Determine all possible value(s) of a non-leading zero, 5-digit positive integer N that satisfy each of these given conditions:
(i) Product of the digits of N is equal to the sum of its digits.
(ii) N is divisible by the sum of its digits.
(iii) N does NOT contain the digit 3.

Added for completeness:
What is the total number of values of N if we disregard condition (iii)?