Ana is investigating a function $f(n)$ defined for all positive integers $n$. She knows that $f(ab) = f(a)\cdot f(b)$ for all relatively prime positive integers $a$ and $b$, and that $f(p+q) = f(p)+f(q)$ for all primes $p$ and $q$. Given these facts, help her find the value of $f(2012)$.