#include <bits/stdc++.h>
using namespace std;
struct iii {
  int a, b, c;
  iii() {}
  iii(int a, int b, int c) : a(a), b(b), c(c) {}
  bool operator<(const iii& e) const {
    return a < e.a || a == e.a && (b < e.b || b == e.b && c < e.c);
  }
};
template <typename T>
T sq(const T& x) {
  return x * x;
}
template <typename T>
void minl(T& a, const T& b) {
  if (a > b) a = b;
}
template <typename T>
void maxl(T& a, const T& b) {
  if (a < b) a = b;
}
template <typename T>
void operator+=(vector<T>& a, const T& x) {
  a.push_back(x);
}
template <typename T>
void operator+=(set<T>& a, const T& x) {
  a.insert(x);
}
template <typename T>
bool operator&(const set<T>& a, const T& x) {
  return a.find(x) != a.end();
}
template <typename A, typename B>
istream& operator>>(istream& i, pair<A, B>& v) {
  return i >> v.first >> v.second;
}
pair<int, int> operator+(const pair<int, int>& a, const pair<int, int>& b) {
  return pair<int, int>(a.first + b.first, a.second + b.second);
}
pair<int, int> operator-(const pair<int, int>& a, const pair<int, int>& b) {
  return pair<int, int>(a.first - b.first, a.second - b.second);
}
template <typename T>
void usort(vector<T>& a) {
  sort((a).begin(), (a).end());
  a.erase(unique((a).begin(), (a).end()), a.end());
}
template <typename T>
int index(const vector<T>& a, const T& x) {
  return lower_bound((a).begin(), (a).end(), x) - a.begin();
}
template <typename T>
T gcd(T a, T b) {
  while (b) {
    T t = a % b;
    a = b;
    b = t;
  }
  return a;
}
long long cross(const pair<int, int>& a, const pair<int, int>& b) {
  return (long long)a.first * b.second - (long long)b.first * a.second;
}
long long dot(const pair<int, int>& a, const pair<int, int>& b) {
  return (long long)a.first * b.first + (long long)a.second * b.second;
}
int bitcnt(unsigned x) { return __builtin_popcount(x); }
int bitlow(unsigned x) { return __builtin_ffs(x); }
const double APS = 1e-10;
const double EPS = 1e-7;
const double PI = acos(-1.0);
inline int sgn(double x) { return x < -EPS ? -1 : x > EPS; }
struct Point {
  double x, y;
  Point() {}
  Point(const double& x, const double& y) : x(x), y(y) {}
  bool operator==(const Point& rs) const {
    return sgn(x - rs.x) == 0 && sgn(y - rs.y) == 0;
  }
  bool operator<(const Point& rs) const {
    return x + EPS < rs.x || x < rs.x + EPS && y + EPS < rs.y;
  }
  Point operator+(const Point& rhs) const {
    return Point(x + rhs.x, y + rhs.y);
  }
  Point operator-(const Point& rhs) const {
    return Point(x - rhs.x, y - rhs.y);
  }
  Point operator*(const double& k) const { return Point(x * k, y * k); }
  Point operator/(const double& k) const { return Point(x / k, y / k); }
  double len2() const { return x * x + y * y; }
  double len() const { return sqrt(len2()); }
  Point to(const double& k) const { return (*this) * (k / len()); }
  Point turn_left() { return Point(-y, x); }
  Point turn_right() { return Point(y, -x); }
  bool read() { return scanf("%lf%lf", &x, &y) != EOF; }
  void print() { printf("%.2f %.2f\n", x, y); }
};
inline double cross(Point p1, Point p2) { return p1.x * p2.y - p2.x * p1.y; }
inline double dot(Point p1, Point p2) { return p1.x * p2.x + p1.y * p2.y; }
bool inter(Point a, Point b, Point c, Point d, Point& x) {
  double s1 = cross(b - a, c - a);
  double s2 = cross(b - a, d - a);
  if (sgn(s2 - s1) == 0) return false;
  x = Point(c.x * s2 - d.x * s1, c.y * s2 - d.y * s1) / (s2 - s1);
  return true;
}
Point foot(Point p, Point s1, Point s2) {
  Point t;
  inter(p, p + (s2 - s1).turn_left(), s1, s2, t);
  return t;
}
double area_triangle(Point p1, Point p2, Point p3) {
  return fabs(cross(p1 - p3, p2 - p3)) / 2;
}
int n;
Point p[50000];
double burn() {
  Point x;
  int a = 0;
  int b = 1;
  Point r = (p[b] - p[a]).turn_right();
  int u = 1, v = ((u) + 1 < (n) ? (u) + 1 : 0);
  double s = 0;
  while (cross(r, p[v] - p[u]) > EPS) {
    s += area_triangle(p[b], p[u], p[v]);
    u = v;
    v = ((u) + 1 < (n) ? (u) + 1 : 0);
  }
  inter(p[a], p[b], p[u], p[u] + r, x);
  double ret = area_triangle(p[b], p[u], x) - s;
  while (1) {
    s -= area_triangle(p[b], p[((b) + 1 < (n) ? (b) + 1 : 0)], p[u]);
    a = b;
    b = ((a) + 1 < (n) ? (a) + 1 : 0);
    if (a == 0) break;
    r = (p[b] - p[a]).turn_right();
    while (cross(r, p[v] - p[u]) > EPS) {
      s += area_triangle(p[b], p[u], p[v]);
      u = v;
      v = ((u) + 1 < (n) ? (u) + 1 : 0);
    }
    inter(p[a], p[b], p[u], p[u] + r, x);
    double d = area_triangle(p[b], p[u], x) - s;
    minl(ret, d);
  }
  return ret;
}
void york() {
  scanf("%d", &n);
  for (int i = 0; i < (n); ++i) p[i].read();
  if (cross(p[1] - p[0], p[2] - p[0]) > 0) reverse(p, p + n);
  double s1 = burn();
  for (int i = 0; i < (n); ++i) p[i].y = -p[i].y;
  reverse(p, p + n);
  double s2 = burn();
  double ans = min(s1, s2);
  printf("%.10f", ans);
}
int main() {
  ios_base::sync_with_stdio(false);
  york();
  return 0;
}
