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;
const int N = 302;
pair<int, int> pts[N];
bool comp(int x, int y, int z) {
  int x1 = pts[x].first - pts[z].first, x2 = pts[y].first - pts[z].first,
      y1 = pts[x].second - pts[z].second, y2 = pts[y].second - pts[z].second;
  return x1 * y2 < x2 * y1;
}
int area(int x, int y, int z) {
  return abs(pts[x].first * (pts[y].second - pts[z].second) +
             pts[y].first * (pts[z].second - pts[x].second) +
             pts[z].first * (pts[x].second - pts[y].second));
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, i, j, k, l, max1, max2, ans = 0;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> pts[i].first >> pts[i].second;
  }
  for (i = 1; i <= n; i++) {
    for (j = i + 1; j <= n; j++) {
      max1 = 0, max2 = 0;
      for (k = 1; k <= n; k++) {
        if (k == i || k == j) {
          continue;
        }
        if (comp(j, k, i)) {
          max1 = max(max1, area(i, j, k));
        } else {
          max2 = max(max2, area(i, j, k));
        }
      }
      if (max1 && max2) {
        ans = max(ans, max1 + max2);
      }
    }
  }
  if (!(ans & 1)) {
    cout << (ans >> 1);
  } else {
    cout << (ans >> 1) << ".5";
  }
}