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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class MaximalAreaQuadrilateral_R198B {
	public static void main(String[] args) throws IOException {
		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 < n; i++) {
			x[i] = sc.nextInt();
			y[i] = sc.nextInt();
		}
		int max = 0;
		for (int i = 0; i < n; i++)
			for (int j = i + 1; j < n; j++) {
				int maxLeft = 0, maxRight = 0;
				Point a = new Point(x[i], y[i]);
				Point b = new Point(x[j], y[j]);
				for (int k = 0; k < n; k++) {
					if (k != i && k != j) {
						Point c = new Point(x[k], y[k]);
						int area = area(a, c, b);
						if (ccw(a, b, c))
							maxLeft = Math.max(maxLeft, area);
						else
							maxRight = Math.max(maxRight, area);
					}
				}
				if (maxLeft != 0 && maxRight != 0)
					max = Math.max(max, Math.abs(maxLeft + maxRight));
			}
		System.out.println(max / 2.0);
	}

	static int area(Point a, Point b, Point c) {
		return Math.abs(a.x * b.y - a.y * b.x + b.x * c.y - b.y * c.x + c.x * a.y - c.y * a.x);
	}

	static boolean ccw(Point p, Point q, Point r) {
		return new Vector(p, q).cross(new Vector(p, r)) > 0;
	}

	static class Point {
		int x, y;

		public Point(int a, int b) {
			x = a;
			y = b;
		}
	}

	static class Vector {
		int x, y;

		Vector(int a, int b) {
			x = a;
			y = b;
		}

		Vector(Point a, Point b) {
			this(b.x - a.x, b.y - a.y);
		}

		int cross(Vector v) {
			return x * v.y - y * v.x;
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}
	}
}