\[\large{\begin{array} &&&&F&A&T&H&E&R \\ &+&&M&O&T&H&E&R \\ \hline &&&A&L&F&R&E&D \end{array}}\]

Every letter in the above cryptarithm represents a distinct single-digit **positive** integer except for \(L \) which represents 0. Compute the 6-digit integer \(\overline{ALFRED}\).

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