Hexadecimal (base-$16$) numbers are written using numeric digits $0$ through $9$ as well as the letters $A$ through $F$ to represent $10$ through $15$. Among the first $1000$ positive integers, there are $n$ whose hexadecimal representation contains only numeric digits. Find the sum of the digits of $n$.

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