***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew <info@findstat.org> * * * * 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: St001502 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. We use the code below to translate them to Dyck paths. The algebras where the statistic returns 0 are exactly the higher Auslander algebras and are of special interest. It seems like they are counted by the number of divisors function. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0,1,0] => 0 [1,1,0,0] => 0 [1,0,1,0,1,0] => 0 [1,0,1,1,0,0] => 1 [1,1,0,0,1,0] => 1 [1,1,0,1,0,0] => 0 [1,1,1,0,0,0] => 0 [1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,1,0,0] => 3 [1,0,1,1,0,0,1,0] => 3 [1,0,1,1,0,1,0,0] => 1 [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] => 2 [1,1,0,1,0,1,0,0] => 0 [1,1,0,1,1,0,0,0] => 2 [1,1,1,0,0,0,1,0] => 1 [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] => 0 [1,0,1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,0,1,1,0,0] => 5 [1,0,1,0,1,1,0,0,1,0] => 5 [1,0,1,0,1,1,0,1,0,0] => 1 [1,0,1,0,1,1,1,0,0,0] => 3 [1,0,1,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,0,1,1,0,0] => 3 [1,0,1,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,1,0,0] => 3 [1,0,1,1,0,1,1,0,0,0] => 2 [1,0,1,1,1,0,0,0,1,0] => 3 [1,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,0] => 5 [1,1,0,0,1,0,1,1,0,0] => 3 [1,1,0,0,1,1,0,0,1,0] => 3 [1,1,0,0,1,1,0,1,0,0] => 2 [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] => 3 [1,1,0,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,0] => 0 [1,1,0,1,0,1,1,0,0,0] => 4 [1,1,0,1,1,0,0,0,1,0] => 3 [1,1,0,1,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,0,0] => 4 [1,1,0,1,1,1,0,0,0,0] => 2 [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] => 4 [1,1,1,0,0,1,1,0,0,0] => 2 [1,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,1,0,0,0] => 0 [1,1,1,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,0,0,0,1,0] => 1 [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] => 0 [1,0,1,0,1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,0,1,0,1,1,0,0] => 7 [1,0,1,0,1,0,1,1,0,0,1,0] => 7 [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] => 5 [1,0,1,0,1,1,0,0,1,0,1,0] => 7 [1,0,1,0,1,1,0,0,1,1,0,0] => 5 [1,0,1,0,1,1,0,1,0,0,1,0] => 6 [1,0,1,0,1,1,0,1,0,1,0,0] => 1 [1,0,1,0,1,1,0,1,1,0,0,0] => 3 [1,0,1,0,1,1,1,0,0,0,1,0] => 5 [1,0,1,0,1,1,1,0,0,1,0,0] => 3 [1,0,1,0,1,1,1,0,1,0,0,0] => 3 [1,0,1,0,1,1,1,1,0,0,0,0] => 3 [1,0,1,1,0,0,1,0,1,0,1,0] => 7 [1,0,1,1,0,0,1,0,1,1,0,0] => 5 [1,0,1,1,0,0,1,1,0,0,1,0] => 5 [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] => 3 [1,0,1,1,0,1,0,0,1,0,1,0] => 6 [1,0,1,1,0,1,0,0,1,1,0,0] => 5 [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] => 5 [1,0,1,1,0,1,0,1,1,0,0,0] => 4 [1,0,1,1,0,1,1,0,0,0,1,0] => 5 [1,0,1,1,0,1,1,0,0,1,0,0] => 3 [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] => 2 [1,0,1,1,1,0,0,0,1,0,1,0] => 5 [1,0,1,1,1,0,0,0,1,1,0,0] => 3 [1,0,1,1,1,0,0,1,0,0,1,0] => 5 [1,0,1,1,1,0,0,1,0,1,0,0] => 4 [1,0,1,1,1,0,0,1,1,0,0,0] => 2 [1,0,1,1,1,0,1,0,0,0,1,0] => 5 [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] => 1 [1,0,1,1,1,0,1,1,0,0,0,0] => 2 [1,0,1,1,1,1,0,0,0,0,1,0] => 3 [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] => 2 [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] => 7 [1,1,0,0,1,0,1,0,1,1,0,0] => 5 [1,1,0,0,1,0,1,1,0,0,1,0] => 5 [1,1,0,0,1,0,1,1,0,1,0,0] => 3 [1,1,0,0,1,0,1,1,1,0,0,0] => 3 [1,1,0,0,1,1,0,0,1,0,1,0] => 5 [1,1,0,0,1,1,0,0,1,1,0,0] => 3 [1,1,0,0,1,1,0,1,0,0,1,0] => 5 [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] => 2 [1,1,0,0,1,1,1,0,0,0,1,0] => 3 [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] => 2 [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] => 6 [1,1,0,1,0,0,1,0,1,1,0,0] => 5 [1,1,0,1,0,0,1,1,0,0,1,0] => 5 [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] => 3 [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] => 3 [1,1,0,1,0,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,1,0,1,0,0] => 0 [1,1,0,1,0,1,0,1,1,0,0,0] => 6 [1,1,0,1,0,1,1,0,0,0,1,0] => 3 [1,1,0,1,0,1,1,0,0,1,0,0] => 5 [1,1,0,1,0,1,1,0,1,0,0,0] => 6 [1,1,0,1,0,1,1,1,0,0,0,0] => 4 [1,1,0,1,1,0,0,0,1,0,1,0] => 5 [1,1,0,1,1,0,0,0,1,1,0,0] => 3 [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] => 5 [1,1,0,1,1,0,0,1,1,0,0,0] => 4 [1,1,0,1,1,0,1,0,0,0,1,0] => 3 [1,1,0,1,1,0,1,0,0,1,0,0] => 6 [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] => 4 [1,1,0,1,1,1,0,0,0,0,1,0] => 3 [1,1,0,1,1,1,0,0,0,1,0,0] => 4 [1,1,0,1,1,1,0,0,1,0,0,0] => 4 [1,1,0,1,1,1,0,1,0,0,0,0] => 4 [1,1,0,1,1,1,1,0,0,0,0,0] => 2 [1,1,1,0,0,0,1,0,1,0,1,0] => 5 [1,1,1,0,0,0,1,0,1,1,0,0] => 3 [1,1,1,0,0,0,1,1,0,0,1,0] => 3 [1,1,1,0,0,0,1,1,0,1,0,0] => 2 [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] => 5 [1,1,1,0,0,1,0,0,1,1,0,0] => 3 [1,1,1,0,0,1,0,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,0,1,0,0] => 6 [1,1,1,0,0,1,0,1,1,0,0,0] => 4 [1,1,1,0,0,1,1,0,0,0,1,0] => 3 [1,1,1,0,0,1,1,0,0,1,0,0] => 4 [1,1,1,0,0,1,1,0,1,0,0,0] => 4 [1,1,1,0,0,1,1,1,0,0,0,0] => 2 [1,1,1,0,1,0,0,0,1,0,1,0] => 5 [1,1,1,0,1,0,0,0,1,1,0,0] => 3 [1,1,1,0,1,0,0,1,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,0,1,0,0] => 6 [1,1,1,0,1,0,0,1,1,0,0,0] => 4 [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] => 2 [1,1,1,0,1,1,0,0,0,0,1,0] => 3 [1,1,1,0,1,1,0,0,0,1,0,0] => 4 [1,1,1,0,1,1,0,0,1,0,0,0] => 4 [1,1,1,0,1,1,0,1,0,0,0,0] => 2 [1,1,1,0,1,1,1,0,0,0,0,0] => 2 [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] => 4 [1,1,1,1,0,0,0,1,1,0,0,0] => 2 [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] => 4 [1,1,1,1,0,0,1,0,1,0,0,0] => 2 [1,1,1,1,0,0,1,1,0,0,0,0] => 2 [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] => 4 [1,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,1,0,0,0,0] => 2 [1,1,1,1,0,1,1,0,0,0,0,0] => 2 [1,1,1,1,1,0,0,0,0,0,1,0] => 1 [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] => 0 [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9 [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 9 [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5 [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7 [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 9 [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 7 [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 8 [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1 [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5 [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 7 [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5 [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] => 5 [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 9 [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 7 [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 7 [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 5 [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5 [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 8 [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 7 [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 5 [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] => 4 [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 7 [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] => 4 [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3 [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7 [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5 [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 7 [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4 [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3 [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 7 [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 4 [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1 [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3 [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 5 [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3 [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3 [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3 [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3 [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 9 [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 7 [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 7 [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5 [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5 [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 7 [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5 [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 7 [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] => 3 [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 5 [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3 [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] => 3 [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 8 [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 7 [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 7 [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4 [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5 [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 5 [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] => 7 [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6 [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5 [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] => 6 [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 4 [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 7 [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 5 [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 6 [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] => 4 [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] => 6 [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] => 4 [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 5 [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4 [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] => 2 [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7 [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5 [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 5 [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] => 3 [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 7 [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 5 [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5 [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6 [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 4 [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 5 [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4 [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 4 [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2 [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 7 [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 5 [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] => 6 [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 4 [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4 [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] => 5 [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] => 2 [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2 [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 5 [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3 [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 5 [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4 [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2 [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 5 [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 4 [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2 [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 5 [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] => 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] => 2 [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3 [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] => 2 [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] => 9 [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 7 [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 7 [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] => 5 [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 7 [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 5 [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 7 [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4 [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3 [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 5 [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3 [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3 [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3 [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 7 [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 5 [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5 [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] => 3 [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 7 [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 5 [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] => 6 [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 4 [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 5 [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] => 2 [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 5 [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3 [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5 [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 4 [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2 [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 5 [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] => 2 [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2 [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3 [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] => 2 [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] => 8 [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 7 [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 7 [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4 [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5 [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 7 [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 5 [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 6 [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] => 3 [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 5 [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 3 [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3 [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3 [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5 [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 5 [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 5 [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1 [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3 [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] => 5 [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0 [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 8 [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 5 [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 7 [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 8 [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6 [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5 [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3 [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4 [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 7 [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 6 [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 5 [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 8 [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] => 6 [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 3 [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6 [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 6 [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 6 [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 4 [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 7 [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 5 [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 5 [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] => 3 [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 6 [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 5 [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4 [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 7 [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 6 [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 5 [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 5 [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 6 [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 4 [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] => 3 [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] => 8 [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 6 [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] => 3 [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] => 4 [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 3 [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 6 [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 6 [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4 [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 4 [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 5 [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 3 [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 5 [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6 [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 4 [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 5 [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 6 [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 4 [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3 [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 6 [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] => 4 [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 4 [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3 [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 4 [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 4 [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 4 [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 4 [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2 [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7 [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 5 [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 5 [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3 [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3 [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 5 [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3 [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 5 [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] => 2 [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3 [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] => 2 [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] => 7 [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 5 [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5 [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3 [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 3 [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] => 3 [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5 [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 8 [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 6 [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 6 [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 6 [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 4 [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 5 [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 3 [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 5 [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 6 [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 4 [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 6 [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 4 [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 4 [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 3 [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 4 [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 4 [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 4 [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2 [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 7 [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 5 [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 5 [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3 [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3 [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] => 3 [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5 [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 8 [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 6 [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 6 [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 6 [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 4 [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4 [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3 [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] => 4 [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1 [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] => 0 [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 4 [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3 [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3 [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 4 [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4 [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2 [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 5 [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 3 [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 5 [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 6 [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 4 [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 6 [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 4 [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 4 [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3 [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] => 4 [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2 [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 3 [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4 [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 4 [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 4 [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2 [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2 [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5 [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3 [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3 [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2 [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] => 5 [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 3 [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3 [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 6 [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 4 [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 3 [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 4 [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 4 [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 2 [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5 [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 3 [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 6 [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 4 [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3 [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4 [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4 [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 3 [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 4 [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 4 [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2 [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2 [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 5 [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3 [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 6 [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 4 [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3 [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4 [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4 [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3 [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4 [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4 [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0 [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2 [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3 [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 4 [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 4 [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2 [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2 [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2 [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] => 4 [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 2 [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] => 4 [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2 [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 2 [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] => 4 [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2 [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 2 [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] => 4 [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2 [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2 [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2 [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1 [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] => 0 ----------------------------------------------------------------------------- Created: Nov 17, 2019 at 19:14 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Nov 17, 2019 at 19:14 by Rene Marczinzik