Define $H_n = 1+\frac{1}{2}+\cdots+\frac{1}{n}$. Let the sum of all $H_n$ that are terminating in base 10 be $S$. If $S = \frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers, find $100m+n$.

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