Smallest Rectangle

Hyunsoo placed N points on a coordinate plane. Every point has nonnegative integer coordinates.

He wants to draw one rectangle whose four vertices all have integer coordinates and whose sides are parallel to the x-axis or the y-axis. The interior of the rectangle must contain at least N/2 of the given points. A point on an edge of the rectangle is not considered to be inside it.

Find the minimum possible area of a rectangle that satisfies these conditions.

The first line contains N, the number of points. N is an even positive integer no greater than 100.

Each of the next N lines contains two integers x and y, the coordinates of one point. Each coordinate is an integer between 0 and 10,000 inclusive. All given points are distinct.

Print the minimum area of a rectangle satisfying the conditions.

For the first visible test case, one valid rectangle has vertices (9, 4), (9, 6), (14, 4), and (14, 6).