Each of the small letters in bold represents a different nonzero base n digit from 1 to n-1 to satisfy this cryptarithmetic equation.

a.b + c.d = (a.b)*(c.d)

Determine all possible positive integer values of n ≤ 36 such that:

(I) The above equation has at least two valid solutions.

(II) a+b+c+d is a perfect square.

Notes:

(A) Solve parts (I) and (II) separately.

(B) Adjacent numerals are multi-digit base n numbers, and not the product. For example, if n = 36, a=1, b=2, c=3 and d=4, then a.b represents the base-36 number 1.2 and, c.d represents the base 36 number 3.4.