L-Shape Covering

An L-shape is an axis-aligned rectilinear hexagon with exactly one reflex corner: it is the smallest bounding rectangle of the shape with only its top-right corner cut away. See Figures (a) and (b). The cut may degenerate so that three corners become collinear, as in Figure (b).

Figure (a)

Figure (b)

Given a set of $N$ points in the plane, an L-shape is said to cover the points if every point lies inside it or on its boundary. Write a program that computes the area of the smallest L-shape covering all of the given points.

Figure (c)

Figure (d)

Figure (c) shows a set of points, and Figure (d) shows the minimum-area L-shape that covers them.

Note that the resulting area may be $0$, and the input may contain several points with identical coordinates.

The first line contains the number of test cases $T$ ($1 \le T \le 20$).

Each test case begins with a line containing the number of points $N$ ($1 \le N \le 50000$). Each of the next $N$ lines contains the two integer coordinates of one point separated by a single space; each coordinate is an integer between $-30000$ and $30000$.

For each test case, print a single line containing the area of the smallest L-shape that covers the given points.