Each of the distinct letters in the following addition problem represents a different digit.  Find the number represented by the word MEET.


$ \begin{array}{cccccc}P&U&R&P&L&E\\&C&O&M&E&T\\&&M&E&E&T\\ \hline Z&Z&Z&Z&Z&Z\end{array} $

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