The intersection staircase consists of a list of points c1,...,ck which are not necessarily corners of rectangles, but at least they can uniquely be assigned to rectangles r (t') ∌ Pr(t) ⋃ Qr(t) ∈ Rr(t). Assume that these points are ordered with decreasing y-coordinates. We denote the corresponding diagonals t1,...,tk analogously.