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:
//
// 凸多角形の切断
//
// verified:
//   AOJ Course CGL_4_C Convex Polygon - Convex Cut
//     http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_C&lang=jp
//

/*
    問題例
    ・AOJ 2385
    ・AOJ 2160
*/


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


using DD = double;
const DD INF = 1LL<<60;      // to be set appropriately
const DD EPS = 1e-10;        // to be set appropriately
const DD PI = acos(-1.0);
DD torad(int deg) {return (DD)(deg) * PI / 180;}
DD todeg(DD ang) {return ang * 180 / PI;}

/* Point */
struct Point {
    DD x, y;
    Point(DD x = 0.0, DD y = 0.0) : x(x), y(y) {}
    friend ostream& operator << (ostream &s, const Point &p) {return s << '(' << p.x << ", " << p.y << ')';}
};
inline Point operator + (const Point &p, const Point &q) {return Point(p.x + q.x, p.y + q.y);}
inline Point operator - (const Point &p, const Point &q) {return Point(p.x - q.x, p.y - q.y);}
inline Point operator * (const Point &p, DD a) {return Point(p.x * a, p.y * a);}
inline Point operator * (DD a, const Point &p) {return Point(a * p.x, a * p.y);}
inline Point operator * (const Point &p, const Point &q) {return Point(p.x * q.x - p.y * q.y, p.x * q.y + p.y * q.x);}
inline Point operator / (const Point &p, DD a) {return Point(p.x / a, p.y / a);}
inline Point conj(const Point &p) {return Point(p.x, -p.y);}
inline Point rot(const Point &p, DD ang) {return Point(cos(ang) * p.x - sin(ang) * p.y, sin(ang) * p.x + cos(ang) * p.y);}
inline Point rot90(const Point &p) {return Point(-p.y, p.x);}
inline DD cross(const Point &p, const Point &q) {return p.x * q.y - p.y * q.x;}
inline DD dot(const Point &p, const Point &q) {return p.x * q.x + p.y * q.y;}
inline DD norm(const Point &p) {return dot(p, p);}
inline DD abs(const Point &p) {return sqrt(dot(p, p));}
inline DD amp(const Point &p) {DD res = atan2(p.y, p.x); if (res < 0) res += PI*2; return res;}
inline bool eq(const Point &p, const Point &q) {return abs(p - q) < EPS;}
inline bool operator < (const Point &p, const Point &q) {return (abs(p.x - q.x) > EPS ? p.x < q.x : p.y < q.y);}
inline bool operator > (const Point &p, const Point &q) {return (abs(p.x - q.x) > EPS ? p.x > q.x : p.y > q.y);}
inline Point operator / (const Point &p, const Point &q) {return p * conj(q) / norm(q);}

/* Line */
struct Line : vector<Point> {
    Line(Point a = Point(0.0, 0.0), Point b = Point(0.0, 0.0)) {
        this->push_back(a);
        this->push_back(b);
    }
    friend ostream& operator << (ostream &s, const Line &l) {return s << '{' << l[0] << ", " << l[1] << '}';}
};

/* Circle */
struct Circle : Point {
    DD r;
    Circle(Point p = Point(0.0, 0.0), DD r = 0.0) : Point(p), r(r) {}
    friend ostream& operator << (ostream &s, const Circle &c) {return s << '(' << c.x << ", " << c.y << ", " << c.r << ')';}
};


///////////////////////
// 多角形
///////////////////////

// 多角形の面積
DD Area(const vector<Point> &pol) {
    DD res = 0.0;
    for (int i = 0; i < pol.size(); ++i) {
        res += cross(pol[i], pol[(i+1)%pol.size()]);
    }
    return res/2.0L;
}

// convex cut
int ccw_for_convexcut(const Point &a, const Point &b, const Point &c) {
    if (cross(b-a, c-a) > EPS) return 1;
    if (cross(b-a, c-a) < -EPS) return -1;
    if (dot(b-a, c-a) < 0) return 2;
    if (norm(b-a) < norm(c-a)) return -2;
    return 0;
}
vector<Point> crosspoint_for_convexcut(const Line &l, const Line &m) {
    vector<Point> res;
    DD d = cross(m[1] - m[0], l[1] - l[0]);
    if (abs(d) < EPS) return vector<Point>();
    res.push_back(l[0] + (l[1] - l[0]) * cross(m[1] - m[0], m[1] - l[0]) / d);
    return res;
}
vector<Point> ConvexCut(const vector<Point> &pol, const Line &l) {
    vector<Point> res;
    for (int i = 0; i < pol.size(); ++i) {
        Point p = pol[i], q = pol[(i+1)%pol.size()];
        if (ccw_for_convexcut(l[0], l[1], p) != -1) {
            if (res.size() == 0) res.push_back(p);
            else if (!eq(p, res[res.size()-1])) res.push_back(p);
        }
        if (ccw_for_convexcut(l[0], l[1], p) * ccw_for_convexcut(l[0], l[1], q) < 0) {
            vector<Point> temp = crosspoint_for_convexcut(Line(p, q), l);
            if (temp.size() == 0) continue;
            else if (res.size() == 0) res.push_back(temp[0]);
            else if (!eq(temp[0], res[res.size()-1])) res.push_back(temp[0]);
        }
    }
    return res;
}

// Voronoi-diagram
Line bisector(const Point &p, const Point &q) {
    Point c = (p + q) / 2.0L;
    Point v = (q - p) * Point(0.0L, 1.0L);
    v = v / abs(v);
    return Line(c - v, c + v);
}
vector<Point> Voronoi(vector<Point> pol, const vector<Point> &ps, int ind) {
    for (int i = 0; i < ps.size(); ++i) {
        if (i == ind) continue;
        Line l = bisector(ps[ind], ps[i]);
        pol = ConvexCut(pol, l);
    }
    return pol;
}



int main() {
    int n; cin >> n;
    vector<Point> pol(n);
    for (int i = 0; i < n; ++i) cin >> pol[i].x >> pol[i].y;
    int Q; cin >> Q;
    for (int _ = 0; _ < Q; ++_) {
        Point x, y; cin >> x.x >> x.y >> y.x >> y.y;
        Line l(x, y);
        auto cutted = ConvexCut(pol, l);
        cout << fixed << setprecision(10) << Area(cutted) << endl;
    }
}