Let $$ABCDEF$$ be a regular hexagon. Let G, H, I, J, K, and L be the midpoints of sides AB, BC, CD, DE, EF, and AF, respectively. The segments $$\overline{AH}$$, $$\overline{BI}$$, $$\overline{CJ}$$, $$\overline{DK}$$, $$\overline{EL}$$, and $$\overline{FG}$$ bound a smaller regular hexagon. Let the ratio of the area of the smaller hexagon to the area of $$ABCDEF$$ be expressed as a fraction $$\frac{m}{n}$$ where m and n are relatively prime positive integers. Find m + n.