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\documentclass{standalone}
\usepackage{tikz}
\usepackage{dimer}
\begin{document}
\begin{tikzpicture}
\fill[color=gray](1,0.5)--++(1,0)--++(0.5,0.5)--++(-0.5,0.5)--++(-1,0)--++(-0.5,-0.5)--cycle;
\grid{3}{2}{[color=lightgray](0,0)}
\draw[color=black, line width=5pt](1,0.5)--++(1,0)--++(0.5,0.5)--++(-0.5,0.5)--++(-1,0)--++(-0.5,-0.5)--cycle;
\end{tikzpicture}
\end{document}
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