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 <complex>
#include <cmath>
#include <algorithm>
#include <vector>

template <class T>
inline T sq(T x) { return x * x; }

using Real = long double;
using Point = std::complex<Real>;
using Segment = std::pair<Point, Point>;
using Polygon = std::vector<Point>;

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

const Real EPS = 1e-10;
const Point origin(0, 0);

// 宇宙船演算子
inline Real compare(Real a, Real b) {
    if (std::abs(a - b) < EPS) return 0;
    return a - b > 0 ? 1 : -1;
}

inline Real dist(Point a, Point b) {
    return std::abs(a - b);
}

inline Real length(Segment s) {
    return dist(s.first, s.second);
}

// inner product
inline Real dot(Point x, Point y) {
    return std::real(std::conj(x) * (y));
}

// outer product
inline Real cross(Point x, Point y) {
    return std::imag(std::conj(x) * (y));
}

// lに対するxの正射影
Point proj(Segment s, Point p) {
    Real ratio = dot(s.second - s.first, p - s.first) / sq(length(s));
    return s.first + (s.second - s.first) * ratio;
}

// lを軸としてxに対称な点
Point refl(Segment s, Point p) {
    Point t = proj(s, p);
    return t + (t - p);
}

// lに対するpの位置
// 0: on segment
// 1: counter clockwise  -1: clockwise
// 2: online front       -2: online back
int side(Segment s, Point p) {
    Real c = cross(s.second - s.first, p - s.first);
    if (compare(c, 0) != 0) return compare(c, 0);

    Real d = dot(s.second - s.first, p - s.first);
    if (compare(d, 0) < 0) return -2;

    return (compare(length(Segment(s.first, p)), length(s)) > 0 ? 2 : 0);
}

inline bool isorthogonal(Segment s1, Segment s2) {
    return compare(dot(s1.second - s1.first, s2.second - s2.first), 0) == 0;
}

inline bool isparallel(Segment s1, Segment s2) {
    return compare(cross(s1.second - s1.first, s2.second - s2.first), 0) == 0;
}

inline bool intersect(Segment s1, Segment s2) {
    return (side(s1, s2.first) * side(s1, s2.second) <= 0) &&
           (side(s2, s1.first) * side(s2, s1.second) <= 0);
}

Point intersection(Segment s1, Segment s2) {
    Real c1 = cross(s2.second - s2.first, s1.second - s1.first);
    Real c2 = cross(s2.second - s2.first, s1.first - s2.first);
    return s1.first + (s1.second - s1.first) * (-c2 / c1);
}

// distanceのオーバーロード
Real dist(Segment s, Point p) {
    Point t = proj(s, p);
    if (side(s, t) == 0) return dist(p, t);
    return std::min(dist(p, s.first), dist(p, s.second));
}

Real dist(Segment s1, Segment s2) {
    if (intersect(s1, s2)) return 0;
    return std::min({dist(s1, s2.first),
                     dist(s1, s2.second),
                     dist(s2, s1.first),
                     dist(s2, s1.second)});
}

// signed area
inline Real triangle(Point a, Point b, Point c) {
    return cross(b - a, c - a) / 2;
}

Real area(const Polygon& g) {
    Real S = 0;
    for (int i = 0; i < g.size(); ++i) {
        S += triangle(origin, g[i], g[(i + 1) % g.size()]);
    }
    return S;
}

bool isconvex(const Polygon& g) {
    for (int i = 0; i < g.size(); ++i) {
        if (side(Segment(g[i], g[(i + 1) % g.size()]),
                 g[(i + 2) % g.size()]) == -1) return false;
    }
    return true;
}

// 0: out  1: on  2: in
int contain(const Polygon& g, Point p) {
    bool in = false;
    for (int i = 0; i < g.size(); ++i) {
        if (side(Segment(g[i], g[(i + 1) % g.size()]), p) == 0) return 1;

        Point a = g[i] - p, b = g[(i + 1) % g.size()] - p;
        if (compare(a.imag(), b.imag()) > 0) std::swap(a, b);
        if (compare(a.imag(), 0) <= 0 &&
            compare(b.imag(), 0) > 0 &&
            compare(cross(a, b), 0) < 0) in = !in;
    }
    return in ? 2 : 0;
}

// linearok: 同一直線上の頂点を取るか
Polygon convexhull(Polygon& g, bool linearok) {
    std::sort(g.begin(), g.end());
    int N = g.size();

    Polygon ret(N * 2);
    int k = 0;
    for (int i = 0; i < N; ++i) {
        while (k >= 2 &&
               compare(cross(ret[k - 1] - ret[k - 2], g[i] - ret[k - 2]), 0) < !linearok) --k;
        // linearokならcross = 0も回収する
        ret[k++] = g[i];
    }
    int t = k + 1;
    for (int i = N - 2; i >= 0; --i) {
        while (k >= t &&
               compare(cross(ret[k - 1] - ret[k - 2], g[i] - ret[k - 2]), 0) < !linearok) --k;
        ret[k++] = g[i];
    }

    // 先頭が被っているので除く
    ret.resize(k - 1);
    return ret;
}

Real diameter(const Polygon& g) {
    Real ret = 0;
    int j = 0;
    for (int i = 0; i < g.size(); ++i) {
        while (j < g.size() - 1 &&
               compare(dist(g[i], g[j + 1]), dist(g[i], g[j])) > 0) ++j;
        ret = std::max(ret, dist(g[i], g[j]));
    }
    return ret;
}


#include <iostream>
#include <iomanip>

using namespace std;

int main() {
    cout << fixed << setprecision(10);

    int N;
    cin >> N;

    Polygon g(N);
    for (auto& p : g) {
        Real x, y;
        cin >> x >> y;
        p = Point(x, y);
    }

    int Q;
    cin >> Q;
    for (int q = 0; q < Q; ++q) {
        Real x1, y1, x2, y2;
        cin >> x1 >> y1 >> x2 >> y2;
        Segment s(Point(x1, y1), Point(x2, y2));

        Polygon cut;
        for (int i = 0; i < N; ++i) {
            if (side(s, g[i]) != -1) {
                cut.push_back(g[i]);
            }

            Segment t(g[i], g[(i + 1) % N]);
            if (!isparallel(s, t)) {
                cut.push_back(intersection(s, t));
            }
        }

        cout << area(cut) << endl;
    }
    return 0;
}