Let $$ABC$$ be an equilateral triangle, and let $$D$$ and $$F$$ be points on sides $$BC$$ and $$AB$$, respectively, with $$FA = 5$$ and $$CD = 2$$. Point $$E$$ lies on side $$CA$$ such that angle $$DEF = 60^{\circ}$$. The area of triangle $$DEF$$ is $$14\sqrt{3}$$. The two possible values of the length of side $$AB$$ are $$p \pm q \sqrt{r}$$, where $$p$$ and $$q$$ are rational, and $$r$$ is an integer not divisible by the square of a prime. Find $$r$$.

(第二十五届AIME1 2007 第15题)