In triangle $$ABC,$$ it is given that angles $$B$$ and $$C$$ are congruent. Points $$P$$ and $$Q$$ lie on $$\overline{AC}$$ and $$\overline{AB},$$ respectively, so that $$AP = PQ = QB = BC.$$ Angle $$ACB$$ is $$r$$ times as large as angle $$APQ,$$ where $$r$$ is a positive real number. Find the greatest integer that does not exceed $$1000r$$.

(第十八届AIME1 2000 第14题)