Howdy Integers!

\[\large{n = 10^{m-1}a_m + 10^{m-2}a_{m-1} + \ldots + a_1}\]

A positive integer \(n\) as described above can be written in the decimal notation as \(a_m a_{m-1} \dotsm a_1 \), where \(a_m, a_{m-1}, \ldots, a_1 \in \{0, 1, 2, \ldots, 9 \} \) and \(a_m \neq 0\).

Find the SUM of all \(n\) such that:

\[\large{n = (a_m+1) \times (a_{m-1}+1) \times \dotsm \times (a_1 +1)}\]

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