***************************************************************************** * 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: St001167 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. The top of a module is the cokernel of the inclusion of the radical of the module into the module. For Nakayama algebras with at most 8 simple modules, the statistic also coincides with the number of simple modules with projective dimension at least 3 in the corresponding Nakayama algebra. ----------------------------------------------------------------------------- References: [1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. [[zbMATH:06820683]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 0 [1,0,1,0] => 0 [1,1,0,0] => 0 [1,0,1,0,1,0] => 1 [1,0,1,1,0,0] => 0 [1,1,0,0,1,0] => 0 [1,1,0,1,0,0] => 0 [1,1,1,0,0,0] => 0 [1,0,1,0,1,0,1,0] => 2 [1,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,0] => 0 [1,0,1,1,0,1,0,0] => 1 [1,0,1,1,1,0,0,0] => 0 [1,1,0,0,1,0,1,0] => 1 [1,1,0,0,1,1,0,0] => 0 [1,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,0] => 1 [1,1,0,1,1,0,0,0] => 0 [1,1,1,0,0,0,1,0] => 0 [1,1,1,0,0,1,0,0] => 0 [1,1,1,0,1,0,0,0] => 0 [1,1,1,1,0,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,0] => 3 [1,0,1,0,1,0,1,1,0,0] => 2 [1,0,1,0,1,1,0,0,1,0] => 1 [1,0,1,0,1,1,0,1,0,0] => 2 [1,0,1,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,0,1,0,1,0] => 1 [1,0,1,1,0,0,1,1,0,0] => 0 [1,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,1,0,0] => 2 [1,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,0,0,1,0] => 0 [1,0,1,1,1,0,0,1,0,0] => 0 [1,0,1,1,1,0,1,0,0,0] => 1 [1,0,1,1,1,1,0,0,0,0] => 0 [1,1,0,0,1,0,1,0,1,0] => 2 [1,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,1,0,0,1,0] => 0 [1,1,0,0,1,1,0,1,0,0] => 1 [1,1,0,0,1,1,1,0,0,0] => 0 [1,1,0,1,0,0,1,0,1,0] => 2 [1,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,1,0,0] => 2 [1,1,0,1,0,1,1,0,0,0] => 1 [1,1,0,1,1,0,0,0,1,0] => 0 [1,1,0,1,1,0,0,1,0,0] => 1 [1,1,0,1,1,0,1,0,0,0] => 1 [1,1,0,1,1,1,0,0,0,0] => 0 [1,1,1,0,0,0,1,0,1,0] => 1 [1,1,1,0,0,0,1,1,0,0] => 0 [1,1,1,0,0,1,0,0,1,0] => 1 [1,1,1,0,0,1,0,1,0,0] => 1 [1,1,1,0,0,1,1,0,0,0] => 0 [1,1,1,0,1,0,0,0,1,0] => 1 [1,1,1,0,1,0,0,1,0,0] => 1 [1,1,1,0,1,0,1,0,0,0] => 1 [1,1,1,0,1,1,0,0,0,0] => 0 [1,1,1,1,0,0,0,0,1,0] => 0 [1,1,1,1,0,0,0,1,0,0] => 0 [1,1,1,1,0,0,1,0,0,0] => 0 [1,1,1,1,0,1,0,0,0,0] => 0 [1,1,1,1,1,0,0,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,0] => 4 [1,0,1,0,1,0,1,0,1,1,0,0] => 3 [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] => 3 [1,0,1,0,1,0,1,1,1,0,0,0] => 2 [1,0,1,0,1,1,0,0,1,0,1,0] => 2 [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] => 3 [1,0,1,0,1,1,0,1,0,1,0,0] => 3 [1,0,1,0,1,1,0,1,1,0,0,0] => 2 [1,0,1,0,1,1,1,0,0,0,1,0] => 1 [1,0,1,0,1,1,1,0,0,1,0,0] => 1 [1,0,1,0,1,1,1,0,1,0,0,0] => 2 [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] => 2 [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] => 0 [1,0,1,1,0,0,1,1,0,1,0,0] => 1 [1,0,1,1,0,0,1,1,1,0,0,0] => 0 [1,0,1,1,0,1,0,0,1,0,1,0] => 3 [1,0,1,1,0,1,0,0,1,1,0,0] => 2 [1,0,1,1,0,1,0,1,0,0,1,0] => 3 [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] => 2 [1,0,1,1,0,1,1,0,0,0,1,0] => 1 [1,0,1,1,0,1,1,0,0,1,0,0] => 2 [1,0,1,1,0,1,1,0,1,0,0,0] => 2 [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] => 1 [1,0,1,1,1,0,0,0,1,1,0,0] => 0 [1,0,1,1,1,0,0,1,0,0,1,0] => 1 [1,0,1,1,1,0,0,1,0,1,0,0] => 1 [1,0,1,1,1,0,0,1,1,0,0,0] => 0 [1,0,1,1,1,0,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,0,1,0,0,0] => 2 [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] => 0 [1,0,1,1,1,1,0,0,0,1,0,0] => 0 [1,0,1,1,1,1,0,0,1,0,0,0] => 0 [1,0,1,1,1,1,0,1,0,0,0,0] => 1 [1,0,1,1,1,1,1,0,0,0,0,0] => 0 [1,1,0,0,1,0,1,0,1,0,1,0] => 3 [1,1,0,0,1,0,1,0,1,1,0,0] => 2 [1,1,0,0,1,0,1,1,0,0,1,0] => 1 [1,1,0,0,1,0,1,1,0,1,0,0] => 2 [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] => 1 [1,1,0,0,1,1,0,0,1,1,0,0] => 0 [1,1,0,0,1,1,0,1,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,1,0,0] => 2 [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] => 0 [1,1,0,0,1,1,1,0,0,1,0,0] => 0 [1,1,0,0,1,1,1,0,1,0,0,0] => 1 [1,1,0,0,1,1,1,1,0,0,0,0] => 0 [1,1,0,1,0,0,1,0,1,0,1,0] => 3 [1,1,0,1,0,0,1,0,1,1,0,0] => 2 [1,1,0,1,0,0,1,1,0,0,1,0] => 1 [1,1,0,1,0,0,1,1,0,1,0,0] => 2 [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] => 3 [1,1,0,1,0,1,0,0,1,1,0,0] => 2 [1,1,0,1,0,1,0,1,0,0,1,0] => 3 [1,1,0,1,0,1,0,1,0,1,0,0] => 3 [1,1,0,1,0,1,0,1,1,0,0,0] => 2 [1,1,0,1,0,1,1,0,0,0,1,0] => 1 [1,1,0,1,0,1,1,0,0,1,0,0] => 2 [1,1,0,1,0,1,1,0,1,0,0,0] => 2 [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] => 1 [1,1,0,1,1,0,0,0,1,1,0,0] => 0 [1,1,0,1,1,0,0,1,0,0,1,0] => 2 [1,1,0,1,1,0,0,1,0,1,0,0] => 2 [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] => 2 [1,1,0,1,1,0,1,0,0,1,0,0] => 2 [1,1,0,1,1,0,1,0,1,0,0,0] => 2 [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] => 0 [1,1,0,1,1,1,0,0,0,1,0,0] => 0 [1,1,0,1,1,1,0,0,1,0,0,0] => 1 [1,1,0,1,1,1,0,1,0,0,0,0] => 1 [1,1,0,1,1,1,1,0,0,0,0,0] => 0 [1,1,1,0,0,0,1,0,1,0,1,0] => 2 [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] => 0 [1,1,1,0,0,0,1,1,0,1,0,0] => 1 [1,1,1,0,0,0,1,1,1,0,0,0] => 0 [1,1,1,0,0,1,0,0,1,0,1,0] => 2 [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] => 2 [1,1,1,0,0,1,0,1,0,1,0,0] => 2 [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] => 0 [1,1,1,0,0,1,1,0,0,1,0,0] => 1 [1,1,1,0,0,1,1,0,1,0,0,0] => 1 [1,1,1,0,0,1,1,1,0,0,0,0] => 0 [1,1,1,0,1,0,0,0,1,0,1,0] => 2 [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] => 2 [1,1,1,0,1,0,0,1,0,1,0,0] => 2 [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] => 2 [1,1,1,0,1,0,1,0,0,1,0,0] => 2 [1,1,1,0,1,0,1,0,1,0,0,0] => 2 [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] => 0 [1,1,1,0,1,1,0,0,0,1,0,0] => 1 [1,1,1,0,1,1,0,0,1,0,0,0] => 1 [1,1,1,0,1,1,0,1,0,0,0,0] => 1 [1,1,1,0,1,1,1,0,0,0,0,0] => 0 [1,1,1,1,0,0,0,0,1,0,1,0] => 1 [1,1,1,1,0,0,0,0,1,1,0,0] => 0 [1,1,1,1,0,0,0,1,0,0,1,0] => 1 [1,1,1,1,0,0,0,1,0,1,0,0] => 1 [1,1,1,1,0,0,0,1,1,0,0,0] => 0 [1,1,1,1,0,0,1,0,0,0,1,0] => 1 [1,1,1,1,0,0,1,0,0,1,0,0] => 1 [1,1,1,1,0,0,1,0,1,0,0,0] => 1 [1,1,1,1,0,0,1,1,0,0,0,0] => 0 [1,1,1,1,0,1,0,0,0,0,1,0] => 1 [1,1,1,1,0,1,0,0,0,1,0,0] => 1 [1,1,1,1,0,1,0,0,1,0,0,0] => 1 [1,1,1,1,0,1,0,1,0,0,0,0] => 1 [1,1,1,1,0,1,1,0,0,0,0,0] => 0 [1,1,1,1,1,0,0,0,0,0,1,0] => 0 [1,1,1,1,1,0,0,0,0,1,0,0] => 0 [1,1,1,1,1,0,0,0,1,0,0,0] => 0 [1,1,1,1,1,0,0,1,0,0,0,0] => 0 [1,1,1,1,1,0,1,0,0,0,0,0] => 0 [1,1,1,1,1,1,0,0,0,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 5 [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4 [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3 [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4 [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3 [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] => 2 [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4 [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3 [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] => 3 [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2 [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3 [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2 [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1 [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2 [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] => 4 [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3 [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4 [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4 [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3 [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] => 3 [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3 [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2 [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2 [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] => 2 [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2 [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] => 3 [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3 [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3 [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2 [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1 [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1 [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1 [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2 [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] => 3 [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2 [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1 [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2 [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] => 1 [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0 [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2 [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] => 0 [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0 [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1 [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0 [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 4 [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3 [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] => 3 [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2 [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4 [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3 [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] => 4 [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3 [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] => 3 [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] => 2 [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2 [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] => 3 [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3 [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2 [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3 [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3 [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] => 2 [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1 [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1 [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2 [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2 [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] => 2 [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] => 0 [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1 [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0 [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2 [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] => 2 [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2 [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] => 0 [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1 [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1 [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0 [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3 [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2 [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3 [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] => 2 [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3 [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] => 2 [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1 [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2 [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2 [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] => 1 [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0 [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1 [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1 [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0 [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1 [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1 [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1 [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0 [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2 [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2 [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] => 0 [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0 [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0 [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0 [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1 [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0 [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4 [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3 [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] => 3 [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2 [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] => 3 [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3 [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2 [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1 [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1 [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2 [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] => 2 [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] => 0 [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 1 [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0 [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2 [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3 [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] => 2 [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1 [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2 [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2 [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] => 1 [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0 [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1 [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 1 [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0 [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2 [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 2 [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] => 0 [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0 [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0 [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1 [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0 [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4 [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3 [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] => 3 [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2 [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2 [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] => 3 [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3 [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2 [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1 [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1 [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2 [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] => 4 [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3 [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] => 3 [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2 [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4 [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3 [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4 [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 4 [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3 [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] => 3 [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2 [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2 [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] => 3 [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 2 [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3 [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3 [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 2 [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1 [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1 [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2 [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2 [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] => 2 [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] => 0 [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1 [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0 [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3 [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2 [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 3 [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] => 2 [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1 [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2 [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2 [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] => 3 [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2 [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 3 [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] => 2 [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3 [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3 [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 2 [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1 [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2 [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 2 [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2 [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] => 1 [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0 [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 1 [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1 [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0 [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2 [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2 [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2 [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] => 2 [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 2 [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2 [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] => 0 [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 0 [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0 [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1 [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1 [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0 [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3 [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2 [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1 [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2 [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] => 1 [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0 [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2 [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 2 [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] => 0 [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0 [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 1 [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0 [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 3 [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2 [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1 [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2 [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] => 3 [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2 [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2 [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1 [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2 [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2 [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] => 1 [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0 [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2 [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2 [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] => 2 [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 2 [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 2 [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] => 0 [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0 [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 1 [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 1 [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0 [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 3 [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2 [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1 [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2 [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] => 3 [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2 [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3 [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 2 [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1 [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2 [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2 [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] => 3 [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2 [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 3 [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 2 [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3 [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] => 2 [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1 [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2 [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2 [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2 [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] => 1 [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0 [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2 [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 2 [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] => 2 [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 2 [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 2 [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] => 2 [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2 [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 2 [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2 [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] => 0 [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 0 [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1 [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1 [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1 [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0 [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2 [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] => 0 [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1 [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0 [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2 [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] => 2 [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2 [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] => 0 [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 1 [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1 [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0 [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2 [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] => 2 [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2 [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] => 2 [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2 [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2 [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] => 0 [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 1 [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 1 [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 1 [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0 [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2 [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] => 2 [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2 [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] => 2 [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2 [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2 [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] => 2 [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2 [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2 [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] => 0 [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1 [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1 [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1 [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1 [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0 [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1 [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0 [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1 [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1 [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0 [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1 [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1 [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1 [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0 [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1 [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1 [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 1 [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1 [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0 [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1 [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1 [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1 [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0 [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 0 [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 0 [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 0 [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0 [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0 ----------------------------------------------------------------------------- Created: Apr 28, 2018 at 12:02 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Dec 17, 2018 at 13:33 by Rene Marczinzik