Problem: <image>


As shown in the figure above, cut a convex polygon g by a line p1p2 and print the area of the cut polygon which is on the left-hand side of the line.

g is represented by a sequence of points p1, p2,..., pn where line segments connecting pi and pi+1 (1 ≤ i ≤ n−1) are sides of the convex polygon. The line segment connecting pn and p1 is also a side of the polygon.

Constraints

* 3 ≤ n ≤ 100
* 1 ≤ q ≤ 100
* -10000 ≤ xi, yi ≤ 10000
* -10000 ≤ p1x,p1y,p2x,p2y ≤ 10000
* No point in g will occur more than once.
* p1 ≠ p2

Input

The input is given in the following format:


g (the sequence of the points of the polygon)
q (the number of queries = the number of target lines)
1st query
2nd query
:
qth query


g is given as a sequence of points p1,..., pn in the following format:


n
x1 y1
x2 y2
:
xn yn


The first integer n is the number of points. The coordinate of the i-th point pi is given by two integers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them. Note that all interior angles of given convex polygons are less than or equal to 180.

For each query, a line represented by two points p1 and p2 is given. The coordinates of the points are given by four integers p1x, p1y, p2x and p2y.

Output

For each query, print the area of the cut polygon. The output values should be in a decimal fraction with an error less than 0.00001.

Example

Input

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


Output

2.00000000
4.00000000

Solution (in CPP):

Solution:
#include <algorithm>
#include <cmath>
#include <complex>
#include <iomanip>
#include <iostream>
#include <vector>
using namespace std;

const double EPS = 1e-8, PI = acos(-1);

inline bool eq(double a, double b) {
  return fabs(b - a) < EPS;
}

using Point = complex<double>;
istream &operator>>(istream &is, Point &p) {
  double a, b;
  is >> a >> b;
  p = Point(a, b);
  return is;
}
ostream &operator<<(ostream &os, Point &p) {
  os << fixed << setprecision(10) << p.real() << " " << p.imag();
}

namespace std {
bool operator<(const Point &a, const Point &b) {
  return a.real() != b.real() ? a.real() < b.real() : a.imag() < b.imag();
}
} // namespace std

double cross(const Point &a, const Point &b) {
  return a.real() * b.imag() - a.imag() * b.real();
}

double dot(const Point &a, const Point &b) {
  return a.real() * b.real() + a.imag() * b.imag();
}

double RadianToDegree(double r) {
  return (r * 180.0 / acos(-1));
}

double DegreeToRadian(double d) {
  return (d * acos(-1) / 180.0);
}

double GetAngle(const Point &a, const Point &b, const Point &c) {
  const Point v(b - a), w(c - b);
  double alpha = atan2(v.imag(), v.real()), beta = atan2(w.imag(), w.real());
  if (alpha > beta) swap(alpha, beta);
  double theta = (beta - alpha);
  return min(theta, 2 * acos(-1) - theta);
}

struct Line {
  Point a, b;

  Line(){};
  Line(Point a, Point b) : a(a), b(b){};

  // Ax + By = C
  Line(double A, double B, double C) {
    if (eq(A, 0)) {
      a = Point(0, C / B);
      b = Point(1, C / B);
    } else if (eq(B, 0)) {
      a = Point(C / A, 0);
      b = Point(C / A, 1);
    } else {
      a = Point(0, C / B);
      b = Point(C / A, 0);
    }
  }

  friend ostream &operator<<(ostream &os, Line &p) {
    return os << p.a << " to " << p.b;
  }

  friend istream &operator>>(istream &is, Line &a) {
    return is >> a.a >> a.b;
  }
};

struct Segment {
  Point a, b;

  Segment(){};
  Segment(Point a, Point b) : a(a), b(b){};

  friend ostream &operator<<(ostream &os, Segment &p) {
    return os << p.a << " to " << p.b;
  }

  friend istream &operator>>(istream &is, Segment &a) {
    return is >> a.a >> a.b;
  }
};

struct Circle {
  Point p;
  double r;

  Circle(){};

  Circle(Point p, double r) : p(p), r(r){};
};

using Polygon = vector<Point>;
using Segments = vector<Segment>;
using Lines = vector<Line>;
using Circles = vector<Circle>;
using PointPoint = pair<Point, Point>;

int ccw(const Point &a, Point b, Point c) {
  b = b - a, c = c - a;
  if (cross(b, c) > EPS) return +1;  // "COUNTER_CLOCKWISE"
  if (cross(b, c) < -EPS) return -1; // "CLOCKWISE"
  if (dot(b, c) < 0) return +2;      // "ONLINE_BACK"
  if (norm(b) < norm(c)) return -2;  // "ONLINE_FRONT"
  return 0;                          // "ON_SEGMENT"
}

bool Parallel(const Line &a, const Line &b) {
  return abs(cross(a.b - a.a, b.b - b.a)) < EPS;
}

bool Orthogonal(const Line &a, const Line &b) {
  return abs(dot(a.a - a.b, b.a - b.b)) < EPS;
}

Point Projection(const Line &l, const Point &p) {
  double t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}
Point Projection(const Segment &l, const Point &p) {
  double t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}

Point Reflection(const Line &l, const Point &p) {
  return p + (Projection(l, p) - p) * 2.0;
}

double Distance(const Point &a, const Point &b) {
  return abs(a - b);
}

double Distance(const Line &l, const Point &p) {
  return abs(p - Projection(l, p));
}

bool Intersect(const Line &l, const Line &m);
double Distance(const Line &l, const Line &m) {
  return Intersect(l, m) ? 0 : Distance(l, m.a);
}

bool Intersect(const Segment &s, const Point &p);
double Distance(const Segment &s, const Point &p) {
  Point r = Projection(s, p);
  if (Intersect(s, r)) return abs(r - p);
  return min(abs(s.a - p), abs(s.b - p));
}

bool Intersect(const Segment &s, const Segment &t);
double Distance(const Segment &a, const Segment &b) {
  if (Intersect(a, b)) return 0;
  return min(min(Distance(a, b.a), Distance(a, b.b)), min(Distance(b, a.a), Distance(b, a.b)));
}

bool Intersect(const Line &l, const Segment &s);
double Distance(const Line &l, const Segment &s) {
  if (Intersect(l, s)) return 0;
  return min(Distance(l, s.a), Distance(l, s.b));
}

bool Intersect(const Line &l, const Point &p) {
  return abs(ccw(l.a, l.b, p)) != 1;
}

bool Intersect(const Line &l, const Line &m) {
  return abs(cross(l.b - l.a, m.b - m.a)) > EPS || abs(cross(l.b - l.a, m.b - l.a)) < EPS;
}

bool Intersect(const Segment &s, const Point &p) {
  return ccw(s.a, s.b, p) == 0;
}

bool Intersect(const Line &l, const Segment &s) {
  return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < EPS;
}

bool Intersect(const Segment &s, const Segment &t) {
  return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

double Distance(const Line &l, const Point &p);
bool Intersect(const Circle &c, const Line &l) {
  return Distance(l, c.p) <= c.r + EPS;
}

bool Intersect(const Circle &c, const Point &p) {
  return abs(abs(p - c.p) - c.r) < EPS;
}

int Intersect(const Circle &c, const Segment &l) {
  if (norm(Projection(l, c.p) - c.p) - c.r * c.r > EPS) return 0;
  const double d1 = abs(c.p - l.a), d2 = abs(c.p - l.b);
  if (d1 < c.r + EPS && d2 < c.r + EPS) return 0;
  if (d1 < c.r - EPS && d2 > c.r + EPS || d1 > c.r + EPS && d2 < c.r - EPS) return 1;
  const Point h = Projection(l, c.p);
  if (dot(l.a - h, l.b - h) < 0) return 2;
  return 0;
}

Point Crosspoint(const Line &l, const Line &m) {
  double A = cross(l.b - l.a, m.b - m.a);
  double B = cross(l.b - l.a, l.b - m.a);
  if (abs(A) < EPS && abs(B) < EPS) return m.a;
  return m.a + (m.b - m.a) * B / A;
}

Point Crosspoint(const Segment &l, const Segment &m) {
  double A = cross(l.b - l.a, m.b - m.a);
  double B = cross(l.b - l.a, l.b - m.a);
  if (abs(A) < EPS && abs(B) < EPS) return m.a;
  return m.a + (m.b - m.a) * B / A;
}

PointPoint Crosspoint(const Circle &c, const Line l) {
  Point hp = Projection(l, c.p), h = hp - c.p;
  const double d2 = norm(h);
  Point v = (l.b - l.a) * sqrt(c.r * c.r - d2) / abs(l.b - l.a);
  return PointPoint(hp - v, hp + v);
}

PointPoint Crosspoint(const Circle &c, const Segment &l) {
  Line aa = Line(l.a, l.b);
  if (Intersect(c, l) == 2) return Crosspoint(c, aa);
  PointPoint ret = Crosspoint(c, aa);
  if (dot(l.a - ret.first, l.b - ret.first) < 0)
    ret.second = ret.first;
  else
    ret.first = ret.second;
  return ret;
}

PointPoint Crosspoint(const Circle &c1, const Circle &c2) {
  double d = abs(c1.p - c2.p);
  double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
  double t = atan2(c2.p.imag() - c1.p.imag(), c2.p.real() - c1.p.real());
  Point p1 = c1.p + Point(cos(t + a) * c1.r, sin(t + a) * c1.r);
  Point p2 = c1.p + Point(cos(t - a) * c1.r, sin(t - a) * c1.r);
  return (PointPoint(p1, p2));
}

bool IsConvex(const Polygon &p) {
  int n = p.size();
  for (int i = 0; i < n; i++) {
    if (ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]) == -1) return false;
  }
  return true;
}

Polygon Convex_Hull(Polygon &p) {
  int n = p.size(), k = 0;
  if (n >= 3) {
    sort(p.begin(), p.end());
    vector<Point> ch(2 * n);
    for (int i = 0; i < n; ch[k++] = p[i++]) {
      while (k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < 0) --k;
    }
    for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
      while (k >= t && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < 0) --k;
    }
    ch.resize(k - 1);
    return ch;
  } else {
    return p;
  }
}

enum { OUT, ON, IN };
int Contains(const Polygon &Q, const Point &p) {
  bool in = false;
  for (int i = 0; i < Q.size(); i++) {
    Point a = Q[i] - p, b = Q[(i + 1) % Q.size()] - p;
    if (a.imag() > b.imag()) swap(a, b);
    if (a.imag() <= 0 && 0 < b.imag() && cross(a, b) < 0) in = !in;
    if (cross(a, b) == 0 && dot(a, b) <= 0) return ON;
  }
  return in ? IN : OUT;
}

bool MergeIfAble(Segment &s1, Segment s2) {
  if (abs(cross(s1.b - s1.a, s2.b - s2.a)) > EPS) return false;
  if (ccw(s1.a, s2.a, s1.b) == 1 || ccw(s1.a, s2.a, s1.b) == -1) return false;
  if (ccw(s1.a, s1.b, s2.a) == -2 || ccw(s2.a, s2.b, s1.a) == -2) return false;
  s1 = Segment(min(s1.a, s2.a), max(s1.b, s2.b));
  return true;
}

void MergeSegments(vector<Segment> &segs) {
  for (int i = 0; i < segs.size(); i++) {
    if (segs[i].b < segs[i].a) swap(segs[i].a, segs[i].b);
  }
  for (int i = 0; i < segs.size(); i++) {
    for (int j = i + 1; j < segs.size(); j++) {
      if (MergeIfAble(segs[i], segs[j])) {
        segs[j--] = segs.back(), segs.pop_back();
      }
    }
  }
}

vector<vector<int>> SegmentArrangement(vector<Segment> &segs, vector<Point> &ps) {
  vector<vector<int>> g;
  const int N = (int)segs.size();
  for (int i = 0; i < N; i++) {
    ps.emplace_back(segs[i].a);
    ps.emplace_back(segs[i].b);
    for (int j = i + 1; j < N; j++) {
      const Point p1 = segs[i].b - segs[i].a;
      const Point p2 = segs[j].b - segs[j].a;
      if (cross(p1, p2) == 0) continue;
      if (Intersect(segs[i], segs[j])) {
        ps.emplace_back(Crosspoint(segs[i], segs[j]));
      }
    }
  }
  sort(begin(ps), end(ps));
  ps.erase(unique(begin(ps), end(ps)), end(ps));

  const int M = (int)ps.size();
  g.resize(M);
  for (int i = 0; i < N; i++) {
    vector<int> vec;
    for (int j = 0; j < M; j++) {
      if (Intersect(segs[i], ps[j])) {
        vec.emplace_back(j);
      }
    }
    for (int j = 1; j < vec.size(); j++) {
      g[vec[j - 1]].push_back(vec[j]);
      g[vec[j]].push_back(vec[j - 1]);
    }
  }
  return (g);
}

Polygon ConvexCut(Polygon &U, Line l) {
  Polygon ret;
  for (int i = 0; i < U.size(); i++) {
    Point now = U[i], nxt = U[(i + 1) % U.size()];
    if (ccw(l.a, l.b, now) != -1) ret.push_back(now);
    if (ccw(l.a, l.b, now) * ccw(l.a, l.b, nxt) < 0) {
      ret.push_back(Crosspoint(Line(now, nxt), l));
    }
  }
  return (ret);
}

double Area2(const Polygon &p) {
  double A = 0;
  for (int i = 0; i < p.size(); ++i) {
    A += cross(p[i], p[(i + 1) % p.size()]);
  }
  return A;
}

double Convex_Diameter(Polygon &p) {
  int n = p.size();
  int is = 0, js = 0;
  for (int i = 1; i < n; i++) {
    if (p[i].imag() > p[is].imag()) is = i;
    if (p[i].imag() < p[js].imag()) js = i;
  }
  double maxdis = norm(p[is] - p[js]);

  int maxi, maxj, i, j;
  i = maxi = is;
  j = maxj = js;
  do {
    if (cross(p[(i + 1) % n] - p[i], p[(j + 1) % n] - p[j]) >= 0) {
      j = (j + 1) % n;
    } else {
      i = (i + 1) % n;
    }
    if (norm(p[i] - p[j]) > maxdis) {
      maxdis = norm(p[i] - p[j]);
      maxi = i;
      maxj = j;
    }
  } while (i != is || j != js);
  return sqrt(maxdis);
}

// int main() {}

// Projection
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/1/CGL_1_A
// int main() {
//   Line l;
//   cin >> l;
//
//   int q;
//   cin >> q;
//   while (q--) {
//     Point p;
//     cin >> p;
//     Point ans = Projection(l, p);
//     cout << ans << endl;
//   }
// }

// Reflection
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/1/CGL_1_B
// int main() {
//   Line l;
//   cin >> l;
//
//   int q;
//   cin >> q;
//   while (q--) {
//     Point p;
//     cin >> p;
//     Point ans = Reflection(l, p);
//     cout << ans << endl;
//   }
// }

// ccw
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/1/CGL_1_C
// int main() {
//   const vector<string> ans{"ONLINE_FRONT", "CLOCKWISE", "ON_SEGMENT", "COUNTER_CLOCKWISE", "ONLINE_BACK"};
//   Point p0, p1;
//   cin >> p0 >> p1;
//
//   int q;
//   cin >> q;
//   while (q--) {
//     Point p2;
//     cin >> p2;
//     cout << ans[ccw(p0, p1, p2) + 2] << endl;
//   }
// }

// Parallel and Orthogonal
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/2/CGL_2_A
// int main() {
//   int n;
//   cin >> n;
//   while (n--) {
//     Line a, b;
//     cin >> a >> b;
//     if (Parallel(a, b))
//       puts("2");
//     else if (Orthogonal(a, b))
//       puts("1");
//     else
//       puts("0");
//   }
// }

// Intersect(S, S)
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/2/CGL_2_B
// int main() {
//   int q;
//   cin >> q;
//   while (q--) {
//     Segment a, b;
//     cin >> a >> b;
//     cout << Intersect(a, b) << endl;
//   }
// }

// Crosspoint(S, S)
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/2/CGL_2_C
// int main() {
//   int q;
//   cin >> q;
//   while (q--) {
//     Segment a, b;
//     cin >> a >> b;
//     Point ans = Crosspoint(a, b);
//     cout << ans << endl;
//   }
// }

// Distance(S, S);
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/2/CGL_2_D
// int main() {
//   int q;
//   cin >> q;
//   while (q--) {
//     Segment a, b;
//     cin >> a >> b;
//     cout << fixed << setprecision(10) << Distance(a, b) << endl;
//   }
// }

// Area2
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/3/CGL_3_A
// int main() {
//   int n;
//   cin >> n;
//   Polygon p(n);
//   for (auto &i : p) cin >> i;
//
//   cout << fixed << setprecision(1) << Area2(p) / 2.0 << endl;
// }

// IsConvex
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/3/CGL_3_B
// int main() {
//   int n;
//   cin >> n;
//   Polygon p(n);
//   for (auto &i : p) cin >> i;
//
//   cout << IsConvex(p) << endl;
// }

// Contains
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/3/CGL_3_C
// int main() {
//   int n;
//   cin >> n;
//   Polygon p(n);
//   for (auto &i : p) cin >> i;
//
//   int q;
//   cin >> q;
//   while (q--) {
//     Point a;
//     cin >> a;
//
//     cout << Contains(p, a) << endl;
//   }
// }

// Convex_Hull
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/4/CGL_4_A
// int main() {
//   int n;
//   cin >> n;
//   Polygon p;
//   for (int i = 0; i < n; ++i) {
//     int a, b;
//     cin >> a >> b;
//     p.push_back(Point(a, b));
//   }
//
//   p = Convex_Hull(p);
//   cout << p.size() << endl;
//
//   // 最悪
//   Point minp = p[0];
//   int idx = 0;
//   for (int i = 0; i < p.size(); ++i) {
//     if (p[i].imag() < minp.imag() ? true : p[i].imag() == minp.imag() && p[i].real() < minp.real()) {
//       minp = p[i];
//       idx = i;
//     }
//   }
//
//   for (int i = 0; i < p.size(); ++i) {
//     Point latte = p[(i + idx) % p.size()];
//     cout << latte.real() << " " << latte.imag() << endl;
//   }
// }

// Convex_Diameter
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/4/CGL_4_B
// int main() {
//   int n;
//   cin >> n;
//
//   Polygon p(n);
//   for (auto &i : p) cin >> i;
//
//   cout << fixed << setprecision(10) << Convex_Diameter(p) << endl;
// }

// ConvexCut
// verified https://onlinejudge.u-aizu.ac.jp/#/courses/library/4/CGL/4/CGL_4_C
int main() {
  int n;
  cin >> n;

  Polygon p(n);
  for (auto &i : p) cin >> i;

  int q;
  cin >> q;
  while (q--) {
    Line l;
    cin >> l;

    cout << fixed << setprecision(10) << Area2(ConvexCut(p, l)) / 2 << endl;
  }
}