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)