Baltic Olympiad in Informatics: 2009 Day 2, Problem 1

You are given ~n~ points on the coordinate plane. Write a program which calculates the largest possible area of a rectangle such that each of its vertices is one of the given points. You may assume that such a rectangle exists.

Input Specification

The first line of input contains an integer ~n~, the number of given points.

Each of the following ~n~ lines contains the coordinates of one point, two integers separated by a space. The coordinates will be between ~-10^8~ and ~10^8~.

No two points will be located at the same coordinates.

Output Specification

The first and only line of output should contain a single integer, the largest possible area of a rectangle.

Sample Input

8
-2 3
-2 -1
0 3
0 -1
1 -1
2 1
-3 1
-2 1

Sample Output

10

Explanation

Constraints

~4 \le n \le 1\,500~

Grading

For test cases worth 20% of the total score, ~n \le 500~.