Let $$A = (0,0)$$ and $$B = (b,2)$$ be points on the coordinate plane. Let $$ABCDEF$$ be a convex equilateral hexagon such that $$\angle FAB = 120^\circ,$$ $$\overline{AB}\parallel \overline{DE},$$ $$\overline{BC}\parallel \overline{EF,}$$ $$\overline{CD}\parallel \overline{FA},$$ and the y-coordinates of its vertices are distinct elements of the set $$\{0,2,4,6,8,10\}.$$ The area of the hexagon can be written in the form $$m\sqrt {n},$$ where $$m$$ and $$n$$ are positive integers and n is not divisible by the square of any prime. Find $$m + n.$$

(第二十一届AIME2 2003 第14题)