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:

//be naame khodaa
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair <int, int> pii;
typedef complex<ld> PT;
typedef vector<PT> Poly;
typedef pair<PT, PT> LS;
#define F first
#define S second
#define X real()
#define Y imag()
#define pb push_back

inline int in(){int x, y; y = scanf("%d", &x); return x; }

const int N = -1;
const ld EPS = 1e-12;

const int ON = 0, LEFT = 1, RIGHT = -1, BACK = -2, FRONT = 2, IN = 3, OUT = -3;

inline bool Geq(ld a, ld b){ return a + EPS > b; }
inline bool Grt(ld a, ld b){ return a > b + EPS; }
inline bool Leq(ld a, ld b){ return a < b + EPS; }
inline bool Lss(ld a, ld b){ return a + EPS < b; }
inline bool Equ(ld a, ld b){ return Geq(a, b) && Geq(b, a); }

istream& operator>> (istream& is, complex<ld>& p){
	ld val;
	is >> val;
	p.real(val);
	is >> val;
	p.imag(val);
	return is;
}

bool cmpXY(PT a, PT b){
	if (Equ(a.X, b.X))
		return Lss(a.Y, b.Y);
	return Lss(a.X, b.X);
}

ld dot(PT a, PT b){ return real(conj(a)*b); }
ld cross(PT a, PT b){ return imag(conj(a)*b); }
ld sqlen(PT a){ return dot(a, a); }
ld len(PT a){ return sqrt(sqlen(a)); }

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

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

PT rotate(PT a, PT b, ld theta){
	return (b-a)*polar<ld>(1, theta) + a;
}

int relpos(PT a, PT b, PT c){
	b -= a, c -= a;
	c /= b;
	if (Grt(c.imag(), 0)) return LEFT;
	if (Lss(c.imag(), 0)) return RIGHT;
	if (Lss(c.real(), 0)) return BACK;
	if (Grt(c.real(), 1)) return FRONT;
	return ON;
}

int side(PT a, PT b, PT c){
	b -= a, c -= a;
	ld cr = (c/b).Y;
	return Grt(cr, 0) ? 1 : (Lss(cr, 0) ? -1 : 0);
}

bool intersect(PT a, PT b, PT c, PT d){
	int as = side(c, d, a), bs = side(c, d, b), cs = side(a, b, c), ds = side(a, b, d);
	if (as && as == bs || cs && cs == ds) return false;
	else if (as || bs || cs || ds) return true;
	for (int j = 0; j < 2; j++, swap(a, c), swap(b, d)){
		ld mx = min(a.X, b.X), Mx = max(a.X, b.X), my = min(a.Y, b.Y), My = max(a.Y, b.Y);
		for (int k = 0; k < 2; k++, swap(c, d))
			if (Geq(c.X, mx) && Leq(c.X, Mx) && Geq(c.Y, my) && Leq(c.Y, My))
				return true;
	}
	return false;
}

PT intersection(PT a, PT b, PT c, PT d){
	ld c1 = cross(b-a, c-a), c2 = cross(b-a, d-a);
	return (c1*d - c2*c)/(c1-c2);
}

ld distLSP(PT a, PT b, PT c){
	int rpos = relpos(a, b, proj(a, b, c));
	if (rpos == BACK) return len(c-a);
	if (rpos == FRONT) return len(c-b);
	b -= a, c -= a;
	return abs(cross(b, c)/len(b));
}

ld distLS(PT a, PT b, PT c, PT d){
	if (intersect(a, b, c, d)) return 0;
	return min(min(distLSP(a, b, c), distLSP(a, b, d)), min(distLSP(c, d, a), distLSP(c, d, b)));
}

ld signedArea(Poly &po){
	int n = po.size();
	ld res = 0;
	for (int i = 0; i < n; i++)
		res += cross(po[i], po[(i+1)%n]);
	return res/2;
}

ld area(Poly &poly){
	return abs(signedArea(poly));
}

bool isConvex(Poly &po){
	int n = po.size();
	bool neg = false, pos = false;
	for (int i = 0; i < n; i++){
		int rpos = relpos(po[i], po[(i+1)%n], po[(i+2)%n]);
		if (rpos == LEFT) pos = true;
		if (rpos == RIGHT) neg = true;
	}	
	return (neg&pos) == false;
}

int crossingN(Poly &po, PT a){
	int n = po.size();
	PT b = a;
	for (PT p : po)
		b.real(max(b.X, p.X));
	int cn = 0;
	for (int i = 0; i < n; i++){
		PT p = po[i], q = po[(i+1)%n];
		if (intersect(a, b, p, q) && (side(a, b, p) == 1 || side(a, b, q) == 1))
			cn++;
	}
	return cn;
}

int windingN(Poly &po, PT a){
	int n = po.size();
	PT b = a;
	for (PT p : po)
		b.real(max(b.X, p.X));
	int wn = 0;
	for (int i = 0; i < n; i++){
		PT p = po[i], q = po[(i+1)%n];
		if (intersect(a, b, p, q)){
			int ps = side(a, b, p), qs = side(a, b, q);
			if (qs >= 0) wn++;
			if (ps >= 0) wn--;
		}
	}
	return wn;
}

int pointInPoly(Poly &po, PT a){
	int n = po.size();
	for (int i = 0; i < n; i++)
		if (relpos(po[i], po[(i+1)%n], a) == ON)
			return ON;	
	return (crossingN(po, a)%2 ? IN : OUT);
}

Poly getHull(Poly &po, bool lower){
	sort(po.begin(), po.end(), cmpXY);
	Poly res;
	int n = res.size();
	for (auto p : po){
		while (n >= 2 && side(res[n-2], res[n-1], p) == (lower ? RIGHT : LEFT))
			res.pop_back(), n--;
		res.pb(p), n++;
	}
	return res;
}

Poly convexHull(Poly &po){
	int n = po.size();
	Poly lower = getHull(po, true),
		 upper = getHull(po, false);
	Poly res = lower;
	for (int i = (int)upper.size()-2; i; i--)
		res.pb(upper[i]);
	return res;
}

pair <PT, PT> farthestPair(Poly &po){
	int n = po.size();
	pair <PT, PT> res = {po[0], po[0]};
	int j = 0;
	for (int i = 0; i < n; i++){
		while (Grt(len(po[(j+1)%n] - po[i]), len(po[j] - po[i])))
			j = (j+1)%n;
		if (Grt(len(po[j]-po[i]), len(res.S-res.F)))
			res = {po[i], po[j]};
	}
	return res;
}

ld diameter(Poly &po){
	auto p = farthestPair(po);
	return len(p.S-p.F);
}

Poly convexCut(Poly &po, PT a, PT b){
	int n = po.size();
	Poly res;
	for (int i = 0; i < n; i++){
		if (side(a, b, po[i]) >= 0) 
			res.pb(po[i]);
		if (abs(side(a, b, po[i]) - side(a, b, po[(i+1)%n])) == 2)
			res.pb(intersection(a, b, po[i], po[(i+1)%n]));
	}
	return res;
}

int main(){	
	cout << setprecision(10) << fixed;
	Poly poly;
	for (int i = in(); i; i--){
		PT p;
		cin >> p;
		poly.pb(p);
	}
	for (int i = in(); i; i--){
		PT p, q;
		cin >> p >> q;
		Poly cut = convexCut(poly, p, q);
		cout << area(cut) << '\n';
	}
	return 0;
}