***************************************************************************** * 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: St000686 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The finitistic dominant dimension of a Dyck path. To every LNakayama algebra there is a corresponding Dyck path, see also [[St000684]]. We associate the finitistic dominant dimension of the algebra to the corresponding Dyck path. ----------------------------------------------------------------------------- References: [1] Marczinzik, R. Upper bounds for the dominant dimension of Nakayama and related algebras [[arXiv:1605.09634]] [2] [[https://en.wikipedia.org/wiki/Nakayama_algebra]] [3] [[https://www.math.uni-bielefeld.de/~ringel/lectures/tachi/tachikawa/dominant.htm]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 2 [1,1,0,0] => 1 [1,0,1,0,1,0] => 3 [1,0,1,1,0,0] => 2 [1,1,0,0,1,0] => 2 [1,1,0,1,0,0] => 2 [1,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,0] => 4 [1,0,1,0,1,1,0,0] => 3 [1,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,0] => 3 [1,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,0,0] => 2 [1,1,0,1,0,0,1,0] => 3 [1,1,0,1,0,1,0,0] => 2 [1,1,0,1,1,0,0,0] => 2 [1,1,1,0,0,0,1,0] => 2 [1,1,1,0,0,1,0,0] => 2 [1,1,1,0,1,0,0,0] => 2 [1,1,1,1,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0] => 5 [1,0,1,0,1,0,1,1,0,0] => 4 [1,0,1,0,1,1,0,0,1,0] => 3 [1,0,1,0,1,1,0,1,0,0] => 4 [1,0,1,0,1,1,1,0,0,0] => 3 [1,0,1,1,0,0,1,0,1,0] => 3 [1,0,1,1,0,0,1,1,0,0] => 2 [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] => 3 [1,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,0,0,0] => 3 [1,0,1,1,1,1,0,0,0,0] => 2 [1,1,0,0,1,0,1,0,1,0] => 4 [1,1,0,0,1,0,1,1,0,0] => 3 [1,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,0] => 3 [1,1,0,0,1,1,1,0,0,0] => 2 [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] => 3 [1,1,0,1,0,1,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,0,0] => 2 [1,1,0,1,1,0,0,0,1,0] => 2 [1,1,0,1,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,0,0] => 2 [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] => 2 [1,1,1,0,0,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,0,0] => 2 [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] => 2 [1,1,1,0,1,0,1,0,0,0] => 2 [1,1,1,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,0,0,0,1,0] => 2 [1,1,1,1,0,0,0,1,0,0] => 2 [1,1,1,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,0] => 6 [1,0,1,0,1,0,1,0,1,1,0,0] => 5 [1,0,1,0,1,0,1,1,0,0,1,0] => 4 [1,0,1,0,1,0,1,1,0,1,0,0] => 5 [1,0,1,0,1,0,1,1,1,0,0,0] => 4 [1,0,1,0,1,1,0,0,1,0,1,0] => 3 [1,0,1,0,1,1,0,0,1,1,0,0] => 3 [1,0,1,0,1,1,0,1,0,0,1,0] => 5 [1,0,1,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,0,1,1,0,1,1,0,0,0] => 4 [1,0,1,0,1,1,1,0,0,0,1,0] => 3 [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] => 4 [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] => 4 [1,0,1,1,0,0,1,0,1,1,0,0] => 3 [1,0,1,1,0,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,0,1,1,0,1,0,0] => 3 [1,0,1,1,0,0,1,1,1,0,0,0] => 2 [1,0,1,1,0,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,1,0,0,1,1,0,0] => 4 [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] => 4 [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] => 3 [1,0,1,1,0,1,1,0,0,1,0,0] => 4 [1,0,1,1,0,1,1,0,1,0,0,0] => 3 [1,0,1,1,0,1,1,1,0,0,0,0] => 3 [1,0,1,1,1,0,0,0,1,0,1,0] => 3 [1,0,1,1,1,0,0,0,1,1,0,0] => 2 [1,0,1,1,1,0,0,1,0,0,1,0] => 3 [1,0,1,1,1,0,0,1,0,1,0,0] => 2 [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] => 4 [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] => 3 [1,0,1,1,1,1,0,0,0,0,1,0] => 2 [1,0,1,1,1,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,1,0,0,0,0] => 3 [1,0,1,1,1,1,1,0,0,0,0,0] => 2 [1,1,0,0,1,0,1,0,1,0,1,0] => 5 [1,1,0,0,1,0,1,0,1,1,0,0] => 4 [1,1,0,0,1,0,1,1,0,0,1,0] => 3 [1,1,0,0,1,0,1,1,0,1,0,0] => 4 [1,1,0,0,1,0,1,1,1,0,0,0] => 3 [1,1,0,0,1,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,0,0,1,1,0,0] => 2 [1,1,0,0,1,1,0,1,0,0,1,0] => 4 [1,1,0,0,1,1,0,1,0,1,0,0] => 3 [1,1,0,0,1,1,0,1,1,0,0,0] => 3 [1,1,0,0,1,1,1,0,0,0,1,0] => 2 [1,1,0,0,1,1,1,0,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,1,0,0,0] => 3 [1,1,0,0,1,1,1,1,0,0,0,0] => 2 [1,1,0,1,0,0,1,0,1,0,1,0] => 5 [1,1,0,1,0,0,1,0,1,1,0,0] => 4 [1,1,0,1,0,0,1,1,0,0,1,0] => 3 [1,1,0,1,0,0,1,1,0,1,0,0] => 4 [1,1,0,1,0,0,1,1,1,0,0,0] => 3 [1,1,0,1,0,1,0,0,1,0,1,0] => 4 [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] => 4 [1,1,0,1,0,1,0,1,0,1,0,0] => 4 [1,1,0,1,0,1,0,1,1,0,0,0] => 3 [1,1,0,1,0,1,1,0,0,0,1,0] => 2 [1,1,0,1,0,1,1,0,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,0,1,1,1,0,0,0,0] => 2 [1,1,0,1,1,0,0,0,1,0,1,0] => 3 [1,1,0,1,1,0,0,0,1,1,0,0] => 2 [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] => 3 [1,1,0,1,1,0,0,1,1,0,0,0] => 3 [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] => 3 [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] => 2 [1,1,0,1,1,1,0,0,0,1,0,0] => 2 [1,1,0,1,1,1,0,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,1,0,0,0,0] => 2 [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] => 4 [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] => 2 [1,1,1,0,0,0,1,1,0,1,0,0] => 3 [1,1,1,0,0,0,1,1,1,0,0,0] => 2 [1,1,1,0,0,1,0,0,1,0,1,0] => 4 [1,1,1,0,0,1,0,0,1,1,0,0] => 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] => 3 [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] => 2 [1,1,1,0,0,1,1,0,0,1,0,0] => 3 [1,1,1,0,0,1,1,0,1,0,0,0] => 2 [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] => 4 [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] => 3 [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] => 3 [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] => 2 [1,1,1,0,1,1,0,0,0,1,0,0] => 3 [1,1,1,0,1,1,0,0,1,0,0,0] => 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] => 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] => 2 [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] => 2 [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] => 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] => 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] => 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] => 2 [1,1,1,1,1,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,0,0,0,0,1,0,0] => 2 [1,1,1,1,1,0,0,0,1,0,0,0] => 2 [1,1,1,1,1,0,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,1,0,0,0,0,0] => 2 [1,1,1,1,1,1,0,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7 [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6 [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5 [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6 [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5 [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 4 [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4 [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6 [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5 [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] => 4 [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4 [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] => 4 [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4 [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3 [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3 [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3 [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3 [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6 [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5 [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] => 5 [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] => 4 [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5 [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4 [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4 [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3 [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3 [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3 [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3 [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3 [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5 [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 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] => 4 [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3 [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] => 4 [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] => 5 [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4 [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3 [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4 [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3 [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3 [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2 [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3 [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] => 2 [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3 [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2 [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6 [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5 [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5 [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4 [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] => 5 [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4 [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3 [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] => 4 [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] => 3 [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 3 [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5 [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4 [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] => 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] => 4 [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] => 3 [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3 [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] => 3 [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3 [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4 [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3 [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2 [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3 [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2 [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4 [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3 [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3 [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3 [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2 [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3 [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2 [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] => 5 [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 4 [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] => 4 [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] => 3 [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4 [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] => 3 [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3 [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] => 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] => 3 [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3 [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2 [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3 [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2 [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] => 3 [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] => 2 [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4 [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 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] => 3 [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2 [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2 [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2 [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3 [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2 [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6 [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5 [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4 [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] => 4 [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3 [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5 [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4 [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4 [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3 [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] => 4 [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] => 4 [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3 [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3 [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 5 [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4 [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] => 4 [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] => 3 [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] => 3 [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 3 [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2 [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3 [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2 [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] => 4 [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] => 3 [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2 [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2 [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2 [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3 [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2 [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6 [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5 [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 4 [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5 [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4 [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3 [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 3 [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4 [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4 [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3 [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] => 4 [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] => 4 [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3 [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] => 5 [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4 [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 4 [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 4 [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3 [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4 [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 4 [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3 [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3 [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 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] => 4 [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] => 4 [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3 [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] => 3 [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] => 4 [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 3 [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2 [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 3 [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 2 [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5 [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 4 [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] => 4 [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] => 3 [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3 [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] => 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] => 4 [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3 [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3 [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] => 2 [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3 [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2 [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3 [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 2 [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3 [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2 [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 2 [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4 [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 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] => 3 [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] => 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] => 3 [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] => 2 [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2 [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2 [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 3 [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2 [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] => 5 [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4 [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3 [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4 [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3 [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3 [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2 [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4 [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3 [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 3 [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2 [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2 [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3 [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2 [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5 [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4 [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4 [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 3 [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] => 4 [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 4 [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3 [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] => 3 [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] => 3 [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2 [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4 [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3 [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] => 2 [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3 [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 2 [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2 [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2 [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 3 [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2 [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] => 5 [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 4 [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 3 [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4 [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3 [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] => 4 [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4 [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3 [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] => 3 [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] => 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] => 3 [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] => 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] => 3 [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] => 3 [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2 [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4 [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3 [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 3 [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] => 2 [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3 [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 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] => 2 [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] => 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] => 2 [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2 [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 3 [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 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] => 2 [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4 [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3 [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2 [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 3 [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2 [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4 [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 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] => 3 [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] => 2 [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 3 [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2 [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] => 4 [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] => 3 [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] => 3 [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] => 2 [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 3 [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 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] => 2 [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4 [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 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] => 3 [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] => 3 [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] => 3 [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] => 2 [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 3 [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 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] => 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] => 2 [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] => 2 [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] => 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] => 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] => 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] => 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] => 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] => 2 [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2 [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2 [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2 [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2 [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2 [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1 ----------------------------------------------------------------------------- Created: Jan 10, 2017 at 15:17 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Oct 21, 2017 at 09:40 by Martin Rubey