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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St001643
-----------------------------------------------------------------------------
Collection: Dyck paths
-----------------------------------------------------------------------------
Description: The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path.
-----------------------------------------------------------------------------
References: [1] Artenstein, D., González, A., Mata, G. Nearly Frobenius dimension on Frobenius algebras [[arXiv:2011.09790]]
-----------------------------------------------------------------------------
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)
A = gap.NakayamaAlgebra(K, gap.GF(3))
injA = gap.IndecInjectiveModules(A)
projA = gap.IndecProjectiveModules(A)
CoRegA = gap.DirectSumOfQPAModules(injA)
RegA = gap.DirectSumOfQPAModules(projA)
return gap.Size(gap.HomOverAlgebra(CoRegA, RegA))
-----------------------------------------------------------------------------
Statistic values:
[1,0] => 1
[1,0,1,0] => 3
[1,1,0,0] => 1
[1,0,1,0,1,0] => 5
[1,0,1,1,0,0] => 4
[1,1,0,0,1,0] => 4
[1,1,0,1,0,0] => 3
[1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,0] => 4
[1,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,0,1,1,0,0,1,0] => 9
[1,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,0,0] => 7
[1,0,1,1,0,0,1,0,1,0] => 9
[1,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,0,1,0,0,1,0] => 9
[1,0,1,1,0,1,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,0] => 9
[1,0,1,1,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,0] => 7
[1,1,0,0,1,1,0,0,1,0] => 9
[1,1,0,0,1,1,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,1,0,0,0] => 8
[1,1,0,1,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,1,1,0,0,0,0] => 5
[1,1,1,0,0,0,1,0,1,0] => 7
[1,1,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,0,1,0,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,0] => 7
[1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => 11
[1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0] => 11
[1,0,1,0,1,0,1,1,0,1,0,0] => 10
[1,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,0,1,0,1,1,0,0,1,0,1,0] => 11
[1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,0,1,1,0,1,0,0,1,0] => 11
[1,0,1,0,1,1,0,1,0,1,0,0] => 11
[1,0,1,0,1,1,0,1,1,0,0,0] => 9
[1,0,1,0,1,1,1,0,0,0,1,0] => 11
[1,0,1,0,1,1,1,0,0,1,0,0] => 10
[1,0,1,0,1,1,1,0,1,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,0] => 11
[1,0,1,1,0,0,1,0,1,1,0,0] => 10
[1,0,1,1,0,0,1,1,0,0,1,0] => 12
[1,0,1,1,0,0,1,1,0,1,0,0] => 11
[1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,1,0,1,0,0,1,0,1,0] => 11
[1,0,1,1,0,1,0,0,1,1,0,0] => 11
[1,0,1,1,0,1,0,1,0,0,1,0] => 12
[1,0,1,1,0,1,0,1,0,1,0,0] => 12
[1,0,1,1,0,1,0,1,1,0,0,0] => 11
[1,0,1,1,0,1,1,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,0,0,1,0,0] => 10
[1,0,1,1,0,1,1,0,1,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,1,1,0,0,0,1,0,1,0] => 11
[1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,0,0,1,0,0,1,0] => 11
[1,0,1,1,1,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,0,0,1,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,0,0,1,0] => 11
[1,0,1,1,1,0,1,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,0,1,0,0,0] => 10
[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] => 11
[1,0,1,1,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,1,0,0,0,0] => 8
[1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,0,1,1,0,0,1,0] => 10
[1,1,0,0,1,0,1,1,0,1,0,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,0] => 8
[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] => 11
[1,1,0,0,1,1,0,1,0,0,1,0] => 11
[1,1,0,0,1,1,0,1,0,1,0,0] => 11
[1,1,0,0,1,1,0,1,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,0,0,1,1,1,0,0,1,0,0] => 11
[1,1,0,0,1,1,1,0,1,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,0,1,0,1,0,1,0] => 10
[1,1,0,1,0,0,1,0,1,1,0,0] => 9
[1,1,0,1,0,0,1,1,0,0,1,0] => 11
[1,1,0,1,0,0,1,1,0,1,0,0] => 10
[1,1,0,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,0,1,0,1,0] => 11
[1,1,0,1,0,1,0,0,1,1,0,0] => 11
[1,1,0,1,0,1,0,1,0,0,1,0] => 12
[1,1,0,1,0,1,0,1,0,1,0,0] => 12
[1,1,0,1,0,1,0,1,1,0,0,0] => 11
[1,1,0,1,0,1,1,0,0,0,1,0] => 12
[1,1,0,1,0,1,1,0,0,1,0,0] => 11
[1,1,0,1,0,1,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,1,1,0,0,0,0] => 10
[1,1,0,1,1,0,0,0,1,0,1,0] => 10
[1,1,0,1,1,0,0,0,1,1,0,0] => 11
[1,1,0,1,1,0,0,1,0,0,1,0] => 10
[1,1,0,1,1,0,0,1,0,1,0,0] => 11
[1,1,0,1,1,0,0,1,1,0,0,0] => 9
[1,1,0,1,1,0,1,0,0,0,1,0] => 11
[1,1,0,1,1,0,1,0,0,1,0,0] => 11
[1,1,0,1,1,0,1,0,1,0,0,0] => 10
[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] => 10
[1,1,0,1,1,1,0,0,0,1,0,0] => 9
[1,1,0,1,1,1,0,0,1,0,0,0] => 8
[1,1,0,1,1,1,0,1,0,0,0,0] => 8
[1,1,0,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0] => 9
[1,1,1,0,0,0,1,0,1,1,0,0] => 8
[1,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,1,1,0,0,0,1,1,0,1,0,0] => 10
[1,1,1,0,0,0,1,1,1,0,0,0] => 11
[1,1,1,0,0,1,0,0,1,0,1,0] => 9
[1,1,1,0,0,1,0,0,1,1,0,0] => 9
[1,1,1,0,0,1,0,1,0,0,1,0] => 11
[1,1,1,0,0,1,0,1,0,1,0,0] => 11
[1,1,1,0,0,1,0,1,1,0,0,0] => 11
[1,1,1,0,0,1,1,0,0,0,1,0] => 10
[1,1,1,0,0,1,1,0,0,1,0,0] => 9
[1,1,1,0,0,1,1,0,1,0,0,0] => 10
[1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,1,1,0,1,0,0,0,1,0,1,0] => 9
[1,1,1,0,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,1,0,0,1,0,0,1,0] => 10
[1,1,1,0,1,0,0,1,0,1,0,0] => 11
[1,1,1,0,1,0,0,1,1,0,0,0] => 10
[1,1,1,0,1,0,1,0,0,0,1,0] => 10
[1,1,1,0,1,0,1,0,0,1,0,0] => 10
[1,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,1,0,1,0,1,1,0,0,0,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,1,0,1,1,0,0,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,1,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,0,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,0] => 10
[1,1,1,1,0,0,0,1,1,0,0,0] => 8
[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] => 8
[1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,0] => 7
[1,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 12
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 13
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 12
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 13
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 13
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 13
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 11
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 13
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 12
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 14
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 13
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 13
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 13
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 14
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 14
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 13
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 13
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 12
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 13
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 14
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 13
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 13
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 13
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 12
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 13
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 12
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 12
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 14
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 15
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 13
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 13
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 13
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 14
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 14
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 15
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 14
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 13
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 13
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 9
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 13
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 15
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 13
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 13
[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] => 9
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 13
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 15
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 13
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 13
[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] => 13
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 11
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 11
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 12
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 11
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 12
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 11
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 12
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 12
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 12
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 12
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 10
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 13
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 13
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 14
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 14
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 12
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 14
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 13
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 13
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 11
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 15
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 14
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 13
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 12
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 12
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 11
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 11
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 13
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 12
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 13
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 14
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 14
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 15
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 15
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 14
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 15
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 14
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 13
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 14
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 15
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 13
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 15
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 14
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 13
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 13
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 12
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 14
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 14
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 15
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 12
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 14
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 12
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 14
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 12
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 9
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 9
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 11
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 10
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 10
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 15
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 14
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 11
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 10
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 11
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 13
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 14
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 14
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 14
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 13
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 13
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 13
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 13
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 11
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 12
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 14
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 13
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 12
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 13
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 14
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 13
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 14
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 13
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 13
[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] => 12
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 10
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 13
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 10
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 9
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 14
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 10
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 12
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 11
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 12
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 12
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 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] => 10
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 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
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 11
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 9
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 9
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 12
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 9
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 9
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 9
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 10
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 9
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 9
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 14
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 14
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 15
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 14
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 14
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 14
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 14
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 14
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 16
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 15
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 15
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 16
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 15
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 15
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 15
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 15
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 15
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 12
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 11
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 14
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 15
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 14
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 14
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 17
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 15
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 15
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 15
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 15
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 18
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 18
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 16
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 15
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 16
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 15
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 15
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 15
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 17
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 10
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 15
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 18
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 11
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 10
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 14
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 13
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 14
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 13
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 12
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 14
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 14
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 15
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 16
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 15
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 15
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 17
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 16
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 17
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 15
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 19
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 15
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 18
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 17
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 16
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 15
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 14
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 13
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 13
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 16
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 15
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 17
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 17
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 18
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 18
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 17
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 17
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 17
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 16
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 18
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 17
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 16
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 18
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 14
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 17
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 17
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 16
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 17
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 10
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 10
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 13
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 12
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 12
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 19
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 17
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 17
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 16
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 15
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 15
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 16
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 17
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 18
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 14
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 17
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 16
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 17
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 18
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 18
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 18
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 17
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 15
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 16
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 14
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 15
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 16
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 13
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 12
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 13
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 11
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 10
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 10
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 15
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 16
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 18
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 17
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 15
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 15
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 14
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 13
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 12
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 15
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 12
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 12
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 11
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 10
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 10
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 8
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 12
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 13
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 14
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 11
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 13
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 12
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 12
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 14
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 12
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 12
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 10
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 11
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 10
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 9
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 8
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 14
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 12
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 10
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 11
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 9
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 8
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 7
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 6
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 5
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 11
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 12
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 13
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 13
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 16
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 16
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 17
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 16
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 16
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 15
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 17
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 17
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 13
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 18
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 18
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 19
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 18
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 18
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 12
-----------------------------------------------------------------------------
Created: Nov 20, 2020 at 09:14 by Rene Marczinzik
-----------------------------------------------------------------------------
Last Updated: Nov 20, 2020 at 12:53 by Martin Rubey