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

$4\le n\le 1500$

Grading

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