The following figure consists of8horizontal lines and13vertical lines. The goal of this problem is to count the number of rectangles (squares are a kind of rectangle, but line segments are not).

LetVbe the set of all sets of two vertical lines, and letHbe the set of all sets of two horizontal lines. LetRbe the set of all rectangles in the figure. Define a functionf:RVH

byf

({AB,CD}, {AC,BD}).

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