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
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
#include <bits/stdc++.h>
using namespace std;


// Half-plane intersection was taken from 
// https://github.com/bicsi/kactl/tree/master/content/geometry
using K = long double;
#define double __float128


using Point = complex<double>;

struct Angle {
	int x, y;
  int id;
  Angle() {}
	Angle(int x, int y) : x(x), y(y) {}
  Angle(int x, int y, int id): x(x), y(y), id(id) {}
	Angle operator-(Angle a) const { return {x-a.x, y-a.y, id}; }
  Angle reflect(Angle a) {
    return Angle(2 * x - a.x, 2 * y - a.y, -1);
  }
	int upper() const {
    return y > 0 || (y == 0 && x > 0);
	}
  Point p() const {
    return Point(x, y);
  }
};
bool operator<(Angle a, Angle b) {
	return make_tuple(!a.upper(), 1LL * a.y * b.x) < make_tuple(!b.upper(), 1LL * a.x * b.y);
}
bool operator==(Angle a, Angle b) {
	return !(a < b || b < a);
}
bool operator!=(Angle a, Angle b) {
  return !(a == b);
}


Angle operator+(Angle a, Angle b) { // where b is a vector
	Angle r(a.x + b.x, a.y + b.y, -1);
  return r;
}

const double kPi = 4.0 * atan(1.0);
const double kEps = 1e-11;
const double kInf = 1e9;

#define X() real()
#define Y() imag()

double dot(Point a, Point b) { return (conj(a) * b).X(); }
double cross(Point a, Point b) { return (conj(a) * b).Y(); }
Point perp(Point a) { return Point{-a.Y(), a.X()}; } // +90deg

double det(Point a, Point b, Point c) {
return cross(b - a, c - a); }

int sgn(double x) {
  if (x < -kEps) return -1;
  if (x > kEps) return +1;
  return 0;
}

Point LineIntersection(Point a, Point b, Point p, Point q) {
  double c1 = det(a, b, p), c2 = det(a, b, q);
  assert(sgn(c1 - c2)); // undefined if parallel
  return (q * c1 - p * c2) / (c1 - c2);
}

struct HalfplaneSet : multimap<Angle, Point> {
  using Iter = multimap<Angle, Point>::iterator;
  
  HalfplaneSet() {
    insert({{+1, 0}, {-kInf, -kInf}});
    insert({{0, +1}, {+kInf, -kInf}});
    insert({{-1, 0}, {+kInf, +kInf}});
    insert({{0, -1}, {-kInf, +kInf}});
  }
  
  Iter get_next(Iter it) {
    return (next(it) == end() ? begin() : next(it)); }
  Iter get_prev(Iter it) {
    return (it == begin() ? prev(end()) : prev(it)); }
  Iter fix(Iter it) { return it == end() ? begin() : it; }
  
  // Cuts everything to the RIGHT of a, b
  // For LEFT, just swap a with b
  void Cut(Angle a, Angle b) {
    //auto c = a; a = b; b = c;
    if (empty()) return;
    int old_size = size();
    
    auto eval = [&](Iter it) {
      return sgn(det(a.p(), b.p(), it->second)); };
    auto intersect = [&](Iter it)  {
      return LineIntersection(a.p(), b.p(),
          it->second, it->first.p() + it->second);
    };
    
    auto it = fix(lower_bound(b - a));
    if (eval(it) >= 0) return;
    
    while (size() && eval(get_prev(it)) < 0)
      fix(erase(get_prev(it)));
    while (size() && eval(get_next(it)) < 0)
      it = fix(erase(it));
    
    if (empty()) return;
    
    if (eval(get_next(it)) > 0) it->second = intersect(it);
    else it = fix(erase(it));
    if (old_size <= 2) return;
    it = get_prev(it);
    insert(it, {b - a, intersect(it)});
    if (eval(it) == 0) erase(it);
  }
  
  double Area() {
    if (size() <= 2) return 0;
    double ret = 0;
    for (auto it = begin(); it != end(); ++it)
      ret += cross(it->second, get_next(it)->second);
    return ret / 2.0;
  }
};

double solve() {
  int n;
  cin >> n;
  vector<Angle> a;
  for (int i = 0; i < n; ++i) {
    Angle x, y;
    cin >> x.x >> x.y;
    cin >> y.x >> y.y;
    x.id = y.id = i;
    a.push_back(x);
    a.push_back(y);
  }
  
  HalfplaneSet s;
  for (int i = 0; i < 2 * n; ++i) {
    vector<Angle> pts;
    Angle orig = {0, 0};
    for (int j = 0; j < 2 * n; ++j) {
      if (i == j) {
        continue;
      }
      auto cur = a[j] - a[i];
      pts.push_back(cur);
      pts.push_back(orig.reflect(cur));
    }
    pts.push_back({1, 0, -1});
    pts.push_back({-1, 0, -1});
    sort(pts.begin(), pts.end());
    
    vector<int> cnt(n);
    int t = 0;
    
    auto add = [&cnt, &t](int id, int mul) {
      if (id == -1) {
        return;
      }
      cnt[id] += mul;
      if (cnt[id] == 1 && mul == -1) --t;
      if (cnt[id] == 2) ++t;
    };
    
    int m = (int) pts.size();
    int it = 0;
    while (pts[it].upper()) {
      add(pts[it].id, +1);
      ++it;
    }
    for (int j = 0; j < m; ++j) {
      int cur = j;
      while (cur < m && pts[cur] == pts[j]) {
        add(pts[cur].id, -1);
        ++cur;
      }
      
      auto ref = orig.reflect(pts[j]);
      while (pts[it] != ref) {
        add(pts[it].id, +1);
        it = (it + 1) % m;
      }
      while (pts[it] == ref) {
        add(pts[it].id, +1);
        it = (it + 1) % m;
      }
      
      if (!t) {
        s.Cut(pts[j] + a[i], orig + a[i]);
        s.Cut(pts[cur % m] + a[i], orig + a[i]);
      }
      
      j = cur - 1;
    }
  }
  return s.Area();
}

void test() {
  HalfplaneSet s;
  s.Cut({1, 0}, {0, 0});
  s.Cut({0, 1}, {1, 0});
  s.Cut({0, 0}, {0, 1});
  cout << (K)s.Area() << endl;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  
  cout << setprecision(17) << fixed << (K)solve() << '\n';
}