A transformation of the first quadrant of the coordinate plane maps each point $$(x,y)$$ to the point $$(\sqrt{x},\sqrt{y}).$$ The vertices of quadrilateral $$ABCD$$ are $$A=(900,300), B=(1800,600), C=(600,1800),$$ and $$D=(300,900).$$ Let $$k_{}$$ be the area of the region enclosed by the image of quadrilateral $$ABCD.$$ Find the greatest integer that does not exceed $$k_{}.$$

(第十七届AIME1999 第6题)