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*       www.FindStat.org - The Combinatorial Statistic Finder               *
*                                                                           *
*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
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-----------------------------------------------------------------------------
Statistic identifier: St000445

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

-----------------------------------------------------------------------------
Description: The number of rises of length 1 of a Dyck path.

-----------------------------------------------------------------------------
References: [1]   Kangro, K., Pourmoradnasseri, M., Theis, D. O. Short note on the number of 1-ascents in dispersed dyck paths [[arXiv:1603.01422]]

-----------------------------------------------------------------------------
Code:
def statistic(D):
    return list(D.rise_composition()).count(1)


-----------------------------------------------------------------------------
Statistic values:

[]                                                                                                                    => 0
[1,0]                                                                                                                 => 1
[1,0,1,0]                                                                                                             => 2
[1,1,0,0]                                                                                                             => 0
[1,0,1,0,1,0]                                                                                                         => 3
[1,0,1,1,0,0]                                                                                                         => 1
[1,1,0,0,1,0]                                                                                                         => 1
[1,1,0,1,0,0]                                                                                                         => 1
[1,1,1,0,0,0]                                                                                                         => 0
[1,0,1,0,1,0,1,0]                                                                                                     => 4
[1,0,1,0,1,1,0,0]                                                                                                     => 2
[1,0,1,1,0,0,1,0]                                                                                                     => 2
[1,0,1,1,0,1,0,0]                                                                                                     => 2
[1,0,1,1,1,0,0,0]                                                                                                     => 1
[1,1,0,0,1,0,1,0]                                                                                                     => 2
[1,1,0,0,1,1,0,0]                                                                                                     => 0
[1,1,0,1,0,0,1,0]                                                                                                     => 2
[1,1,0,1,0,1,0,0]                                                                                                     => 2
[1,1,0,1,1,0,0,0]                                                                                                     => 0
[1,1,1,0,0,0,1,0]                                                                                                     => 1
[1,1,1,0,0,1,0,0]                                                                                                     => 1
[1,1,1,0,1,0,0,0]                                                                                                     => 1
[1,1,1,1,0,0,0,0]                                                                                                     => 0
[1,0,1,0,1,0,1,0,1,0]                                                                                                 => 5
[1,0,1,0,1,0,1,1,0,0]                                                                                                 => 3
[1,0,1,0,1,1,0,0,1,0]                                                                                                 => 3
[1,0,1,0,1,1,0,1,0,0]                                                                                                 => 3
[1,0,1,0,1,1,1,0,0,0]                                                                                                 => 2
[1,0,1,1,0,0,1,0,1,0]                                                                                                 => 3
[1,0,1,1,0,0,1,1,0,0]                                                                                                 => 1
[1,0,1,1,0,1,0,0,1,0]                                                                                                 => 3
[1,0,1,1,0,1,0,1,0,0]                                                                                                 => 3
[1,0,1,1,0,1,1,0,0,0]                                                                                                 => 1
[1,0,1,1,1,0,0,0,1,0]                                                                                                 => 2
[1,0,1,1,1,0,0,1,0,0]                                                                                                 => 2
[1,0,1,1,1,0,1,0,0,0]                                                                                                 => 2
[1,0,1,1,1,1,0,0,0,0]                                                                                                 => 1
[1,1,0,0,1,0,1,0,1,0]                                                                                                 => 3
[1,1,0,0,1,0,1,1,0,0]                                                                                                 => 1
[1,1,0,0,1,1,0,0,1,0]                                                                                                 => 1
[1,1,0,0,1,1,0,1,0,0]                                                                                                 => 1
[1,1,0,0,1,1,1,0,0,0]                                                                                                 => 0
[1,1,0,1,0,0,1,0,1,0]                                                                                                 => 3
[1,1,0,1,0,0,1,1,0,0]                                                                                                 => 1
[1,1,0,1,0,1,0,0,1,0]                                                                                                 => 3
[1,1,0,1,0,1,0,1,0,0]                                                                                                 => 3
[1,1,0,1,0,1,1,0,0,0]                                                                                                 => 1
[1,1,0,1,1,0,0,0,1,0]                                                                                                 => 1
[1,1,0,1,1,0,0,1,0,0]                                                                                                 => 1
[1,1,0,1,1,0,1,0,0,0]                                                                                                 => 1
[1,1,0,1,1,1,0,0,0,0]                                                                                                 => 0
[1,1,1,0,0,0,1,0,1,0]                                                                                                 => 2
[1,1,1,0,0,0,1,1,0,0]                                                                                                 => 0
[1,1,1,0,0,1,0,0,1,0]                                                                                                 => 2
[1,1,1,0,0,1,0,1,0,0]                                                                                                 => 2
[1,1,1,0,0,1,1,0,0,0]                                                                                                 => 0
[1,1,1,0,1,0,0,0,1,0]                                                                                                 => 2
[1,1,1,0,1,0,0,1,0,0]                                                                                                 => 2
[1,1,1,0,1,0,1,0,0,0]                                                                                                 => 2
[1,1,1,0,1,1,0,0,0,0]                                                                                                 => 0
[1,1,1,1,0,0,0,0,1,0]                                                                                                 => 1
[1,1,1,1,0,0,0,1,0,0]                                                                                                 => 1
[1,1,1,1,0,0,1,0,0,0]                                                                                                 => 1
[1,1,1,1,0,1,0,0,0,0]                                                                                                 => 1
[1,1,1,1,1,0,0,0,0,0]                                                                                                 => 0
[1,0,1,0,1,0,1,0,1,0,1,0]                                                                                             => 6
[1,0,1,0,1,0,1,0,1,1,0,0]                                                                                             => 4
[1,0,1,0,1,0,1,1,0,0,1,0]                                                                                             => 4
[1,0,1,0,1,0,1,1,0,1,0,0]                                                                                             => 4
[1,0,1,0,1,0,1,1,1,0,0,0]                                                                                             => 3
[1,0,1,0,1,1,0,0,1,0,1,0]                                                                                             => 4
[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]                                                                                             => 4
[1,0,1,0,1,1,0,1,0,1,0,0]                                                                                             => 4
[1,0,1,0,1,1,0,1,1,0,0,0]                                                                                             => 2
[1,0,1,0,1,1,1,0,0,0,1,0]                                                                                             => 3
[1,0,1,0,1,1,1,0,0,1,0,0]                                                                                             => 3
[1,0,1,0,1,1,1,0,1,0,0,0]                                                                                             => 3
[1,0,1,0,1,1,1,1,0,0,0,0]                                                                                             => 2
[1,0,1,1,0,0,1,0,1,0,1,0]                                                                                             => 4
[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]                                                                                             => 2
[1,0,1,1,0,0,1,1,1,0,0,0]                                                                                             => 1
[1,0,1,1,0,1,0,0,1,0,1,0]                                                                                             => 4
[1,0,1,1,0,1,0,0,1,1,0,0]                                                                                             => 2
[1,0,1,1,0,1,0,1,0,0,1,0]                                                                                             => 4
[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]                                                                                             => 2
[1,0,1,1,0,1,1,0,0,0,1,0]                                                                                             => 2
[1,0,1,1,0,1,1,0,0,1,0,0]                                                                                             => 2
[1,0,1,1,0,1,1,0,1,0,0,0]                                                                                             => 2
[1,0,1,1,0,1,1,1,0,0,0,0]                                                                                             => 1
[1,0,1,1,1,0,0,0,1,0,1,0]                                                                                             => 3
[1,0,1,1,1,0,0,0,1,1,0,0]                                                                                             => 1
[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]                                                                                             => 3
[1,0,1,1,1,0,0,1,1,0,0,0]                                                                                             => 1
[1,0,1,1,1,0,1,0,0,0,1,0]                                                                                             => 3
[1,0,1,1,1,0,1,0,0,1,0,0]                                                                                             => 3
[1,0,1,1,1,0,1,0,1,0,0,0]                                                                                             => 3
[1,0,1,1,1,0,1,1,0,0,0,0]                                                                                             => 1
[1,0,1,1,1,1,0,0,0,0,1,0]                                                                                             => 2
[1,0,1,1,1,1,0,0,0,1,0,0]                                                                                             => 2
[1,0,1,1,1,1,0,0,1,0,0,0]                                                                                             => 2
[1,0,1,1,1,1,0,1,0,0,0,0]                                                                                             => 2
[1,0,1,1,1,1,1,0,0,0,0,0]                                                                                             => 1
[1,1,0,0,1,0,1,0,1,0,1,0]                                                                                             => 4
[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]                                                                                             => 2
[1,1,0,0,1,0,1,1,1,0,0,0]                                                                                             => 1
[1,1,0,0,1,1,0,0,1,0,1,0]                                                                                             => 2
[1,1,0,0,1,1,0,0,1,1,0,0]                                                                                             => 0
[1,1,0,0,1,1,0,1,0,0,1,0]                                                                                             => 2
[1,1,0,0,1,1,0,1,0,1,0,0]                                                                                             => 2
[1,1,0,0,1,1,0,1,1,0,0,0]                                                                                             => 0
[1,1,0,0,1,1,1,0,0,0,1,0]                                                                                             => 1
[1,1,0,0,1,1,1,0,0,1,0,0]                                                                                             => 1
[1,1,0,0,1,1,1,0,1,0,0,0]                                                                                             => 1
[1,1,0,0,1,1,1,1,0,0,0,0]                                                                                             => 0
[1,1,0,1,0,0,1,0,1,0,1,0]                                                                                             => 4
[1,1,0,1,0,0,1,0,1,1,0,0]                                                                                             => 2
[1,1,0,1,0,0,1,1,0,0,1,0]                                                                                             => 2
[1,1,0,1,0,0,1,1,0,1,0,0]                                                                                             => 2
[1,1,0,1,0,0,1,1,1,0,0,0]                                                                                             => 1
[1,1,0,1,0,1,0,0,1,0,1,0]                                                                                             => 4
[1,1,0,1,0,1,0,0,1,1,0,0]                                                                                             => 2
[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]                                                                                             => 4
[1,1,0,1,0,1,0,1,1,0,0,0]                                                                                             => 2
[1,1,0,1,0,1,1,0,0,0,1,0]                                                                                             => 2
[1,1,0,1,0,1,1,0,0,1,0,0]                                                                                             => 2
[1,1,0,1,0,1,1,0,1,0,0,0]                                                                                             => 2
[1,1,0,1,0,1,1,1,0,0,0,0]                                                                                             => 1
[1,1,0,1,1,0,0,0,1,0,1,0]                                                                                             => 2
[1,1,0,1,1,0,0,0,1,1,0,0]                                                                                             => 0
[1,1,0,1,1,0,0,1,0,0,1,0]                                                                                             => 2
[1,1,0,1,1,0,0,1,0,1,0,0]                                                                                             => 2
[1,1,0,1,1,0,0,1,1,0,0,0]                                                                                             => 0
[1,1,0,1,1,0,1,0,0,0,1,0]                                                                                             => 2
[1,1,0,1,1,0,1,0,0,1,0,0]                                                                                             => 2
[1,1,0,1,1,0,1,0,1,0,0,0]                                                                                             => 2
[1,1,0,1,1,0,1,1,0,0,0,0]                                                                                             => 0
[1,1,0,1,1,1,0,0,0,0,1,0]                                                                                             => 1
[1,1,0,1,1,1,0,0,0,1,0,0]                                                                                             => 1
[1,1,0,1,1,1,0,0,1,0,0,0]                                                                                             => 1
[1,1,0,1,1,1,0,1,0,0,0,0]                                                                                             => 1
[1,1,0,1,1,1,1,0,0,0,0,0]                                                                                             => 0
[1,1,1,0,0,0,1,0,1,0,1,0]                                                                                             => 3
[1,1,1,0,0,0,1,0,1,1,0,0]                                                                                             => 1
[1,1,1,0,0,0,1,1,0,0,1,0]                                                                                             => 1
[1,1,1,0,0,0,1,1,0,1,0,0]                                                                                             => 1
[1,1,1,0,0,0,1,1,1,0,0,0]                                                                                             => 0
[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]                                                                                             => 1
[1,1,1,0,0,1,0,1,0,0,1,0]                                                                                             => 3
[1,1,1,0,0,1,0,1,0,1,0,0]                                                                                             => 3
[1,1,1,0,0,1,0,1,1,0,0,0]                                                                                             => 1
[1,1,1,0,0,1,1,0,0,0,1,0]                                                                                             => 1
[1,1,1,0,0,1,1,0,0,1,0,0]                                                                                             => 1
[1,1,1,0,0,1,1,0,1,0,0,0]                                                                                             => 1
[1,1,1,0,0,1,1,1,0,0,0,0]                                                                                             => 0
[1,1,1,0,1,0,0,0,1,0,1,0]                                                                                             => 3
[1,1,1,0,1,0,0,0,1,1,0,0]                                                                                             => 1
[1,1,1,0,1,0,0,1,0,0,1,0]                                                                                             => 3
[1,1,1,0,1,0,0,1,0,1,0,0]                                                                                             => 3
[1,1,1,0,1,0,0,1,1,0,0,0]                                                                                             => 1
[1,1,1,0,1,0,1,0,0,0,1,0]                                                                                             => 3
[1,1,1,0,1,0,1,0,0,1,0,0]                                                                                             => 3
[1,1,1,0,1,0,1,0,1,0,0,0]                                                                                             => 3
[1,1,1,0,1,0,1,1,0,0,0,0]                                                                                             => 1
[1,1,1,0,1,1,0,0,0,0,1,0]                                                                                             => 1
[1,1,1,0,1,1,0,0,0,1,0,0]                                                                                             => 1
[1,1,1,0,1,1,0,0,1,0,0,0]                                                                                             => 1
[1,1,1,0,1,1,0,1,0,0,0,0]                                                                                             => 1
[1,1,1,0,1,1,1,0,0,0,0,0]                                                                                             => 0
[1,1,1,1,0,0,0,0,1,0,1,0]                                                                                             => 2
[1,1,1,1,0,0,0,0,1,1,0,0]                                                                                             => 0
[1,1,1,1,0,0,0,1,0,0,1,0]                                                                                             => 2
[1,1,1,1,0,0,0,1,0,1,0,0]                                                                                             => 2
[1,1,1,1,0,0,0,1,1,0,0,0]                                                                                             => 0
[1,1,1,1,0,0,1,0,0,0,1,0]                                                                                             => 2
[1,1,1,1,0,0,1,0,0,1,0,0]                                                                                             => 2
[1,1,1,1,0,0,1,0,1,0,0,0]                                                                                             => 2
[1,1,1,1,0,0,1,1,0,0,0,0]                                                                                             => 0
[1,1,1,1,0,1,0,0,0,0,1,0]                                                                                             => 2
[1,1,1,1,0,1,0,0,0,1,0,0]                                                                                             => 2
[1,1,1,1,0,1,0,0,1,0,0,0]                                                                                             => 2
[1,1,1,1,0,1,0,1,0,0,0,0]                                                                                             => 2
[1,1,1,1,0,1,1,0,0,0,0,0]                                                                                             => 0
[1,1,1,1,1,0,0,0,0,0,1,0]                                                                                             => 1
[1,1,1,1,1,0,0,0,0,1,0,0]                                                                                             => 1
[1,1,1,1,1,0,0,0,1,0,0,0]                                                                                             => 1
[1,1,1,1,1,0,0,1,0,0,0,0]                                                                                             => 1
[1,1,1,1,1,0,1,0,0,0,0,0]                                                                                             => 1
[1,1,1,1,1,1,0,0,0,0,0,0]                                                                                             => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                         => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                                         => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]                                                                                         => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                                         => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]                                                                                         => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]                                                                                         => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]                                                                                         => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]                                                                                         => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]                                                                                         => 5
[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]                                                                                         => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]                                                                                         => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]                                                                                         => 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]                                                                                         => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]                                                                                         => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]                                                                                         => 3
[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]                                                                                         => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]                                                                                         => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]                                                                                         => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]                                                                                         => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]                                                                                         => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]                                                                                         => 3
[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]                                                                                         => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]                                                                                         => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]                                                                                         => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]                                                                                         => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]                                                                                         => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]                                                                                         => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]                                                                                         => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]                                                                                         => 2
[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]                                                                                         => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]                                                                                         => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]                                                                                         => 2
[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]                                                                                         => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]                                                                                         => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]                                                                                         => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]                                                                                         => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]                                                                                         => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]                                                                                         => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]                                                                                         => 3
[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]                                                                                         => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]                                                                                         => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                                         => 1
[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]                                                                                         => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]                                                                                         => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]                                                                                         => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]                                                                                         => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]                                                                                         => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]                                                                                         => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]                                                                                         => 5
[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]                                                                                         => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]                                                                                         => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]                                                                                         => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]                                                                                         => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]                                                                                         => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]                                                                                         => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]                                                                                         => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]                                                                                         => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]                                                                                         => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]                                                                                         => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]                                                                                         => 2
[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]                                                                                         => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]                                                                                         => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]                                                                                         => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]                                                                                         => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]                                                                                         => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]                                                                                         => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]                                                                                         => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]                                                                                         => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]                                                                                         => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]                                                                                         => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]                                                                                         => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]                                                                                         => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]                                                                                         => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]                                                                                         => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]                                                                                         => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]                                                                                         => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]                                                                                         => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]                                                                                         => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]                                                                                         => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]                                                                                         => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]                                                                                         => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]                                                                                         => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]                                                                                         => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]                                                                                         => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]                                                                                         => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]                                                                                         => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]                                                                                         => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]                                                                                         => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]                                                                                         => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]                                                                                         => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]                                                                                         => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]                                                                                         => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]                                                                                         => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]                                                                                         => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]                                                                                         => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]                                                                                         => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]                                                                                         => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]                                                                                         => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]                                                                                         => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]                                                                                         => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]                                                                                         => 1
[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]                                                                                         => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]                                                                                         => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]                                                                                         => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]                                                                                         => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]                                                                                         => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]                                                                                         => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]                                                                                         => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]                                                                                         => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]                                                                                         => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]                                                                                         => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]                                                                                         => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]                                                                                         => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]                                                                                         => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]                                                                                         => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]                                                                                         => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]                                                                                         => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]                                                                                         => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]                                                                                         => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                         => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                         => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]                                                                                         => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]                                                                                         => 3
[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]                                                                                         => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]                                                                                         => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]                                                                                         => 1
[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]                                                                                         => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]                                                                                         => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]                                                                                         => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]                                                                                         => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]                                                                                         => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]                                                                                         => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]                                                                                         => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]                                                                                         => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                                         => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]                                                                                         => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]                                                                                         => 0
[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]                                                                                         => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]                                                                                         => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]                                                                                         => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]                                                                                         => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]                                                                                         => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]                                                                                         => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]                                                                                         => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]                                                                                         => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]                                                                                         => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]                                                                                         => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]                                                                                         => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]                                                                                         => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]                                                                                         => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]                                                                                         => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                                         => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]                                                                                         => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]                                                                                         => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]                                                                                         => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]                                                                                         => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]                                                                                         => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                         => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                         => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                         => 5
[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]                                                                                         => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]                                                                                         => 2
[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]                                                                                         => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]                                                                                         => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]                                                                                         => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]                                                                                         => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]                                                                                         => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]                                                                                         => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]                                                                                         => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]                                                                                         => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]                                                                                         => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]                                                                                         => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]                                                                                         => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]                                                                                         => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]                                                                                         => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]                                                                                         => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]                                                                                         => 3
[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]                                                                                         => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]                                                                                         => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]                                                                                         => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]                                                                                         => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                                         => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]                                                                                         => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]                                                                                         => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]                                                                                         => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]                                                                                         => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]                                                                                         => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]                                                                                         => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]                                                                                         => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]                                                                                         => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                                         => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]                                                                                         => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]                                                                                         => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]                                                                                         => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]                                                                                         => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]                                                                                         => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]                                                                                         => 1
[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]                                                                                         => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]                                                                                         => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]                                                                                         => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]                                                                                         => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]                                                                                         => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]                                                                                         => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]                                                                                         => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]                                                                                         => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]                                                                                         => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]                                                                                         => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]                                                                                         => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]                                                                                         => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]                                                                                         => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]                                                                                         => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]                                                                                         => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]                                                                                         => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]                                                                                         => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]                                                                                         => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]                                                                                         => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]                                                                                         => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                                         => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]                                                                                         => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]                                                                                         => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]                                                                                         => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]                                                                                         => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                                         => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]                                                                                         => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]                                                                                         => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]                                                                                         => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]                                                                                         => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]                                                                                         => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]                                                                                         => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]                                                                                         => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]                                                                                         => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]                                                                                         => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]                                                                                         => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]                                                                                         => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]                                                                                         => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                                         => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]                                                                                         => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]                                                                                         => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]                                                                                         => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]                                                                                         => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]                                                                                         => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]                                                                                         => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]                                                                                         => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]                                                                                         => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                         => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]                                                                                         => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]                                                                                         => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]                                                                                         => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]                                                                                         => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]                                                                                         => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]                                                                                         => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]                                                                                         => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]                                                                                         => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]                                                                                         => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]                                                                                         => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]                                                                                         => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]                                                                                         => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]                                                                                         => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]                                                                                         => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]                                                                                         => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]                                                                                         => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]                                                                                         => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]                                                                                         => 1
[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]                                                                                         => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]                                                                                         => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]                                                                                         => 4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]                                                                                         => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]                                                                                         => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]                                                                                         => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]                                                                                         => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]                                                                                         => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]                                                                                         => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]                                                                                         => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]                                                                                         => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]                                                                                         => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]                                                                                         => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]                                                                                         => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]                                                                                         => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]                                                                                         => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]                                                                                         => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]                                                                                         => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]                                                                                         => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]                                                                                         => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]                                                                                         => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]                                                                                         => 0
[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]                                                                                         => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]                                                                                         => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                                         => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]                                                                                         => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]                                                                                         => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]                                                                                         => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]                                                                                         => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                         => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]                                                                                         => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]                                                                                         => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]                                                                                         => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                                                                         => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]                                                                                         => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]                                                                                         => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]                                                                                         => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]                                                                                         => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]                                                                                         => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]                                                                                         => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                         => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                         => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                         => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]                                                                                         => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]                                                                                         => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]                                                                                         => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]                                                                                         => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]                                                                                         => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]                                                                                         => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]                                                                                         => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]                                                                                         => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]                                                                                         => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]                                                                                         => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]                                                                                         => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]                                                                                         => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]                                                                                         => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]                                                                                         => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]                                                                                         => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]                                                                                         => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                                                                         => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]                                                                                         => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]                                                                                         => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]                                                                                         => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]                                                                                         => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]                                                                                         => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]                                                                                         => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]                                                                                         => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]                                                                                         => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]                                                                                         => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]                                                                                         => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]                                                                                         => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]                                                                                         => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]                                                                                         => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]                                                                                         => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]                                                                                         => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]                                                                                         => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]                                                                                         => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]                                                                                         => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]                                                                                         => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]                                                                                         => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]                                                                                         => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]                                                                                         => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]                                                                                         => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]                                                                                         => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]                                                                                         => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]                                                                                         => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]                                                                                         => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]                                                                                         => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]                                                                                         => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]                                                                                         => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]                                                                                         => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]                                                                                         => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]                                                                                         => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]                                                                                         => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]                                                                                         => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]                                                                                         => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]                                                                                         => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]                                                                                         => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]                                                                                         => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]                                                                                         => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]                                                                                         => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]                                                                                         => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                                         => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                                                                         => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]                                                                                         => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]                                                                                         => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]                                                                                         => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]                                                                                         => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]                                                                                         => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                         => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]                                                                                         => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]                                                                                         => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]                                                                                         => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]                                                                                         => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]                                                                                         => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]                                                                                         => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]                                                                                         => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]                                                                                         => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]                                                                                         => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]                                                                                         => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                         => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]                                                                                         => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]                                                                                         => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]                                                                                         => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]                                                                                         => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]                                                                                         => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]                                                                                         => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]                                                                                         => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]                                                                                         => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]                                                                                         => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]                                                                                         => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]                                                                                         => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]                                                                                         => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]                                                                                         => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]                                                                                         => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]                                                                                         => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]                                                                                         => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                         => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]                                                                                         => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                         => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]                                                                                         => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]                                                                                         => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]                                                                                         => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]                                                                                         => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                     => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                                     => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]                                                                                     => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                                     => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]                                                                                     => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]                                                                                     => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]                                                                                     => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]                                                                                     => 6
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]                                                                                     => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]                                                                                     => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]                                                                                     => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]                                                                                     => 4
[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]                                                                                     => 6
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]                                                                                     => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]                                                                                     => 6
[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]                                                                                     => 4
[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]                                                                                     => 4
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]                                                                                     => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]                                                                                     => 5
[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]                                                                                     => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]                                                                                     => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]                                                                                     => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]                                                                                     => 5
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]                                                                                     => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]                                                                                     => 4
[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]                                                                                     => 4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]                                                                                     => 4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]                                                                                     => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]                                                                                     => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]                                                                                     => 4
[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]                                                                                     => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                                     => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]                                                                                     => 4
[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]                                                                                     => 2
[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]                                                                                     => 3
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]                                                                                     => 6
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]                                                                                     => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]                                                                                     => 4
[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]                                                                                     => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]                                                                                     => 6
[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]                                                                                     => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]                                                                                     => 6
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]                                                                                     => 4
[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]                                                                                     => 4
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]                                                                                     => 4
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]                                                                                     => 2
[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]                                                                                     => 4
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]                                                                                     => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]                                                                                     => 4
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]                                                                                     => 4
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]                                                                                     => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]                                                                                     => 3
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]                                                                                     => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]                                                                                     => 5
[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]                                                                                     => 3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]                                                                                     => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]                                                                                     => 3
[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]                                                                                     => 5
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]                                                                                     => 5
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]                                                                                     => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]                                                                                     => 2
[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]                                                                                     => 4
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]                                                                                     => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]                                                                                     => 4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]                                                                                     => 4
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]                                                                                     => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]                                                                                     => 4
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]                                                                                     => 4
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]                                                                                     => 4
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]                                                                                     => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]                                                                                     => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]                                                                                     => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                     => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]                                                                                     => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]                                                                                     => 4
[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]                                                                                     => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]                                                                                     => 4
[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]                                                                                     => 2
[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]                                                                                     => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]                                                                                     => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]                                                                                     => 4
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]                                                                                     => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]                                                                                     => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]                                                                                     => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]                                                                                     => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]                                                                                     => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]                                                                                     => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]                                                                                     => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                     => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                     => 6
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]                                                                                     => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]                                                                                     => 4
[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]                                                                                     => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]                                                                                     => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]                                                                                     => 4
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]                                                                                     => 6
[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]                                                                                     => 4
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]                                                                                     => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]                                                                                     => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]                                                                                     => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]                                                                                     => 6
[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]                                                                                     => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]                                                                                     => 4
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                                     => 4
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]                                                                                     => 3
[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]                                                                                     => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]                                                                                     => 4
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]                                                                                     => 4
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                                     => 4
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]                                                                                     => 3
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]                                                                                     => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]                                                                                     => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                                     => 4
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]                                                                                     => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]                                                                                     => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]                                                                                     => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]                                                                                     => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]                                                                                     => 3
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]                                                                                     => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]                                                                                     => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]                                                                                     => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]                                                                                     => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]                                                                                     => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                     => 5
[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]                                                                                     => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]                                                                                     => 2
[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]                                                                                     => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]                                                                                     => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]                                                                                     => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]                                                                                     => 3
[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]                                                                                     => 5
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]                                                                                     => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]                                                                                     => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]                                                                                     => 2
[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]                                                                                     => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                     => 5
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]                                                                                     => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]                                                                                     => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]                                                                                     => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]                                                                                     => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]                                                                                     => 4
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]                                                                                     => 4
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                                                                     => 4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]                                                                                     => 4
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]                                                                                     => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]                                                                                     => 4
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]                                                                                     => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                     => 4
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]                                                                                     => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]                                                                                     => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]                                                                                     => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]                                                                                     => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                     => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]                                                                                     => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]                                                                                     => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                                                                                     => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                     => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                                     => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]                                                                                     => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                                     => 4
[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]                                                                                     => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]                                                                                     => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]                                                                                     => 4
[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]                                                                                     => 2
[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]                                                                                     => 3
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]                                                                                     => 3
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]                                                                                     => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]                                                                                     => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]                                                                                     => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]                                                                                     => 4
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]                                                                                     => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]                                                                                     => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]                                                                                     => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]                                                                                     => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]                                                                                     => 3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]                                                                                     => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]                                                                                     => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]                                                                                     => 3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]                                                                                     => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]                                                                                     => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]                                                                                     => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                                     => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]                                                                                     => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]                                                                                     => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]                                                                                     => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]                                                                                     => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]                                                                                     => 1
[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]                                                                                     => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]                                                                                     => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]                                                                                     => 4
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]                                                                                     => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]                                                                                     => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]                                                                                     => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]                                                                                     => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]                                                                                     => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]                                                                                     => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]                                                                                     => 0
[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]                                                                                     => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]                                                                                     => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]                                                                                     => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]                                                                                     => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]                                                                                     => 3
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]                                                                                     => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]                                                                                     => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]                                                                                     => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]                                                                                     => 3
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]                                                                                     => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]                                                                                     => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]                                                                                     => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]                                                                                     => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]                                                                                     => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]                                                                                     => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]                                                                                     => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]                                                                                     => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]                                                                                     => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]                                                                                     => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]                                                                                     => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                     => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                     => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]                                                                                     => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]                                                                                     => 4
[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]                                                                                     => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]                                                                                     => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]                                                                                     => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]                                                                                     => 4
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]                                                                                     => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]                                                                                     => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]                                                                                     => 3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]                                                                                     => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]                                                                                     => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                                     => 2
[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]                                                                                     => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]                                                                                     => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]                                                                                     => 3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]                                                                                     => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                                     => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]                                                                                     => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                     => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                     => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                     => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]                                                                                     => 4
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]                                                                                     => 3
[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]                                                                                     => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]                                                                                     => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]                                                                                     => 3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]                                                                                     => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]                                                                                     => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]                                                                                     => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]                                                                                     => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]                                                                                     => 4
[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]                                                                                     => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]                                                                                     => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]                                                                                     => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                                     => 4
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]                                                                                     => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]                                                                                     => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]                                                                                     => 3
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]                                                                                     => 3
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]                                                                                     => 3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]                                                                                     => 2
[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]                                                                                     => 4
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]                                                                                     => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]                                                                                     => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]                                                                                     => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]                                                                                     => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]                                                                                     => 4
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                                     => 4
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                                     => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]                                                                                     => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]                                                                                     => 3
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]                                                                                     => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                                     => 3
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]                                                                                     => 3
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]                                                                                     => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]                                                                                     => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]                                                                                     => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]                                                                                     => 2
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]                                                                                     => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]                                                                                     => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]                                                                                     => 0
[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]                                                                                     => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]                                                                                     => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]                                                                                     => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]                                                                                     => 4
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]                                                                                     => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]                                                                                     => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]                                                                                     => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]                                                                                     => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]                                                                                     => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]                                                                                     => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]                                                                                     => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]                                                                                     => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]                                                                                     => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]                                                                                     => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                                     => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                     => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]                                                                                     => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                     => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                     => 4
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                     => 4
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]                                                                                     => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                                                                                     => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]                                                                                     => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]                                                                                     => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]                                                                                     => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]                                                                                     => 3
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]                                                                                     => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]                                                                                     => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]                                                                                     => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]                                                                                     => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]                                                                                     => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                                     => 3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]                                                                                     => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                     => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]                                                                                     => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]                                                                                     => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]                                                                                     => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                     => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]                                                                                     => 0
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]                                                                                     => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]                                                                                     => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]                                                                                     => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]                                                                                     => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]                                                                                     => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                     => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]                                                                                     => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                     => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]                                                                                     => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]                                                                                     => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                     => 5
[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]                                                                                     => 3
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]                                                                                     => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]                                                                                     => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]                                                                                     => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]                                                                                     => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]                                                                                     => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]                                                                                     => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]                                                                                     => 2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]                                                                                     => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]                                                                                     => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]                                                                                     => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                     => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                     => 5
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]                                                                                     => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]                                                                                     => 5
[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]                                                                                     => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                     => 5
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]                                                                                     => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]                                                                                     => 3
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]                                                                                     => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]                                                                                     => 3
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]                                                                                     => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]                                                                                     => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]                                                                                     => 3
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]                                                                                     => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]                                                                                     => 1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]                                                                                     => 0
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]                                                                                     => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]                                                                                     => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]                                                                                     => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]                                                                                     => 1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]                                                                                     => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                     => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]                                                                                     => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]                                                                                     => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]                                                                                     => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]                                                                                     => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]                                                                                     => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                                                                                     => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]                                                                                     => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]                                                                                     => 5
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]                                                                                     => 5
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]                                                                                     => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                     => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]                                                                                     => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                     => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                     => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                     => 5
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]                                                                                     => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]                                                                                     => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]                                                                                     => 3
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]                                                                                     => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]                                                                                     => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]                                                                                     => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]                                                                                     => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]                                                                                     => 3
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]                                                                                     => 3
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]                                                                                     => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                     => 3
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]                                                                                     => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                     => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]                                                                                     => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]                                                                                     => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]                                                                                     => 2
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]                                                                                     => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]                                                                                     => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                     => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]                                                                                     => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]                                                                                     => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]                                                                                     => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]                                                                                     => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]                                                                                     => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]                                                                                     => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]                                                                                     => 0
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]                                                                                     => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]                                                                                     => 0
[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]                                                                                     => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]                                                                                     => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]                                                                                     => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]                                                                                     => 4
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]                                                                                     => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]                                                                                     => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]                                                                                     => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]                                                                                     => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]                                                                                     => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]                                                                                     => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]                                                                                     => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]                                                                                     => 4
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]                                                                                     => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]                                                                                     => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                                                                                     => 4
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]                                                                                     => 0
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]                                                                                     => 1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]                                                                                     => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]                                                                                     => 1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]                                                                                     => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]                                                                                     => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]                                                                                     => 4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]                                                                                     => 4
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]                                                                                     => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]                                                                                     => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]                                                                                     => 4
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]                                                                                     => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]                                                                                     => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                                     => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]                                                                                     => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]                                                                                     => 0
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]                                                                                     => 0
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]                                                                                     => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                                                                                     => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]                                                                                     => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]                                                                                     => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]                                                                                     => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]                                                                                     => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]                                                                                     => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]                                                                                     => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]                                                                                     => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]                                                                                     => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]                                                                                     => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]                                                                                     => 3
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]                                                                                     => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]                                                                                     => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]                                                                                     => 1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]                                                                                     => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]                                                                                     => 3
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]                                                                                     => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]                                                                                     => 3
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]                                                                                     => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]                                                                                     => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]                                                                                     => 3
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]                                                                                     => 3
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                                                                                     => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                                                                                     => 3
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]                                                                                     => 3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]                                                                                     => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]                                                                                     => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]                                                                                     => 3
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]                                                                                     => 3
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]                                                                                     => 3
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]                                                                                     => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]                                                                                     => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]                                                                                     => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]                                                                                     => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]                                                                                     => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]                                                                                     => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]                                                                                     => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                                                                                     => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]                                                                                     => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]                                                                                     => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                                                                                     => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                     => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]                                                                                 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]                                                                                 => 2
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                                                                                 => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]                                                                                 => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]                                                                                 => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]                                                                                 => 2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]                                                                                 => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]                                                                                 => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]                                                                                 => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]                                                                                 => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]                                                                                 => 3
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]                                                                                 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]                                                                                 => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                                                                                 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]                                                                                 => 0
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]                                                                                 => 4
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                                                                                 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]                                                                                 => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                                                                                 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]                                                                                 => 1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]                                                                                 => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                                                                                 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]                                                                                 => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]                                                                                 => 0
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]                                                                                 => 1
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]                                                                                 => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]                                                                                 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]                                                                                 => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]                                                                                 => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]                                                                                 => 4
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]                                                                                 => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]                                                                                 => 4
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]                                                                                 => 4
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]                                                                                 => 4
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]                                                                                 => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]                                                                                 => 4
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                                 => 4
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]                                                                                 => 4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]                                                                                 => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]                                                                                 => 5
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 5
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]                                                                                 => 4
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]                                                                                 => 4
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]                                                                                 => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 5
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]                                                                                 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]                                                                                 => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                 => 5
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 5
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]                                                                                 => 4
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 4
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]                                                                                 => 3
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]                                                                                 => 0
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]                                                                                 => 2
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]                                                                                 => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]                                                                                 => 1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]                                                                                 => 1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]                                                                                 => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                                                                                 => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 6
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]                                                                                 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                 => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 6
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]                                                                                 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]                                                                                 => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 5
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                 => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 5
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]                                                                                 => 5
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]                                                                                 => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 5
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]                                                                                 => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]                                                                                 => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]                                                                                 => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 4
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]                                                                                 => 2
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]                                                                                 => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]                                                                                 => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]                                                                                 => 3
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]                                                                                 => 3
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]                                                                                 => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]                                                                                 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]                                                                                 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]                                                                                 => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]                                                                                 => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]                                                                                 => 2
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]                                                                                 => 2
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]                                                                                 => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]                                                                                 => 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]                                                                                 => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]                                                                                 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]                                                                                 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                                 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                                 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                                 => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]                                                                                 => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]                                                                                 => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]                                                                                 => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]                                                                                 => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]                                                                                 => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]                                                                                 => 6
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]                                                                                 => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]                                                                                 => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]                                                                                 => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                 => 6
[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]                                                                                 => 6
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]                                                                                 => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]                                                                                 => 4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]                                                                                 => 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]                                                                                 => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                 => 4
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                                                                 => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                                                                                 => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]                                                                                 => 3
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]                                                                                 => 4
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]                                                                                 => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 6
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                 => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]                                                                                 => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]                                                                                 => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]                                                                                 => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 7
[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]                                                                                 => 7
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]                                                                                 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]                                                                                 => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]                                                                                 => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                 => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                                 => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                                 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]                                                                                 => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]                                                                                 => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]                                                                                 => 1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                 => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 6
[1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]                                                                                 => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]                                                                                 => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]                                                                                 => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]                                                                                 => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]                                                                                 => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]                                                                                 => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]                                                                                 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]                                                                                 => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]                                                                                 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                                 => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]                                                                                 => 5
[1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]                                                                                 => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]                                                                                 => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]                                                                                 => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 5
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]                                                                                 => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                                 => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]                                                                                 => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]                                                                                 => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]                                                                                 => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]                                                                                 => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]                                                                                 => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]                                                                                 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 6
[1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]                                                                                 => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]                                                                                 => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]                                                                                 => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]                                                                                 => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]                                                                                 => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                                 => 0
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]                                                                                 => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]                                                                                 => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]                                                                                 => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]                                                                                 => 2
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                 => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]                                                                                 => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0]                                                                                 => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]                                                                                 => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0]                                                                                 => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]                                                                                 => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]                                                                                 => 2
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                 => 0
[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]                                                                                 => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]                                                                                 => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]                                                                                 => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]                                                                                 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]                                                                                 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]                                                                                 => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                 => 5
[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]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]                                                                                 => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                                 => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                                 => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                                 => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                                 => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                 => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]                                                                                 => 6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]                                                                                 => 6
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]                                                                                 => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]                                                                                 => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]                                                                                 => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                                 => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]                                                                                 => 4
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 4
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                                                                                 => 5
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                                 => 1
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]                                                                                 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]                                                                                 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 7
[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]                                                                                 => 5
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                                                                                 => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]                                                                                 => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]                                                                                 => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]                                                                                 => 4
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]                                                                                 => 3
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                 => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]                                                                                 => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                                 => 3
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]                                                                                 => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]                                                                                 => 0
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]                                                                                 => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]                                                                                 => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]                                                                                 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]                                                                                 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]                                                                                 => 1
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]                                                                                 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]                                                                                 => 5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]                                                                                 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]                                                                                 => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]                                                                                 => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]                                                                                 => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]                                                                                 => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]                                                                                 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]                                                                                 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]                                                                                 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]                                                                                 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]                                                                                 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                                 => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]                                                                                 => 2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]                                                                                 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]                                                                                 => 3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]                                                                                 => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]                                                                                 => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]                                                                                 => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]                                                                                 => 5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]                                                                                 => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]                                                                                 => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]                                                                                 => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]                                                                                 => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]                                                                                 => 4
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]                                                                                 => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]                                                                             => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]                                                                             => 2
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]                                                                             => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]                                                                             => 1
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]                                                                             => 2
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]                                                                             => 3
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]                                                                             => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]                                                                             => 0
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                             => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]                                                                             => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]                                                                             => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]                                                                             => 1
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                                                                             => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                             => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                             => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                             => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]                                                                             => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]                                                                             => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]                                                                             => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                             => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                             => 8
[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]                                                                             => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                             => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]                                                                             => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]                                                                             => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                                                                             => 7
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                                                                             => 7
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]                                                                             => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]                                                                             => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                             => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                             => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                                                                             => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                             => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]                                                                             => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]                                                                             => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]                                                                             => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]                                                                             => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]                                                                             => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]                                                                             => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]                                                                             => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                             => 6
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]                                                                             => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]                                                                             => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                             => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]                                                                             => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]                                                                             => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]                                                                             => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]                                                                             => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 7
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]                                                                             => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]                                                                             => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]                                                                             => 1
[1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]                                                                             => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]                                                                             => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]                                                                             => 1
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                                                                             => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]                                                                             => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]                                                                             => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]                                                                             => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]                                                                             => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]                                                                             => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]                                                                             => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                             => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]                                                                             => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]                                                                             => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]                                                                             => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]                                                                             => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]                                                                             => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]                                                                             => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                                                                             => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                                                                             => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]                                                                             => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]                                                                             => 8
[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]                                                                             => 3
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]                                                                             => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]                                                                             => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                                                                             => 6
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]                                                                             => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]                                                                             => 1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]                                                                             => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                             => 6
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]                                                                             => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]                                                                             => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]                                                                             => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 0
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 0
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 0
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 0
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                             => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]                                                                             => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]                                                                             => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                                                                             => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                                                                             => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]                                                                             => 6
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]                                                                             => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]                                                                             => 5
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]                                                                             => 5
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]                                                                             => 5
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 5
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 5
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                             => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]                                                                             => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]                                                                             => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]                                                                             => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]                                                                             => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]                                                                             => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                             => 6
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]                                                                             => 3
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]                                                                             => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                                                             => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]                                                                             => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]                                                                             => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]                                                                             => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]                                                                             => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]                                                                             => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                             => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]                                                                             => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                             => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                             => 6
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 6
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]                                                                             => 5
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]                                                                             => 5
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]                                                                             => 5
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 5
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 5
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                             => 6
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                                                                             => 2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                                                                             => 3
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                                                                             => 3
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                                                                             => 3
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                                                                             => 4
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]                                                                             => 3
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]                                                                             => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]                                                                             => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]                                                                             => 4
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                                                                             => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                                                                             => 4
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]                                                                             => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]                                                                             => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]                                                                             => 5
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                             => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                             => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                                                             => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                                                             => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                                                             => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]                                                                             => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]                                                                             => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                                                                             => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                             => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]                                                                             => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]                                                                             => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                             => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]                                                                             => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]                                                                             => 4
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]                                                                             => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]                                                                             => 3
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]                                                                             => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]                                                                             => 3
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]                                                                             => 4
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                                                                             => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                             => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]                                                                             => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]                                                                             => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]                                                                             => 3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]                                                                             => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]                                                                             => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]                                                                             => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]                                                                             => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                                                                             => 7
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]                                                                             => 1
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]                                                                             => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]                                                                             => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]                                                                             => 1
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]                                                                             => 1
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]                                                                             => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]                                                                             => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]                                                                             => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]                                                                             => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]                                                                             => 4
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]                                                                             => 4
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]                                                                         => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]                                                                         => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]                                                                         => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]                                                                         => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0]                                                                         => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                         => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                                                         => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                                                         => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                                                                         => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]                                                                         => 8
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 8
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]                                                                         => 4
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]                                                                         => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                                                                         => 9
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]                                                                         => 0
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]                                                                         => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]                                                                         => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]                                                                         => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]                                                                         => 2
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]                                                                         => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                                                                         => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                                                                         => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                                                                         => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                                                                         => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 7
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 7
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 7
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                                                         => 8
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]                                                                         => 0
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                                                                         => 0
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]                                                                         => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]                                                                         => 0
[1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                                                                         => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]                                                                         => 6
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                                                         => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]                                                                         => 3
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]                                                                         => 3
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]                                                                         => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]                                                                     => 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]                                                                     => 12
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]                                                                     => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]                                                                     => 3
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]                                                                     => 3
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]                                                                     => 3
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]                                                                     => 4
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]                                                                     => 3
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]                                                                     => 4
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]                                                                     => 3
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]                                                                     => 4
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]                                                                     => 3
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]                                                                     => 4
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]                                                                     => 4
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]                                                                     => 4
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]                                                                     => 5
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                                                                     => 3
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                                                                     => 4
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                                                                     => 4
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                                                                     => 4
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                                                                     => 5
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]                                                                     => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]                                                                     => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]                                                                     => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]                                                                     => 5
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]                                                                     => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]                                                                     => 4
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]                                                                     => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]                                                                     => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]                                                                     => 5
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]                                                                     => 3
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]                                                                     => 4
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]                                                                     => 4
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]                                                                     => 4
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]                                                                     => 5
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                                                                     => 4
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                                                                     => 5
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]                                                                     => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]                                                                     => 5
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]                                                                     => 4
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]                                                                     => 5
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]                                                                     => 5
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]                                                                     => 5
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]                                                                     => 6
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                                                                     => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                                                                     => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                                                                     => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                                                                     => 3
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                                                                     => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]                                                                     => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]                                                                     => 4
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]                                                                     => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]                                                                     => 4
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                                                                     => 3
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                                                                     => 4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]                                                                     => 4
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]                                                                     => 4
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]                                                                     => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                     => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                     => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                                                     => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                                                     => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                                                     => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                                                     => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                                                     => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                                                     => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                                                     => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                                                     => 5
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]                                                                     => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]                                                                     => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]                                                                     => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]                                                                     => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]                                                                     => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]                                                                     => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                                                                     => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                     => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                                                                     => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                                                                     => 5
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]                                                                     => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]                                                                     => 3
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]                                                                     => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]                                                                     => 3
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]                                                                     => 4
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]                                                                     => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]                                                                     => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                     => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                                                                     => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]                                                                     => 3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]                                                                     => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]                                                                     => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]                                                                     => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]                                                                     => 5
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]                                                                     => 2
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]                                                                     => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]                                                                     => 3
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]                                                                     => 3
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]                                                                     => 4
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]                                                                     => 3
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]                                                                     => 4
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]                                                                     => 3
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]                                                                     => 4
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]                                                                     => 3
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]                                                                     => 4
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]                                                                     => 4
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]                                                                     => 4
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]                                                                     => 5
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]                                                                     => 3
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]                                                                     => 4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]                                                                     => 4
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]                                                                     => 4
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]                                                                     => 5
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                                                                     => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                     => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                                                                     => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                                                                     => 5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]                                                                     => 3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]                                                                     => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]                                                                     => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]                                                                     => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]                                                                     => 5
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]                                                                     => 3
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]                                                                     => 4
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]                                                                     => 4
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]                                                                     => 4
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]                                                                     => 5
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]                                                                     => 4
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]                                                                     => 5
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]                                                                     => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]                                                                     => 5
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]                                                                     => 4
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]                                                                     => 5
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]                                                                     => 5
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]                                                                     => 5
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]                                                                     => 6
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]                                                                     => 1
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]                                                                     => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]                                                                     => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                                     => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]                                                                     => 7
[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]                                                                 => 1
[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]                                                                 => 2
[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]                                                                 => 13
[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]                                                                 => 10
[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]                                                                 => 6
[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]                                                             => 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]                                                             => 14
[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]                                                             => 0
[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]                                                         => 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]                                                         => 15
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]                                                     => 1
[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]                                                     => 6
[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]                                                     => 13
[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]                                                     => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                                                 => 13
[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]                                                 => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]                                                 => 0
[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]                                             => 0
[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]     => 18
[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] => 0

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Created: Mar 07, 2016 at 20:06 by Christian Stump

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Last Updated: Feb 22, 2024 at 12:17 by Martin Rubey