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 pu push
#define pb push_back
#define mp make_pair
#define eps 1e-9
#define Vector Point
#define INF 2000000000
#define DOUBLE_INF 1e50
#define sq(x) ((x)*(x))
#define fi first
#define sec second
#define all(x) (x).begin(),(x).end()
#define EQ(a,b) (abs((a)-(b))<eps)

// Geometry Library
// written by okuraofvegetable

inline double add(double a,double b){
	if(abs(a+b)<eps*(abs(a)+abs(b)))return 0;
	return a+b;
}

struct Point{
	double x,y;
	Point() {}
	Point(double x,double y) : x(x),y(y){}
	Point operator + (Point p){return Point(add(x,p.x),add(y,p.y));}
	Point operator - (Point p){return Point(add(x,-p.x),add(y,-p.y));}
	Point operator * (double d){return Point(x*d,y*d);}
	double dot(Point p){return add(x*p.x,y*p.y);}
	double det(Point p){return add(x*p.y,-y*p.x);}
	double norm(){return sqrt(x*x+y*y);}
	double norm2(){return x*x+y*y;}
	double dist(Point p){return ((*this)-p).norm();}
	double dist2(Point p){return sq(x-p.x)+sq(y-p.y);}
	Point vert(){return Point(y,-x);}
	void dump(const char* msg=""){printf("%s%.12f %.12f\n",msg,x,y);return;}
	
	// following functions for vector operation

	// signed area of triange (0,0) (x,y) (p.x,p.y)
	double area(Point p){
		return (x*p.y-p.x*y)/2.0;
	}
};
// direction a -> b -> c
// verified AOJ CGL_1_C
enum {COUNTER_CLOCKWISE,
		CLOCKWISE,
		ONLINE_BACK,
		ONLINE_FRONT,
		ON_SEGMENT};
int ccw(Point a,Point b,Point c){
	Vector p = b-a;
	Vector q = c-a;
	if(p.det(q)>0.0)return COUNTER_CLOCKWISE; // counter clockwise
	if(p.det(q)<0.0)return CLOCKWISE; // clockwise
	if(p.dot(q)<0.0)return ONLINE_BACK; // c--a--b online_back
	if(p.norm()<q.norm())return ONLINE_FRONT; // a--b--c online_front 
	return ON_SEGMENT;// a--c--b on_segment
}
struct Line{
	Point a,b;
	Line(){}
	Line(Point a,Point b):a(a),b(b){}
	bool on(Point q){
		return (a-q).det(b-q)==0; 
	}
	// folloing 2 functions verified AOJ CGL_2_A
	bool is_parallel(Line l){return (a-b).det(l.a-l.b)==0;}
	bool is_orthogonal(Line l){return (a-b).dot(l.a-l.b)==0;}
	Point intersection(Line l){
		assert(!is_parallel(l));
		return a+(b-a)*((l.b-l.a).det(l.a-a)/(l.b-l.a).det(b-a));
	}
	// projection of p to this line
	// verified AOJ CGL_1_A
	Point projection(Point p){
		return (b-a)*((b-a).dot(p-a)/(b-a).norm2())+a;
	}
	// reflection point of p onto this line
	// verified AOJ CGL_1_B
	Point refl(Point p){
		Point proj = projection(p);
		return p+((proj-p)*2.0);
	}
};
struct Segment{
	Point a,b;
	Segment(){}
	Segment(Point a,Point b):a(a),b(b){}
	Line line(){
		return Line(a,b);
	}
	bool on(Point q){
		return ((a-q).det(b-q)==0&&(a-q).dot(b-q)<=0); 
	}
	// verified AOJ CGL_2_B
	bool is_intersect(Segment s){
		if(line().is_parallel(s.line())){
			if(on(s.a)||on(s.b))return true;
			if(s.on(a)||s.on(b))return true;
			return false;
		}
		Point p = line().intersection(s.line());
		if(on(p)&&s.on(p))return true;
		else return false;
	}
	bool is_intersect(Line l){
		if(line().is_parallel(l)){
			if(l.on(a)||l.on(b))return true;
			else return false;
		}
		Point p = line().intersection(l);
		if(on(p))return true;
		else return false;
	}
	// following 2 distance functions verified AOJ CGL_2_D
	double distance(Point p){
		double res = DOUBLE_INF;
		Point q = line().projection(p);
		if(on(q))res = min(res,p.dist(q));
		res = min(res,min(p.dist(a),p.dist(b)));
		return res;
	}
	double distance(Segment s){
		if(is_intersect(s))return 0.0;
		double res = DOUBLE_INF;
		res = min(res,s.distance(a));
		res = min(res,s.distance(b));
		res = min(res,this->distance(s.a));
		res = min(res,this->distance(s.b));
		return res;
	}
};

// Polygon 

typedef vector<Point> Polygon;
// verified AOJ CGL_3_A
// Polygon don't need to be convex
double area(Polygon& pol){
	vector<Point> vec;
	double res = 0.0;
	int M = pol.size();
	for(int i=0;i<M;i++){
		res += (pol[i]-pol[0]).area(pol[(i+1)%M]-pol[0]);	
	}
	return res;
}
bool is_convex(Polygon& pol){
	int n = pol.size();
	for(int i=0;i<n-1;i++){
		if(ccw(pol[i],pol[i+1],pol[(i+2)%n])==CLOCKWISE){
			return false;
		}
	}
	return true;
}
// vecrified AOJ CGL_3_C
enum {OUT,ON,IN};
int contained(Polygon& pol,Point p){
	int n = pol.size();
	Point outer(1e9,p.y);
	Segment s = Segment(outer,p);
	int cnt = 0;
	for(int i=0;i<n;i++){
		Segment e = Segment(pol[i],pol[(i+1)%n]);
		if(e.on(p))return ON;
		Vector a = pol[i]-p;
		Vector b = pol[(i+1)%n]-p;
		if(a.y>b.y)swap(a,b);
		if(a.y<=0.0&&b.y>0.0){
			if(a.det(b)<0.0)cnt++;
		}
	}
	if((cnt&1)==1)return IN;
	else return OUT;
}
// compare function for convex_hull
// sort points by (x-y) lexicographical order.
// you can change (y-x) order with no change in convex_hull
bool comp(const Point& p,const Point& q){
	if(p.x!=q.x)return p.x<q.x;
	else return p.y<q.y;
}
// Convex hull
// if you want not to contain points on boundary,
// change while(....<=0.0)
// verified AOJ CGL_4_A
Polygon convex_hull(vector<Point> ps){
	sort(all(ps),comp);
	int k = 0;
	int n = ps.size();
	Polygon qs(2*n);
	for(int i=0;i<n;i++){
		while(k>1&&(qs[k-1]-qs[k-2]).det(ps[i]-qs[k-1])<0.0)k--;
		qs[k++]=ps[i];
	}
	for(int i=n-2,t=k;i>=0;i--){
		while(k>t&&(qs[k-1]-qs[k-2]).det(ps[i]-qs[k-1])<0.0)k--;
		qs[k++]=ps[i];
	}
	qs.resize(k-1);
	return qs;
}
// Caliper method
// verified AOJ CGL_4_B
double convex_diameter(Polygon& cv){
	int i=0,j=0;
	int n = cv.size();
	for(int k=0;k<n;k++){
		if(!comp(cv[i],cv[k]))i=k;
		if(comp(cv[j],cv[k]))j=k;
	}
	int si=i,sj=j;
	double res = 0.0;
	while(i!=sj||j!=si){
		res = max(res,cv[i].dist(cv[j]));
		if((cv[(i+1)%n]-cv[i]).det(cv[(j+1)%n]-cv[j])<0.0)i=(i+1)%n;
		else j=(j+1)%n;
	}
	return res;
}
// Cut conovex polygon by a line and return left polygon
Polygon convex_cut(Polygon& cv,Line l){
	int n = cv.size();
	Polygon left; 
	for(int i=0;i<n;i++){
		Segment e = Segment(cv[i],cv[(i+1)%n]);
		if(ccw(l.a,l.b,cv[i])!=CLOCKWISE)left.pb(cv[i]);
		if(e.is_intersect(l)){
			if(!e.line().is_parallel(l)){
				left.pb(e.line().intersection(l));
			}
		}
	}
	return left;
}
// for input
Point input_point(){
	Point p;
	cin >> p.x >> p.y;
	return p;
}
Segment input_segment(){
	Point a,b;
	a = input_point();
	b = input_point();
	return Segment(a,b);
}
Line input_line(){
	Point a,b;
	a = input_point();
	b = input_point();
	return Line(a,b);
}

int main(){
	int n;
	cin >> n;
	vector<Point> pol;
	for(int i=0;i<n;i++){
		pol.pb(input_point());
	}
	int q;
	cin >> q;
	for(int i=0;i<q;i++){
		Line l = input_line();
		Polygon cvl = convex_cut(pol,l);
		cout << setprecision(30) << area(cvl) << endl;
	}
	return 0;
}