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;

using CP = complex<long double>;
#define X real()
#define Y imag()
const long double PI = acos(-1.0L);
const long double EPS = 1e-10;
// conj(x) : complex conjugate,(0,1)->(0,-1)
// abs(x) : dist between(0,0) and x
// norm(x) : abs(x) * abs(x)
// arg(x) : argment,[-PI,PI]

// dot(a,b) = |a||b|cos x
long double dot(CP a, CP b) { return (conj(a) * b).X; }
// cross(a,b) : area of parallelogram
// sign : a-> b ,counter clockwise? + : -
long double cross(CP a, CP b) { return (conj(a) * b).Y; }
long double corner(CP a, CP b) {
  //[0,PI]
  return acos(dot(a, b) / (abs(a) * abs(b)));
}

CP projection(CP p, CP s, CP t) {
  CP base = t - s;
  long double r = dot(p - s, base) / norm(base);
  return s + base * r;
}

CP reflection(CP p, CP s, CP t) {
  CP tmp = (projection(p, s, t) - p);
  tmp *= 2;
  return p + tmp;
}

CP intersectionLL(CP a, CP b, CP c, CP d) {
  return a + (b - a) * (cross(d - c, c - a) /
                        cross(d - c, b - a));
}

bool on_seg(CP a, CP b, CP p) {
  // if not use end point, dot(a - p, b - p) < 0
  return abs(cross(a - p, b - p)) <= 1e-10 &&
         dot(a - p, b - p) <= 0;
}

// crossing lines? (a,b) and (c,d)
bool iscross(CP a, CP b, CP c, CP d) {
  // parallel
  if(abs(cross(a - b, c - d)) <= 1e-10) {
    return on_seg(a, b, c) || on_seg(a, b, d) ||
           on_seg(c, d, a) || on_seg(c, d, b);
  }
  CP isp = intersectionLL(a, b, c, d);
  return on_seg(a, b, isp) && on_seg(c, d, isp);
}

long double distLP(CP a, CP b, CP p) {
  return abs(cross(b - a, p - a) / abs(b - a));
}

// segmentver.
long double distSP(CP a, CP b, CP p) {
  if(dot(b - a, p - a) < 0) return abs(p - a);
  if(dot(a - b, p - b) < 0) return abs(p - b);
  return distLP(a, b, p);
}

// segment and segment
long double distSS(CP a, CP b, CP c, CP d) {
  long double res = 1e18;
  if(iscross(a, b, c, d)) return 0.0L;
  res = min(res, distSP(a, b, c));
  res = min(res, distSP(a, b, d));
  res = min(res, distSP(c, d, a));
  res = min(res, distSP(c, d, b));
  return res;
}

// counter clockwise
bool is_convex(const vector<CP> &v) {
  int n = v.size();
  for(int i = 0; i < n; ++i)
    if(cross(v[(i + 1) % n] - v[i],
             v[(i + 2) % n] - v[(i + 1) % n]) < -EPS)
      return 0;
  return 1;
}

vector<CP> convex_hull(vector<CP> &ps) {
  auto lmd = [&](const CP &l, const CP &r) {
    if(l.X != r.X) return l.X < r.X;
    return l.Y < r.Y;
  };
  vector<CP> qs;
  int psize = ps.size();
  sort(ps.begin(), ps.end(), lmd);
  int k = 0;
  qs.resize(psize * 2);
  for(int i = 0; i < psize; ++i) {
    while(k > 1 && cross(qs[k - 1] - qs[k - 2],
                         ps[i] - qs[k - 1]) <= 0)
      --k;
    qs[k++] = ps[i];
  }
  for(int i = psize - 2, t = k; i >= 0; --i) {
    while(k > t && cross(qs[k - 1] - qs[k - 2],
                         ps[i] - qs[k - 1]) <= 0)
      --k;
    qs[k++] = ps[i];
  }
  qs.resize(k - 1);
  return qs;
}

long double convex_diameter(vector<CP> &newv) {
  vector<CP> v = convex_hull(newv);
  int n = v.size(), i = 0, j = 0;
  if(n == 2) return abs(v[0] - v[1]);
  for(int k = 0; k < n; ++k) {
    if(v[k].X < v[i].X) i = k;
    if(v[k].X > v[j].X) j = k;
  }
  long double res = 0;
  int si = i, sj = j;
  while(i != sj || j != si) {
    res = max(res, abs(v[i] - v[j]));
    if(cross(v[(i + 1) % n] - v[i], v[(j + 1) % n] - v[j]) <
       0)
      (++i) %= n;
    else
      (++j) %= n;
  }
  return res;
}

vector<CP> convex_cut(const vector<CP> &v, const CP &s,
                      const CP &t) {
  vector<CP> res;
  int n = v.size();
  for(int i = 0; i < n; ++i) {
    CP nows = v[i], nowt = v[(i + 1) % n];
    if(cross(t - s, nows - s) >= -EPS) res.push_back(nows);
    if(cross(t - s, nows - s) * cross(t - s, nowt - s) < 0)
      res.push_back(intersectionLL(s, t, nows, nowt));
  }
  return res;
}

struct Circle {
  CP o;
  long double r;
  Circle(long double _x = 0.0L, long double _y = 0.0L,
         long double _r = 0.0L)
      : o(CP(_x, _y)), r(_r) {}
};

void intersectionCL(Circle ci, CP s, CP t, CP &res1,
                    CP &res2) {
  res1 = res2 = projection(ci.o, s, t);
  long double r = sqrtl(ci.r * ci.r - norm(res1 - ci.o));
  t -= s;
  t *= r / abs(t);
  res1 += t;
  res2 -= t;
  if(res1.X > res2.X ||
     (res1.X == res2.X && res1.Y > res2.Y))
    swap(res1, res2);
}

long double polygonarea(const vector<CP> &v) {
  int n = v.size();
  long double res = 0;
  for(int i = 0; i < n; ++i)
    res +=
        (v[(i - 1 + n) % n].X - v[(i + 1) % n].X) * v[i].Y;
  return res / 2.0L;
}

long long n, q;
vector<CP> v;

int main() {
  cout << fixed << setprecision(10);
  cin >> n;
  for(int i = 0; i < n; ++i) {
    long long a, b;
    cin >> a >> b;
    v.emplace_back(a, b);
  }
  cin >> q;
  while(q--) {
    long long a, b, c, d;
    cin >> a >> b >> c >> d;
    cout << polygonarea(convex_cut(v, CP(a, b), CP(c, d)))
         << endl;
  }
  return 0;
}