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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n;
struct point {
  int x, y;
} input[512];
int a, b;
int ans = 0;
int cross(int i1, int i2, int i3) {
  int x1 = input[i1].x - input[i3].x, y1 = input[i1].y - input[i3].y;
  int x2 = input[i2].x - input[i3].x, y2 = input[i2].y - input[i3].y;
  return x1 * y2 - y1 * x2;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> input[i].x >> input[i].y;
  }
  for (int i1 = 0; i1 < n; i1++) {
    for (int i2 = i1 + 1; i2 < n; i2++) {
      a = 0;
      b = 0;
      for (int i3 = 0; i3 < n; i3++) {
        if (cross(i1, i2, i3) > 0) {
          a = max(a, cross(i1, i2, i3));
        } else {
          b = max(b, -cross(i1, i2, i3));
        }
      }
      if (a && b) {
        ans = max(ans, a + b);
      }
    }
  }
  if (ans % 2) {
    cout << ans / 2 << ".5\n";
  } else {
    cout << ans / 2 << "\n";
  }
  return 0;
}