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*                                                                           *
*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
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-----------------------------------------------------------------------------
Statistic identifier: St001135

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

-----------------------------------------------------------------------------
Description: The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path.

-----------------------------------------------------------------------------
References: [1]   Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. [[zbMATH:06820683]]

-----------------------------------------------------------------------------
Code:
gap('LoadPackage("QPA");')

def kupisch(D):
    H = D.heights()
    return [1+H[i] for i, s in enumerate(D) if s == 0] + [1]

def statistic(D):
    D = DyckWord(D)
    K = kupisch(D.reverse())
    A = gap.NakayamaAlgebra(K, gap.GF(3))
    S = gap.SimpleModules(A)
    return ZZ(gap.ProjDimensionOfModule(S[1], 100))


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

[1,0]                         => 1
[1,0,1,0]                     => 2
[1,1,0,0]                     => 1
[1,0,1,0,1,0]                 => 3
[1,0,1,1,0,0]                 => 1
[1,1,0,0,1,0]                 => 2
[1,1,0,1,0,0]                 => 2
[1,1,1,0,0,0]                 => 1
[1,0,1,0,1,0,1,0]             => 4
[1,0,1,0,1,1,0,0]             => 1
[1,0,1,1,0,0,1,0]             => 2
[1,0,1,1,0,1,0,0]             => 3
[1,0,1,1,1,0,0,0]             => 1
[1,1,0,0,1,0,1,0]             => 3
[1,1,0,0,1,1,0,0]             => 1
[1,1,0,1,0,0,1,0]             => 3
[1,1,0,1,0,1,0,0]             => 3
[1,1,0,1,1,0,0,0]             => 1
[1,1,1,0,0,0,1,0]             => 2
[1,1,1,0,0,1,0,0]             => 2
[1,1,1,0,1,0,0,0]             => 2
[1,1,1,1,0,0,0,0]             => 1
[1,0,1,0,1,0,1,0,1,0]         => 5
[1,0,1,0,1,0,1,1,0,0]         => 1
[1,0,1,0,1,1,0,0,1,0]         => 2
[1,0,1,0,1,1,0,1,0,0]         => 4
[1,0,1,0,1,1,1,0,0,0]         => 1
[1,0,1,1,0,0,1,0,1,0]         => 3
[1,0,1,1,0,0,1,1,0,0]         => 1
[1,0,1,1,0,1,0,0,1,0]         => 4
[1,0,1,1,0,1,0,1,0,0]         => 4
[1,0,1,1,0,1,1,0,0,0]         => 1
[1,0,1,1,1,0,0,0,1,0]         => 2
[1,0,1,1,1,0,0,1,0,0]         => 2
[1,0,1,1,1,0,1,0,0,0]         => 3
[1,0,1,1,1,1,0,0,0,0]         => 1
[1,1,0,0,1,0,1,0,1,0]         => 4
[1,1,0,0,1,0,1,1,0,0]         => 1
[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]         => 1
[1,1,0,1,0,0,1,0,1,0]         => 4
[1,1,0,1,0,0,1,1,0,0]         => 1
[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]         => 1
[1,1,0,1,1,0,0,0,1,0]         => 2
[1,1,0,1,1,0,0,1,0,0]         => 3
[1,1,0,1,1,0,1,0,0,0]         => 3
[1,1,0,1,1,1,0,0,0,0]         => 1
[1,1,1,0,0,0,1,0,1,0]         => 3
[1,1,1,0,0,0,1,1,0,0]         => 1
[1,1,1,0,0,1,0,0,1,0]         => 3
[1,1,1,0,0,1,0,1,0,0]         => 3
[1,1,1,0,0,1,1,0,0,0]         => 1
[1,1,1,0,1,0,0,0,1,0]         => 3
[1,1,1,0,1,0,0,1,0,0]         => 3
[1,1,1,0,1,0,1,0,0,0]         => 3
[1,1,1,0,1,1,0,0,0,0]         => 1
[1,1,1,1,0,0,0,0,1,0]         => 2
[1,1,1,1,0,0,0,1,0,0]         => 2
[1,1,1,1,0,0,1,0,0,0]         => 2
[1,1,1,1,0,1,0,0,0,0]         => 2
[1,1,1,1,1,0,0,0,0,0]         => 1
[1,0,1,0,1,0,1,0,1,0,1,0]     => 6
[1,0,1,0,1,0,1,0,1,1,0,0]     => 1
[1,0,1,0,1,0,1,1,0,0,1,0]     => 2
[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]     => 1
[1,0,1,0,1,1,0,0,1,0,1,0]     => 3
[1,0,1,0,1,1,0,0,1,1,0,0]     => 1
[1,0,1,0,1,1,0,1,0,0,1,0]     => 5
[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]     => 1
[1,0,1,0,1,1,1,0,0,0,1,0]     => 2
[1,0,1,0,1,1,1,0,0,1,0,0]     => 2
[1,0,1,0,1,1,1,0,1,0,0,0]     => 4
[1,0,1,0,1,1,1,1,0,0,0,0]     => 1
[1,0,1,1,0,0,1,0,1,0,1,0]     => 4
[1,0,1,1,0,0,1,0,1,1,0,0]     => 1
[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]     => 1
[1,0,1,1,0,1,0,0,1,0,1,0]     => 5
[1,0,1,1,0,1,0,0,1,1,0,0]     => 1
[1,0,1,1,0,1,0,1,0,0,1,0]     => 5
[1,0,1,1,0,1,0,1,0,1,0,0]     => 3
[1,0,1,1,0,1,0,1,1,0,0,0]     => 1
[1,0,1,1,0,1,1,0,0,0,1,0]     => 2
[1,0,1,1,0,1,1,0,0,1,0,0]     => 4
[1,0,1,1,0,1,1,0,1,0,0,0]     => 4
[1,0,1,1,0,1,1,1,0,0,0,0]     => 1
[1,0,1,1,1,0,0,0,1,0,1,0]     => 3
[1,0,1,1,1,0,0,0,1,1,0,0]     => 1
[1,0,1,1,1,0,0,1,0,0,1,0]     => 3
[1,0,1,1,1,0,0,1,0,1,0,0]     => 3
[1,0,1,1,1,0,0,1,1,0,0,0]     => 1
[1,0,1,1,1,0,1,0,0,0,1,0]     => 4
[1,0,1,1,1,0,1,0,0,1,0,0]     => 4
[1,0,1,1,1,0,1,0,1,0,0,0]     => 4
[1,0,1,1,1,0,1,1,0,0,0,0]     => 1
[1,0,1,1,1,1,0,0,0,0,1,0]     => 2
[1,0,1,1,1,1,0,0,0,1,0,0]     => 2
[1,0,1,1,1,1,0,0,1,0,0,0]     => 2
[1,0,1,1,1,1,0,1,0,0,0,0]     => 3
[1,0,1,1,1,1,1,0,0,0,0,0]     => 1
[1,1,0,0,1,0,1,0,1,0,1,0]     => 5
[1,1,0,0,1,0,1,0,1,1,0,0]     => 1
[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]     => 4
[1,1,0,0,1,0,1,1,1,0,0,0]     => 1
[1,1,0,0,1,1,0,0,1,0,1,0]     => 3
[1,1,0,0,1,1,0,0,1,1,0,0]     => 1
[1,1,0,0,1,1,0,1,0,0,1,0]     => 4
[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]     => 1
[1,1,0,0,1,1,1,0,0,0,1,0]     => 2
[1,1,0,0,1,1,1,0,0,1,0,0]     => 2
[1,1,0,0,1,1,1,0,1,0,0,0]     => 3
[1,1,0,0,1,1,1,1,0,0,0,0]     => 1
[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]     => 1
[1,1,0,1,0,0,1,1,0,0,1,0]     => 2
[1,1,0,1,0,0,1,1,0,1,0,0]     => 4
[1,1,0,1,0,0,1,1,1,0,0,0]     => 1
[1,1,0,1,0,1,0,0,1,0,1,0]     => 5
[1,1,0,1,0,1,0,0,1,1,0,0]     => 1
[1,1,0,1,0,1,0,1,0,0,1,0]     => 4
[1,1,0,1,0,1,0,1,0,1,0,0]     => 4
[1,1,0,1,0,1,0,1,1,0,0,0]     => 1
[1,1,0,1,0,1,1,0,0,0,1,0]     => 2
[1,1,0,1,0,1,1,0,0,1,0,0]     => 4
[1,1,0,1,0,1,1,0,1,0,0,0]     => 3
[1,1,0,1,0,1,1,1,0,0,0,0]     => 1
[1,1,0,1,1,0,0,0,1,0,1,0]     => 3
[1,1,0,1,1,0,0,0,1,1,0,0]     => 1
[1,1,0,1,1,0,0,1,0,0,1,0]     => 4
[1,1,0,1,1,0,0,1,0,1,0,0]     => 4
[1,1,0,1,1,0,0,1,1,0,0,0]     => 1
[1,1,0,1,1,0,1,0,0,0,1,0]     => 4
[1,1,0,1,1,0,1,0,0,1,0,0]     => 4
[1,1,0,1,1,0,1,0,1,0,0,0]     => 3
[1,1,0,1,1,0,1,1,0,0,0,0]     => 1
[1,1,0,1,1,1,0,0,0,0,1,0]     => 2
[1,1,0,1,1,1,0,0,0,1,0,0]     => 2
[1,1,0,1,1,1,0,0,1,0,0,0]     => 3
[1,1,0,1,1,1,0,1,0,0,0,0]     => 3
[1,1,0,1,1,1,1,0,0,0,0,0]     => 1
[1,1,1,0,0,0,1,0,1,0,1,0]     => 4
[1,1,1,0,0,0,1,0,1,1,0,0]     => 1
[1,1,1,0,0,0,1,1,0,0,1,0]     => 2
[1,1,1,0,0,0,1,1,0,1,0,0]     => 3
[1,1,1,0,0,0,1,1,1,0,0,0]     => 1
[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]     => 1
[1,1,1,0,0,1,0,1,0,0,1,0]     => 4
[1,1,1,0,0,1,0,1,0,1,0,0]     => 3
[1,1,1,0,0,1,0,1,1,0,0,0]     => 1
[1,1,1,0,0,1,1,0,0,0,1,0]     => 2
[1,1,1,0,0,1,1,0,0,1,0,0]     => 3
[1,1,1,0,0,1,1,0,1,0,0,0]     => 3
[1,1,1,0,0,1,1,1,0,0,0,0]     => 1
[1,1,1,0,1,0,0,0,1,0,1,0]     => 4
[1,1,1,0,1,0,0,0,1,1,0,0]     => 1
[1,1,1,0,1,0,0,1,0,0,1,0]     => 4
[1,1,1,0,1,0,0,1,0,1,0,0]     => 3
[1,1,1,0,1,0,0,1,1,0,0,0]     => 1
[1,1,1,0,1,0,1,0,0,0,1,0]     => 4
[1,1,1,0,1,0,1,0,0,1,0,0]     => 3
[1,1,1,0,1,0,1,0,1,0,0,0]     => 3
[1,1,1,0,1,0,1,1,0,0,0,0]     => 1
[1,1,1,0,1,1,0,0,0,0,1,0]     => 2
[1,1,1,0,1,1,0,0,0,1,0,0]     => 3
[1,1,1,0,1,1,0,0,1,0,0,0]     => 3
[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]     => 1
[1,1,1,1,0,0,0,0,1,0,1,0]     => 3
[1,1,1,1,0,0,0,0,1,1,0,0]     => 1
[1,1,1,1,0,0,0,1,0,0,1,0]     => 3
[1,1,1,1,0,0,0,1,0,1,0,0]     => 3
[1,1,1,1,0,0,0,1,1,0,0,0]     => 1
[1,1,1,1,0,0,1,0,0,0,1,0]     => 3
[1,1,1,1,0,0,1,0,0,1,0,0]     => 3
[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]     => 1
[1,1,1,1,0,1,0,0,0,0,1,0]     => 3
[1,1,1,1,0,1,0,0,0,1,0,0]     => 3
[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]     => 3
[1,1,1,1,0,1,1,0,0,0,0,0]     => 1
[1,1,1,1,1,0,0,0,0,0,1,0]     => 2
[1,1,1,1,1,0,0,0,0,1,0,0]     => 2
[1,1,1,1,1,0,0,0,1,0,0,0]     => 2
[1,1,1,1,1,0,0,1,0,0,0,0]     => 2
[1,1,1,1,1,0,1,0,0,0,0,0]     => 2
[1,1,1,1,1,1,0,0,0,0,0,0]     => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[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] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6
[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] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[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] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[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] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[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] => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[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] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[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] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[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] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[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] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[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] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[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] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5
[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] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[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] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[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] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[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] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 3
[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] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3
[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] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3
[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] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[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] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1

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Created: Apr 06, 2018 at 21:39 by Rene Marczinzik

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Last Updated: Dec 05, 2020 at 18:41 by Martin Rubey