1,1] => 0 [5,2,1,1,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1,1,1] => 0 [4,4,4,3] => 0 [4,4,4,2,1] => 0 [4,4,4,1,1,1] => 0 [4,4,3,3,1] => 0 [4,4,3,2,2] => 0 [4,4,3,2,1,1] => 20 [4,4,3,1,1,1,1] => 0 [4,4,2,2,2,1] => 0 [4,4,2,2,1,1,1] => 0 [4,4,2,1,1,1,1,1] => 0 [4,4,1,1,1,1,1,1,1] => 0 [4,3,3,3,2] => 0 [4,3,3,3,1,1] => 0 [4,3,3,2,2,1] => 18 [4,3,3,2,1,1,1] => 12 [4,3,3,1,1,1,1,1] => 0 [4,3,2,2,2,2] => 0 [4,3,2,2,2,1,1] => 6 [4,3,2,2,1,1,1,1] => 8 [4,3,2,1,1,1,1,1,1] => 2 [4,3,1,1,1,1,1,1,1,1] => 0 [4,2,2,2,2,2,1] => 0 [4,2,2,2,2,1,1,1] => 0 [4,2,2,2,1,1,1,1,1] => 0 [4,2,2,1,1,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,3] => 0 [3,3,3,3,2,1] => 4 [3,3,3,3,1,1,1] => 0 [3,3,3,2,2,2] => 0 [3,3,3,2,2,1,1] => 18 [3,3,3,2,1,1,1,1] => 6 [3,3,3,1,1,1,1,1,1] => 0 [3,3,2,2,2,2,1] => 6 [3,3,2,2,2,1,1,1] => 8 [3,3,2,2,1,1,1,1,1] => 12 [3,3,2,1,1,1,1,1,1,1] => 6 [3,3,1,1,1,1,1,1,1,1,1] => 0 [3,2,2,2,2,2,2] => 0 [3,2,2,2,2,2,1,1] => 6 [3,2,2,2,2,1,1,1,1] => 4 [3,2,2,2,1,1,1,1,1,1] => 4 [3,2,2,1,1,1,1,1,1,1,1] => 6 [3,2,1,1,1,1,1,1,1,1,1,1] => 2 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2,2,1] => 3 [2,2,2,2,2,2,1,1,1] => 4 [2,2,2,2,2,1,1,1,1,1] => 4 [2,2,2,2,1,1,1,1,1,1,1] => 4 [2,2,2,1,1,1,1,1,1,1,1,1] => 4 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [16] => 0 [15,1] => 0 [14,2] => 0 [14,1,1] => 0 [13,3] => 0 [13,2,1] => 0 [13,1,1,1] => 0 [12,4] => 0 [12,3,1] => 0 [12,2,2] => 0 [12,2,1,1] => 0 [12,1,1,1,1] => 0 [11,5] => 0 [11,4,1] => 0 [11,3,2] => 0 [11,3,1,1] => 0 [11,2,2,1] => 0 [11,2,1,1,1] => 0 [11,1,1,1,1,1] => 0 [10,6] => 0 [10,5,1] => 0 [10,4,2] => 0 [10,4,1,1] => 0 [10,3,3] => 0 [10,3,2,1] => 0 [10,3,1,1,1] => 0 [10,2,2,2] => 0 [10,2,2,1,1] => 0 [10,2,1,1,1,1] => 0 [10,1,1,1,1,1,1] => 0 [9,7] => 0 [9,6,1] => 0 [9,5,2] => 0 [9,5,1,1] => 0 [9,4,3] => 0 [9,4,2,1] => 0 [9,4,1,1,1] => 0 [9,3,3,1] => 0 [9,3,2,2] => 0 [9,3,2,1,1] => 0 [9,3,1,1,1,1] => 0 [9,2,2,2,1] => 0 [9,2,2,1,1,1] => 0 [9,2,1,1,1,1,1] => 0 [9,1,1,1,1,1,1,1] => 0 [8,8] => 0 [8,7,1] => 0 [8,6,2] => 0 [8,6,1,1] => 0 [8,5,3] => 0 [8,5,2,1] => 0 [8,5,1,1,1] => 0 [8,4,4] => 0 [8,4,3,1] => 0 [8,4,2,2] => 0 [8,4,2,1,1] => 0 [8,4,1,1,1,1] => 0 [8,3,3,2] => 0 [8,3,3,1,1] => 0 [8,3,2,2,1] => 0 [8,3,2,1,1,1] => 0 [8,3,1,1,1,1,1] => 0 [8,2,2,2,2] => 0 [8,2,2,2,1,1] => 0 [8,2,2,1,1,1,1] => 0 [8,2,1,1,1,1,1,1] => 0 [8,1,1,1,1,1,1,1,1] => 0 [7,7,2] => 0 [7,7,1,1] => 0 [7,6,3] => 0 [7,6,2,1] => 0 [7,6,1,1,1] => 0 [7,5,4] => 0 [7,5,3,1] => 0 [7,5,2,2] => 0 [7,5,2,1,1] => 0 [7,5,1,1,1,1] => 0 [7,4,4,1] => 0 [7,4,3,2] => 0 [7,4,3,1,1] => 0 [7,4,2,2,1] => 0 [7,4,2,1,1,1] => 0 [7,4,1,1,1,1,1] => 0 [7,3,3,3] => 0 [7,3,3,2,1] => 0 [7,3,3,1,1,1] => 0 [7,3,2,2,2] => 0 [7,3,2,2,1,1] => 0 [7,3,2,1,1,1,1] => 0 [7,3,1,1,1,1,1,1] => 0 [7,2,2,2,2,1] => 0 [7,2,2,2,1,1,1] => 0 [7,2,2,1,1,1,1,1] => 0 [7,2,1,1,1,1,1,1,1] => 0 [7,1,1,1,1,1,1,1,1,1] => 0 [6,6,4] => 0 [6,6,3,1] => 0 [6,6,2,2] => 0 [6,6,2,1,1] => 0 [6,6,1,1,1,1] => 0 [6,5,5] => 0 [6,5,4,1] => 0 [6,5,3,2] => 0 [6,5,3,1,1] => 0 [6,5,2,2,1] => 0 [6,5,2,1,1,1] => 0 [6,5,1,1,1,1,1] => 0 [6,4,4,2] => 0 [6,4,4,1,1] => 0 [6,4,3,3] => 0 [6,4,3,2,1] => 0 [6,4,3,1,1,1] => 0 [6,4,2,2,2] => 0 [6,4,2,2,1,1] => 0 [6,4,2,1,1,1,1] => 0 [6,4,1,1,1,1,1,1] => 0 [6,3,3,3,1] => 0 [6,3,3,2,2] => 0 [6,3,3,2,1,1] => 0 [6,3,3,1,1,1,1] => 0 [6,3,2,2,2,1] => 0 [6,3,2,2,1,1,1] => 0 [6,3,2,1,1,1,1,1] => 0 [6,3,1,1,1,1,1,1,1] => 0 [6,2,2,2,2,2] => 0 [6,2,2,2,2,1,1] => 0 [6,2,2,2,1,1,1,1] => 0 [6,2,2,1,1,1,1,1,1] => 0 [6,2,1,1,1,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1,1,1,1] => 0 [5,5,5,1] => 0 [5,5,4,2] => 0 [5,5,4,1,1] => 0 [5,5,3,3] => 0 [5,5,3,2,1] => 0 [5,5,3,1,1,1] => 0 [5,5,2,2,2] => 0 [5,5,2,2,1,1] => 0 [5,5,2,1,1,1,1] => 0 [5,5,1,1,1,1,1,1] => 0 [5,4,4,3] => 0 [5,4,4,2,1] => 0 [5,4,4,1,1,1] => 0 [5,4,3,3,1] => 0 [5,4,3,2,2] => 0 [5,4,3,2,1,1] => 6 [5,4,3,1,1,1,1] => 0 [5,4,2,2,2,1] => 0 [5,4,2,2,1,1,1] => 0 [5,4,2,1,1,1,1,1] => 0 [5,4,1,1,1,1,1,1,1] => 0 [5,3,3,3,2] => 0 [5,3,3,3,1,1] => 0 [5,3,3,2,2,1] => 0 [5,3,3,2,1,1,1] => 0 [5,3,3,1,1,1,1,1] => 0 [5,3,2,2,2,2] => 0 [5,3,2,2,2,1,1] => 0 [5,3,2,2,1,1,1,1] => 0 [5,3,2,1,1,1,1,1,1] => 0 [5,3,1,1,1,1,1,1,1,1] => 0 [5,2,2,2,2,2,1] => 0 [5,2,2,2,2,1,1,1] => 0 [5,2,2,2,1,1,1,1,1] => 0 [5,2,2,1,1,1,1,1,1,1] => 0 [5,2,1,1,1,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1,1,1,1] => 0 [4,4,4,4] => 0 [4,4,4,3,1] => 0 [4,4,4,2,2] => 0 [4,4,4,2,1,1] => 0 [4,4,4,1,1,1,1] => 0 [4,4,3,3,2] => 0 [4,4,3,3,1,1] => 0 [4,4,3,2,2,1] => 30 [4,4,3,2,1,1,1] => 8 [4,4,3,1,1,1,1,1] => 0 [4,4,2,2,2,2] => 0 [4,4,2,2,2,1,1] => 0 [4,4,2,2,1,1,1,1] => 0 [4,4,2,1,1,1,1,1,1] => 0 [4,4,1,1,1,1,1,1,1,1] => 0 [4,3,3,3,3] => 0 [4,3,3,3,2,1] => 4 [4,3,3,3,1,1,1] => 0 [4,3,3,2,2,2] => 0 [4,3,3,2,2,1,1] => 27 [4,3,3,2,1,1,1,1] => 12 [4,3,3,1,1,1,1,1,1] => 0 [4,3,2,2,2,2,1] => 3 [4,3,2,2,2,1,1,1] => 4 [4,3,2,2,1,1,1,1,1] => 8 [4,3,2,1,1,1,1,1,1,1] => 2 [4,3,1,1,1,1,1,1,1,1,1] => 0 [4,2,2,2,2,2,2] => 0 [4,2,2,2,2,2,1,1] => 0 [4,2,2,2,2,1,1,1,1] => 0 [4,2,2,2,1,1,1,1,1,1] => 0 [4,2,2,1,1,1,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,3,1] => 0 [3,3,3,3,2,2] => 0 [3,3,3,3,2,1,1] => 12 [3,3,3,3,1,1,1,1] => 0 [3,3,3,2,2,2,1] => 6 [3,3,3,2,2,1,1,1] => 12 [3,3,3,2,1,1,1,1,1] => 6 [3,3,3,1,1,1,1,1,1,1] => 0 [3,3,2,2,2,2,2] => 0 [3,3,2,2,2,2,1,1] => 12 [3,3,2,2,2,1,1,1,1] => 8 [3,3,2,2,1,1,1,1,1,1] => 12 [3,3,2,1,1,1,1,1,1,1,1] => 6 [3,3,1,1,1,1,1,1,1,1,1,1] => 0 [3,2,2,2,2,2,2,1] => 3 [3,2,2,2,2,2,1,1,1] => 4 [3,2,2,2,2,1,1,1,1,1] => 4 [3,2,2,2,1,1,1,1,1,1,1] => 4 [3,2,2,1,1,1,1,1,1,1,1,1] => 6 [3,2,1,1,1,1,1,1,1,1,1,1,1] => 2 [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2,2,2] => 0 [2,2,2,2,2,2,2,1,1] => 6 [2,2,2,2,2,2,1,1,1,1] => 4 [2,2,2,2,2,1,1,1,1,1,1] => 4 [2,2,2,2,1,1,1,1,1,1,1,1] => 4 [2,2,2,1,1,1,1,1,1,1,1,1,1] => 4 [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [17] => 0 [16,1] => 0 [15,2] => 0 [15,1,1] => 0 [14,3] => 0 [14,2,1] => 0 [14,1,1,1] => 0 [13,4] => 0 [13,3,1] => 0 [13,2,2] => 0 [13,2,1,1] => 0 [13,1,1,1,1] => 0 [12,5] => 0 [12,4,1] => 0 [12,3,2] => 0 [12,3,1,1] => 0 [12,2,2,1] => 0 [12,2,1,1,1] => 0 [12,1,1,1,1,1] => 0 [11,6] => 0 [11,5,1] => 0 [11,4,2] => 0 [11,4,1,1] => 0 [11,3,3] => 0 [11,3,2,1] => 0 [11,3,1,1,1] => 0 [11,2,2,2] => 0 [11,2,2,1,1] => 0 [11,2,1,1,1,1] => 0 [11,1,1,1,1,1,1] => 0 [10,7] => 0 [10,6,1] => 0 [10,5,2] => 0 [10,5,1,1] => 0 [10,4,3] => 0 [10,4,2,1] => 0 [10,4,1,1,1] => 0 [10,3,3,1] => 0 [10,3,2,2] => 0 [10,3,2,1,1] => 0 [10,3,1,1,1,1] => 0 [10,2,2,2,1] => 0 [10,2,2,1,1,1] => 0 [10,2,1,1,1,1,1] => 0 [10,1,1,1,1,1,1,1] => 0 [9,8] => 0 [9,7,1] => 0 [9,6,2] => 0 [9,6,1,1] => 0 [9,5,3] => 0 [9,5,2,1] => 0 [9,5,1,1,1] => 0 [9,4,4] => 0 [9,4,3,1] => 0 [9,4,2,2] => 0 [9,4,2,1,1] => 0 [9,4,1,1,1,1] => 0 [9,3,3,2] => 0 [9,3,3,1,1] => 0 [9,3,2,2,1] => 0 [9,3,2,1,1,1] => 0 [9,3,1,1,1,1,1] => 0 [9,2,2,2,2] => 0 [9,2,2,2,1,1] => 0 [9,2,2,1,1,1,1] => 0 [9,2,1,1,1,1,1,1] => 0 [9,1,1,1,1,1,1,1,1] => 0 [8,8,1] => 0 [8,7,2] => 0 [8,7,1,1] => 0 [8,6,3] => 0 [8,6,2,1] => 0 [8,6,1,1,1] => 0 [8,5,4] => 0 [8,5,3,1] => 0 [8,5,2,2] => 0 [8,5,2,1,1] => 0 [8,5,1,1,1,1] => 0 [8,4,4,1] => 0 [8,4,3,2] => 0 [8,4,3,1,1] => 0 [8,4,2,2,1] => 0 [8,4,2,1,1,1] => 0 [8,4,1,1,1,1,1] => 0 [8,3,3,3] => 0 [8,3,3,2,1] => 0 [8,3,3,1,1,1] => 0 [8,3,2,2,2] => 0 [8,3,2,2,1,1] => 0 [8,3,2,1,1,1,1] => 0 [8,3,1,1,1,1,1,1] => 0 [8,2,2,2,2,1] => 0 [8,2,2,2,1,1,1] => 0 [8,2,2,1,1,1,1,1] => 0 [8,2,1,1,1,1,1,1,1] => 0 [8,1,1,1,1,1,1,1,1,1] => 0 [7,7,3] => 0 [7,7,2,1] => 0 [7,7,1,1,1] => 0 [7,6,4] => 0 [7,6,3,1] => 0 [7,6,2,2] => 0 [7,6,2,1,1] => 0 [7,6,1,1,1,1] => 0 [7,5,5] => 0 [7,5,4,1] => 0 [7,5,3,2] => 0 [7,5,3,1,1] => 0 [7,5,2,2,1] => 0 [7,5,2,1,1,1] => 0 [7,5,1,1,1,1,1] => 0 [7,4,4,2] => 0 [7,4,4,1,1] => 0 [7,4,3,3] => 0 [7,4,3,2,1] => 0 [7,4,3,1,1,1] => 0 [7,4,2,2,2] => 0 [7,4,2,2,1,1] => 0 [7,4,2,1,1,1,1] => 0 [7,4,1,1,1,1,1,1] => 0 [7,3,3,3,1] => 0 [7,3,3,2,2] => 0 [7,3,3,2,1,1] => 0 [7,3,3,1,1,1,1] => 0 [7,3,2,2,2,1] => 0 [7,3,2,2,1,1,1] => 0 [7,3,2,1,1,1,1,1] => 0 [7,3,1,1,1,1,1,1,1] => 0 [7,2,2,2,2,2] => 0 [7,2,2,2,2,1,1] => 0 [7,2,2,2,1,1,1,1] => 0 [7,2,2,1,1,1,1,1,1] => 0 [7,2,1,1,1,1,1,1,1,1] => 0 [7,1,1,1,1,1,1,1,1,1,1] => 0 [6,6,5] => 0 [6,6,4,1] => 0 [6,6,3,2] => 0 [6,6,3,1,1] => 0 [6,6,2,2,1] => 0 [6,6,2,1,1,1] => 0 [6,6,1,1,1,1,1] => 0 [6,5,5,1] => 0 [6,5,4,2] => 0 [6,5,4,1,1] => 0 [6,5,3,3] => 0 [6,5,3,2,1] => 0 [6,5,3,1,1,1] => 0 [6,5,2,2,2] => 0 [6,5,2,2,1,1] => 0 [6,5,2,1,1,1,1] => 0 [6,5,1,1,1,1,1,1] => 0 [6,4,4,3] => 0 [6,4,4,2,1] => 0 [6,4,4,1,1,1] => 0 [6,4,3,3,1] => 0 [6,4,3,2,2] => 0 [6,4,3,2,1,1] => 0 [6,4,3,1,1,1,1] => 0 [6,4,2,2,2,1] => 0 [6,4,2,2,1,1,1] => 0 [6,4,2,1,1,1,1,1] => 0 [6,4,1,1,1,1,1,1,1] => 0 [6,3,3,3,2] => 0 [6,3,3,3,1,1] => 0 [6,3,3,2,2,1] => 0 [6,3,3,2,1,1,1] => 0 [6,3,3,1,1,1,1,1] => 0 [6,3,2,2,2,2] => 0 [6,3,2,2,2,1,1] => 0 [6,3,2,2,1,1,1,1] => 0 [6,3,2,1,1,1,1,1,1] => 0 [6,3,1,1,1,1,1,1,1,1] => 0 [6,2,2,2,2,2,1] => 0 [6,2,2,2,2,1,1,1] => 0 [6,2,2,2,1,1,1,1,1] => 0 [6,2,2,1,1,1,1,1,1,1] => 0 [6,2,1,1,1,1,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1,1,1,1,1] => 0 [5,5,5,2] => 0 [5,5,5,1,1] => 0 [5,5,4,3] => 0 [5,5,4,2,1] => 0 [5,5,4,1,1,1] => 0 [5,5,3,3,1] => 0 [5,5,3,2,2] => 0 [5,5,3,2,1,1] => 0 [5,5,3,1,1,1,1] => 0 [5,5,2,2,2,1] => 0 [5,5,2,2,1,1,1] => 0 [5,5,2,1,1,1,1,1] => 0 [5,5,1,1,1,1,1,1,1] => 0 [5,4,4,4] => 0 [5,4,4,3,1] => 0 [5,4,4,2,2] => 0 [5,4,4,2,1,1] => 0 [5,4,4,1,1,1,1] => 0 [5,4,3,3,2] => 0 [5,4,3,3,1,1] => 0 [5,4,3,2,2,1] => 15 [5,4,3,2,1,1,1] => 2 [5,4,3,1,1,1,1,1] => 0 [5,4,2,2,2,2] => 0 [5,4,2,2,2,1,1] => 0 [5,4,2,2,1,1,1,1] => 0 [5,4,2,1,1,1,1,1,1] => 0 [5,4,1,1,1,1,1,1,1,1] => 0 [5,3,3,3,3] => 0 [5,3,3,3,2,1] => 0 [5,3,3,3,1,1,1] => 0 [5,3,3,2,2,2] => 0 [5,3,3,2,2,1,1] => 0 [5,3,3,2,1,1,1,1] => 0 [5,3,3,1,1,1,1,1,1] => 0 [5,3,2,2,2,2,1] => 0 [5,3,2,2,2,1,1,1] => 0 [5,3,2,2,1,1,1,1,1] => 0 [5,3,2,1,1,1,1,1,1,1] => 0 [5,3,1,1,1,1,1,1,1,1,1] => 0 [5,2,2,2,2,2,2] => 0 [5,2,2,2,2,2,1,1] => 0 [5,2,2,2,2,1,1,1,1] => 0 [5,2,2,2,1,1,1,1,1,1] => 0 [5,2,2,1,1,1,1,1,1,1,1] => 0 [5,2,1,1,1,1,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [4,4,4,4,1] => 0 [4,4,4,3,2] => 0 [4,4,4,3,1,1] => 0 [4,4,4,2,2,1] => 0 [4,4,4,2,1,1,1] => 0 [4,4,4,1,1,1,1,1] => 0 [4,4,3,3,3] => 0 [4,4,3,3,2,1] => 20 [4,4,3,3,1,1,1] => 0 [4,4,3,2,2,2] => 0 [4,4,3,2,2,1,1] => 36 [4,4,3,2,1,1,1,1] => 8 [4,4,3,1,1,1,1,1,1] => 0 [4,4,2,2,2,2,1] => 0 [4,4,2,2,2,1,1,1] => 0 [4,4,2,2,1,1,1,1,1] => 0 [4,4,2,1,1,1,1,1,1,1] => 0 [4,4,1,1,1,1,1,1,1,1,1] => 0 [4,3,3,3,3,1] => 0 [4,3,3,3,2,2] => 0 [4,3,3,3,2,1,1] => 12 [4,3,3,3,1,1,1,1] => 0 [4,3,3,2,2,2,1] => 9 [4,3,3,2,2,1,1,1] => 18 [4,3,3,2,1,1,1,1,1] => 12 [4,3,3,1,1,1,1,1,1,1] => 0 [4,3,2,2,2,2,2] => 0 [4,3,2,2,2,2,1,1] => 6 [4,3,2,2,2,1,1,1,1] => 4 [4,3,2,2,1,1,1,1,1,1] => 8 [4,3,2,1,1,1,1,1,1,1,1] => 2 [4,3,1,1,1,1,1,1,1,1,1,1] => 0 [4,2,2,2,2,2,2,1] => 0 [4,2,2,2,2,2,1,1,1] => 0 [4,2,2,2,2,1,1,1,1,1] => 0 [4,2,2,2,1,1,1,1,1,1,1] => 0 [4,2,2,1,1,1,1,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,3,2] => 0 [3,3,3,3,3,1,1] => 0 [3,3,3,3,2,2,1] => 12 [3,3,3,3,2,1,1,1] => 6 [3,3,3,3,1,1,1,1,1] => 0 [3,3,3,2,2,2,2] => 0 [3,3,3,2,2,2,1,1] => 12 [3,3,3,2,2,1,1,1,1] => 12 [3,3,3,2,1,1,1,1,1,1] => 6 [3,3,3,1,1,1,1,1,1,1,1] => 0 [3,3,2,2,2,2,2,1] => 6 [3,3,2,2,2,2,1,1,1] => 8 [3,3,2,2,2,1,1,1,1,1] => 8 [3,3,2,2,1,1,1,1,1,1,1] => 12 [3,3,2,1,1,1,1,1,1,1,1,1] => 6 [3,3,1,1,1,1,1,1,1,1,1,1,1] => 0 [3,2,2,2,2,2,2,2] => 0 [3,2,2,2,2,2,2,1,1] => 6 [3,2,2,2,2,2,1,1,1,1] => 4 [3,2,2,2,2,1,1,1,1,1,1] => 4 [3,2,2,2,1,1,1,1,1,1,1,1] => 4 [3,2,2,1,1,1,1,1,1,1,1,1,1] => 6 ----------------------------------------------------------------------------- Created: Apr 14, 2022 at 15:39 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 14, 2022 at 15:39 by Martin Rubey