Compute the only element of the set \[ \{1, 2, 3, 4, \ldots\} \cap \left\{\frac{404}{r^2-4} \;\bigg| \; r \in \mathbb{Q} \setminus \{-2, 2\}\right\}. \]

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