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The following figure consists of 8 horizontal lines and 12 vertical lines. The goal of this problem is to count the number of rectangles (squares are a kind of rectangle, but line segments are not). Let V be the set of all sets of two vertical lines, and let H be the set of all sets of two horizontal lines. Let R be the set of all rectangles in the figure. Define a function f : R → V × Hby f ({AB, CD}, {AC, BD}). Compute |R|, the number of rectangles in the figure.

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