*****************************************************************************
*       www.FindStat.org - The Combinatorial Statistic Finder               *
*                                                                           *
*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
*                                                                           *
*    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: St000394

-----------------------------------------------------------------------------
Collection: Dyck paths

-----------------------------------------------------------------------------
Description: The sum of the heights of the peaks of a Dyck path minus the number of peaks.

-----------------------------------------------------------------------------
References: [1]   Feinberg, G., Lee, K.-H. Homogeneous representations of Type A KLR-algebras and Dyck paths [[arXiv:1505.04075]]
[2]   Cheng, S.-E., Elizalde, S., Kasraoui, A., Sagan, B. Inversion polynomials for 321-avoiding permutations [[arXiv:1112.6014]]

-----------------------------------------------------------------------------
Code:
def statistic(D):
    heights = D.heights()
    return sum(heights[i+1]-1 for i in D.peaks())


-----------------------------------------------------------------------------
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]                                                                                                         => 2
[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]                                                                                                     => 2
[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]                                                                                                     => 3
[1,1,1,0,0,0,1,0]                                                                                                     => 2
[1,1,1,0,0,1,0,0]                                                                                                     => 3
[1,1,1,0,1,0,0,0]                                                                                                     => 4
[1,1,1,1,0,0,0,0]                                                                                                     => 3
[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]                                                                                                 => 2
[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]                                                                                                 => 3
[1,0,1,1,1,0,0,0,1,0]                                                                                                 => 2
[1,0,1,1,1,0,0,1,0,0]                                                                                                 => 3
[1,0,1,1,1,0,1,0,0,0]                                                                                                 => 4
[1,0,1,1,1,1,0,0,0,0]                                                                                                 => 3
[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]                                                                                                 => 3
[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]                                                                                                 => 4
[1,1,0,1,1,0,0,0,1,0]                                                                                                 => 3
[1,1,0,1,1,0,0,1,0,0]                                                                                                 => 4
[1,1,0,1,1,0,1,0,0,0]                                                                                                 => 5
[1,1,0,1,1,1,0,0,0,0]                                                                                                 => 4
[1,1,1,0,0,0,1,0,1,0]                                                                                                 => 2
[1,1,1,0,0,0,1,1,0,0]                                                                                                 => 3
[1,1,1,0,0,1,0,0,1,0]                                                                                                 => 3
[1,1,1,0,0,1,0,1,0,0]                                                                                                 => 4
[1,1,1,0,0,1,1,0,0,0]                                                                                                 => 4
[1,1,1,0,1,0,0,0,1,0]                                                                                                 => 4
[1,1,1,0,1,0,0,1,0,0]                                                                                                 => 5
[1,1,1,0,1,0,1,0,0,0]                                                                                                 => 6
[1,1,1,0,1,1,0,0,0,0]                                                                                                 => 5
[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]                                                                                                 => 5
[1,1,1,1,0,1,0,0,0,0]                                                                                                 => 6
[1,1,1,1,1,0,0,0,0,0]                                                                                                 => 4
[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]                                                                                             => 2
[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]                                                                                             => 3
[1,0,1,0,1,1,1,0,0,0,1,0]                                                                                             => 2
[1,0,1,0,1,1,1,0,0,1,0,0]                                                                                             => 3
[1,0,1,0,1,1,1,0,1,0,0,0]                                                                                             => 4
[1,0,1,0,1,1,1,1,0,0,0,0]                                                                                             => 3
[1,0,1,1,0,0,1,0,1,0,1,0]                                                                                             => 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]                                                                                             => 3
[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]                                                                                             => 4
[1,0,1,1,0,1,1,0,0,0,1,0]                                                                                             => 3
[1,0,1,1,0,1,1,0,0,1,0,0]                                                                                             => 4
[1,0,1,1,0,1,1,0,1,0,0,0]                                                                                             => 5
[1,0,1,1,0,1,1,1,0,0,0,0]                                                                                             => 4
[1,0,1,1,1,0,0,0,1,0,1,0]                                                                                             => 2
[1,0,1,1,1,0,0,0,1,1,0,0]                                                                                             => 3
[1,0,1,1,1,0,0,1,0,0,1,0]                                                                                             => 3
[1,0,1,1,1,0,0,1,0,1,0,0]                                                                                             => 4
[1,0,1,1,1,0,0,1,1,0,0,0]                                                                                             => 4
[1,0,1,1,1,0,1,0,0,0,1,0]                                                                                             => 4
[1,0,1,1,1,0,1,0,0,1,0,0]                                                                                             => 5
[1,0,1,1,1,0,1,0,1,0,0,0]                                                                                             => 6
[1,0,1,1,1,0,1,1,0,0,0,0]                                                                                             => 5
[1,0,1,1,1,1,0,0,0,0,1,0]                                                                                             => 3
[1,0,1,1,1,1,0,0,0,1,0,0]                                                                                             => 4
[1,0,1,1,1,1,0,0,1,0,0,0]                                                                                             => 5
[1,0,1,1,1,1,0,1,0,0,0,0]                                                                                             => 6
[1,0,1,1,1,1,1,0,0,0,0,0]                                                                                             => 4
[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]                                                                                             => 3
[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]                                                                                             => 4
[1,1,0,0,1,1,1,0,0,0,1,0]                                                                                             => 3
[1,1,0,0,1,1,1,0,0,1,0,0]                                                                                             => 4
[1,1,0,0,1,1,1,0,1,0,0,0]                                                                                             => 5
[1,1,0,0,1,1,1,1,0,0,0,0]                                                                                             => 4
[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]                                                                                             => 4
[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]                                                                                             => 5
[1,1,0,1,0,1,1,0,0,0,1,0]                                                                                             => 4
[1,1,0,1,0,1,1,0,0,1,0,0]                                                                                             => 5
[1,1,0,1,0,1,1,0,1,0,0,0]                                                                                             => 6
[1,1,0,1,0,1,1,1,0,0,0,0]                                                                                             => 5
[1,1,0,1,1,0,0,0,1,0,1,0]                                                                                             => 3
[1,1,0,1,1,0,0,0,1,1,0,0]                                                                                             => 4
[1,1,0,1,1,0,0,1,0,0,1,0]                                                                                             => 4
[1,1,0,1,1,0,0,1,0,1,0,0]                                                                                             => 5
[1,1,0,1,1,0,0,1,1,0,0,0]                                                                                             => 5
[1,1,0,1,1,0,1,0,0,0,1,0]                                                                                             => 5
[1,1,0,1,1,0,1,0,0,1,0,0]                                                                                             => 6
[1,1,0,1,1,0,1,0,1,0,0,0]                                                                                             => 7
[1,1,0,1,1,0,1,1,0,0,0,0]                                                                                             => 6
[1,1,0,1,1,1,0,0,0,0,1,0]                                                                                             => 4
[1,1,0,1,1,1,0,0,0,1,0,0]                                                                                             => 5
[1,1,0,1,1,1,0,0,1,0,0,0]                                                                                             => 6
[1,1,0,1,1,1,0,1,0,0,0,0]                                                                                             => 7
[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]                                                                                             => 2
[1,1,1,0,0,0,1,0,1,1,0,0]                                                                                             => 3
[1,1,1,0,0,0,1,1,0,0,1,0]                                                                                             => 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]                                                                                             => 3
[1,1,1,0,0,1,0,0,1,1,0,0]                                                                                             => 4
[1,1,1,0,0,1,0,1,0,0,1,0]                                                                                             => 4
[1,1,1,0,0,1,0,1,0,1,0,0]                                                                                             => 5
[1,1,1,0,0,1,0,1,1,0,0,0]                                                                                             => 5
[1,1,1,0,0,1,1,0,0,0,1,0]                                                                                             => 4
[1,1,1,0,0,1,1,0,0,1,0,0]                                                                                             => 5
[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]                                                                                             => 5
[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]                                                                                             => 6
[1,1,1,0,1,0,1,0,0,1,0,0]                                                                                             => 7
[1,1,1,0,1,0,1,0,1,0,0,0]                                                                                             => 8
[1,1,1,0,1,0,1,1,0,0,0,0]                                                                                             => 7
[1,1,1,0,1,1,0,0,0,0,1,0]                                                                                             => 5
[1,1,1,0,1,1,0,0,0,1,0,0]                                                                                             => 6
[1,1,1,0,1,1,0,0,1,0,0,0]                                                                                             => 7
[1,1,1,0,1,1,0,1,0,0,0,0]                                                                                             => 8
[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]                                                                                             => 3
[1,1,1,1,0,0,0,0,1,1,0,0]                                                                                             => 4
[1,1,1,1,0,0,0,1,0,0,1,0]                                                                                             => 4
[1,1,1,1,0,0,0,1,0,1,0,0]                                                                                             => 5
[1,1,1,1,0,0,0,1,1,0,0,0]                                                                                             => 5
[1,1,1,1,0,0,1,0,0,0,1,0]                                                                                             => 5
[1,1,1,1,0,0,1,0,0,1,0,0]                                                                                             => 6
[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]                                                                                             => 6
[1,1,1,1,0,1,0,0,0,0,1,0]                                                                                             => 6
[1,1,1,1,0,1,0,0,0,1,0,0]                                                                                             => 7
[1,1,1,1,0,1,0,0,1,0,0,0]                                                                                             => 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]                                                                                             => 7
[1,1,1,1,1,0,0,0,0,0,1,0]                                                                                             => 4
[1,1,1,1,1,0,0,0,0,1,0,0]                                                                                             => 5
[1,1,1,1,1,0,0,0,1,0,0,0]                                                                                             => 6
[1,1,1,1,1,0,0,1,0,0,0,0]                                                                                             => 7
[1,1,1,1,1,0,1,0,0,0,0,0]                                                                                             => 8
[1,1,1,1,1,1,0,0,0,0,0,0]                                                                                             => 5
[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]                                                                                         => 2
[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]                                                                                         => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]                                                                                         => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]                                                                                         => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]                                                                                         => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]                                                                                         => 3
[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]                                                                                         => 3
[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]                                                                                         => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]                                                                                         => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]                                                                                         => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]                                                                                         => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]                                                                                         => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]                                                                                         => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]                                                                                         => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]                                                                                         => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]                                                                                         => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]                                                                                         => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]                                                                                         => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]                                                                                         => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]                                                                                         => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]                                                                                         => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]                                                                                         => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]                                                                                         => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]                                                                                         => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]                                                                                         => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]                                                                                         => 4
[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]                                                                                         => 3
[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]                                                                                         => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]                                                                                         => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]                                                                                         => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]                                                                                         => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]                                                                                         => 4
[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]                                                                                         => 4
[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]                                                                                         => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]                                                                                         => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]                                                                                         => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]                                                                                         => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]                                                                                         => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]                                                                                         => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]                                                                                         => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]                                                                                         => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]                                                                                         => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]                                                                                         => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]                                                                                         => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]                                                                                         => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]                                                                                         => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]                                                                                         => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]                                                                                         => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]                                                                                         => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]                                                                                         => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]                                                                                         => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]                                                                                         => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]                                                                                         => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]                                                                                         => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]                                                                                         => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]                                                                                         => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]                                                                                         => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]                                                                                         => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]                                                                                         => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]                                                                                         => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]                                                                                         => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]                                                                                         => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]                                                                                         => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]                                                                                         => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]                                                                                         => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]                                                                                         => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]                                                                                         => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]                                                                                         => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]                                                                                         => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]                                                                                         => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]                                                                                         => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]                                                                                         => 6
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]                                                                                         => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]                                                                                         => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]                                                                                         => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]                                                                                         => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]                                                                                         => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]                                                                                         => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]                                                                                         => 8
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]                                                                                         => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]                                                                                         => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]                                                                                         => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]                                                                                         => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]                                                                                         => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]                                                                                         => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]                                                                                         => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]                                                                                         => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]                                                                                         => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]                                                                                         => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]                                                                                         => 6
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]                                                                                         => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]                                                                                         => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]                                                                                         => 9
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]                                                                                         => 7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]                                                                                         => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]                                                                                         => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]                                                                                         => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]                                                                                         => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]                                                                                         => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                         => 5
[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]                                                                                         => 3
[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]                                                                                         => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]                                                                                         => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]                                                                                         => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]                                                                                         => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]                                                                                         => 4
[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]                                                                                         => 4
[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]                                                                                         => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]                                                                                         => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]                                                                                         => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]                                                                                         => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]                                                                                         => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]                                                                                         => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]                                                                                         => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]                                                                                         => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]                                                                                         => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]                                                                                         => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]                                                                                         => 5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                                         => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]                                                                                         => 7
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]                                                                                         => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]                                                                                         => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]                                                                                         => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]                                                                                         => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                         => 7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                         => 5
[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]                                                                                         => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]                                                                                         => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]                                                                                         => 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]                                                                                         => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]                                                                                         => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]                                                                                         => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]                                                                                         => 6
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]                                                                                         => 5
[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]                                                                                         => 5
[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]                                                                                         => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]                                                                                         => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]                                                                                         => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                                         => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]                                                                                         => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]                                                                                         => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]                                                                                         => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]                                                                                         => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]                                                                                         => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]                                                                                         => 6
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]                                                                                         => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]                                                                                         => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                                         => 8
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]                                                                                         => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]                                                                                         => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]                                                                                         => 6
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]                                                                                         => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]                                                                                         => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]                                                                                         => 6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]                                                                                         => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]                                                                                         => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]                                                                                         => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]                                                                                         => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]                                                                                         => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]                                                                                         => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]                                                                                         => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]                                                                                         => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]                                                                                         => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]                                                                                         => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]                                                                                         => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]                                                                                         => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]                                                                                         => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]                                                                                         => 6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]                                                                                         => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]                                                                                         => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]                                                                                         => 6
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]                                                                                         => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]                                                                                         => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]                                                                                         => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]                                                                                         => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                                         => 9
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]                                                                                         => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]                                                                                         => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]                                                                                         => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]                                                                                         => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                                         => 9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]                                                                                         => 7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]                                                                                         => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]                                                                                         => 5
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]                                                                                         => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]                                                                                         => 6
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]                                                                                         => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]                                                                                         => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]                                                                                         => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]                                                                                         => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]                                                                                         => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]                                                                                         => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]                                                                                         => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                                         => 9
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]                                                                                         => 10
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]                                                                                         => 8
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]                                                                                         => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]                                                                                         => 6
[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]                                                                                         => 9
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]                                                                                         => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                         => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]                                                                                         => 3
[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]                                                                                         => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]                                                                                         => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]                                                                                         => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]                                                                                         => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]                                                                                         => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]                                                                                         => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]                                                                                         => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]                                                                                         => 6
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]                                                                                         => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]                                                                                         => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]                                                                                         => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]                                                                                         => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]                                                                                         => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]                                                                                         => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]                                                                                         => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]                                                                                         => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]                                                                                         => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]                                                                                         => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]                                                                                         => 6
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]                                                                                         => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]                                                                                         => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]                                                                                         => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]                                                                                         => 6
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]                                                                                         => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]                                                                                         => 5
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]                                                                                         => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]                                                                                         => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]                                                                                         => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]                                                                                         => 6
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]                                                                                         => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]                                                                                         => 8
[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]                                                                                         => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]                                                                                         => 6
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]                                                                                         => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]                                                                                         => 8
[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]                                                                                         => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]                                                                                         => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]                                                                                         => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                                         => 6
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]                                                                                         => 6
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]                                                                                         => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]                                                                                         => 6
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]                                                                                         => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                         => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]                                                                                         => 7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]                                                                                         => 6
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]                                                                                         => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                                                                         => 8
[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]                                                                                         => 6
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]                                                                                         => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]                                                                                         => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]                                                                                         => 8
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]                                                                                         => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                         => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                         => 9
[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]                                                                                         => 9
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]                                                                                         => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]                                                                                         => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]                                                                                         => 9
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]                                                                                         => 10
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]                                                                                         => 8
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]                                                                                         => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]                                                                                         => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]                                                                                         => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]                                                                                         => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]                                                                                         => 7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]                                                                                         => 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]                                                                                         => 9
[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]                                                                                         => 10
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]                                                                                         => 11
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]                                                                                         => 9
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]                                                                                         => 6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]                                                                                         => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]                                                                                         => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]                                                                                         => 9
[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]                                                                                         => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]                                                                                         => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]                                                                                         => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]                                                                                         => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]                                                                                         => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]                                                                                         => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]                                                                                         => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]                                                                                         => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]                                                                                         => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]                                                                                         => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]                                                                                         => 6
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]                                                                                         => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]                                                                                         => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]                                                                                         => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]                                                                                         => 6
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]                                                                                         => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]                                                                                         => 6
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]                                                                                         => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]                                                                                         => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]                                                                                         => 7
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]                                                                                         => 7
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]                                                                                         => 8
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]                                                                                         => 9
[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]                                                                                         => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]                                                                                         => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]                                                                                         => 8
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]                                                                                         => 9
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]                                                                                         => 7
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]                                                                                         => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]                                                                                         => 7
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]                                                                                         => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]                                                                                         => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]                                                                                         => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                                         => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                                                                         => 9
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]                                                                                         => 10
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]                                                                                         => 9
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]                                                                                         => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]                                                                                         => 10
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]                                                                                         => 11
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                         => 12
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]                                                                                         => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]                                                                                         => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]                                                                                         => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]                                                                                         => 9
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]                                                                                         => 10
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]                                                                                         => 11
[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]                                                                                         => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]                                                                                         => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]                                                                                         => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                         => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]                                                                                         => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]                                                                                         => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]                                                                                         => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]                                                                                         => 8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]                                                                                         => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]                                                                                         => 7
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]                                                                                         => 8
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]                                                                                         => 9
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]                                                                                         => 10
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]                                                                                         => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]                                                                                         => 8
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]                                                                                         => 9
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]                                                                                         => 10
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]                                                                                         => 11
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]                                                                                         => 12
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]                                                                                         => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                         => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]                                                                                         => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                         => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]                                                                                         => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]                                                                                         => 9
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]                                                                                         => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]                                                                                         => 6
[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]                                                                                     => 2
[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]                                                                                     => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]                                                                                     => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]                                                                                     => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]                                                                                     => 3
[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]                                                                                     => 3
[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]                                                                                     => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]                                                                                     => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]                                                                                     => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]                                                                                     => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]                                                                                     => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]                                                                                     => 6
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]                                                                                     => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]                                                                                     => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]                                                                                     => 5
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]                                                                                     => 6
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]                                                                                     => 4
[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]                                                                                     => 3
[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]                                                                                     => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]                                                                                     => 4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]                                                                                     => 5
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]                                                                                     => 4
[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]                                                                                     => 4
[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]                                                                                     => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]                                                                                     => 6
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]                                                                                     => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]                                                                                     => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]                                                                                     => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]                                                                                     => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]                                                                                     => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]                                                                                     => 6
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]                                                                                     => 7
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]                                                                                     => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]                                                                                     => 6
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]                                                                                     => 7
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]                                                                                     => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]                                                                                     => 4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]                                                                                     => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]                                                                                     => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]                                                                                     => 6
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]                                                                                     => 6
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]                                                                                     => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]                                                                                     => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]                                                                                     => 7
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]                                                                                     => 8
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]                                                                                     => 7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]                                                                                     => 6
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]                                                                                     => 7
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]                                                                                     => 8
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]                                                                                     => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]                                                                                     => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]                                                                                     => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]                                                                                     => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]                                                                                     => 6
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]                                                                                     => 7
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]                                                                                     => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]                                                                                     => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]                                                                                     => 7
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]                                                                                     => 8
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]                                                                                     => 9
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]                                                                                     => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]                                                                                     => 6
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]                                                                                     => 7
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]                                                                                     => 8
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                     => 5
[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]                                                                                     => 3
[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]                                                                                     => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]                                                                                     => 4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]                                                                                     => 5
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]                                                                                     => 4
[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]                                                                                     => 4
[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]                                                                                     => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]                                                                                     => 5
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]                                                                                     => 6
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]                                                                                     => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]                                                                                     => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]                                                                                     => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]                                                                                     => 5
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]                                                                                     => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]                                                                                     => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                                     => 6
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]                                                                                     => 7
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]                                                                                     => 6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]                                                                                     => 5
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]                                                                                     => 6
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                     => 7
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                     => 5
[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]                                                                                     => 4
[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]                                                                                     => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]                                                                                     => 5
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]                                                                                     => 6
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]                                                                                     => 5
[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]                                                                                     => 5
[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]                                                                                     => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]                                                                                     => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]                                                                                     => 6
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                                     => 7
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]                                                                                     => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]                                                                                     => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]                                                                                     => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]                                                                                     => 6
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]                                                                                     => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]                                                                                     => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]                                                                                     => 7
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                                     => 8
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]                                                                                     => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]                                                                                     => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]                                                                                     => 6
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]                                                                                     => 7
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]                                                                                     => 8
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]                                                                                     => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]                                                                                     => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]                                                                                     => 5
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]                                                                                     => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]                                                                                     => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]                                                                                     => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]                                                                                     => 6
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]                                                                                     => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]                                                                                     => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]                                                                                     => 6
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]                                                                                     => 7
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]                                                                                     => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]                                                                                     => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]                                                                                     => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]                                                                                     => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]                                                                                     => 7
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]                                                                                     => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]                                                                                     => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]                                                                                     => 8
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                                     => 9
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]                                                                                     => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]                                                                                     => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]                                                                                     => 7
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]                                                                                     => 8
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                                     => 9
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]                                                                                     => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]                                                                                     => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]                                                                                     => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]                                                                                     => 6
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]                                                                                     => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]                                                                                     => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]                                                                                     => 7
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]                                                                                     => 8
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]                                                                                     => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]                                                                                     => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]                                                                                     => 8
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                                     => 9
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]                                                                                     => 10
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]                                                                                     => 8
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]                                                                                     => 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]                                                                                     => 6
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]                                                                                     => 7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]                                                                                     => 8
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]                                                                                     => 9
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]                                                                                     => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                     => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]                                                                                     => 4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]                                                                                     => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]                                                                                     => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]                                                                                     => 5
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]                                                                                     => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]                                                                                     => 5
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]                                                                                     => 6
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]                                                                                     => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]                                                                                     => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]                                                                                     => 5
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]                                                                                     => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]                                                                                     => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]                                                                                     => 6
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]                                                                                     => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]                                                                                     => 6
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]                                                                                     => 7
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]                                                                                     => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]                                                                                     => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]                                                                                     => 6
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]                                                                                     => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]                                                                                     => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]                                                                                     => 7
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]                                                                                     => 8
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]                                                                                     => 7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]                                                                                     => 6
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]                                                                                     => 7
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]                                                                                     => 8
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]                                                                                     => 6
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                                     => 6
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]                                                                                     => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]                                                                                     => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]                                                                                     => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                     => 7
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]                                                                                     => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]                                                                                     => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]                                                                                     => 7
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                                                                     => 8
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]                                                                                     => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]                                                                                     => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]                                                                                     => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]                                                                                     => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]                                                                                     => 8
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]                                                                                     => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                     => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                     => 9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                     => 10
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]                                                                                     => 9
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]                                                                                     => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]                                                                                     => 8
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]                                                                                     => 9
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]                                                                                     => 10
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]                                                                                     => 8
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]                                                                                     => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]                                                                                     => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]                                                                                     => 7
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]                                                                                     => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]                                                                                     => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]                                                                                     => 8
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]                                                                                     => 9
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]                                                                                     => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]                                                                                     => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                                                                     => 9
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]                                                                                     => 10
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]                                                                                     => 11
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]                                                                                     => 9
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]                                                                                     => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]                                                                                     => 7
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]                                                                                     => 8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]                                                                                     => 9
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]                                                                                     => 10
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]                                                                                     => 7
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]                                                                                     => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]                                                                                     => 5
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]                                                                                     => 5
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]                                                                                     => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]                                                                                     => 6
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]                                                                                     => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]                                                                                     => 6
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]                                                                                     => 7
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]                                                                                     => 6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]                                                                                     => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]                                                                                     => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]                                                                                     => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]                                                                                     => 7
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]                                                                                     => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]                                                                                     => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]                                                                                     => 8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]                                                                                     => 9
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]                                                                                     => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]                                                                                     => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]                                                                                     => 7
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]                                                                                     => 8
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]                                                                                     => 9
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]                                                                                     => 7
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]                                                                                     => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]                                                                                     => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]                                                                                     => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]                                                                                     => 8
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]                                                                                     => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                                     => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                                                                     => 9
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]                                                                                     => 10
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]                                                                                     => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]                                                                                     => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]                                                                                     => 10
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]                                                                                     => 11
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                     => 12
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]                                                                                     => 10
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]                                                                                     => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]                                                                                     => 8
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]                                                                                     => 9
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]                                                                                     => 10
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]                                                                                     => 11
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]                                                                                     => 8
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]                                                                                     => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                     => 6
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]                                                                                     => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]                                                                                     => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]                                                                                     => 7
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]                                                                                     => 8
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]                                                                                     => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]                                                                                     => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]                                                                                     => 8
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]                                                                                     => 9
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]                                                                                     => 10
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]                                                                                     => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]                                                                                     => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]                                                                                     => 9
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]                                                                                     => 10
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]                                                                                     => 11
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]                                                                                     => 12
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]                                                                                     => 9
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]                                                                                     => 6
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                     => 7
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]                                                                                     => 8
[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]                                                                                     => 6
[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]                                                                                     => 3
[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]                                                                                     => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]                                                                                     => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]                                                                                     => 4
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]                                                                                     => 5
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]                                                                                     => 4
[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]                                                                                     => 4
[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]                                                                                     => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]                                                                                     => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]                                                                                     => 5
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]                                                                                     => 6
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]                                                                                     => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]                                                                                     => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]                                                                                     => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]                                                                                     => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]                                                                                     => 5
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]                                                                                     => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]                                                                                     => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]                                                                                     => 6
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]                                                                                     => 7
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]                                                                                     => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]                                                                                     => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]                                                                                     => 5
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]                                                                                     => 6
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]                                                                                     => 7
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]                                                                                     => 5
[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]                                                                                     => 4
[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]                                                                                     => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]                                                                                     => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]                                                                                     => 5
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]                                                                                     => 6
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]                                                                                     => 5
[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]                                                                                     => 5
[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]                                                                                     => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]                                                                                     => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]                                                                                     => 6
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]                                                                                     => 7
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]                                                                                     => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]                                                                                     => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]                                                                                     => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]                                                                                     => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]                                                                                     => 6
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]                                                                                     => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]                                                                                     => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]                                                                                     => 7
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]                                                                                     => 8
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]                                                                                     => 7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]                                                                                     => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]                                                                                     => 6
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]                                                                                     => 7
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]                                                                                     => 8
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]                                                                                     => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]                                                                                     => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]                                                                                     => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]                                                                                     => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]                                                                                     => 5
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]                                                                                     => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]                                                                                     => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]                                                                                     => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]                                                                                     => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]                                                                                     => 6
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]                                                                                     => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]                                                                                     => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]                                                                                     => 6
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]                                                                                     => 7
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]                                                                                     => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]                                                                                     => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]                                                                                     => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]                                                                                     => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]                                                                                     => 7
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]                                                                                     => 7
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]                                                                                     => 7
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]                                                                                     => 8
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]                                                                                     => 9
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]                                                                                     => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]                                                                                     => 6
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]                                                                                     => 7
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]                                                                                     => 8
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]                                                                                     => 9
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]                                                                                     => 7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]                                                                                     => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]                                                                                     => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]                                                                                     => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]                                                                                     => 6
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]                                                                                     => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]                                                                                     => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]                                                                                     => 7
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]                                                                                     => 8
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]                                                                                     => 7
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]                                                                                     => 7
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]                                                                                     => 8
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]                                                                                     => 9
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]                                                                                     => 10
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]                                                                                     => 8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]                                                                                     => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]                                                                                     => 6
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]                                                                                     => 7
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]                                                                                     => 8
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]                                                                                     => 9
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                     => 6
[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]                                                                                     => 4
[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]                                                                                     => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]                                                                                     => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]                                                                                     => 5
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]                                                                                     => 6
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]                                                                                     => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]                                                                                     => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                                     => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                                                                                     => 7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]                                                                                     => 5
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]                                                                                     => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                                     => 7
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]                                                                                     => 7
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                     => 8
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                     => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                     => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]                                                                                     => 5
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]                                                                                     => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]                                                                                     => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]                                                                                     => 6
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]                                                                                     => 5
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]                                                                                     => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]                                                                                     => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]                                                                                     => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]                                                                                     => 6
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]                                                                                     => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]                                                                                     => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]                                                                                     => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]                                                                                     => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                     => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                                                                                     => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]                                                                                     => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]                                                                                     => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                                     => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]                                                                                     => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]                                                                                     => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]                                                                                     => 7
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]                                                                                     => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]                                                                                     => 7
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                                     => 9
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]                                                                                     => 8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]                                                                                     => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]                                                                                     => 7
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]                                                                                     => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]                                                                                     => 9
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]                                                                                     => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]                                                                                     => 7
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]                                                                                     => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]                                                                                     => 7
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]                                                                                     => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]                                                                                     => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]                                                                                     => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]                                                                                     => 9
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                                     => 10
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                                     => 10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]                                                                                     => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]                                                                                     => 7
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]                                                                                     => 7
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]                                                                                     => 9
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                                     => 10
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]                                                                                     => 11
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]                                                                                     => 9
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]                                                                                     => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]                                                                                     => 7
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]                                                                                     => 8
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]                                                                                     => 10
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]                                                                                     => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                     => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]                                                                                     => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]                                                                                     => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]                                                                                     => 5
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]                                                                                     => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]                                                                                     => 7
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]                                                                                     => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]                                                                                     => 7
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]                                                                                     => 7
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]                                                                                     => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]                                                                                     => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]                                                                                     => 7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]                                                                                     => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]                                                                                     => 7
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]                                                                                     => 8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]                                                                                     => 9
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]                                                                                     => 7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]                                                                                     => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                                     => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                     => 8
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]                                                                                     => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                     => 9
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                     => 10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                     => 11
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]                                                                                     => 10
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                                                                                     => 9
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]                                                                                     => 12
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]                                                                                     => 11
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]                                                                                     => 8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]                                                                                     => 7
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]                                                                                     => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]                                                                                     => 7
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]                                                                                     => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]                                                                                     => 7
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]                                                                                     => 10
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]                                                                                     => 9
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                                     => 9
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]                                                                                     => 11
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]                                                                                     => 12
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                     => 13
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]                                                                                     => 10
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]                                                                                     => 12
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]                                                                                     => 9
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]                                                                                     => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                     => 7
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]                                                                                     => 7
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]                                                                                     => 9
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]                                                                                     => 9
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]                                                                                     => 11
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]                                                                                     => 12
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]                                                                                     => 13
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]                                                                                     => 10
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                     => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]                                                                                     => 7
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                     => 8
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]                                                                                     => 9
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]                                                                                     => 10
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]                                                                                     => 11
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]                                                                                     => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                     => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]                                                                                     => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]                                                                                     => 4
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]                                                                                     => 6
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]                                                                                     => 8
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]                                                                                     => 7
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]                                                                                     => 5
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                     => 8
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                     => 6
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                     => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]                                                                                     => 6
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]                                                                                     => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]                                                                                     => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                     => 7
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]                                                                                     => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]                                                                                     => 7
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]                                                                                     => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]                                                                                     => 7
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]                                                                                     => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]                                                                                     => 7
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]                                                                                     => 7
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]                                                                                     => 7
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]                                                                                     => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]                                                                                     => 7
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]                                                                                     => 7
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]                                                                                     => 10
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]                                                                                     => 7
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]                                                                                     => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]                                                                                     => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]                                                                                     => 7
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]                                                                                     => 8
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]                                                                                     => 10
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]                                                                                     => 7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]                                                                                     => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]                                                                                     => 6
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]                                                                                     => 8
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]                                                                                     => 7
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]                                                                                     => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]                                                                                     => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                                                                                     => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]                                                                                     => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]                                                                                     => 6
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]                                                                                     => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]                                                                                     => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]                                                                                     => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]                                                                                     => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                     => 9
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]                                                                                     => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]                                                                                     => 9
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]                                                                                     => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                     => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                     => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                     => 12
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]                                                                                     => 11
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]                                                                                     => 11
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]                                                                                     => 12
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]                                                                                     => 10
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]                                                                                     => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]                                                                                     => 9
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]                                                                                     => 11
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]                                                                                     => 10
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]                                                                                     => 11
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]                                                                                     => 12
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]                                                                                     => 13
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]                                                                                     => 11
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]                                                                                     => 10
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]                                                                                     => 11
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]                                                                                     => 12
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]                                                                                     => 9
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]                                                                                     => 8
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]                                                                                     => 11
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]                                                                                     => 10
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]                                                                                     => 10
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]                                                                                     => 11
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]                                                                                     => 9
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]                                                                                     => 9
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]                                                                                     => 9
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]                                                                                     => 10
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]                                                                                     => 12
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]                                                                                     => 11
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]                                                                                     => 12
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]                                                                                     => 13
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                     => 14
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]                                                                                     => 12
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]                                                                                     => 11
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]                                                                                     => 12
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                                                                                     => 13
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]                                                                                     => 10
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]                                                                                     => 7
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                     => 8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]                                                                                     => 10
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]                                                                                     => 9
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]                                                                                     => 10
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]                                                                                     => 11
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]                                                                                     => 12
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]                                                                                     => 10
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]                                                                                     => 11
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]                                                                                     => 12
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                                                                                     => 13
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]                                                                                     => 14
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]                                                                                     => 11
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                     => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]                                                                                     => 8
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                     => 9
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]                                                                                     => 10
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]                                                                                     => 11
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]                                                                                     => 12
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]                                                                                     => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]                                                                                     => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]                                                                                     => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]                                                                                     => 5
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]                                                                                     => 7
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]                                                                                     => 6
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]                                                                                     => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]                                                                                     => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]                                                                                     => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]                                                                                     => 7
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]                                                                                     => 7
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]                                                                                     => 7
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]                                                                                     => 7
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]                                                                                     => 7
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]                                                                                     => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]                                                                                     => 7
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]                                                                                     => 9
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]                                                                                     => 7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]                                                                                     => 5
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]                                                                                     => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]                                                                                     => 10
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                                                                                     => 11
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]                                                                                     => 10
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]                                                                                     => 10
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]                                                                                     => 11
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]                                                                                     => 9
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]                                                                                     => 10
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]                                                                                     => 9
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]                                                                                     => 11
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]                                                                                     => 12
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]                                                                                     => 10
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]                                                                                     => 8
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]                                                                                     => 9
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]                                                                                     => 10
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]                                                                                     => 11
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]                                                                                     => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]                                                                                     => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]                                                                                     => 9
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]                                                                                     => 9
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]                                                                                     => 12
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]                                                                                     => 11
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]                                                                                     => 11
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                                                                                     => 12
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]                                                                                     => 10
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]                                                                                     => 10
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]                                                                                     => 11
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]                                                                                     => 13
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]                                                                                     => 12
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]                                                                                     => 13
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]                                                                                     => 14
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                                     => 15
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]                                                                                     => 13
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]                                                                                     => 10
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]                                                                                     => 12
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]                                                                                     => 13
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]                                                                                     => 14
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]                                                                                     => 11
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]                                                                                     => 8
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]                                                                                     => 9
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]                                                                                     => 11
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]                                                                                     => 10
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]                                                                                     => 12
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]                                                                                     => 13
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]                                                                                     => 11
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                                                                                     => 12
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                                                                                     => 13
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]                                                                                     => 14
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]                                                                                     => 15
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]                                                                                     => 12
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]                                                                                     => 8
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]                                                                                     => 9
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]                                                                                     => 10
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]                                                                                     => 11
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]                                                                                     => 12
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]                                                                                     => 13
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]                                                                                     => 9
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]                                                                                     => 6
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]                                                                                     => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]                                                                                     => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]                                                                                     => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]                                                                                     => 7
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]                                                                                     => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]                                                                                     => 7
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]                                                                                     => 8
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]                                                                                     => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]                                                                                     => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]                                                                                     => 7
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]                                                                                     => 10
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]                                                                                     => 9
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]                                                                                     => 7
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]                                                                                     => 9
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]                                                                                     => 10
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]                                                                                     => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]                                                                                     => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]                                                                                     => 8
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]                                                                                     => 8
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]                                                                                     => 11
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]                                                                                     => 10
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]                                                                                     => 12
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]                                                                                     => 13
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]                                                                                     => 11
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]                                                                                     => 8
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]                                                                                     => 9
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]                                                                                     => 10
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]                                                                                     => 11
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]                                                                                     => 12
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]                                                                                     => 9
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]                                                                                     => 9
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]                                                                                     => 10
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]                                                                                     => 11
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]                                                                                     => 12
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]                                                                                     => 11
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                                                                                     => 12
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                                                                                     => 13
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]                                                                                     => 14
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]                                                                                     => 12
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]                                                                                     => 12
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]                                                                                     => 13
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]                                                                                     => 14
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]                                                                                     => 15
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]                                                                                     => 16
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]                                                                                     => 13
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]                                                                                     => 9
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]                                                                                     => 10
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]                                                                                     => 11
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]                                                                                     => 12
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]                                                                                     => 13
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]                                                                                     => 14
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]                                                                                     => 10
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]                                                                                     => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]                                                                                     => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]                                                                                     => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]                                                                                     => 7
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]                                                                                     => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]                                                                                     => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]                                                                                     => 8
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]                                                                                     => 9
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]                                                                                     => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]                                                                                     => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]                                                                                     => 9
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]                                                                                     => 10
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]                                                                                     => 11
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]                                                                                     => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]                                                                                     => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]                                                                                     => 10
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]                                                                                     => 11
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]                                                                                     => 12
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]                                                                                     => 13
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]                                                                                     => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]                                                                                     => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]                                                                                     => 11
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]                                                                                     => 12
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]                                                                                     => 13
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]                                                                                     => 14
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]                                                                                     => 15
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]                                                                                     => 11
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                                                                                     => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]                                                                                     => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]                                                                                     => 8
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]                                                                                     => 9
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]                                                                                     => 10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]                                                                                     => 11
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                                                                                     => 12
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                     => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]                                                                                 => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]                                                                                 => 12
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                                                                                 => 12
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]                                                                                 => 11
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]                                                                                 => 11
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]                                                                                 => 11
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]                                                                                 => 11
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]                                                                                 => 10
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]                                                                                 => 10
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]                                                                                 => 15
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]                                                                                 => 10
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]                                                                                 => 13
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]                                                                                 => 13
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]                                                                                 => 7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                                                                                 => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]                                                                                 => 7
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]                                                                                 => 16
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                                                                                 => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]                                                                                 => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                                                                                 => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]                                                                                 => 11
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]                                                                                 => 11
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                                                                                 => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]                                                                                 => 10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]                                                                                 => 10
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]                                                                                 => 10
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]                                                                                 => 10
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]                                                                                 => 9
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]                                                                                 => 13
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]                                                                                 => 13
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                                                                                 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]                                                                                 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                                 => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]                                                                                 => 8
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]                                                                                 => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]                                                                                 => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                                 => 10
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]                                                                                 => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]                                                                                 => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]                                                                                 => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]                                                                                 => 10
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]                                                                                 => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]                                                                                 => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                                 => 11
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]                                                                                 => 10
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                                 => 11
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]                                                                                 => 12
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]                                                                                 => 9
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]                                                                                 => 10
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 12
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]                                                                                 => 11
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]                                                                                 => 12
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 14
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]                                                                                 => 10
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]                                                                                 => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]                                                                                 => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                 => 12
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 13
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 12
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]                                                                                 => 13
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 16
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]                                                                                 => 11
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]                                                                                 => 11
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]                                                                                 => 16
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]                                                                                 => 12
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]                                                                                 => 8
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]                                                                                 => 11
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]                                                                                 => 12
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                                                                                 => 13
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 8
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]                                                                                 => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                 => 13
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 14
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]                                                                                 => 15
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]                                                                                 => 10
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 13
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 15
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                 => 10
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 14
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]                                                                                 => 15
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]                                                                                 => 15
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 18
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]                                                                                 => 16
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]                                                                                 => 12
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 10
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 12
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]                                                                                 => 15
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 16
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]                                                                                 => 12
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]                                                                                 => 17
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]                                                                                 => 15
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]                                                                                 => 11
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]                                                                                 => 14
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]                                                                                 => 16
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 11
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]                                                                                 => 17
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]                                                                                 => 14
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]                                                                                 => 15
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]                                                                                 => 12
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]                                                                                 => 15
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]                                                                                 => 16
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]                                                                                 => 16
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]                                                                                 => 12
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]                                                                                 => 16
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]                                                                                 => 17
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 12
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]                                                                                 => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]                                                                                 => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]                                                                                 => 11
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]                                                                                 => 12
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]                                                                                 => 15
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]                                                                                 => 16
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]                                                                                 => 13
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]                                                                                 => 18
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]                                                                                 => 13
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]                                                                                 => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]                                                                                 => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]                                                                                 => 10
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]                                                                                 => 11
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]                                                                                 => 12
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]                                                                                 => 13
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]                                                                                 => 14
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                                 => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                                 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                                 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]                                                                                 => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]                                                                                 => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]                                                                                 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]                                                                                 => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]                                                                                 => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]                                                                                 => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]                                                                                 => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]                                                                                 => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]                                                                                 => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                 => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]                                                                                 => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]                                                                                 => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                 => 9
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]                                                                                 => 7
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]                                                                                 => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]                                                                                 => 9
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                 => 6
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                                                                 => 9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                 => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                 => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]                                                                                 => 11
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]                                                                                 => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 12
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                 => 5
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]                                                                                 => 10
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 15
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]                                                                                 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]                                                                                 => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                                 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]                                                                                 => 4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                 => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                                 => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                                 => 4
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                 => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]                                                                                 => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]                                                                                 => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                                 => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]                                                                                 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                                 => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                 => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                                 => 5
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                 => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                 => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]                                                                                 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]                                                                                 => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]                                                                                 => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]                                                                                 => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]                                                                                 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]                                                                                 => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                 => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]                                                                                 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]                                                                                 => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                                 => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                                 => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                                 => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                                 => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                 => 12
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]                                                                                 => 10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]                                                                                 => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                 => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]                                                                                 => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]                                                                                 => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]                                                                                 => 11
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 11
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                 => 11
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                 => 7
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                 => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]                                                                                 => 9
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]                                                                                 => 10
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]                                                                                 => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 11
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]                                                                                 => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                                                                                 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]                                                                                 => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]                                                                                 => 7
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]                                                                                 => 7
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                 => 9
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]                                                                                 => 11
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 13
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]                                                                                 => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]                                                                                 => 8
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]                                                                                 => 8
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]                                                                                 => 9
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                 => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]                                                                                 => 7
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]                                                                                 => 8
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]                                                                                 => 10
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]                                                                                 => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                 => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]                                                                                 => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]                                                                                 => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]                                                                                 => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]                                                                                 => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]                                                                                 => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]                                                                                 => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]                                                                                 => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]                                                                                 => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                                 => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]                                                                                 => 7
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]                                                                                 => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]                                                                                 => 6
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]                                                                                 => 7
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]                                                                                 => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]                                                                                 => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]                                                                                 => 6
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]                                                                                 => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]                                                                                 => 8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]                                                                                 => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]                                                                                 => 7
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]                                                                                 => 7
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]                                                                                 => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]                                                                             => 8
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]                                                                             => 14
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]                                                                             => 14
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]                                                                             => 13
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]                                                                             => 13
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]                                                                             => 18
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]                                                                             => 20
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]                                                                             => 8
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                             => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]                                                                             => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]                                                                             => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]                                                                             => 13
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                                                                             => 13
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                             => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                             => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                             => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]                                                                             => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]                                                                             => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]                                                                             => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                             => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                             => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                             => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                             => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                             => 9
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]                                                                             => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]                                                                             => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                                                                             => 12
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                                                                             => 15
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 18
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]                                                                             => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]                                                                             => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                             => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                             => 4
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                                                                             => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                             => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]                                                                             => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                             => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                             => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 2
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                                                                             => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                             => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]                                                                             => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]                                                                             => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]                                                                             => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]                                                                             => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]                                                                             => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]                                                                             => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                             => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]                                                                             => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]                                                                             => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]                                                                             => 8
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]                                                                             => 21
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]                                                                             => 21
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]                                                                             => 19
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 19
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                                                                             => 9
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 15
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]                                                                             => 15
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]                                                                             => 19
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]                                                                             => 19
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                             => 3
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]                                                                             => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]                                                                             => 15
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]                                                                             => 16
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 14
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 13
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 12
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 11
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 15
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]                                                                             => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]                                                                             => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                                                                             => 11
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                                                                             => 10
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]                                                                             => 9
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]                                                                             => 20
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]                                                                             => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]                                                                             => 11
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]                                                                             => 13
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 15
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 17
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 19
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 21
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]                                                                             => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]                                                                             => 11
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]                                                                             => 12
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]                                                                             => 13
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]                                                                             => 14
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                             => 12
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]                                                                             => 19
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]                                                                             => 19
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                             => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]                                                                             => 7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]                                                                             => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]                                                                             => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]                                                                             => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]                                                                             => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                             => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                             => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                             => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                             => 11
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 13
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 16
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]                                                                             => 10
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]                                                                             => 11
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]                                                                             => 12
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 13
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 14
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 15
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                                                                             => 14
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                                                                             => 14
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                                                                             => 13
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                                                                             => 14
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                                                                             => 14
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]                                                                             => 12
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]                                                                             => 12
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]                                                                             => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]                                                                             => 12
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                                                                             => 14
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                                                                             => 14
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]                                                                             => 13
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]                                                                             => 14
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]                                                                             => 14
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                             => 11
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                             => 11
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                                                             => 10
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                                                             => 11
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                                                             => 11
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]                                                                             => 10
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]                                                                             => 10
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                                                                             => 10
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                             => 10
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]                                                                             => 11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]                                                                             => 11
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                             => 10
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]                                                                             => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]                                                                             => 11
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]                                                                             => 14
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]                                                                             => 14
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]                                                                             => 13
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]                                                                             => 14
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]                                                                             => 14
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                                                                             => 12
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                             => 12
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]                                                                             => 12
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]                                                                             => 12
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]                                                                             => 14
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]                                                                             => 14
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]                                                                             => 13
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]                                                                             => 14
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]                                                                             => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                                                                             => 14
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]                                                                             => 20
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]                                                                             => 15
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]                                                                             => 14
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]                                                                             => 14
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]                                                                             => 14
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]                                                                             => 14
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]                                                                             => 25
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]                                                                             => 9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]                                                                             => 12
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]                                                                             => 10
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]                                                                             => 10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]                                                                         => 9
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]                                                                         => 9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]                                                                         => 16
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]                                                                         => 15
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0]                                                                         => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                         => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                         => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                         => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                         => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]                                                                         => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 10
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]                                                                         => 25
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]                                                                         => 25
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                         => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]                                                                         => 17
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]                                                                         => 17
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]                                                                         => 10
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]                                                                         => 18
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]                                                                         => 17
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]                                                                         => 17
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                                                                         => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                         => 11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                         => 12
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                         => 13
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 14
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 15
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 16
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 17
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 18
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]                                                                         => 10
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                         => 9
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]                                                                         => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]                                                                         => 9
[1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                         => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]                                                                         => 20
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                         => 9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]                                                                         => 7
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]                                                                         => 7
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]                                                                         => 12
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]                                                                     => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                     => 0
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]                                                                     => 20
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]                                                                     => 20
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]                                                                     => 19
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]                                                                     => 20
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]                                                                     => 20
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]                                                                     => 18
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]                                                                     => 18
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]                                                                     => 18
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]                                                                     => 18
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]                                                                     => 20
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]                                                                     => 20
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]                                                                     => 19
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]                                                                     => 20
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]                                                                     => 20
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                                                                     => 17
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                                                                     => 17
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                                                                     => 16
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                                                                     => 17
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                                                                     => 17
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]                                                                     => 16
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]                                                                     => 16
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]                                                                     => 16
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]                                                                     => 16
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]                                                                     => 17
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]                                                                     => 17
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]                                                                     => 16
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]                                                                     => 17
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]                                                                     => 17
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]                                                                     => 20
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]                                                                     => 20
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]                                                                     => 19
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]                                                                     => 20
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]                                                                     => 20
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                                                                     => 18
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                                                                     => 18
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]                                                                     => 18
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]                                                                     => 18
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]                                                                     => 20
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]                                                                     => 20
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]                                                                     => 19
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]                                                                     => 20
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]                                                                     => 20
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                                                                     => 16
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                                                                     => 16
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                                                                     => 15
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                                                                     => 16
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                                                                     => 16
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]                                                                     => 14
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]                                                                     => 14
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]                                                                     => 14
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]                                                                     => 14
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                                                                     => 16
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                                                                     => 16
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]                                                                     => 15
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]                                                                     => 16
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]                                                                     => 16
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                     => 14
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                     => 14
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                                                     => 13
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                                                     => 14
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                                                     => 14
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                     => 14
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                     => 14
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                                                     => 13
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                                                     => 14
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                                                     => 14
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]                                                                     => 14
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]                                                                     => 14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]                                                                     => 14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]                                                                     => 14
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]                                                                     => 13
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]                                                                     => 13
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                                                                     => 14
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                     => 14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                                                                     => 14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                     => 14
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]                                                                     => 16
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]                                                                     => 16
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]                                                                     => 15
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]                                                                     => 16
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]                                                                     => 16
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]                                                                     => 14
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]                                                                     => 14
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                     => 14
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                     => 14
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]                                                                     => 16
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]                                                                     => 16
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]                                                                     => 15
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]                                                                     => 16
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]                                                                     => 16
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]                                                                     => 20
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]                                                                     => 20
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]                                                                     => 19
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]                                                                     => 20
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]                                                                     => 20
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]                                                                     => 18
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]                                                                     => 18
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]                                                                     => 18
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]                                                                     => 18
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]                                                                     => 20
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]                                                                     => 20
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]                                                                     => 19
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]                                                                     => 20
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]                                                                     => 20
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]                                                                     => 17
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]                                                                     => 17
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]                                                                     => 16
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]                                                                     => 17
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]                                                                     => 17
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                                                                     => 16
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                     => 16
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                                                                     => 16
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                     => 16
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]                                                                     => 17
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]                                                                     => 17
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]                                                                     => 16
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]                                                                     => 17
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]                                                                     => 17
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]                                                                     => 20
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]                                                                     => 20
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]                                                                     => 19
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]                                                                     => 20
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]                                                                     => 20
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]                                                                     => 18
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]                                                                     => 18
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]                                                                     => 18
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]                                                                     => 18
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]                                                                     => 20
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]                                                                     => 20
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]                                                                     => 19
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]                                                                     => 20
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]                                                                     => 20
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]                                                                     => 11
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]                                                                     => 11
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]                                                                     => 10
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                     => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]                                                                     => 8
[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]                                                                 => 11
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]                                                                 => 17
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]                                                                 => 6
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]                                                                 => 42
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]                                                             => 12
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                             => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]                                                             => 12
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]                                                         => 13
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                         => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]                                                     => 14
[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]                                                     => 63
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                     => 28
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]                                                     => 21
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                 => 42
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]                                                 => 12
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]                                                 => 15
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]                                                 => 15
[1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]                                             => 16
[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]     => 171
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] => 27

-----------------------------------------------------------------------------
Created: Feb 17, 2016 at 20:41 by Christian Stump

-----------------------------------------------------------------------------
Last Updated: Dec 30, 2023 at 12:12 by Martin Rubey