We call a positive integer a "good number", if the product of all its divisors equals its cube.

For example, 12 is a good number, because the divisors of 12 are 1, 2, 3, 4, 6, 12, and 1*2*3*4*6*12=1728=12^3.

If n is a good number, what is the minimum number of divisors that n^2 has?