Impossible Cryptarithm

\[ \begin{array}{ccccc} & A & B & C & D\\ \times & & & & E\\ \hline & F & G & H & I \end{array} \]

Given that \(A, B, C, D, E, F, G, H, I\) are distinct non-zero digits, find \(A+E+H+I\).

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