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:
bool debug=false;
#include <stdio.h>
#include <math.h>
#include <vector>
#include <algorithm>
using namespace std;
#define PB push_back
const double eps=1e-9;
const double INF=1e9;
double ABS(double n){return n>=0?n:-n;}
int dcmp(double n){return ABS(n)<eps?0:n>0?1:-1;}
double min(double a,double b){return a>b?b:a;}
double max(double a,double b){return a>b?a:b;}
bool same(double a,double b){return ABS(a-b)<eps;}
struct point{
	double x;
	double y;
	point(){}
	point(const double a,const double b){x=a;y=b;}
	point(const point &p){x=p.x;y=p.y;}
	point operator +(const point &a){return point(x+a.x,y+a.y);}
	point operator -(const point &a){return point(x-a.x,y-a.y);}
	point operator *(const double &a){return point(x*a,y*a);}
	point operator /(const double &a){return point(x/a,y/a);}
	void operator =(const point &a){x=a.x;y=a.y;}
	void operator +=(const point &a){x+=a.x;y+=a.y;}
	void operator -=(const point &a){x-=a.x;y-=a.y;}
	void operator *=(const double &a){x*=a;y*=a;}
	void operator /=(const double &a){x/=a;y/=a;}
	double length(){return sqrt(x*x+y*y);}
	void in(){scanf("%lf%lf",&x,&y);}
	void out(){printf("(%.3lf,%.3lf)",x,y);}
};
bool operator <(const point &a,const point &b){return a.x-b.x<-eps||(ABS(a.x-b.x)<eps&&a.y-b.y<-eps);}
struct segment{
	point a;
	point b;
	segment(){}
	segment(point x,point y){a=x;b=y;}
	void out(){
		printf("segment::");
		a.out();
		b.out();
		printf("\n");
		return ;
	}
};
struct line{
	double A;
	double B;
	double C;
	void pull(){
		if(ABS(A)<eps){
			A/=B;
			C/=B;
			B/=B;
		}
		else{
			B/=A;
			C/=A;
			A/=A;
		}
		return ;
	}
	line(){}
	line(double a,double b,double c){A=a;B=b;C=c;pull();}
	line(point a,point b){
		A=a.y-b.y;
		B=b.x-a.x;
		C=A*a.x+B*a.y;
		pull();
	}
	line(double a,double b,point p){
		A=a;
		B=b;
		C=A*p.x+B*p.y;
		pull();
	}
	line(segment s){
		A=s.a.y-s.b.y;
		B=s.b.x-s.a.x;
		C=A*s.a.x+B*s.a.y;
		pull();
	}
	void out(){
		printf("line:: A=%.3lf B=%.3lf C=%.3lf\n",A,B,C);
		return ;
	}
};
double distance(point a,point b){return (a-b).length();}
double dot(point a,point b){return a.x*b.x+a.y*b.y;}
double cross(point a,point b){return a.x*b.y-b.x*a.y;}
//angle only returns positive value
double angle(point a,point b){return acos(dot(a,b)/(a.length()*b.length()));}
double area(point a,point b,point c){return ABS(cross(b-a,c-a));}
double distance(point a,line b){return (b.A*a.x+b.B*a.y-b.C)/sqrt(b.A*b.A+b.B*b.B);}
point arbitrary_point(line l){
	if(ABS(l.A)<=eps)return point(0,l.C/l.B);
	else return point(l.C/l.A,0);
}
bool between(point a,point b,point c){
	if((a.x-b.x<=eps&&b.x-c.x<=eps)||(eps>=b.x-a.x&&eps>=c.x-b.x))
	if((a.y-b.y<=eps&&b.y-c.y<=eps)||(eps>=b.y-a.y&&eps>=c.y-b.y))
	return true;
	return false;
}
point intersect(line a,line b){
	double x,y,det;
	x=(a.C*b.B-b.C*a.B);
	y=(a.A*b.C-b.A*a.C);
	det=(a.A*b.B-b.A*a.B);
	return point(x,y)/det;
}
bool parallel(line a,line b){return same(a.A*b.B,b.A*a.B);}
double distance(line a,line b){
	if(parallel(a,b))return distance(arbitrary_point(a),b);
	else return 0;
}
double distance(point p,segment s){
	line l(s);
	point a(intersect(line(l.B,-l.A,l.B*p.x-l.A*p.y),l));
	if(between(s.a,a,s.b))return distance(p,a);
	else return min(distance(p,s.a),distance(p,s.b));
}
double distance(segment a,segment b){
	point l(a.a),lm,rm,r(a.b);
	for(int i=0;i<100;i++){
		lm=(l*2+r)/3;
		rm=(l+r*2)/3;
		if(distance(lm,b)>distance(rm,b))l=lm;
		else r=rm;
	}
	return distance(l,b);
}
bool same(line a,line b){return parallel(a,b)&&ABS(distance(a,b))<=eps;}
bool vertical(line a,line b){return ABS(a.A*b.A+a.B*b.B)<=eps;}
bool hasintersect(segment a,segment b){
	line l(a),r(b);
	if(parallel(l,r)){
		if(same(l,r))return between(a.a,b.a,a.b)||between(a.a,b.b,a.b)||between(b.a,a.a,b.b)||between(b.a,a.b,b.b);
		else return false;
	}
	else{
		point p(intersect(l,r));
		return between(a.a,p,a.b)&&between(b.a,p,b.b);
	}
}
bool hasintersect(segment a,line b){
	line l(a);
	if(parallel(l,b))return same(l,b);
	else return between(a.a,intersect(l,b),a.b);
}
point intersect(segment a,segment b){return intersect(line(a),line(b));}
point intersect(segment a,line b){return intersect(line(a),b);}
point projection(point a,line b){return intersect(line(b.B,-b.A,a),b);}
point reflection(point a,line b){return projection(a,b)*2-a;}
bool online(point p,line l){return ABS(l.A*p.x+l.B*p.y-l.C)<eps;}
bool onsegment(point p,segment s){return online(p,line(s))&&between(s.a,p,s.b);}
double area(vector<point> v){
	if(v.size()<=2)return 0;
	double ans=0;
	int n=(int)v.size();
	for(int i=1;i<n;i++)ans+=cross(v[i],v[i-1]);
	ans+=cross(v[0],v[n-1]);
	return ABS(ans)/2;
}
bool isconvex(vector<point> v){
	bool f=true;
	int n=(int)v.size();
	for(int i=0;i<n;i++)if(cross(v[i+1]-v[i],v[i+2]-v[i])<-eps){
		f=false;
		break;
	}
	if(f)return true;
	f=true;
	reverse(v.begin(),v.end());
	for(int i=0;i<n;i++)if(cross(v[i+1]-v[i],v[i+2]-v[i])<-eps)return false;
	return true;
}
bool onpolygon(point p,vector<point> v){
	int n=(int)v.size();
	for(int i=1;i<n;i++)if(onsegment(p,segment(v[i],v[i-1])))return true;
	return onsegment(p,segment(v[0],v[n-1]));
}
bool inpolygon(point p,vector<point> v){
	bool f=false;
	int n=(int)v.size();
	for(int i=0,j=n-1;i<n;j=i++)if((dcmp(v[i].y-p.y)>0!=dcmp(v[j].y-p.y)>0)&&dcmp(p.x-(p.y-v[i].y)*(v[i].x-v[j].x)/(v[i].y-v[j].y)-v[i].x)<0)f=!f;
	return f;
}
vector<point> make_convex(vector<point> v){
	int n=(int)v.size(),sz=0,lst;
	vector<point> ans;
	sort(v.begin(),v.end());
	for(int i=0;i<n;i++){
		while(sz>=2){
			if(cross(v[i]-ans[sz-2],ans[sz-1]-ans[sz-2])>0){
				ans.pop_back();
				sz--;
			}
			else break;
		}
		ans.PB(v[i]);
		sz++;
	}
	lst=sz;
	for(int i=n-2;i>=0;i--){
		while(sz>lst){
			if(cross(v[i]-ans[sz-2],ans[sz-1]-ans[sz-2])>0){
				ans.pop_back();
				sz--;
			}
			else break;
		}
		ans.PB(v[i]);
		sz++;
	}
	ans.pop_back();
	return ans;
}
double diameter(vector<point> v){
	double ans=0;
	int n=(int)v.size();
	for(int i=0,j=0,nxt=1;i<n;i++){
		while(distance(v[i],v[j])-distance(v[i],v[nxt])<-eps){
			nxt++;
			j++;
			if(nxt>=n)nxt-=n;
			else if(j>=n)j-=n;
		}
		ans=max(ans,distance(v[i],v[j]));
	}
	return ans;
}
vector<point> leftside(vector<point> v,point p1,point p2){
	vector<point> ans;
	line l(p1,p2);
	point p(p2-p1);
	int n=(int)v.size();
	if(!same(line(v[n-1],v[0]),l)&&hasintersect(segment(v[n-1],v[0]),l))ans.PB(intersect(line(v[n-1],v[0]),l));
	if(cross(v[0]-p1,p)<0)ans.PB(v[0]);
	for(int i=1;i<n;i++){
		if(!same(line(v[i-1],v[i]),l)&&hasintersect(segment(v[i-1],v[i]),l))ans.PB(intersect(line(v[i-1],v[i]),l));
		if(cross(v[i]-p1,p)<0)ans.PB(v[i]);
	}
	if(debug){
		for(point i:ans)i.out();
		printf("\n");
	}
	return ans;
}
int main(){
	int n,q;
	vector<point> v;
	point temp,tt;
	scanf("%d",&n);
	for(int i=0;i<n;i++){
		temp.in();
		v.PB(temp);
	}
	scanf("%d",&q);
	while(q--){
		temp.in();
		tt.in();
		printf("%lf\n",area(leftside(v,temp,tt)));
	}
}