Tony allows his customers to create their own pizza. The customers choose exactly one type of crust, sauce, cheese, and meat for their pizza. The following table shows the options available to customers.

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.