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*                                                                           *
*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
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-----------------------------------------------------------------------------
Statistic identifier: St000645

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

-----------------------------------------------------------------------------
Description: The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between.

For a Dyck path $D = D_1 \cdots D_{2n}$ with peaks in positions $i_1 < \ldots < i_k$ and valleys in positions $j_1 < \ldots < j_{k-1}$, this statistic is given by
$$
    \sum_{a=1}^{k-1} (j_a-i_a)(i_{a+1}-j_a)
$$

-----------------------------------------------------------------------------
References: 

-----------------------------------------------------------------------------
Code:
def statistic(D):
    I = D.peaks()
    J = D.valleys()
    return sum( (J[a]-I[a])*(I[a+1]-J[a]) for a in range(len(J)) )


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

[]                                                                => 0
[1,0]                                                             => 0
[1,0,1,0]                                                         => 1
[1,1,0,0]                                                         => 0
[1,0,1,0,1,0]                                                     => 2
[1,0,1,1,0,0]                                                     => 2
[1,1,0,0,1,0]                                                     => 2
[1,1,0,1,0,0]                                                     => 1
[1,1,1,0,0,0]                                                     => 0
[1,0,1,0,1,0,1,0]                                                 => 3
[1,0,1,0,1,1,0,0]                                                 => 3
[1,0,1,1,0,0,1,0]                                                 => 4
[1,0,1,1,0,1,0,0]                                                 => 3
[1,0,1,1,1,0,0,0]                                                 => 3
[1,1,0,0,1,0,1,0]                                                 => 3
[1,1,0,0,1,1,0,0]                                                 => 4
[1,1,0,1,0,0,1,0]                                                 => 3
[1,1,0,1,0,1,0,0]                                                 => 2
[1,1,0,1,1,0,0,0]                                                 => 2
[1,1,1,0,0,0,1,0]                                                 => 3
[1,1,1,0,0,1,0,0]                                                 => 2
[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]                                             => 4
[1,0,1,0,1,0,1,1,0,0]                                             => 4
[1,0,1,0,1,1,0,0,1,0]                                             => 5
[1,0,1,0,1,1,0,1,0,0]                                             => 4
[1,0,1,0,1,1,1,0,0,0]                                             => 4
[1,0,1,1,0,0,1,0,1,0]                                             => 5
[1,0,1,1,0,0,1,1,0,0]                                             => 6
[1,0,1,1,0,1,0,0,1,0]                                             => 5
[1,0,1,1,0,1,0,1,0,0]                                             => 4
[1,0,1,1,0,1,1,0,0,0]                                             => 4
[1,0,1,1,1,0,0,0,1,0]                                             => 6
[1,0,1,1,1,0,0,1,0,0]                                             => 5
[1,0,1,1,1,0,1,0,0,0]                                             => 4
[1,0,1,1,1,1,0,0,0,0]                                             => 4
[1,1,0,0,1,0,1,0,1,0]                                             => 4
[1,1,0,0,1,0,1,1,0,0]                                             => 4
[1,1,0,0,1,1,0,0,1,0]                                             => 6
[1,1,0,0,1,1,0,1,0,0]                                             => 5
[1,1,0,0,1,1,1,0,0,0]                                             => 6
[1,1,0,1,0,0,1,0,1,0]                                             => 4
[1,1,0,1,0,0,1,1,0,0]                                             => 5
[1,1,0,1,0,1,0,0,1,0]                                             => 4
[1,1,0,1,0,1,0,1,0,0]                                             => 3
[1,1,0,1,0,1,1,0,0,0]                                             => 3
[1,1,0,1,1,0,0,0,1,0]                                             => 5
[1,1,0,1,1,0,0,1,0,0]                                             => 4
[1,1,0,1,1,0,1,0,0,0]                                             => 3
[1,1,0,1,1,1,0,0,0,0]                                             => 3
[1,1,1,0,0,0,1,0,1,0]                                             => 4
[1,1,1,0,0,0,1,1,0,0]                                             => 6
[1,1,1,0,0,1,0,0,1,0]                                             => 4
[1,1,1,0,0,1,0,1,0,0]                                             => 3
[1,1,1,0,0,1,1,0,0,0]                                             => 4
[1,1,1,0,1,0,0,0,1,0]                                             => 4
[1,1,1,0,1,0,0,1,0,0]                                             => 3
[1,1,1,0,1,0,1,0,0,0]                                             => 2
[1,1,1,0,1,1,0,0,0,0]                                             => 2
[1,1,1,1,0,0,0,0,1,0]                                             => 4
[1,1,1,1,0,0,0,1,0,0]                                             => 3
[1,1,1,1,0,0,1,0,0,0]                                             => 2
[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]                                         => 5
[1,0,1,0,1,0,1,0,1,1,0,0]                                         => 5
[1,0,1,0,1,0,1,1,0,0,1,0]                                         => 6
[1,0,1,0,1,0,1,1,0,1,0,0]                                         => 5
[1,0,1,0,1,0,1,1,1,0,0,0]                                         => 5
[1,0,1,0,1,1,0,0,1,0,1,0]                                         => 6
[1,0,1,0,1,1,0,0,1,1,0,0]                                         => 7
[1,0,1,0,1,1,0,1,0,0,1,0]                                         => 6
[1,0,1,0,1,1,0,1,0,1,0,0]                                         => 5
[1,0,1,0,1,1,0,1,1,0,0,0]                                         => 5
[1,0,1,0,1,1,1,0,0,0,1,0]                                         => 7
[1,0,1,0,1,1,1,0,0,1,0,0]                                         => 6
[1,0,1,0,1,1,1,0,1,0,0,0]                                         => 5
[1,0,1,0,1,1,1,1,0,0,0,0]                                         => 5
[1,0,1,1,0,0,1,0,1,0,1,0]                                         => 6
[1,0,1,1,0,0,1,0,1,1,0,0]                                         => 6
[1,0,1,1,0,0,1,1,0,0,1,0]                                         => 8
[1,0,1,1,0,0,1,1,0,1,0,0]                                         => 7
[1,0,1,1,0,0,1,1,1,0,0,0]                                         => 8
[1,0,1,1,0,1,0,0,1,0,1,0]                                         => 6
[1,0,1,1,0,1,0,0,1,1,0,0]                                         => 7
[1,0,1,1,0,1,0,1,0,0,1,0]                                         => 6
[1,0,1,1,0,1,0,1,0,1,0,0]                                         => 5
[1,0,1,1,0,1,0,1,1,0,0,0]                                         => 5
[1,0,1,1,0,1,1,0,0,0,1,0]                                         => 7
[1,0,1,1,0,1,1,0,0,1,0,0]                                         => 6
[1,0,1,1,0,1,1,0,1,0,0,0]                                         => 5
[1,0,1,1,0,1,1,1,0,0,0,0]                                         => 5
[1,0,1,1,1,0,0,0,1,0,1,0]                                         => 7
[1,0,1,1,1,0,0,0,1,1,0,0]                                         => 9
[1,0,1,1,1,0,0,1,0,0,1,0]                                         => 7
[1,0,1,1,1,0,0,1,0,1,0,0]                                         => 6
[1,0,1,1,1,0,0,1,1,0,0,0]                                         => 7
[1,0,1,1,1,0,1,0,0,0,1,0]                                         => 7
[1,0,1,1,1,0,1,0,0,1,0,0]                                         => 6
[1,0,1,1,1,0,1,0,1,0,0,0]                                         => 5
[1,0,1,1,1,0,1,1,0,0,0,0]                                         => 5
[1,0,1,1,1,1,0,0,0,0,1,0]                                         => 8
[1,0,1,1,1,1,0,0,0,1,0,0]                                         => 7
[1,0,1,1,1,1,0,0,1,0,0,0]                                         => 6
[1,0,1,1,1,1,0,1,0,0,0,0]                                         => 5
[1,0,1,1,1,1,1,0,0,0,0,0]                                         => 5
[1,1,0,0,1,0,1,0,1,0,1,0]                                         => 5
[1,1,0,0,1,0,1,0,1,1,0,0]                                         => 5
[1,1,0,0,1,0,1,1,0,0,1,0]                                         => 6
[1,1,0,0,1,0,1,1,0,1,0,0]                                         => 5
[1,1,0,0,1,0,1,1,1,0,0,0]                                         => 5
[1,1,0,0,1,1,0,0,1,0,1,0]                                         => 7
[1,1,0,0,1,1,0,0,1,1,0,0]                                         => 8
[1,1,0,0,1,1,0,1,0,0,1,0]                                         => 7
[1,1,0,0,1,1,0,1,0,1,0,0]                                         => 6
[1,1,0,0,1,1,0,1,1,0,0,0]                                         => 6
[1,1,0,0,1,1,1,0,0,0,1,0]                                         => 9
[1,1,0,0,1,1,1,0,0,1,0,0]                                         => 8
[1,1,0,0,1,1,1,0,1,0,0,0]                                         => 7
[1,1,0,0,1,1,1,1,0,0,0,0]                                         => 8
[1,1,0,1,0,0,1,0,1,0,1,0]                                         => 5
[1,1,0,1,0,0,1,0,1,1,0,0]                                         => 5
[1,1,0,1,0,0,1,1,0,0,1,0]                                         => 7
[1,1,0,1,0,0,1,1,0,1,0,0]                                         => 6
[1,1,0,1,0,0,1,1,1,0,0,0]                                         => 7
[1,1,0,1,0,1,0,0,1,0,1,0]                                         => 5
[1,1,0,1,0,1,0,0,1,1,0,0]                                         => 6
[1,1,0,1,0,1,0,1,0,0,1,0]                                         => 5
[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]                                         => 4
[1,1,0,1,0,1,1,0,0,0,1,0]                                         => 6
[1,1,0,1,0,1,1,0,0,1,0,0]                                         => 5
[1,1,0,1,0,1,1,0,1,0,0,0]                                         => 4
[1,1,0,1,0,1,1,1,0,0,0,0]                                         => 4
[1,1,0,1,1,0,0,0,1,0,1,0]                                         => 6
[1,1,0,1,1,0,0,0,1,1,0,0]                                         => 8
[1,1,0,1,1,0,0,1,0,0,1,0]                                         => 6
[1,1,0,1,1,0,0,1,0,1,0,0]                                         => 5
[1,1,0,1,1,0,0,1,1,0,0,0]                                         => 6
[1,1,0,1,1,0,1,0,0,0,1,0]                                         => 6
[1,1,0,1,1,0,1,0,0,1,0,0]                                         => 5
[1,1,0,1,1,0,1,0,1,0,0,0]                                         => 4
[1,1,0,1,1,0,1,1,0,0,0,0]                                         => 4
[1,1,0,1,1,1,0,0,0,0,1,0]                                         => 7
[1,1,0,1,1,1,0,0,0,1,0,0]                                         => 6
[1,1,0,1,1,1,0,0,1,0,0,0]                                         => 5
[1,1,0,1,1,1,0,1,0,0,0,0]                                         => 4
[1,1,0,1,1,1,1,0,0,0,0,0]                                         => 4
[1,1,1,0,0,0,1,0,1,0,1,0]                                         => 5
[1,1,1,0,0,0,1,0,1,1,0,0]                                         => 5
[1,1,1,0,0,0,1,1,0,0,1,0]                                         => 8
[1,1,1,0,0,0,1,1,0,1,0,0]                                         => 7
[1,1,1,0,0,0,1,1,1,0,0,0]                                         => 9
[1,1,1,0,0,1,0,0,1,0,1,0]                                         => 5
[1,1,1,0,0,1,0,0,1,1,0,0]                                         => 6
[1,1,1,0,0,1,0,1,0,0,1,0]                                         => 5
[1,1,1,0,0,1,0,1,0,1,0,0]                                         => 4
[1,1,1,0,0,1,0,1,1,0,0,0]                                         => 4
[1,1,1,0,0,1,1,0,0,0,1,0]                                         => 7
[1,1,1,0,0,1,1,0,0,1,0,0]                                         => 6
[1,1,1,0,0,1,1,0,1,0,0,0]                                         => 5
[1,1,1,0,0,1,1,1,0,0,0,0]                                         => 6
[1,1,1,0,1,0,0,0,1,0,1,0]                                         => 5
[1,1,1,0,1,0,0,0,1,1,0,0]                                         => 7
[1,1,1,0,1,0,0,1,0,0,1,0]                                         => 5
[1,1,1,0,1,0,0,1,0,1,0,0]                                         => 4
[1,1,1,0,1,0,0,1,1,0,0,0]                                         => 5
[1,1,1,0,1,0,1,0,0,0,1,0]                                         => 5
[1,1,1,0,1,0,1,0,0,1,0,0]                                         => 4
[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]                                         => 3
[1,1,1,0,1,1,0,0,0,0,1,0]                                         => 6
[1,1,1,0,1,1,0,0,0,1,0,0]                                         => 5
[1,1,1,0,1,1,0,0,1,0,0,0]                                         => 4
[1,1,1,0,1,1,0,1,0,0,0,0]                                         => 3
[1,1,1,0,1,1,1,0,0,0,0,0]                                         => 3
[1,1,1,1,0,0,0,0,1,0,1,0]                                         => 5
[1,1,1,1,0,0,0,0,1,1,0,0]                                         => 8
[1,1,1,1,0,0,0,1,0,0,1,0]                                         => 5
[1,1,1,1,0,0,0,1,0,1,0,0]                                         => 4
[1,1,1,1,0,0,0,1,1,0,0,0]                                         => 6
[1,1,1,1,0,0,1,0,0,0,1,0]                                         => 5
[1,1,1,1,0,0,1,0,0,1,0,0]                                         => 4
[1,1,1,1,0,0,1,0,1,0,0,0]                                         => 3
[1,1,1,1,0,0,1,1,0,0,0,0]                                         => 4
[1,1,1,1,0,1,0,0,0,0,1,0]                                         => 5
[1,1,1,1,0,1,0,0,0,1,0,0]                                         => 4
[1,1,1,1,0,1,0,0,1,0,0,0]                                         => 3
[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]                                         => 2
[1,1,1,1,1,0,0,0,0,0,1,0]                                         => 5
[1,1,1,1,1,0,0,0,0,1,0,0]                                         => 4
[1,1,1,1,1,0,0,0,1,0,0,0]                                         => 3
[1,1,1,1,1,0,0,1,0,0,0,0]                                         => 2
[1,1,1,1,1,0,1,0,0,0,0,0]                                         => 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]                                     => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                     => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]                                     => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                     => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]                                     => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]                                     => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]                                     => 8
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]                                     => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]                                     => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]                                     => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]                                     => 8
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]                                     => 7
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]                                     => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]                                     => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]                                     => 7
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]                                     => 7
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]                                     => 9
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]                                     => 8
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]                                     => 9
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]                                     => 7
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]                                     => 8
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]                                     => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]                                     => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]                                     => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]                                     => 8
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]                                     => 7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]                                     => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]                                     => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]                                     => 8
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]                                     => 10
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]                                     => 8
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]                                     => 7
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]                                     => 8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]                                     => 8
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]                                     => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]                                     => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]                                     => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]                                     => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]                                     => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]                                     => 7
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]                                     => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]                                     => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]                                     => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]                                     => 7
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]                                     => 8
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]                                     => 7
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]                                     => 7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]                                     => 9
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]                                     => 10
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]                                     => 9
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]                                     => 8
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]                                     => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]                                     => 11
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]                                     => 10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]                                     => 9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]                                     => 10
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]                                     => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]                                     => 7
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]                                     => 9
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]                                     => 8
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]                                     => 9
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]                                     => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]                                     => 8
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]                                     => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]                                     => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]                                     => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]                                     => 8
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]                                     => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]                                     => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]                                     => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]                                     => 8
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]                                     => 10
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]                                     => 8
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]                                     => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]                                     => 8
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]                                     => 8
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]                                     => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]                                     => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]                                     => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]                                     => 9
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]                                     => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]                                     => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]                                     => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]                                     => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]                                     => 8
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]                                     => 8
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]                                     => 11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]                                     => 10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]                                     => 12
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]                                     => 8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]                                     => 9
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]                                     => 8
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]                                     => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]                                     => 7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]                                     => 10
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]                                     => 9
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]                                     => 8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]                                     => 9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]                                     => 8
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]                                     => 10
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]                                     => 8
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]                                     => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]                                     => 8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]                                     => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]                                     => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]                                     => 6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]                                     => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]                                     => 9
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]                                     => 8
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]                                     => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]                                     => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]                                     => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]                                     => 9
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]                                     => 12
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]                                     => 9
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]                                     => 8
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]                                     => 10
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]                                     => 9
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]                                     => 8
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]                                     => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]                                     => 8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]                                     => 9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]                                     => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]                                     => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]                                     => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]                                     => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]                                     => 10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]                                     => 9
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]                                     => 8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]                                     => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]                                     => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]                                     => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]                                     => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]                                     => 6
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]                                     => 7
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]                                     => 6
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]                                     => 6
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]                                     => 7
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]                                     => 8
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]                                     => 7
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]                                     => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]                                     => 6
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]                                     => 8
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]                                     => 7
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]                                     => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]                                     => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]                                     => 8
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]                                     => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]                                     => 10
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]                                     => 9
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]                                     => 10
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]                                     => 8
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]                                     => 9
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]                                     => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]                                     => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]                                     => 7
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]                                     => 9
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]                                     => 8
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]                                     => 7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]                                     => 7
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]                                     => 10
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]                                     => 12
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]                                     => 10
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]                                     => 9
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]                                     => 10
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]                                     => 10
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]                                     => 9
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]                                     => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]                                     => 8
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]                                     => 12
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]                                     => 11
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]                                     => 10
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]                                     => 9
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]                                     => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]                                     => 6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]                                     => 6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]                                     => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]                                     => 6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]                                     => 6
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]                                     => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]                                     => 9
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]                                     => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]                                     => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]                                     => 7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]                                     => 10
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]                                     => 9
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]                                     => 8
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]                                     => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]                                     => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]                                     => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]                                     => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]                                     => 7
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]                                     => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]                                     => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]                                     => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]                                     => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]                                     => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]                                     => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]                                     => 7
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]                                     => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]                                     => 5
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]                                     => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]                                     => 7
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]                                     => 9
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]                                     => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]                                     => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]                                     => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]                                     => 7
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]                                     => 6
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]                                     => 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]                                     => 5
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]                                     => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]                                     => 7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]                                     => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]                                     => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]                                     => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]                                     => 7
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]                                     => 7
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]                                     => 10
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]                                     => 9
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]                                     => 11
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]                                     => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]                                     => 8
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]                                     => 7
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]                                     => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]                                     => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]                                     => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]                                     => 8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]                                     => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]                                     => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]                                     => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]                                     => 9
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]                                     => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]                                     => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]                                     => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]                                     => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]                                     => 6
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]                                     => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]                                     => 5
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]                                     => 8
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]                                     => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]                                     => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                     => 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]                                     => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]                                     => 8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]                                     => 11
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]                                     => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]                                     => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]                                     => 9
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]                                     => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]                                     => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]                                     => 6
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]                                     => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]                                     => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]                                     => 7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                     => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]                                     => 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]                                     => 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]                                     => 9
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]                                     => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]                                     => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]                                     => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]                                     => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]                                     => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]                                     => 6
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]                                     => 6
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]                                     => 7
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]                                     => 6
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]                                     => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]                                     => 9
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]                                     => 10
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]                                     => 9
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]                                     => 8
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]                                     => 8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]                                     => 12
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]                                     => 11
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]                                     => 10
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]                                     => 12
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]                                     => 6
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]                                     => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]                                     => 8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]                                     => 7
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]                                     => 8
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]                                     => 6
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]                                     => 7
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]                                     => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]                                     => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]                                     => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]                                     => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]                                     => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]                                     => 5
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]                                     => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]                                     => 8
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]                                     => 10
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]                                     => 8
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]                                     => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]                                     => 8
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]                                     => 8
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]                                     => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]                                     => 6
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]                                     => 6
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]                                     => 10
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]                                     => 9
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]                                     => 8
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]                                     => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]                                     => 8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]                                     => 6
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]                                     => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]                                     => 9
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]                                     => 8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]                                     => 10
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]                                     => 6
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]                                     => 7
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]                                     => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]                                     => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]                                     => 5
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]                                     => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]                                     => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                     => 6
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]                                     => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]                                     => 6
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]                                     => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]                                     => 6
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]                                     => 5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]                                     => 6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]                                     => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]                                     => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]                                     => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]                                     => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]                                     => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]                                     => 6
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]                                     => 5
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]                                     => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]                                     => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]                                     => 7
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]                                     => 10
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]                                     => 7
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]                                     => 6
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]                                     => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]                                     => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]                                     => 6
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]                                     => 5
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]                                     => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]                                     => 7
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                     => 6
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]                                     => 5
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]                                     => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]                                     => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]                                     => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]                                     => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]                                     => 6
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]                                     => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]                                     => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]                                     => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]                                     => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]                                     => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]                                     => 10
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]                                     => 9
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]                                     => 12
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]                                     => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]                                     => 7
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]                                     => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]                                     => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]                                     => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]                                     => 9
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]                                     => 8
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]                                     => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]                                     => 9
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]                                     => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]                                     => 8
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]                                     => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]                                     => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]                                     => 6
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]                                     => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]                                     => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]                                     => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]                                     => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]                                     => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]                                     => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]                                     => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]                                     => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]                                     => 6
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]                                     => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]                                     => 9
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]                                     => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]                                     => 5
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]                                     => 7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]                                     => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                     => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]                                     => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]                                     => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]                                     => 6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]                                     => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]                                     => 4
[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]                                     => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]                                     => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]                                     => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]                                     => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]                                     => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]                                     => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]                                     => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]                                     => 6
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]                                     => 10
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]                                     => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]                                     => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]                                     => 8
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]                                     => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]                                     => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]                                     => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]                                     => 6
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]                                     => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]                                     => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]                                     => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]                                     => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]                                     => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]                                     => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]                                     => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]                                     => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]                                     => 3
[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]                                     => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]                                     => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]                                     => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]                                     => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]                                     => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]                                     => 2
[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]                                 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                                 => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]                                 => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                                 => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]                                 => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]                                 => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]                                 => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]                                 => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]                                 => 7
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]                                 => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]                                 => 9
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]                                 => 8
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]                                 => 7
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]                                 => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]                                 => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]                                 => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]                                 => 10
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]                                 => 9
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]                                 => 10
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]                                 => 8
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]                                 => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]                                 => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]                                 => 7
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]                                 => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]                                 => 9
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]                                 => 8
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]                                 => 7
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]                                 => 7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]                                 => 9
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]                                 => 11
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]                                 => 9
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]                                 => 8
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]                                 => 9
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]                                 => 9
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]                                 => 8
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]                                 => 7
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]                                 => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]                                 => 10
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]                                 => 9
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]                                 => 8
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]                                 => 7
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]                                 => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]                                 => 8
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]                                 => 8
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]                                 => 9
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]                                 => 8
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]                                 => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]                                 => 10
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]                                 => 11
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]                                 => 10
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]                                 => 9
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]                                 => 9
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]                                 => 12
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]                                 => 11
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]                                 => 10
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]                                 => 11
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]                                 => 8
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]                                 => 8
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]                                 => 10
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]                                 => 9
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]                                 => 10
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]                                 => 8
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]                                 => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]                                 => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]                                 => 7
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]                                 => 7
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]                                 => 9
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]                                 => 8
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]                                 => 7
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]                                 => 7
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]                                 => 9
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]                                 => 11
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]                                 => 9
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]                                 => 8
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]                                 => 9
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]                                 => 9
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]                                 => 8
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]                                 => 7
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]                                 => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]                                 => 10
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]                                 => 9
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]                                 => 8
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]                                 => 7
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]                                 => 7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]                                 => 9
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]                                 => 9
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]                                 => 12
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]                                 => 11
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]                                 => 13
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]                                 => 9
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]                                 => 10
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]                                 => 9
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]                                 => 8
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]                                 => 8
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]                                 => 11
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]                                 => 10
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]                                 => 9
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]                                 => 10
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]                                 => 9
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]                                 => 11
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]                                 => 9
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]                                 => 8
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]                                 => 9
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]                                 => 9
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]                                 => 8
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]                                 => 7
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]                                 => 7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]                                 => 10
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]                                 => 9
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]                                 => 8
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]                                 => 7
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]                                 => 7
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]                                 => 10
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]                                 => 13
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]                                 => 10
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]                                 => 9
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]                                 => 11
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]                                 => 10
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]                                 => 9
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]                                 => 8
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]                                 => 9
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]                                 => 10
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]                                 => 9
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]                                 => 8
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]                                 => 7
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]                                 => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]                                 => 11
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]                                 => 10
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]                                 => 9
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]                                 => 8
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]                                 => 7
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]                                 => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]                                 => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]                                 => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]                                 => 9
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]                                 => 8
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]                                 => 8
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]                                 => 9
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]                                 => 10
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]                                 => 9
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]                                 => 8
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]                                 => 8
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]                                 => 10
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]                                 => 9
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]                                 => 8
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]                                 => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]                                 => 10
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]                                 => 10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]                                 => 12
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]                                 => 11
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]                                 => 12
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]                                 => 10
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]                                 => 11
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]                                 => 10
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]                                 => 9
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]                                 => 9
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]                                 => 11
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]                                 => 10
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]                                 => 9
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]                                 => 9
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]                                 => 12
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]                                 => 14
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]                                 => 12
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]                                 => 11
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]                                 => 12
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]                                 => 12
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]                                 => 11
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]                                 => 10
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]                                 => 10
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]                                 => 14
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]                                 => 13
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]                                 => 12
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]                                 => 11
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]                                 => 12
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]                                 => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]                                 => 8
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]                                 => 9
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]                                 => 8
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]                                 => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]                                 => 10
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]                                 => 11
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]                                 => 10
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]                                 => 9
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]                                 => 9
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]                                 => 12
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]                                 => 11
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]                                 => 10
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]                                 => 11
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]                                 => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]                                 => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]                                 => 10
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]                                 => 9
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]                                 => 10
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]                                 => 8
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]                                 => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]                                 => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]                                 => 7
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]                                 => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]                                 => 9
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]                                 => 8
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]                                 => 7
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]                                 => 7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]                                 => 9
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]                                 => 11
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]                                 => 9
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]                                 => 8
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]                                 => 9
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]                                 => 9
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]                                 => 8
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]                                 => 7
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]                                 => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]                                 => 10
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]                                 => 9
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]                                 => 8
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]                                 => 7
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]                                 => 7
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]                                 => 9
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]                                 => 9
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]                                 => 12
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]                                 => 11
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]                                 => 13
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]                                 => 9
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]                                 => 10
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]                                 => 9
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]                                 => 8
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]                                 => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]                                 => 11
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]                                 => 10
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]                                 => 9
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]                                 => 10
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]                                 => 9
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]                                 => 11
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]                                 => 9
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]                                 => 8
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]                                 => 9
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]                                 => 9
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]                                 => 8
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]                                 => 7
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]                                 => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]                                 => 10
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]                                 => 9
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]                                 => 8
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                                 => 7
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]                                 => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]                                 => 10
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]                                 => 13
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]                                 => 10
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]                                 => 9
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]                                 => 11
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]                                 => 10
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]                                 => 9
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]                                 => 8
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]                                 => 9
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]                                 => 10
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]                                 => 9
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                                 => 8
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]                                 => 7
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]                                 => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]                                 => 11
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]                                 => 10
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]                                 => 9
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]                                 => 8
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]                                 => 7
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]                                 => 7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]                                 => 9
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]                                 => 9
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]                                 => 10
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]                                 => 9
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]                                 => 9
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]                                 => 12
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]                                 => 13
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]                                 => 12
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]                                 => 11
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]                                 => 11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]                                 => 15
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]                                 => 14
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]                                 => 13
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]                                 => 15
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]                                 => 9
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]                                 => 9
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]                                 => 11
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]                                 => 10
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]                                 => 11
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]                                 => 9
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]                                 => 10
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]                                 => 9
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]                                 => 8
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]                                 => 8
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]                                 => 10
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]                                 => 9
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]                                 => 8
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]                                 => 8
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]                                 => 11
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]                                 => 13
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]                                 => 11
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]                                 => 10
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]                                 => 11
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]                                 => 11
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]                                 => 10
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]                                 => 9
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]                                 => 9
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]                                 => 13
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]                                 => 12
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]                                 => 11
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]                                 => 10
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]                                 => 11
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]                                 => 9
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]                                 => 9
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]                                 => 12
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]                                 => 11
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]                                 => 13
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]                                 => 9
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]                                 => 10
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]                                 => 9
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]                                 => 8
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]                                 => 8
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]                                 => 11
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]                                 => 10
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                                 => 9
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]                                 => 10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]                                 => 9
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]                                 => 11
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]                                 => 9
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]                                 => 8
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]                                 => 9
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]                                 => 9
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]                                 => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]                                 => 7
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]                                 => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]                                 => 10
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]                                 => 9
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]                                 => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]                                 => 7
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]                                 => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]                                 => 10
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]                                 => 13
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]                                 => 10
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]                                 => 9
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]                                 => 11
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]                                 => 10
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]                                 => 9
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]                                 => 8
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]                                 => 9
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]                                 => 10
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                                 => 9
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]                                 => 8
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]                                 => 7
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]                                 => 7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]                                 => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]                                 => 10
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]                                 => 9
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]                                 => 8
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]                                 => 7
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]                                 => 7
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]                                 => 10
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]                                 => 10
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]                                 => 14
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]                                 => 13
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]                                 => 16
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]                                 => 10
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]                                 => 11
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]                                 => 10
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]                                 => 9
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]                                 => 9
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]                                 => 13
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]                                 => 12
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]                                 => 11
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]                                 => 13
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]                                 => 10
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]                                 => 12
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]                                 => 10
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]                                 => 9
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]                                 => 10
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]                                 => 10
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]                                 => 9
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]                                 => 8
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]                                 => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]                                 => 12
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]                                 => 11
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]                                 => 10
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]                                 => 9
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]                                 => 10
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]                                 => 10
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]                                 => 13
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]                                 => 10
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]                                 => 9
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]                                 => 11
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]                                 => 10
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                                 => 9
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]                                 => 8
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]                                 => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]                                 => 10
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]                                 => 9
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]                                 => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]                                 => 7
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]                                 => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]                                 => 11
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]                                 => 10
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]                                 => 9
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]                                 => 8
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]                                 => 7
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]                                 => 7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]                                 => 11
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]                                 => 15
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]                                 => 11
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]                                 => 10
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]                                 => 13
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]                                 => 11
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]                                 => 10
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]                                 => 9
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]                                 => 11
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]                                 => 11
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]                                 => 10
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]                                 => 9
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]                                 => 8
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]                                 => 9
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]                                 => 11
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]                                 => 10
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]                                 => 9
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]                                 => 8
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]                                 => 7
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]                                 => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]                                 => 12
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]                                 => 11
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]                                 => 10
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]                                 => 9
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]                                 => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]                                 => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                                 => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                                 => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]                                 => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]                                 => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]                                 => 7
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]                                 => 7
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]                                 => 8
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]                                 => 9
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]                                 => 8
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]                                 => 7
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]                                 => 7
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]                                 => 9
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]                                 => 8
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]                                 => 7
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]                                 => 7
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]                                 => 8
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]                                 => 8
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]                                 => 10
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]                                 => 9
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]                                 => 10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]                                 => 8
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]                                 => 9
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]                                 => 8
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]                                 => 7
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]                                 => 7
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]                                 => 9
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]                                 => 8
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]                                 => 7
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]                                 => 7
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]                                 => 9
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]                                 => 11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]                                 => 9
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]                                 => 8
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]                                 => 9
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]                                 => 9
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]                                 => 8
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]                                 => 7
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]                                 => 7
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]                                 => 10
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]                                 => 9
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]                                 => 8
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]                                 => 7
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]                                 => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]                                 => 9
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]                                 => 9
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]                                 => 10
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]                                 => 9
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]                                 => 9
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]                                 => 11
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                                 => 12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]                                 => 11
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]                                 => 10
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]                                 => 10
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]                                 => 13
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]                                 => 12
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]                                 => 11
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]                                 => 12
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]                                 => 9
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]                                 => 9
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]                                 => 11
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]                                 => 10
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]                                 => 11
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]                                 => 9
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]                                 => 10
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]                                 => 9
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]                                 => 8
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]                                 => 8
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]                                 => 10
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]                                 => 9
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]                                 => 8
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]                                 => 8
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]                                 => 10
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]                                 => 12
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]                                 => 10
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]                                 => 9
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]                                 => 10
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]                                 => 10
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]                                 => 9
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]                                 => 8
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]                                 => 8
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]                                 => 11
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]                                 => 10
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]                                 => 9
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]                                 => 8
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]                                 => 8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]                                 => 11
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]                                 => 11
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]                                 => 14
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]                                 => 13
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]                                 => 15
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]                                 => 11
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]                                 => 12
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]                                 => 11
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]                                 => 10
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]                                 => 10
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]                                 => 13
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]                                 => 12
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]                                 => 11
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]                                 => 12
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]                                 => 11
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]                                 => 13
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]                                 => 11
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]                                 => 10
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]                                 => 11
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]                                 => 11
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]                                 => 10
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]                                 => 9
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]                                 => 9
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]                                 => 12
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]                                 => 11
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]                                 => 10
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]                                 => 9
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]                                 => 9
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]                                 => 13
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]                                 => 16
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]                                 => 13
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]                                 => 12
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]                                 => 14
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]                                 => 13
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]                                 => 12
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]                                 => 11
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]                                 => 12
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]                                 => 13
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]                                 => 12
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]                                 => 11
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]                                 => 10
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]                                 => 10
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]                                 => 15
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]                                 => 14
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]                                 => 13
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]                                 => 12
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]                                 => 11
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                                 => 12
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                                 => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]                                 => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]                                 => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]                                 => 7
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]                                 => 7
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]                                 => 8
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]                                 => 9
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]                                 => 8
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]                                 => 7
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]                                 => 7
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]                                 => 9
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]                                 => 8
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]                                 => 7
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]                                 => 7
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]                                 => 9
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]                                 => 11
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]                                 => 9
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                                 => 8
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]                                 => 11
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]                                 => 11
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]                                 => 11
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                                 => 10
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]                                 => 9
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]                                 => 10
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]                                 => 11
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                                 => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]                                 => 7
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]                                 => 7
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]                                 => 9
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]                                 => 9
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]                                 => 8
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]                                 => 11
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]                                 => 10
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]                                 => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]                                 => 7
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]                                 => 9
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]                                 => 8
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]                                 => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]                                 => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]                                 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]                                 => 7
[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]                                 => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]                                 => 8
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]                                 => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                                 => 6
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]                                 => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]                                 => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]                                 => 7
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]                                 => 8
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]                                 => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                                 => 6
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]                                 => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]                                 => 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]                                 => 8
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]                                 => 7
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]                                 => 6
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]                                 => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]                                 => 8
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]                                 => 7
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]                                 => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]                                 => 9
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]                                 => 9
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]                                 => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]                                 => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]                                 => 7
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                                 => 6
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]                                 => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]                                 => 9
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]                                 => 8
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]                                 => 10
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]                                 => 7
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]                                 => 7
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]                                 => 6
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]                                 => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]                                 => 10
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]                                 => 9
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]                                 => 8
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]                                 => 6
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]                                 => 6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]                                 => 8
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]                                 => 12
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]                                 => 8
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]                                 => 8
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]                                 => 10
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]                                 => 10
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]                                 => 7
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]                                 => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]                                 => 8
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]                                 => 7
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]                                 => 12
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]                                 => 10
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]                                 => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]                                 => 10
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]                                 => 11
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]                                 => 10
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]                                 => 9
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]                                 => 10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]                                 => 8
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                                 => 10
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]                                 => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]                                 => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]                                 => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]                                 => 7
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                                 => 6
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]                                 => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                                 => 9
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]                                 => 6
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]                                 => 6
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]                                 => 6
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]                                 => 9
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]                                 => 8
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]                                 => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]                                 => 11
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]                                 => 12
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]                                 => 11
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]                                 => 7
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]                                 => 9
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                                 => 9
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]                                 => 7
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]                                 => 7
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]                                 => 6
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]                                 => 8
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]                                 => 6
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]                                 => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]                                 => 14
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]                                 => 9
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]                                 => 12
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]                                 => 8
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]                                 => 8
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]                                 => 8
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]                                 => 7
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]                                 => 6
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]                                 => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]                                 => 11
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]                                 => 10
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]                                 => 9
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]                                 => 8
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]                                 => 7
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]                                 => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]                                 => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                                 => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]                                 => 7
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]                                 => 7
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]                                 => 7
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]                                 => 11
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]                                 => 11
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]                                 => 16
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]                                 => 13
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]                                 => 15
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]                                 => 7
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]                                 => 10
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]                                 => 7
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]                                 => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]                                 => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                                 => 6
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]                                 => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]                                 => 7
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]                                 => 6
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]                                 => 7
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]                                 => 8
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]                                 => 8
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]                                 => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]                                 => 8
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]                                 => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]                                 => 10
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]                                 => 10
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]                                 => 7
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]                                 => 10
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]                                 => 12
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]                                 => 12
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]                                 => 9
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]                                 => 10
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]                                 => 7
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]                                 => 7
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]                                 => 11
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]                                 => 11
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]                                 => 13
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]                                 => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]                                 => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                                 => 6
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]                                 => 9
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]                                 => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]                                 => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]                                 => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]                                 => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]                                 => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]                                 => 6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]                                 => 7
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]                                 => 9
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]                                 => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                                 => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                                 => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                                 => 5
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]                                 => 5
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]                                 => 6
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]                                 => 5
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]                                 => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]                                 => 11
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]                                 => 7
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]                                 => 6
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]                                 => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]                                 => 7
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]                                 => 6
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]                                 => 5
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]                                 => 5
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]                                 => 7
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]                                 => 6
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]                                 => 5
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]                                 => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]                                 => 10
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]                                 => 6
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]                                 => 6
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]                                 => 8
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]                                 => 7
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]                                 => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]                                 => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]                                 => 7
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]                                 => 6
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]                                 => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]                                 => 7
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]                                 => 6
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]                                 => 5
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]                                 => 5
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]                                 => 7
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]                                 => 6
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                                 => 5
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]                                 => 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]                                 => 13
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]                                 => 8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]                                 => 7
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]                                 => 9
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]                                 => 8
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]                                 => 7
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]                                 => 6
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]                                 => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]                                 => 8
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]                                 => 7
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                                 => 6
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]                                 => 5
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]                                 => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]                                 => 10
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]                                 => 9
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]                                 => 8
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]                                 => 7
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]                                 => 6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]                                 => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]                                 => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]                                 => 7
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]                                 => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]                                 => 12
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]                                 => 13
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]                                 => 16
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]                                 => 7
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]                                 => 7
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]                                 => 7
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]                                 => 6
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]                                 => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]                                 => 7
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]                                 => 6
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]                                 => 9
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]                                 => 10
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]                                 => 12
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]                                 => 10
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]                                 => 12
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]                                 => 7
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]                                 => 11
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]                                 => 6
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                                 => 5
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]                                 => 5
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]                                 => 6
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]                                 => 5
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]                                 => 5
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]                                 => 7
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]                                 => 8
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]                                 => 7
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]                                 => 6
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]                                 => 6
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]                                 => 9
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]                                 => 8
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]                                 => 7
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]                                 => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]                                 => 13
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]                                 => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]                                 => 7
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]                                 => 5
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]                                 => 5
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]                                 => 7
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                                 => 6
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]                                 => 7
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]                                 => 10
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]                                 => 6
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]                                 => 5
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]                                 => 6
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]                                 => 6
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]                                 => 5
[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]                                 => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]                                 => 8
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]                                 => 6
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]                                 => 5
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]                                 => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]                                 => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]                                 => 12
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]                                 => 6
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]                                 => 8
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]                                 => 6
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]                                 => 5
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]                                 => 6
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                                 => 7
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                                 => 6
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]                                 => 5
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]                                 => 4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]                                 => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]                                 => 9
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]                                 => 8
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]                                 => 7
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]                                 => 6
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]                                 => 5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]                                 => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]                                 => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]                                 => 7
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]                                 => 11
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]                                 => 15
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]                                 => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]                                 => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]                                 => 6
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]                                 => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]                                 => 10
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]                                 => 9
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]                                 => 12
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]                                 => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]                                 => 9
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]                                 => 5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]                                 => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]                                 => 10
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]                                 => 8
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]                                 => 7
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]                                 => 9
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]                                 => 10
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]                                 => 5
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]                                 => 6
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]                                 => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]                                 => 4
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]                                 => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]                                 => 9
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]                                 => 8
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]                                 => 7
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]                                 => 6
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]                                 => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]                                 => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]                                 => 11
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]                                 => 6
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]                                 => 5
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]                                 => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                                 => 6
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                                 => 5
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]                                 => 4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]                                 => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]                                 => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]                                 => 6
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]                                 => 5
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]                                 => 4
[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]                                 => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]                                 => 8
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]                                 => 7
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]                                 => 6
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]                                 => 5
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]                                 => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]                                 => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]                                 => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]                                 => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]                                 => 12
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]                                 => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]                                 => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]                                 => 10
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]                                 => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]                                 => 6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]                                 => 5
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]                                 => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]                                 => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]                                 => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]                                 => 5
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]                                 => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]                                 => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]                                 => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]                                 => 6
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]                                 => 5
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]                                 => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]                                 => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]                                 => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]                                 => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]                                 => 6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]                                 => 5
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]                                 => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]                                 => 3
[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]                                 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                                 => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]                                 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]                                 => 5
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]                                 => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]                                 => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]                                 => 2
[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]                             => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                             => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]                             => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                             => 8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]                             => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]                             => 9
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]                             => 9
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]                             => 8
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]                             => 10
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]                             => 8
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]                             => 10
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]                             => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]                             => 8
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                             => 13
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]                             => 14
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]                             => 8
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                             => 14
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]                             => 8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                             => 14
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]                             => 13
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]                             => 13
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                             => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]                             => 12
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]                             => 14
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]                             => 14
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]                             => 12
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]                             => 9
[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]                             => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]                             => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                             => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]                             => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]                             => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]                             => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                             => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]                             => 7
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]                             => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]                             => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]                             => 7
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]                             => 7
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]                             => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                             => 7
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]                             => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]                             => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]                             => 7
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]                             => 9
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]                             => 8
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                             => 7
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]                             => 8
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]                             => 8
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]                             => 7
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]                             => 9
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                             => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]                             => 12
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]                             => 12
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                             => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                             => 7
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                             => 8
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]                             => 8
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                             => 7
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]                             => 9
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]                             => 7
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]                             => 7
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]                             => 7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]                             => 12
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]                             => 9
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]                             => 8
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                             => 7
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                             => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                             => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                             => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                             => 7
[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]                             => 6
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]                             => 10
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                             => 6
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]                             => 6
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]                             => 7
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]                             => 6
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]                             => 6
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]                             => 7
[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]                             => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]                             => 8
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]                             => 5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]                             => 6
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]                             => 6
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]                             => 5
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]                             => 4
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]                             => 4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]                             => 9
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]                             => 6
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]                             => 4
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]                             => 4
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]                             => 4
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]                             => 5
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]                             => 5
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]                             => 7
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]                             => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]                             => 8
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]                             => 4
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]                             => 3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]                             => 3
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]                             => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]                             => 7
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]                             => 4
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]                             => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]                             => 7
[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]                             => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]                             => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]                             => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]                             => 5
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]                             => 4
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]                             => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]                             => 2
[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]                             => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                             => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                             => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]                             => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]                             => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]                             => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]                             => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                             => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]                             => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]                             => 9
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]                             => 9
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]                             => 9
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]                             => 9
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                             => 9
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]                             => 9
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]                             => 10
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]                             => 9
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]                             => 9
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]                             => 10
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]                             => 10
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]                             => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]                             => 11
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                             => 10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                             => 9
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]                             => 11
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]                             => 10
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]                             => 11
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                             => 8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]                             => 11
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                             => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]                             => 10
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]                             => 12
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]                             => 9
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]                             => 12
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]                             => 9
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]                             => 14
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                             => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]                             => 9
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]                             => 11
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                             => 14
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                             => 14
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                             => 10
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]                             => 18
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                             => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                             => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]                             => 9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]                             => 10
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]                             => 14
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]                             => 18
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                             => 8
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                             => 14
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                             => 18
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]                             => 8
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]                             => 20
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]                             => 8
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]                             => 20
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]                             => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]                             => 18
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                             => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                             => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                             => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]                             => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]                             => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]                             => 8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                             => 9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]                             => 9
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]                             => 9
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]                             => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]                             => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                             => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]                             => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]                             => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]                             => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                             => 8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]                             => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]                             => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]                             => 8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                             => 8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]                             => 8
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]                             => 8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]                             => 8
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                             => 8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]                             => 10
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]                             => 10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                             => 9
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                             => 13
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]                             => 16
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]                             => 17
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]                             => 16
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                             => 9
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]                             => 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]                             => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]                             => 10
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                             => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]                             => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                             => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]                             => 9
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]                             => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]                             => 10
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]                             => 11
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]                             => 11
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]                             => 11
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]                             => 11
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]                             => 9
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]                             => 16
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]                             => 12
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]                             => 17
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]                             => 17
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]                             => 13
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]                             => 16
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]                             => 16
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]                             => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]                             => 10
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]                             => 10
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]                             => 10
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]                             => 10
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]                             => 14
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]                             => 14
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]                             => 13
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]                             => 12
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]                             => 12
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                             => 13
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]                             => 13
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]                             => 13
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]                             => 11
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]                             => 12
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]                             => 13
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]                             => 13
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]                             => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]                         => 9
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                         => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]                         => 9
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]                         => 9
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]                         => 10
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]                         => 10
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]                         => 9
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]                         => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]                         => 16
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                         => 16
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]                         => 9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]                         => 16
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]                         => 15
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                         => 15
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                         => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                         => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                         => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                         => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]                         => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]                         => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]                         => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]                         => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                         => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                         => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                         => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                         => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                         => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                         => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                         => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                         => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]                         => 11
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]                         => 10
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]                         => 13
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                         => 15
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]                         => 16
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                         => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                         => 9
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                         => 16
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                         => 9
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                         => 21
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                         => 9
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                         => 24
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]                         => 9
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]                         => 25
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]                         => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]                         => 24
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]                         => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]                         => 21
[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]                         => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                         => 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                         => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                         => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]                         => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]                         => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]                         => 9
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]                         => 5
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]                         => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]                         => 6
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                         => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                         => 8
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]                         => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]                         => 2
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]                         => 3
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]                         => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                         => 9
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                         => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]                         => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]                         => 8
[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]                         => 3
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]                         => 4
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                         => 5
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                         => 6
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]                         => 7
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                         => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]                         => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]                         => 10
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                         => 9
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                         => 9
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]                         => 9
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]                         => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]                         => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]                         => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]                         => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]                         => 8
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                         => 8
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]                         => 8
[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]                         => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]                         => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]                         => 5
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]                         => 4
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]                         => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                         => 8
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]                         => 8
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]                         => 8
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]                         => 16
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]                         => 16
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]                         => 16
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]                         => 14
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]                         => 14
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]                         => 14
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]                         => 14
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]                         => 15
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                         => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                         => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                         => 8
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                         => 8
[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]                         => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]                         => 9
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]                         => 9
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                         => 9
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]                         => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                         => 7
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                         => 9
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                         => 10
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                         => 11
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                         => 11
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                         => 11
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]                         => 11
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]                         => 13
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]                         => 13
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]                         => 12
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                         => 12
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                         => 12
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]                         => 13
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]                         => 12
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]                         => 12
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                         => 10
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                         => 11
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                         => 13
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                         => 13
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                         => 14
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]                         => 12
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]                         => 15
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                         => 10
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                         => 12
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]                         => 14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]                         => 13
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                         => 13
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]                         => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]                         => 10
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]                         => 12
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]                         => 12
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]                         => 13
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]                         => 12
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]                         => 12
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                         => 12
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                         => 13
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]                         => 13
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]                         => 11
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]                         => 11
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]                         => 11
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]                         => 11
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]                         => 10
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]                         => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                         => 9
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]                         => 3
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]                         => 8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]                         => 8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]                         => 9
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]                         => 9
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]                         => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]                     => 10
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]                     => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]                     => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                     => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                     => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                     => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                     => 9
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]                     => 6
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]                     => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                     => 10
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]                     => 2
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]                     => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]                     => 9
[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]                     => 9
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]                     => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                     => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                     => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                     => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                     => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                     => 9
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                     => 9
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                     => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                     => 9
[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]                     => 18
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]                     => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]                     => 18
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]                 => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                 => 11
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]                 => 11
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]                 => 12
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]                 => 13
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]                 => 13
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]                 => 13
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]                 => 13
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]                 => 15
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]                 => 15
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]                 => 14
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]                 => 14
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]                 => 14
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]                 => 15
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]                 => 14
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]                 => 14
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                 => 13
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                 => 14
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                 => 16
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                 => 16
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                 => 17
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]                 => 15
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]                 => 18
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]                 => 14
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]                 => 16
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]                 => 17
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]                 => 16
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]                 => 17
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]                 => 15
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]                 => 15
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]                 => 15
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]                 => 15
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]                 => 16
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]                 => 15
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]                 => 15
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                 => 16
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                 => 17
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]                 => 17
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]                 => 16
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]                 => 15
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]                 => 15
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]                 => 16
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]                 => 15
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]                 => 15
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                 => 12
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                 => 13
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                 => 14
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                 => 14
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                 => 14
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]                 => 15
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]                 => 17
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]                 => 17
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]                 => 17
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                 => 16
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                 => 16
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]                 => 18
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]                 => 17
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]                 => 18
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                 => 14
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                 => 15
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                 => 18
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                 => 18
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                 => 20
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                 => 12
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                 => 13
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                 => 15
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                 => 15
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                 => 16
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]                 => 16
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]                 => 20
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]                 => 15
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]                 => 18
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]                 => 15
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]                 => 18
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                 => 13
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                 => 15
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                 => 12
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                 => 14
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]                 => 18
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]                 => 17
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]                 => 18
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]                 => 16
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]                 => 16
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]                 => 17
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]                 => 17
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                 => 17
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                 => 15
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]                 => 14
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]                 => 14
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]                 => 14
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]                 => 13
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]                 => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]                 => 15
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]                 => 15
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]                 => 16
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]                 => 15
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]                 => 15
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]                 => 16
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]                 => 17
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]                 => 17
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]                 => 16
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]                 => 15
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]                 => 15
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]                 => 16
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]                 => 15
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]                 => 15
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]                 => 15
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]                 => 15
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]                 => 17
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]                 => 16
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]                 => 17
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                 => 16
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                 => 18
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                 => 14
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                 => 15
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]                 => 17
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]                 => 16
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]                 => 16
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]                 => 14
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]                 => 13
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]                 => 14
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]                 => 14
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]                 => 15
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]                 => 14
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]                 => 14
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]                 => 14
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]                 => 15
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]                 => 15
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]                 => 13
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]                 => 13
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]                 => 13
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]                 => 13
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]                 => 12
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]                 => 11
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]                 => 10
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]                 => 10
[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]             => 12
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]             => 12
[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]         => 13
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]         => 13
[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]     => 14
[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]     => 14
[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] => 15

-----------------------------------------------------------------------------
Created: Nov 10, 2016 at 11:59 by Christian Stump

-----------------------------------------------------------------------------
Last Updated: Apr 12, 2023 at 15:53 by Martin Rubey