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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        MaximalQuad solver = new MaximalQuad();
        solver.solve(1, in, out);
        out.close();
    }

    static class MaximalQuad {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            Point points[] = new Point[n];

            for (int i = 0; i < n; i++) {
                points[i] = new Point(in.nextInt(), in.nextInt());
            }


            double maxarea = Double.MIN_VALUE;
            for (int i = 0; i < n; i++) {
                for (int j = i + 1; j < n; j++) {
                    double maxn = 0;
                    double maxp = 0;
                    for (int k = 0; k < n; k++) {
                        if (i != k && j != k) {

                            double crossprod = cross(points[i], points[j], points[k]);
                            if (crossprod > 0) {
                                maxp = Math.max(maxp, crossprod);
                            } else {
                                maxn = Math.max(maxn, -crossprod);
                            }

                        }
                    }

                    if (maxn > 0 && maxp > 0) {
                        maxarea = Math.max(maxarea, maxp + maxn);
                    }

                }
            }

            out.println(maxarea);
        }

        double cross(Point a, Point b, Point c) {
            return 0.5 * (((a.x - b.x) * (b.y - c.y)) - ((a.y - b.y) * (b.x - c.x)));
        }

        public class Point {
            double x;
            double y;

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

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}