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:

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