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-----------------------------------------------------------------------------
Statistic identifier: St000012

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

-----------------------------------------------------------------------------
Description: The area of a Dyck path.

This is the number of complete squares in the integer lattice which are below the path and above the x-axis. The 'half-squares' directly above the axis do not contribute to this statistic.

1. Dyck paths are bijection with '''area sequences''' $(a_1,\ldots,a_n)$ such that $a_1 = 0, a_{k+1} \leq a_k + 1$.

2. The generating function $\mathbf{D}_n(q) = \sum_{D \in \mathfrak{D}_n} q^{\operatorname{area}(D)}$ satisfy the recurrence $$\mathbf{D}_{n+1}(q) = \sum q^k \mathbf{D}_k(q) \mathbf{D}_{n-k}(q).$$

3. The area is equidistributed with [[St000005]] and [[St000006]]. Pairs of these statistics play an important role in the theory of $q,t$-Catalan numbers.

-----------------------------------------------------------------------------
References: [1]   Haglund, J. The $q$,$t$-Catalan numbers and the space of diagonal harmonics [[MathSciNet:2371044]]

-----------------------------------------------------------------------------
Code:
def statistic(x):
    return x.area()

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

[1,0]                             => 0
[1,0,1,0]                         => 0
[1,1,0,0]                         => 1
[1,0,1,0,1,0]                     => 0
[1,0,1,1,0,0]                     => 1
[1,1,0,0,1,0]                     => 1
[1,1,0,1,0,0]                     => 2
[1,1,1,0,0,0]                     => 3
[1,0,1,0,1,0,1,0]                 => 0
[1,0,1,0,1,1,0,0]                 => 1
[1,0,1,1,0,0,1,0]                 => 1
[1,0,1,1,0,1,0,0]                 => 2
[1,0,1,1,1,0,0,0]                 => 3
[1,1,0,0,1,0,1,0]                 => 1
[1,1,0,0,1,1,0,0]                 => 2
[1,1,0,1,0,0,1,0]                 => 2
[1,1,0,1,0,1,0,0]                 => 3
[1,1,0,1,1,0,0,0]                 => 4
[1,1,1,0,0,0,1,0]                 => 3
[1,1,1,0,0,1,0,0]                 => 4
[1,1,1,0,1,0,0,0]                 => 5
[1,1,1,1,0,0,0,0]                 => 6
[1,0,1,0,1,0,1,0,1,0]             => 0
[1,0,1,0,1,0,1,1,0,0]             => 1
[1,0,1,0,1,1,0,0,1,0]             => 1
[1,0,1,0,1,1,0,1,0,0]             => 2
[1,0,1,0,1,1,1,0,0,0]             => 3
[1,0,1,1,0,0,1,0,1,0]             => 1
[1,0,1,1,0,0,1,1,0,0]             => 2
[1,0,1,1,0,1,0,0,1,0]             => 2
[1,0,1,1,0,1,0,1,0,0]             => 3
[1,0,1,1,0,1,1,0,0,0]             => 4
[1,0,1,1,1,0,0,0,1,0]             => 3
[1,0,1,1,1,0,0,1,0,0]             => 4
[1,0,1,1,1,0,1,0,0,0]             => 5
[1,0,1,1,1,1,0,0,0,0]             => 6
[1,1,0,0,1,0,1,0,1,0]             => 1
[1,1,0,0,1,0,1,1,0,0]             => 2
[1,1,0,0,1,1,0,0,1,0]             => 2
[1,1,0,0,1,1,0,1,0,0]             => 3
[1,1,0,0,1,1,1,0,0,0]             => 4
[1,1,0,1,0,0,1,0,1,0]             => 2
[1,1,0,1,0,0,1,1,0,0]             => 3
[1,1,0,1,0,1,0,0,1,0]             => 3
[1,1,0,1,0,1,0,1,0,0]             => 4
[1,1,0,1,0,1,1,0,0,0]             => 5
[1,1,0,1,1,0,0,0,1,0]             => 4
[1,1,0,1,1,0,0,1,0,0]             => 5
[1,1,0,1,1,0,1,0,0,0]             => 6
[1,1,0,1,1,1,0,0,0,0]             => 7
[1,1,1,0,0,0,1,0,1,0]             => 3
[1,1,1,0,0,0,1,1,0,0]             => 4
[1,1,1,0,0,1,0,0,1,0]             => 4
[1,1,1,0,0,1,0,1,0,0]             => 5
[1,1,1,0,0,1,1,0,0,0]             => 6
[1,1,1,0,1,0,0,0,1,0]             => 5
[1,1,1,0,1,0,0,1,0,0]             => 6
[1,1,1,0,1,0,1,0,0,0]             => 7
[1,1,1,0,1,1,0,0,0,0]             => 8
[1,1,1,1,0,0,0,0,1,0]             => 6
[1,1,1,1,0,0,0,1,0,0]             => 7
[1,1,1,1,0,0,1,0,0,0]             => 8
[1,1,1,1,0,1,0,0,0,0]             => 9
[1,1,1,1,1,0,0,0,0,0]             => 10
[1,0,1,0,1,0,1,0,1,0,1,0]         => 0
[1,0,1,0,1,0,1,0,1,1,0,0]         => 1
[1,0,1,0,1,0,1,1,0,0,1,0]         => 1
[1,0,1,0,1,0,1,1,0,1,0,0]         => 2
[1,0,1,0,1,0,1,1,1,0,0,0]         => 3
[1,0,1,0,1,1,0,0,1,0,1,0]         => 1
[1,0,1,0,1,1,0,0,1,1,0,0]         => 2
[1,0,1,0,1,1,0,1,0,0,1,0]         => 2
[1,0,1,0,1,1,0,1,0,1,0,0]         => 3
[1,0,1,0,1,1,0,1,1,0,0,0]         => 4
[1,0,1,0,1,1,1,0,0,0,1,0]         => 3
[1,0,1,0,1,1,1,0,0,1,0,0]         => 4
[1,0,1,0,1,1,1,0,1,0,0,0]         => 5
[1,0,1,0,1,1,1,1,0,0,0,0]         => 6
[1,0,1,1,0,0,1,0,1,0,1,0]         => 1
[1,0,1,1,0,0,1,0,1,1,0,0]         => 2
[1,0,1,1,0,0,1,1,0,0,1,0]         => 2
[1,0,1,1,0,0,1,1,0,1,0,0]         => 3
[1,0,1,1,0,0,1,1,1,0,0,0]         => 4
[1,0,1,1,0,1,0,0,1,0,1,0]         => 2
[1,0,1,1,0,1,0,0,1,1,0,0]         => 3
[1,0,1,1,0,1,0,1,0,0,1,0]         => 3
[1,0,1,1,0,1,0,1,0,1,0,0]         => 4
[1,0,1,1,0,1,0,1,1,0,0,0]         => 5
[1,0,1,1,0,1,1,0,0,0,1,0]         => 4
[1,0,1,1,0,1,1,0,0,1,0,0]         => 5
[1,0,1,1,0,1,1,0,1,0,0,0]         => 6
[1,0,1,1,0,1,1,1,0,0,0,0]         => 7
[1,0,1,1,1,0,0,0,1,0,1,0]         => 3
[1,0,1,1,1,0,0,0,1,1,0,0]         => 4
[1,0,1,1,1,0,0,1,0,0,1,0]         => 4
[1,0,1,1,1,0,0,1,0,1,0,0]         => 5
[1,0,1,1,1,0,0,1,1,0,0,0]         => 6
[1,0,1,1,1,0,1,0,0,0,1,0]         => 5
[1,0,1,1,1,0,1,0,0,1,0,0]         => 6
[1,0,1,1,1,0,1,0,1,0,0,0]         => 7
[1,0,1,1,1,0,1,1,0,0,0,0]         => 8
[1,0,1,1,1,1,0,0,0,0,1,0]         => 6
[1,0,1,1,1,1,0,0,0,1,0,0]         => 7
[1,0,1,1,1,1,0,0,1,0,0,0]         => 8
[1,0,1,1,1,1,0,1,0,0,0,0]         => 9
[1,0,1,1,1,1,1,0,0,0,0,0]         => 10
[1,1,0,0,1,0,1,0,1,0,1,0]         => 1
[1,1,0,0,1,0,1,0,1,1,0,0]         => 2
[1,1,0,0,1,0,1,1,0,0,1,0]         => 2
[1,1,0,0,1,0,1,1,0,1,0,0]         => 3
[1,1,0,0,1,0,1,1,1,0,0,0]         => 4
[1,1,0,0,1,1,0,0,1,0,1,0]         => 2
[1,1,0,0,1,1,0,0,1,1,0,0]         => 3
[1,1,0,0,1,1,0,1,0,0,1,0]         => 3
[1,1,0,0,1,1,0,1,0,1,0,0]         => 4
[1,1,0,0,1,1,0,1,1,0,0,0]         => 5
[1,1,0,0,1,1,1,0,0,0,1,0]         => 4
[1,1,0,0,1,1,1,0,0,1,0,0]         => 5
[1,1,0,0,1,1,1,0,1,0,0,0]         => 6
[1,1,0,0,1,1,1,1,0,0,0,0]         => 7
[1,1,0,1,0,0,1,0,1,0,1,0]         => 2
[1,1,0,1,0,0,1,0,1,1,0,0]         => 3
[1,1,0,1,0,0,1,1,0,0,1,0]         => 3
[1,1,0,1,0,0,1,1,0,1,0,0]         => 4
[1,1,0,1,0,0,1,1,1,0,0,0]         => 5
[1,1,0,1,0,1,0,0,1,0,1,0]         => 3
[1,1,0,1,0,1,0,0,1,1,0,0]         => 4
[1,1,0,1,0,1,0,1,0,0,1,0]         => 4
[1,1,0,1,0,1,0,1,0,1,0,0]         => 5
[1,1,0,1,0,1,0,1,1,0,0,0]         => 6
[1,1,0,1,0,1,1,0,0,0,1,0]         => 5
[1,1,0,1,0,1,1,0,0,1,0,0]         => 6
[1,1,0,1,0,1,1,0,1,0,0,0]         => 7
[1,1,0,1,0,1,1,1,0,0,0,0]         => 8
[1,1,0,1,1,0,0,0,1,0,1,0]         => 4
[1,1,0,1,1,0,0,0,1,1,0,0]         => 5
[1,1,0,1,1,0,0,1,0,0,1,0]         => 5
[1,1,0,1,1,0,0,1,0,1,0,0]         => 6
[1,1,0,1,1,0,0,1,1,0,0,0]         => 7
[1,1,0,1,1,0,1,0,0,0,1,0]         => 6
[1,1,0,1,1,0,1,0,0,1,0,0]         => 7
[1,1,0,1,1,0,1,0,1,0,0,0]         => 8
[1,1,0,1,1,0,1,1,0,0,0,0]         => 9
[1,1,0,1,1,1,0,0,0,0,1,0]         => 7
[1,1,0,1,1,1,0,0,0,1,0,0]         => 8
[1,1,0,1,1,1,0,0,1,0,0,0]         => 9
[1,1,0,1,1,1,0,1,0,0,0,0]         => 10
[1,1,0,1,1,1,1,0,0,0,0,0]         => 11
[1,1,1,0,0,0,1,0,1,0,1,0]         => 3
[1,1,1,0,0,0,1,0,1,1,0,0]         => 4
[1,1,1,0,0,0,1,1,0,0,1,0]         => 4
[1,1,1,0,0,0,1,1,0,1,0,0]         => 5
[1,1,1,0,0,0,1,1,1,0,0,0]         => 6
[1,1,1,0,0,1,0,0,1,0,1,0]         => 4
[1,1,1,0,0,1,0,0,1,1,0,0]         => 5
[1,1,1,0,0,1,0,1,0,0,1,0]         => 5
[1,1,1,0,0,1,0,1,0,1,0,0]         => 6
[1,1,1,0,0,1,0,1,1,0,0,0]         => 7
[1,1,1,0,0,1,1,0,0,0,1,0]         => 6
[1,1,1,0,0,1,1,0,0,1,0,0]         => 7
[1,1,1,0,0,1,1,0,1,0,0,0]         => 8
[1,1,1,0,0,1,1,1,0,0,0,0]         => 9
[1,1,1,0,1,0,0,0,1,0,1,0]         => 5
[1,1,1,0,1,0,0,0,1,1,0,0]         => 6
[1,1,1,0,1,0,0,1,0,0,1,0]         => 6
[1,1,1,0,1,0,0,1,0,1,0,0]         => 7
[1,1,1,0,1,0,0,1,1,0,0,0]         => 8
[1,1,1,0,1,0,1,0,0,0,1,0]         => 7
[1,1,1,0,1,0,1,0,0,1,0,0]         => 8
[1,1,1,0,1,0,1,0,1,0,0,0]         => 9
[1,1,1,0,1,0,1,1,0,0,0,0]         => 10
[1,1,1,0,1,1,0,0,0,0,1,0]         => 8
[1,1,1,0,1,1,0,0,0,1,0,0]         => 9
[1,1,1,0,1,1,0,0,1,0,0,0]         => 10
[1,1,1,0,1,1,0,1,0,0,0,0]         => 11
[1,1,1,0,1,1,1,0,0,0,0,0]         => 12
[1,1,1,1,0,0,0,0,1,0,1,0]         => 6
[1,1,1,1,0,0,0,0,1,1,0,0]         => 7
[1,1,1,1,0,0,0,1,0,0,1,0]         => 7
[1,1,1,1,0,0,0,1,0,1,0,0]         => 8
[1,1,1,1,0,0,0,1,1,0,0,0]         => 9
[1,1,1,1,0,0,1,0,0,0,1,0]         => 8
[1,1,1,1,0,0,1,0,0,1,0,0]         => 9
[1,1,1,1,0,0,1,0,1,0,0,0]         => 10
[1,1,1,1,0,0,1,1,0,0,0,0]         => 11
[1,1,1,1,0,1,0,0,0,0,1,0]         => 9
[1,1,1,1,0,1,0,0,0,1,0,0]         => 10
[1,1,1,1,0,1,0,0,1,0,0,0]         => 11
[1,1,1,1,0,1,0,1,0,0,0,0]         => 12
[1,1,1,1,0,1,1,0,0,0,0,0]         => 13
[1,1,1,1,1,0,0,0,0,0,1,0]         => 10
[1,1,1,1,1,0,0,0,0,1,0,0]         => 11
[1,1,1,1,1,0,0,0,1,0,0,0]         => 12
[1,1,1,1,1,0,0,1,0,0,0,0]         => 13
[1,1,1,1,1,0,1,0,0,0,0,0]         => 14
[1,1,1,1,1,1,0,0,0,0,0,0]         => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]     => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]     => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]     => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]     => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]     => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]     => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]     => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]     => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]     => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]     => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]     => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]     => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]     => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]     => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]     => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]     => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]     => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]     => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]     => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]     => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]     => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]     => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]     => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]     => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]     => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]     => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]     => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]     => 7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]     => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]     => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]     => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]     => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]     => 6
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]     => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]     => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]     => 7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]     => 8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]     => 6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]     => 7
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]     => 8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]     => 9
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]     => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]     => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]     => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]     => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]     => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]     => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]     => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]     => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]     => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]     => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]     => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]     => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]     => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]     => 6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]     => 7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]     => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]     => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]     => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]     => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]     => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]     => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]     => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]     => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]     => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]     => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]     => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]     => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]     => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]     => 8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]     => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]     => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]     => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]     => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]     => 7
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]     => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]     => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]     => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]     => 9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]     => 7
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]     => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]     => 9
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]     => 10
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]     => 11
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]     => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]     => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]     => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]     => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]     => 6
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]     => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]     => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]     => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]     => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]     => 7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]     => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]     => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]     => 8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]     => 9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]     => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]     => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]     => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]     => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]     => 8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]     => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]     => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]     => 9
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]     => 10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]     => 8
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]     => 9
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]     => 10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]     => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]     => 12
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]     => 6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]     => 7
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]     => 7
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]     => 8
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]     => 9
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]     => 8
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]     => 9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]     => 10
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]     => 11
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]     => 9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]     => 10
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]     => 11
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]     => 12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]     => 13
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]     => 10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]     => 11
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]     => 12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]     => 13
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]     => 14
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]     => 15
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]     => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]     => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]     => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]     => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]     => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]     => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]     => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]     => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]     => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]     => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]     => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]     => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]     => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]     => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]     => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]     => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]     => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]     => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]     => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]     => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]     => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]     => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]     => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]     => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]     => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]     => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]     => 7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]     => 8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]     => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]     => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]     => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]     => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]     => 7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]     => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]     => 7
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]     => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]     => 9
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]     => 7
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]     => 8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]     => 9
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]     => 10
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]     => 11
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]     => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]     => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]     => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]     => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]     => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]     => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]     => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]     => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]     => 5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]     => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]     => 5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]     => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]     => 7
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]     => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]     => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]     => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]     => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]     => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]     => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]     => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]     => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]     => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]     => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]     => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]     => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]     => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]     => 8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]     => 9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]     => 5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]     => 6
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]     => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]     => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]     => 8
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]     => 7
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]     => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]     => 9
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]     => 10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]     => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]     => 9
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]     => 10
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]     => 11
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]     => 12
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]     => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]     => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]     => 5
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]     => 6
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]     => 7
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]     => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]     => 6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]     => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]     => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]     => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]     => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]     => 8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]     => 9
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]     => 10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]     => 6
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]     => 7
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]     => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]     => 8
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]     => 9
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]     => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]     => 9
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]     => 10
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]     => 11
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]     => 9
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]     => 10
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]     => 11
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]     => 12
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]     => 13
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]     => 7
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]     => 8
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]     => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]     => 9
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]     => 10
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]     => 9
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]     => 10
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]     => 11
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]     => 12
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]     => 10
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]     => 11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]     => 12
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]     => 13
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]     => 14
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]     => 11
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]     => 12
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]     => 13
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]     => 14
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]     => 15
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]     => 16
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]     => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]     => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]     => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]     => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]     => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]     => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]     => 5
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]     => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]     => 6
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]     => 7
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]     => 6
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]     => 7
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]     => 8
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]     => 9
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]     => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]     => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]     => 5
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]     => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]     => 7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]     => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]     => 6
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]     => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]     => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]     => 8
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]     => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]     => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]     => 9
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]     => 10
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]     => 6
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]     => 7
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]     => 7
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]     => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]     => 9
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]     => 8
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]     => 9
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]     => 10
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]     => 11
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]     => 9
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]     => 10
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]     => 11
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]     => 12
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]     => 13
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]     => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]     => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]     => 6
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]     => 7
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]     => 8
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]     => 6
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]     => 7
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]     => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]     => 8
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]     => 9
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]     => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]     => 9
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]     => 10
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]     => 11
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]     => 7
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]     => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]     => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]     => 9
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]     => 10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]     => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]     => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]     => 11
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]     => 12
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]     => 10
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]     => 11
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]     => 12
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]     => 13
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]     => 14
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]     => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]     => 9
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]     => 9
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]     => 10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]     => 11
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]     => 10
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]     => 11
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]     => 12
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]     => 13
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]     => 11
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]     => 12
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]     => 13
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]     => 14
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]     => 15
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]     => 12
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]     => 13
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]     => 14
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]     => 15
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]     => 16
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]     => 17
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]     => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]     => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]     => 7
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]     => 8
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]     => 9
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]     => 7
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]     => 8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]     => 8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]     => 9
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]     => 10
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]     => 9
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]     => 10
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]     => 11
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]     => 12
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]     => 8
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]     => 9
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]     => 9
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]     => 10
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]     => 11
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]     => 10
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]     => 11
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]     => 12
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]     => 13
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]     => 11
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]     => 12
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]     => 13
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]     => 14
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]     => 15
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]     => 9
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]     => 10
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]     => 10
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]     => 11
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]     => 12
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]     => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]     => 12
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]     => 13
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]     => 14
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]     => 12
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]     => 13
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]     => 14
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]     => 15
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]     => 16
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]     => 13
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]     => 14
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]     => 15
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]     => 16
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]     => 17
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]     => 18
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]     => 10
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]     => 11
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]     => 11
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]     => 12
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]     => 13
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]     => 12
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]     => 13
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]     => 14
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]     => 15
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]     => 13
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]     => 14
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]     => 15
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]     => 16
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]     => 17
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]     => 14
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]     => 15
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]     => 16
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]     => 17
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]     => 18
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]     => 19
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]     => 15
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]     => 16
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]     => 17
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]     => 18
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]     => 19
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]     => 20
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]     => 21
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 8
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 8
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 9
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 10
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 7
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 10
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 11
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 12
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 8
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 9
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 13
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 14
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 14
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 15
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 16
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 9
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 8
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 9
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 10
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 13
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 13
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 14
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 8
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 9
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 10
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 13
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 14
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 15
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 12
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 13
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 14
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 15
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 16
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 17
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 7
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 8
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 10
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 8
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 9
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 10
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 11
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 14
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 15
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 9
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 10
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 14
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 13
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 14
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 16
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 15
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 16
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 17
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 18
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 10
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 15
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 15
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 17
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 15
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 16
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 17
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 18
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 19
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 16
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 17
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 18
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 19
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 20
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 21
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 8
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 8
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 9
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 11
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 10
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 13
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 14
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 14
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 15
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 16
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8

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Created: Sep 27, 2011 at 19:29 by Chris Berg

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Last Updated: Jun 17, 2019 at 17:03 by Christian Stump