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.*;
import java.util.*;

public class cf340b {
  public static void main(String[] args) {
    FastIO in = new FastIO(), out = in;
    int n = in.nextInt();
    vec2[] v = new vec2[n];
    double ans = 0;
    for(int i=0; i<n; i++) v[i] = new vec2(in.nextDouble(),in.nextDouble());
    for(int i=0; i<n; i++)
      for(int j=0; j<i; j++) {
        double max = -1, min = 1;
        for(int k=0; k<n; k++) {
          if(k==i || k==j) continue;
          double z = area(v[i],v[j],v[k]);
          max = Math.max(max,z);
          min = Math.min(min,z);
        }
        if(max > -.5 && min < .5)
          ans = Math.max(ans,max-min);
      }
    out.printf("%.10f%n", ans);
    out.close();
  }
  static double area(vec2 a, vec2 b, vec2 c) {
    return b.sub(a).cross(c.sub(a))/2.0;
  }
  static class vec2 {
    double x,y;
    vec2(double a, double b) {
      x=a;y=b;
    }
    vec2 sub(vec2 rhs) {
      return new vec2(x-rhs.x, y-rhs.y);
    }
    double cross(vec2 rhs) {
      return x*rhs.y - y*rhs.x;
    }
  }

  static class FastIO extends PrintWriter {
    BufferedReader br;
    StringTokenizer st;

    public FastIO() {
      this(System.in, System.out);
    }

    public FastIO(InputStream in, OutputStream out) {
      super(new BufferedWriter(new OutputStreamWriter(out)));
      br = new BufferedReader(new InputStreamReader(in));
      scanLine();
    }

    public void scanLine() {
      try {
        st = new StringTokenizer(br.readLine().trim());
      } catch (Exception e) {
        throw new RuntimeException(e.getMessage());
      }
    }

    public int numTokens() {
      if (!st.hasMoreTokens()) {
        scanLine();
        return numTokens();
      }
      return st.countTokens();
    }

    public String next() {
      if (!st.hasMoreTokens()) {
        scanLine();
        return next();
      }
      return st.nextToken();
    }

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

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

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