#include <bits/stdc++.h>
using namespace std;
const int maxn = 4e4 + 5;
double sqr(double x) { return x * x; }
struct P {
  double x, y;
  P() {}
  P(double _x, double _y) : x(_x), y(_y) {}
  friend P operator-(const P &a, const P &b) { return P(a.x - b.x, a.y - b.y); }
  friend double operator*(const P &a, const P &b) {
    return a.x * b.x + a.y * b.y;
  }
  friend double operator^(const P &a, const P &b) {
    return a.x * b.y - a.y * b.x;
  }
} p[maxn];
double dis(P a, P b) { return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y)); }
int n;
int dec(int x) { return x - 1; }
int inc(int x) { return (x + 1) % n; }
double solve() {
  double ans = 1e18, s = 0;
  for (int i = 0, j = 1; i < n; ++i) {
    while ((p[inc(j)] - p[j]) * (p[inc(i)] - p[i]) > 0) {
      s += fabs((p[i] - p[j]) ^ (p[i] - p[inc(j)]));
      j = inc(j);
    }
    double a = fabs((p[i] - p[inc(i)]) ^ (p[i] - p[j])) / dis(p[i], p[inc(i)]);
    double c = dis(p[i], p[j]);
    double b = sqrt(sqr(c) - sqr(a));
    double area = a * b;
    ans = min(ans, fabs(fabs(area) - fabs(s)));
    s -= fabs((p[j] - p[i]) ^ (p[inc(i)] - p[i]));
  }
  return ans * 0.5;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%lf%lf", &p[i].x, &p[i].y);
  double ans = solve();
  reverse(p, p + n);
  printf("%.15f\n", min(ans, solve()));
  return 0;
}
