SMO 2012 Senior Round 1 Question 18

Let $f(x)=(x-a_1)(x-a_2)(x-a_3)(x-a_4)(x-a_5)$, where $a_1,\ldots,a_5$ are distinct integers. Given $f(104)=2012$, evaluate $a_1+a_2+a_3+a_4+a_5$.