Making life hard

Sea f:\mathcal{P}(\mathbb{Z}^2) \to \mathcal{P}(\mathbb{Z}^2) la función definida por

\displaystyle \left\lfloor\frac{\left|\{y\in S | d_{\infty}(y, x) = 1\}\right|}{2}\right\rfloor = 1 \wedge x \in S \rightarrow x \in f(S)
\displaystyle \left|\{y\in S | d_{\infty}(y, x) = 1\}\right| = 3 \wedge x \notin S \rightarrow x \in f(S)

de modo que |f(S)| tome el mínimo valor posible.

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