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;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define INF 1<<30
#define LINF 1LL<<60

typedef long double ld;
typedef complex<ld> Point;
const ld eps = 1e-9, pi = acos(-1.0);
namespace std {
    bool operator<(const Point &lhs, const Point &rhs) {
        if (lhs.real() < rhs.real() - eps) return true;
        if (lhs.real() > rhs.real() + eps) return false;
        return lhs.imag() < rhs.imag();
    }
}
Point input_point() {ld x, y; cin >> x >> y; return Point(x, y);} // ????????\???
bool eq(ld a, ld b) {return (abs(a - b) < eps);} // ????????????????????????
ld dot(Point a, Point b) {return real(conj(a) * b);} // ??????
ld cross(Point a, Point b) {return imag(conj(a) * b);} // ??????

// ??´????????????
class Line {
public:
    Point a, b;
    Line() : a(Point(0, 0)), b(Point(0, 0)) {}
    Line(Point a, Point b) : a(a), b(b) {}
    Point operator[](const int _num) {
        if (_num == 0)return a;
        else if (_num == 1)return b;
        else assert(false);
    }
};

// ????????????
class Circle {
public:
    Point p;
    ld r;
    Circle() : p(Point(0, 0)), r(0) {}
    Circle(Point p, ld r) : p(p), r(r) {}
};

// ??????????¶?
Point proj(Line l, Point p) {
    ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
    return l.a + t * (l.a - l.b);
}

// CCW
int ccw(Point a, Point b, Point c) {
    b -= a; c -= a;
    if (cross(b, c) > eps) return 1;   // a,b,c??????????¨???¨?????????????????¶
    if (cross(b, c) < -eps) return -1; // a,b,c???????¨???¨?????????????????¶
    if (dot(b, c) < 0) return 2;       // c,a,b???????????´???????????¶
    if (norm(b) < norm(c)) return -2;  // a,b,c???????????´???????????¶
    return 0;                          // a,c,b???????????´???????????¶
}

/* ???????????? */
// ??´?????¨??´??????????????????
bool isis_ll(Line l, Line m) {return !eq(cross(l.b - l.a, m.b - m.a), 0);}
// ??´?????¨?????????????????????
bool isis_ls(Line l, Line s) {
    return isis_ll(l, s) &&
    (cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}
// ????????¨?????????????????????
bool isis_ss(Line s, Line t) {
    return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
    ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}
// ????????´????????????
bool isis_lp(Line l, Point p) {return (abs(cross(l.b - p, l.a - p)) < eps);}
// ?????????????????????
bool isis_sp(Line s, Point p) {return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);}

/* ?????¢ */
// ??´?????¨??´????????????
Point is_ll(Line s, Line t) {
    Point sv = s.b - s.a, tv = t.b - t.a;
    assert(cross(sv, tv) != 0);
    return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

// ??´?????¨???????????¢
ld dist_lp(Line l, Point p) {
    return abs(p - proj(l, p));
}

// ??´?????¨??´???????????¢
ld dist_ll(Line l, Line m) {
    return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// ??´?????¨??????????????¢
ld dist_ls(Line l, Line s) {
    return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// ????????¨???????????¢
ld dist_sp(Line s, Point p) {
    Point r = proj(s, p);
    return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// ????????¨??????????????¢
ld dist_ss(Line s, Line t) {
    if (isis_ss(s, t)) return 0;
    return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) });
}

/* ????§???¢ */
typedef vector<Point> Polygon;
// ??¢???
ld area(const Polygon &p) {
    ld res = 0;
    int n = (int)p.size();
    for (int j = 0;j < n;j++) res += cross(p[j], p[(j + 1) % n]);
    return res / 2;
}
// ???????????? ????????????????????´???????§???¢????????´
Polygon convex_cut(const Polygon &ps, Line l) {
    int n = (int)ps.size();
    Polygon Q;
    for (int i = 0;i < n;i++) {
        Point A = ps[i], B = ps[(i + 1) % n];
        Line m = Line(A, B);
        if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
        if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
            Q.push_back(is_ll(l, m));
    }
    return Q;
}

int main(void) {
    cin.tie(0); ios::sync_with_stdio(false);
    int n; cin >> n;
    Polygon ps;
    for(int i = 0; i < n;i++) ps.emplace_back(input_point());
    int q; cin >> q;
    for(int i = 0; i < q;i++){
        /* ?????\???(??´???)??§???????????????????????´???????§???¢?????¢????????????*/
        Point p1 = input_point(), p2 = input_point();
        Line l(p1,p2);
        ld res = area(convex_cut(ps, l));
        cout << fixed << setprecision(10) << res << endl;
    }
    return 0;
}