Let t be the hypotenuse of the lowest semi-square in the cliques, and let r (t) denote the whole square defined by the diagonal t. Note that it makes sense to use t in the two different but related contexts. Using the same notation as in [9], P(t) denotes the set of semi-squares that include the left endpoint of t, Q(t) is the set of semi-squares that include t's right endpoint, and R (t) denotes the set of semi-squares that intersect t but include none of its endpoints. Ps(t), Qs(t), and Rs(t) denote the set of the full squares corresponding to the set of semi-squares P(t), Q(t) and R (t), while more importantly, we will consider the sets Pr(t), Qr(t) and Rr(t) which denote the set of rectangles given by the intersection of r (t) with each single element of Ps(t), Qs(t) and Rs(t).