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 java.io.*;
public class MaximalAreaQuadrilateral
{
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		
		int n = in.nextInt();
		
		Point[] points = new Point[n];
		for(int x = 0; x < n; x++)
		{
			points[x] = new Point(in.nextInt(), in.nextInt());
		}
		
		int best = 0;
		for(int y = 0; y < points.length; y++)
		{
			for(int z = y + 1; z < points.length; z++)
			{
				int max = Integer.MIN_VALUE;
				int min = Integer.MAX_VALUE;
				
				for(int a = 0; a < points.length; a++)
				{
					if(a != y && a != z)
					{
						int d = cross(points[y], points[z], points[a]);
						
						max = Math.max(max, d);
						min = Math.min(min, d);
					}
				}
				
				int current = Math.abs(max - min);
				best = Math.max(best, current);
			}
		}
		
		System.out.println((double)best / 2);
	}
	
	public static int cross(Point a, Point b, Point c)
	{
		return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
	}
}

class Point
{
	int x;
	int y;
	
	public Point(int x, int y)
	{
		this.x = x;
		this.y = y;
	}
}

//class Vector
//{
//	Point p1;
//	Point p2;
//	
//	public Vector(Point p1, Point p2)
//	{
//		this.p1 = p1;
//		this.p2 = p2;
//	}
//}