Let $O$ be the set of odd numbers between 0 and 100. Let $T$ be the set of subsets of $O$ of size 25. For any finite subset of integers $S$, let $P(S)$ be the product of the elements of $S$. Define $n = \sum_{S \in T} P(S)$. If you divide $n$ by 17, what is the remainder?

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