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<cmath>
#include<algorithm>
#include<iostream>
#include<vector>
#include<climits>
#include<cfloat>
#include<cstdio>
#include<cassert>
#define all(c) (c).begin(),(c).end()
#define curr(P,i) P[(i)%P.size()]
#define next(P,i) P[(i+1)%P.size()]
#define prev(P,i) P[(i+P.size()-1)%P.size()]


using namespace std;

typedef double Real;

Real EPS = 1e-7;
const Real PI = acos(-1);

int sgn(Real a, Real b=0){return a<b-EPS?-1:a>b+EPS?1:0;}
Real sqr(Real a){return sqrt(max(a,(Real)0));}

struct Point{  
  Real add(Real a, Real b){
    if(abs(a+b) < EPS*(abs(a)+abs(b)))return 0;
    return a+b;
  }

  Real x, y;
  Point(){}
  Point(Real x,Real 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 * (Real d){return Point(x*d,y*d);}
  Point operator / (Real d){return Point(x/d,y/d);}
  bool operator == (Point p){return !sgn(dist(p));}
  //bool operator < (Point p)const{return (p.x!=x)?x<p.x:y<p.y;}
bool operator < (Point p)const{return (p.y!=y)?y<p.y:x<p.x;}
  Real norm(){return sqr(x*x+y*y);}
  Real dist(Point a){return (*this-a).norm();}
  Real dot(Point a){return x*a.x+y*a.y;}
  Real cross(Point a){return x*a.y-y*a.x;}
};

//a -> b -> c

int ccw(Point a, Point b, Point c) {
  b = b-a; c = c-a;
  
  if (b.cross(c) > 0)   return +1;       // counter clockwise
  if (b.cross(c) < 0)   return -1;       // clockwise
  if (b.dot(c) < 0)     return +2;       // c--a--b on line
  if (b.dot(b) < c.dot(c)) return -2;    // a--b--c on line
  /*
  if(sgn(b.cross(c))>0)return +1;
  if(sgn(b.cross(c))<0)return -1;
  if(sgn(b.dot(c))<0)return +2;
  if(sgn(b.norm(),c.norm())<0)return -2;
  */
  return 0;                              // a--c--b on line
}

struct Line{
  Point a,b;

  Line(){}
  Line(Point a,Point b):a(a),b(b){}

  bool on(Point c){return abs(ccw(a,b,c))!=1;}
  Real dist(Point c){return abs((b-a).cross(c-a))/(b-a).norm();}

  Point intersectionPoint(Line l){
    return a+(b-a)*((l.b-l.a).cross(l.a-a)/(l.b-l.a).cross(b-a));
  }
};

struct Segment: public Line{
  
  Segment(){}
  Segment(Point a,Point b):Line(a,b){}

  bool on(Point c){return ccw(a,b,c)==0;}
  bool on(Line l){return l.on(a)&&l.on(b);}

  bool isParallel(Segment s){return (a-b).cross(s.a-s.b)==0.0;}

  Real dist(Point c){
    if((b-a).dot(c-a)<EPS)return c.dist(a);
    if((a-b).dot(c-b)<EPS)return c.dist(b);
    return abs((b-a).cross(c-a))/b.dist(a);    
  }

  bool isIntersection(Line l){
    return (ccw(l.a,l.b,a)*ccw(l.a,l.b,b)<0);
  }
};

struct Polygon{
  //頂点。反時計回りに順番で与えられていること。
  vector<Point>v;
  
  Polygon(){}
  Polygon(int n){v.resize(n);}
  Polygon(vector<Point>v):v(v){}
  /*
    Verified. AOJ CGL_3/A
    多角形の面積計算。
    多角形の頂点が時計回りまたは反時計回り
  */
  Real area(){
    Real area=0;
    for(int i=0;i<v.size();i++)
      area+=(curr(v,i).x-next(v,i).x)*(curr(v,i).y+next(v,i).y);
    return abs(area)/2.0;
  }
  
  /*
    凸多角形の切断
    凸多角形psを直線abで切断し、
    左側の多角形を返す。
  */
  Polygon convexCut(Line l){
    vector<Point>res;
    for(int i=0;i<v.size();i++){
      Point a=curr(v,i),b=next(v,i),p=l.b-l.a;
      if(ccw(l.a,l.b,a)!=-1)res.push_back(a);
      if(sgn(p.cross(a-l.a)*p.cross(b-l.a))<0)
	res.push_back(Segment(a,b).intersectionPoint(l));
    }
    return res;
  }
  
};

int main(void){

  int n;
  cin >> n;
  Polygon p(n);

  for(int i=0;i<n;i++)
    cin >> p.v[i].x >> p.v[i].y;
  
  //assert(sgn(p.area())>0);

  int q;
  cin >> q;
  while(q--){
    Line l;
    cin >> l.a.x >> l.a.y >> l.b.x >> l.b.y;

    //bool fg=false;
    //for(int i=0;i<n;i++){
      //assert(!l.on(p.v[i]));
      //assert(!Segment(p.v[i],p.v[(i+1)%n]).on(l));
      //fg|=Segment(p.v[i],p.v[(i+1)%n]).isIntersection(l);
    //}
    //assert(fg);
    //assert(sgn(p.convexCut(l).area(),p.area())<1);
    //assert(sgn(p.convexCut(l).area())>0);
    printf("%.8f",p.convexCut(l).area());
    cout << endl;
  }
  return 0;
}