Lillian bought four hairbrushes as $3.99 each. she had a coupon for $1 off. her mom paid for half of the remaining cost. write an evaluate a numerical expression to find how much lillian paid toward the purchase of the hairbrushes.

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.