In triangle $$ABC$$, point $$D$$ is on $$\overline{BC}$$ with $$CD=2$$ and $$DB=5$$, point $$E$$ is on $$\overline{AC}$$ with $$CE=1$$ and $$EA=3$$, $$AB=8$$, and $$\overline{AD}$$ and $$\overline{BE}$$ intersect at $$P$$. Points $$Q$$ and $$R$$ lie on $$\overline{AB}$$ so that $$\overline{PQ}$$ is parallel to $$\overline{CA}$$ and $$\overline{PR}$$ is parallel to $$\overline{CB}$$. It is given that the ratio of the area of triangle $$PQR$$ to the area of triangle $$ABC$$ is $$m/n$$, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m+n$$.

(第二十届AIME2 2002 第13题)