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;
using LL = long long;
using ULL = unsigned long long;
const double PI = acos(-1);
template<class T>constexpr T INF() { return ::std::numeric_limits<T>::max(); }
template<class T>constexpr T HINF() { return INF<T>() / 2; }
template <typename T_char>T_char TL(T_char cX) { return tolower(cX); };
template <typename T_char>T_char TU(T_char cX) { return toupper(cX); };
typedef pair<LL, LL> pii;
const int vy[] = { -1, -1, -1, 0, 1, 1, 1, 0 }, vx[] = { -1, 0, 1, 1, 1, 0, -1, -1 };
const int dx[4] = { 0,1,0,-1 }, dy[4] = { 1,0,-1,0 };
int popcnt(unsigned long long n) { int cnt = 0; for (int i = 0; i < 64; i++)if ((n >> i) & 1)cnt++; return cnt; }
int d_sum(LL n) { int ret = 0; while (n > 0) { ret += n % 10; n /= 10; }return ret; }
int d_cnt(LL n) { int ret = 0; while (n > 0) { ret++; n /= 10; }return ret; }
LL gcd(LL a, LL b) { if (b == 0)return a; return gcd(b, a%b); };
LL lcm(LL a, LL b) { LL g = gcd(a, b); return a / g*b; };
# define ALL(qpqpq)           (qpqpq).begin(),(qpqpq).end()
# define UNIQUE(wpwpw)        sort(ALL((wpwpw)));(wpwpw).erase(unique(ALL((wpwpw))),(wpwpw).end())
# define LOWER(epepe)         transform(ALL((epepe)),(epepe).begin(),TL<char>)
# define UPPER(rprpr)         transform(ALL((rprpr)),(rprpr).begin(),TU<char>)
# define FOR(i,tptpt,ypypy)   for(LL i=(tptpt);i<(ypypy);i++)
# define REP(i,upupu)         FOR(i,0,upupu)
# define INIT                 std::ios::sync_with_stdio(false);std::cin.tie(0)
# pragma warning(disable:4996)

//定義系

double EPS = 1e-10;

//誤差を考慮して足し算を行う
double add(double a, double b) {
	if (abs(a + b) < EPS*(abs(a) + abs(b)))return 0;
	return a + b;
}

//Point
struct Point {
	double x, y;
	Point() {}
	Point(double x, double 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 * (double d) {
		return Point(x*d, y*d);
	}
	Point operator / (double d) {
		return Point(x / d, y / d);
	}
	//内積
	double dot(Point p) {
		return add(x*p.x, y*p.y);
	}
	//外積
	double det(Point p) {
		return add(x*p.y, -y*p.x);
	}
	//点の大小比較
	bool operator <(const Point &p)const {
		if (fabs(add(x, -p.x)) < EPS)return y < p.y;
		return x < p.x;
	}
	bool operator ==(const Point &p)const {
		return fabs(x - p.x) < EPS&&fabs(y - p.y) < EPS;
	}
};

//ベクトル。使い分けるといいかも
typedef Point Vector;

//ベクトルの大きさの2乗
double norm(Vector p) {
	return p.x*p.x + p.y*p.y;
}

//ベクトルの大きさ
double abs(Vector p) {
	return sqrt(norm(p));
}

//線分
struct Segment {
	Point p1, p2;
};

//直線
typedef Segment Line;

//中心c,半径rの円
struct Circle {
	Point c;
	double r;
	Circle(Point c = Point(), double r = 0.0) :c(c), r(r) {}
};

//多角形
typedef vector<Point> Polygon;

//頂点集合
typedef vector<Point> Points;




//計算・アルゴリズム系


//反時計回りCCW
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 (a.det(b) > EPS)return COUNTER_CLOCKWISE;
	if (a.det(b) < -EPS)return CLOCKWISE;
	if (a.dot(b) < -EPS)return ONLINE_BACK;
	if (norm(a) < norm(b))return ONLINE_FRONT;

	return ON_SEGMENT;
}

//線分p1p2と線分p3p4の交差判定
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);
}

//ベクトルa,bの直交判定
bool isOrthogonal(Vector a, Vector b) {
	return a.dot(b) == 0.0;
}
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
	return isOrthogonal(a1 - a2, b1 - b2);
}
bool isOrthogonal(Segment s1, Segment s2) {
	return (s1.p2 - s1.p1).dot(s2.p2 - s2.p1) == 0.0;
}

//ベクトルa,bの並行判定
bool isParallel(Vector a, Vector b) {
	return a.det(b) == 0.0;
}
bool isParallel(Point a1, Point a2, Point b1, Point b2) {
	return isParallel(a1 - a2, b1 - b2);
}
bool isParallel(Segment s1, Segment s2) {
	return (s1.p2 - s1.p1).det(s2.p2 - s2.p1) == 0.0;
}

//射影(点p1と点p2を通る直線に点pから垂線を引いた交点xを求める)
Point project(Segment s, Point p) {
	Vector base = s.p2 - s.p1;
	double r = (p - s.p1).dot(base) / norm(base);
	return s.p1 + base*r;
}

//反射(点p1と点p2を通る直線を対象軸として点pと線対称の位置にある点xを求める)
Point reflect(Segment s, Point p) {
	return p + (project(s, p) - p)*2.0;
}

//点aと点bの距離
double getDistance(Point a, Point b) {
	return abs(a - b);
}

//直線lと点pの距離
double getDistanceLP(Line l, Point p) {
	return abs((l.p2 - l.p1).det(p - l.p1) / abs(l.p2 - l.p1));
}

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

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

//線分s1と線分s2の交点
Point getCrossPoint(Segment l, Segment m) {
	double d1 = (l.p2 - l.p1).det( m.p2 - m.p1);
	double d2 = (l.p2 - l.p1).det( l.p2 - m.p1);
	if (abs(d1) < EPS && abs(d2) < EPS) return m.p1;
	return m.p1 + (m.p2 - m.p1) * d2 / d1;
}

//円cと線分lの交点
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 make_pair(pr + e*base, pr - e*base);
}

//円c1と円c2の交点
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 make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

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

//凸包を求める
Polygon convex_hull(Polygon s) {
	Polygon u, l;
	if (s.size() <= 2)return s;
	sort(s.begin(), s.end(), [](const Point &p1, const Point &p2) {return p1.y == p2.y ? p1.x<p2.x : p1.y<p2.y; });
	u.push_back(s[0]);
	u.push_back(s[1]);
	l.push_back(s[s.size() - 1]);
	l.push_back(s[s.size() - 2]);

	for (int i = 2; i<s.size(); i++){
		for (int n = u.size(); n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) != CLOCKWISE&&ccw(u[n - 2], u[n - 1], s[i]) != ONLINE_FRONT; n--){
			u.pop_back();
		}
		u.push_back(s[i]);
	}

	for (int i = s.size() - 3; i >= 0; i--){
		for (int n = l.size(); n >= 2 && ccw(l[n - 2], l[n - 1], s[i]) != CLOCKWISE&&ccw(l[n - 2], l[n - 1], s[i]) != ONLINE_FRONT; n--){
			l.pop_back();
		}
		l.push_back(s[i]);
	}

	reverse(l.begin(), l.end());
	for (int i = u.size() - 2; i >= 1; i--)l.push_back(u[i]);

	return l;
}

//y座標の昇順でマージするための比較関数
bool compare_y(Point a, Point b) {
	return a.y < b.y;
}

//最近点対
double closest_pair(Point *a, int n) {
	if (n <= 1)return INF<double>();
	sort(a, a + n);
	int m = n / 2;
	double x = a[m].x;
	double d = min({ closest_pair(a,m),closest_pair(a + m,n - m) });//p,qが違う区間にある
	inplace_merge(a, a + m, a + n, compare_y);//2つのソートされた列をマージ

											  //p,qが同じ区間にある
	Points b;//直線から距離d未満の頂点を入れていく
	for (int i = 0; i < n; i++) {
		if (add(fabs(add(a[i].x, -x)), -d) >= 0.0)continue;

		//bに入っている頂点を、末尾からy座標の差がd以上になるまで見ていく
		for (int j = 0; j < b.size(); j++) {
			Point dd;
			dd.x = add(a[i].x, -b[b.size() - j - 1].x);
			dd.y = add(a[i].y, -b[b.size() - j - 1].y);
			if (add(dd.y, -d) >= 0.0)break;
			d = min(d, abs(dd));
		}
		b.emplace_back(a[i]);
	}
	return d;
}

//多角形の面積
double area(Polygon p) {
	int n = p.size();
	double sum = 0.0;
	for (int i = 0; i < n; i++) {
		sum = add(sum,0.5*p[i].det(p[(i + 1) % n]));
	}
	return sum < 0.0 ? -sum : sum;
}

//凸性判定
bool is_convex(Polygon p) {
	for (int i = 0; i < p.size(); i++) {
		if (ccw(p[(i - 1 + p.size()) % p.size()], p[i], p[(i + 1) % p.size()]) == -1)return false;
	}
	return true;
}

//切断
Polygon convex_cut(Polygon p, Line l) {
	Polygon ret;
	for (int i = 0; i < p.size(); i++) {
		Point cur = p[i], nxt = p[(i + 1) % p.size()];
		if (ccw(l.p1, l.p2, cur) != -1)ret.emplace_back(cur);
		if (ccw(l.p1, l.p2, cur)*ccw(l.p1, l.p2, nxt) < 0) {
			Segment seg;
			seg.p1 = cur;
			seg.p2 = nxt;
			ret.emplace_back(getCrossPoint(seg, l));
		}
	}
	return ret;
}
int main() {
	int n;
	cin >> n;
	Polygon g;
	REP(i, n) {
		Point p;
		cin >> p.x >> p.y;
		g.emplace_back(p);
	}
	int q;
	cin >> q;
	REP(qqq, q) {
		Line l;
		cin >> l.p1.x >> l.p1.y >> l.p2.x >> l.p2.y;
		cout << fixed << setprecision(13) << area(convex_cut(g,l)) << endl;
	}
}