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)