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:
#define _USE_MATH_DEFINES
#include<bits/stdc++.h>
using namespace std;

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

#define EPS 1e-10
#define INF 1e10

typedef complex<double> Point;
typedef complex<double> Vector;
typedef vector<Point> Polygon;

struct Line
{
	Point a, b;
	Line() {}
	Line(const Point &_a, const Point &_b)
	{
		a = _a; b = _b;
	}
};

//?????????Line???¨??????(??????????????????????????????????????????)
struct Segment
{
	Point a, b;
	Segment() {}
	Segment(const Point &_a, const Point &_b)
	{
		a = _a; b = _b;
	}
};

struct Circle
{
	Point c;
	double r;

	Circle() {}

	Circle(const Point &_c, const double &_r)
	{
		c = _c; r = _r;
	}
};

istream& operator >> (istream& is, Point &p)
{
	double x, y;
	is >> x >> y;
	p.real(x); p.imag(y);
	return is;
}

Segment ToSegment(const Line l)
{
	return Segment(l.a, l.b);
}

Line ToLine(const Segment s)
{
	return Line(s.a, s.b);
}

//????????¨?±???==
bool equals(const double &a, const double &b)
{
	return abs(a - b) < EPS;
}

//????????¨?±???==
bool equals(const Vector &a, const Vector &b)
{
	return equals(a.real(), b.real()) && equals(a.imag(), b.imag());
}

bool comp(const Point &a, const Point &b)
{
	//return equals(a.real(), b.real()) ? a.imag() < b.imag() : a.real() < b.real();
	return a.real() < b.real();
}

//??????
double dot(const Vector &a, const Vector &b)
{
	return a.real()*b.real() + a.imag()*b.imag();
}

//??????
double cross(const Vector &a, const Vector &b)
{
	return a.real()*b.imag() - a.imag()*b.real();
}

//?????§????¢??????¢???
double GetArea(const Polygon &g)
{
	double res = 0;
	for (int i = 1; i < g.size() - 1; i++)
	{
		res += cross(g[i] - g[0], g[i + 1] - g[0]);
	}
	return abs(res / 2);
}

//????????¨???????(O(1))
//??????¶:?????????¨??????°??????
int CCW(const Point &p0, const Point &p1, const Point &p2)
{
	Vector v1 = (Vector)(p1 - p0), v2 = p2 - p0;
	if (cross(v1, v2) > EPS) return COUNTER_CLOCKWISE;
	if (cross(v1, v2) < -EPS) return CLOCKWISE;
	if (dot(v1, v2) < -EPS) return ONLINE_BACK;
	if (abs(v1) < abs(v2)) return ONLINE_FRONT;
	return ON_SEGMENT;
}

//???´?????????(O(1))
//??????¶:?????????°??????
bool IsOrthogonal(const Vector &a, const Vector &b)
{
	return equals(dot(a, b), 0.0);
}

bool IsOrthogonal(const Line &l1, const Line &l2)
{
	return equals(dot(l1.b - l1.a, l2.b - l2.a), 0.0);
}

//????????????(O(1))
bool IsParallel(const Vector &a, const Vector &b)
{
	return equals(cross(a, b), 0.0);
}

bool IsParallel(const Line &l1, const Line &l2)
{
	return equals(cross(l1.b - l1.a, l2.b - l2.a), 0.0);
}

//??°????±(O(1))
Point Project(const Line &s, const Point &p) {
	Vector v1 = s.b - s.a;
	Vector v2 = p - s.a;
	double r = dot(v1, v2) / norm(v1);
	return s.a + v1 * r;
}

//?????°?(O(1))
Point Reflect(const Line &s, const Point &p) {
	return p + (Project(s, p) - p) * 2.0;
}

//???´??????¨?????????????????????(O(1))
bool Intersects(const Line &l, const Segment &s)
{
	return CCW(l.a, l.b, s.a)*CCW(l.a, l.b, s.b) != 1;
}

//?????????????????????(O(1))
bool Intersects(const Segment &l1, const Segment &l2)
{
	return CCW(l1.a, l1.b, l2.a)*CCW(l1.a, l1.b, l2.b) <= 0 &&
		CCW(l2.a, l2.b, l1.a)*CCW(l2.a, l2.b, l1.b) <= 0;
}

//???´????????????(O(1))
//??????¶:???´???????????????§??????
Point GetIntersection(const Line &l1, const Line &l2)
{
	Vector a1 = l1.b - l1.a, a2 = l2.b - l2.a;
	Vector b1 = l2.a - l1.a, b2 = l1.a - l2.b;
	double s1 = cross(a1, b1) / 2, s2 = cross(a1, b2) / 2;
	return Point(l2.a.real() + a2.real()*s1 / (s1 + s2), l2.a.imag() + a2.imag()*s1 / (s1 + s2));
}

//????????????(O(1))
//??????¶:?????????°??????
vector<Point> GetIntersection(const Circle &c1, const Circle &c2)
{
	vector<Point> res;
	double d, a, t;
	d = sqrt(norm((c2.c - c1.c)));
	if (d < abs(c1.r - c2.r) || c1.r + c2.r < d) return res; //???¢?????????????????????
	a = acos((c1.r*c1.r + d*d - c2.r*c2.r) / (2 * c1.r*d));
	t = atan2(c2.c.imag() - c1.c.imag(), c2.c.real() - c1.c.real());
	res.push_back(Point(c1.c.real() + c1.r*cos(t + a), c1.c.imag() + c1.r*sin(t + a)));
	res.push_back(Point(c1.c.real() + c1.r*cos(t - a), c1.c.imag() + c1.r*sin(t - a)));
	if (equals(res[0], res[1])) res.pop_back(); //?????????1???
	return res;
}

//?????§????¢??????????????????(O(n))
//?????????
//  0:?????????????????????
//  1:??????????????????
//  2:?????????
int Contains(const Polygon &g, const Point &p)
{
	Line l = Line(p, Point(INF, p.imag()));
	int cnt = 0, n = g.size();
	for (int i = 0; i < n; i++)
	{
		Vector a = g[i] - p;
		Vector b = g[(i + 1) % n] - p;
		if (CCW(g[i], g[(i + 1) % n], p) == 0) return 2; //?????????
		if (a.imag() > b.imag()) swap(a, b);
		if (a.imag() <= EPS && EPS < b.imag() && cross(a, b) > EPS) cnt++;
	}
	if ((cnt & 1) == 1) return 1; //??????????????????
	return 0; //?????????????????????
}

//??????(O(n))
Polygon AndrewScan(Polygon &s)
{
	if (s.size() <= 2) return s;
	sort(s.begin(), s.end(), comp);
	Polygon g;
	for (int i = 0; i < s.size(); 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]);
	}
	int upper_n = g.size();
	for (int i = s.size() - 2; i >= 0; i--)
	{
		for (int n = g.size(); n > upper_n && 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;
}

//?????§????¢?????????
Polygon ConvexCut(const Polygon &g, const Line &l)
{
	Polygon res;
	for (int i = 0; i < g.size(); i++)
	{
		Segment s = Segment(g[i], g[(i + 1) % g.size()]);
		if (CCW(l.a, l.b, s.a) != -1) res.push_back(s.a);
		if (CCW(l.a, l.b, s.a)*CCW(l.a, l.b, s.b) == -1) 
			res.push_back(GetIntersection(l, ToLine(s)));
	}
	return res;
}

int N, Q;
Polygon g;

signed main()
{
	cin >> N;
	for (int i = 0; i < N; i++)
	{
		g.push_back(Point());
		cin >> g.back();
	}
	cin >> Q;
	for (int i = 0; i < Q; i++)
	{
		Line l;
		cin >> l.a >> l.b;
		Polygon left = ConvexCut(g, l);
		double ans;
		if (left.size() < 3) ans = 0;
		else ans = GetArea(left);
		printf("%.16f\n", ans);
	}
	return 0;
}