Problem p01562 (C++) — buggy submission, verdict: Runtime Error

#include <bits/stdc++.h>

#define REP(i, s, n) for (int i = s; i < n; i++)
#define rep(i, n) REP(i, 0, n)
#define EPS (1e-7)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0
#define equals(a, b) (fabs((a) - (b)) < EPS)

using namespace std;

class Point {
public:
  double x, y;

  Point(double x = 0, double y = 0) : x(x), y(y) {}

  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  Point operator*(double a) { return Point(a * x, a * y); }
  Point operator/(double a) { return Point(x / a, y / a); }
  Point operator*(Point a) {
    return Point(x * a.x - y * a.y, x * a.y + y * a.x);
  }

  bool operator<(const Point &p) const {
    return !equals(x, p.x) ? x < p.x : (!equals(y, p.y) && y < p.y);
  }

  bool operator==(const Point &p) const {
    return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
  }
};

struct Segment {
  Point p1, p2;
  Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
  bool operator==(const Segment &p) const {
    return (p.p1 == p1 && p.p2 == p2) || (p.p1 == p2 && p.p2 == p1);
  }
};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;

ostream &operator<<(ostream &os, const Point &a) {
  os << "(" << a.x << "," << a.y << ")";
}

ostream &operator<<(ostream &os, const Segment &a) {
  os << "( " << a.p1 << " , " << a.p2 << " )";
}

double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }

double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }

double norm(Point a) { return a.x * a.x + a.y * a.y; }

double abs(Point a) { return sqrt(norm(a)); }

// rad は角度をラジアンで持たせること
Point rotate(Point a, double rad) {
  return Point(cos(rad) * a.x - sin(rad) * a.y,
               sin(rad) * a.x + cos(rad) * a.y);
}

// 度をラジアンに変換
double toRad(double agl) { return agl * M_PI / 180.0; }

// a => prev, b => cur, c=> next
// prev から cur へ行って next へ行く際の角度を求める
double getArg(Point a, Point b, Point c) {
  double arg1 = atan2(b.y - a.y, b.x - a.x);
  double arg2 = atan2(c.y - b.y, c.x - b.x);
  double arg = fabs(arg1 - arg2);
  while (arg > M_PI)
    arg -= 2.0 * M_PI;
  return fabs(arg);
}

int ccw(Point p0, Point p1, Point p2) {
  Point a = p1 - p0;
  Point b = p2 - p0;
  if (cross(a, b) > EPS)
    return COUNTER_CLOCKWISE;
  if (cross(a, b) < -EPS)
    return CLOCKWISE;
  if (dot(a, b) < -EPS)
    return ONLINE_BACK;
  if (norm(a) < norm(b))
    return ONLINE_FRONT;
  return ON_SEGMENT;
}

bool intersectLL(Line l, Line m) {
  return abs(cross(l.p2 - l.p1, m.p2 - m.p1)) > EPS || // non-parallel
         abs(cross(l.p2 - l.p1, m.p1 - l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2 - l.p1, s.p1 - l.p1) * // s[0] is left of l
             cross(l.p2 - l.p1, s.p2 - l.p1) <
         EPS; // s[1] is right of l
}
bool intersectLP(Line l, Point p) {
  return abs(cross(l.p2 - p, l.p1 - p)) < EPS;
}
bool intersectSS(Line s, Line t) {
  return ccw(s.p1, s.p2, t.p1) * ccw(s.p1, s.p2, t.p2) <= 0 &&
         ccw(t.p1, t.p2, s.p1) * ccw(t.p1, t.p2, s.p2) <= 0;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1 - p) + abs(s.p2 - p) - abs(s.p2 - s.p1) <
         EPS; // triangle inequality
}

Point projection(Line l, Point p) {
  double t = dot(p - l.p1, l.p1 - l.p2) / norm(l.p1 - l.p2);
  return l.p1 + (l.p1 - l.p2) * t;
}
Point reflection(Line l, Point p) { return p + (projection(l, p) - p) * 2; }
double distanceLP(Line l, Point p) { return abs(p - projection(l, p)); }
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s))
    return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r))
    return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t))
    return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.p2)));
}

Point crosspoint(Line l, Line m) {
  double A = cross(l.p2 - l.p1, m.p2 - m.p1);
  double B = cross(l.p2 - l.p1, l.p2 - m.p1);
  if (abs(A) < EPS && abs(B) < EPS) {
    vector<Point> vec;
    vec.push_back(l.p1), vec.push_back(l.p2), vec.push_back(m.p1),
        vec.push_back(m.p2);
    sort(vec.begin(), vec.end());
    assert(vec[1] == vec[2]); // 同じセグメントかもよ
    return vec[1];
    // return m.p1;
  }
  if (abs(A) < EPS)
    assert(false);
  return m.p1 + (m.p2 - m.p1) * (B / A);
}

// cross product of pq and pr
double cross3p(Point p, Point q, Point r) {
  return (r.x - q.x) * (p.y - q.y) - (r.y - q.y) * (p.x - q.x);
}

// returns true if point r is on the same line as the line pq
bool collinear(Point p, Point q, Point r) {
  return fabs(cross3p(p, q, r)) < EPS;
}

// returns true if point t is on the left side of line pq
bool ccwtest(Point p, Point q, Point r) {
  return cross3p(p, q, r) > 0; // can be modified to accept collinear points
}

bool onSegment(Point p, Point q, Point r) {
  return collinear(p, q, r) &&
         equals(sqrt(pow(p.x - r.x, 2) + pow(p.y - r.y, 2)) +
                    sqrt(pow(r.x - q.x, 2) + pow(r.y - q.y, 2)),
                sqrt(pow(p.x - q.x, 2) + pow(p.y - q.y, 2)));
}

double getArea(vector<Point> &vec) {
  double sum = 0;
  for (int i = 0; i < (int)vec.size(); i++)
    sum += cross(vec[i], vec[(i + 1) % vec.size()]);
  return fabs(sum) / 2.0;
}

bool DEBUG = false;
int N;
vector<Point> ps;

bool comp_dist(const Point &a, const Point &b) { return abs(a) < abs(b); }

void makeSegments(vector<Segment> &segs) {
  // int dex = 0;
  vector<Point> vp;

  rep(i, N - 1) {
    vp.clear();
    vp.push_back(ps[i]);
    vp.push_back(ps[i + 1]);
    Segment cur_seg = Segment(ps[i], ps[i + 1]);
    rep(j, N - 1) if (i != j) {
      Segment seg = Segment(ps[j], ps[j + 1]);
      if (equals(cross(cur_seg.p1 - cur_seg.p2, seg.p1 - seg.p2), 0.0)) {
        if (onSegment(cur_seg.p1, cur_seg.p2, seg.p1)) {
          vp.push_back(seg.p1);
        }
        if (onSegment(cur_seg.p1, cur_seg.p2, seg.p2)) {
          vp.push_back(seg.p2);
        }
      } else if (intersectSS(seg, cur_seg)) {
        vp.push_back(crosspoint(cur_seg, seg));
      }

      rep(k, vp.size()) vp[k] = vp[k] - ps[i];
      sort(vp.begin(), vp.end(), comp_dist);
      vp.erase(unique(vp.begin(), vp.end()), vp.end());
      rep(k, vp.size()) vp[k] = vp[k] + ps[i];
    }
    rep(k, vp.size()) vp[k] = vp[k] - ps[i];
    sort(vp.begin(), vp.end(), comp_dist);
    vp.erase(unique(vp.begin(), vp.end()), vp.end());
    rep(k, vp.size()) vp[k] = vp[k] + ps[i];
    rep(j, (int)vp.size() - 1) {
      segs.push_back(Segment(vp[j], vp[j + 1]));
      // segs[dex++] = Segment(vp[j],vp[j+1]);
    }
  }
  // segs.resize(dex);
}

vector<Point> angle_ps;

struct Data {
  int from, to, rev;
  bool operator<(const Data &a) const {
    // cout << from << "," << to << " " << a.from << "," << a.to<< endl;
    int tmp = max(from, to);
    int tmp2 = max(a.from, a.to);
    tmp = max(tmp, tmp2);
    // if( tmp >= angle_ps.size() ) return false;
    Vector vec_a = angle_ps[a.to] - angle_ps[a.from];
    Vector vec_b = angle_ps[to] - angle_ps[from];
    double arg_a = atan2(vec_b.y, vec_b.x);
    double arg_b = atan2(vec_a.y, vec_a.x);
    return !equals(arg_a, arg_b) && arg_a < arg_b;
  }
};
/*
  bool comp_angle(const Data& a,const Data& b){
  cout << a.from << "," << a.to << " " << b.from << "," << b.to << endl;
  Vector vec_a = angle_ps[a.to] - angle_ps[a.from];
  Vector vec_b = angle_ps[b.to] - angle_ps[b.from];
  return atan2(vec_a.y,vec_a.x) <= atan2(vec_b.y,vec_b.x);
  }*/

vector<vector<Data>> G;
vector<Point> vp;

void makeGraph(const vector<Segment> &segs) {
  map<Point, int> mp;
  int V = 0;
  rep(i, segs.size()) if (!mp.count(segs[i].p1)) mp[segs[i].p1] = V++;
  if (!mp.count(segs.back().p2))
    mp[segs.back().p2] = V++;
  vp.resize(V);
  for (map<Point, int>::iterator it = mp.begin(); it != mp.end(); it++) {
    vp[it->second] = it->first;
  }
  angle_ps = vp;
  G.resize(V, vector<Data>());
  rep(i, segs.size()) {
    int s = mp[segs[i].p1], t = mp[segs[i].p2];
    G[s].push_back((Data){s, t, -1});
    G[t].push_back((Data){t, s, -1});
  }

  rep(i, V) { sort(G[i].begin(), G[i].end()); }
  rep(i, V) rep(j, (int)G[i].size()) if (G[i][j].rev == -1) {
    int to = G[i][j].to;
    rep(k, (int)G[to].size()) if (G[to][k].to == i) {
      G[i][j].rev = k;
      G[to][k].rev = j;
      break;
    }
  }
}

const int MAX_V = 6000;
bool visited[MAX_V][MAX_V];

bool getPath(int start_node, int node, int edge, vector<Point> &buf) {
  if (visited[node][edge]) {
    if (!buf.empty() && node == start_node)
      return true;
    return false;
  }
  visited[node][edge] = true;

  int next_node = G[node][edge].to;
  int next_edge = (G[node][edge].rev + 1) % ((int)G[next_node].size());
  buf.push_back(vp[G[node][edge].from]);
  if (getPath(start_node, next_node, next_edge, buf))
    return true;
  else
    return visited[node][edge] = false;
}

void compute() {
  vector<Segment> segs;
  segs.clear();
  makeSegments(segs);

  makeGraph(segs);

  segs.clear();
  ps.clear();
  angle_ps.clear();
  int V = vp.size();
  assert(V < MAX_V);
  rep(i, V) rep(j, V) visited[i][j] = false;

  double area = 0;
  rep(i, V) rep(j, (int)G[i].size()) if (!visited[i][j]) {
    vector<Point> buf;
    if (getPath(i, i, j, buf) && !buf.empty())
      area += getArea(buf);
  }
  printf("%.10lf\\n", area / 2.0);
}

int main() {
  cin >> N;
  ps.resize(N);
  rep(i, N) cin >> ps[i].x >> ps[i].y;

  if (N == 43) {
    bool ok = true;
    Point test[43] = {
        Point(720, 400), Point(380, 400), Point(400, 460), Point(720, 400),
        Point(400, 460), Point(520, 560), Point(720, 400), Point(520, 560),
        Point(600, 580), Point(720, 400), Point(600, 580), Point(820, 580),
        Point(720, 400), Point(820, 580), Point(920, 500), Point(720, 400),
        Point(920, 500), Point(960, 400), Point(720, 400), Point(960, 400),
        Point(960, 300), Point(720, 400), Point(920, 240), Point(860, 180),
        Point(720, 400), Point(860, 180), Point(720, 180), Point(720, 400),
        Point(720, 180), Point(600, 200), Point(720, 400), Point(600, 200),
        Point(520, 240), Point(720, 400), Point(520, 240), Point(480, 280),
        Point(720, 400), Point(480, 280), Point(420, 320), Point(720, 400),
        Point(420, 320), Point(380, 400), Point(720, 400)};
    rep(i, N) if (!(test[i] == ps[i])) ok = false;
    if (ok)
      DEBUG = true;
  }

  compute();
  return 0;
}

Error: WA

Fixed submission:

#include <bits/stdc++.h>

#define REP(i, s, n) for (int i = s; i < n; i++)
#define rep(i, n) REP(i, 0, n)
#define EPS (1e-5)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0
#define equals(a, b) (fabs((a) - (b)) < EPS)

using namespace std;

class Point {
public:
  double x, y;

  Point(double x = 0, double y = 0) : x(x), y(y) {}

  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  Point operator*(double a) { return Point(a * x, a * y); }
  Point operator/(double a) { return Point(x / a, y / a); }
  Point operator*(Point a) {
    return Point(x * a.x - y * a.y, x * a.y + y * a.x);
  }

  bool operator<(const Point &p) const {
    return !equals(x, p.x) ? x < p.x : (!equals(y, p.y) && y < p.y);
  }

  bool operator==(const Point &p) const {
    return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
  }
};

struct Segment {
  Point p1, p2;
  Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
  bool operator==(const Segment &p) const {
    return (p.p1 == p1 && p.p2 == p2) || (p.p1 == p2 && p.p2 == p1);
  }
};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;

ostream &operator<<(ostream &os, const Point &a) {
  os << "(" << a.x << "," << a.y << ")";
}

ostream &operator<<(ostream &os, const Segment &a) {
  os << "( " << a.p1 << " , " << a.p2 << " )";
}

double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }

double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }

double norm(Point a) { return a.x * a.x + a.y * a.y; }

double abs(Point a) { return sqrt(norm(a)); }

// rad は角度をラジアンで持たせること
Point rotate(Point a, double rad) {
  return Point(cos(rad) * a.x - sin(rad) * a.y,
               sin(rad) * a.x + cos(rad) * a.y);
}

// 度をラジアンに変換
double toRad(double agl) { return agl * M_PI / 180.0; }

// a => prev, b => cur, c=> next
// prev から cur へ行って next へ行く際の角度を求める
double getArg(Point a, Point b, Point c) {
  double arg1 = atan2(b.y - a.y, b.x - a.x);
  double arg2 = atan2(c.y - b.y, c.x - b.x);
  double arg = fabs(arg1 - arg2);
  while (arg > M_PI)
    arg -= 2.0 * M_PI;
  return fabs(arg);
}

int ccw(Point p0, Point p1, Point p2) {
  Point a = p1 - p0;
  Point b = p2 - p0;
  if (cross(a, b) > EPS)
    return COUNTER_CLOCKWISE;
  if (cross(a, b) < -EPS)
    return CLOCKWISE;
  if (dot(a, b) < -EPS)
    return ONLINE_BACK;
  if (norm(a) < norm(b))
    return ONLINE_FRONT;
  return ON_SEGMENT;
}

bool intersectLL(Line l, Line m) {
  return abs(cross(l.p2 - l.p1, m.p2 - m.p1)) > EPS || // non-parallel
         abs(cross(l.p2 - l.p1, m.p1 - l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2 - l.p1, s.p1 - l.p1) * // s[0] is left of l
             cross(l.p2 - l.p1, s.p2 - l.p1) <
         EPS; // s[1] is right of l
}
bool intersectLP(Line l, Point p) {
  return abs(cross(l.p2 - p, l.p1 - p)) < EPS;
}
bool intersectSS(Line s, Line t) {
  return ccw(s.p1, s.p2, t.p1) * ccw(s.p1, s.p2, t.p2) <= 0 &&
         ccw(t.p1, t.p2, s.p1) * ccw(t.p1, t.p2, s.p2) <= 0;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1 - p) + abs(s.p2 - p) - abs(s.p2 - s.p1) <
         EPS; // triangle inequality
}

Point projection(Line l, Point p) {
  double t = dot(p - l.p1, l.p1 - l.p2) / norm(l.p1 - l.p2);
  return l.p1 + (l.p1 - l.p2) * t;
}
Point reflection(Line l, Point p) { return p + (projection(l, p) - p) * 2; }
double distanceLP(Line l, Point p) { return abs(p - projection(l, p)); }
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s))
    return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r))
    return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t))
    return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.p2)));
}

Point crosspoint(Line l, Line m) {
  double A = cross(l.p2 - l.p1, m.p2 - m.p1);
  double B = cross(l.p2 - l.p1, l.p2 - m.p1);
  if (abs(A) < EPS && abs(B) < EPS) {
    vector<Point> vec;
    vec.push_back(l.p1), vec.push_back(l.p2), vec.push_back(m.p1),
        vec.push_back(m.p2);
    sort(vec.begin(), vec.end());
    assert(vec[1] == vec[2]); // 同じセグメントかもよ
    return vec[1];
    // return m.p1;
  }
  if (abs(A) < EPS)
    assert(false);
  return m.p1 + (m.p2 - m.p1) * (B / A);
}

// cross product of pq and pr
double cross3p(Point p, Point q, Point r) {
  return (r.x - q.x) * (p.y - q.y) - (r.y - q.y) * (p.x - q.x);
}

// returns true if point r is on the same line as the line pq
bool collinear(Point p, Point q, Point r) {
  return fabs(cross3p(p, q, r)) < EPS;
}

// returns true if point t is on the left side of line pq
bool ccwtest(Point p, Point q, Point r) {
  return cross3p(p, q, r) > 0; // can be modified to accept collinear points
}

bool onSegment(Point p, Point q, Point r) {
  return collinear(p, q, r) &&
         equals(sqrt(pow(p.x - r.x, 2) + pow(p.y - r.y, 2)) +
                    sqrt(pow(r.x - q.x, 2) + pow(r.y - q.y, 2)),
                sqrt(pow(p.x - q.x, 2) + pow(p.y - q.y, 2)));
}

double getArea(vector<Point> &vec) {
  double sum = 0;
  for (int i = 0; i < (int)vec.size(); i++)
    sum += cross(vec[i], vec[(i + 1) % vec.size()]);
  return fabs(sum) / 2.0;
}

bool DEBUG = false;
int N;
vector<Point> ps;

bool comp_dist(const Point &a, const Point &b) { return abs(a) < abs(b); }

void makeSegments(vector<Segment> &segs) {
  // int dex = 0;
  vector<Point> vp;

  rep(i, N - 1) {
    vp.clear();
    vp.push_back(ps[i]);
    vp.push_back(ps[i + 1]);
    Segment cur_seg = Segment(ps[i], ps[i + 1]);
    rep(j, N - 1) if (i != j) {
      Segment seg = Segment(ps[j], ps[j + 1]);
      if (equals(cross(cur_seg.p1 - cur_seg.p2, seg.p1 - seg.p2), 0.0)) {
        if (onSegment(cur_seg.p1, cur_seg.p2, seg.p1)) {
          vp.push_back(seg.p1);
        }
        if (onSegment(cur_seg.p1, cur_seg.p2, seg.p2)) {
          vp.push_back(seg.p2);
        }
      } else if (intersectSS(seg, cur_seg)) {
        vp.push_back(crosspoint(cur_seg, seg));
      }

      rep(k, vp.size()) vp[k] = vp[k] - ps[i];
      sort(vp.begin(), vp.end(), comp_dist);
      vp.erase(unique(vp.begin(), vp.end()), vp.end());
      rep(k, vp.size()) vp[k] = vp[k] + ps[i];
    }
    rep(k, vp.size()) vp[k] = vp[k] - ps[i];
    sort(vp.begin(), vp.end(), comp_dist);
    vp.erase(unique(vp.begin(), vp.end()), vp.end());
    rep(k, vp.size()) vp[k] = vp[k] + ps[i];
    rep(j, (int)vp.size() - 1) {
      segs.push_back(Segment(vp[j], vp[j + 1]));
      // segs[dex++] = Segment(vp[j],vp[j+1]);
    }
  }
  // segs.resize(dex);
}

vector<Point> angle_ps;

struct Data {
  int from, to, rev;
  bool operator<(const Data &a) const {
    // cout << from << "," << to << " " << a.from << "," << a.to<< endl;
    int tmp = max(from, to);
    int tmp2 = max(a.from, a.to);
    tmp = max(tmp, tmp2);
    if (tmp >= angle_ps.size())
      return false;
    Vector vec_a = angle_ps[a.to] - angle_ps[a.from];
    Vector vec_b = angle_ps[to] - angle_ps[from];
    return atan2(vec_b.y, vec_b.x) <= atan2(vec_a.y, vec_a.x);
  }
};
/*
  bool comp_angle(const Data& a,const Data& b){
  cout << a.from << "," << a.to << " " << b.from << "," << b.to << endl;
  Vector vec_a = angle_ps[a.to] - angle_ps[a.from];
  Vector vec_b = angle_ps[b.to] - angle_ps[b.from];
  return atan2(vec_a.y,vec_a.x) <= atan2(vec_b.y,vec_b.x);
  }*/

vector<vector<Data>> G;
vector<Point> vp;

void makeGraph(const vector<Segment> &segs) {
  map<Point, int> mp;
  int V = 0;
  rep(i, segs.size()) if (!mp.count(segs[i].p1)) mp[segs[i].p1] = V++;
  if (!mp.count(segs.back().p2))
    mp[segs.back().p2] = V++;
  vp.resize(V);
  for (map<Point, int>::iterator it = mp.begin(); it != mp.end(); it++) {
    vp[it->second] = it->first;
  }
  angle_ps = vp;
  G.resize(V, vector<Data>());
  rep(i, segs.size()) {
    int s = mp[segs[i].p1], t = mp[segs[i].p2];
    G[s].push_back((Data){s, t, -1});
    G[t].push_back((Data){t, s, -1});
  }

  rep(i, V) { sort(G[i].begin(), G[i].end()); }
  rep(i, V) rep(j, (int)G[i].size()) if (G[i][j].rev == -1) {
    int to = G[i][j].to;
    rep(k, (int)G[to].size()) if (G[to][k].to == i) {
      G[i][j].rev = k;
      G[to][k].rev = j;
      break;
    }
  }
}

const int MAX_V = 6000;
bool visited[MAX_V][MAX_V];

bool getPath(int start_node, int node, int edge, vector<Point> &buf) {
  if (visited[node][edge]) {
    if (!buf.empty() && node == start_node)
      return true;
    return false;
  }
  visited[node][edge] = true;

  int next_node = G[node][edge].to;
  int next_edge = (G[node][edge].rev + 1) % ((int)G[next_node].size());
  buf.push_back(vp[G[node][edge].from]);
  if (getPath(start_node, next_node, next_edge, buf))
    return true;
  else
    return visited[node][edge] = false;
}

void compute() {
  vector<Segment> segs;
  segs.clear();
  makeSegments(segs);

  makeGraph(segs);

  segs.clear();
  ps.clear();
  angle_ps.clear();
  int V = vp.size();
  assert(V < MAX_V);
  rep(i, V) rep(j, V) visited[i][j] = false;

  double area = 0;
  rep(i, V) rep(j, (int)G[i].size()) if (!visited[i][j]) {
    vector<Point> buf;
    if (getPath(i, i, j, buf) && !buf.empty())
      area += getArea(buf);
  }
  printf("%.10lf\\n", area / 2.0);
}

int main() {
  cin >> N;
  ps.resize(N);
  rep(i, N) cin >> ps[i].x >> ps[i].y;

  if (N == 43) {
    bool ok = true;
    Point test[43] = {
        Point(720, 400), Point(380, 400), Point(400, 460), Point(720, 400),
        Point(400, 460), Point(520, 560), Point(720, 400), Point(520, 560),
        Point(600, 580), Point(720, 400), Point(600, 580), Point(820, 580),
        Point(720, 400), Point(820, 580), Point(920, 500), Point(720, 400),
        Point(920, 500), Point(960, 400), Point(720, 400), Point(960, 400),
        Point(960, 300), Point(720, 400), Point(920, 240), Point(860, 180),
        Point(720, 400), Point(860, 180), Point(720, 180), Point(720, 400),
        Point(720, 180), Point(600, 200), Point(720, 400), Point(600, 200),
        Point(520, 240), Point(720, 400), Point(520, 240), Point(480, 280),
        Point(720, 400), Point(480, 280), Point(420, 320), Point(720, 400),
        Point(420, 320), Point(380, 400), Point(720, 400)};
    rep(i, N) if (!(test[i] == ps[i])) ok = false;
    if (ok)
      DEBUG = true;
  }

  compute();
  return 0;
}