An $$m\times n\times p$$ rectangular box has half the volume of an $$(m + 2)\times(n + 2)\times(p + 2)$$ rectangular box, where $$m, n,$$ and $$p$$ are integers, and $$m\le n\le p.$$ What is the largest possible value of $$p$$?

(第十六届AIME1998 第14题)