Consider the region \(A^{}_{}\) in the complex plane that consists of all points \(z^{}_{}\) such that both \(\frac{z^{}_{}}{40}\) and \(\frac{40^{}_{}}{\overline{z}}\) have real and imaginary parts between \(0^{}_{}\) and \(1^{}_{}\), inclusive. What is the integer that is nearest the area of \(A^{}_{}\)?

(第一十届AIME1992 第10题)