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 f first
#define s second
#define mp make_pair
#define inf 100000000
#define eps (1e-11)
#define equals(a,b) (fabs((a)-(b))<eps)
using namespace std;

class Point{
public:
  double x,y;
  Point(double x=0,double y=0):x(x),y(y){}

  Point operator+(Point p){ return Point(x+p.x,y+p.y);}
  Point operator-(Point p){ return Point(x-p.x,y-p.y);}
  Point operator*(double k){ return Point(x*k,y*k);}
  Point operator/(double k){ return Point(x/k,y/k);}
  bool operator<(Point p)const{ return (x!=p.x ? x<p.x : y<p.y);}
  bool operator==(Point p)const{ return fabs(x-p.x)<eps && fabs(y-p.y)<eps;}

  double abs(){ return sqrt(norm());}
  double norm(){ return (x*x+y*y);}
};
typedef Point Vector;
typedef vector<Point> Polygon;

class Segment{
public:
  Point p1,p2;
  Segment(Point p1,Point p2):p1(p1),p2(p2){}
};
typedef Segment Line;

class Circle{
public:
  Point c;
  double r;
  Circle(Point c=Point(),double r=0.0):c(c),r(r){}
};

double norm(Vector a){ return (a.x*a.x+a.y*a.y);}
double abs(Vector a){ return sqrt(norm(a));}
double dot(Vector a,Vector b){ return (a.x*b.x+a.y*b.y);}
double cross(Vector a,Vector b){ return (a.x*b.y-a.y*b.x);}

Point project(Segment s,Point p){
  Vector base=(s.p2-s.p1);
  double r=(dot(p-s.p1,base)/base.norm());
  return (s.p1+base*r);
}

Point reflect(Segment s,Point p){
  return p+(project(s,p)-p)*2;
}

bool isOrthogonal(Vector a,Vector b){
  return equals(dot(a,b),0.0);
}

bool isParallel(Vector a,Vector b){
  return equals(cross(a,b),0.0);
}

static const int COUNTER_CLOCKWISE=1;
static const int CLOCKWISE=-1;
static const int ONLINE_BACK=2;
static const int ONLINE_FRONT=-2;
static const int ON_SEGMENT=0;

int ccw(Point p0,Point p1,Point p2){
  Vector a=p1-p0;
  Vector b=p2-p0;
  if(cross(a,b)>eps)return COUNTER_CLOCKWISE;
  if(cross(a,b)<-eps)return CLOCKWISE;
  if(dot(a,b)<-eps)return ONLINE_BACK;
  if(a.norm()<b.norm())return ONLINE_FRONT;
  return ON_SEGMENT;
}

bool intersect(Point p1,Point p2,Point p3,Point p4){
  return (ccw(p1,p2,p3)*ccw(p1,p2,p4)<=0 &&
          ccw(p3,p4,p1)*ccw(p3,p4,p2)<=0);
}

bool intersect(Segment s1,Segment s2){
  return intersect(s1.p1,s1.p2,s2.p1,s2.p2);
}

Point getCrossPointSS(Segment s1,Segment s2){
  Vector base=s2.p2-s2.p1;
  double d1=abs(cross(base,s1.p1-s2.p1));
  double d2=abs(cross(base,s1.p2-s2.p1));
  double t=d1/(d1+d2);
  return (s1.p1+(s1.p2-s1.p1)*t);
}

Point getCrossPointLL(Line a,Line b){
  double A=cross(a.p2-a.p1,b.p2-b.p1);
  double B=cross(a.p2-a.p1,a.p2-b.p1);
  if(abs(A)<eps && abs(B)<eps)return b.p1;
  return b.p1+(b.p2-b.p1)*(B/A);
}

double getDistanceLP(Line l,Point p){
  return abs(cross(l.p2-l.p1,p-l.p1)/abs(l.p2-l.p1));
}

double getDistanceSP(Segment s,Point p){
  if(dot(s.p2-s.p1,p-s.p1)<0.0)return abs(p-s.p1);
  if(dot(s.p1-s.p2,p-s.p2)<0.0)return abs(p-s.p2);
  return getDistanceLP(s,p);
}

double getDistance(Segment s1,Segment s2){
  if(intersect(s1,s2))return 0.0;
  return min(min(getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)),
             min(getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2)));
}

pair<Point,Point> getCrossPoints(Circle c,Line l){
  Vector pr=project(l,c.c);
  Vector e=(l.p2-l.p1)/abs(l.p2-l.p1);
  double base=sqrt(c.r*c.r-norm(pr-c.c));
  return mp(pr+e*base,pr-e*base);
}

double arg(Vector p){ return atan2(p.y,p.x);}
Vector polar(double a,double r){ return Point(cos(r)*a,sin(r)*a);}

pair<Point,Point> getCrossPoints(Circle c1,Circle c2){
  double d=abs(c1.c-c2.c);
  double a=acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d));
  double t=arg(c2.c-c1.c);
  return mp(c1.c+polar(c1.r,t+a),c1.c+polar(c1.r,t-a));
}

double getPolygonArea(Polygon p){
  double area=0.0;
  int n=p.size();
  for(int i=0;i<n;i++)area+=cross(p[i%n],p[(i+1)%n]);
  return area/2;
}

bool isConvex(Polygon p){
  int n=p.size();
  for(int i=0;i<n;i++){
    if(ccw(p[(i+1)%n],p[i%n],p[(i+2)%n])==1)return false;
  }
  return true;
}

// in 2,out 0,on 1
int contains(Polygon g,Point p){
  int n=g.size();
  bool x=false;
  for(int i=0;i<n;i++){
    Vector a=g[i]-p,b=g[(i+1)%n]-p;
    if(abs(cross(a,b))<eps && dot(a,b)<eps)return 1;
    if(a.y>b.y)swap(a,b);
    if(a.y<eps && eps<b.y && cross(a,b)>eps)x=!x;
  }
  if(x)return 2;
  return 0;
}

Polygon convex_hull(Polygon s){
  Polygon g;
  int n=s.size();
  if(n<3)return s;

  sort(s.begin(),s.end());

  for(int i=0;i<n;i++){
    for(int n=g.size();n>=2&&ccw(g[n-2],g[n-1],s[i])==1;n--){
      g.pop_back();
    }
    g.push_back(s[i]);
  }
  for(int i=n-2;i>=0;i--){
    for(int n=g.size();n>=2&&ccw(g[n-2],g[n-1],s[i])==1;n--){
      g.pop_back();
    }
    g.push_back(s[i]);
  }
  reverse(g.begin(),g.end());
  g.pop_back();
  return g;
}

double convex_diameter(Polygon p){
  int n=p.size();
  int i=0,j=0;

  for(int k=0;k<n;k++){
    if(p[i]<p[k])i=k;
    if(p[k]<p[j])j=k;
  }
  int si=i,sj=j;
  double ans=0.0;
  while(i!=sj || j!=si){
    ans=max(ans,abs(p[i]-p[j]));
    if(cross((p[(i+1)%n]-p[i]),(p[(j+1)%n]-p[j]))<0)i=(i+1)%n;
    else j=(j+1)%n;
  }
  return ans;
}

Polygon convex_cut(Polygon p,Line l){
  Polygon ans;
  for(int i=0;i<p.size();i++){
    Point A=p[i],B=p[(i+1)%p.size()];
    if(ccw(l.p1,l.p2,A)!=-1)ans.push_back(A);
    if(ccw(l.p1,l.p2,A)*ccw(l.p1,l.p2,B)<0)
      ans.push_back(getCrossPointLL(l,Segment(A,B)));
  }
  return ans;
}

int main()
{
  int n,q;
  Point A,B;
  Polygon p,cutp;

  cin>>n;
  p.resize(n);
  for(int i=0;i<n;i++)cin>>p[i].x>>p[i].y;
  cin>>q;
  for(int i=0;i<q;i++){
    cin>>A.x>>A.y>>B.x>>B.y;
    cutp=convex_cut(p,Line(A,B));
    printf("%.10f\n",getPolygonArea(cutp));
  }
  return 0;
}