In triangle $$ABC$$ the medians $$\overline{AD}$$ and $$\overline{CE}$$ have lengths 18 and 27, respectively, and $$AB = 24$$. Extend $$\overline{CE}$$ to intersect the circumcircle of $$ABC$$ at $$F$$. The area of triangle $$AFB$$ is $$m\sqrt {n}$$, where $$m$$ and $$n$$ are positive integers and $$n$$ is not divisible by the square of any prime. Find $$m + n$$.

(第二十届AIME1 2002 第13题)