**Given an integer, n, find the smallest integer m such that is divisible by n (i.e.n, is a factor of m ) and satisfies the following properties:**
1. **m** must not contain zeroes in its decimal representation.
2. The sum of **m's** digits must be greater than or equal to the product of **m's** digits.
Given **n**, find the number of digits in **m's** decimal representation.
*Note: n is not divisible by 10.*