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 pi = acos(-1.0);
const double eps = 1E-7;
const int inf = int(1e9) + 7;
int sgn(double x) {
  if (x < -eps) return -1;
  if (x > eps) return 1;
  return 0;
}
struct Point {
  double x, y;
  Point(double _x, double _y) : x(_x), y(_y) {}
  Point() {}
};
struct Seg {
  Point p0, p1;
  Seg(Point _p0, Point _p1) : p0(_p0), p1(_p1) {}
  Seg() {}
};
struct Circle {
  Point o;
  double r;
  Circle() {}
  Circle(Point _o, double _r) : o(_o), r(_r) {}
};
inline Point operator+(const Point &p1, const Point &p2) {
  return Point(p1.x + p2.x, p1.y + p2.y);
}
inline Point operator-(const Point &p1, const Point &p2) {
  return Point(p1.x - p2.x, p1.y - p2.y);
}
inline Point operator*(const Point &p, double k) {
  return Point(p.x * k, p.y * k);
}
inline double operator^(const Point &p1, const Point &p2) {
  return (p1.x * p2.y - p2.x * p1.y);
}
inline double operator*(const Point &p1, const Point &p2) {
  return p1.x * p2.x + p1.y * p2.y;
}
inline double cross(Point &p0, Point &p1, Point &p2) {
  return (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y);
}
inline double get_dis(const Point &p1, const Point &p2) {
  return sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y));
}
bool seg_jiao(Seg s1, Seg s2, Point &p) {
  double area1 = cross(s1.p0, s1.p1, s2.p0);
  double area2 = cross(s1.p0, s1.p1, s2.p1);
  if (sgn(area1 - area2) == 0) return false;
  p = Point((s2.p0.x * area2 - s2.p1.x * area1) / (area2 - area1),
            (s2.p0.y * area2 - s2.p1.y * area1) / (area2 - area1));
  if (get_dis(p, s2.p0) + get_dis(p, s2.p1) > get_dis(s2.p0, s2.p1) + eps)
    return false;
  if (get_dis(p, s1.p0) + get_dis(p, s1.p1) > get_dis(s1.p0, s1.p1) + eps)
    return false;
  if (sgn(get_dis(p, s1.p0)) == 0 || sgn(get_dis(p, s1.p1)) == 0 ||
      sgn(get_dis(p, s2.p0)) == 0 || sgn(get_dis(p, s2.p1)) == 0)
    return false;
  return true;
}
bool seg_jiao2(Seg &s1, Seg &s2, Point &p) {
  double area1 = cross(s1.p0, s1.p1, s2.p0);
  double area2 = cross(s1.p0, s1.p1, s2.p1);
  if (sgn(area1 - area2) == 0) return false;
  p = Point((s2.p0.x * area2 - s2.p1.x * area1) / (area2 - area1),
            (s2.p0.y * area2 - s2.p1.y * area1) / (area2 - area1));
  if (get_dis(p, s2.p0) + get_dis(p, s2.p1) > get_dis(s2.p0, s2.p1) + eps)
    return false;
  return true;
}
bool strictOnSeg(Point p, Seg s) {
  if (get_dis(p, s.p0) + get_dis(p, s.p1) > get_dis(s.p0, s.p1) + eps)
    return false;
  if (sgn(get_dis(p, s.p0)) == 0 || sgn(get_dis(p, s.p1)) == 0) return false;
  return true;
}
const int maxN = 2000 + 5;
Seg sa[maxN];
int n, m;
double totArea;
bool inside(Point p) {
  for (int(i) = 0; (i) < (n); ++(i)) {
    double base = cross(sa[i * 4].p0, sa[i * 4].p1, p);
    int tmp;
    bool in = true;
    for (int(j) = (1); (j) < (4); ++(j)) {
      if (sgn(base) * sgn(cross(sa[i * 4 + j].p0, sa[i * 4 + j].p1, p)) <= 0)
        in = false;
    }
    if (in) return true;
  }
  return false;
}
struct node {
  int tag;
  double x;
} na[maxN];
bool cmp1(const node &a1, const node &a2) { return (a1.x < a2.x); }
struct line {
  double y, len;
} la[100000];
bool cmp2(const line &a1, const line &a2) { return (a1.y < a2.y); }
bool operator<(const Point &p1, const Point &p2) { return (p1.y + eps < p2.y); }
set<Point> mp;
int lineNum;
void add2(Point p) {
  if (mp.count(p)) return;
  mp.insert(p);
  Seg s = Seg(p, Point(p.x + 10, p.y));
  double tmp[4];
  int nodeNum = 0;
  for (int(i) = 0; (i) < (n); ++(i)) {
    int np = 0;
    for (int(j) = 0; (j) < (4); ++(j))
      if (seg_jiao2(s, sa[i * 4 + j], p)) {
        tmp[np++] = p.x;
      }
    if (np == 2) {
      if (tmp[0] > tmp[1]) swap(tmp[0], tmp[1]);
      na[nodeNum].tag = 1;
      na[nodeNum].x = tmp[0];
      nodeNum++;
      na[nodeNum].tag = -1;
      na[nodeNum].x = tmp[1];
      nodeNum++;
    }
  }
  sort(na, na + nodeNum, cmp1);
  int tag = 0;
  double len = 0;
  for (int(i) = 0; (i) < (nodeNum); ++(i)) {
    if (tag > 0) len += na[i].x - na[i - 1].x;
    tag += na[i].tag;
  }
  la[lineNum].y = s.p0.y;
  la[lineNum].len = len;
  lineNum++;
}
int rr, rc;
void add(Point p, bool flag) {
  rr++;
  if (!flag)
    if (inside(p)) return;
  add2(Point(p.x, p.y - eps));
  add2(Point(p.x, p.y + eps));
  rc++;
}
void work() {
  sort(la, la + lineNum, cmp2);
  double ans = 0;
  for (int(i) = (1); (i) < (lineNum); ++(i)) {
    ans += (la[i].y - la[i - 1].y) * (la[i].len + la[i - 1].len);
  }
  printf("%.8lf\n", totArea / ans);
}
void init() {
  Point tmp[5];
  scanf("%d", &n);
  m = 0;
  for (int(r) = 0; (r) < (n); ++(r)) {
    for (int(i) = 0; (i) < (4); ++(i)) scanf("%lf%lf", &tmp[i].x, &tmp[i].y);
    tmp[4] = tmp[0];
    for (int(i) = 0; (i) < (4); ++(i)) sa[m++] = Seg(tmp[i], tmp[i + 1]);
    totArea +=
        abs(cross(tmp[0], tmp[2], tmp[1])) + abs(cross(tmp[0], tmp[2], tmp[3]));
  }
  Point p;
  for (int(i1) = 0; (i1) < (n); ++(i1))
    for (int(j1) = 0; (j1) < (4); ++(j1))
      for (int(i2) = (i1); (i2) < (n); ++(i2))
        for (int(j2) = 0; (j2) < (4); ++(j2))
          if (i1 != i2) {
            if (seg_jiao(sa[i1 * 4 + j1], sa[i2 * 4 + j2], p)) add(p, 0);
          }
  for (int(i) = 0; (i) < (n); ++(i)) {
    add(sa[i * 4].p0, 0);
    add(sa[i * 4].p1, 0);
    add(sa[i * 4 + 2].p0, 0);
    add(sa[i * 4 + 2].p1, 0);
  }
}
int main() {
  init();
  work();
  return 0;
}