Problem: The night after the graduation ceremony graduate students of German University in Cairo (GUC) are playing darts. As there's no real dart board available, the photographs of members of the GUC upper management are being used.

So, n rectangular photos are placed on the wall. They can overlap arbitrary and even coincide. The photos are not necessarily placed horizontally or vertically, they could also be rotated before being pinned to the wall.

The score of one dart throw is simply the number of photos the dart went through.

Fatma has made a throw but her score was not recorded. She only remembers that she did make it into at least one photo.

Assuming that the probability distribution of the throw is equal across the whole wall, what would be the expectation of Fatma's score?

Input

The first line of input contains integer n (1 ≤ n ≤ 500) — the number of photos on the wall. Then follow n lines describing the photos, each containing 8 single-space-separated integers (coordinates of 4 vertices): x1, y1, x2, y2, x3, y3, x4, y4. Each photo is a rectangle with a nonzero area. The coordinates are integers, not exceeding 104 by absolute value. The coordinates of the rectangle are given in either clockwise or counterclockwise order.

Output

Print the expected score of the throw. The answer will be accepted if it has absolute or relative error not exceeding 10 - 6.

Examples

Input

1
0 0 0 2 2 2 2 0


Output

1.0000000000


Input

1
-1 0 0 1 1 0 0 -1


Output

1.0000000000


Input

4
0 0 0 1 3 1 3 0
0 0 0 3 1 3 1 0
3 3 2 3 2 0 3 0
3 3 3 2 0 2 0 3


Output

1.5000000000


Input

2
-1 0 0 1 1 0 0 -1
0 0 1 1 2 0 1 -1


Output

1.1428571429

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double EPS = 1e-9;
const double INF = 1e6;
const double PI = atan2(0, -1);
const int maxn = 550;
inline int sgn(double x) {
  if (fabs(x) < EPS) return 0;
  return x < 0 ? -1 : 1;
}
inline int iseq(double x, double y) { return sgn(x - y) == 0; }
struct Point {
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  double Angle() { return atan2(y, x); }
};
inline Point operator+(Point A, Point B) { return Point(A.x + B.x, A.y + B.y); }
inline Point operator-(Point A, Point B) { return Point(A.x - B.x, A.y - B.y); }
inline Point operator*(double x, Point A) { return Point(x * A.x, x * A.y); }
inline double operator*(Point A, Point B) { return A.x * B.x + A.y * B.y; }
inline double operator%(Point A, Point B) { return A.x * B.y - A.y * B.x; }
inline double Length2(Point A) { return A * A; }
inline double Length(Point A) { return sqrt(A * A); }
inline double Distance2(Point A, Point B) { return Length2(A - B); }
inline double Distance(Point A, Point B) { return Length(A - B); }
inline bool operator==(Point A, Point B) { return iseq(Distance(A, B), 0); }
inline bool operator<(Point A, Point B) {
  return iseq(A.x, B.x) ? sgn(A.y - B.y) == -1 : sgn(A.x - B.x) == -1;
}
struct Line {
  Point P, Q;
  Line() {}
  Line(Point A, Point B) {
    P = A;
    Q = B;
  }
  Point Direction() { return Q - P; }
};
inline int IsOnLine(Point P, Line l) { return sgn((l.P - P) % (l.Q - P)) == 0; }
inline int IsOnSegment(Point P, Line l) {
  if (P == l.P || P == l.Q) return 1;
  return sgn((l.P - P) % (l.Q - P)) == 0 && sgn((l.P - P) * (l.Q - P)) <= 0;
}
inline bool IsSegmentOverlap(Line A, Line B) {
  if (iseq(A.Direction() % B.Direction(), 0))
    return IsOnSegment(A.P, B) + IsOnSegment(A.Q, B) + IsOnSegment(B.P, A) +
               IsOnSegment(B.Q, A) >=
           2;
  else
    return false;
}
inline bool IsSegmentIntersected(Line A, Line B) {
  if (IsOnSegment(A.P, B) || IsOnSegment(A.Q, B)) return true;
  if (IsOnSegment(B.P, A) || IsOnSegment(B.Q, A)) return true;
  int sgn1 = sgn((A.P - B.P) % B.Direction()),
      sgn2 = sgn((A.Q - B.P) % B.Direction());
  int sgn3 = sgn((B.P - A.P) % A.Direction()),
      sgn4 = sgn((B.Q - A.P) % A.Direction());
  return sgn1 * sgn2 == -1 && sgn3 * sgn4 == -1;
}
inline Point getLineIntersection(Line A, Line B) {
  Point v = A.Direction(), w = B.Direction();
  Point u = B.P - A.P;
  return A.P + ((w % u) / (w % v)) * v;
}
int n;
vector<Point> Rect[maxn];
double area1, area2;
inline double getPolygonArea(const vector<Point> &A) {
  double ans = 0;
  for (auto j = 1u; j + 1 < A.size(); ++j)
    ans += (A[j] - A[0]) % (A[j] - A[0]) * 0.5;
  return ans;
}
inline bool IsInPolygon(Point P, const vector<Point> &A) {
  double area1 = getPolygonArea(A), area2 = 0.0;
  for (auto j = 0u; j + 1 < A.size(); ++j)
    area2 += (A[j] - P) % (A[j + 1] - P) * 0.5;
  return iseq(area1, area2);
}
inline bool IsPolygonOverlap(vector<Point> P[], int i, int j) {
  int sgn = 1;
  for (auto k = 0u; k < P[i].size(); ++k)
    if (!IsInPolygon(P[i][k], P[j])) {
      sgn = 0;
      break;
    }
  if (!sgn) return false;
  if (iseq(getPolygonArea(P[i]), getPolygonArea(P[j]))) return i < j;
  return true;
}
struct info {
  Point P;
  double ang;
  int delta;
  info() {}
  info(Point x, double y, int z) {
    P = x;
    ang = y;
    delta = z;
  }
};
inline int operator<(const info &A, const info &B) {
  if (iseq(A.ang, B.ang))
    return A.delta > B.delta;
  else
    return A.ang < B.ang;
}
inline double getPosition(Point P, Line l) {
  return ((P - l.P) * l.Direction()) / (l.Direction() * l.Direction());
  return (P.x - l.P.x) / (l.Q.x - l.P.x);
}
double ans[maxn];
double getAreaUnion(vector<Point> P[], int n, double *ans) {
  for (int i = 1; i <= n; ++i) ans[i] = 0.0;
  static vector<pair<double, int>> PointList;
  double aans = 0;
  for (int i = 1; i <= n; ++i)
    for (auto j = 0u; j + 1 < P[i].size(); ++j) {
      Line A(P[i][j], P[i][j + 1]);
      PointList.clear();
      for (int k = 1; k <= n; ++k)
        if (i != k)
          for (auto w = 0u; w + 1 < P[k].size(); ++w) {
            Line B(P[k][w], P[k][w + 1]);
            int p1 = sgn((B.P - A.P) % A.Direction());
            int p2 = sgn((B.Q - A.P) % A.Direction());
            if (!p1 && !p2) {
              if (i < k && sgn(A.Direction() * B.Direction()) == 1) {
                PointList.push_back(
                    make_pair(min(1.0, max(getPosition(B.P, A), 0.0)), -1));
                PointList.push_back(
                    make_pair(min(1.0, max(getPosition(B.Q, A), 0.0)), 1));
              }
            } else {
              Point tp = getLineIntersection(A, B);
              if (p1 >= 0 && p2 < 0)
                PointList.push_back(
                    make_pair(min(1.0, max(getPosition(tp, A), 0.0)), -1));
              if (p1 < 0 && p2 >= 0)
                PointList.push_back(
                    make_pair(min(1.0, max(getPosition(tp, A), 0.0)), 1));
            }
          }
      PointList.push_back(make_pair(0.0, 1));
      PointList.push_back(make_pair(1.0, -1));
      sort(PointList.begin(), PointList.end());
      double S0 = A.P % A.Q * 0.5;
      double lst = 0;
      int now = 0;
      for (auto l = 0u, r = 0u; l < PointList.size();) {
        ans[now] += S0 * (PointList[l].first - lst);
        lst = PointList[l].first;
        for (r = l + 1; r < PointList.size() && iseq(PointList[r].first, lst);
             ++r)
          ;
        for (auto w = l; w < r; ++w) now += PointList[w].second;
        l = r;
      }
    }
  return ans[1];
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= 4; ++j) {
      Point P;
      scanf("%lf%lf", &P.x, &P.y);
      Rect[i].push_back(P);
    }
    if (sgn((Rect[i][1] - Rect[i][0]) % (Rect[i][2] - Rect[i][0])) == -1)
      reverse(Rect[i].begin(), Rect[i].end());
    area1 += (Rect[i][1] - Rect[i][0]) % (Rect[i][3] - Rect[i][0]);
    Rect[i].push_back(Rect[i][0]);
  }
  area2 = getAreaUnion(Rect, n, ans);
  printf("%.10lf\n", area1 / area2);
  return 0;
}