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 complex<double> P;
typedef complex<double> V;
typedef vector<P> vecP;
typedef pair<P,P> L;
typedef pair<P,P> S;
typedef pair<P,double> C;
const double eps=1e-8;
const double PI=acos(-1);
const double PI2=PI*2.0;

namespace std{
  bool operator < (const P &a,const P &b){
    return (a.imag()==b.imag()?
            a.real()<b.real():
            a.imag()<b.imag());
  }
};

V normal(V a){
  assert( abs(a)>0 );
  return a/abs(a);
}

double Sqrt( double x ){
  if(x<0)return 0;
  else return sqrt(x);
}

P Vector(L a){
  return a.second-a.first;
}

bool eq(double a,double b){
  return (-eps<a-b&&a-b<eps);
}

bool eq(P a,P b){
  return ( eq(a.real(),b.real()) && eq(a.imag(),b.imag()) );
}

double dot(P a,P b){
  return real(b*conj(a));
}

double cross(P a,P b){
  return imag(b*conj(a));
}

double getArg(P a,P b){
  return arg(b*conj(a));
}

double getTime(V a,V b){
  assert( eq(cross(a,b),0) );
  return ( dot(a,b) < 0 ? -1.0 : 1.0 ) * abs(b) / abs(a);
}


P project(P a,P b,P c){
  b-=a,c-=a;
  return a+b*real(c/b);
}

P reflect(P a,P b,P c){
  b-=a,c-=a;
  return a+b*conj(c/b);
}

int ccw(P a,P b,P c){
  P ab=b-a,ac=c-a;
  P k=ac*conj(ab);
  if(k.imag()>0)return 1;
  if(k.imag()<0)return -1;
  if(k.real()<0)return 2;
  if(abs(ab)<abs(ac))return -2;
  return 0;
}

bool isParallel(P a,P b){
  return eq(0, cross(a,b));
}

bool isParallel(S a,S b){
  return eq(0, cross( Vector(a) , Vector(b) ) );
}

bool onLP(L l,P p){
  P a=l.first, b=l.second;
  return eq(0, cross(b-a,p-a));
}

bool onSP(S s,P p){
  P a=s.first, b=s.second;
  return eq( abs(b-a) , abs(a-p)+abs(b-p) );
}

bool isCrossSS(S s0,S s1){
  P a=s0.first, b=s0.second;
  P c=s1.first, d=s1.second;
  int f0 = ccw(a,b,c) * ccw(a,b,d);
  int f1 = ccw(c,d,a) * ccw(c,d,b);
  return (f0<=0 && f1<=0);
}

bool isCrossLS(L l,S s){
  P a=l.first, b=l.second;
  P c=s.first, d=s.second;
  return ( ccw(a,b,c) * ccw(a,b,d) <= 0 );
}

double distLP(L l,P p){
  P a=l.first, b=l.second;
  double res = cross(b-a,p-a) / abs(b-a);
  return abs(res);
}

double distSP(S s,P p){
  P a=s.first, b=s.second;
  if( dot(b-a,p-a) < eps )return abs(p-a);
  if( dot(a-b,p-b) < eps )return abs(p-b);
  return distLP(s,p);
}

double distSS(S s0,S s1){
  if( isCrossSS(s0,s1) )return 0;
  double res0 = min( distSP( s0, s1.first ) , distSP(s0, s1.second) );
  double res1 = min( distSP( s1, s0.first ) , distSP(s1, s0.second) );
  return min(res0,res1);
}

P getCrossLL(L l0,L l1){
  P a=l0.first, b=l0.second;
  P c=l1.first, d=l1.second;
  a-=d;b-=d;c-=d;
  return d+a+(b-a)*imag(a/c)/imag(a/c-b/c);
}


 
int inPolygon(vecP &t,P p){
  int n=t.size();
  double sum=0;
  for(int i=0;i<n;i++){
    P a=t[i],b=t[(i+1==n?0:i+1)];
    if( ccw(a,b,p)==0 )return 1;
    sum+= getArg(a-p,b-p);
  }
  if( abs(sum) < eps )return 0;
  else return 2;
}

vecP andrewScan(vecP &t){
  int N=t.size(),C=0;
  vecP R(N);
  for(int i=0;i<N;i++){
    while(2<=C&&ccw(R[C-2],R[C-1],t[i])==-1)C--;
    R[C++]=t[i];
  }
  vecP res(C);
  for(int i=0;i<C;i++)res[i]=R[i];
  return res;
}
 
vecP convexHull(vecP &t){
  sort(t.begin(),t.end());
  vecP u=andrewScan(t);
  reverse(t.begin(),t.end());
  vecP l=andrewScan(t);
  for(int i=1;i+1<(int)l.size();i++)u.push_back(l[i]);
  return u;
}

vecP cutConvex(vecP &t,L l){
  P a=l.first, b=l.second;
  int N=t.size();
  vecP res;
  for(int i=0;i<N;i++){
    P c=t[i],d=t[(i+1)%N];
    int C=ccw(a,b,c),D=ccw(a,b,d);
    if(C!=-1)res.push_back(c);
    if(C==-D&&abs(C)==1)res.push_back(getCrossLL( l ,L(c,d) ));
  }
  return res;
}

P getVector(const vecP &t, int id){
  int n=t.size();
  return t[ (id+1)%n ] - t[id%n];
}

double convex_diameter(vecP &t) {
  int n = t.size();
  int is = 0, js = 0;
  for (int i = 1; i < n; ++i) {
    if (imag(t[i]) > imag(t[is])) is = i;
    if (imag(t[i]) < imag(t[js])) js = i;
  }
  double maxd = norm(t[is]-t[js]);
 
  int i, maxi, j, maxj;
  i = maxi = is;
  j = maxj = js;
  do {
    
    if (cross( getVector(t,i), getVector(t,j)) >= 0) j = (j+1) % n;
    
    else i = (i+1) % n;
    if (norm(t[i]-t[j]) > maxd) {
      maxd = norm(t[i]-t[j]);
      maxi = i; maxj = j;
    }
  } while (i != is || j != js);
  return sqrt(maxd); /* farthest pair is (maxi, maxj). */
}

bool compare_y(const P &a,const P &b){
  return a.imag() < b.imag();
}

double closest_pair(P *a, int n){
  if(n <= 1) return 1e30;
  int m = n / 2;
  double x = a[m].real();
  double d = min(closest_pair(a, m), closest_pair(a + m, n - m));
  inplace_merge(a, a + m, a + n, compare_y);
  vector<P> b;
  for(int i=0;i<n;i++){
    if( abs(a[i].real() - x) >= d) continue;
    for(int j=0;j<(int)b.size();j++){
      double dx = real(a[i] - b[b.size() - j - 1]);
      double dy = imag(a[i] - b[b.size() - j - 1]);
      if(dy >= d) break;
      d = min(d, sqrt(dx * dx + dy * dy));
    }
    b.push_back(a[i]);
  }
  return d;
}

P _pool[200005];
double minDist(vecP &t){
  int n=t.size();
  for(int i=0;i<n;i++)_pool[i]=t[i];
  sort( _pool, _pool+n);
  return closest_pair(_pool, n);
}

int getStateCC(C a,C b){
  double ar=a.second, br=b.second;
  double dist=abs(a.first-b.first);
  if(dist>ar+br+eps)return 4;
  if(dist>ar+br-eps)return 3;
  if(dist>abs(ar-br)+eps)return 2;
  if(dist>abs(ar-br)-eps)return 1;
  return 0;
}

P getCrossCC(C a,C b){
  P p1=a.first, p2=a.second;
  double r1=a.second, r2=b.second;
  double cA = (r1*r1+norm(p1-p2)-r2*r2) / (2.0*r1*abs(p1-p2));
  return p1+(p2-p1)/abs(p1-p2)*r1*P(cA,Sqrt(1.0-cA*cA));
}

S getTangentCP(C a,P p){
  P base=a.first-p;
  double ar=a.second;
  double w=Sqrt(norm(base)-ar*ar);
  P s=p+base*P(w,ar)/norm(base)*w;
  P t=p+base*P(w,-ar)/norm(base)*w;
  return S(s,t);
}

S getInTangent(C a,C b,double flg=1.0){
  P ap=a.first,bp=b.first;
  double ar=a.second,br=b.second;
  
  P base=bp-ap;
  double w=ar+br;
  double h=Sqrt(norm(base)-w*w);
  P k=base*P(w,h*flg)/norm(base);
  return S(ap+k*ar,bp-k*br);
}
  
S getOutTangent(C a,C b,double flg=1.0){
  P ap=a.first,bp=b.first;
  double ar=a.second,br=b.second;
  
  P base=bp-ap;
  double h=br-ar;
  
  double w=Sqrt(norm(base)-h*h);
  P k=base*P(w,h*flg)/norm(base)*P(0,flg);
  return S(ap+k*ar,bp+k*br);
}
  
vector<S> getTangent(C a,C b){
  P ap=a.first,bp=b.first;
  double ar=a.second,br=b.second;
  
  vector<S> res;
  double dist=abs(ap-bp);
    
  if(dist>ar+br+eps)
    res.push_back(getInTangent(a,b,1));
  
  if(dist>ar+br-eps)
    res.push_back(getInTangent(a,b,-1));
  
  if(dist>abs(ar-br)+eps)
    res.push_back(getOutTangent(a,b,1));
  
  if(dist>abs(ar-br)-eps)
    res.push_back(getOutTangent(a,b,-1));
  
  return res;
}


vecP getCrossCS(C cir,S s, bool debug=false){
  P a=s.first, b=s.second;
  double cr=cir.second;
  P cp=cir.first;
  
  vecP res;
  P base=b-a,  target=project(a,b,cp);
  
  double length=abs(base), h=abs(cp-target);
  base/=length;
  
  if(cr+eps<h)return res;
  double w=Sqrt(cr*cr-h*h);
  double L=getTime( normal(b-a) ,target-a)-w,  R=L+w*2.0;
  
  if( -eps<L && L< length+eps )res.push_back(a+base*L);
  if( eq(L,R) )return res;
  if( -eps<R && R< length+eps )res.push_back(a+base*R);
  return res;
}
 
double getArea(C c,P a,P b){
  P cp=c.first;
  double cr=c.second;
  
  P va=cp-a,  vb=cp-b;
  double A=abs(va), B=abs(vb);
  double f=cross(va,vb), d=distSP( S(a,b) ,cp), res=0;
  
  if( eq(0, f ) )return 0;
  if(A<cr+eps&&B<cr+eps)return f*0.5;
  if(d>cr-eps)return cr*cr*PI*getArg(va,vb)/PI2;
   
  vecP u=getCrossCS(c, S(a,b) );
  
  assert( !u.empty() );
  u.insert(u.begin(), a),  u.push_back(b);
 
  for(int i=0;i+1<(int)u.size();i++) res+=getArea(c,u[i],u[i+1]);
  return res;
}
 
double getCrossArea(vecP t,C c){
  int n=t.size();
  if(n<3)return 0;
  double res=0;
  for(int i=0;i<n;i++){
    P a=t[i], b=t[(i+1)%n];
    res+=getArea(c,a,b);
  }
  return res;
}


double calcArea(const vecP &t){
  double res=0;
  int n=t.size();
  for(int i=0;i<n;i++){
    res+= cross( t[ (i+1)%n ],t[i] );
  }
  return abs(res)*0.5;
}

P input(){
  double x,y;
  cin>>x>>y;
  return P(x,y);
}

void pr(P p,string str){
  printf("%.10f %.10f",p.real(),p.imag());
  cout<<str;
}


int main(){
  int Tc;
  cin>>Tc;

  vecP polygon;
  while(Tc--){
    polygon.push_back( input() );
  }
  int q;
  cin>>q;
  while(q--){
    P s=input();
    P t=input();
    printf("%.10f\n", calcArea( cutConvex( polygon , L(s,t) ) ) );
  }

  return 0;
}