If distinct digits $D, E, L, M, Q$ (between $0$ and $9$ inclusive) satisfy the following equation:
\[
\begin{array}{c@{\,}c@{\,}c@{\,}c}
  &   & E & L \\
+ & M & E & M \\\hline
  & Q & E & D \\
\end{array}
\]
What is the maximum possible value of the three-digit integer $QED$?

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