Triangle $$ABC$$ has $$AB=21$$, $$AC=22$$ and $$BC=20$$. Points $$D$$ and $$E$$ are located on $$\overline{AB}$$ and $$\overline{AC}$$, respectively, such that $$\overline{DE}$$ is parallel to $$\overline{BC}$$ and contains the center of the inscribed circle of triangle $$ABC$$. Then $$DE=m/n$$, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m+n$$.

(第十九届AIME1 2001 第7题)