AMC 12 2000 Problem 1

In the year $2001$, the United States will host the International Mathematical Olympiad. Let $I,M,$ and $O$ be distinct positive integers such that the product $I \cdot M \cdot O = 2001$. What is the largest possible value of the sum $I + M + O$?

\textbf{(A)}\ 23 \textbf{(B)}\ 55 \textbf{(C)}\ 99 \textbf{(D)}\ 111 \textbf{(E)}\ 671