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 _overload(_1,_2,_3,name,...) name
#define _rep(i,n) _range(i,0,n)
#define _range(i,a,b) for(int i=int(a);i<int(b);++i)
#define rep(...) _overload(__VA_ARGS__,_range,_rep,)(__VA_ARGS__)

#define _rrep(i,n) _rrange(i,n,0)
#define _rrange(i,a,b) for(int i=int(a)-1;i>=int(b);--i)
#define rrep(...) _overload(__VA_ARGS__,_rrange,_rrep,)(__VA_ARGS__)

#define _all(arg) begin(arg),end(arg)
#define uniq(arg) sort(_all(arg)),(arg).erase(unique(_all(arg)),end(arg))
#define getidx(ary,key) lower_bound(_all(ary),key)-begin(ary)
#define clr(a,b) memset((a),(b),sizeof(a))
#define bit(n) (1LL<<(n))
#define popcount(n) (__builtin_popcountll(n))

using namespace std;

template<class T>bool chmax(T &a, const T &b) { return (a<b)?(a=b,1):0;}
template<class T>bool chmin(T &a, const T &b) { return (b<a)?(a=b,1):0;}

using ll=long long;
using R=long double;
const R EPS=1e-9L; // [-1000,1000]->EPS=1e-8 [-10000,10000]->EPS=1e-7
inline int sgn(const R& r){return(r > EPS)-(r < -EPS);}
inline R sq(R x){return sqrt(max(x,0.0L));}

const int dx[8]={1,0,-1,0,1,-1,-1,1};
const int dy[8]={0,1,0,-1,1,1,-1,-1};

// Problem Specific Parameter:

// Description: ????????????
// Verifyed: various problem 
const R INF = 1E40L;
const R PI = acos(-1.0L);
using P=complex<R>;
const P O=0.0L;
using L=struct{P s,t;};
using VP=vector<P>;
using C=struct{P p;R c;};

istream& operator >> (istream& is,P& p){ R x,y;is >> x >> y; p=P(x,y); return is;}
ostream& operator << (ostream& os,P& p){ os << real(p) << " " << imag(p); return os;}

inline R dot(P o,P a,P b){return real(conj(a-o)*(b-o));}
inline R det(P o,P a,P b){return imag(conj(a-o)*(b-o));}
inline int sdot(P o,P a,P b){return sgn(dot(o,a,b));}
inline int sdet(P o,P a,P b){return sgn(det(o,a,b));}

//projection verify AOJ CGL_1_A
P proj(L l,P p){ R u=real((p-l.s)/(l.t-l.s)); return (1-u)*l.s+u*l.t;}

//reflection verify AOJ CGL_1_B
P refl(L l,P p){return 2.0L*proj(l,p)-p;}

// CCW verify AOJ CGL_1_C
enum CCW{ LEFT = 1,RIGHT = 2,BACK = 4,FRONT = 8,ON = 16};
inline int ccw(P o,P a, P b) {
	a-=o,b-=o,o-=o;
	if(sdet(o,a,b) > 0) return LEFT;    // counter clockwise
	if(sdet(o,a,b) < 0) return RIGHT;   // clockwise
	if(sdot(o,a,b) < 0) return BACK;    // b--base--a on line
	if(sgn(norm(a)-norm(b)) < 0) return FRONT;   // base--a--b on line
	return ON; // base--b--a on line  semnet determination betwenn a and b 
}

// vertical parallel
// verified: AOJ CGL_2_A
bool vertical(L a,L b) {return sdot(O,a.t-a.s,b.t-b.s)==0;}
bool parallel(L a,L b) {return sdet(O,a.t-a.s,b.t-b.s)==0;}
bool eql(L a,L b){ return parallel(a,b) and sdet(a.s,a.t,b.s)==0;}

// crossing determination
// verified: AOJ CGL_2_B 
bool iss(L a,L b){
	int sa=sdet(a.s,a.t,b.s)*sdet(a.s,a.t,b.t);
	int sb=sdet(b.s,b.t,a.s)*sdet(b.s,b.t,a.t);
	return max(sa,sb)<0;
}

// crossing point 
// verified: AOJ CGL_2_C
P cross(L a,L b){
	R u=det(a.s,b.s,b.t)/det(O,a.t-a.s,b.t-b.s);
	return (1-u)*a.s+u*a.t;
}
	
// distance 
// verified: AOJ CGL_2_D
R dsp(L l,P p){
	P h=proj(l,p);
	if(sdot(l.s,l.t,p)<=0) h=l.s;
	if(sdot(l.t,l.s,p)<=0) h=l.t;
	return abs(p-h);
}

R dss(L a,L b){return iss(a,b)?0:min({dsp(a,b.s),dsp(a,b.t),dsp(b,a.s),dsp(b,a.t)});}

// Polygon

// area 
// verified: AOJ 1100 CGL_3_A
R area(const VP& pol){
	int n=pol.size();
	R sum=0.0;
	rep(i,n) sum+=det(O,pol[i],pol[(i+1)%n]);
	return abs(sum/2.0L);
}


// convex_polygon determination
// verified: CGL_3_B
bool is_convex(const VP& pol){
	int n=pol.size();
	rep(i,n)if(sdet(pol[i],pol[(i+1)%n],pol[(i+2)%n])<0) return false;
	return true;
}

// polygon realation determination  in  2 on 1 out 0???(possible non-convex) 
// verified: AOJ CGL_3-C
int in_polygon(const VP& pol, const P& p){
	int n=pol.size(),res=0;
	rep(i,n){
		P a=pol[i],b=pol[(i+1)%n];
		if(sdet(p,a,b)==0 and sdot(p,a,b)<=0) return 1;
		bool f=sgn(imag(p-a))>=0,s=sgn(imag(p-b))<0;
		if(sgn(imag(b-a))*sdet(a,b,p)==1 and f==s) res+=(2*f-1);
	}
	return res?2:0;
}


// polygon realation determination???(possible non-convex) 
// verified: AOJ 2514
bool in_polygon(const VP& pol, const L& l){
	VP check{l.s,l.t};
	int n=pol.size();
	rep(i,n){
		L edge={pol[i],pol[(i+1)%n]};
		if(iss(l,edge)) check.emplace_back(cross(l,edge));
	}
	sort(begin(check),end(check),[](P a,P b)->bool{return sgn(real(a)-real(b))?:sgn(imag(a)-imag(b));});
	n=check.size();
	rep(i,n-1){
		P m=(check[i]+check[i+1])/2.0L;
		if(in_polygon(pol,m)==false) return false;
	}
	return true;
}

// convex_cut 
// verified: AOJ CGL_4_C
VP convex_cut(const VP& pol,const L& l) {
	VP res;
	int n=pol.size();
	rep(i,n){
		P a = pol[i],b=pol[(i+1)%n];
		int da=sdet(l.s,l.t,a),db=sdet(l.s,l.t,b);
		if(da>=0) res.emplace_back(a);
		if(da*db<0) res.emplace_back(cross({a,b},l));
	}
	return res;
}

int main(void){
	int n,q;
	cin >> n;
	VP pol;
	rep(i,n){
		P p;
		cin >> p;
		pol.push_back(p); 
	}
	cin >> q;
	cout.precision(20);
	rep(i,q){
		P a,b;
		cin >> a >> b;
		L l={a,b};
		cout << fixed <<  area(convex_cut(pol,l)) << endl;
	}
	return 0;
}