Problem: Iahub has drawn a set of n points in the cartesian plane which he calls "special points". A quadrilateral is a simple polygon without self-intersections with four sides (also called edges) and four vertices (also called corners). Please note that a quadrilateral doesn't have to be convex. A special quadrilateral is one which has all four vertices in the set of special points. Given the set of special points, please calculate the maximal area of a special quadrilateral. 

Input

The first line contains integer n (4 ≤ n ≤ 300). Each of the next n lines contains two integers: xi, yi ( - 1000 ≤ xi, yi ≤ 1000) — the cartesian coordinates of ith special point. It is guaranteed that no three points are on the same line. It is guaranteed that no two points coincide. 

Output

Output a single real number — the maximal area of a special quadrilateral. The answer will be considered correct if its absolute or relative error does't exceed 10 - 9.

Examples

Input

5
0 0
0 4
4 0
4 4
2 3


Output

16.000000

Note

In the test example we can choose first 4 points to be the vertices of the quadrilateral. They form a square by side 4, so the area is 4·4 = 16.

Solution (in JAVA):

Solution:
import java.util.*;
import static java.lang.Math.*;

public class A
{
	public static void main(String[] args)
	{
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		node[] nodes = new node[n];

		for(int i = 0; i < n; i++)
			nodes[i] = new node(scan.nextInt(), scan.nextInt());

		double best = 0;
		for(int i = 0; i < n; i++)
			for(int j = i+1; j < n; j++)
			{
				double max1 = Integer.MIN_VALUE, max2 = Integer.MIN_VALUE;
				for(int k = 0; k < n; k++)
				{
					double ret = cross(nodes[i], nodes[j], nodes[k]);
					if(ret > 0)	max1 = max(max1, ret);
					if(ret < 0)	max2 = max(max2, -ret);
				}
				if(max1 > 0 && max2 > 0)
					best = max(best, max1+max2);
			}

		System.out.println(best/2);
	}

	private static double cross(node pair, node pair1, node pair2)
	{
		int x1 = pair1.x-pair.x, y1 = pair1.y-pair.y;
		int x2 = pair2.x-pair.x, y2 = pair2.y-pair.y;
		return x1*y2-y1*x2;
	}

	private static class node
	{
		int x, y;
		node(int X, int Y)
		{
			x = X;
			y = Y;
		}
	}
}