In convex quadrilateral $$ABCD, \angle A \cong \angle C, AB = CD = 180,$$ and $$AD \neq BC.$$ The perimeter of $$ABCD$$ is 640. Find $$\lfloor 1000 \cos A \rfloor.$$ (The notation $$\lfloor x \rfloor$$ means the greatest integer that is less than or equal to $$x.$$)

(第二十一届AIME1 2003 第12题)