2001 AIME I Problem 10

Let \mathcal{S} be the set of points whose coordinates x, y, and z are integers that satisfy 0 \leq x \leq 2,0 \leq y \leq 3, and 0 \leq z \leq 4. Two distinct points are randomly chosen from \mathcal{S}. The probability that the midpoint of the segment they determine also belongs to \mathcal{S} is m / n, where m and n are relatively prime positive integers. Find m+n.