***************************************************************************** * 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: St001956 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The comajor index for set-valued two-row standard Young tableaux. The comajorindex is the sum $\sum_k (n+1-k)$ over all natural descents $k$. Bijections via bicolored Motzkin paths (with two restrictions, see [1]) give the following for Dyck paths. Let $j$ be smallest integer such that $2j$ is a down step. Then $k$ is a natural descent if * $k-2\ge j$ and positions $2(k-1)-1,2(k-1)$ are a valley i.e. [0,1], or * $k-2\ge j$ and positions $2(k-1)-1,2(k-1)$ are a peak i.e. [1,0], or * $k-1\ge j$ and positions $2(k-1),2k-1,2k$ form [0,1,1], or * $k=j$ and positions $2k-1,2k$ are double down i.e. [0,0], or * $k < j$ and positions $2k-1,2k$ are a valley i.e. [0,1]. ----------------------------------------------------------------------------- References: [1] Alexander Lazar and Svante Linusson, "Two-row Set-Valued Tableaux: Catalan$^+k$ Combinatorics", Extended abstract at FPSAC 2024. ----------------------------------------------------------------------------- Code: def natural_descents(D): for j in range(1, D.semilength()+1): if D[2*j-1] == 0: break else: raise ValueError des = [] for k in range(1, len(D)+2): if k-2 >= j and D[2*(k-1)-2:2*(k-1)] == [0,1]: des.append(k) elif k-2 >= j and D[2*(k-1)-2:2*(k-1)] == [1,0]: des.append(k) elif k-1 >= j and D[2*(k-1)-1:2*k] == [0,1,1]: des.append(k) elif k == j and D[2*k-2:2*k] == [0,0]: des.append(k) elif k < j and D[2*k-2:2*k] == [0,1]: des.append(k) return des def statistic(D): n = D.semilength() return sum(n+1-k for k in natural_descents(D)) ----------------------------------------------------------------------------- Statistic values: [1,0] => 0 [1,0,1,0] => 0 [1,1,0,0] => 1 [1,0,1,0,1,0] => 1 [1,0,1,1,0,0] => 2 [1,1,0,0,1,0] => 2 [1,1,0,1,0,0] => 3 [1,1,1,0,0,0] => 0 [1,0,1,0,1,0,1,0] => 3 [1,0,1,0,1,1,0,0] => 2 [1,0,1,1,0,0,1,0] => 3 [1,0,1,1,0,1,0,0] => 4 [1,0,1,1,1,0,0,0] => 4 [1,1,0,0,1,0,1,0] => 4 [1,1,0,0,1,1,0,0] => 5 [1,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,1,0,0] => 6 [1,1,0,1,1,0,0,0] => 3 [1,1,1,0,0,0,1,0] => 0 [1,1,1,0,0,1,0,0] => 1 [1,1,1,0,1,0,0,0] => 1 [1,1,1,1,0,0,0,0] => 2 [1,0,1,0,1,0,1,0,1,0] => 6 [1,0,1,0,1,0,1,1,0,0] => 5 [1,0,1,0,1,1,0,0,1,0] => 3 [1,0,1,0,1,1,0,1,0,0] => 4 [1,0,1,0,1,1,1,0,0,0] => 4 [1,0,1,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,0,1,1,0,0] => 6 [1,0,1,1,0,1,0,0,1,0] => 6 [1,0,1,1,0,1,0,1,0,0] => 7 [1,0,1,1,0,1,1,0,0,0] => 7 [1,0,1,1,1,0,0,0,1,0] => 6 [1,0,1,1,1,0,0,1,0,0] => 7 [1,0,1,1,1,0,1,0,0,0] => 7 [1,0,1,1,1,1,0,0,0,0] => 4 [1,1,0,0,1,0,1,0,1,0] => 7 [1,1,0,0,1,0,1,1,0,0] => 6 [1,1,0,0,1,1,0,0,1,0] => 7 [1,1,0,0,1,1,0,1,0,0] => 8 [1,1,0,0,1,1,1,0,0,0] => 8 [1,1,0,1,0,0,1,0,1,0] => 8 [1,1,0,1,0,0,1,1,0,0] => 9 [1,1,0,1,0,1,0,0,1,0] => 9 [1,1,0,1,0,1,0,1,0,0] => 10 [1,1,0,1,0,1,1,0,0,0] => 7 [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] => 5 [1,1,0,1,1,1,0,0,0,0] => 6 [1,1,1,0,0,0,1,0,1,0] => 1 [1,1,1,0,0,0,1,1,0,0] => 2 [1,1,1,0,0,1,0,0,1,0] => 2 [1,1,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,1,0,0,0] => 3 [1,1,1,0,1,0,0,0,1,0] => 2 [1,1,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,1,0,0,0] => 3 [1,1,1,0,1,1,0,0,0,0] => 3 [1,1,1,1,0,0,0,0,1,0] => 3 [1,1,1,1,0,0,0,1,0,0] => 4 [1,1,1,1,0,0,1,0,0,0] => 4 [1,1,1,1,0,1,0,0,0,0] => 5 [1,1,1,1,1,0,0,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,0,1,0] => 10 [1,0,1,0,1,0,1,0,1,1,0,0] => 9 [1,0,1,0,1,0,1,1,0,0,1,0] => 7 [1,0,1,0,1,0,1,1,0,1,0,0] => 8 [1,0,1,0,1,0,1,1,1,0,0,0] => 8 [1,0,1,0,1,1,0,0,1,0,1,0] => 5 [1,0,1,0,1,1,0,0,1,1,0,0] => 6 [1,0,1,0,1,1,0,1,0,0,1,0] => 6 [1,0,1,0,1,1,0,1,0,1,0,0] => 7 [1,0,1,0,1,1,0,1,1,0,0,0] => 7 [1,0,1,0,1,1,1,0,0,0,1,0] => 6 [1,0,1,0,1,1,1,0,0,1,0,0] => 7 [1,0,1,0,1,1,1,0,1,0,0,0] => 7 [1,0,1,0,1,1,1,1,0,0,0,0] => 4 [1,0,1,1,0,0,1,0,1,0,1,0] => 8 [1,0,1,1,0,0,1,0,1,1,0,0] => 7 [1,0,1,1,0,0,1,1,0,0,1,0] => 8 [1,0,1,1,0,0,1,1,0,1,0,0] => 9 [1,0,1,1,0,0,1,1,1,0,0,0] => 9 [1,0,1,1,0,1,0,0,1,0,1,0] => 9 [1,0,1,1,0,1,0,0,1,1,0,0] => 10 [1,0,1,1,0,1,0,1,0,0,1,0] => 10 [1,0,1,1,0,1,0,1,0,1,0,0] => 11 [1,0,1,1,0,1,0,1,1,0,0,0] => 11 [1,0,1,1,0,1,1,0,0,0,1,0] => 10 [1,0,1,1,0,1,1,0,0,1,0,0] => 11 [1,0,1,1,0,1,1,0,1,0,0,0] => 11 [1,0,1,1,0,1,1,1,0,0,0,0] => 8 [1,0,1,1,1,0,0,0,1,0,1,0] => 9 [1,0,1,1,1,0,0,0,1,1,0,0] => 10 [1,0,1,1,1,0,0,1,0,0,1,0] => 10 [1,0,1,1,1,0,0,1,0,1,0,0] => 11 [1,0,1,1,1,0,0,1,1,0,0,0] => 11 [1,0,1,1,1,0,1,0,0,0,1,0] => 10 [1,0,1,1,1,0,1,0,0,1,0,0] => 11 [1,0,1,1,1,0,1,0,1,0,0,0] => 11 [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] => 5 [1,0,1,1,1,1,0,0,0,1,0,0] => 6 [1,0,1,1,1,1,0,0,1,0,0,0] => 6 [1,0,1,1,1,1,0,1,0,0,0,0] => 7 [1,0,1,1,1,1,1,0,0,0,0,0] => 7 [1,1,0,0,1,0,1,0,1,0,1,0] => 11 [1,1,0,0,1,0,1,0,1,1,0,0] => 10 [1,1,0,0,1,0,1,1,0,0,1,0] => 8 [1,1,0,0,1,0,1,1,0,1,0,0] => 9 [1,1,0,0,1,0,1,1,1,0,0,0] => 9 [1,1,0,0,1,1,0,0,1,0,1,0] => 10 [1,1,0,0,1,1,0,0,1,1,0,0] => 11 [1,1,0,0,1,1,0,1,0,0,1,0] => 11 [1,1,0,0,1,1,0,1,0,1,0,0] => 12 [1,1,0,0,1,1,0,1,1,0,0,0] => 12 [1,1,0,0,1,1,1,0,0,0,1,0] => 11 [1,1,0,0,1,1,1,0,0,1,0,0] => 12 [1,1,0,0,1,1,1,0,1,0,0,0] => 12 [1,1,0,0,1,1,1,1,0,0,0,0] => 9 [1,1,0,1,0,0,1,0,1,0,1,0] => 12 [1,1,0,1,0,0,1,0,1,1,0,0] => 11 [1,1,0,1,0,0,1,1,0,0,1,0] => 12 [1,1,0,1,0,0,1,1,0,1,0,0] => 13 [1,1,0,1,0,0,1,1,1,0,0,0] => 13 [1,1,0,1,0,1,0,0,1,0,1,0] => 13 [1,1,0,1,0,1,0,0,1,1,0,0] => 14 [1,1,0,1,0,1,0,1,0,0,1,0] => 14 [1,1,0,1,0,1,0,1,0,1,0,0] => 15 [1,1,0,1,0,1,0,1,1,0,0,0] => 12 [1,1,0,1,0,1,1,0,0,0,1,0] => 9 [1,1,0,1,0,1,1,0,0,1,0,0] => 10 [1,1,0,1,0,1,1,0,1,0,0,0] => 10 [1,1,0,1,0,1,1,1,0,0,0,0] => 11 [1,1,0,1,1,0,0,0,1,0,1,0] => 6 [1,1,0,1,1,0,0,0,1,1,0,0] => 7 [1,1,0,1,1,0,0,1,0,0,1,0] => 7 [1,1,0,1,1,0,0,1,0,1,0,0] => 8 [1,1,0,1,1,0,0,1,1,0,0,0] => 8 [1,1,0,1,1,0,1,0,0,0,1,0] => 7 [1,1,0,1,1,0,1,0,0,1,0,0] => 8 [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] => 8 [1,1,0,1,1,1,0,0,0,0,1,0] => 8 [1,1,0,1,1,1,0,0,0,1,0,0] => 9 [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] => 5 [1,1,1,0,0,0,1,0,1,0,1,0] => 3 [1,1,1,0,0,0,1,0,1,1,0,0] => 2 [1,1,1,0,0,0,1,1,0,0,1,0] => 3 [1,1,1,0,0,0,1,1,0,1,0,0] => 4 [1,1,1,0,0,0,1,1,1,0,0,0] => 4 [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] => 6 [1,1,1,0,0,1,1,0,0,0,1,0] => 5 [1,1,1,0,0,1,1,0,0,1,0,0] => 6 [1,1,1,0,0,1,1,0,1,0,0,0] => 6 [1,1,1,0,0,1,1,1,0,0,0,0] => 3 [1,1,1,0,1,0,0,0,1,0,1,0] => 4 [1,1,1,0,1,0,0,0,1,1,0,0] => 5 [1,1,1,0,1,0,0,1,0,0,1,0] => 5 [1,1,1,0,1,0,0,1,0,1,0,0] => 6 [1,1,1,0,1,0,0,1,1,0,0,0] => 6 [1,1,1,0,1,0,1,0,0,0,1,0] => 5 [1,1,1,0,1,0,1,0,0,1,0,0] => 6 [1,1,1,0,1,0,1,0,1,0,0,0] => 6 [1,1,1,0,1,0,1,1,0,0,0,0] => 3 [1,1,1,0,1,1,0,0,0,0,1,0] => 4 [1,1,1,0,1,1,0,0,0,1,0,0] => 5 [1,1,1,0,1,1,0,0,1,0,0,0] => 5 [1,1,1,0,1,1,0,1,0,0,0,0] => 6 [1,1,1,0,1,1,1,0,0,0,0,0] => 6 [1,1,1,1,0,0,0,0,1,0,1,0] => 5 [1,1,1,1,0,0,0,0,1,1,0,0] => 6 [1,1,1,1,0,0,0,1,0,0,1,0] => 6 [1,1,1,1,0,0,0,1,0,1,0,0] => 7 [1,1,1,1,0,0,0,1,1,0,0,0] => 7 [1,1,1,1,0,0,1,0,0,0,1,0] => 6 [1,1,1,1,0,0,1,0,0,1,0,0] => 7 [1,1,1,1,0,0,1,0,1,0,0,0] => 7 [1,1,1,1,0,0,1,1,0,0,0,0] => 7 [1,1,1,1,0,1,0,0,0,0,1,0] => 7 [1,1,1,1,0,1,0,0,0,1,0,0] => 8 [1,1,1,1,0,1,0,0,1,0,0,0] => 8 [1,1,1,1,0,1,0,1,0,0,0,0] => 9 [1,1,1,1,0,1,1,0,0,0,0,0] => 4 [1,1,1,1,1,0,0,0,0,0,1,0] => 0 [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] => 2 [1,1,1,1,1,0,1,0,0,0,0,0] => 2 [1,1,1,1,1,1,0,0,0,0,0,0] => 3 [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 15 [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 14 [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 12 [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 13 [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 13 [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 10 [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11 [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 11 [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 12 [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 12 [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 11 [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 12 [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 12 [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9 [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 8 [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 7 [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 8 [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 9 [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 9 [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 9 [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 10 [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 10 [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 11 [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 11 [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 10 [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 11 [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 11 [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 8 [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 9 [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 10 [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 10 [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 11 [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 11 [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 10 [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 11 [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 11 [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] => 5 [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 6 [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 6 [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 7 [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7 [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 12 [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 11 [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 9 [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 10 [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 10 [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 11 [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12 [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 12 [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 13 [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 13 [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 12 [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 13 [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 13 [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 10 [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 13 [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 12 [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 13 [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 14 [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 14 [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 14 [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 15 [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 15 [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16 [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 16 [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 15 [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 16 [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 16 [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 13 [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 14 [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 15 [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 15 [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 16 [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 16 [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 15 [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 16 [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 16 [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 13 [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 10 [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 11 [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 11 [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 12 [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 12 [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 13 [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 12 [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 13 [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 14 [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 14 [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 14 [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 15 [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 15 [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 16 [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 16 [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 15 [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 16 [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 16 [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 13 [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 14 [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 15 [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 15 [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 16 [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 16 [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 15 [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 16 [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 16 [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 13 [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 10 [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 11 [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11 [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 12 [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] => 7 [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8 [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 8 [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 9 [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] => 9 [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 9 [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] => 10 [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 11 [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 11 [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9 [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10 [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10 [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 11 [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 11 [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6 [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 16 [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 15 [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 13 [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 14 [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 14 [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 11 [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 12 [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 12 [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 13 [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 13 [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 12 [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 13 [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 13 [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 10 [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 14 [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 13 [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 14 [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 15 [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 15 [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 15 [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 16 [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 16 [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 17 [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 17 [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 16 [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 17 [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 17 [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 14 [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 15 [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 16 [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 16 [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 17 [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 17 [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 16 [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 17 [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 17 [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 14 [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11 [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 12 [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 12 [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 13 [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 13 [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 17 [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 16 [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 14 [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 15 [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 15 [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 16 [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 17 [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 17 [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 18 [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 18 [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 17 [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 18 [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 18 [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 15 [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 18 [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 17 [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 18 [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 19 [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 19 [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 19 [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 20 [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 20 [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 21 [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 18 [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 15 [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 16 [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 16 [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 17 [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 12 [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 13 [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 13 [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 14 [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 14 [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 13 [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 14 [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 14 [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 14 [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 14 [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 15 [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 15 [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 16 [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 11 [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 9 [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 8 [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 9 [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 10 [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 10 [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 10 [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 11 [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 11 [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 12 [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 12 [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 11 [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 12 [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 12 [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 9 [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 10 [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 11 [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 11 [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 12 [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 12 [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 11 [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 12 [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 12 [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 9 [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 10 [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 11 [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] => 12 [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 11 [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 12 [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 12 [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 13 [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 13 [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 12 [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 13 [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 13 [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 13 [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 13 [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 14 [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 14 [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 15 [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 10 [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 6 [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7 [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7 [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 8 [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 8 [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 9 [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6 [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 5 [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3 [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4 [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4 [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 5 [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 6 [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 6 [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 7 [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 7 [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 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] => 7 [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4 [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 7 [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 6 [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 7 [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 8 [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 8 [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 8 [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 9 [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 9 [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 10 [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 10 [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 9 [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 10 [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 10 [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7 [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 8 [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 9 [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 9 [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 10 [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 10 [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 9 [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 10 [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] => 7 [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 4 [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 5 [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 5 [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 6 [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 6 [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 7 [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] => 7 [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 8 [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 8 [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 8 [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 9 [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 9 [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 10 [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 10 [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 9 [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 10 [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] => 7 [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 8 [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 9 [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 9 [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 10 [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] => 10 [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 7 [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 4 [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5 [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 5 [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 6 [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 6 [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 6 [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 7 [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 7 [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 8 [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8 [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 7 [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 8 [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 8 [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8 [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 8 [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 9 [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 9 [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 10 [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 10 [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 8 [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 9 [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 9 [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 10 [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 10 [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 5 [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 8 [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7 [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 8 [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 9 [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] => 9 [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 10 [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 10 [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 11 [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 11 [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 10 [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 11 [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] => 8 [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 9 [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 10 [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10 [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 11 [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] => 11 [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 8 [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 9 [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10 [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10 [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 11 [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 11 [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 10 [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 11 [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11 [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 12 [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] => 12 [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 12 [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] => 13 [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 14 [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 9 [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 5 [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 6 [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 6 [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7 [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7 [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8 [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1 [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2 [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2 [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3 [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 3 [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] => 3 [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3 [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 3 [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3 [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 4 [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 4 [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 5 [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 5 [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3 [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 4 [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 4 [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 5 [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5 [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 4 [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 4 [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 5 [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 5 [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6 [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 6 [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7 [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] => 21 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 18 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 19 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 19 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 16 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 17 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 17 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 18 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 18 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 18 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 18 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 15 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 14 [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 13 [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 14 [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 15 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 15 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 15 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 16 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 16 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 17 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 17 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 16 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 17 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 17 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 14 [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 15 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 16 [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 16 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 17 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 17 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 16 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 17 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 17 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 14 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 11 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 12 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 12 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 13 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 13 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 12 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 11 [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 9 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 10 [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 10 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 11 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12 [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 12 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 13 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 13 [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 12 [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 13 [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 13 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 10 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 13 [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 12 [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 13 [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 14 [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 14 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 14 [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 15 [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 15 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 16 [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 15 [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 16 [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 16 [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 13 [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 14 [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 15 [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 15 [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 16 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 16 [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 15 [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 16 [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 16 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 13 [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 10 [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 11 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 11 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 12 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 12 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 13 [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 12 [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 13 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 14 [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 14 [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 14 [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 15 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 15 [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 16 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 16 [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 15 [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 16 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 16 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 13 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 14 [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 15 [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 15 [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 16 [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 16 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 15 [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 16 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 16 [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 13 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 10 [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 11 [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11 [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 12 [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] => 7 [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 8 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 9 [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] => 9 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 9 [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] => 10 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 11 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 11 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9 [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10 [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 11 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 11 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 17 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 16 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 14 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 15 [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 15 [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 12 [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 13 [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 13 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 14 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 14 [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 13 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 14 [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 14 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 11 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 15 [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 14 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 15 [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 16 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 16 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 16 [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 17 [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 17 [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 18 [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 18 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 17 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 18 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 18 [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 15 [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 16 [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 17 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 17 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 18 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 18 [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 17 [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 18 [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 18 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 15 [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 12 [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 13 [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 13 [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 14 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 14 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 18 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 17 [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 15 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 16 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 16 [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 17 [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 18 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 18 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 19 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 19 [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 18 [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 19 [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 19 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 16 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 19 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 18 [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 19 [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 20 [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 20 [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 20 [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 21 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 21 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 22 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 22 [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 21 [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 22 [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 22 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 19 [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 20 [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 21 [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 21 [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 22 [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 22 [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 21 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 22 [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 22 [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 19 [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 16 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 17 [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 17 [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 18 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 18 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 19 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 18 [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 19 [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 20 [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 20 [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 20 [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 21 [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 21 [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 22 [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 22 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 21 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 22 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 22 [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 19 [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 20 [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 21 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 21 [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 22 [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 22 [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 21 [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 22 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 22 [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 19 [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 16 [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 17 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 17 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 18 [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 18 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 13 [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 14 [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 14 [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 15 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 15 [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 14 [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 15 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 15 [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 15 [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 15 [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 16 [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 16 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 17 [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 17 [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 15 [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 16 [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 16 [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 17 [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 17 [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 12 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 18 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 17 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 15 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 16 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 16 [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 17 [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 18 [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 18 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 19 [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 19 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 18 [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 19 [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 19 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 16 [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 19 [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 18 [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 19 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 20 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 20 [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 20 [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 21 [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 21 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 22 [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 22 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 21 [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 22 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 22 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 19 [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 20 [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 21 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 21 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 22 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 22 [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 21 [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 22 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 22 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 19 [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 16 [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 17 [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 17 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 18 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 18 [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 19 [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 18 [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 19 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 20 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 20 [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 20 [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 21 [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 21 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 22 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 22 [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 21 [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 22 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 22 [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 19 [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 20 [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 21 [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 21 [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 22 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 22 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 21 [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 22 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 22 [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 19 [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 16 [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 17 [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 17 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 18 [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 18 [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 13 [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 14 [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 14 [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 15 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 15 [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 14 [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 15 [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 15 [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 15 [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 15 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 16 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 16 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 17 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 17 [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 15 [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 16 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 16 [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 17 [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 17 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 12 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 10 [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9 [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 10 [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 11 [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 11 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 11 [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 12 [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 12 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 13 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 13 [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 12 [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 13 [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 13 [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 10 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 11 [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 12 [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 12 [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 13 [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 13 [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 12 [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 13 [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 13 [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 10 [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] => 12 [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 13 [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 13 [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 12 [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 13 [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 13 [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 14 [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 14 [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 13 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 14 [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 14 [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] => 14 [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 15 [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 15 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 16 [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] => 14 [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 15 [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] => 16 [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 11 [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 12 [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 13 [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 13 [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 14 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 14 [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 13 [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 14 [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] => 14 [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 14 [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 15 [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] => 16 [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] => 15 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 16 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 16 [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 11 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7 [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 8 [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 9 [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 9 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 10 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 10 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 22 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21 [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 19 [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 20 [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 20 [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 17 [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 18 [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 18 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 19 [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 19 [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 18 [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 19 [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 19 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 16 [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 15 [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 14 [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 15 [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 16 [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 16 [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 16 [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 17 [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 17 [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 18 [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 18 [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 17 [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 18 [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 18 [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 15 [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 16 [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 17 [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 17 [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 18 [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 18 [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 17 [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 18 [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 18 [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 15 [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 12 [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 13 [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 13 [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 14 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 14 [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 19 [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18 [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 16 [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 17 [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 17 [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 18 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 19 [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 19 [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 20 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 20 [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 19 [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 20 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 20 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 17 [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 20 [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 19 [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 20 [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 21 [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 21 [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 21 [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 22 [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 22 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 23 [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 23 [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 22 [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 23 [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 23 [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 20 [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 21 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 22 [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 22 [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 23 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 23 [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 22 [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 23 [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 23 [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 20 [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 17 [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 18 [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 18 [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 19 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 19 [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 20 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 19 [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 20 [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 21 [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 21 [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 21 [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 22 [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 22 [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 23 [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 23 [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 22 [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 23 [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 23 [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 20 [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 21 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 22 [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 22 [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 23 [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 23 [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 22 [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 23 [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 23 [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 20 [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 17 [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 18 [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 18 [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 19 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 19 [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 14 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 15 [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 15 [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 16 [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 16 [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 15 [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 16 [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 16 [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 16 [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 16 [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 17 [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 17 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 18 [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 18 [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 16 [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 17 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 17 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 18 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 18 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 13 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 23 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 22 [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 21 [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 21 [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 18 [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 19 [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 19 [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 20 [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 20 [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 19 [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 20 [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 20 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 17 ----------------------------------------------------------------------------- Created: Jul 25, 2024 at 23:26 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jul 25, 2024 at 23:26 by Martin Rubey