Parallelogram
In many computer graphics problems, processing smooth surfaces is essential. Typically, only a finite number of points on such a surface are known, necessitating interpolation of the surface. For ease of calculation, it's beneficial if the projections of these approximation nodes onto a plane are arranged in a regular pattern, such as aligning with the nodes of a two-dimensional grid.
One method to achieve this regular arrangement is to project all given points into a specific parallelogram. The sides of this parallelogram are then divided into equal segments, forming the interpolation grid. Since the total number of grid points at a fixed interval is proportional to the area of the parallelogram, it's important to construct a parallelogram with the smallest possible area that still contains all the points in the set.
Your task is to calculate the area of this minimal parallelogram. You do not need to determine the parallelogram itself, just compute its area.
Input
The first line contains a single integer N (3 ≤ N ≤ 5000) — the number of points on the plane. The following N lines each contain two integers separated by a space, representing the coordinates of the points in the Cartesian coordinate system. The coordinate values do not exceed 500 in absolute value.
It is guaranteed that not all points lie on a single line.
Output
Output the minimal area of the parallelogram that contains all the given points.