Simpsons Cryptogram

Logic Level 4

\[ \large{\begin{array}{ccccccc} && & & M& E & M&O\\ +&& & & F& R & O&M\\ \hline & & & H & O& M & E&R\\ \hline \end{array}} \]

For the above cryptogram, each letter represent a distinct non-negative single digit integer, find the value of the 5-digit integer, \(\overline{HOMER} \).

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