1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <cmath>
#include <set>
#include <cassert>
using namespace std;
using LD = long double;
using LL = long long;
const int N = 101;
const LD eps = 1e-15, INF = 1e30, INF_LL = 1LL<<62;
struct Point {
  LD x, y;
  Point() {}
  Point(LD x, LD y): x(x), y(y) {}
  bool operator==(const Point &other) const { return abs(x - other.x) < eps && abs(y - other.y) < eps; }
  Point operator-(const Point &other) const { return Point(x - other.x, y - other.y); }
  Point operator+(const Point &other) const { return Point(x + other.x, y + other.y); }
  bool operator<(const Point &other) const { return make_pair(x, y) < make_pair(other.x, other.y); }
};
struct IntPoint {
  int x, y;
  IntPoint() {}
  IntPoint(int x, int y): x(x), y(y) {}
  IntPoint operator+(const IntPoint &other) const { return IntPoint(x + other.x, y + other.y); }
  IntPoint operator-(const IntPoint &other) const { return IntPoint(x - other.x, y - other.y); }
  bool operator<(const IntPoint &other) const { return make_pair(x, y) < make_pair(other.x, other.y); }
};
const Point zero(0, 0);
const IntPoint int_zero(0, 0);
/* ostream& operator<<(ostream &out, const Point &p) {
  out << "(" << p.x << ", " << p.y << ")";
  return out;
} */
LD vecprod(const Point &a, const Point &b, const Point &c) {
  return (b.y - a.y) * (c.x - a.x) - (b.x - a.x) * (c.y - a.y);
}
LL int_vecprod(const IntPoint &a, const IntPoint &b, const IntPoint &c) {
  return (b.y - a.y) * 1LL * (c.x - a.x) - (b.x - a.x) * 1LL * (c.y - a.y);
}
LD scalarprod(const Point &a, const Point &b) {
  return a.x * b.x + a.y * b.y;
}
bool active[N];
int n;
IntPoint a[N], b[N];
vector<Point> points;
LD dist2(const Point &a, const Point &b) {
  return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
}
LD intersection_ratio(const IntPoint &c, const IntPoint &d, const IntPoint &a, const IntPoint &b) {
  return -((c.y - a.y) * 1LL * (b.x - a.x) - (c.x - a.x) * 1LL * (b.y - a.y)) / (long double)((c.x - d.x) * 1LL * (b.y - a.y) - (c.y - d.y) * 1LL * (b.x - a.x));
}
int main() {
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(15);

  cin >> n;
  vector<IntPoint> towers;
  for (int i=1; i<=n; i++) {
    cin >> a[i].x >> a[i].y >> b[i].x >> b[i].y;
    towers.push_back(a[i]);
    towers.push_back(b[i]);
  }
  vector<IntPoint> dirs;
  int m = towers.size();
  for (int i=0; i<m; i++) {
    const auto &a = towers[i];
    for (int j=i+1; j<m; j++) {
      const auto &b = towers[j];
      dirs.emplace_back(a.x - b.x, a.y - b.y);
      dirs.emplace_back(a.x - b.x, b.y - a.y);
    }
  }
  
  vector<IntPoint> new_dirs;
  for (int i=0; i<dirs.size(); i++) {
    bool unique = true;
    for (int j=0; j<i && unique; j++)
      unique = (int_vecprod(int_zero, dirs[i], dirs[j]) != 0);
    if (unique) {
      new_dirs.push_back(dirs[i]);
      new_dirs.push_back(int_zero - dirs[i]);
    }
  }
  dirs = new_dirs;
  
  vector<pair<IntPoint, IntPoint>> borders;
  for (const auto &dir: dirs) {
    pair<LL, IntPoint> border = {INF_LL, int_zero};
    for (int i=1; i<=n; i++) {
      LL v1 = int_vecprod(int_zero, dir, a[i]), v2 = int_vecprod(int_zero, dir, b[i]);
      if (v1 > v2) {
        border = min(border, make_pair(v1, a[i]));
      } else
        border = min(border, make_pair(v2, b[i]));
    }
    borders.emplace_back(border.second, border.second + dir);
  }
  
  vector<Point> safe_points;
  random_shuffle(borders.begin(), borders.end());
  for (const auto &b: borders) {
    LD top_ratio = INF, bottom_ratio = -INF;
    bool top_bound = false, bottom_bound = false;
    for (const auto &c: borders) {
      LL v1 = int_vecprod(b.first, b.second, c.first);
      LL v2 = int_vecprod(b.first, b.second, c.second);
      if (v1 == v2) continue;
      LD ratio = intersection_ratio(b.first, b.second, c.first, c.second);
      if (v1 < v2) {
        top_ratio = min(top_ratio, ratio);
        top_bound = true;
      } else {
        bottom_ratio = max(bottom_ratio, ratio);
        bottom_bound = true;
      }
      if (top_bound && bottom_bound && top_ratio < bottom_ratio) break;
    }
    if (top_bound && bottom_bound && top_ratio - bottom_ratio > eps) {
      const IntPoint &p = b.first, &q = b.second;
      // Point x(p.x + top_ratio * (q.x - p.x), p.y + top_ratio * (q.y - p.y));
      // Point y(p.x + bottom_ratio * (q.x - p.x), p.y + bottom_ratio * (q.y - p.y));
      safe_points.emplace_back(p.x + top_ratio * (q.x - p.x), p.y + top_ratio * (q.y - p.y));
      safe_points.emplace_back(p.x + bottom_ratio * (q.x - p.x), p.y + bottom_ratio * (q.y - p.y));
    }
  }

  if (safe_points.size() < 6) {
    cout << 0.0 << endl;
    return 0;
  }

  sort(safe_points.begin(), safe_points.end());
  safe_points.erase(unique(safe_points.begin(), safe_points.end()), safe_points.end());

  for (Point &p: safe_points) {
    Point &first = safe_points[0];
    if (p.x < first.x || (abs(p.x - first.x) < eps && p.y < first.y)) swap(first, p);
  }
  const Point &first = safe_points[0];
  sort(safe_points.begin()+1, safe_points.end(), [&first](const Point &a, const Point &b) {
    return vecprod(first, a, b) > 0;
  });
  
  vector<Point> stack = {safe_points[0], safe_points[1]};
  for (int i=2; i<safe_points.size(); i++) {
    const Point &p = safe_points[i];
    LD v;
    bool ignore = false;
    while (stack.size() >= 2 && (v = vecprod(stack[stack.size()-2], stack[stack.size()-1], p)) < eps) {
      if (abs(v) < eps) {
        if (dist2(stack[stack.size()-2], stack[stack.size()-1]) < dist2(stack[stack.size()-2], p)) stack.pop_back();
        else { ignore = true; break; }
      } else stack.pop_back();
    }
    if (!ignore) stack.push_back(p);
  }
  stack.push_back(stack[0]);

  LD res = 0;
  for (int i=0; i<stack.size()-1; i++)
    res += vecprod(zero, stack[i], stack[i+1]);
  cout << 0.5 * res << "\n";
  return 0;
}