***************************************************************************** * 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: St001994 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The number of simple spherical modules of the corresponding linear Nakayama algebra. A module $M$ with projective dimension $n$ is spherical (in the sense of Auslander and Bridger) if $Ext_A^i(M,A) =0$ for $i=1,\dots,n-1$. By convention all modules of projective dimension at most 1 are spherical. ----------------------------------------------------------------------------- References: [1] Auslander, M., Bridger, M. Stable module theory [[MathSciNet:0269685]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 2 [1,0,1,0] => 3 [1,1,0,0] => 3 [1,0,1,0,1,0] => 4 [1,0,1,1,0,0] => 4 [1,1,0,0,1,0] => 4 [1,1,0,1,0,0] => 4 [1,1,1,0,0,0] => 4 [1,0,1,0,1,0,1,0] => 5 [1,0,1,0,1,1,0,0] => 5 [1,0,1,1,0,0,1,0] => 5 [1,0,1,1,0,1,0,0] => 4 [1,0,1,1,1,0,0,0] => 5 [1,1,0,0,1,0,1,0] => 5 [1,1,0,0,1,1,0,0] => 5 [1,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,1,0,0] => 5 [1,1,0,1,1,0,0,0] => 5 [1,1,1,0,0,0,1,0] => 5 [1,1,1,0,0,1,0,0] => 5 [1,1,1,0,1,0,0,0] => 5 [1,1,1,1,0,0,0,0] => 5 [1,0,1,0,1,0,1,0,1,0] => 6 [1,0,1,0,1,0,1,1,0,0] => 6 [1,0,1,0,1,1,0,0,1,0] => 6 [1,0,1,0,1,1,0,1,0,0] => 5 [1,0,1,0,1,1,1,0,0,0] => 6 [1,0,1,1,0,0,1,0,1,0] => 6 [1,0,1,1,0,0,1,1,0,0] => 6 [1,0,1,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,1,0,0] => 5 [1,0,1,1,0,1,1,0,0,0] => 5 [1,0,1,1,1,0,0,0,1,0] => 6 [1,0,1,1,1,0,0,1,0,0] => 6 [1,0,1,1,1,0,1,0,0,0] => 5 [1,0,1,1,1,1,0,0,0,0] => 6 [1,1,0,0,1,0,1,0,1,0] => 6 [1,1,0,0,1,0,1,1,0,0] => 6 [1,1,0,0,1,1,0,0,1,0] => 6 [1,1,0,0,1,1,0,1,0,0] => 5 [1,1,0,0,1,1,1,0,0,0] => 6 [1,1,0,1,0,0,1,0,1,0] => 6 [1,1,0,1,0,0,1,1,0,0] => 6 [1,1,0,1,0,1,0,0,1,0] => 6 [1,1,0,1,0,1,0,1,0,0] => 6 [1,1,0,1,0,1,1,0,0,0] => 6 [1,1,0,1,1,0,0,0,1,0] => 6 [1,1,0,1,1,0,0,1,0,0] => 5 [1,1,0,1,1,0,1,0,0,0] => 5 [1,1,0,1,1,1,0,0,0,0] => 6 [1,1,1,0,0,0,1,0,1,0] => 6 [1,1,1,0,0,0,1,1,0,0] => 6 [1,1,1,0,0,1,0,0,1,0] => 6 [1,1,1,0,0,1,0,1,0,0] => 6 [1,1,1,0,0,1,1,0,0,0] => 6 [1,1,1,0,1,0,0,0,1,0] => 6 [1,1,1,0,1,0,0,1,0,0] => 6 [1,1,1,0,1,0,1,0,0,0] => 6 [1,1,1,0,1,1,0,0,0,0] => 6 [1,1,1,1,0,0,0,0,1,0] => 6 [1,1,1,1,0,0,0,1,0,0] => 6 [1,1,1,1,0,0,1,0,0,0] => 6 [1,1,1,1,0,1,0,0,0,0] => 6 [1,1,1,1,1,0,0,0,0,0] => 6 [1,0,1,0,1,0,1,0,1,0,1,0] => 7 [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] => 6 [1,0,1,0,1,0,1,1,1,0,0,0] => 7 [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] => 7 [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] => 6 [1,0,1,0,1,1,0,1,1,0,0,0] => 6 [1,0,1,0,1,1,1,0,0,0,1,0] => 7 [1,0,1,0,1,1,1,0,0,1,0,0] => 7 [1,0,1,0,1,1,1,0,1,0,0,0] => 6 [1,0,1,0,1,1,1,1,0,0,0,0] => 7 [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] => 7 [1,0,1,1,0,0,1,1,0,0,1,0] => 7 [1,0,1,1,0,0,1,1,0,1,0,0] => 6 [1,0,1,1,0,0,1,1,1,0,0,0] => 7 [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] => 5 [1,0,1,1,0,1,0,1,0,0,1,0] => 6 [1,0,1,1,0,1,0,1,0,1,0,0] => 6 [1,0,1,1,0,1,0,1,1,0,0,0] => 6 [1,0,1,1,0,1,1,0,0,0,1,0] => 6 [1,0,1,1,0,1,1,0,0,1,0,0] => 5 [1,0,1,1,0,1,1,0,1,0,0,0] => 5 [1,0,1,1,0,1,1,1,0,0,0,0] => 6 [1,0,1,1,1,0,0,0,1,0,1,0] => 7 [1,0,1,1,1,0,0,0,1,1,0,0] => 7 [1,0,1,1,1,0,0,1,0,0,1,0] => 7 [1,0,1,1,1,0,0,1,0,1,0,0] => 7 [1,0,1,1,1,0,0,1,1,0,0,0] => 7 [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] => 5 [1,0,1,1,1,0,1,0,1,0,0,0] => 6 [1,0,1,1,1,0,1,1,0,0,0,0] => 6 [1,0,1,1,1,1,0,0,0,0,1,0] => 7 [1,0,1,1,1,1,0,0,0,1,0,0] => 7 [1,0,1,1,1,1,0,0,1,0,0,0] => 7 [1,0,1,1,1,1,0,1,0,0,0,0] => 6 [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] => 7 [1,1,0,0,1,0,1,0,1,1,0,0] => 7 [1,1,0,0,1,0,1,1,0,0,1,0] => 7 [1,1,0,0,1,0,1,1,0,1,0,0] => 6 [1,1,0,0,1,0,1,1,1,0,0,0] => 7 [1,1,0,0,1,1,0,0,1,0,1,0] => 7 [1,1,0,0,1,1,0,0,1,1,0,0] => 7 [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] => 6 [1,1,0,0,1,1,0,1,1,0,0,0] => 6 [1,1,0,0,1,1,1,0,0,0,1,0] => 7 [1,1,0,0,1,1,1,0,0,1,0,0] => 7 [1,1,0,0,1,1,1,0,1,0,0,0] => 6 [1,1,0,0,1,1,1,1,0,0,0,0] => 7 [1,1,0,1,0,0,1,0,1,0,1,0] => 7 [1,1,0,1,0,0,1,0,1,1,0,0] => 7 [1,1,0,1,0,0,1,1,0,0,1,0] => 7 [1,1,0,1,0,0,1,1,0,1,0,0] => 6 [1,1,0,1,0,0,1,1,1,0,0,0] => 7 [1,1,0,1,0,1,0,0,1,0,1,0] => 7 [1,1,0,1,0,1,0,0,1,1,0,0] => 7 [1,1,0,1,0,1,0,1,0,0,1,0] => 7 [1,1,0,1,0,1,0,1,0,1,0,0] => 7 [1,1,0,1,0,1,0,1,1,0,0,0] => 7 [1,1,0,1,0,1,1,0,0,0,1,0] => 7 [1,1,0,1,0,1,1,0,0,1,0,0] => 6 [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] => 7 [1,1,0,1,1,0,0,0,1,0,1,0] => 7 [1,1,0,1,1,0,0,0,1,1,0,0] => 7 [1,1,0,1,1,0,0,1,0,0,1,0] => 5 [1,1,0,1,1,0,0,1,0,1,0,0] => 6 [1,1,0,1,1,0,0,1,1,0,0,0] => 6 [1,1,0,1,1,0,1,0,0,0,1,0] => 5 [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] => 6 [1,1,0,1,1,0,1,1,0,0,0,0] => 6 [1,1,0,1,1,1,0,0,0,0,1,0] => 7 [1,1,0,1,1,1,0,0,0,1,0,0] => 7 [1,1,0,1,1,1,0,0,1,0,0,0] => 6 [1,1,0,1,1,1,0,1,0,0,0,0] => 6 [1,1,0,1,1,1,1,0,0,0,0,0] => 7 [1,1,1,0,0,0,1,0,1,0,1,0] => 7 [1,1,1,0,0,0,1,0,1,1,0,0] => 7 [1,1,1,0,0,0,1,1,0,0,1,0] => 7 [1,1,1,0,0,0,1,1,0,1,0,0] => 6 [1,1,1,0,0,0,1,1,1,0,0,0] => 7 [1,1,1,0,0,1,0,0,1,0,1,0] => 7 [1,1,1,0,0,1,0,0,1,1,0,0] => 7 [1,1,1,0,0,1,0,1,0,0,1,0] => 7 [1,1,1,0,0,1,0,1,0,1,0,0] => 7 [1,1,1,0,0,1,0,1,1,0,0,0] => 7 [1,1,1,0,0,1,1,0,0,0,1,0] => 7 [1,1,1,0,0,1,1,0,0,1,0,0] => 6 [1,1,1,0,0,1,1,0,1,0,0,0] => 6 [1,1,1,0,0,1,1,1,0,0,0,0] => 7 [1,1,1,0,1,0,0,0,1,0,1,0] => 7 [1,1,1,0,1,0,0,0,1,1,0,0] => 7 [1,1,1,0,1,0,0,1,0,0,1,0] => 7 [1,1,1,0,1,0,0,1,0,1,0,0] => 7 [1,1,1,0,1,0,0,1,1,0,0,0] => 7 [1,1,1,0,1,0,1,0,0,0,1,0] => 7 [1,1,1,0,1,0,1,0,0,1,0,0] => 7 [1,1,1,0,1,0,1,0,1,0,0,0] => 7 [1,1,1,0,1,0,1,1,0,0,0,0] => 7 [1,1,1,0,1,1,0,0,0,0,1,0] => 7 [1,1,1,0,1,1,0,0,0,1,0,0] => 6 [1,1,1,0,1,1,0,0,1,0,0,0] => 6 [1,1,1,0,1,1,0,1,0,0,0,0] => 6 [1,1,1,0,1,1,1,0,0,0,0,0] => 7 [1,1,1,1,0,0,0,0,1,0,1,0] => 7 [1,1,1,1,0,0,0,0,1,1,0,0] => 7 [1,1,1,1,0,0,0,1,0,0,1,0] => 7 [1,1,1,1,0,0,0,1,0,1,0,0] => 7 [1,1,1,1,0,0,0,1,1,0,0,0] => 7 [1,1,1,1,0,0,1,0,0,0,1,0] => 7 [1,1,1,1,0,0,1,0,0,1,0,0] => 7 [1,1,1,1,0,0,1,0,1,0,0,0] => 7 [1,1,1,1,0,0,1,1,0,0,0,0] => 7 [1,1,1,1,0,1,0,0,0,0,1,0] => 7 [1,1,1,1,0,1,0,0,0,1,0,0] => 7 [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] => 7 [1,1,1,1,0,1,1,0,0,0,0,0] => 7 [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] => 7 [1,1,1,1,1,0,0,0,1,0,0,0] => 7 [1,1,1,1,1,0,0,1,0,0,0,0] => 7 [1,1,1,1,1,0,1,0,0,0,0,0] => 7 [1,1,1,1,1,1,0,0,0,0,0,0] => 7 [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8 [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8 [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 8 [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7 [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 8 [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 8 [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 8 [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] => 7 [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 7 [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 8 [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 8 [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 7 [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 8 [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 8 [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 8 [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 8 [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 7 [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 8 [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] => 6 [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 7 [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 7 [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 7 [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] => 6 [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6 [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7 [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 8 [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8 [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 8 [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 8 [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 8 [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 6 [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6 [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7 [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 7 [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 8 [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 8 [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 8 [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 7 [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 8 [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 8 [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 8 [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 8 [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 7 [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8 [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 8 [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 8 [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 6 [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 7 [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 7 [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 8 [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 8 [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 7 [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8 [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] => 5 [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 6 [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] => 6 [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 7 [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 7 [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 7 [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6 [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 7 [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 7 [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6 [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] => 7 [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] => 7 [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] => 5 [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 6 [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] => 6 [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 6 [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7 [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 7 [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 6 [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 6 [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 7 [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 8 [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 8 [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 8 [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 7 [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8 [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 8 [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 8 [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 8 [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 8 [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 8 [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8 [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 7 [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 7 [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8 [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] => 6 [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] => 6 [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 7 [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 7 [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 7 [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 7 [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 7 [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 6 [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 6 [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 6 [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 7 [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 8 [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8 [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 8 [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 8 [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8 [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 8 [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 8 [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 8 [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8 [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 6 [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 6 [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 6 [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 7 [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 7 [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 8 [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 8 [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 8 [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 8 [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7 [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] => 8 [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 8 [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 8 [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 7 [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 8 [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 8 [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 8 [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 6 [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 7 [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 7 [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 8 [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 8 [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 7 [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8 [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 8 [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 8 [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 8 [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 7 [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 8 [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] => 6 [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 7 [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 7 [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 7 [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 7 [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 6 [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 6 [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 7 [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 8 [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 8 [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 8 [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 8 [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 8 [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 6 [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 6 [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 7 [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 7 [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8 [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 8 [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 8 [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 7 [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8 [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] => 8 [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 8 [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 7 [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 8 [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 8 [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 8 [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] => 7 [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 7 [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 8 [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 8 [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 7 [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 8 [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8 [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8 [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8 [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 7 [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 8 [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8 [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8 [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 8 [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8 [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] => 8 [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] => 7 [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 8 [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 8 [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 8 [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 6 [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] => 7 [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 6 [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 7 [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 7 [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 7 [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8 [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 8 [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 7 [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 7 [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 8 [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 8 [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 8 [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 8 [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 7 [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 8 [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] => 6 [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 7 [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] => 7 [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 7 [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 6 [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] => 7 [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] => 6 [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 7 [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 7 [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 7 [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 7 [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 6 [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 7 [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 7 [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 7 [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] => 6 [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 7 [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 8 [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8 [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 8 [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 8 [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8 [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 6 [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] => 7 [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 7 [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 6 [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] => 7 [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 7 [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 7 [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 8 [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 8 [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 8 [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7 [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7 [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8 [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 8 [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 8 [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 8 [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 7 [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 8 [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 8 [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8 [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 6 [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 7 [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 7 [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 8 [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 8 [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 7 [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8 [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 8 [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 8 [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 8 [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 7 [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 8 [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 8 [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 8 [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 8 [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] => 8 [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 8 [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 7 [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 7 [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 8 [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 8 [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 8 [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6 [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 7 [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 7 [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6 [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 7 [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 7 [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 7 [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 8 [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8 [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7 [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7 [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8 [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 8 [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 8 [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 8 [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 7 [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 8 [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 8 [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 8 [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 8 [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] => 8 [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 8 [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 7 [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 7 [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 8 [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 8 [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 8 [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 8 [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 8 [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 8 [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 8 [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 8 [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 8 [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 8 [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 8 [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 7 [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 7 [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 7 [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 8 [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 8 [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8 [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 6 [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 7 [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 7 [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 6 [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 7 [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 7 [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 7 [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 6 [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 7 [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 7 [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 7 [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 7 [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 8 [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 8 [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7 [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7 [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7 [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8 [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 8 [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 8 [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 8 [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 7 [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8 [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 8 [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 8 [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 8 [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 8 [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 8 [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 8 [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7 [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7 [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8 [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 8 [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 8 [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 8 [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 8 [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 8 [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 8 [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 8 [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 8 [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 8 [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 8 [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7 [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7 [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7 [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8 [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 8 [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 8 [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 8 [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 8 [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 8 [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 8 [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 8 [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 8 [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 8 [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 8 [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 8 [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 8 [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 8 [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 8 [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 8 [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7 [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7 [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7 [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] => 8 [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 8 [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8 [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 8 [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 8 [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8 [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 8 [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 8 [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 8 [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] => 8 [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8 [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 8 [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 8 [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8 [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 8 [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 8 [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] => 8 [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 8 [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8 [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] => 8 [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8 [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 8 [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 8 [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 8 [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8 ----------------------------------------------------------------------------- Created: May 12, 2026 at 14:20 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: May 12, 2026 at 14:43 by Martin Rubey