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.Scanner;


public class a198b {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int[] x =new int[n];
		int[]y=new int[n];
		int min=0,max=0;
		double ans=0;
		for (int i=0;i<n;i++){
			x[i]=sc.nextInt();
			y[i]=sc.nextInt();}
		for (int i=0;i<n;i++)
			for (int j=i+1;j<n;j++)
			{
				min=0;max=0;
				for (int j1=0;j1<n;j1++)
					if (j1!=i && j1!=j)
					{
						int s=surface(x[i],y[i],x[j1],y[j1],x[j],y[j]);
						if (s>0)
							max=Math.max(max,s);
						else min=Math.min(min,s);
						if (max>0 && min<0)
						ans=Math.max(ans,(max-min)/2.0);
					}
			}
	System.out.println(ans);			
	}
	private static int surface(int x1,int y1,int x2,int y2,int x3,int y3)
	{
		return (x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));		
	}

}