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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, N) for (int i = 0; i < (int)N; ++i)
#define all(a) (a).begin(), (a).end()
const double EPS = 1e-10;
bool equals(double a, double b) { return fabs(a - b) < EPS; }

class Point {
  double add(double a, double b) const {
    if (fabs(a + b) < EPS * (fabs(a) + fabs(b))) return 0;
    return a + b;
  }

 public:
  double x, y;

  Point(double x = 0, double y = 0) : x(x), y(y) {}

  Point operator+(const Point &p) const {
    return Point(add(x, p.x), add(y, p.y));
  }
  Point operator-(const Point &p) const {
    return Point(add(x, -p.x), add(y, -p.y));
  }
  Point operator*(const double a) { return Point(a * x, a * y); }
  Point operator/(const double a) { return Point(x / a, y / a); }

  double abs() const { return sqrt(norm()); }
  double norm() const { return x * x + y * y; }

  Point rotate(double theta) const {
    return Point(cos(theta) * x - sin(theta) * y,
                 sin(theta) * x + cos(theta) * y);
  }

  Point normalize() const { return Point(*this) / abs(); }

  bool operator<(const Point &p) const { return x != p.x ? x < p.x : y < p.y; }

  bool operator==(const Point &p) const {
    return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
  }

  friend istream &operator>>(istream &is, Point &p) { return is >> p.x >> p.y; }
};

double abs(const Point &p) { return p.abs(); }
double norm(const Point &p) { return p.norm(); }

typedef Point Vector;

class Segment {
 public:
  Point p1, p2;
  Segment() {}
  Segment(Point p1, Point p2) : p1(p1), p2(p2) {}
  friend istream &operator>>(istream &is, Segment &s) {
    return is >> s.p1 >> s.p2;
  }
};

typedef Segment Line;

class Circle {
 public:
  Point c;
  double r;
  Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}

  int contains(const Point &p) const {
    double d = abs(c - p);
    if (equals(d, r)) return 1;  // ON
    if (d < r + EPS) return 2;   // IN
    return 0;                    // OUT
  }
};

typedef vector<Point> Polygon;

double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }

bool isOrthogonal(Vector a, Vector b) { return equals(dot(a, b), 0.0); }

bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
  return isOrthogonal(a1 - a2, b1 - b2);
}

bool isOrthogonal(Segment s1, Segment s2) {
  return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

bool isParallel(Vector a, Vector b) { return equals(cross(a, b), 0.0); }

bool isParallel(Point a1, Point a2, Point b1, Point b2) {
  return isParallel(a1 - a2, b1 - b2);
}

bool isParallel(Segment s1, Segment s2) {
  return equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

Point project(Segment s, Point p) {
  Vector base = s.p2 - s.p1;
  double r = dot(p - s.p1, base) / base.norm();
  return s.p1 + base * r;
}

Point reflect(Segment s, Point p) { return p + (project(s, p) - p) * 2.0; }

double distance(Point a, Point b) { return (a - b).abs(); }

double distanceLP(Line l, Point p) {
  return abs(cross(l.p2 - l.p1, p - l.p1)) / (l.p2 - l.p1).abs();
}

double distanceSP(Segment s, Point p) {
  if (dot(s.p2 - s.p1, p - s.p1) < -EPS) return (p - s.p1).abs();
  if (dot(s.p1 - s.p2, p - s.p2) < -EPS) return (p - s.p2).abs();
  return distanceLP(s, p);
}

bool intersect(Segment s1, Segment s2);
double distance(Segment s1, Segment s2) {
  if (intersect(s1, s2)) return 0.0;
  return min({distanceSP(s1, s2.p1), distanceSP(s1, s2.p2),
              distanceSP(s2, s1.p1), distanceSP(s2, s1.p2)});
}

enum CCW {
  COUNTER_CLOCKWISE = 1,
  CLOCKWISE = -1,
  ONLINE_BACK = 2,
  ONLINE_FRONT = -2,
  ON_SEGMENT = 0,
};

CCW ccw(Point p0, Point p1, Point p2) {
  Vector a = p1 - p0;
  Vector b = p2 - p0;
  if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
  if (cross(a, b) < -EPS) return CLOCKWISE;
  if (dot(a, b) < -EPS) return ONLINE_BACK;      // p2, p0, p1
  if (a.norm() < b.norm()) return ONLINE_FRONT;  // p0, p1, p2
  return ON_SEGMENT;                             // p0, p2, p1
}

bool onLine(Line l, Point p) {
  int c = ccw(l.p1, l.p2, p);
  return c != CLOCKWISE && c != COUNTER_CLOCKWISE;
}

bool intersect(Point p1, Point p2, Point p3, Point p4) {
  return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
          ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}

bool intersect(Segment s1, Segment s2) {
  return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}

Point crossPoint(Line s1, Line s2) {
  assert(!isParallel(s1, s2));
  Vector base = s2.p2 - s2.p1;
  double d1 = cross(base, s2.p1 - s1.p1);
  double d2 = cross(base, s1.p2 - s1.p1);
  double t = d1 / d2;
  return s1.p1 + (s1.p2 - s1.p1) * t;
}

bool intersect(Circle c, Line l) { return distanceLP(l, c.c) < c.r; }

pair<Point, Point> crossPoint(Circle c, Line l) {
  assert(intersect(c, l));
  Vector pr = project(l, c.c);
  Vector e = (l.p2 - l.p1) / (l.p2 - l.p1).abs();
  double base = sqrt(c.r * c.r - norm(pr - c.c));
  return make_pair(pr + e * base, pr - e * base);
}

double arg(Vector p) { return atan2(p.y, p.x); }
Vector polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }

bool intersect(Circle c1, Circle c2) {
  return (c1.c - c2.c).abs() < c1.r + c2.r;
}

pair<Point, Point> crossPoint(Circle c1, Circle c2) {
  assert(intersect(c1, c2));
  double d = abs(c1.c - c2.c);
  double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
  double t = arg(c2.c - c1.c);
  return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

/*
  IN 2
  ON 1
  OUT 0
*/
int contains(const Polygon &g, Point p) {
  int n = g.size();
  bool x = false;
  for (int i = 0; i < n; ++i) {
    Point a = g[i] - p, b = g[(i + 1) % n] - p;
    if (abs(cross(a, b)) < EPS && dot(a, b) < EPS) return 1;
    if (a.y > b.y) swap(a, b);
    if (a.y < EPS & EPS < b.y && cross(a, b) > EPS) x = !x;
  }
  return (x ? 2 : 0);
}

Polygon convexHull(Polygon s, bool includeOnSegment = false) {
  Polygon u, l;

  if (s.size() < 3) return s;
  sort(s.begin(), s.end());

  u.push_back(s[0]);
  u.push_back(s[1]);
  l.push_back(s[s.size() - 1]);
  l.push_back(s[s.size() - 2]);

  auto bad = [&](Point p1, Point p2, Point p3) {
    if (includeOnSegment) {
      return ccw(p1, p2, p3) == COUNTER_CLOCKWISE;
    } else {
      return ccw(p1, p2, p3) != CLOCKWISE;
    }
  };

  for (int i = 2; i < s.size(); ++i) {
    for (int n = u.size(); n >= 2 && bad(u[n - 2], u[n - 1], s[i]); --n) {
      u.pop_back();
    }
    u.push_back(s[i]);
  }

  for (int i = s.size() - 3; i >= 0; i--) {
    for (int n = l.size(); n >= 2 && bad(l[n - 2], l[n - 1], s[i]); --n) {
      l.pop_back();
    }
    l.push_back(s[i]);
  }

  reverse(l.begin(), l.end());
  for (int i = u.size() - 2; i >= 1; --i) l.push_back(u[i]);

  return l;
}

Circle circumscribedCircle(const Point &a, const Point &b, const Point &c) {
  double a1, a2, b1, b2, c1, c2;
  a1 = 2 * (b.x - a.x);
  b1 = 2 * (b.y - a.y);
  c1 = a.x * a.x - b.x * b.x + a.y * a.y - b.y * b.y;
  a2 = 2 * (c.x - a.x);
  b2 = 2 * (c.y - a.y);
  c2 = a.x * a.x - c.x * c.x + a.y * a.y - c.y * c.y;
  Point p;
  p.x = (b1 * c2 - b2 * c1) / (a1 * b2 - a2 * b1);
  p.y = (c1 * a2 - c2 * a1) / (a1 * b2 - a2 * b1);

  return Circle(p, abs(p - a));
}

// https://en.wikipedia.org/wiki/Green's_theorem#Area_Calculation
double area(const Polygon &p) {
  double ans = 0;
  const int N = p.size();
  for (int i = 0; i < N; ++i) {
    Point q = p[(i + 1) % N];
    ans += (p[i].y + q.y) * (q.x - p[i].x);
  }
  ans /= 2.0;
  return fabs(ans);
}

// The points must be counter-clockwise order
bool isConvex(const Polygon &p) {
  const int N = p.size();

  for (int i = 0; i < N; ++i) {
    Point pn = p[(i + 1) % N], pnn = p[(i + 2) % N];
    int d = ccw(p[i], pn, pnn);
    if (d == CLOCKWISE) return false;
  }
  return true;
}

// Rotating calipers or Shamos's algorithm
pair<Point, Point> farthestPoints(const Polygon &p) {
  Polygon ch = convexHull(p);

  int n = ch.size();
  if (n == 2) return make_pair(ch[0], ch[1]);
  int i = 0, j = 0;
  for (int k = 0; k < n; ++k) {
    if (!(ch[i] < ch[k])) i = k;
    if (ch[j] < ch[k]) j = k;
  }

  pair<Point, Point> res;
  double d = 0;
  int si = i, sj = j;
  while (i != sj || j != si) {
    double cd = abs(ch[i] - ch[j]);
    if (cd > d) {
      d = cd;
      res = make_pair(ch[i], ch[j]);
    }

    if (cross(ch[(i + 1) % n] - ch[i], ch[(j + 1) % n] - ch[j]) < 0) {
      i = (i + 1) % n;
    } else {
      j = (j + 1) % n;
    }
  }
  return res;
}

double diameter(const Polygon &p) {
  pair<Point, Point> pts = farthestPoints(p);
  return abs(pts.first - pts.second);
}

Polygon convexCut(const Polygon &p, const Line &l) {
  const int n = p.size();
  Polygon res;

  for (int i = 0; i < n; ++i) {
    int j = (i + 1) % n;
    Segment s = Segment(p[i], p[j]);

    if (isParallel(s, l)) continue;
    Point q = crossPoint(s, l);
    if (ccw(p[i], p[j], q) != ON_SEGMENT) continue;
    if (cross(l.p2 - l.p1, s.p2 - s.p1) < EPS) continue;
    res.push_back(q);

    for (;; j = (j + 1) % n) {
      res.push_back(p[j]);
      Segment s = Segment(p[j], p[(j + 1) % n]);
      if (isParallel(s, l)) continue;

      Point q = crossPoint(Segment(p[j], p[(j + 1) % n]), l);
      if (ccw(p[j], p[(j + 1) % n], q) != ON_SEGMENT) continue;
      if (cross(l.p2 - l.p1, s.p2 - s.p1) > -EPS) continue;
      res.push_back(q);
      return res;
    }
  }

  // no intersection
  if (ccw(l.p1, l.p2, p[0]) == COUNTER_CLOCKWISE) return p;
  return res;
}

int main() {
  int n;
  cin >> n;
  Polygon p(n);
  rep(i, n) cin >> p[i];

  int q;
  cin >> q;
  rep(i, q) {
    Line l;
    cin >> l;
    printf("%.8lf\n", area(convexCut(p, l)));
  }

  return 0;
}