***************************************************************************** * 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: St000688 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. The global dimension is given by [[St000684]] and the dominant dimension is given by [[St000685]]. To every Dyck path there is an LNakayama algebra associated as described in [[St000684]]. Dyck paths for which the global dimension and the dominant dimension of the the LNakayama algebra coincide and both dimensions at least $2$ correspond to the LNakayama algebras that are higher Auslander algebras in the sense of [1]. ----------------------------------------------------------------------------- References: [1] Iyama, O. Auslander correspondence [[MathSciNet:2298820]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 0 [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] => 1 [1,1,1,0,0,0] => 0 [1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,1,0,0] => 2 [1,0,1,1,0,0,1,0] => 0 [1,0,1,1,0,1,0,0] => 2 [1,0,1,1,1,0,0,0] => 1 [1,1,0,0,1,0,1,0] => 2 [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] => 1 [1,1,0,1,1,0,0,0] => 1 [1,1,1,0,0,0,1,0] => 1 [1,1,1,0,0,1,0,0] => 1 [1,1,1,0,1,0,0,0] => 1 [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] => 3 [1,0,1,0,1,1,0,0,1,0] => 1 [1,0,1,0,1,1,0,1,0,0] => 3 [1,0,1,0,1,1,1,0,0,0] => 2 [1,0,1,1,0,0,1,0,1,0] => 1 [1,0,1,1,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,0,1,0] => 3 [1,0,1,1,0,1,0,1,0,0] => 2 [1,0,1,1,0,1,1,0,0,0] => 2 [1,0,1,1,1,0,0,0,1,0] => 1 [1,0,1,1,1,0,0,1,0,0] => 1 [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] => 3 [1,1,0,0,1,0,1,1,0,0] => 2 [1,1,0,0,1,1,0,0,1,0] => 1 [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] => 3 [1,1,0,1,0,0,1,1,0,0] => 2 [1,1,0,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,1,0,0] => 0 [1,1,0,1,0,1,1,0,0,0] => 2 [1,1,0,1,1,0,0,0,1,0] => 1 [1,1,0,1,1,0,0,1,0,0] => 2 [1,1,0,1,1,0,1,0,0,0] => 2 [1,1,0,1,1,1,0,0,0,0] => 1 [1,1,1,0,0,0,1,0,1,0] => 2 [1,1,1,0,0,0,1,1,0,0] => 1 [1,1,1,0,0,1,0,0,1,0] => 2 [1,1,1,0,0,1,0,1,0,0] => 2 [1,1,1,0,0,1,1,0,0,0] => 1 [1,1,1,0,1,0,0,0,1,0] => 2 [1,1,1,0,1,0,0,1,0,0] => 2 [1,1,1,0,1,0,1,0,0,0] => 2 [1,1,1,0,1,1,0,0,0,0] => 1 [1,1,1,1,0,0,0,0,1,0] => 1 [1,1,1,1,0,0,0,1,0,0] => 1 [1,1,1,1,0,0,1,0,0,0] => 1 [1,1,1,1,0,1,0,0,0,0] => 1 [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] => 4 [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] => 4 [1,0,1,0,1,0,1,1,1,0,0,0] => 3 [1,0,1,0,1,1,0,0,1,0,1,0] => 0 [1,0,1,0,1,1,0,0,1,1,0,0] => 2 [1,0,1,0,1,1,0,1,0,0,1,0] => 4 [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] => 3 [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] => 3 [1,0,1,0,1,1,1,1,0,0,0,0] => 2 [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] => 2 [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] => 2 [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] => 4 [1,0,1,1,0,1,0,0,1,1,0,0] => 3 [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] => 1 [1,0,1,1,0,1,0,1,1,0,0,0] => 3 [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] => 3 [1,0,1,1,0,1,1,0,1,0,0,0] => 3 [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] => 2 [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] => 2 [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] => 1 [1,0,1,1,1,0,1,0,0,0,1,0] => 3 [1,0,1,1,1,0,1,0,0,1,0,0] => 3 [1,0,1,1,1,0,1,0,1,0,0,0] => 3 [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] => 1 [1,0,1,1,1,1,0,0,0,1,0,0] => 1 [1,0,1,1,1,1,0,0,1,0,0,0] => 1 [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] => 4 [1,1,0,0,1,0,1,0,1,1,0,0] => 3 [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] => 3 [1,1,0,0,1,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,1,0,0,1,0,1,0] => 2 [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] => 3 [1,1,0,0,1,1,0,1,0,1,0,0] => 3 [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] => 1 [1,1,0,0,1,1,1,0,0,1,0,0] => 1 [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] => 4 [1,1,0,1,0,0,1,0,1,1,0,0] => 3 [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] => 3 [1,1,0,1,0,0,1,1,1,0,0,0] => 2 [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] => 1 [1,1,0,1,0,1,0,1,0,1,0,0] => 1 [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] => 3 [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] => 2 [1,1,0,1,1,0,0,0,1,0,1,0] => 2 [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] => 3 [1,1,0,1,1,0,0,1,0,1,0,0] => 3 [1,1,0,1,1,0,0,1,1,0,0,0] => 2 [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] => 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] => 2 [1,1,0,1,1,1,0,0,0,0,1,0] => 1 [1,1,0,1,1,1,0,0,0,1,0,0] => 1 [1,1,0,1,1,1,0,0,1,0,0,0] => 2 [1,1,0,1,1,1,0,1,0,0,0,0] => 2 [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] => 3 [1,1,1,0,0,0,1,0,1,1,0,0] => 2 [1,1,1,0,0,0,1,1,0,0,1,0] => 1 [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] => 3 [1,1,1,0,0,1,0,0,1,1,0,0] => 2 [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] => 2 [1,1,1,0,0,1,0,1,1,0,0,0] => 2 [1,1,1,0,0,1,1,0,0,0,1,0] => 1 [1,1,1,0,0,1,1,0,0,1,0,0] => 2 [1,1,1,0,0,1,1,0,1,0,0,0] => 2 [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] => 3 [1,1,1,0,1,0,0,0,1,1,0,0] => 2 [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] => 2 [1,1,1,0,1,0,0,1,1,0,0,0] => 2 [1,1,1,0,1,0,1,0,0,0,1,0] => 3 [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] => 1 [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] => 1 [1,1,1,0,1,1,0,0,0,1,0,0] => 2 [1,1,1,0,1,1,0,0,1,0,0,0] => 2 [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] => 1 [1,1,1,1,0,0,0,0,1,0,1,0] => 2 [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] => 2 [1,1,1,1,0,0,0,1,0,1,0,0] => 2 [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] => 2 [1,1,1,1,0,0,1,0,0,1,0,0] => 2 [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] => 1 [1,1,1,1,0,1,0,0,0,0,1,0] => 2 [1,1,1,1,0,1,0,0,0,1,0,0] => 2 [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] => 1 [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] => 1 [1,1,1,1,1,0,0,0,1,0,0,0] => 1 [1,1,1,1,1,0,0,1,0,0,0,0] => 1 [1,1,1,1,1,0,1,0,0,0,0,0] => 1 [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] => 5 [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] => 5 [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4 [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1 [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3 [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5 [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] => 4 [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3 [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3 [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4 [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3 [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1 [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] => 2 [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5 [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4 [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] => 2 [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] => 3 [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4 [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] => 2 [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2 [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] => 1 [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2 [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4 [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] => 4 [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] => 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] => 3 [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2 [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] => 3 [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] => 3 [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2 [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] => 1 [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3 [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] => 2 [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1 [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1 [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2 [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] => 5 [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4 [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3 [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] => 3 [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] => 4 [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0 [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2 [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] => 4 [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] => 3 [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] => 2 [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4 [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4 [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3 [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 4 [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] => 3 [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] => 3 [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3 [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] => 3 [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2 [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1 [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2 [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] => 3 [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2 [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] => 1 [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2 [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1 [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2 [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] => 4 [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3 [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4 [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] => 3 [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] => 2 [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3 [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] => 3 [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3 [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3 [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] => 2 [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] => 2 [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2 [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] => 2 [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2 [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] => 1 [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3 [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3 [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3 [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3 [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] => 1 [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1 [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1 [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1 [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] => 5 [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4 [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3 [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4 [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3 [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] => 2 [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4 [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] => 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] => 3 [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2 [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3 [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2 [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1 [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2 [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] => 4 [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 3 [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4 [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] => 3 [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] => 3 [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3 [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] => 2 [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] => 2 [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2 [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] => 3 [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3 [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3 [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] => 1 [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 1 [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 1 [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] => 5 [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4 [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3 [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] => 3 [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] => 2 [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4 [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4 [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] => 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] => 3 [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2 [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] => 4 [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] => 4 [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] => 2 [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] => 2 [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1 [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] => 1 [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] => 1 [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 2 [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] => 3 [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3 [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] => 2 [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] => 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] => 3 [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] => 2 [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3 [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2 [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1 [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2 [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] => 4 [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3 [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] => 3 [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3 [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] => 3 [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 2 [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4 [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] => 3 [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 2 [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 3 [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] => 2 [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] => 2 [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 3 [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] => 2 [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2 [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] => 2 [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2 [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] => 3 [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3 [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] => 2 [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] => 3 [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3 [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] => 2 [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1 [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1 [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1 [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2 [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2 [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] => 4 [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3 [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] => 3 [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2 [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2 [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] => 3 [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3 [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] => 1 [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 1 [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] => 4 [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3 [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] => 3 [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2 [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4 [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] => 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] => 2 [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3 [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] => 2 [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2 [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] => 3 [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2 [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] => 3 [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] => 2 [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 1 [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 1 [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2 [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2 [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] => 4 [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3 [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] => 3 [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2 [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4 [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] => 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] => 2 [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 3 [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] => 2 [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] => 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] => 2 [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2 [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] => 2 [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] => 3 [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] => 2 [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2 [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] => 3 [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3 [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 2 [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] => 3 [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] => 2 [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] => 3 [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] => 2 [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1 [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1 [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2 [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2 [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] => 1 [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3 [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2 [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1 [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] => 3 [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2 [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] => 2 [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2 [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1 [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2 [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2 [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] => 3 [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2 [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] => 2 [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2 [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] => 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] => 2 [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1 [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2 [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2 [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] => 1 [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3 [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2 [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] => 2 [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 2 [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] => 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] => 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] => 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] => 2 [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1 [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2 [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2 [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] => 1 [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2 [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] => 2 [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2 [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] => 2 [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2 [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] => 1 [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2 [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2 [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] => 1 [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2 [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] => 1 [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] => 1 [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1 [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1 [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1 [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1 [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0 ----------------------------------------------------------------------------- Created: Jan 12, 2017 at 14:05 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Jan 12, 2017 at 15:19 by Christian Stump