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:
//#define NDEBUG
#include "bits/stdc++.h"
#include <iostream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <array>
#include <random>
#ifdef _MSC_VER
#include <ppl.h>
//#include <boost/multiprecision/cpp_dec_float.hpp>
//#include <boost/multiprecision/cpp_int.hpp>
//#include <boost/rational.hpp>
//#include <opencv2/core.hpp>
//#include <opencv2/imgproc.hpp>
//#include <opencv2/highgui.hpp>
//#else
//#include <omp.h>
#endif


using namespace std;

#define DUMPOUT cerr
#define dump(...) DUMPOUT<<"  ";DUMPOUT<<#__VA_ARGS__<<" :["<<__LINE__<<":"<<__FUNCTION__<<"]"<<endl;DUMPOUT<<"    ";dump_func(__VA_ARGS__)

using uint = unsigned; using ll = long long; using ull = unsigned long long; using pii = pair<int, int>; using pll = pair<ll, ll>; using pdd = pair<double, double>; using pss = pair<string, string>;
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const pair<_KTy, _Ty>& m) { o << "{" << m.first << ", " << m.second << "}"; return o; }
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const map<_KTy, _Ty>& m) { if (m.empty()) { o << "{ }"; return o; } o << "{" << *m.begin(); for (auto itr = ++m.begin(); itr != m.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const unordered_map<_KTy, _Ty>& m) { if (m.empty()) { o << "{ }"; return o; } o << "{" << *m.begin(); for (auto itr = ++m.begin(); itr != m.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const vector<_Ty>& v) { if (v.empty()) { o << "{ }"; return o; } o << "{" << v.front(); for (auto itr = ++v.begin(); itr != v.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const deque<_Ty>& v) { if (v.empty()) { o << "{ }"; return o; } o << "{" << v.front(); for (auto itr = ++v.begin(); itr != v.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const set<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } o << "{" << *(s.begin()); for (auto itr = ++s.begin(); itr != s.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const unordered_set<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } o << "{" << *(s.begin()); for (auto itr = ++s.begin(); itr != s.end(); itr++) { o << ", " << *itr; }	o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const stack<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } stack<_Ty> t(s); o << "{" << t.top(); t.pop(); while (!t.empty()) { o << ", " << t.top(); t.pop(); } o << "}";	return o; }
template <typename _Ty> ostream& operator << (ostream& o, const list<_Ty>& l) { if (l.empty()) { o << "{ }"; return o; } o << "{" << l.front(); for (auto itr = ++l.begin(); itr != l.end(); ++itr) { o << ", " << *itr; } o << "}"; return o; }
template <typename _KTy, typename _Ty> istream& operator >> (istream& is, pair<_KTy, _Ty>& m) { is >> m.first >> m.second; return is; }
template <typename _Ty> istream& operator >> (istream& is, vector<_Ty>& v) { for (size_t t = 0; t < v.size(); t++) is >> v[t]; return is; }
template <typename _Ty> istream& operator >> (istream& is, deque<_Ty>& v) { for (size_t t = 0; t < v.size(); t++) is >> v[t]; return is; }
namespace aux { // print tuple
  template<typename Ty, unsigned N, unsigned L> struct tp { static void print(ostream& os, const Ty& v) { os << get<N>(v) << ", "; tp<Ty, N + 1, L>::print(os, v); } };
  template<typename Ty, unsigned N> struct tp<Ty, N, N> { static void print(ostream& os, const Ty& v) { os << get<N>(v); } };
}

template<typename... Tys> ostream& operator<<(ostream& os, const tuple<Tys...>& t) { os << "{"; aux::tp<tuple<Tys...>, 0, sizeof...(Tys) - 1>::print(os, t); os << "}"; return os; }

template<typename A, size_t N, typename T> inline void Fill(A(&array)[N], const T& val) { fill((T*)array, (T*)(array + N), val); }

template <typename ... Args>
std::string format(const std::string& fmt, Args ... args) {
  size_t len = std::snprintf(nullptr, 0, fmt.c_str(), args ...);
  std::vector<char> buf(len + 1);
  std::snprintf(&buf[0], len + 1, fmt.c_str(), args ...);
  return std::string(&buf[0], &buf[0] + len);
}

void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head&& head, Tail&&... tail) { DUMPOUT << head; if (sizeof...(Tail) == 0) { DUMPOUT << " "; } else { DUMPOUT << ", "; } dump_func(move(tail)...); }

#define PI 3.14159265358979323846
#define EPS 1e-8
#define rep(t,n) for(int t=0;t<(n);++t)
#define ALL(j) (j).begin(), (j).end()
#define SZ(j) ((int)(j).size())
#define fake false

class Timer {
public:
  double t = 0;
  Timer() {}
  static double time() {
#ifdef _MSC_VER
    return __rdtsc() / 2.8e9;
#else
    unsigned long long a, d;
    __asm__ volatile("rdtsc"
      : "=a"(a), "=d"(d));
    return (d << 32 | a) / 2.8e9;
#endif
  }
  void measure() { t = time() - t; }
  double elapsedMs() { return (time() - t) * 1000.0; }
} timer;

struct Xorshift {
  uint64_t x = 88172645463325252LL;
  unsigned next_int() {
    x = x ^ (x << 7);
    return x = x ^ (x >> 9);
  }
  unsigned next_int(unsigned mod) {
    x = x ^ (x << 7);
    x = x ^ (x >> 9);
    return x % mod;
  }
  unsigned next_int(unsigned l, unsigned r) {
    x = x ^ (x << 7);
    x = x ^ (x >> 9);
    return x % (r - l + 1) + l;
  }
  double next_double() {
    return double(next_int()) / UINT_MAX;
  }
} rnd;

template<typename T>
void shuffle_vector(vector<T>& v, Xorshift& rnd) {
  int n = v.size();
  for (int i = n - 1; i >= 1; i--) {
    int r = rnd.next_int(i);
    swap(v[i], v[r]);
  }
}



namespace geom {
  constexpr double eps = 1e-8;

  /* point */
  struct Point {
    double x, y;
    Point() : x(0.0), y(0.0) {}
    Point(double x, double y) : x(x), y(y) {}
    Point operator+(const Point& p) const { return Point(this->x + p.x, this->y + p.y); }
    Point operator-(const Point& p) const { return Point(this->x - p.x, this->y - p.y); }
    Point operator-() const { return Point(-this->x, -this->y); }
    Point& operator+=(const Point& p) { return *this = *this + p; }
    Point& operator-=(const Point& p) { return *this = *this - p; }
    bool operator==(const Point& p) const { return x == p.x && y == p.y; }
    bool operator!=(const Point& p) const { return !(*this == p); }
    bool operator<(const Point& p) const { return x == p.x ? y < p.y : x < p.x; }
    bool operator<=(const Point& p) const { return *this == p || *this < p; }
    bool operator>(const Point& p) const { return !(*this <= p); }
    bool operator>=(const Point& p) const { return !(*this < p); }
    double length() const { return std::sqrt(x * x + y * y); }
    double length2() const { return x * x + y * y; }
    double distance(const Point& p) const { return sqrt(pow(x - p.x, 2.0) + pow(y - p.y, 2.0)); }
    friend std::ostream& operator<<(std::ostream& o, const Point& p) {
      o << '(' << p.x << ',' << p.y << ')';
      return o;
    }
    friend std::istream& operator>>(std::istream& i, Point& p) {
      i >> p.x >> p.y;
      return i;
    }
  };
  
  /* vector */
  using Vector = Point;
  double cross_product(const Vector& v1, const Vector& v2) {
    return v1.x * v2.y - v2.x * v1.y;
  }
  double inner_product(const Vector& v1, const Vector& v2) {
    return v1.x * v2.x + v1.y * v2.y;
  }
  enum struct ccw_t {
    COUNTER_CLOCKWISE,
    CLOCKWISE,
    ONLINE_BACK,
    ONLINE_FRONT,
    ON_SEGMENT
  };
  ccw_t ccw(const Point& p0, const Point& p1, const Point& p2) {
    Vector v1 = p1 - p0, v2 = p2 - p0;
    if (cross_product(v1, v2) > eps) return ccw_t::COUNTER_CLOCKWISE;
    if (cross_product(v1, v2) < -eps) return ccw_t::CLOCKWISE;
    if (inner_product(v1, v2) < -eps) return ccw_t::ONLINE_BACK;
    if (v1.length2() < v2.length2()) return ccw_t::ONLINE_FRONT;
    return ccw_t::ON_SEGMENT;
  }

  /* line */
  struct Line {
    Point p1, p2;
    Line() {}
    Line(const Point& p1, const Point& p2) : p1(p1), p2(p2) {}
    Line(double x1, double y1, double x2, double y2) : p1(Point(x1, y1)), p2(Point(x2, y2)) {}
    Vector to_vector() const { return p2 - p1; }
    Point projection(const Point& p) const {
      Vector v12(p2 - p1);
      double det = v12.length2();
      double a = v12.y * p1.x - v12.x * p1.y, b = v12.y * p.y + v12.x * p.x;
      double x = v12.y * a + v12.x * b, y = v12.y * b - v12.x * a;
      return Point(x / det, y / det);
    }
    Point reflection(const Point& p) const {
      Point proj = projection(p);
      return proj + proj - p;
    }
    double distance(const Point& p) const {
      return projection(p).distance(p);
    }
    bool is_parallel(const Line& l) const {
      return abs(cross_product(this->to_vector(), l.to_vector())) < eps;
    }
    bool is_orthogonal(const Line& l) const {
      return abs(inner_product(this->to_vector(), l.to_vector())) < eps;
    }
    Point intersection(const Line& l) const {
      Point p0(this->p1), p1(this->p2), p2(l.p1), p3(l.p2);
      Vector v01(p1 - p0), v23(p3 - p2);
      double det = cross_product(v01, v23);
      double a = v01.y * p0.x - v01.x * p0.y, b = v23.y * p2.x - v23.x * p2.y;
      double x = v01.x * b - v23.x * a;
      double y = v01.y * b - v23.y * a;
      return Point(x / det, y / det);
    }
    friend std::ostream& operator<<(std::ostream& o, const Line& l) {
      o << '(' << l.p1 << ',' << l.p2 << ')';
      return o;
    }
    friend std::istream& operator>>(std::istream& i, Line& l) {
      i >> l.p1 >> l.p2;
      return i;
    }
  };

  /* segment */
  using Segment = Line;
  bool is_intersect_segments(const Segment& s1, const Segment& s2) {
    Vector v2 = s2.to_vector(), p1(s1.p1 - s2.p1), p2(s1.p2 - s2.p1);
    if (cross_product(v2, p1) * cross_product(v2, p2) > eps) return false;
    Vector v1 = s1.to_vector(), p3(s2.p1 - s1.p1), p4(s2.p2 - s1.p1);
    if (cross_product(v1, p3) * cross_product(v1, p4) > eps) return false;
    if (inner_product(s2.p1 - s1.p1, s2.p2 - s1.p1) < eps) return true;
    if (inner_product(s2.p1 - s1.p2, s2.p2 - s1.p2) < eps) return true;
    if (inner_product(s1.p1 - s2.p1, s1.p2 - s2.p1) < eps) return true;
    if (inner_product(s1.p1 - s2.p2, s1.p2 - s2.p2) < eps) return true;
    return false;
  }
  bool is_intersect_segment_line(const Segment s, const Line& l) {
    if (l.is_parallel(s)) return false;
    Vector vst = l.to_vector();
    Point ps = l.p1;
    return cross_product(vst, s.p1 - ps) * cross_product(vst, s.p2 - ps) < eps;
  }
  double segment_distance(const Segment& s, const Point& p) {
    Point proj = s.projection(p);
    if (ccw(s.p1, proj, s.p2) == ccw_t::ONLINE_FRONT) return p.distance(proj);
    return min(p.distance(s.p1), p.distance(s.p2));
  }
  double segment_distance(const Segment& s1, const Segment& s2) {
    if (is_intersect_segments(s1, s2)) return 0.0;
    return min({
      segment_distance(s1, s2.p1), segment_distance(s1, s2.p2),
      segment_distance(s2, s1.p1), segment_distance(s2, s1.p2)
      });
  }


  /* polygon */
  using Polygon = std::vector<Point>;
  double area(const Polygon& poly) {
    if (poly.size() <= 2) return 0;
    Point b(DBL_MAX, DBL_MAX);
    for (const Point& p : poly) {
      b.x = min(b.x, p.x); b.y = min(b.y, p.y);
    }
    b.x -= 1.0; b.y -= 1.0;
    int n = (int)poly.size();
    double area = 0.0;
    for (int i = 0; i < n; i++) {
      area += cross_product(poly[i] - b, poly[(i + 1) % n] - b) * 0.5;
    }
    return area;
  }
  bool is_convex(const Polygon& poly) {
    if (poly.size() <= 2) return false;
    int n = (int)poly.size();
    for (int i = 0; i < n; i++) {
      if (ccw(poly[i], poly[(i + 1) % n], poly[(i + 2) % n]) == ccw_t::CLOCKWISE) {
        return false;
      }
    }
    return true;
  }
  enum struct poly_t {
    EXTERNAL = 0,
    ON_SEGMENT = 1,
    INTERNAL = 2
  };
  poly_t is_inside(const Point& p, const Polygon& poly) {
    int n = (int)poly.size();
    double rad = 0.0;
    for (int i = 0; i < n; i++) {
      const Point& p1 = poly[i];
      const Point& p2 = poly[(i + 1) % n];
      double d1 = p.distance(p1), d2 = p.distance(p2);
      if (segment_distance(Segment(p1, p2), p) < eps) return poly_t::ON_SEGMENT;
      Vector v1(p1 - p), v2(p2 - p);
      double r = atan2(cross_product(v1, v2), inner_product(v1, v2));
      rad += r;
    }
    return rad < eps ? poly_t::EXTERNAL : poly_t::INTERNAL;
  }

  /* convex hull */
  using Hull = Polygon;
  Hull convex_hull(std::vector<Point> points, bool strict = true) {
    double e = strict ? eps : -eps;
    std::sort(points.begin(), points.end());
    int n = (int)points.size(), k = 0;
    Hull hull(2 * n);
    for (int i = 0; i < n; i++) {
      while (k > 1 && cross_product(hull[k - 1] - hull[k - 2], points[i] - hull[k - 1]) < e) k--;
      hull[k++] = points[i];
    }
    for (int i = n - 2, t = k; i >= 0; i--) {
      while (k > t && cross_product(hull[k - 1] - hull[k - 2], points[i] - hull[k - 1]) < e) k--;
      hull[k++] = points[i];
    }
    hull.resize(k - 1);
    return hull;
  }
  double convex_diameter(const Hull& hull) {
    int n = (int)hull.size();
    if (n == 2) return hull.front().distance(hull.back());
    int i = 0, j = 0;
    for (int k = 0; k < n; k++) {
      if (hull[k] < hull[i]) i = k;
      if (hull[j] < hull[k]) j = k;
    }
    double d = 0.0;
    int si = i, sj = j;
    while (i != sj || j != si) {
      d = max(d, hull[i].distance(hull[j]));
      if (cross_product(hull[(i + 1) % n] - hull[i], hull[(j + 1) % n] - hull[j]) < 0.0) {
        i = (i + 1) % n;
      }
      else {
        j = (j + 1) % n;
      }
    }
    return d;
  }
  std::pair<Hull, Hull> convex_cut(const Hull& hull, const Line& l) {
    int n = (int)hull.size(), i = -1, j = -1;
    Point pi, pj;
    for (int k = 0; k < n; k++) {
      Segment s(hull[k], hull[(k + 1) % n]);
      if (is_intersect_segment_line(s, l)) {
        if (cross_product(l.to_vector(), s.to_vector()) < 0) {
          i = k;
          pi = l.intersection(s);
        }
        else {
          j = k;
          pj = l.intersection(s);
        }
      }
    }
    if (i < 0) {
      // no cut
      // 左か右か判定
      if (cross_product(l.to_vector(), hull.front() - l.p1) > 0) {
        // left
        return std::make_pair(hull, Hull());
      }
      else {
        return std::make_pair(Hull(), hull);
      }
    }
    Hull left({ pi, pj }), right({ pj, pi });
    for (int k = (j + 1) % n, e = (i + 1) % n; k != e; k = (k + 1) % n) {
      if(left.back().distance(hull[k]) > eps) left.push_back(hull[k]);
    }
    for (int k = (i + 1) % n, e = (j + 1) % n; k != e; k = (k + 1) % n) {
      if(right.back().distance(hull[k]) > eps) right.push_back(hull[k]);
    }
    if (left.front().distance(left.back()) < eps) left.pop_back();
    if (right.front().distance(right.back()) < eps) right.pop_back();
    return std::make_pair(left, right);
  }
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  using namespace geom;

  int n;
  cin >> n;
  Hull hull(n);
  cin >> hull;

  int q;
  cin >> q;
  cout << fixed << setprecision(15);
  rep(_, q) {
    Line line;
    cin >> line;
    auto res = convex_cut(hull, line);
    cout << area(res.first) << '\n';
  }

  return 0;
}