The following figure consists of 7 horizontal lines and 12 vertical lines. The goal of this problem is to count the number of rectangles (squares are...

The following figure consists of 7 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 × H

by

 f↦ ({AB, CD}, {AC, BD}).

Compute |R|, the number of rectangles in the figure.