***************************************************************************** * 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: St001643 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. ----------------------------------------------------------------------------- References: [1] Artenstein, D., González, A., Mata, G. Nearly Frobenius dimension on Frobenius algebras [[arXiv:2011.09790]] ----------------------------------------------------------------------------- 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) A = gap.NakayamaAlgebra(K, gap.GF(3)) injA = gap.IndecInjectiveModules(A) projA = gap.IndecProjectiveModules(A) CoRegA = gap.DirectSumOfQPAModules(injA) RegA = gap.DirectSumOfQPAModules(projA) return gap.Size(gap.HomOverAlgebra(CoRegA, RegA)) ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 3 [1,1,0,0] => 1 [1,0,1,0,1,0] => 5 [1,0,1,1,0,0] => 4 [1,1,0,0,1,0] => 4 [1,1,0,1,0,0] => 3 [1,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,0] => 7 [1,0,1,0,1,1,0,0] => 6 [1,0,1,1,0,0,1,0] => 7 [1,0,1,1,0,1,0,0] => 6 [1,0,1,1,1,0,0,0] => 5 [1,1,0,0,1,0,1,0] => 6 [1,1,0,0,1,1,0,0] => 6 [1,1,0,1,0,0,1,0] => 6 [1,1,0,1,0,1,0,0] => 6 [1,1,0,1,1,0,0,0] => 4 [1,1,1,0,0,0,1,0] => 5 [1,1,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,0,0] => 3 [1,1,1,1,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0] => 9 [1,0,1,0,1,0,1,1,0,0] => 8 [1,0,1,0,1,1,0,0,1,0] => 9 [1,0,1,0,1,1,0,1,0,0] => 8 [1,0,1,0,1,1,1,0,0,0] => 7 [1,0,1,1,0,0,1,0,1,0] => 9 [1,0,1,1,0,0,1,1,0,0] => 9 [1,0,1,1,0,1,0,0,1,0] => 9 [1,0,1,1,0,1,0,1,0,0] => 9 [1,0,1,1,0,1,1,0,0,0] => 7 [1,0,1,1,1,0,0,0,1,0] => 9 [1,0,1,1,1,0,0,1,0,0] => 8 [1,0,1,1,1,0,1,0,0,0] => 7 [1,0,1,1,1,1,0,0,0,0] => 6 [1,1,0,0,1,0,1,0,1,0] => 8 [1,1,0,0,1,0,1,1,0,0] => 7 [1,1,0,0,1,1,0,0,1,0] => 9 [1,1,0,0,1,1,0,1,0,0] => 8 [1,1,0,0,1,1,1,0,0,0] => 8 [1,1,0,1,0,0,1,0,1,0] => 8 [1,1,0,1,0,0,1,1,0,0] => 8 [1,1,0,1,0,1,0,0,1,0] => 9 [1,1,0,1,0,1,0,1,0,0] => 9 [1,1,0,1,0,1,1,0,0,0] => 8 [1,1,0,1,1,0,0,0,1,0] => 8 [1,1,0,1,1,0,0,1,0,0] => 7 [1,1,0,1,1,0,1,0,0,0] => 7 [1,1,0,1,1,1,0,0,0,0] => 5 [1,1,1,0,0,0,1,0,1,0] => 7 [1,1,1,0,0,0,1,1,0,0] => 8 [1,1,1,0,0,1,0,0,1,0] => 7 [1,1,1,0,0,1,0,1,0,0] => 8 [1,1,1,0,0,1,1,0,0,0] => 6 [1,1,1,0,1,0,0,0,1,0] => 7 [1,1,1,0,1,0,0,1,0,0] => 7 [1,1,1,0,1,0,1,0,0,0] => 6 [1,1,1,0,1,1,0,0,0,0] => 4 [1,1,1,1,0,0,0,0,1,0] => 6 [1,1,1,1,0,0,0,1,0,0] => 5 [1,1,1,1,0,0,1,0,0,0] => 4 [1,1,1,1,0,1,0,0,0,0] => 3 [1,1,1,1,1,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,0] => 11 [1,0,1,0,1,0,1,0,1,1,0,0] => 10 [1,0,1,0,1,0,1,1,0,0,1,0] => 11 [1,0,1,0,1,0,1,1,0,1,0,0] => 10 [1,0,1,0,1,0,1,1,1,0,0,0] => 9 [1,0,1,0,1,1,0,0,1,0,1,0] => 11 [1,0,1,0,1,1,0,0,1,1,0,0] => 11 [1,0,1,0,1,1,0,1,0,0,1,0] => 11 [1,0,1,0,1,1,0,1,0,1,0,0] => 11 [1,0,1,0,1,1,0,1,1,0,0,0] => 9 [1,0,1,0,1,1,1,0,0,0,1,0] => 11 [1,0,1,0,1,1,1,0,0,1,0,0] => 10 [1,0,1,0,1,1,1,0,1,0,0,0] => 9 [1,0,1,0,1,1,1,1,0,0,0,0] => 8 [1,0,1,1,0,0,1,0,1,0,1,0] => 11 [1,0,1,1,0,0,1,0,1,1,0,0] => 10 [1,0,1,1,0,0,1,1,0,0,1,0] => 12 [1,0,1,1,0,0,1,1,0,1,0,0] => 11 [1,0,1,1,0,0,1,1,1,0,0,0] => 11 [1,0,1,1,0,1,0,0,1,0,1,0] => 11 [1,0,1,1,0,1,0,0,1,1,0,0] => 11 [1,0,1,1,0,1,0,1,0,0,1,0] => 12 [1,0,1,1,0,1,0,1,0,1,0,0] => 12 [1,0,1,1,0,1,0,1,1,0,0,0] => 11 [1,0,1,1,0,1,1,0,0,0,1,0] => 11 [1,0,1,1,0,1,1,0,0,1,0,0] => 10 [1,0,1,1,0,1,1,0,1,0,0,0] => 10 [1,0,1,1,0,1,1,1,0,0,0,0] => 8 [1,0,1,1,1,0,0,0,1,0,1,0] => 11 [1,0,1,1,1,0,0,0,1,1,0,0] => 12 [1,0,1,1,1,0,0,1,0,0,1,0] => 11 [1,0,1,1,1,0,0,1,0,1,0,0] => 12 [1,0,1,1,1,0,0,1,1,0,0,0] => 10 [1,0,1,1,1,0,1,0,0,0,1,0] => 11 [1,0,1,1,1,0,1,0,0,1,0,0] => 11 [1,0,1,1,1,0,1,0,1,0,0,0] => 10 [1,0,1,1,1,0,1,1,0,0,0,0] => 8 [1,0,1,1,1,1,0,0,0,0,1,0] => 11 [1,0,1,1,1,1,0,0,0,1,0,0] => 10 [1,0,1,1,1,1,0,0,1,0,0,0] => 9 [1,0,1,1,1,1,0,1,0,0,0,0] => 8 [1,0,1,1,1,1,1,0,0,0,0,0] => 7 [1,1,0,0,1,0,1,0,1,0,1,0] => 10 [1,1,0,0,1,0,1,0,1,1,0,0] => 9 [1,1,0,0,1,0,1,1,0,0,1,0] => 10 [1,1,0,0,1,0,1,1,0,1,0,0] => 9 [1,1,0,0,1,0,1,1,1,0,0,0] => 8 [1,1,0,0,1,1,0,0,1,0,1,0] => 11 [1,1,0,0,1,1,0,0,1,1,0,0] => 11 [1,1,0,0,1,1,0,1,0,0,1,0] => 11 [1,1,0,0,1,1,0,1,0,1,0,0] => 11 [1,1,0,0,1,1,0,1,1,0,0,0] => 9 [1,1,0,0,1,1,1,0,0,0,1,0] => 12 [1,1,0,0,1,1,1,0,0,1,0,0] => 11 [1,1,0,0,1,1,1,0,1,0,0,0] => 10 [1,1,0,0,1,1,1,1,0,0,0,0] => 10 [1,1,0,1,0,0,1,0,1,0,1,0] => 10 [1,1,0,1,0,0,1,0,1,1,0,0] => 9 [1,1,0,1,0,0,1,1,0,0,1,0] => 11 [1,1,0,1,0,0,1,1,0,1,0,0] => 10 [1,1,0,1,0,0,1,1,1,0,0,0] => 10 [1,1,0,1,0,1,0,0,1,0,1,0] => 11 [1,1,0,1,0,1,0,0,1,1,0,0] => 11 [1,1,0,1,0,1,0,1,0,0,1,0] => 12 [1,1,0,1,0,1,0,1,0,1,0,0] => 12 [1,1,0,1,0,1,0,1,1,0,0,0] => 11 [1,1,0,1,0,1,1,0,0,0,1,0] => 12 [1,1,0,1,0,1,1,0,0,1,0,0] => 11 [1,1,0,1,0,1,1,0,1,0,0,0] => 11 [1,1,0,1,0,1,1,1,0,0,0,0] => 10 [1,1,0,1,1,0,0,0,1,0,1,0] => 10 [1,1,0,1,1,0,0,0,1,1,0,0] => 11 [1,1,0,1,1,0,0,1,0,0,1,0] => 10 [1,1,0,1,1,0,0,1,0,1,0,0] => 11 [1,1,0,1,1,0,0,1,1,0,0,0] => 9 [1,1,0,1,1,0,1,0,0,0,1,0] => 11 [1,1,0,1,1,0,1,0,0,1,0,0] => 11 [1,1,0,1,1,0,1,0,1,0,0,0] => 10 [1,1,0,1,1,0,1,1,0,0,0,0] => 9 [1,1,0,1,1,1,0,0,0,0,1,0] => 10 [1,1,0,1,1,1,0,0,0,1,0,0] => 9 [1,1,0,1,1,1,0,0,1,0,0,0] => 8 [1,1,0,1,1,1,0,1,0,0,0,0] => 8 [1,1,0,1,1,1,1,0,0,0,0,0] => 6 [1,1,1,0,0,0,1,0,1,0,1,0] => 9 [1,1,1,0,0,0,1,0,1,1,0,0] => 8 [1,1,1,0,0,0,1,1,0,0,1,0] => 11 [1,1,1,0,0,0,1,1,0,1,0,0] => 10 [1,1,1,0,0,0,1,1,1,0,0,0] => 11 [1,1,1,0,0,1,0,0,1,0,1,0] => 9 [1,1,1,0,0,1,0,0,1,1,0,0] => 9 [1,1,1,0,0,1,0,1,0,0,1,0] => 11 [1,1,1,0,0,1,0,1,0,1,0,0] => 11 [1,1,1,0,0,1,0,1,1,0,0,0] => 11 [1,1,1,0,0,1,1,0,0,0,1,0] => 10 [1,1,1,0,0,1,1,0,0,1,0,0] => 9 [1,1,1,0,0,1,1,0,1,0,0,0] => 10 [1,1,1,0,0,1,1,1,0,0,0,0] => 8 [1,1,1,0,1,0,0,0,1,0,1,0] => 9 [1,1,1,0,1,0,0,0,1,1,0,0] => 10 [1,1,1,0,1,0,0,1,0,0,1,0] => 10 [1,1,1,0,1,0,0,1,0,1,0,0] => 11 [1,1,1,0,1,0,0,1,1,0,0,0] => 10 [1,1,1,0,1,0,1,0,0,0,1,0] => 10 [1,1,1,0,1,0,1,0,0,1,0,0] => 10 [1,1,1,0,1,0,1,0,1,0,0,0] => 10 [1,1,1,0,1,0,1,1,0,0,0,0] => 8 [1,1,1,0,1,1,0,0,0,0,1,0] => 9 [1,1,1,0,1,1,0,0,0,1,0,0] => 8 [1,1,1,0,1,1,0,0,1,0,0,0] => 8 [1,1,1,0,1,1,0,1,0,0,0,0] => 7 [1,1,1,0,1,1,1,0,0,0,0,0] => 5 [1,1,1,1,0,0,0,0,1,0,1,0] => 8 [1,1,1,1,0,0,0,0,1,1,0,0] => 10 [1,1,1,1,0,0,0,1,0,0,1,0] => 8 [1,1,1,1,0,0,0,1,0,1,0,0] => 10 [1,1,1,1,0,0,0,1,1,0,0,0] => 8 [1,1,1,1,0,0,1,0,0,0,1,0] => 8 [1,1,1,1,0,0,1,0,0,1,0,0] => 9 [1,1,1,1,0,0,1,0,1,0,0,0] => 8 [1,1,1,1,0,0,1,1,0,0,0,0] => 6 [1,1,1,1,0,1,0,0,0,0,1,0] => 8 [1,1,1,1,0,1,0,0,0,1,0,0] => 8 [1,1,1,1,0,1,0,0,1,0,0,0] => 7 [1,1,1,1,0,1,0,1,0,0,0,0] => 6 [1,1,1,1,0,1,1,0,0,0,0,0] => 4 [1,1,1,1,1,0,0,0,0,0,1,0] => 7 [1,1,1,1,1,0,0,0,0,1,0,0] => 6 [1,1,1,1,1,0,0,0,1,0,0,0] => 5 [1,1,1,1,1,0,0,1,0,0,0,0] => 4 [1,1,1,1,1,0,1,0,0,0,0,0] => 3 [1,1,1,1,1,1,0,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 12 [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 13 [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 12 [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 13 [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 13 [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 13 [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 11 [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 13 [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 12 [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12 [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 14 [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 13 [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 13 [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 13 [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 14 [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 14 [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 13 [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 13 [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 12 [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 13 [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 14 [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 13 [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 13 [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 13 [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13 [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 12 [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 11 [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10 [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 9 [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 13 [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 12 [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 12 [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 14 [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 15 [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 13 [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 13 [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 12 [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 13 [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 14 [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 14 [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 15 [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 14 [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 13 [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 12 [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 13 [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 11 [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 11 [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 9 [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 13 [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 15 [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 13 [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 13 [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11 [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 9 [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 13 [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 15 [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 13 [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 13 [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 13 [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 11 [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 13 [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12 [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 11 [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 9 [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 13 [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 12 [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 11 [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10 [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 9 [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8 [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 12 [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 11 [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 12 [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 11 [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 10 [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 12 [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 12 [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 12 [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 12 [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 10 [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 12 [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 9 [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 13 [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 12 [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 13 [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 14 [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 14 [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 12 [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 10 [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 14 [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 13 [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 14 [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 13 [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 11 [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 15 [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 14 [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 13 [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 12 [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 12 [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 12 [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 11 [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 11 [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 14 [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 13 [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 12 [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 13 [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 14 [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 14 [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 15 [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 15 [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 14 [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 15 [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 14 [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 14 [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 13 [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 14 [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 15 [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 13 [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 15 [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 14 [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 13 [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 13 [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 12 [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 14 [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 14 [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 15 [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 14 [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 12 [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 14 [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12 [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 12 [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 14 [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 12 [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 11 [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 9 [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 9 [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 7 [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 11 [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 10 [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 10 [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 15 [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 14 [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 11 [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 10 [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 11 [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 13 [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 14 [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 14 [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 14 [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 13 [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 13 [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 13 [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 13 [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 11 [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 10 [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 12 [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 14 [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 14 [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 13 [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 12 [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 13 [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 14 [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 13 [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 14 [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 14 [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 14 [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 13 [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 13 [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 12 [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 12 [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 10 [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 13 [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 12 [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12 [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11 [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 10 [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 9 [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 8 [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 6 [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9 [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13 [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 14 [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 10 [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 12 [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 11 [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 12 [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 12 [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 13 [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11 [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10 [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 12 [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11 [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 12 [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11 [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 11 [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 10 [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 10 [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 9 [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 9 [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 8 [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7 [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 5 [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 12 [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 9 [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12 [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 9 [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11 [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8 [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 9 [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 10 [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 9 [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 6 [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 9 [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 9 [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 8 [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 7 [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6 [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 4 [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8 [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7 [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6 [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 5 [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 4 [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3 [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 14 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 14 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 15 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 14 [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 14 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 14 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 14 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 14 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 16 [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 15 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 15 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 16 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 15 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 15 [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 15 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 15 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 15 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 12 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 11 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 14 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 15 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 14 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 14 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 17 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 15 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 15 [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 15 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 15 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 18 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 18 [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 16 [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 15 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 16 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 15 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 15 [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 15 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 17 [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 10 [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 15 [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 18 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 12 [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 12 [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 11 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 10 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 9 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 14 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 13 [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 14 [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 13 [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 12 [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 14 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 14 [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 15 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 16 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 15 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 15 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 17 [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 16 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 17 [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 15 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 19 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 15 [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13 [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 18 [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 17 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 16 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 15 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 14 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 13 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 13 [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 14 [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 16 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16 [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 15 [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 17 [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 17 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 18 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 18 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 17 [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 17 [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 17 [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 16 [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 18 [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 17 [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 16 [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 18 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 14 [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 17 [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 16 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 17 [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 16 [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 17 [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 10 [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 10 [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 13 [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 12 [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 12 [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 19 [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 16 [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 17 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 17 [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 16 [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 15 [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 15 [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 16 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 14 [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 17 [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 18 [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 14 [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 17 [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 16 [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 17 [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 18 [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 18 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 18 [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 17 [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 15 [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 16 [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 14 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 15 [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 16 [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 13 [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 12 [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 13 [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 11 [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 10 [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 10 [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 9 [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 7 [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 15 [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 16 [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 18 [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 17 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 15 [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 15 [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 14 [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 13 [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 12 [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 10 [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 15 [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 12 [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 9 [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 12 [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 11 [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 10 [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 10 [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 8 [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 6 [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 12 [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 13 [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 14 [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 11 [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 13 [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 12 [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 12 [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 8 [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 14 [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 12 [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 12 [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 10 [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 8 [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 11 [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 10 [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 10 [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 9 [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 8 [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 7 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 5 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 14 [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 10 [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 12 [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 10 [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 8 [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 10 [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 11 [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 9 [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 8 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6 [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 10 [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 10 [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 8 [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 7 [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 6 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 4 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 9 [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 8 [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 7 [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 6 [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 5 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 4 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 3 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 10 [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 10 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 11 [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 11 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 11 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 12 [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 12 [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 11 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 13 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 13 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 16 [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 16 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 17 [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 16 [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 16 [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 11 [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 15 [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 17 [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 17 [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 15 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11 [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 11 [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 12 [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 12 [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 13 [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 13 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 18 [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 18 [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 19 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 18 [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 18 [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 12 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 12 [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 12 ----------------------------------------------------------------------------- Created: Nov 20, 2020 at 09:14 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Nov 20, 2020 at 12:53 by Martin Rubey