Let $$S$$ be the set of points whose coordinates $$x,$$ $$y,$$ and $$z$$ are integers that satisfy $$0\le x\le2,$$ $$0\le y\le3,$$ and $$0\le z\le4.$$ Two distinct points are randomly chosen from $$S.$$ The probability that the midpoint of the segment they determine also belongs to $$S$$ is $$m/n,$$ where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m + n.$$

(第十九届AIME1 2001 第10题)