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-8;
const double pi = acos(-1.0);
inline int dcmp(const double &x) { return x > eps ? 1 : (x < -eps ? -1 : 0); }
inline double sqr(const double &x) { return x * x; }
struct Point {
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(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/(double scale) const { return Point(x / scale, y / scale); }
  Point operator*(double scale) const { return Point(x * scale, y * scale); }
  double operator*(const Point &rhs) const { return x * rhs.x + y * rhs.y; }
  double operator^(const Point &rhs) const { return x * rhs.y - y * rhs.x; }
  Point operator-=(const Point &rhs) { return *this = *this - rhs; }
  Point operator+=(const Point &rhs) { return *this = *this + rhs; }
  Point operator/=(double scale) { return *this = *this / scale; }
  Point operator*=(double scale) { return *this = *this * scale; }
  bool operator<(const Point &rhs) const {
    return dcmp(x - rhs.x) < 0 || (dcmp(x - rhs.x) == 0 && dcmp(y - rhs.y) < 0);
  }
  bool operator==(const Point &rhs) const {
    return dcmp(x - rhs.x) == 0 && dcmp(y - rhs.y) == 0;
  }
  double vlen() const { return sqrt(sqr(x) + sqr(y)); }
  Point normal() const {
    double L = this->vlen();
    return Point(-y / L, x / L);
  }
  bool read() { return scanf("%lf%lf", &x, &y) == 2; }
  void print() const { printf("(%f, %f)\n", x, y); }
};
struct Line {
  Point P;
  Point v;
  double ang;
  Line() {}
  Line(Point P, Point v) : P(P), v(v) { ang = atan2(v.y, v.x); }
  bool operator<(const Line &rhs) const { return ang < rhs.ang; }
};
inline double Dist(const Point &A, const Point &B) {
  return sqrt(sqr(A.x - B.x) + sqr(A.y - B.y));
}
inline Point Rotate(const Point &P, double rad) {
  return Point(P.x * cos(rad) - P.y * sin(rad),
               P.x * sin(rad) + P.y * cos(rad));
}
double Cross(Point A, Point B) { return A ^ B; }
double Cross(Point O, Point A, Point B) { return Cross(A - O, B - O); }
double Dot(Point A, Point B) { return A * B; }
Point Rotate(Point P, Point O, double alpha) {
  P -= O;
  O.x += P.x * cos(alpha) - P.y * sin(alpha);
  O.y += P.y * cos(alpha) + P.x * sin(alpha);
  return O;
}
double Angle(const Point &A, const Point &B) {
  return acos(A * B / A.vlen() / B.vlen());
}
double Area2(Point A, Point B, Point C) { return (B - A) ^ (C - A); }
Point GetLineIntersection(Point P, Point v, Point Q, Point w) {
  Point u = P - Q;
  double t = (w ^ u) / (v ^ w);
  return P + v * t;
}
bool OnSegment(Point p, Point a1, Point a2) {
  return dcmp((a1 - p) ^ (a2 - p)) == 0 && dcmp((a1 - p) * (a2 - p)) < 0;
}
int seg_inter_seg(Point a, Point b, Point c, Point d, Point &k) {
  double s1, s2, s3, s4;
  int d1, d2, d3, d4;
  d1 = dcmp(s1 = (b - a) ^ (c - a));
  d2 = dcmp(s2 = (b - a) ^ (d - a));
  d3 = dcmp(s3 = (d - c) ^ (a - c));
  d4 = dcmp(s4 = (d - c) ^ (b - c));
  if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) {
    k = Point((c.x * s2 - d.x * s1) / (s2 - s1),
              (c.y * s2 - d.y * s1) / (s2 - s1));
    return 1;
  } else if (d1 == 0 && dcmp((a - c) * (b - c)) <= 0) {
    k = c;
    return 2;
  } else if (d2 == 0 && dcmp((a - d) * (b - d)) <= 0) {
    k = d;
    return 2;
  } else if (d3 == 0 && dcmp((c - a) * (d - a)) <= 0) {
    k = a;
    return 2;
  } else if (d4 == 0 && dcmp((c - b) * (d - b)) <= 0) {
    k = b;
    return 2;
  } else
    return 0;
}
double pnt_to_line(Point p, Point l1, Point l2) {
  return fabs((l1 - p) ^ (l2 - p)) / Dist(l1, l2);
}
double DistanceToSegment(Point P, Point A, Point B) {
  if (A == B) return (P - A).vlen();
  Point v1 = B - A, v2 = P - A, v3 = P - B;
  if (dcmp((Dot(v1, v2))) < 0)
    return v2.vlen();
  else if (dcmp(Dot(v1, v3)) > 0)
    return v3.vlen();
  else
    return fabs(Cross(v1, v2)) / v1.vlen();
}
Point intersection(Point u1, Point u2, Point v1, Point v2) {
  double t = ((u1 - v1) ^ (v1 - v2)) / ((u1 - u2) ^ (v1 - v2));
  return u1 + (u2 - u1) * t;
}
bool OnLeft(Line L, Point P) { return dcmp(Cross(L.v, P - L.P)) > 0; }
Point GetIntersection(Line a, Line b) {
  Point u = a.P - b.P;
  double t = Cross(b.v, u) / Cross(a.v, b.v);
  return a.P + a.v * t;
}
int HalfPlaneIntersection(Line *L, int n, Point *poly) {
  sort(L, L + n);
  int first, last;
  Point *p = new Point[n];
  Line *q = new Line[n];
  q[first = last = 0] = L[0];
  for (int i = 1; i < n; ++i) {
    while (first < last && !OnLeft(L[i], p[last - 1])) --last;
    while (first < last && !OnLeft(L[i], p[first])) ++first;
    q[++last] = L[i];
    if (fabs(Cross(q[last].v, q[last - 1].v)) < eps) {
      --last;
      if (OnLeft(q[last], L[i].P)) q[last] = L[i];
    }
    if (first < last) p[last - 1] = GetIntersection(q[last - 1], q[last]);
  }
  while (first < last && !OnLeft(q[first], p[last - 1])) --last;
  if (last - first <= 1) return 0;
  p[last] = GetIntersection(q[last], q[first]);
  int m = 0;
  for (int i = first; i <= last; ++i) poly[m++] = p[i];
  return m;
}
void GetLineVectorPoint(double A, double B, double C, Point &p, Point &v) {
  v = Point(B, -A);
  if (fabs(A) > fabs(B))
    p = Point(-C / A, 0);
  else
    p = Point(0, -C / B);
}
int ConvexHull(Point *p, int n, Point *ch) {
  sort(p, p + n);
  int m = 0;
  for (int i = 0; i < n; ++i) {
    while (m > 1 && dcmp(Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2])) <= 0)
      --m;
    ch[m++] = p[i];
  }
  int k = m;
  for (int i = n - 2; i >= 0; --i) {
    while (m > k && dcmp(Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2])) <= 0)
      --m;
    ch[m++] = p[i];
  }
  if (n > 1) --m;
  return m;
}
int isPointInPolygon(Point p, Point *poly, int n) {
  int wn = 0;
  for (int i = 0; i < n; ++i) {
    Point &p1 = poly[i], p2 = poly[(i + 1) % n];
    if (p == p1 || p == p2 || OnSegment(p, p1, p2)) return -1;
    int k = dcmp(Cross(p2 - p1, p - p1));
    int d1 = dcmp(p1.y - p.y);
    int d2 = dcmp(p2.y - p.y);
    if (k > 0 && d1 <= 0 && d2 > 0) ++wn;
    if (k < 0 && d2 <= 0 && d1 > 0) --wn;
  }
  if (wn) return 1;
  return 0;
}
double dispallseg(Point p0, Point p1, Point p2, Point p3) {
  double ans1 =
      min(DistanceToSegment(p0, p2, p3), DistanceToSegment(p1, p2, p3));
  double ans2 =
      min(DistanceToSegment(p2, p0, p1), DistanceToSegment(p3, p0, p1));
  return min(ans1, ans2);
}
double GetAngle(Point a1, Point a2, Point b1, Point b2) {
  return (a2 - a1) ^ (b1 - b2);
}
double rotating_calipers_min_dist(Point p[], int np, Point q[], int nq,
                                  int flag = true) {
  if (flag)
    return min(rotating_calipers_min_dist(p, np, q, nq, false),
               rotating_calipers_min_dist(q, nq, p, np, false));
  int sp = 0, sq = 0;
  for (int i = 0; i < np; i++)
    if (dcmp(p[i].y - p[sp].y) < 0) sp = i;
  for (int i = 0; i < nq; i++)
    if (dcmp(q[i].y - q[sq].y) > 0) sq = i;
  double tmp;
  double ans = Dist(p[sp], q[sq]);
  for (int i = 0; i < np; i++) {
    while (dcmp(tmp = GetAngle(p[sp], p[(sp + 1) % np], q[sq],
                               q[(sq + 1) % nq])) < 0)
      sq = (sq + 1) % nq;
    if (dcmp(tmp) == 0)
      ans = min(ans,
                dispallseg(p[sp], p[(sp + 1) % np], q[sq], q[(sq + 1) % nq]));
    else
      ans = min(ans, DistanceToSegment(q[sq], p[sp], p[(sp + 1) % np]));
    sp = (sp + 1) % np;
  }
  return ans;
}
double PolygonArea(Point *p, int n) {
  double area = 0;
  for (int i = 1; i < n - 1; ++i) area += Cross(p[i] - p[0], p[i + 1] - p[0]);
  return area / 2;
}
const int N = 1024;
int n;
pair<double, int> c[10000];
double segP(Point p1, Point p2, Point p3) {
  if (dcmp(p2.x - p3.x))
    return (p1.x - p2.x) / (p3.x - p2.x);
  else
    return (p1.y - p2.y) / (p3.y - p2.y);
}
Point p[600][5];
double polyUnion() {
  int i, j, ii, jj, ta, tb, r, d;
  double z, w, s, sum, tc, td;
  Point tmp1, tmp2;
  sum = 0;
  for (i = 0; i < n; ++i)
    for (ii = 0; ii < 4; ++ii) {
      r = 0;
      c[r++] = make_pair(0., 0);
      c[r++] = make_pair(1., 0);
      for (j = 0; j < n; ++j)
        if (i - j)
          for (jj = 0; jj < 4; ++jj) {
            ta = dcmp(Cross(p[i][ii], p[i][ii + 1], p[j][jj]));
            tb = dcmp(Cross(p[i][ii], p[i][ii + 1], p[j][jj + 1]));
            if (!ta && !tb) {
              tmp1.x = p[j][jj + 1].x - p[j][jj].x;
              tmp1.y = p[j][jj + 1].y - p[j][jj].y;
              tmp2.x = p[i][ii + 1].x - p[i][ii].x;
              tmp2.y = p[i][ii + 1].y - p[i][ii].y;
              if (dcmp(Dot(tmp1, tmp2)) > 0 && j < i) {
                c[r++] = make_pair(segP(p[j][jj], p[i][ii], p[i][ii + 1]), 1);
                c[r++] =
                    make_pair(segP(p[j][jj + 1], p[i][ii], p[i][ii + 1]), -1);
              }
            } else if (ta >= 0 && tb < 0) {
              tc = Cross(p[j][jj], p[j][jj + 1], p[i][ii]);
              td = Cross(p[j][jj], p[j][jj + 1], p[i][ii + 1]);
              c[r++] = make_pair(tc / (tc - td), 1);
            } else if (ta < 0 && tb >= 0) {
              tc = Cross(p[j][jj], p[j][jj + 1], p[i][ii]);
              td = Cross(p[j][jj], p[j][jj + 1], p[i][ii + 1]);
              c[r++] = make_pair(tc / (tc - td), -1);
            }
          }
      sort(c, c + r);
      z = min(max(c[0].first, 0.), 1.);
      d = c[0].second;
      s = 0;
      for (j = 1; j < r; ++j) {
        w = min(max(c[j].first, 0.), 1.);
        if (!d) s += w - z;
        d += c[j].second;
        z = w;
      }
      tmp1.x = tmp1.y = 0;
      sum += Cross(tmp1, p[i][ii], p[i][ii + 1]) * s;
    }
  return 0.5 * sum;
}
Point tp[12];
int main() {
  while (~scanf("%d", &n)) {
    double sum = 0;
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < 4; ++j) tp[j].read();
      ConvexHull(tp, 4, p[i]);
      p[i][4] = p[i][0];
      sum += fabs(PolygonArea(p[i], 4));
    }
    double fuck = polyUnion();
    printf("%.10f\n", sum / fuck);
  }
  return 0;
}