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 maxarea {
    static Point[] points;
    public static void main(String[] args)
    {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        points = new Point[n];
        for(int i = 0; i < n; i++)
            points[i]=new Point(in.nextInt(), in.nextInt());
        double best=0;
        for(int i = 0; i < n; i++)
        {
            for(int j = i+1; j < n; j++)
            {
                int pos = Integer.MIN_VALUE;
                int neg = Integer.MAX_VALUE;
                for(int k = 0; k < n; k++)
                {
                    int curr = cross(points[k],points[i],points[j]);
                    if(curr<0)
                        neg= Math.min(neg,curr);
                    if(curr>0)
                        pos= Math.max(pos,curr);                    
                }       
                best = Math.max(best,pos-neg);
            }
        }
        System.out.println(best/2);     
    }
    public static int cross(Point s, Point e1, Point e2)
    {
        int x1 = e1.x-s.x; int y1 = e1.y-s.y;
        int x2 = e2.x-s.x; int y2= e2.y-s.y;
        return x1*y2-y1*x2;
    }
}
class Point {
    int x; int y;
    public Point(int a, int b) {x=a; y=b;}
}