For $$n\in\mathbb{N}$$, let $$P(n)$$ denote the product of the digits in $$n$$ and $$S(n)$$ denote the sum of the digits in $$n$$. Consider the set $$A=\{n\in\mathbb{N}:P(n)\text{ is non-zero, square free and }S(n)\text{ is a proper divisor of }P(n)\}$$. Find the maximum possible number of digits of the numbers in $$A$$.