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;
/*******************??????********************/
const double EPS = 1e-8;
const double INF = 1e12;
#define X real()
#define Y imag()
#define curr(P, i) P[i]
#define next(P, i) P[(i+1)%P.size()]
#define prev(P, i) P[(i+P.size()-1) % P.size()]
#define diff(P, i) (next(P, i) - curr(P, i))
#define EQ(a,b) (abs((a)-(b)) < EPS)

typedef complex<double> P;
namespace std {
	bool operator < (const P& a, const P& b) {
		return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
	}
	bool operator == (const P& a, const P& b) {
		return abs(a-b) < EPS;
	}
}
double cross(const P& a, const P& b) {//??????
	return imag(conj(a)*b);
}
double dot(const P& a, const P& b) {//??????
	return real(conj(a)*b);
}

struct L : public vector<P> {//??????
	L(const P &a, const P &b) {
		push_back(a); push_back(b);
	}
};

typedef vector<P> G;
struct C {//???
	P p; double r;
	C(const P &p, double r) : p(p), r(r) { }
};

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

bool intersectLL(const L& l,const L& m){
	//non-parallel || sameline
	return abs(cross(l[1]-l[0],m[1]-m[0])) > EPS || abs(cross(l[1]-l[0],m[0]-l[0])) < EPS;
}
bool intersectLS(const L& l,const L& s){
	// s[0] is left of l,s[1] is right of l
	return cross(l[1]-l[0],s[0]-l[0]) * cross(l[1]-l[0],s[1]-l[0]) < EPS;
}
bool intersectSS(const L &s, const L &t) {
	return ccw(s[0],s[1],t[0])*ccw(s[0],s[1],t[1]) <= 0 &&
		ccw(t[0],t[1],s[0])*ccw(t[0],t[1],s[1]) <= 0;
}
bool intersectLP(const L& l,const P& p){
	return abs(cross(l[1]-p,l[0]-p)) < EPS;
}
bool intersectSP(const L& s,const P& p){
	return abs(s[0]-p)+abs(s[1]-p) - abs(s[1]-s[0]) < EPS;// triangle inequality
}
// ??´???????????????
bool orthogonalLL(const L &l1, const L &l2){
	return (dot(l1[0]-l1[1], l2[0]-l2[1]) <= EPS && dot(l1[0]-l1[1], l2[0]-l2[1]) >= -EPS);
}
// ??????????????????
bool parallelLL(const L &l1, const L &l2){
	return (cross(l1[0]-l1[1], l2[0]-l2[1]) <= EPS && cross(l1[0]-l1[1], l2[0]-l2[1]) >= -EPS);
}
// p??????l?????????????????????????????????
P projection(const L& l,const P& p){
	double t = dot(p-l[0],l[0]-l[1]) / norm(l[0]-l[1]);
	return l[0] + t*(l[0]-l[1]);
}
// l???????§°?????¨????????????p??¨???????§°?????????????????????
P reflection(const L& l,const P& p){
	return p + 2. * (projection(l,p) - p);
}
double distancePP(const P &a, const P &b){
	return abs(a - b);
}
double distanceSP(const L &s, const P &p) {
	const P r = projection(s, p);
	if (intersectSP(s, r)) return abs(r - p);
	return min(abs(s[0] - p), abs(s[1] - p));
}
double distanceLP(const L& l,const P& p){
	return abs(p - projection(l,p));
}
double distanceLL(const L& l,const L& m){
	return intersectLL(l,m) ? 0 : distanceLP(l,m[0]);
}
double distanceLS(const L& l,const L& s){
	if(intersectLS(l,s)) return 0;
	return min(distanceLP(l, s[0]),distanceLP(l, s[1]));
}
double distanceSS(const L &s, const L &t) {
	if (intersectSS(s, t)) return 0;
	return min(min(distanceSP(s, t[0]), distanceSP(s, t[1])),
		min(distanceSP(t, s[0]), distanceSP(t, s[1])));
}
// ??????
P crosspointLL(const L &l, const L &m) {
	double A = cross(l[1] - l[0], m[1] - m[0]);
	double B = cross(l[1] - l[0], l[1] - m[0]);
	if (abs(A) < EPS && abs(B) < EPS) return m[0]; // same line
	if (abs(A) < EPS) assert(false); // !!!PRECONDITION NOT SATISFIED!!!
	return m[0] + B / A * (m[1] - m[0]);
}
// ????§???¢?????¢???
double area(const G &g){
	double A = 0.0;
	for(int i=0;i<g.size();i++)
		A += cross(g[i],g[(i+1)%g.size()]);
	return A / 2.0;
}
// ?????????
bool isconvex(const G &g){
	for(int i=0;i<g.size();i++){
		if(ccw(g[(i-1+g.size())%g.size()], g[i], g[(i+1)%g.size()]) == -1)return false;
	}
	return true;
}
// convex full
G convex_full(G &ps){
	int n = ps.size(), k = 0;
	sort(ps.begin(), ps.end());
	G ch(2*n);
	for (int i = 0; i < n; ch[k++] = ps[i++])//lower-hull
		while (k >= 2 && ccw(ch[k-2], ch[k-1], ps[i]) == -1) --k;
	for (int i = n-2, t = k+1; i >= 0; ch[k++] = ps[i--])//upper-hull
		while (k >= t && ccw(ch[k-2], ch[k-1], ps[i]) == -1) --k;
	ch.resize(k-1);
	return ch;
}
// ????§???¢?????´??????????????????????????¢
double convex_diameter(const G &pt){
	const int n = pt.size();
	int is = 0, js = 0;
	for(int i=1;i<n;i++){
		if(imag(pt[i]) > imag(pt[is])) is = i;
		if(imag(pt[i]) < imag(pt[js])) js = i;
	}
	double maxd = norm(pt[is]-pt[js]);
	int i, maxi, j, maxj;
	i = maxi = is;
	j = maxj = js;
	do {
		if (cross(diff(pt,i), diff(pt,j)) >= 0) j = (j+1) % n;
		else i = (i+1) % n;
		if (norm(pt[i]-pt[j]) > maxd) {
			maxd = norm(pt[i]-pt[j]);
			maxi = i; maxj = j;
	    }
	} while (i != is || j != js);
	return sqrt(maxd); /* farthest pair is (maxi, maxj). */
}
// ???????§???¢?????????
// ???????§???¢?????´?????§???????????????????????´???????????????
G convex_cut(const G &g, const L &l){
	G Q;
	for(int i=0;i<g.size();i++){
		P A = curr(g, i), B = next(g, i);
		if(ccw(l[0], l[1], A) != -1) Q.push_back(A);
	if(ccw(l[0], l[1], A) * ccw(l[0], l[1], B) < 0) Q.push_back(crosspointLL(L(A, B), l));
	}
	return Q;
}
// ??????????????§??????
bool is_convex(G &g){
	G cf = convex_full(g);
	if(cf.size() == g.size())return true;
	return false;
}
// ??????????§???¢????????????
enum{ OUT, ON, IN};
int contains(const G &g, const P &p){
	bool in = false;
	for(int i=0;i<g.size();i++){
		P a = g[i] - p, b = g[(i+1)%g.size()] - p;
		if( imag(a) > imag(b) )swap(a, b);
		if( imag(a) <= 0 && 0 < imag(b) )
			if( cross(a, b) < 0) in = !in;
		if( cross(a, b) == 0 && dot(a, b) <= 0 )return ON;
	}
	return in ? IN : OUT;
}
int main(void){
	int n;
	cin >> n;
	G g(n);
	for(int i=0;i<n;i++){
		int x,y;
		cin >> x >> y;
		g[i] = P(x,y);
	}
	int q;
	cin >> q;
	for(int i=0;i<q;i++){
		int x0,y0,x1,y1;
		cin >> x0 >> y0 >> x1 >> y1;
		L l(P(x0,y0),P(x1,y1));
		cout << fixed << setprecision(20) << area(convex_cut( g, l)) << endl;
	}
	return 0;
}