Consider the set of points that are inside or within one unit of a rectangular parallelepiped (box) that measures 3 by 4 by 5 units. Given that the volume of this set is $$(m + n \pi)/p,$$ where $$m, n,$$ and $$p$$ are positive integers, and $$n$$ and $$p$$ are relatively prime, find $$m + n + p.$$

(第二十一届AIME1 2003 第5题)