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>
#include <cmath>

using namespace std;
typedef long long ll;
//typedef unsigned long long ll;

#define rep(i, n) for (int i = 0; i < (n); ++i)
//#define rep(i, n) for (ll i = 0; i < (n); ++i)
//#define sz(x) ll(x.size())
//typedef pair<ll, int> P;
//typedef pair<ll, ll> P;
//const double INF = 1e10;
//const ll INF = LONG_LONG_MAX / 100;
//const ll INF = (1ll << 31) - 1;
//const ll INF = 1e15;
const ll MINF = LONG_LONG_MIN;
//const int INF = INT_MAX / 10;
#define cmin(x, y) x = min(x, y)
#define cmax(x, y) x = max(x, y)
//typedef pair<int, int> P;
//typedef pair<double, double> P;

//bool contain(set<P> &s, P a) { return s.find(a) != s.end(); }

//ifstream myfile("C:\\Users\\riku\\Downloads\\0_00.txt");
//ofstream outfile("log.txt");
//outfile << setw(6) << setfill('0') << prefecture << setw(6) << setfill('0') << rank << endl;
// std::cout << std::bitset<8>(9);
const int mod = 1000000007;
typedef priority_queue<long long, vector<long long>, greater<long long>> PQ_ASK;


void print_line(vector<string> &line) {
    if (line.size() == 0ll) {
        cout << endl;
        return;
    }
    for (ll i = 0; i < line.size(); i++) {
        cout << line[i];
        if (i == line.size() - 1) cout << endl;
        else cout << ' ';
    }
}

#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

struct Point {
    double x, y;

    Point(double x = 0, double y = 0) : x(x), y(y) {}

    Point operator+(Point p) { return Point(x + p.x, y + p.y); }

    Point operator-(Point p) { return Point(x - p.x, y - p.y); }

    Point operator*(double a) { return Point(a * x, a * y); }

    Point operator/(double a) { return Point(x / a, y / a); }

    double abs() { return sqrt(norm()); }

    double norm() { return x * x + y * y; }

    bool operator<(const Point &p) const {
        return x != p.x ? x < p.x : y < p.y;
    }

    bool operator==(const Point &p) const {
        return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
    }
};

typedef Point Vector;
typedef vector<Point> Polygon;


static const int IN = 2;
static const int ON = 1;
static const int OUT = 0;

double dot(Vector a, Vector b) {
    return a.x * b.x + a.y * b.y;
}

double cross(Vector a, Vector b) {
    return a.x * b.y - a.y * b.x;
}

static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;   // p2->p0->p1
static const int ONLINE_FRONT = -2; // p0->p1->p2
static const int ON_SEGMENT = 0;    // p0->p2->p1

double norm(Point a) {
    return a.x * a.x + a.y * a.y;
}

int ccw(Point p0, Point p1, Point p2) {
    Vector a = p1 - p0;
    Vector b = p2 - p0;
    if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
    if (cross(a, b) < -EPS) return CLOCKWISE;
    if (dot(a, b) < -EPS) return ONLINE_BACK;
    if (norm(a) < norm(b)) return ONLINE_FRONT;
    return ON_SEGMENT;
}

Polygon f(Polygon g) {
    Polygon u, l;
    if (g.size() < 3) return g;
    sort(g.begin(), g.end());
    u.push_back(g[0]);
    u.push_back(g[1]);
    l.push_back(g[g.size() - 1]);
    l.push_back(g[g.size() - 2]);

    // upper
    for (int i = 2; i < g.size(); i++) {
        for (int n = u.size(); n >= 2 && ccw(u[n - 2], u[n - 1], g[i]) == COUNTER_CLOCKWISE; n--) {
            u.pop_back();
        }
        u.push_back(g[i]);
    }

    // lower
    for (int i = g.size() - 3; i >= 0; i--) {
        for (int n = l.size(); n >= 2 && ccw(l[n - 2], l[n - 1], g[i]) == COUNTER_CLOCKWISE; n--) {
            l.pop_back();
        }
        l.push_back(g[i]);
    }

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

    return l;
}


double abs(Point a) {
    return sqrt(norm(a));
}


double getDistance(Point a, Point b) {
    return abs(a - b);
}


double convexDiameter(Polygon g) {
    double d = 0.0;
    int n = g.size();
    int is = 0, js = 0;
    for (int i = 1; i < n; i++) {
        if (g[i].y > g[is].y) is = i;
        if (g[i].y < g[js].y) js = i;
    }
    d = getDistance(g[is], g[js]);

    int i = is, j = js, maxi = is, maxj = js;
    do {
        if (cross(g[(i + 1) % n] - g[i], g[(j + 1) % n] - g[j]) >= 0.0) j = (j + 1) % n;
        else i = (i + 1) % n;
        if (getDistance(g[i], g[j]) > d) {
            d = getDistance(g[i], g[j]);
            maxi = i, maxj = j;
        }
    } while (i != is || j != js);

    return d;
}

struct Segment {
    Point p1, p2;

    Segment(Point p1, Point p2) : p1(p1), p2(p2) {}
};

typedef Segment Line;

bool isParallel(Vector a, Vector b) {
    return equals(cross(a, 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 equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}



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);
}



Point getCrossPoint(Segment s1, Segment s2){
    Vector base = s2.p2 - s2.p1;
    double d1 = abs(cross(base, s1.p1-s2.p1));
    double d2 = abs(cross(base, s1.p2-s2.p1));
    double t = d1 / (d1 + d2);
    return s1.p1 + (s1.p2 - s1.p1) * t;
}



Polygon andrewScan(Polygon g){
    Polygon u, l;
    if(g.size() < 3)    return g;
    sort(g.begin(), g.end());
    u.push_back(g[0]);
    u.push_back(g[1]);
    l.push_back(g[g.size()-1]);
    l.push_back(g[g.size()-2]);

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

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

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

    return l;
}


double area(Polygon g){
    if(g.size() < 3)    return 0;
    int n = g.size();
    Point o(0.0, 0.0);
    double s = 0.0;
    for(int i = 0; i < n; i++)  s += cross(g[i]-o, g[(i+1)%n]-o);
    return abs(s) / 2.0;
}

int main() {
    int n;
    cin >> n;
    Polygon g;
    for (int i = 0; i < n; i++) {
        double x, y;
        cin >> x >> y;
        g.push_back(Point(x, y));
    }
    int q;
    cin >> q;
    while (q-- > 0) {
        double px, py, qx, qy;
        cin >> px >> py >> qx >> qy;
        Point a(px, py), b(qx, qy);
        Vector diff = b - a;
        a = a - diff * 10001;
        b = b + diff * 10001;
        Polygon h;
        for (int i = 0; i < n; i++) {
            if (!isParallel(g[i], g[(i + 1) % n], a, b) && intersect(g[i], g[(i + 1) % n], a, b))
                h.push_back(getCrossPoint(Segment(g[i], g[(i + 1) % n]), Segment(a, b)));
        }
        for (int i = 0; i < n; i++) {
            if (cross(b - a, g[i] - a) >= 0.0) h.push_back(g[i]);
        }
        h = andrewScan(h);
        cout << fixed << setprecision(12) << area(h) << endl;
    }
    return 0;
}