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.Arrays;
import java.util.Scanner;

public class B340 {

    /**
     * @param args
     */
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        int n = in.nextInt();
        int x[] = new int[n];
        int y[] = new int[n];
        for (int i = 0; i < n; i++) {
            x[i] = in.nextInt();
            y[i] = in.nextInt();
        }

        int ii = -1;
        int jj = -1;

        double d = 0;

        double a = 0;
        double b = 0;
        double c = 0;

        double max = 0;

        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                ii = i;
                jj = j;

                double maxminus = 0;
                double maxplus = 0;

                for (int k = 0; k < n; k++) {
                    if (k != ii & k != jj) {
                        if (sideOfLine(x[ii], y[ii], x[jj], y[jj], x[k], y[k]) < -0.0000001) {
                            // minus = true;
                            double f = pointToPoint(x[ii], y[ii], x[jj], y[jj]);
                            double s = pointToPoint(x[ii], y[ii], x[k], y[k]);
                            double t = pointToPoint(x[jj], y[jj], x[k], y[k]);

                            double S = (f + s + t) / 2;
                            double area = Math.sqrt(S * (S - f) * (S - s)
                                    * (S - t));

                            if (area > maxminus) {
                                maxminus = area;
                            }

                        }
                        if (sideOfLine(x[ii], y[ii], x[jj], y[jj], x[k], y[k]) > 0.00000001) {
                            // plus = true;
                            double f = pointToPoint(x[ii], y[ii], x[jj], y[jj]);
                            double s = pointToPoint(x[ii], y[ii], x[k], y[k]);
                            double t = pointToPoint(x[jj], y[jj], x[k], y[k]);

                            double S = (f + s + t) / 2;
                            double area = Math.sqrt(S * (S - f) * (S - s)
                                    * (S - t));

                            if (area > maxplus) {
                                maxplus = area;
                            }
                        }
                    }

                }

                if (maxplus > 0 && maxminus > 0 && max < maxplus + maxminus) {
                    max = maxplus + maxminus;
                }

            }
        }
        System.out.println(max);
    }

    public static double pointToLine(double aa, double bb, double cc, int x,
            int y) {
        return (aa * x + bb * y + cc) / Math.sqrt(aa * aa + bb * bb);
    }

    public static double pointToPoint(int x1, int y1, int x2, int y2) {
        return Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
    }

    public static double sideOfLine(int x1, int y1, int x2, int y2, int x3,
            int y3) {
        return (y3 - y1) * (x2 - x1) - (y2 - y1) * (x3 - x1);
    }
}