Square $$ABCD$$ has sides of length 1. Points $$E$$ and $$F$$ are on $$\overline{BC}$$ and $$\overline{CD},$$ respectively, so that $$\triangle AEF$$ is equilateral. A square with vertex $$B$$ has sides that are parallel to those of $$ABCD$$ and a vertex on $$\overline{AE}.$$ The length of a side of this smaller square is $$\frac{a-\sqrt{b}}{c},$$ where $$a, b,$$ and $$c$$ are positive integers and $$b$$ is not divisible by the square of any prime. Find $$a+b+c.$$

(第二十四届AIME2 2006 第6题)