Problem 60431. Calculating the Union Area of Overlapping Rectangles

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Calculate the area covered by a union of multiple rectangles. Each rectangle is represented by 4 integers: the first two integers denote the coordinates of the bottom-left corner, and the next two integers denote the coordinates of the top-right corner. The input is provided as a matrix where each row represents one rectangle.
The rectangles can overlap, meaning that simply summing up the areas of each rectangle will not yield the correct total area. Instead, the overlapping regions should be counted only once.
Example:
Given the rectangles [ 4  8 11 10;  6  3  8 10; 16  8 19 11 ] the area covered by the union of these rectangles is 33.