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 cd {
	static int cross(int a,int s,int d,int f)
	{
		return a*f-s*d;
	}
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		int[] x=new int[n];
		int[] y=new int[n];
//		int[] z=new int[n];
		for(int q=0;q<n;q++)
		{
			x[q]=scan.nextInt();
			y[q]=scan.nextInt();
		}
		int max=0;
		int a,s,d;
		for(int q=0;q<n;q++)
			for(int w=q+1;w<n;w++)
			{
				a=-1;
				s=-1;
				for(int e=0;e<n;e++)
if(e!=q&&e!=w)
				{
					d=cross(x[w]-x[q],y[w]-y[q],x[e]-x[q],y[e]-y[q]);
					if(d>=0)
					{
						if(a<d)
							a=d;
					}
					if(d<=0)
					{
						if(s<-d)
							s=-d;
					}
				}
				if(a+s>max&&a>=0&&s>=0)
					max=a+s;
			}
		if(max%2==0)
			System.out.println(max/2+".000000");
		else
			System.out.println(max/2+".500000");
	}

}