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\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\hfil\begin{tikzpicture}
\foreach\i in {0,...,5}{
\draw(0,\i)--++(5,0);
\draw(\i,0)--++(0,5);
}
\foreach\i in {0,...,5}{
\foreach\j in {0,...,5}{
\fill[color=red](\i,\j)circle(0.1);
\draw(\i,\j)circle(0.1);
}
}
\foreach\i in {0,...,4}{
\foreach\j in {0,...,5}{
\fill[color=blue](\i+0.5,\j)circle(0.1);
\draw(\i+0.5,\j)circle(0.1);
}
}
\foreach\i in {0,...,5}{
\foreach\j in {0,...,4}{
\fill[color=blue](\i,\j+0.5)circle(0.1);
\draw(\i,\j+0.5)circle(0.1);
}
}
\end{tikzpicture}
\end{document}
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