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 B {
	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];
		for (int i = 0; i < y.length; i++) {
			x[i] = sc.nextInt();
			y[i] = sc.nextInt();
		}
		int ans = 0;
		for (int i = 0; i < y.length; i++) {
			for (int j = i + 1; j < y.length; j++) {
				int min = 0;
				int max = 0;
				for (int k = 0; k < y.length; k++) {
					int s = yuza(x[i], y[i], x[k], y[k], x[j], y[j]);
					max = Math.max(max, s);
					min = Math.min(min, s);
				}
				if (max > 0 && min < 0 && ans < (max - min)) {
					ans = max - min;
				}
			}
		}
		System.out.println(ans/2.0);
	}

	private static int yuza(int x1, int y1, int x2, int y2, int x3, int y3) {
		return (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1);
	}

}