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)