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.InputStreamReader;
import java.io.PrintWriter;
import static java.lang.Math.*;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author Trung Pham
 */
public class B {

    public static void main(String[] args) {
        Scanner in = new Scanner();

        PrintWriter out = new PrintWriter(System.out);
        int n = in.nextInt();
        Point[] data = new Point[n];
        for (int i = 0; i < n; i++) {
            data[i] = new Point(in.nextInt(), in.nextInt());
        }
        double result = 0;
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                double left = 0;
                double right = 0;
                for (int k = 0; k < n; k++) {
                    if (k != j && k != i) {
                        double val = cross(minus(data[i], data[k]), minus(data[j], data[k]));
                        if (cross(minus(data[i], data[k]), minus(data[j], data[k])) > 0) {
                            right = max(right, val);
                        } else {
                            left = max(left,-val);
                        }
                    }
                }
                if (right > 0 && left > 0) {
                    result = max(result, (right + left)/2);
                }
            }
        }
        out.println(result);
        out.close();


    }

    static double area(Point a, Point b, Point c) {
        double i = distance(a, b);
        double j = distance(b, c);
        double k = distance(a, c);
        double s = (i + j + k) / 2;
        double result = s * (s - j) * (s - i) * (s - k);
        return Math.sqrt(result);

    }

    static class Point {

        double x, y;

        Point(double x, double y) {
            this.x = x;
            this.y = y;
        }

        Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Point: " + x + " " + y;
        }
    }

    static double distance(Point a, Point b) {
        return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
    }

    static Point intersect(Point a, Point b, Point c) {
        double D = cross(a, b);
        if (D != 0) {
            return new Point(cross(c, b) / D, cross(a, c) / D);
        }
        return null;
    }

    static Point convert(Point a, double angle) {
        double x = a.x * cos(angle) - a.y * sin(angle);
        double y = a.x * sin(angle) + a.y * cos(angle);
        return new Point(x, y);
    }

    static Point minus(Point a, Point b) {
        return new Point(a.x - b.x, a.y - b.y);
    }

    static Point add(Point a, Point b) {
        return new Point(a.x + b.x, a.y + b.y);
    }

    static double cross(Point a, Point b) {
        return a.x * b.y - a.y * b.x;
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() {
            //System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() {


            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}