Total Area of Intersecting Rectangles?

At first blush it seems that an O(n^2) algorithm should be straightforward since we can just check all pairwise points. However, that would create the problem of double counting, as all points that are in 3 rectangles would get counted 3 times! After realizing that, an O(n^2) algorithm doesn't look bad to me now.

If you can think of a trivial O(n^2) algorithm, please post.

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