Consider all the positive integers $N$ with the property that all of the divisors of $N$ can be written as $p-2$ for some prime number $p$. Then, there exists an integer $m$ such that $m$ is the maximum possible number of divisors of all numbers $N$ with such property. Find the sum of all possible values of $N$ such that $N$ has $m$ divisors.

Let's think step by step and output the final answer within \boxed{}.
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