***************************************************************************** * 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: St000386 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The number of factors DDU in a Dyck path. ----------------------------------------------------------------------------- References: [1] Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n, having k ddu's [here u=(1,1) and d=(1,-1)]. [[OEIS:A091894]] ----------------------------------------------------------------------------- Code: def statistic(D): return len(list(Word([0,0,1]).factor_occurrences_in(Word(D)))) ----------------------------------------------------------------------------- Statistic values: [] => 0 [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] => 0 [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] => 0 [1,0,1,1,0,0,1,0] => 1 [1,0,1,1,0,1,0,0] => 0 [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] => 1 [1,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,0] => 0 [1,1,0,1,1,0,0,0] => 0 [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] => 0 [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] => 0 [1,0,1,0,1,1,0,0,1,0] => 1 [1,0,1,0,1,1,0,1,0,0] => 0 [1,0,1,0,1,1,1,0,0,0] => 0 [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] => 1 [1,0,1,1,0,1,0,1,0,0] => 0 [1,0,1,1,0,1,1,0,0,0] => 0 [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] => 0 [1,0,1,1,1,1,0,0,0,0] => 0 [1,1,0,0,1,0,1,0,1,0] => 1 [1,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,0] => 1 [1,1,0,0,1,1,1,0,0,0] => 1 [1,1,0,1,0,0,1,0,1,0] => 1 [1,1,0,1,0,0,1,1,0,0] => 1 [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] => 0 [1,1,0,1,1,0,0,0,1,0] => 1 [1,1,0,1,1,0,0,1,0,0] => 1 [1,1,0,1,1,0,1,0,0,0] => 0 [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] => 1 [1,1,1,0,0,1,0,0,1,0] => 2 [1,1,1,0,0,1,0,1,0,0] => 1 [1,1,1,0,0,1,1,0,0,0] => 1 [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] => 0 [1,1,1,0,1,1,0,0,0,0] => 0 [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] => 0 [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] => 0 [1,0,1,0,1,0,1,1,0,0,1,0] => 1 [1,0,1,0,1,0,1,1,0,1,0,0] => 0 [1,0,1,0,1,0,1,1,1,0,0,0] => 0 [1,0,1,0,1,1,0,0,1,0,1,0] => 1 [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] => 1 [1,0,1,0,1,1,0,1,0,1,0,0] => 0 [1,0,1,0,1,1,0,1,1,0,0,0] => 0 [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] => 0 [1,0,1,0,1,1,1,1,0,0,0,0] => 0 [1,0,1,1,0,0,1,0,1,0,1,0] => 1 [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] => 2 [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] => 1 [1,0,1,1,0,1,0,0,1,0,1,0] => 1 [1,0,1,1,0,1,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,1,0,0,1,0] => 1 [1,0,1,1,0,1,0,1,0,1,0,0] => 0 [1,0,1,1,0,1,0,1,1,0,0,0] => 0 [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] => 1 [1,0,1,1,0,1,1,0,1,0,0,0] => 0 [1,0,1,1,0,1,1,1,0,0,0,0] => 0 [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] => 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] => 1 [1,0,1,1,1,0,1,0,0,1,0,0] => 1 [1,0,1,1,1,0,1,0,1,0,0,0] => 0 [1,0,1,1,1,0,1,1,0,0,0,0] => 0 [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] => 0 [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] => 1 [1,1,0,0,1,0,1,0,1,1,0,0] => 1 [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] => 1 [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] => 2 [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] => 2 [1,1,0,0,1,1,0,1,0,1,0,0] => 1 [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] => 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] => 1 [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] => 1 [1,1,0,1,0,0,1,0,1,1,0,0] => 1 [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] => 1 [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] => 1 [1,1,0,1,0,1,0,0,1,1,0,0] => 1 [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] => 0 [1,1,0,1,0,1,0,1,1,0,0,0] => 0 [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] => 1 [1,1,0,1,0,1,1,0,1,0,0,0] => 0 [1,1,0,1,0,1,1,1,0,0,0,0] => 0 [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] => 1 [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] => 1 [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] => 1 [1,1,0,1,1,0,1,0,0,1,0,0] => 1 [1,1,0,1,1,0,1,0,1,0,0,0] => 0 [1,1,0,1,1,0,1,1,0,0,0,0] => 0 [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] => 1 [1,1,0,1,1,1,0,1,0,0,0,0] => 0 [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] => 1 [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] => 2 [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] => 1 [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] => 2 [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] => 1 [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] => 2 [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] => 1 [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] => 1 [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] => 1 [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] => 1 [1,1,1,0,1,0,1,0,0,1,0,0] => 1 [1,1,1,0,1,0,1,0,1,0,0,0] => 0 [1,1,1,0,1,0,1,1,0,0,0,0] => 0 [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] => 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] => 0 [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] => 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] => 1 [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] => 1 [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] => 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] => 0 [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] => 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] => 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] => 0 [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0 [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1 [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0 [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0 [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] => 1 [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1 [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0 [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 0 [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1 [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1 [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 0 [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0 [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] => 1 [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2 [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1 [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] => 1 [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1 [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0 [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 0 [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1 [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1 [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0 [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0 [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1 [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] => 1 [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] => 1 [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1 [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0 [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0 [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] => 0 [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0 [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1 [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1 [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] => 2 [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] => 2 [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1 [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] => 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] => 1 [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] => 1 [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1 [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] => 1 [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1 [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1 [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0 [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0 [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1 [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1 [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0 [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0 [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1 [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] => 2 [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1 [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1 [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1 [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1 [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0 [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0 [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] => 1 [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0 [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0 [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1 [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] => 2 [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] => 1 [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] => 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] => 1 [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] => 2 [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] => 1 [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1 [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1 [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2 [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1 [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1 [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1 [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0 [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0 [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] => 1 [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1 [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0 [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0 [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] => 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] => 1 [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] => 1 [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] => 1 [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1 [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1 [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0 [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0 [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] => 0 [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] => 1 [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1 [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] => 1 [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1 [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] => 2 [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1 [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1 [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] => 1 [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] => 2 [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3 [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] => 2 [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2 [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] => 2 [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1 [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1 [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] => 2 [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1 [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] => 2 [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] => 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] => 1 [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] => 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] => 1 [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] => 1 [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1 [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] => 1 [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1 [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] => 2 [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1 [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1 [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] => 1 [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] => 1 [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1 [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] => 1 [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1 [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1 [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] => 0 [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] => 1 [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0 [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0 [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] => 1 [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1 [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1 [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1 [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1 [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0 [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0 [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] => 1 [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0 [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0 [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1 [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] => 2 [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] => 1 [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2 [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] => 2 [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1 [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1 [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] => 2 [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1 [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] => 1 [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1 [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2 [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1 [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1 [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1 [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1 [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0 [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0 [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] => 1 [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1 [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0 [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0 [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] => 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] => 1 [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] => 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] => 1 [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] => 1 [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1 [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1 [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0 [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0 [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] => 1 [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0 [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] => 1 [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1 [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] => 1 [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] => 2 [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] => 2 [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1 [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] => 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] => 1 [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] => 2 [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] => 3 [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] => 2 [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2 [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] => 2 [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1 [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1 [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] => 2 [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1 [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] => 2 [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] => 3 [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] => 2 [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] => 1 [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] => 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] => 2 [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] => 1 [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1 [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1 [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] => 1 [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] => 2 [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] => 2 [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1 [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1 [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] => 2 [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1 [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] => 1 [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1 [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2 [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1 [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1 [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] => 1 [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] => 0 [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] => 1 [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1 [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0 [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0 [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] => 1 [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] => 1 [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] => 1 [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] => 1 [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1 [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1 [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0 [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0 [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] => 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] => 0 [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] => 1 [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] => 2 [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] => 1 [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] => 2 [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] => 1 [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] => 2 [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] => 1 [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] => 2 [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] => 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] => 1 [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] => 2 [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] => 1 [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] => 1 [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] => 1 [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] => 1 [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] => 1 [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1 [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1 [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] => 0 [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] => 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] => 0 [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] => 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] => 1 [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] => 1 [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] => 1 [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] => 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] => 0 [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] => 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] => 0 [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1 [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2 [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 0 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0 [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1 [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 0 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1 [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2 [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2 [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1 [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1 [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0 [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1 [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1 [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0 [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0 [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1 [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2 [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1 [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1 [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1 [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0 [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1 [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1 [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1 [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1 [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2 [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2 [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1 [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2 [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1 [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1 [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2 [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1 [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1 [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0 [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1 [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1 [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1 [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0 [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1 [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1 [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1 [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2 [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1 [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1 [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1 [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1 [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1 [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2 [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2 [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2 [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3 [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2 [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2 [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2 [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1 [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1 [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1 [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2 [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2 [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2 [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2 [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1 [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2 [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2 [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2 [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2 [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1 [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1 [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0 [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1 [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1 [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0 [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1 [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1 [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1 [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1 [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0 [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0 [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1 [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1 [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1 [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2 [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2 [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2 [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1 [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1 [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1 [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1 [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2 [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1 [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1 [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1 [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0 [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0 [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1 [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0 [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1 [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2 [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1 [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2 [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1 [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1 [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1 [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1 [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0 [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0 [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1 [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1 [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1 [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1 [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0 [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1 [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2 [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2 [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1 [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 1 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1 [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2 [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2 [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2 [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2 [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2 [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1 [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1 [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2 [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2 [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1 [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 1 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1 [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1 [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1 [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1 [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2 [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2 [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1 [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1 [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1 [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1 [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2 [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1 [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0 [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0 [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1 [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1 [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0 [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0 [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1 [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1 [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2 [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1 [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1 [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0 [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1 [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1 [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1 [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1 [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2 [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1 [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2 [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2 [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1 [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2 [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1 [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2 [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2 [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3 [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2 [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2 [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2 [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1 [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1 [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2 [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 1 [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1 [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1 [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1 [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2 [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1 [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1 [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1 [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1 [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1 [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0 [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0 [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1 [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1 [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0 [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0 [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1 [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1 [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2 [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1 [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2 [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2 [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1 [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1 [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2 [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2 [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1 [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1 [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1 [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0 [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1 [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1 [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2 [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2 [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1 [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2 [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2 [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1 [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2 [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2 [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3 [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2 [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2 [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2 [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2 [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1 [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1 [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2 [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2 [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1 [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1 [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2 [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2 [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3 [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2 [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2 [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2 [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2 [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1 [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1 [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2 [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2 [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2 [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1 [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2 [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2 [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3 [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2 [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3 [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3 [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2 [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3 [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2 [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2 [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3 [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2 [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2 [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1 [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1 [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2 [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1 [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1 [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2 [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3 [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2 [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2 [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1 [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1 [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2 [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2 [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1 [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2 [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3 [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3 [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3 [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2 [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3 [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3 [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2 [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2 [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2 [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3 [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2 [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2 [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1 [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1 [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2 [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2 [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1 [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2 [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3 [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2 [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2 [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3 [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3 [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2 [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2 [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2 [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2 [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1 [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1 [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2 [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1 [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1 [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2 [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2 [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1 [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1 [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2 [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2 [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1 [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2 [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1 [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0 [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1 [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0 [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0 [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1 [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0 [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1 [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1 [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1 [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1 [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2 [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1 [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1 [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0 [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 1 [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2 [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 2 [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 2 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1 [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 2 [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 2 [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 1 [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 1 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 2 [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1 [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2 [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 1 [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 1 [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1 [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 1 [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1 [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0 [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 0 [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 2 [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 2 [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 1 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 2 [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1 [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 1 [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 1 [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1 [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 1 [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 1 [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 1 [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 0 [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0 [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2 [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 1 [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1 [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 1 [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 1 [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 1 [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 0 [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 0 [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1 [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 1 [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 0 [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1 [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 1 [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 1 [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 1 [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 0 [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 2 [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2 [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 2 [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1 [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 2 [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 2 [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1 [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 1 [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0 [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 0 [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1 [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 1 [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 1 [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1 [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 2 [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 2 [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1 [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1 [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 2 [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 2 [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1 [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1 [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1 [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1 [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1 [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1 [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1 [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 1 [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1 [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 2 [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1 [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2 [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0 [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1 [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1 [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0 [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1 [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0 [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 1 [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 2 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 1 [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1 [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1 [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 1 [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 2 [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => 1 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1 [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1 [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 1 [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1 [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1 [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0 [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1 [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 0 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0 [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 0 [1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 1 [1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 1 [1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 1 [1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 2 [1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 1 [1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 1 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 2 [1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 1 [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 2 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 3 [1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1 [1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2 [1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2 [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 1 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 2 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2 [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 1 [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 2 [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 2 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 3 [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 1 [1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 2 [1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 2 [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 2 [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2 [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 2 [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 2 [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 3 [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 4 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1 [1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 0 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 1 [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 1 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 0 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0 [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0 [1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 1 [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 1 [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1 [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0 [1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1 [1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 1 [1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 1 [1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 2 [1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => 1 [1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 2 [1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => 1 [1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => 2 [1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => 1 [1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 2 [1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => 2 [1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 2 [1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 3 [1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 1 [1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 2 [1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 2 [1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 2 [1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 3 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 1 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 2 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 3 [1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 1 [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 2 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 3 [1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 1 [1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 3 [1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 3 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 3 [1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 3 [1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 3 [1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 3 [1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 4 [1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 1 [1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 2 [1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 2 [1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 2 [1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 3 [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 2 [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 3 [1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 2 [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 2 [1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 3 [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 3 [1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 3 [1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1 [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2 [1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3 [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3 [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3 [1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => 1 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 2 [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 2 [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 2 [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 1 [1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 2 [1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 2 [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 2 [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 3 [1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 2 [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 3 [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2 [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3 [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 2 [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 3 [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 3 [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 3 [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 4 [1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 1 [1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 2 [1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 2 [1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 2 [1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 3 [1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 2 [1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 3 [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => 2 [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 3 [1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 2 [1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 3 [1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 3 [1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 3 [1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 4 [1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 2 [1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 4 [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2 [1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3 [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3 [1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4 [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 2 [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 4 [1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 2 [1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 3 [1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 3 [1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 3 [1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 4 [1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 4 [1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 3 [1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 4 [1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 4 [1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 4 [1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 4 [1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 5 ----------------------------------------------------------------------------- Created: Feb 10, 2016 at 14:31 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jan 11, 2018 at 15:02 by Martin Rubey