***************************************************************************** * 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: St001135 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. ----------------------------------------------------------------------------- References: [1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. [[zbMATH:06820683]] ----------------------------------------------------------------------------- Code: gap('LoadPackage("QPA");') def kupisch(D): H = D.heights() return [1+H[i] for i, s in enumerate(D) if s == 0] + [1] def statistic(D): D = DyckWord(D) K = kupisch(D.reverse()) A = gap.NakayamaAlgebra(K, gap.GF(3)) S = gap.SimpleModules(A) return ZZ(gap.ProjDimensionOfModule(S[1], 100)) ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 2 [1,1,0,0] => 1 [1,0,1,0,1,0] => 3 [1,0,1,1,0,0] => 1 [1,1,0,0,1,0] => 2 [1,1,0,1,0,0] => 2 [1,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,0] => 4 [1,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,0] => 3 [1,0,1,1,1,0,0,0] => 1 [1,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,0,1,0] => 3 [1,1,0,1,0,1,0,0] => 3 [1,1,0,1,1,0,0,0] => 1 [1,1,1,0,0,0,1,0] => 2 [1,1,1,0,0,1,0,0] => 2 [1,1,1,0,1,0,0,0] => 2 [1,1,1,1,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0] => 5 [1,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,0,1,0] => 2 [1,0,1,0,1,1,0,1,0,0] => 4 [1,0,1,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,0,1,0,1,0] => 3 [1,0,1,1,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,0,0,0] => 3 [1,0,1,1,1,1,0,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,0] => 4 [1,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,0] => 3 [1,1,0,0,1,1,1,0,0,0] => 1 [1,1,0,1,0,0,1,0,1,0] => 4 [1,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,0,1,0] => 4 [1,1,0,1,0,1,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,0,0] => 1 [1,1,0,1,1,0,0,0,1,0] => 2 [1,1,0,1,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,0,0,0] => 1 [1,1,1,0,0,0,1,0,1,0] => 3 [1,1,1,0,0,0,1,1,0,0] => 1 [1,1,1,0,0,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,1,0,0,0] => 1 [1,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,1,0,0,0] => 3 [1,1,1,0,1,1,0,0,0,0] => 1 [1,1,1,1,0,0,0,0,1,0] => 2 [1,1,1,1,0,0,0,1,0,0] => 2 [1,1,1,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,0] => 6 [1,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,0,1,0,1,1,0,0,1,0] => 2 [1,0,1,0,1,0,1,1,0,1,0,0] => 5 [1,0,1,0,1,0,1,1,1,0,0,0] => 1 [1,0,1,0,1,1,0,0,1,0,1,0] => 3 [1,0,1,0,1,1,0,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,1,0,0,1,0] => 5 [1,0,1,0,1,1,0,1,0,1,0,0] => 5 [1,0,1,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,0,1,1,1,0,1,0,0,0] => 4 [1,0,1,0,1,1,1,1,0,0,0,0] => 1 [1,0,1,1,0,0,1,0,1,0,1,0] => 4 [1,0,1,1,0,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,0,1,1,0,1,0,0] => 3 [1,0,1,1,0,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,1,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,1,0,0,1,0] => 5 [1,0,1,1,0,1,0,1,0,1,0,0] => 3 [1,0,1,1,0,1,0,1,1,0,0,0] => 1 [1,0,1,1,0,1,1,0,0,0,1,0] => 2 [1,0,1,1,0,1,1,0,0,1,0,0] => 4 [1,0,1,1,0,1,1,0,1,0,0,0] => 4 [1,0,1,1,0,1,1,1,0,0,0,0] => 1 [1,0,1,1,1,0,0,0,1,0,1,0] => 3 [1,0,1,1,1,0,0,0,1,1,0,0] => 1 [1,0,1,1,1,0,0,1,0,0,1,0] => 3 [1,0,1,1,1,0,0,1,0,1,0,0] => 3 [1,0,1,1,1,0,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,1,0,0,0,1,0] => 4 [1,0,1,1,1,0,1,0,0,1,0,0] => 4 [1,0,1,1,1,0,1,0,1,0,0,0] => 4 [1,0,1,1,1,0,1,1,0,0,0,0] => 1 [1,0,1,1,1,1,0,0,0,0,1,0] => 2 [1,0,1,1,1,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,1,0,0,0,0] => 3 [1,0,1,1,1,1,1,0,0,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,0] => 5 [1,1,0,0,1,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,0,1,1,0,1,0,0] => 4 [1,1,0,0,1,0,1,1,1,0,0,0] => 1 [1,1,0,0,1,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,0,0,1,1,0,0] => 1 [1,1,0,0,1,1,0,1,0,0,1,0] => 4 [1,1,0,0,1,1,0,1,0,1,0,0] => 4 [1,1,0,0,1,1,0,1,1,0,0,0] => 1 [1,1,0,0,1,1,1,0,0,0,1,0] => 2 [1,1,0,0,1,1,1,0,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,1,0,0,0] => 3 [1,1,0,0,1,1,1,1,0,0,0,0] => 1 [1,1,0,1,0,0,1,0,1,0,1,0] => 5 [1,1,0,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,1,0,0,1,1,0,1,0,0] => 4 [1,1,0,1,0,0,1,1,1,0,0,0] => 1 [1,1,0,1,0,1,0,0,1,0,1,0] => 5 [1,1,0,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,1,0,0,1,0] => 4 [1,1,0,1,0,1,0,1,0,1,0,0] => 4 [1,1,0,1,0,1,0,1,1,0,0,0] => 1 [1,1,0,1,0,1,1,0,0,0,1,0] => 2 [1,1,0,1,0,1,1,0,0,1,0,0] => 4 [1,1,0,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,0,1,1,1,0,0,0,0] => 1 [1,1,0,1,1,0,0,0,1,0,1,0] => 3 [1,1,0,1,1,0,0,0,1,1,0,0] => 1 [1,1,0,1,1,0,0,1,0,0,1,0] => 4 [1,1,0,1,1,0,0,1,0,1,0,0] => 4 [1,1,0,1,1,0,0,1,1,0,0,0] => 1 [1,1,0,1,1,0,1,0,0,0,1,0] => 4 [1,1,0,1,1,0,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,1,0,1,0,0,0] => 3 [1,1,0,1,1,0,1,1,0,0,0,0] => 1 [1,1,0,1,1,1,0,0,0,0,1,0] => 2 [1,1,0,1,1,1,0,0,0,1,0,0] => 2 [1,1,0,1,1,1,0,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,1,0,0,0,0] => 3 [1,1,0,1,1,1,1,0,0,0,0,0] => 1 [1,1,1,0,0,0,1,0,1,0,1,0] => 4 [1,1,1,0,0,0,1,0,1,1,0,0] => 1 [1,1,1,0,0,0,1,1,0,0,1,0] => 2 [1,1,1,0,0,0,1,1,0,1,0,0] => 3 [1,1,1,0,0,0,1,1,1,0,0,0] => 1 [1,1,1,0,0,1,0,0,1,0,1,0] => 4 [1,1,1,0,0,1,0,0,1,1,0,0] => 1 [1,1,1,0,0,1,0,1,0,0,1,0] => 4 [1,1,1,0,0,1,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,0,1,1,0,0,0] => 1 [1,1,1,0,0,1,1,0,0,0,1,0] => 2 [1,1,1,0,0,1,1,0,0,1,0,0] => 3 [1,1,1,0,0,1,1,0,1,0,0,0] => 3 [1,1,1,0,0,1,1,1,0,0,0,0] => 1 [1,1,1,0,1,0,0,0,1,0,1,0] => 4 [1,1,1,0,1,0,0,0,1,1,0,0] => 1 [1,1,1,0,1,0,0,1,0,0,1,0] => 4 [1,1,1,0,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,1,0,0,1,1,0,0,0] => 1 [1,1,1,0,1,0,1,0,0,0,1,0] => 4 [1,1,1,0,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,1,0,1,0,0,0] => 3 [1,1,1,0,1,0,1,1,0,0,0,0] => 1 [1,1,1,0,1,1,0,0,0,0,1,0] => 2 [1,1,1,0,1,1,0,0,0,1,0,0] => 3 [1,1,1,0,1,1,0,0,1,0,0,0] => 3 [1,1,1,0,1,1,0,1,0,0,0,0] => 3 [1,1,1,0,1,1,1,0,0,0,0,0] => 1 [1,1,1,1,0,0,0,0,1,0,1,0] => 3 [1,1,1,1,0,0,0,0,1,1,0,0] => 1 [1,1,1,1,0,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,0,0,1,0,1,0,0] => 3 [1,1,1,1,0,0,0,1,1,0,0,0] => 1 [1,1,1,1,0,0,1,0,0,0,1,0] => 3 [1,1,1,1,0,0,1,0,0,1,0,0] => 3 [1,1,1,1,0,0,1,0,1,0,0,0] => 3 [1,1,1,1,0,0,1,1,0,0,0,0] => 1 [1,1,1,1,0,1,0,0,0,0,1,0] => 3 [1,1,1,1,0,1,0,0,0,1,0,0] => 3 [1,1,1,1,0,1,0,0,1,0,0,0] => 3 [1,1,1,1,0,1,0,1,0,0,0,0] => 3 [1,1,1,1,0,1,1,0,0,0,0,0] => 1 [1,1,1,1,1,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,0,0,0,0,1,0,0] => 2 [1,1,1,1,1,0,0,0,1,0,0,0] => 2 [1,1,1,1,1,0,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,1,0,0,0,0,0] => 2 [1,1,1,1,1,1,0,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7 [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2 [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6 [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3 [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1 [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6 [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 6 [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5 [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1 [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4 [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2 [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3 [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1 [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6 [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 6 [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3 [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1 [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2 [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5 [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 5 [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1 [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3 [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1 [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3 [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3 [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1 [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5 [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5 [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 5 [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1 [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2 [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2 [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2 [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4 [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1 [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5 [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4 [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3 [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3 [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1 [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6 [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5 [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 6 [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5 [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1 [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2 [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5 [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3 [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1 [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3 [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5 [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 5 [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1 [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 5 [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 5 [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3 [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1 [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2 [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2 [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4 [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4 [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1 [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4 [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1 [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2 [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3 [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1 [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4 [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1 [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4 [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3 [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3 [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3 [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1 [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5 [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1 [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5 [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3 [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 5 [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3 [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3 [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1 [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2 [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4 [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4 [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4 [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1 [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3 [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1 [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3 [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3 [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1 [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3 [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3 [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3 [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1 [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4 [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4 [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 4 [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4 [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1 [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2 [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2 [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2 [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3 [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6 [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5 [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1 [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1 [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5 [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5 [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1 [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2 [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2 [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 4 [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1 [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4 [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3 [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1 [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 5 [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 5 [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3 [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1 [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 4 [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4 [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1 [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1 [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3 [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3 [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1 [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 4 [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4 [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 4 [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1 [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2 [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2 [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2 [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3 [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1 [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6 [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1 [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2 [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5 [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1 [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3 [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5 [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1 [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2 [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2 [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 4 [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1 [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6 [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5 [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1 [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5 [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 5 [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1 [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2 [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4 [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 4 [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1 [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3 [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1 [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 5 [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 5 [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1 [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 4 [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 4 [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 4 [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1 [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2 [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2 [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 4 [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3 [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1 [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4 [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1 [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2 [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 3 [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1 [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5 [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1 [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 5 [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3 [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1 [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2 [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 4 [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1 [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5 [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1 [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 5 [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1 [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4 [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4 [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1 [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2 [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 4 [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 4 [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3 [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1 [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3 [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1 [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3 [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3 [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1 [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4 [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 4 [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 4 [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1 [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 4 [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 4 [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4 [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3 [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1 [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2 [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2 [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2 [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 3 [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 3 [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1 [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5 [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1 [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2 [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4 [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1 [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3 [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1 [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4 [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 4 [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1 [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2 [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2 [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3 [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1 [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5 [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1 [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2 [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4 [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1 [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5 [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1 [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4 [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 4 [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1 [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2 [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 4 [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3 [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1 [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3 [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1 [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4 [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 4 [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1 [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 4 [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 4 [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3 [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1 [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2 [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2 [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 3 [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3 [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1 [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5 [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1 [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2 [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4 [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1 [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5 [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1 [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4 [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4 [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1 [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2 [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3 [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1 [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5 [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1 [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4 [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4 [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1 [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4 [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3 [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1 [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2 [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 4 [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 3 [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 3 [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1 [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3 [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1 [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4 [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4 [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1 [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 4 [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 4 [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3 [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1 [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4 [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4 [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3 [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3 [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1 [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2 [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2 [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 3 [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 3 [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 3 [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1 [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4 [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1 [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2 [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 3 [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1 [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4 [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1 [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4 [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3 [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1 [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2 [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 3 [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 3 [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1 [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4 [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1 [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4 [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 3 [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1 [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4 [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 3 [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 3 [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1 [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2 [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 3 [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 3 [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 3 [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1 [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4 [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1 [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4 [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3 [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1 [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4 [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3 [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 3 [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1 [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4 [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3 [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 3 [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3 [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1 [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2 [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 3 [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 3 [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 3 [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 3 [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1 [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3 [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1 [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3 [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3 [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1 [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3 [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3 [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3 [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1 [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3 [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3 [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3 [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3 [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1 [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3 [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3 [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3 [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3 [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 3 [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1 [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2 [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2 [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2 [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2 [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2 [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1 ----------------------------------------------------------------------------- Created: Apr 06, 2018 at 21:39 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Dec 05, 2020 at 18:41 by Martin Rubey