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>
#define REP(i,n) for (long long i=0;i<(n);i++)
using namespace std;
constexpr long loINF = 2147483647;
constexpr double eps = (1e-10);
bool eq(double a,double b){ return a>b?a-b<eps:b-a<eps; }
class Point { //位置ベクトルと作用ベクトルを同一視
public:
	double x;
	double y;
	Point(double X=0.0,double Y=0.0):x(X),y(Y){}
	Point(const Point &m):x(m.x),y(m.y) {}
	Point operator+(const Point &p){return Point(x+p.x,y+p.y);}
	Point operator-(const Point &p){return Point(x-p.x,y-p.y);}
	Point operator*(const double k){return Point(x*k,y*k);}
	Point operator/(const double k){return Point(x/k,y/k);}
	Point operator=(const Point &p){x=p.x;y=p.y;return *this;}
	Point rev() {return Point(-x,-y);}
	bool operator<(const Point &p){return x!=p.x?x<p.x:y<p.y;}
	bool operator>(const Point &p){return x!=p.x?x>p.x:y>p.y;}
	bool operator==(const Point &p){return eq(x,p.x)&&eq(y,p.y);}
	double norm(){ return x*x+y*y; }
	double abs() { return sqrt(norm());}
	double dist(const Point &a) { return (Point(x,y)-a).abs(); }
	double dot(const Point &a) { return x*a.x + y*a.y; }
	//外積 -> 2vec向き付き角度判定,平行四辺形面積
	double det(const Point &a) { return x*a.y - y*a.x; }
	bool is_parallel(const Point &a) { return eq((x*a.y - y*a.x),0); }
	// a -> this の正射影
	Point proj(const Point &a) { return Point(x,y)*(dot(a)/norm()); }
	//2ベクトルのなす角 (正 : 時計回り, 負 : 反時計)
	double ang(const Point &v) {
		double g1 = atan2(v.y,v.x);
		double g2 = atan2(y,x);
		if (g1 < 0) g1 += (2 * M_PI);
		if (g2 < 0) g2 += (2 * M_PI);
		return (g2 - g1);
	}
	//2ベクトルのなす角(正値)を出す。
	double absAng(Point &v){ 
    	return acos(dot(v)/sqrt(norm() * v.norm()));
  	}

};

class Segment {
public:
	Point p1;
	Point p2;
	Segment(double x1,double y1,double x2,double y2) : p1(x1,y1),p2(x2,y2) {}
	Segment(const Point &a,const Point &b) : p1(a),p2(b) {}
	double len (const Segment &l) { return (p2 - p1).norm(); }
	inline Point toVec() { return (p2 - p1); }
};

// 線分Xと線分Yの交点
Point intersection(Segment X,Segment Y) {
	return X.p1 + (X.p2 - X.p1) * (Y.p2 - Y.p1).det((Y.p1 - X.p1)) / (Y.p2 - Y.p1).det(X.p2 - X.p1);
}

// 線分X上に点qがあるか
bool on_seq(Segment X,Point q) {
	return (eq((X.p1 - q).det(X.p2 - q),0) && (X.p1 - q).dot(X.p2 - q) < eps);
}

// 線分Xと線分Yが交点を持つか
bool have_intersection(Segment X,Segment Y) {
	if (!(X.toVec()).is_parallel(Y.toVec())) {
		Point r = intersection(X,Y);
		return (on_seq(X,r) && on_seq(Y,r));
    }
    else return (on_seq(X,Y.p1) || on_seq(X,Y.p2) || on_seq(Y,X.p1) || on_seq(Y,X.p2));
}

// 二つの線分の位置関係
int ccw(Point a,Point b,Point c) { // aが支点
	complex<double> v1(b.x-a.x,b.y-a.y),v2(c.x-a.x,c.y-a.y);
	complex<double> v = (v2*conj(v1));
	if(v.imag()>eps)return 1;        //反時計回り
	if(v.imag()<-eps)return -1;      //時計回り
	if(v.real()<-eps)return 2;       //真逆
	if(abs(v1)+eps<abs(v2))return -2;//同じ側超えてる
	return 0;                        //同じ側近い側
}
// 線分Xと点qの距離
double distance1 (Segment X,Point q) { 
	if (eq((X.p1 - X.p2).dot(q - X.p2),0)) return X.p2.dist(q);
	if (eq((X.p2 - X.p1).dot(q - X.p1),0)) return X.p1.dist(q);
	else return (X.p1 + (X.p2-X.p1).proj(q-X.p1)).dist(q);
}

//線分Xと線分Yの距離
double distance2 (Segment X,Segment Y) { 
	if (have_intersection(X,Y)) return 0.0;
	else return min({distance1(X,Y.p1),distance1(X,Y.p2),distance1(Y,X.p1),distance1(Y,X.p2)});
}

//点列をx座標で昇順ソート
inline void sort_x(vector<Point> &p) { 
	struct comp { bool operator() (const Point &a,const Point &b) {return (a.x!=b.x?a.x<b.x:a.y<b.y);} };
	sort(p.begin(),p.end(),comp());
}

//点列をy座標で昇順ソート
inline void sort_y(vector<Point> &p) { 
	struct comp { bool operator() (const Point &a,const Point &b) {return (a.y!=b.y?a.y<b.y:a.x<b.x);} };
	sort(p.begin(),p.end(),comp());
}

//多角形の面積 (point列は順番になっていること)
double getArea(vector<Point> &point){
	double s = 0;
	int n = point.size();
	for (int i = 0;i < n;i++ ) s += point[i%n].det(point[(i+1)%n]);
	return abs(s) * 0.5;
}

//0: outside, 1: on line, 2: inside (Winding Number)
int contains(const vector<Point> &point, Point p) {
    int flg = -1;
    Point _a, _b = point.back();
    for (int i = 0; i < int(point.size()); i++) {
        _a = _b; _b = point[i];
        Point a = _a, b = _b;
        if (ccw(a, b, p) == 0) return 1;
        if (a.y > b.y) swap(a, b);
        if (!(a.y <= p.y && p.y < b.y)) continue;
        // (a-p).det(b-p) > eps) : 線の内側
        if (eq(a.y,p.y) ? (a.x > p.x):((a-p).det(b-p) > eps)) flg *= -1;
    }
    return flg + 1;
}

//凸包(グラハムスキャン)
vector<Point> convexHull(vector<Point> &point){
	int n = point.size(),k = 0;
	vector<Point> qs(n*2);
	sort_x(point);
	for(int i = 0;i < n;i++){ //下側凸包の作成
		while(k > 1 && (qs[k-1] - qs[k-2]).det(point[i] - qs[k-1]) < (-eps)) k--;
		// 平行な点を削除 -> while(k > 1 && (qs[k-1] - qs[k-2]).det(point[i] - qs[k-1]) < (eps)) k--;
		qs[k++] = point[i];
	}
	for(int i = n - 2, t = k; i >= 0; i--){ //上側凸包の作成
		while(k > t && (qs[k-1] - qs[k-2]).det(point[i] - qs[k-1]) <= (-eps)) k--;
		// 平行な点を削除 -> while(k > t && (qs[k-1] - qs[k-2]).det(point[i] - qs[k-1]) <= (eps)) k--;
		qs[k++] = point[i];
	}
	qs.resize(k-1);
	return qs;
}

//最遠頂点対間距離 (pはConvex)
double diameter(vector<Point> &p) {
    int n = int(p.size());
    int x = 0, y = 0;
    for (int i = 1; i < n; i++) {
        if (p[i] < p[x]) x = i;
        if (p[y] < p[i]) y = i;
    }
    double ans = 0;
    int sx = x, sy = y;
    while (sx != y || sy != x) {
        ans = max(ans, (p[x]).dist(p[y]));
        int nx = ((x+1) % n),ny = ((y+1)%n);
        if ((p[nx] - p[x]).det(p[ny] - p[y]) < 0.0) x = nx;
        else y = ny;
    }
    return ans;
}

vector<Point> convex_cut(vector<Point> &p,Segment &l) {
    if (!p.size()) return vector<Point>{};
    int n = int(p.size());
    vector<Point> q;
    Point a, b = p.back();
    for (int i = 0; i < n; i++) {
        a = b; b = p[i];
        if ((ccw(l.p1,l.p2, a)%2)*(ccw(l.p1,l.p2, b)%2) < 0) {
            q.push_back(intersection(Segment(a,b),l));
        }
        if (ccw(l.p1,l.p2,b) != -1) q.push_back(b);
    }
    return q;
}

int main(void){
	 cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(20) << fixed;
 
    int n;
    cin >> n;
    vector<Point> p(n);
    for (int i = 0; i < n; i++) {
        double x, y;
        cin >> x >> y;
        p[i] = Point(x, y);
    }
    int q;
    cin >> q;
    for (int ph = 0; ph < q; ph++) {
        double x, y, w, s;
        cin >> x >> y >> w >> s;
       	Segment l(x,y,w,s);
       	vector<Point> a = convex_cut(p,l);
        cout <<	getArea(a) << endl;
    }
 
    return 0;
}