Suppose that f : \mathbb{Z} \times \mathbb{Z} \rightarrow \mathbb{R} such that f(x, y) = f(3x + y, 2x + 2y) for all x,y \in \mathbb{Z}. Determine the maximal number of distinct values of f(x, y) for 1 \leq x, y \leq 100.
Suppose that f : \mathbb{Z} \times \mathbb{Z} \rightarrow \mathbb{R} such that f(x, y) = f(3x + y, 2x + 2y) for all x,y \in \mathbb{Z}. Determine the maximal number of distinct values of f(x, y) for 1 \leq x, y \leq 100.