***************************************************************************** * 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: St000012 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The area of a Dyck path. This is the number of complete squares in the integer lattice which are below the path and above the x-axis. The 'half-squares' directly above the axis do not contribute to this statistic. 1. Dyck paths are bijection with '''area sequences''' $(a_1,\ldots,a_n)$ such that $a_1 = 0, a_{k+1} \leq a_k + 1$. 2. The generating function $\mathbf{D}_n(q) = \sum_{D \in \mathfrak{D}_n} q^{\operatorname{area}(D)}$ satisfy the recurrence $$\mathbf{D}_{n+1}(q) = \sum q^k \mathbf{D}_k(q) \mathbf{D}_{n-k}(q).$$ 3. The area is equidistributed with [[St000005]] and [[St000006]]. Pairs of these statistics play an important role in the theory of $q,t$-Catalan numbers. ----------------------------------------------------------------------------- References: [1] Haglund, J. The $q$,$t$-Catalan numbers and the space of diagonal harmonics [[MathSciNet:2371044]] ----------------------------------------------------------------------------- Code: def statistic(x): return x.area() ----------------------------------------------------------------------------- Statistic values: [1,0] => 0 [1,0,1,0] => 0 [1,1,0,0] => 1 [1,0,1,0,1,0] => 0 [1,0,1,1,0,0] => 1 [1,1,0,0,1,0] => 1 [1,1,0,1,0,0] => 2 [1,1,1,0,0,0] => 3 [1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,0] => 1 [1,0,1,1,0,1,0,0] => 2 [1,0,1,1,1,0,0,0] => 3 [1,1,0,0,1,0,1,0] => 1 [1,1,0,0,1,1,0,0] => 2 [1,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,0] => 3 [1,1,0,1,1,0,0,0] => 4 [1,1,1,0,0,0,1,0] => 3 [1,1,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,0,0] => 5 [1,1,1,1,0,0,0,0] => 6 [1,0,1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,0,1,0] => 1 [1,0,1,0,1,1,0,1,0,0] => 2 [1,0,1,0,1,1,1,0,0,0] => 3 [1,0,1,1,0,0,1,0,1,0] => 1 [1,0,1,1,0,0,1,1,0,0] => 2 [1,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,1,0,0] => 3 [1,0,1,1,0,1,1,0,0,0] => 4 [1,0,1,1,1,0,0,0,1,0] => 3 [1,0,1,1,1,0,0,1,0,0] => 4 [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] => 1 [1,1,0,0,1,0,1,1,0,0] => 2 [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] => 4 [1,1,0,1,0,0,1,0,1,0] => 2 [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] => 4 [1,1,0,1,0,1,1,0,0,0] => 5 [1,1,0,1,1,0,0,0,1,0] => 4 [1,1,0,1,1,0,0,1,0,0] => 5 [1,1,0,1,1,0,1,0,0,0] => 6 [1,1,0,1,1,1,0,0,0,0] => 7 [1,1,1,0,0,0,1,0,1,0] => 3 [1,1,1,0,0,0,1,1,0,0] => 4 [1,1,1,0,0,1,0,0,1,0] => 4 [1,1,1,0,0,1,0,1,0,0] => 5 [1,1,1,0,0,1,1,0,0,0] => 6 [1,1,1,0,1,0,0,0,1,0] => 5 [1,1,1,0,1,0,0,1,0,0] => 6 [1,1,1,0,1,0,1,0,0,0] => 7 [1,1,1,0,1,1,0,0,0,0] => 8 [1,1,1,1,0,0,0,0,1,0] => 6 [1,1,1,1,0,0,0,1,0,0] => 7 [1,1,1,1,0,0,1,0,0,0] => 8 [1,1,1,1,0,1,0,0,0,0] => 9 [1,1,1,1,1,0,0,0,0,0] => 10 [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] => 1 [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] => 2 [1,0,1,0,1,0,1,1,1,0,0,0] => 3 [1,0,1,0,1,1,0,0,1,0,1,0] => 1 [1,0,1,0,1,1,0,0,1,1,0,0] => 2 [1,0,1,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,0,1,1,0,1,0,1,0,0] => 3 [1,0,1,0,1,1,0,1,1,0,0,0] => 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] => 4 [1,0,1,0,1,1,1,0,1,0,0,0] => 5 [1,0,1,0,1,1,1,1,0,0,0,0] => 6 [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] => 2 [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] => 4 [1,0,1,1,0,1,0,0,1,0,1,0] => 2 [1,0,1,1,0,1,0,0,1,1,0,0] => 3 [1,0,1,1,0,1,0,1,0,0,1,0] => 3 [1,0,1,1,0,1,0,1,0,1,0,0] => 4 [1,0,1,1,0,1,0,1,1,0,0,0] => 5 [1,0,1,1,0,1,1,0,0,0,1,0] => 4 [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] => 6 [1,0,1,1,0,1,1,1,0,0,0,0] => 7 [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] => 4 [1,0,1,1,1,0,0,1,0,0,1,0] => 4 [1,0,1,1,1,0,0,1,0,1,0,0] => 5 [1,0,1,1,1,0,0,1,1,0,0,0] => 6 [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] => 6 [1,0,1,1,1,0,1,0,1,0,0,0] => 7 [1,0,1,1,1,0,1,1,0,0,0,0] => 8 [1,0,1,1,1,1,0,0,0,0,1,0] => 6 [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] => 8 [1,0,1,1,1,1,0,1,0,0,0,0] => 9 [1,0,1,1,1,1,1,0,0,0,0,0] => 10 [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] => 2 [1,1,0,0,1,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,0,1,1,0,1,0,0] => 3 [1,1,0,0,1,0,1,1,1,0,0,0] => 4 [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] => 3 [1,1,0,0,1,1,0,1,0,0,1,0] => 3 [1,1,0,0,1,1,0,1,0,1,0,0] => 4 [1,1,0,0,1,1,0,1,1,0,0,0] => 5 [1,1,0,0,1,1,1,0,0,0,1,0] => 4 [1,1,0,0,1,1,1,0,0,1,0,0] => 5 [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] => 2 [1,1,0,1,0,0,1,0,1,1,0,0] => 3 [1,1,0,1,0,0,1,1,0,0,1,0] => 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] => 5 [1,1,0,1,0,1,0,0,1,0,1,0] => 3 [1,1,0,1,0,1,0,0,1,1,0,0] => 4 [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] => 5 [1,1,0,1,0,1,0,1,1,0,0,0] => 6 [1,1,0,1,0,1,1,0,0,0,1,0] => 5 [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] => 7 [1,1,0,1,0,1,1,1,0,0,0,0] => 8 [1,1,0,1,1,0,0,0,1,0,1,0] => 4 [1,1,0,1,1,0,0,0,1,1,0,0] => 5 [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] => 7 [1,1,0,1,1,0,1,0,0,0,1,0] => 6 [1,1,0,1,1,0,1,0,0,1,0,0] => 7 [1,1,0,1,1,0,1,0,1,0,0,0] => 8 [1,1,0,1,1,0,1,1,0,0,0,0] => 9 [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] => 8 [1,1,0,1,1,1,0,0,1,0,0,0] => 9 [1,1,0,1,1,1,0,1,0,0,0,0] => 10 [1,1,0,1,1,1,1,0,0,0,0,0] => 11 [1,1,1,0,0,0,1,0,1,0,1,0] => 3 [1,1,1,0,0,0,1,0,1,1,0,0] => 4 [1,1,1,0,0,0,1,1,0,0,1,0] => 4 [1,1,1,0,0,0,1,1,0,1,0,0] => 5 [1,1,1,0,0,0,1,1,1,0,0,0] => 6 [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] => 5 [1,1,1,0,0,1,0,1,0,0,1,0] => 5 [1,1,1,0,0,1,0,1,0,1,0,0] => 6 [1,1,1,0,0,1,0,1,1,0,0,0] => 7 [1,1,1,0,0,1,1,0,0,0,1,0] => 6 [1,1,1,0,0,1,1,0,0,1,0,0] => 7 [1,1,1,0,0,1,1,0,1,0,0,0] => 8 [1,1,1,0,0,1,1,1,0,0,0,0] => 9 [1,1,1,0,1,0,0,0,1,0,1,0] => 5 [1,1,1,0,1,0,0,0,1,1,0,0] => 6 [1,1,1,0,1,0,0,1,0,0,1,0] => 6 [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] => 8 [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] => 8 [1,1,1,0,1,0,1,0,1,0,0,0] => 9 [1,1,1,0,1,0,1,1,0,0,0,0] => 10 [1,1,1,0,1,1,0,0,0,0,1,0] => 8 [1,1,1,0,1,1,0,0,0,1,0,0] => 9 [1,1,1,0,1,1,0,0,1,0,0,0] => 10 [1,1,1,0,1,1,0,1,0,0,0,0] => 11 [1,1,1,0,1,1,1,0,0,0,0,0] => 12 [1,1,1,1,0,0,0,0,1,0,1,0] => 6 [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] => 8 [1,1,1,1,0,0,0,1,1,0,0,0] => 9 [1,1,1,1,0,0,1,0,0,0,1,0] => 8 [1,1,1,1,0,0,1,0,0,1,0,0] => 9 [1,1,1,1,0,0,1,0,1,0,0,0] => 10 [1,1,1,1,0,0,1,1,0,0,0,0] => 11 [1,1,1,1,0,1,0,0,0,0,1,0] => 9 [1,1,1,1,0,1,0,0,0,1,0,0] => 10 [1,1,1,1,0,1,0,0,1,0,0,0] => 11 [1,1,1,1,0,1,0,1,0,0,0,0] => 12 [1,1,1,1,0,1,1,0,0,0,0,0] => 13 [1,1,1,1,1,0,0,0,0,0,1,0] => 10 [1,1,1,1,1,0,0,0,0,1,0,0] => 11 [1,1,1,1,1,0,0,0,1,0,0,0] => 12 [1,1,1,1,1,0,0,1,0,0,0,0] => 13 [1,1,1,1,1,0,1,0,0,0,0,0] => 14 [1,1,1,1,1,1,0,0,0,0,0,0] => 15 [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] => 1 [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] => 2 [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3 [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] => 2 [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3 [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4 [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3 [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => 6 [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2 [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2 [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] => 4 [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2 [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3 [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3 [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4 [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5 [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] => 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] => 3 [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4 [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4 [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5 [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 6 [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] => 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] => 8 [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6 [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 7 [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] => 9 [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10 [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] => 2 [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] => 3 [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4 [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] => 3 [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3 [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 5 [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4 [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5 [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 6 [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7 [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2 [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3 [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3 [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4 [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5 [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3 [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4 [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 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] => 6 [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5 [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6 [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 7 [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8 [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4 [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 5 [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5 [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6 [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 7 [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6 [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7 [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 8 [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 9 [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] => 8 [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 9 [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 10 [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 11 [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3 [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4 [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4 [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5 [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6 [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] => 5 [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5 [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6 [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7 [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 6 [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] => 8 [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9 [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] => 6 [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7 [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 8 [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] => 8 [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9 [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10 [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 8 [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 9 [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 10 [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11 [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12 [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6 [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 7 [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 7 [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] => 9 [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] => 9 [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 10 [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 11 [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 9 [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10 [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 11 [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12 [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13 [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10 [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 11 [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 12 [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 13 [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14 [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 15 [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] => 2 [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] => 3 [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] => 2 [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] => 3 [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] => 5 [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4 [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5 [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6 [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7 [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] => 3 [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] => 4 [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5 [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3 [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] => 4 [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5 [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 6 [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 5 [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 6 [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7 [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8 [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4 [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5 [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5 [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 6 [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7 [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] => 7 [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 8 [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 9 [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7 [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] => 9 [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 10 [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11 [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2 [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3 [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3 [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4 [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5 [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] => 4 [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4 [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5 [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 6 [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 5 [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 6 [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] => 3 [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] => 4 [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5 [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6 [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4 [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5 [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6 [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7 [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 6 [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 7 [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 8 [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9 [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5 [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 6 [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] => 8 [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7 [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 8 [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 9 [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 10 [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] => 9 [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 10 [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11 [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 12 [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] => 5 [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 5 [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 6 [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7 [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] => 6 [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] => 8 [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] => 8 [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 9 [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 10 [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 6 [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 7 [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] => 8 [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 9 [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 8 [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 9 [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 10 [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11 [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 9 [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 10 [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 11 [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12 [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 13 [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 7 [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] => 9 [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10 [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 9 [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 10 [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11 [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 12 [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 10 [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 11 [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 12 [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13 [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 14 [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11 [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 12 [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 13 [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 14 [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 15 [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 16 [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3 [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] => 4 [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 5 [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6 [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4 [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5 [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 5 [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 6 [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] => 6 [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 7 [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 8 [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 9 [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4 [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 5 [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5 [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 6 [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7 [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5 [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 6 [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6 [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7 [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] => 7 [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 8 [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 9 [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 10 [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6 [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 7 [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 7 [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 8 [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 9 [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 8 [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 9 [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 10 [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 11 [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9 [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 10 [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 11 [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 12 [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 13 [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] => 6 [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 6 [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] => 6 [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 7 [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 7 [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] => 9 [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] => 9 [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 10 [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 11 [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7 [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] => 9 [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 10 [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9 [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 10 [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11 [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12 [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 10 [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11 [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 12 [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 13 [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 14 [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] => 9 [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 9 [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 10 [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11 [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 10 [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 11 [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 12 [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 13 [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11 [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12 [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 13 [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 14 [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 15 [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 12 [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 13 [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 14 [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 15 [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 16 [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 17 [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6 [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7 [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7 [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 8 [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 9 [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 7 [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] => 9 [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 10 [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9 [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10 [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 11 [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 12 [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] => 9 [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 9 [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 10 [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 11 [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 10 [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 11 [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 12 [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 13 [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11 [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 12 [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13 [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 14 [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 15 [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 9 [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 10 [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 10 [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 11 [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12 [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11 [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 12 [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 13 [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 14 [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 12 [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 13 [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 14 [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15 [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 16 [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 13 [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 14 [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 15 [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 16 [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 17 [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 18 [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 10 [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11 [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11 [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12 [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13 [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 12 [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 13 [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14 [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 15 [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 13 [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14 [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 15 [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 16 [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 17 [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14 [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 15 [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 16 [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 17 [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 18 [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 19 [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15 [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 16 [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 17 [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 18 [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 19 [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 20 [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 21 [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] => 1 [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] => 2 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3 [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] => 2 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6 [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] => 2 [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] => 3 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7 [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4 [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 6 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 8 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 7 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 8 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 9 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10 [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] => 2 [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] => 3 [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4 [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] => 3 [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 5 [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4 [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5 [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 6 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2 [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3 [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3 [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4 [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3 [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4 [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6 [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5 [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6 [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 7 [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8 [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4 [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 5 [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5 [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 7 [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6 [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7 [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 8 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 9 [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7 [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 8 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 9 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 10 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 11 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3 [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4 [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5 [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6 [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4 [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 5 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5 [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7 [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 6 [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 7 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 8 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5 [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 6 [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 6 [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7 [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 8 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 7 [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9 [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 8 [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 9 [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 10 [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11 [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6 [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 7 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 7 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 8 [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 9 [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 8 [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 9 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 10 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 11 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 9 [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10 [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 11 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10 [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 11 [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 12 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 13 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 15 [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] => 2 [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] => 3 [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4 [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] => 3 [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 5 [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5 [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7 [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] => 3 [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] => 4 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3 [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4 [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5 [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 6 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 5 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 6 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7 [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8 [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4 [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 6 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7 [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 6 [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 7 [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 8 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 9 [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7 [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 8 [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 9 [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 10 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3 [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5 [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3 [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 6 [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 5 [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 6 [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 7 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 8 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4 [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5 [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6 [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4 [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7 [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 6 [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 7 [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 8 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9 [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5 [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 6 [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 6 [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 7 [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 8 [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 8 [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 9 [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 10 [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 9 [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 10 [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 12 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 5 [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 5 [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 6 [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7 [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 6 [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 6 [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 7 [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 8 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 7 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 8 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 9 [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 10 [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 6 [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 7 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 7 [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 8 [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 9 [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 8 [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 9 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 10 [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11 [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 9 [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 10 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 11 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12 [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 13 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 7 [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8 [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 8 [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 9 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10 [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 9 [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 10 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11 [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 12 [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 10 [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 11 [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 12 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13 [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 14 [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11 [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 12 [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 13 [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 14 [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 15 [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 16 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 5 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6 [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4 [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5 [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 5 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 6 [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 7 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6 [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 7 [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 8 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 9 [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4 [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 5 [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 6 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7 [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5 [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 6 [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7 [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 8 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 7 [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 8 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 9 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 10 [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6 [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 7 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 7 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 8 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 9 [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 8 [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 9 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 10 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 11 [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9 [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 10 [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 11 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 12 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 13 [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5 [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6 [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 6 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 7 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 8 [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 6 [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 7 [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 7 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 8 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 9 [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 8 [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 9 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 10 [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 11 [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7 [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 8 [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 8 [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 9 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 10 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9 [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 10 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11 [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12 [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 10 [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11 [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 12 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 13 [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 14 [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 8 [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 9 [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 9 [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 10 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11 [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 10 [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 11 [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 12 [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 13 [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 13 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 14 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 15 [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 12 [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 13 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 14 [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 15 [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 16 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 17 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6 [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7 [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7 [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 8 [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 9 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 7 [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 8 [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 8 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 9 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 10 [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9 [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10 [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 11 [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 12 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 8 [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 9 [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 9 [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 10 [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 11 [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 10 [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 11 [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 12 [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 13 [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11 [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 12 [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13 [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 14 [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 15 [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 9 [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 10 [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 10 [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 11 [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12 [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 12 [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 13 [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 14 [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 12 [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 13 [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 14 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15 [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 16 [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 13 [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 14 [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 15 [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 16 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 17 [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 18 [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 10 [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11 [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11 [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13 [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 12 [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 13 [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14 [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 15 [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 13 [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14 [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 15 [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 16 [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 17 [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14 [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 15 [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 16 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 17 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 18 [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 19 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15 [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 16 [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 17 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 18 [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 19 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 20 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 21 [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] => 2 [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] => 3 [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4 [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] => 3 [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4 [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5 [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4 [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5 [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 7 [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] => 3 [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] => 4 [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5 [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4 [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4 [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5 [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 6 [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5 [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 6 [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 7 [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 8 [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4 [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5 [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5 [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 6 [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 7 [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 6 [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 7 [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 8 [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 9 [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7 [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 8 [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 9 [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 11 [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] => 3 [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] => 4 [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5 [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] => 4 [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4 [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 5 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 6 [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 5 [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 6 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 7 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8 [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3 [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4 [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4 [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5 [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 6 [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4 [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 5 [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6 [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 7 [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 6 [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 7 [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 8 [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 9 [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 5 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 6 [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 6 [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 7 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 8 [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 7 [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 8 [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 9 [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 10 [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 8 [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 9 [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 10 [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 11 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 12 [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5 [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 5 [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 6 [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7 [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5 [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 6 [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 6 [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 7 [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 8 [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 7 [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 8 [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 9 [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 10 [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 6 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 7 [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 7 [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 8 [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 9 [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 8 [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 9 [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 10 [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 11 [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 9 [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 10 [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11 [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 12 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 13 [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8 [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 8 [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 9 [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 10 [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 9 [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 10 [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 11 [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 12 [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 10 [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 11 [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 13 [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 14 [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 11 [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 12 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 13 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 14 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 15 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 16 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3 [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4 [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 5 [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3 [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4 [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4 [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5 [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 6 [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 5 [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 6 [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 7 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8 ----------------------------------------------------------------------------- Created: Sep 27, 2011 at 19:29 by Chris Berg ----------------------------------------------------------------------------- Last Updated: Jun 17, 2019 at 17:03 by Christian Stump