Rectangle $$ABCD$$ is given with $$AB=63$$ and $$BC=448.$$ Points $$E$$ and $$F$$ lie on $$AD$$ and $$BC$$ respectively, such that $$AE=CF=84.$$ The inscribed circle of triangle $$BEF$$ is tangent to $$EF$$ at point $$P,$$ and the inscribed circle of triangle $$DEF$$ is tangent to $$EF$$ at point $$Q.$$ Find $$PQ.$$

(第二十五届AIME2 2007 第9题)