In convex hexagon $$ABCDEF$$, all six sides are congruent, $$\angle A$$ and $$\angle D$$ are right angles, and $$\angle B, \angle C, \angle E,$$ and $$\angle F$$ are congruent. The area of the hexagonal region is $$2116(\sqrt{2}+1).$$ Find $$AB$$.

(第二十四届AIME2 2006 第1题)