Problem 85

Counting Rectangles

By counting carefully it can be seen that a rectangular grid measuring $3$ by $2$ contains eighteen rectangles:

Although there exists no rectangular grid that contains exactly two million rectangles, find the area of the grid with the nearest solution.

在一个 $3 \times 2$ 的长方形网格中包含有 $18$ 个不同大小的长方形，如下图所示：

不存在任意大小的长方形网格中包含有恰好两百万个长方形。求包含长方形的数目最接近两百万的长方形网格的面积。