***************************************************************************** * 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: St001937 ----------------------------------------------------------------------------- Collection: Parking functions ----------------------------------------------------------------------------- Description: The size of the center of a parking function. The center of a parking function $p_1,\dots,p_n$ is the longest subsequence $a_1,\dots,a_k$ such that $a_i\leq i$. ----------------------------------------------------------------------------- References: [1] Duarte, R., Guedes de Oliveira, António The number of parking functions with center of a given length [[arXiv:1611.03707]] ----------------------------------------------------------------------------- Code: def statistic(p): c = [] j = 1 for e in p: if e <= j: c.append(e) j += 1 return len(c) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,1] => 2 [1,2] => 2 [2,1] => 1 [1,1,1] => 3 [1,1,2] => 3 [1,2,1] => 3 [2,1,1] => 2 [1,1,3] => 3 [1,3,1] => 2 [3,1,1] => 2 [1,2,2] => 3 [2,1,2] => 2 [2,2,1] => 1 [1,2,3] => 3 [1,3,2] => 2 [2,1,3] => 1 [2,3,1] => 1 [3,1,2] => 2 [3,2,1] => 1 [1,1,1,1] => 4 [1,1,1,2] => 4 [1,1,2,1] => 4 [1,2,1,1] => 4 [2,1,1,1] => 3 [1,1,1,3] => 4 [1,1,3,1] => 4 [1,3,1,1] => 3 [3,1,1,1] => 3 [1,1,1,4] => 4 [1,1,4,1] => 3 [1,4,1,1] => 3 [4,1,1,1] => 3 [1,1,2,2] => 4 [1,2,1,2] => 4 [1,2,2,1] => 4 [2,1,1,2] => 3 [2,1,2,1] => 3 [2,2,1,1] => 2 [1,1,2,3] => 4 [1,1,3,2] => 4 [1,2,1,3] => 4 [1,2,3,1] => 4 [1,3,1,2] => 3 [1,3,2,1] => 3 [2,1,1,3] => 3 [2,1,3,1] => 2 [2,3,1,1] => 2 [3,1,1,2] => 3 [3,1,2,1] => 3 [3,2,1,1] => 2 [1,1,2,4] => 4 [1,1,4,2] => 3 [1,2,1,4] => 4 [1,2,4,1] => 3 [1,4,1,2] => 3 [1,4,2,1] => 3 [2,1,1,4] => 2 [2,1,4,1] => 2 [2,4,1,1] => 2 [4,1,1,2] => 3 [4,1,2,1] => 3 [4,2,1,1] => 2 [1,1,3,3] => 4 [1,3,1,3] => 3 [1,3,3,1] => 2 [3,1,1,3] => 3 [3,1,3,1] => 2 [3,3,1,1] => 2 [1,1,3,4] => 4 [1,1,4,3] => 3 [1,3,1,4] => 2 [1,3,4,1] => 2 [1,4,1,3] => 3 [1,4,3,1] => 2 [3,1,1,4] => 2 [3,1,4,1] => 2 [3,4,1,1] => 2 [4,1,1,3] => 3 [4,1,3,1] => 2 [4,3,1,1] => 2 [1,2,2,2] => 4 [2,1,2,2] => 3 [2,2,1,2] => 2 [2,2,2,1] => 1 [1,2,2,3] => 4 [1,2,3,2] => 4 [1,3,2,2] => 3 [2,1,2,3] => 3 [2,1,3,2] => 2 [2,2,1,3] => 1 [2,2,3,1] => 1 [2,3,1,2] => 2 [2,3,2,1] => 1 [3,1,2,2] => 3 [3,2,1,2] => 2 [3,2,2,1] => 1 [1,2,2,4] => 4 [1,2,4,2] => 3 [1,4,2,2] => 3 [2,1,2,4] => 2 [2,1,4,2] => 2 [2,2,1,4] => 1 [2,2,4,1] => 1 [2,4,1,2] => 2 [2,4,2,1] => 1 [4,1,2,2] => 3 [4,2,1,2] => 2 [4,2,2,1] => 1 [1,2,3,3] => 4 [1,3,2,3] => 3 [1,3,3,2] => 2 [2,1,3,3] => 1 [2,3,1,3] => 1 [2,3,3,1] => 1 [3,1,2,3] => 3 [3,1,3,2] => 2 [3,2,1,3] => 1 [3,2,3,1] => 1 [3,3,1,2] => 2 [3,3,2,1] => 1 [1,2,3,4] => 4 [1,2,4,3] => 3 [1,3,2,4] => 2 [1,3,4,2] => 2 [1,4,2,3] => 3 [1,4,3,2] => 2 [2,1,3,4] => 1 [2,1,4,3] => 1 [2,3,1,4] => 1 [2,3,4,1] => 1 [2,4,1,3] => 1 [2,4,3,1] => 1 [3,1,2,4] => 2 [3,1,4,2] => 2 [3,2,1,4] => 1 [3,2,4,1] => 1 [3,4,1,2] => 2 [3,4,2,1] => 1 [4,1,2,3] => 3 [4,1,3,2] => 2 [4,2,1,3] => 1 [4,2,3,1] => 1 [4,3,1,2] => 2 [4,3,2,1] => 1 [1,1,1,1,1] => 5 [1,1,1,1,2] => 5 [1,1,1,2,1] => 5 [1,1,2,1,1] => 5 [1,2,1,1,1] => 5 [2,1,1,1,1] => 4 [1,1,1,1,3] => 5 [1,1,1,3,1] => 5 [1,1,3,1,1] => 5 [1,3,1,1,1] => 4 [3,1,1,1,1] => 4 [1,1,1,1,4] => 5 [1,1,1,4,1] => 5 [1,1,4,1,1] => 4 [1,4,1,1,1] => 4 [4,1,1,1,1] => 4 [1,1,1,1,5] => 5 [1,1,1,5,1] => 4 [1,1,5,1,1] => 4 [1,5,1,1,1] => 4 [5,1,1,1,1] => 4 [1,1,1,2,2] => 5 [1,1,2,1,2] => 5 [1,1,2,2,1] => 5 [1,2,1,1,2] => 5 [1,2,1,2,1] => 5 [1,2,2,1,1] => 5 [2,1,1,1,2] => 4 [2,1,1,2,1] => 4 [2,1,2,1,1] => 4 [2,2,1,1,1] => 3 [1,1,1,2,3] => 5 [1,1,1,3,2] => 5 [1,1,2,1,3] => 5 [1,1,2,3,1] => 5 [1,1,3,1,2] => 5 [1,1,3,2,1] => 5 [1,2,1,1,3] => 5 [1,2,1,3,1] => 5 [1,2,3,1,1] => 5 [1,3,1,1,2] => 4 [1,3,1,2,1] => 4 [1,3,2,1,1] => 4 [2,1,1,1,3] => 4 [2,1,1,3,1] => 4 [2,1,3,1,1] => 3 [2,3,1,1,1] => 3 [3,1,1,1,2] => 4 [3,1,1,2,1] => 4 [3,1,2,1,1] => 4 [3,2,1,1,1] => 3 [1,1,1,2,4] => 5 [1,1,1,4,2] => 5 [1,1,2,1,4] => 5 [1,1,2,4,1] => 5 [1,1,4,1,2] => 4 [1,1,4,2,1] => 4 [1,2,1,1,4] => 5 [1,2,1,4,1] => 5 [1,2,4,1,1] => 4 [1,4,1,1,2] => 4 [1,4,1,2,1] => 4 [1,4,2,1,1] => 4 [2,1,1,1,4] => 4 [2,1,1,4,1] => 3 [2,1,4,1,1] => 3 [2,4,1,1,1] => 3 [4,1,1,1,2] => 4 [4,1,1,2,1] => 4 [4,1,2,1,1] => 4 [4,2,1,1,1] => 3 [1,1,1,2,5] => 5 [1,1,1,5,2] => 4 [1,1,2,1,5] => 5 [1,1,2,5,1] => 4 [1,1,5,1,2] => 4 [1,1,5,2,1] => 4 [1,2,1,1,5] => 5 [1,2,1,5,1] => 4 [1,2,5,1,1] => 4 [1,5,1,1,2] => 4 [1,5,1,2,1] => 4 [1,5,2,1,1] => 4 [2,1,1,1,5] => 3 [2,1,1,5,1] => 3 [2,1,5,1,1] => 3 [2,5,1,1,1] => 3 [5,1,1,1,2] => 4 [5,1,1,2,1] => 4 [5,1,2,1,1] => 4 [5,2,1,1,1] => 3 [1,1,1,3,3] => 5 [1,1,3,1,3] => 5 [1,1,3,3,1] => 5 [1,3,1,1,3] => 4 [1,3,1,3,1] => 4 [1,3,3,1,1] => 3 [3,1,1,1,3] => 4 [3,1,1,3,1] => 4 [3,1,3,1,1] => 3 [3,3,1,1,1] => 3 [1,1,1,3,4] => 5 [1,1,1,4,3] => 5 [1,1,3,1,4] => 5 [1,1,3,4,1] => 5 [1,1,4,1,3] => 4 [1,1,4,3,1] => 4 [1,3,1,1,4] => 4 [1,3,1,4,1] => 3 [1,3,4,1,1] => 3 [1,4,1,1,3] => 4 [1,4,1,3,1] => 4 [1,4,3,1,1] => 3 [3,1,1,1,4] => 4 [3,1,1,4,1] => 3 [3,1,4,1,1] => 3 [3,4,1,1,1] => 3 [4,1,1,1,3] => 4 [4,1,1,3,1] => 4 [4,1,3,1,1] => 3 [4,3,1,1,1] => 3 [1,1,1,3,5] => 5 [1,1,1,5,3] => 4 [1,1,3,1,5] => 5 [1,1,3,5,1] => 4 [1,1,5,1,3] => 4 [1,1,5,3,1] => 4 [1,3,1,1,5] => 3 [1,3,1,5,1] => 3 [1,3,5,1,1] => 3 [1,5,1,1,3] => 4 [1,5,1,3,1] => 4 [1,5,3,1,1] => 3 [3,1,1,1,5] => 3 [3,1,1,5,1] => 3 [3,1,5,1,1] => 3 [3,5,1,1,1] => 3 [5,1,1,1,3] => 4 [5,1,1,3,1] => 4 [5,1,3,1,1] => 3 [5,3,1,1,1] => 3 [1,1,1,4,4] => 5 [1,1,4,1,4] => 4 [1,1,4,4,1] => 3 [1,4,1,1,4] => 4 [1,4,1,4,1] => 3 [1,4,4,1,1] => 3 [4,1,1,1,4] => 4 [4,1,1,4,1] => 3 [4,1,4,1,1] => 3 [4,4,1,1,1] => 3 [1,1,1,4,5] => 5 [1,1,1,5,4] => 4 [1,1,4,1,5] => 3 [1,1,4,5,1] => 3 [1,1,5,1,4] => 4 [1,1,5,4,1] => 3 [1,4,1,1,5] => 3 [1,4,1,5,1] => 3 [1,4,5,1,1] => 3 [1,5,1,1,4] => 4 [1,5,1,4,1] => 3 [1,5,4,1,1] => 3 [4,1,1,1,5] => 3 [4,1,1,5,1] => 3 [4,1,5,1,1] => 3 [4,5,1,1,1] => 3 [5,1,1,1,4] => 4 [5,1,1,4,1] => 3 [5,1,4,1,1] => 3 [5,4,1,1,1] => 3 [1,1,2,2,2] => 5 [1,2,1,2,2] => 5 [1,2,2,1,2] => 5 [1,2,2,2,1] => 5 [2,1,1,2,2] => 4 [2,1,2,1,2] => 4 [2,1,2,2,1] => 4 [2,2,1,1,2] => 3 [2,2,1,2,1] => 3 [2,2,2,1,1] => 2 [1,1,2,2,3] => 5 [1,1,2,3,2] => 5 [1,1,3,2,2] => 5 [1,2,1,2,3] => 5 [1,2,1,3,2] => 5 [1,2,2,1,3] => 5 [1,2,2,3,1] => 5 [1,2,3,1,2] => 5 [1,2,3,2,1] => 5 [1,3,1,2,2] => 4 [1,3,2,1,2] => 4 [1,3,2,2,1] => 4 [2,1,1,2,3] => 4 [2,1,1,3,2] => 4 [2,1,2,1,3] => 4 [2,1,2,3,1] => 4 [2,1,3,1,2] => 3 [2,1,3,2,1] => 3 [2,2,1,1,3] => 3 [2,2,1,3,1] => 2 [2,2,3,1,1] => 2 [2,3,1,1,2] => 3 [2,3,1,2,1] => 3 [2,3,2,1,1] => 2 [3,1,1,2,2] => 4 [3,1,2,1,2] => 4 [3,1,2,2,1] => 4 [3,2,1,1,2] => 3 [3,2,1,2,1] => 3 [3,2,2,1,1] => 2 [1,1,2,2,4] => 5 [1,1,2,4,2] => 5 [1,1,4,2,2] => 4 [1,2,1,2,4] => 5 [1,2,1,4,2] => 5 [1,2,2,1,4] => 5 [1,2,2,4,1] => 5 [1,2,4,1,2] => 4 [1,2,4,2,1] => 4 [1,4,1,2,2] => 4 [1,4,2,1,2] => 4 [1,4,2,2,1] => 4 [2,1,1,2,4] => 4 [2,1,1,4,2] => 3 [2,1,2,1,4] => 4 [2,1,2,4,1] => 3 [2,1,4,1,2] => 3 [2,1,4,2,1] => 3 [2,2,1,1,4] => 2 [2,2,1,4,1] => 2 [2,2,4,1,1] => 2 [2,4,1,1,2] => 3 [2,4,1,2,1] => 3 [2,4,2,1,1] => 2 [4,1,1,2,2] => 4 [4,1,2,1,2] => 4 [4,1,2,2,1] => 4 [4,2,1,1,2] => 3 [4,2,1,2,1] => 3 [4,2,2,1,1] => 2 [1,1,2,2,5] => 5 [1,1,2,5,2] => 4 [1,1,5,2,2] => 4 [1,2,1,2,5] => 5 [1,2,1,5,2] => 4 [1,2,2,1,5] => 5 [1,2,2,5,1] => 4 [1,2,5,1,2] => 4 [1,2,5,2,1] => 4 [1,5,1,2,2] => 4 [1,5,2,1,2] => 4 [1,5,2,2,1] => 4 [2,1,1,2,5] => 3 [2,1,1,5,2] => 3 [2,1,2,1,5] => 3 [2,1,2,5,1] => 3 [2,1,5,1,2] => 3 [2,1,5,2,1] => 3 [2,2,1,1,5] => 2 [2,2,1,5,1] => 2 [2,2,5,1,1] => 2 [2,5,1,1,2] => 3 [2,5,1,2,1] => 3 [2,5,2,1,1] => 2 [5,1,1,2,2] => 4 [5,1,2,1,2] => 4 [5,1,2,2,1] => 4 [5,2,1,1,2] => 3 [5,2,1,2,1] => 3 [5,2,2,1,1] => 2 [1,1,2,3,3] => 5 [1,1,3,2,3] => 5 [1,1,3,3,2] => 5 [1,2,1,3,3] => 5 [1,2,3,1,3] => 5 [1,2,3,3,1] => 5 [1,3,1,2,3] => 4 [1,3,1,3,2] => 4 [1,3,2,1,3] => 4 [1,3,2,3,1] => 4 [1,3,3,1,2] => 3 [1,3,3,2,1] => 3 [2,1,1,3,3] => 4 [2,1,3,1,3] => 3 [2,1,3,3,1] => 2 [2,3,1,1,3] => 3 [2,3,1,3,1] => 2 [2,3,3,1,1] => 2 [3,1,1,2,3] => 4 [3,1,1,3,2] => 4 [3,1,2,1,3] => 4 [3,1,2,3,1] => 4 [3,1,3,1,2] => 3 [3,1,3,2,1] => 3 [3,2,1,1,3] => 3 [3,2,1,3,1] => 2 [3,2,3,1,1] => 2 [3,3,1,1,2] => 3 [3,3,1,2,1] => 3 [3,3,2,1,1] => 2 [1,1,2,3,4] => 5 [1,1,2,4,3] => 5 [1,1,3,2,4] => 5 [1,1,3,4,2] => 5 [1,1,4,2,3] => 4 [1,1,4,3,2] => 4 [1,2,1,3,4] => 5 [1,2,1,4,3] => 5 [1,2,3,1,4] => 5 [1,2,3,4,1] => 5 [1,2,4,1,3] => 4 [1,2,4,3,1] => 4 [1,3,1,2,4] => 4 [1,3,1,4,2] => 3 [1,3,2,1,4] => 4 [1,3,2,4,1] => 3 [1,3,4,1,2] => 3 [1,3,4,2,1] => 3 [1,4,1,2,3] => 4 [1,4,1,3,2] => 4 [1,4,2,1,3] => 4 [1,4,2,3,1] => 4 [1,4,3,1,2] => 3 [1,4,3,2,1] => 3 [2,1,1,3,4] => 4 [2,1,1,4,3] => 3 [2,1,3,1,4] => 2 [2,1,3,4,1] => 2 [2,1,4,1,3] => 3 [2,1,4,3,1] => 2 [2,3,1,1,4] => 2 [2,3,1,4,1] => 2 [2,3,4,1,1] => 2 [2,4,1,1,3] => 3 [2,4,1,3,1] => 2 [2,4,3,1,1] => 2 [3,1,1,2,4] => 4 [3,1,1,4,2] => 3 [3,1,2,1,4] => 4 [3,1,2,4,1] => 3 [3,1,4,1,2] => 3 [3,1,4,2,1] => 3 [3,2,1,1,4] => 2 [3,2,1,4,1] => 2 [3,2,4,1,1] => 2 [3,4,1,1,2] => 3 [3,4,1,2,1] => 3 [3,4,2,1,1] => 2 [4,1,1,2,3] => 4 [4,1,1,3,2] => 4 [4,1,2,1,3] => 4 [4,1,2,3,1] => 4 [4,1,3,1,2] => 3 [4,1,3,2,1] => 3 [4,2,1,1,3] => 3 [4,2,1,3,1] => 2 [4,2,3,1,1] => 2 [4,3,1,1,2] => 3 [4,3,1,2,1] => 3 [4,3,2,1,1] => 2 [1,1,2,3,5] => 5 [1,1,2,5,3] => 4 [1,1,3,2,5] => 5 [1,1,3,5,2] => 4 [1,1,5,2,3] => 4 [1,1,5,3,2] => 4 [1,2,1,3,5] => 5 [1,2,1,5,3] => 4 [1,2,3,1,5] => 5 [1,2,3,5,1] => 4 [1,2,5,1,3] => 4 [1,2,5,3,1] => 4 [1,3,1,2,5] => 3 [1,3,1,5,2] => 3 [1,3,2,1,5] => 3 [1,3,2,5,1] => 3 [1,3,5,1,2] => 3 [1,3,5,2,1] => 3 [1,5,1,2,3] => 4 [1,5,1,3,2] => 4 [1,5,2,1,3] => 4 [1,5,2,3,1] => 4 [1,5,3,1,2] => 3 [1,5,3,2,1] => 3 [2,1,1,3,5] => 3 [2,1,1,5,3] => 3 [2,1,3,1,5] => 2 [2,1,3,5,1] => 2 [2,1,5,1,3] => 3 [2,1,5,3,1] => 2 [2,3,1,1,5] => 2 [2,3,1,5,1] => 2 [2,3,5,1,1] => 2 [2,5,1,1,3] => 3 [2,5,1,3,1] => 2 [2,5,3,1,1] => 2 [3,1,1,2,5] => 3 [3,1,1,5,2] => 3 [3,1,2,1,5] => 3 [3,1,2,5,1] => 3 [3,1,5,1,2] => 3 [3,1,5,2,1] => 3 [3,2,1,1,5] => 2 [3,2,1,5,1] => 2 [3,2,5,1,1] => 2 [3,5,1,1,2] => 3 [3,5,1,2,1] => 3 [3,5,2,1,1] => 2 [5,1,1,2,3] => 4 [5,1,1,3,2] => 4 [5,1,2,1,3] => 4 [5,1,2,3,1] => 4 [5,1,3,1,2] => 3 [5,1,3,2,1] => 3 [5,2,1,1,3] => 3 [5,2,1,3,1] => 2 [5,2,3,1,1] => 2 [5,3,1,1,2] => 3 [5,3,1,2,1] => 3 [5,3,2,1,1] => 2 [1,1,2,4,4] => 5 [1,1,4,2,4] => 4 [1,1,4,4,2] => 3 [1,2,1,4,4] => 5 [1,2,4,1,4] => 4 [1,2,4,4,1] => 3 [1,4,1,2,4] => 4 [1,4,1,4,2] => 3 [1,4,2,1,4] => 4 [1,4,2,4,1] => 3 [1,4,4,1,2] => 3 [1,4,4,2,1] => 3 [2,1,1,4,4] => 2 [2,1,4,1,4] => 2 [2,1,4,4,1] => 2 [2,4,1,1,4] => 2 [2,4,1,4,1] => 2 [2,4,4,1,1] => 2 [4,1,1,2,4] => 4 [4,1,1,4,2] => 3 [4,1,2,1,4] => 4 [4,1,2,4,1] => 3 [4,1,4,1,2] => 3 [4,1,4,2,1] => 3 [4,2,1,1,4] => 2 [4,2,1,4,1] => 2 [4,2,4,1,1] => 2 [4,4,1,1,2] => 3 [4,4,1,2,1] => 3 [4,4,2,1,1] => 2 [1,1,2,4,5] => 5 [1,1,2,5,4] => 4 [1,1,4,2,5] => 3 [1,1,4,5,2] => 3 [1,1,5,2,4] => 4 [1,1,5,4,2] => 3 [1,2,1,4,5] => 5 [1,2,1,5,4] => 4 [1,2,4,1,5] => 3 [1,2,4,5,1] => 3 [1,2,5,1,4] => 4 [1,2,5,4,1] => 3 [1,4,1,2,5] => 3 [1,4,1,5,2] => 3 [1,4,2,1,5] => 3 [1,4,2,5,1] => 3 [1,4,5,1,2] => 3 [1,4,5,2,1] => 3 [1,5,1,2,4] => 4 [1,5,1,4,2] => 3 [1,5,2,1,4] => 4 [1,5,2,4,1] => 3 [1,5,4,1,2] => 3 [1,5,4,2,1] => 3 [2,1,1,4,5] => 2 [2,1,1,5,4] => 2 [2,1,4,1,5] => 2 [2,1,4,5,1] => 2 [2,1,5,1,4] => 2 [2,1,5,4,1] => 2 [2,4,1,1,5] => 2 [2,4,1,5,1] => 2 [2,4,5,1,1] => 2 [2,5,1,1,4] => 2 [2,5,1,4,1] => 2 [2,5,4,1,1] => 2 [4,1,1,2,5] => 3 [4,1,1,5,2] => 3 [4,1,2,1,5] => 3 [4,1,2,5,1] => 3 [4,1,5,1,2] => 3 [4,1,5,2,1] => 3 [4,2,1,1,5] => 2 [4,2,1,5,1] => 2 [4,2,5,1,1] => 2 [4,5,1,1,2] => 3 [4,5,1,2,1] => 3 [4,5,2,1,1] => 2 [5,1,1,2,4] => 4 [5,1,1,4,2] => 3 [5,1,2,1,4] => 4 [5,1,2,4,1] => 3 [5,1,4,1,2] => 3 [5,1,4,2,1] => 3 [5,2,1,1,4] => 2 [5,2,1,4,1] => 2 [5,2,4,1,1] => 2 [5,4,1,1,2] => 3 [5,4,1,2,1] => 3 [5,4,2,1,1] => 2 [1,1,3,3,3] => 5 [1,3,1,3,3] => 4 [1,3,3,1,3] => 3 [1,3,3,3,1] => 2 [3,1,1,3,3] => 4 [3,1,3,1,3] => 3 [3,1,3,3,1] => 2 [3,3,1,1,3] => 3 [3,3,1,3,1] => 2 [3,3,3,1,1] => 2 [1,1,3,3,4] => 5 [1,1,3,4,3] => 5 [1,1,4,3,3] => 4 [1,3,1,3,4] => 4 [1,3,1,4,3] => 3 [1,3,3,1,4] => 2 [1,3,3,4,1] => 2 [1,3,4,1,3] => 3 [1,3,4,3,1] => 2 [1,4,1,3,3] => 4 [1,4,3,1,3] => 3 [1,4,3,3,1] => 2 [3,1,1,3,4] => 4 [3,1,1,4,3] => 3 [3,1,3,1,4] => 2 [3,1,3,4,1] => 2 [3,1,4,1,3] => 3 [3,1,4,3,1] => 2 [3,3,1,1,4] => 2 [3,3,1,4,1] => 2 [3,3,4,1,1] => 2 [3,4,1,1,3] => 3 [3,4,1,3,1] => 2 [3,4,3,1,1] => 2 [4,1,1,3,3] => 4 [4,1,3,1,3] => 3 [4,1,3,3,1] => 2 [4,3,1,1,3] => 3 [4,3,1,3,1] => 2 [4,3,3,1,1] => 2 [1,1,3,3,5] => 5 [1,1,3,5,3] => 4 [1,1,5,3,3] => 4 [1,3,1,3,5] => 3 [1,3,1,5,3] => 3 [1,3,3,1,5] => 2 [1,3,3,5,1] => 2 [1,3,5,1,3] => 3 [1,3,5,3,1] => 2 [1,5,1,3,3] => 4 [1,5,3,1,3] => 3 [1,5,3,3,1] => 2 [3,1,1,3,5] => 3 [3,1,1,5,3] => 3 [3,1,3,1,5] => 2 [3,1,3,5,1] => 2 [3,1,5,1,3] => 3 [3,1,5,3,1] => 2 [3,3,1,1,5] => 2 [3,3,1,5,1] => 2 [3,3,5,1,1] => 2 [3,5,1,1,3] => 3 [3,5,1,3,1] => 2 [3,5,3,1,1] => 2 [5,1,1,3,3] => 4 [5,1,3,1,3] => 3 [5,1,3,3,1] => 2 [5,3,1,1,3] => 3 [5,3,1,3,1] => 2 [5,3,3,1,1] => 2 [1,1,3,4,4] => 5 [1,1,4,3,4] => 4 [1,1,4,4,3] => 3 [1,3,1,4,4] => 2 [1,3,4,1,4] => 2 [1,3,4,4,1] => 2 [1,4,1,3,4] => 4 [1,4,1,4,3] => 3 [1,4,3,1,4] => 2 [1,4,3,4,1] => 2 [1,4,4,1,3] => 3 [1,4,4,3,1] => 2 [3,1,1,4,4] => 2 [3,1,4,1,4] => 2 [3,1,4,4,1] => 2 [3,4,1,1,4] => 2 [3,4,1,4,1] => 2 [3,4,4,1,1] => 2 [4,1,1,3,4] => 4 [4,1,1,4,3] => 3 [4,1,3,1,4] => 2 [4,1,3,4,1] => 2 [4,1,4,1,3] => 3 [4,1,4,3,1] => 2 [4,3,1,1,4] => 2 [4,3,1,4,1] => 2 [4,3,4,1,1] => 2 [4,4,1,1,3] => 3 [4,4,1,3,1] => 2 [4,4,3,1,1] => 2 [1,1,3,4,5] => 5 [1,1,3,5,4] => 4 [1,1,4,3,5] => 3 [1,1,4,5,3] => 3 [1,1,5,3,4] => 4 [1,1,5,4,3] => 3 [1,3,1,4,5] => 2 [1,3,1,5,4] => 2 [1,3,4,1,5] => 2 [1,3,4,5,1] => 2 [1,3,5,1,4] => 2 [1,3,5,4,1] => 2 [1,4,1,3,5] => 3 [1,4,1,5,3] => 3 [1,4,3,1,5] => 2 [1,4,3,5,1] => 2 [1,4,5,1,3] => 3 [1,4,5,3,1] => 2 [1,5,1,3,4] => 4 [1,5,1,4,3] => 3 [1,5,3,1,4] => 2 [1,5,3,4,1] => 2 [1,5,4,1,3] => 3 [1,5,4,3,1] => 2 [3,1,1,4,5] => 2 [3,1,1,5,4] => 2 [3,1,4,1,5] => 2 [3,1,4,5,1] => 2 [3,1,5,1,4] => 2 [3,1,5,4,1] => 2 [3,4,1,1,5] => 2 [3,4,1,5,1] => 2 [3,4,5,1,1] => 2 [3,5,1,1,4] => 2 [3,5,1,4,1] => 2 [3,5,4,1,1] => 2 [4,1,1,3,5] => 3 [4,1,1,5,3] => 3 [4,1,3,1,5] => 2 [4,1,3,5,1] => 2 [4,1,5,1,3] => 3 [4,1,5,3,1] => 2 [4,3,1,1,5] => 2 [4,3,1,5,1] => 2 [4,3,5,1,1] => 2 [4,5,1,1,3] => 3 [4,5,1,3,1] => 2 [4,5,3,1,1] => 2 [5,1,1,3,4] => 4 [5,1,1,4,3] => 3 [5,1,3,1,4] => 2 [5,1,3,4,1] => 2 [5,1,4,1,3] => 3 [5,1,4,3,1] => 2 [5,3,1,1,4] => 2 [5,3,1,4,1] => 2 [5,3,4,1,1] => 2 [5,4,1,1,3] => 3 [5,4,1,3,1] => 2 [5,4,3,1,1] => 2 [1,2,2,2,2] => 5 [2,1,2,2,2] => 4 [2,2,1,2,2] => 3 [2,2,2,1,2] => 2 [2,2,2,2,1] => 1 [1,2,2,2,3] => 5 [1,2,2,3,2] => 5 [1,2,3,2,2] => 5 [1,3,2,2,2] => 4 [2,1,2,2,3] => 4 [2,1,2,3,2] => 4 [2,1,3,2,2] => 3 [2,2,1,2,3] => 3 [2,2,1,3,2] => 2 [2,2,2,1,3] => 1 [2,2,2,3,1] => 1 [2,2,3,1,2] => 2 [2,2,3,2,1] => 1 [2,3,1,2,2] => 3 [2,3,2,1,2] => 2 [2,3,2,2,1] => 1 [3,1,2,2,2] => 4 [3,2,1,2,2] => 3 [3,2,2,1,2] => 2 [3,2,2,2,1] => 1 [1,2,2,2,4] => 5 [1,2,2,4,2] => 5 [1,2,4,2,2] => 4 [1,4,2,2,2] => 4 [2,1,2,2,4] => 4 [2,1,2,4,2] => 3 [2,1,4,2,2] => 3 [2,2,1,2,4] => 2 [2,2,1,4,2] => 2 [2,2,2,1,4] => 1 [2,2,2,4,1] => 1 [2,2,4,1,2] => 2 [2,2,4,2,1] => 1 [2,4,1,2,2] => 3 [2,4,2,1,2] => 2 [2,4,2,2,1] => 1 [4,1,2,2,2] => 4 [4,2,1,2,2] => 3 [4,2,2,1,2] => 2 [4,2,2,2,1] => 1 [1,2,2,2,5] => 5 [1,2,2,5,2] => 4 [1,2,5,2,2] => 4 [1,5,2,2,2] => 4 [2,1,2,2,5] => 3 [2,1,2,5,2] => 3 [2,1,5,2,2] => 3 [2,2,1,2,5] => 2 [2,2,1,5,2] => 2 [2,2,2,1,5] => 1 [2,2,2,5,1] => 1 [2,2,5,1,2] => 2 [2,2,5,2,1] => 1 [2,5,1,2,2] => 3 [2,5,2,1,2] => 2 [2,5,2,2,1] => 1 [5,1,2,2,2] => 4 [5,2,1,2,2] => 3 [5,2,2,1,2] => 2 [5,2,2,2,1] => 1 [1,2,2,3,3] => 5 [1,2,3,2,3] => 5 [1,2,3,3,2] => 5 [1,3,2,2,3] => 4 [1,3,2,3,2] => 4 [1,3,3,2,2] => 3 [2,1,2,3,3] => 4 [2,1,3,2,3] => 3 [2,1,3,3,2] => 2 [2,2,1,3,3] => 1 [2,2,3,1,3] => 1 [2,2,3,3,1] => 1 [2,3,1,2,3] => 3 [2,3,1,3,2] => 2 [2,3,2,1,3] => 1 [2,3,2,3,1] => 1 [2,3,3,1,2] => 2 [2,3,3,2,1] => 1 [3,1,2,2,3] => 4 [3,1,2,3,2] => 4 [3,1,3,2,2] => 3 [3,2,1,2,3] => 3 [3,2,1,3,2] => 2 [3,2,2,1,3] => 1 [3,2,2,3,1] => 1 [3,2,3,1,2] => 2 [3,2,3,2,1] => 1 [3,3,1,2,2] => 3 [3,3,2,1,2] => 2 [3,3,2,2,1] => 1 [1,2,2,3,4] => 5 [1,2,2,4,3] => 5 [1,2,3,2,4] => 5 [1,2,3,4,2] => 5 [1,2,4,2,3] => 4 [1,2,4,3,2] => 4 [1,3,2,2,4] => 4 [1,3,2,4,2] => 3 [1,3,4,2,2] => 3 [1,4,2,2,3] => 4 [1,4,2,3,2] => 4 [1,4,3,2,2] => 3 [2,1,2,3,4] => 4 [2,1,2,4,3] => 3 [2,1,3,2,4] => 2 [2,1,3,4,2] => 2 [2,1,4,2,3] => 3 [2,1,4,3,2] => 2 [2,2,1,3,4] => 1 [2,2,1,4,3] => 1 [2,2,3,1,4] => 1 [2,2,3,4,1] => 1 [2,2,4,1,3] => 1 [2,2,4,3,1] => 1 [2,3,1,2,4] => 2 [2,3,1,4,2] => 2 [2,3,2,1,4] => 1 [2,3,2,4,1] => 1 [2,3,4,1,2] => 2 [2,3,4,2,1] => 1 [2,4,1,2,3] => 3 [2,4,1,3,2] => 2 [2,4,2,1,3] => 1 [2,4,2,3,1] => 1 [2,4,3,1,2] => 2 [2,4,3,2,1] => 1 [3,1,2,2,4] => 4 [3,1,2,4,2] => 3 [3,1,4,2,2] => 3 [3,2,1,2,4] => 2 [3,2,1,4,2] => 2 [3,2,2,1,4] => 1 [3,2,2,4,1] => 1 [3,2,4,1,2] => 2 [3,2,4,2,1] => 1 [3,4,1,2,2] => 3 [3,4,2,1,2] => 2 [3,4,2,2,1] => 1 [4,1,2,2,3] => 4 [4,1,2,3,2] => 4 [4,1,3,2,2] => 3 [4,2,1,2,3] => 3 [4,2,1,3,2] => 2 [4,2,2,1,3] => 1 [4,2,2,3,1] => 1 [4,2,3,1,2] => 2 [4,2,3,2,1] => 1 [4,3,1,2,2] => 3 [4,3,2,1,2] => 2 [4,3,2,2,1] => 1 [1,2,2,3,5] => 5 [1,2,2,5,3] => 4 [1,2,3,2,5] => 5 [1,2,3,5,2] => 4 [1,2,5,2,3] => 4 [1,2,5,3,2] => 4 [1,3,2,2,5] => 3 [1,3,2,5,2] => 3 [1,3,5,2,2] => 3 [1,5,2,2,3] => 4 [1,5,2,3,2] => 4 [1,5,3,2,2] => 3 [2,1,2,3,5] => 3 [2,1,2,5,3] => 3 [2,1,3,2,5] => 2 [2,1,3,5,2] => 2 [2,1,5,2,3] => 3 [2,1,5,3,2] => 2 [2,2,1,3,5] => 1 [2,2,1,5,3] => 1 [2,2,3,1,5] => 1 [2,2,3,5,1] => 1 [2,2,5,1,3] => 1 [2,2,5,3,1] => 1 [2,3,1,2,5] => 2 [2,3,1,5,2] => 2 [2,3,2,1,5] => 1 [2,3,2,5,1] => 1 [2,3,5,1,2] => 2 [2,3,5,2,1] => 1 [2,5,1,2,3] => 3 [2,5,1,3,2] => 2 [2,5,2,1,3] => 1 [2,5,2,3,1] => 1 [2,5,3,1,2] => 2 [2,5,3,2,1] => 1 [3,1,2,2,5] => 3 [3,1,2,5,2] => 3 [3,1,5,2,2] => 3 [3,2,1,2,5] => 2 [3,2,1,5,2] => 2 [3,2,2,1,5] => 1 [3,2,2,5,1] => 1 [3,2,5,1,2] => 2 [3,2,5,2,1] => 1 [3,5,1,2,2] => 3 [3,5,2,1,2] => 2 [3,5,2,2,1] => 1 [5,1,2,2,3] => 4 [5,1,2,3,2] => 4 [5,1,3,2,2] => 3 [5,2,1,2,3] => 3 [5,2,1,3,2] => 2 [5,2,2,1,3] => 1 [5,2,2,3,1] => 1 [5,2,3,1,2] => 2 [5,2,3,2,1] => 1 [5,3,1,2,2] => 3 [5,3,2,1,2] => 2 [5,3,2,2,1] => 1 [1,2,2,4,4] => 5 [1,2,4,2,4] => 4 [1,2,4,4,2] => 3 [1,4,2,2,4] => 4 [1,4,2,4,2] => 3 [1,4,4,2,2] => 3 [2,1,2,4,4] => 2 [2,1,4,2,4] => 2 [2,1,4,4,2] => 2 [2,2,1,4,4] => 1 [2,2,4,1,4] => 1 [2,2,4,4,1] => 1 [2,4,1,2,4] => 2 [2,4,1,4,2] => 2 [2,4,2,1,4] => 1 [2,4,2,4,1] => 1 [2,4,4,1,2] => 2 [2,4,4,2,1] => 1 [4,1,2,2,4] => 4 [4,1,2,4,2] => 3 [4,1,4,2,2] => 3 [4,2,1,2,4] => 2 [4,2,1,4,2] => 2 [4,2,2,1,4] => 1 [4,2,2,4,1] => 1 [4,2,4,1,2] => 2 [4,2,4,2,1] => 1 [4,4,1,2,2] => 3 [4,4,2,1,2] => 2 [4,4,2,2,1] => 1 [1,2,2,4,5] => 5 [1,2,2,5,4] => 4 [1,2,4,2,5] => 3 [1,2,4,5,2] => 3 [1,2,5,2,4] => 4 [1,2,5,4,2] => 3 [1,4,2,2,5] => 3 [1,4,2,5,2] => 3 [1,4,5,2,2] => 3 [1,5,2,2,4] => 4 [1,5,2,4,2] => 3 [1,5,4,2,2] => 3 [2,1,2,4,5] => 2 [2,1,2,5,4] => 2 [2,1,4,2,5] => 2 [2,1,4,5,2] => 2 [2,1,5,2,4] => 2 [2,1,5,4,2] => 2 [2,2,1,4,5] => 1 [2,2,1,5,4] => 1 [2,2,4,1,5] => 1 [2,2,4,5,1] => 1 [2,2,5,1,4] => 1 [2,2,5,4,1] => 1 [2,4,1,2,5] => 2 [2,4,1,5,2] => 2 [2,4,2,1,5] => 1 [2,4,2,5,1] => 1 [2,4,5,1,2] => 2 [2,4,5,2,1] => 1 [2,5,1,2,4] => 2 [2,5,1,4,2] => 2 [2,5,2,1,4] => 1 [2,5,2,4,1] => 1 [2,5,4,1,2] => 2 [2,5,4,2,1] => 1 [4,1,2,2,5] => 3 [4,1,2,5,2] => 3 [4,1,5,2,2] => 3 [4,2,1,2,5] => 2 [4,2,1,5,2] => 2 [4,2,2,1,5] => 1 [4,2,2,5,1] => 1 [4,2,5,1,2] => 2 [4,2,5,2,1] => 1 [4,5,1,2,2] => 3 [4,5,2,1,2] => 2 [4,5,2,2,1] => 1 [5,1,2,2,4] => 4 [5,1,2,4,2] => 3 [5,1,4,2,2] => 3 [5,2,1,2,4] => 2 [5,2,1,4,2] => 2 [5,2,2,1,4] => 1 [5,2,2,4,1] => 1 [5,2,4,1,2] => 2 [5,2,4,2,1] => 1 [5,4,1,2,2] => 3 [5,4,2,1,2] => 2 [5,4,2,2,1] => 1 [1,2,3,3,3] => 5 [1,3,2,3,3] => 4 [1,3,3,2,3] => 3 [1,3,3,3,2] => 2 [2,1,3,3,3] => 1 [2,3,1,3,3] => 1 [2,3,3,1,3] => 1 [2,3,3,3,1] => 1 [3,1,2,3,3] => 4 [3,1,3,2,3] => 3 [3,1,3,3,2] => 2 [3,2,1,3,3] => 1 [3,2,3,1,3] => 1 [3,2,3,3,1] => 1 [3,3,1,2,3] => 3 [3,3,1,3,2] => 2 [3,3,2,1,3] => 1 [3,3,2,3,1] => 1 [3,3,3,1,2] => 2 [3,3,3,2,1] => 1 [1,2,3,3,4] => 5 [1,2,3,4,3] => 5 [1,2,4,3,3] => 4 [1,3,2,3,4] => 4 [1,3,2,4,3] => 3 [1,3,3,2,4] => 2 [1,3,3,4,2] => 2 [1,3,4,2,3] => 3 [1,3,4,3,2] => 2 [1,4,2,3,3] => 4 [1,4,3,2,3] => 3 [1,4,3,3,2] => 2 [2,1,3,3,4] => 1 [2,1,3,4,3] => 1 [2,1,4,3,3] => 1 [2,3,1,3,4] => 1 [2,3,1,4,3] => 1 [2,3,3,1,4] => 1 [2,3,3,4,1] => 1 [2,3,4,1,3] => 1 [2,3,4,3,1] => 1 [2,4,1,3,3] => 1 [2,4,3,1,3] => 1 [2,4,3,3,1] => 1 [3,1,2,3,4] => 4 [3,1,2,4,3] => 3 [3,1,3,2,4] => 2 [3,1,3,4,2] => 2 [3,1,4,2,3] => 3 [3,1,4,3,2] => 2 [3,2,1,3,4] => 1 [3,2,1,4,3] => 1 [3,2,3,1,4] => 1 [3,2,3,4,1] => 1 [3,2,4,1,3] => 1 [3,2,4,3,1] => 1 [3,3,1,2,4] => 2 [3,3,1,4,2] => 2 [3,3,2,1,4] => 1 [3,3,2,4,1] => 1 [3,3,4,1,2] => 2 [3,3,4,2,1] => 1 [3,4,1,2,3] => 3 [3,4,1,3,2] => 2 [3,4,2,1,3] => 1 [3,4,2,3,1] => 1 [3,4,3,1,2] => 2 [3,4,3,2,1] => 1 [4,1,2,3,3] => 4 [4,1,3,2,3] => 3 [4,1,3,3,2] => 2 [4,2,1,3,3] => 1 [4,2,3,1,3] => 1 [4,2,3,3,1] => 1 [4,3,1,2,3] => 3 [4,3,1,3,2] => 2 [4,3,2,1,3] => 1 [4,3,2,3,1] => 1 [4,3,3,1,2] => 2 ----------------------------------------------------------------------------- Created: Dec 30, 2023 at 10:45 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Dec 30, 2023 at 10:45 by Martin Rubey