In triangle $$ABC$$, $$AB=13$$, $$BC=15$$ and $$CA=17$$. Point $$D$$ is on $$\overline{AB}$$, $$E$$ is on $$\overline{BC}$$, and $$F$$ is on $$\overline{CA}$$. Let $$AD=p\cdot AB$$, $$BE=q\cdot BC$$, and $$CF=r\cdot CA$$, where $$p$$, $$q$$, and $$r$$ are positive and satisfy $$p+q+r=2/3$$ and $$p^2+q^2+r^2=2/5$$. The ratio of the area of triangle $$DEF$$ to the area of triangle $$ABC$$ can be written in the form $$m/n$$, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m+n$$.

(第十九届AIME1 2001 第9题)