+199 The number 12 can be broken up to \(x^2*y^2\), since the number of factors is \((2+1)(2+1)=3\cdot3=9.\) The three numbers do not work here since there are no possible outcomes.
Thus, we can have: \(2^2*3^2=36.\)
\(2^2*5^2=100.\)
\(2^2*7^2=196.\)
I do not think any more possible outcomes are there, and you can still check my work.
Thus, the answer is \(36+100+196=\boxed{332}.\)
