Farthest Pair of Points

Given n points on a two-dimensional plane, choose the two points that are farthest apart and compute the square of the Euclidean distance between them.

The first line contains a natural number n (2 ≤ n ≤ 100,000). Each of the next n lines contains the x-coordinate and y-coordinate of one point. Each coordinate is an integer whose absolute value is at most 10,000. Multiple points may have the same coordinates.

Print the square of the distance between the two farthest points among the given points.