Suppose that $f : Z\times Z \to R$, satisfies the equation $f(x, y) = f(3x+y, 2x+ 2y)$ for all $x, y \in Z$. Determine the maximal number of distinct values of $f(x, y)$ for $1 \le x, y \le  100$.

Let's think step by step and output the final answer within \boxed{}.
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