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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St001137
-----------------------------------------------------------------------------
Collection: Dyck paths
-----------------------------------------------------------------------------
Description: Number of simple modules that are 3-regular in the corresponding Nakayama algebra.
-----------------------------------------------------------------------------
References: [1] Enomoto, H. Classifications of exact structures and Cohen-Macaulay-finite algebras [[arXiv:1705.02163]]
-----------------------------------------------------------------------------
Code:
# has 3-redular condition iff output is [0,0,0].
gap.eval('DeclareOperation("has3regularcondition", [IsList]);')
gap_code_3_regular = r"""
InstallMethod(has3regularcondition, "for a representation of a quiver", [IsList],0,function(LIST)
local A, M, RegA, g1, g2, g3;
A:=LIST[1];
M:=LIST[2];
RegA:=DirectSumOfQPAModules(IndecProjectiveModules(A));
g1:=ProjDimensionOfModule(M,30)-3;
g2:=Size(HomOverAlgebra(M,RegA))+Size(ExtOverAlgebra(M,RegA)[2])+Size(ExtOverAlgebra(NthSyzygy(M,1),RegA)[2]);
g3:=Size(ExtOverAlgebra(NthSyzygy(M,2),RegA)[2])-1;
return([g1,g2,g3]);
end);
"""
gap.eval(gap_code_3_regular)
gap.eval('DeclareOperation("sim3ausreg", [IsList]);')
gap_code_sim3ausreg = r"""
InstallMethod(sim3ausreg, "for a representation of a quiver", [IsList],0,function(LIST)
local A, simA, TT, WU, x;
A:=LIST[1];
simA:=SimpleModules(A);
TT:=[1..Size(simA)];
WU:=Filtered(TT,x->has3regularcondition([A,simA[x]])=[0,0,0]);
return(WU);
end);
"""
gap.eval(gap_code_sim3ausreg)
def kupisch(D):
"""
sage: [kupisch(D) for D in DyckWords(3)]
[[2, 2, 2, 1], [2, 3, 2, 1], [3, 2, 2, 1], [3, 3, 2, 1], [4, 3, 2, 1]]
sage: all(kupisch(D) == [a+2 for a in D.reverse().to_area_sequence()[::-1]] + [1] for D in DyckWords(5))
"""
H = D.heights()
return [1+H[i] for i, s in enumerate(D) if s == 0]+[1]
def statistic(D):
k = kupisch(D)
gap.eval("A := NakayamaAlgebra(" + str(k) + ", GF(3))")
return len(gap.sim3ausreg(["A"]).sage())
-----------------------------------------------------------------------------
Statistic values:
[1,0] => 0
[1,0,1,0] => 0
[1,1,0,0] => 0
[1,0,1,0,1,0] => 1
[1,0,1,1,0,0] => 0
[1,1,0,0,1,0] => 0
[1,1,0,1,0,0] => 0
[1,1,1,0,0,0] => 0
[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] => 0
[1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0] => 0
[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] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => 0
[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] => 0
[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] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => 0
[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] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => 1
[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] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => 0
[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] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => 2
[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] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[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] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[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] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[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] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[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] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[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] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 0
[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] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 0
[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] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[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] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[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] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[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] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[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] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[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] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[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] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[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] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[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] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[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] => 0
[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] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[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] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 0
[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] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1
[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] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[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] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 0
[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] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[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] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[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] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[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] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[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] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[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] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[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] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[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] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => 1
[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] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[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] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[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] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
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Created: Apr 09, 2018 at 13:13 by Rene Marczinzik
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Last Updated: May 10, 2018 at 10:22 by Martin Rubey