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>
#define int long long
#define endl '\n'
#define FOR(i, a, n) for (int i = (a); i < (n); ++i)
#define REP(i, n) FOR(i, 0, n)
using namespace std;

using T = double;
const T EPS = 1e-10;
T torad(int deg) {return (T)(deg) * M_PI / 180;}
T todeg(T ang) {return ang * 180 / M_PI;}

/* Point */
using P = complex<T>;
#define x real()
#define y imag()
template <typename T> inline bool eq(T p, T q) { return abs(p - q) < EPS; }
inline int sgn(T x) { return (T(0) < x) - (x < T(0)); }
inline T dot(P v, P w) { return (conj(v) * w).x; }
inline T cross(P v, P w) { return (conj(v) * w).y; }
inline bool isOrth(P v, P w) { return dot(v, w) == 0; }
inline bool isPara(P v, P w) { return cross(v, w) == 0; }
inline P unit(P v) { return v / abs(v); }
inline P translate(P p, P v) { return p + v; }
inline P scale(P p, P c, T k) { return c + (p - c) * k; }
inline P rot(P p, T a) { return p * polar(1.0, a); }
inline P rot90(P p) { return {-p.y, p.x}; }
inline T orient(P a, P b, P c) { return cross(b - a, c - a); }
istream& operator>>(istream& is, P& p) { T xx, yy; is >> xx >> yy; p = P(xx, yy); return is; }
bool cmpX(const P& a, const P& b) { return a.x != b.x ? a.x < b.x : a.y < b.y; }
namespace std {
    bool operator < (const P& a, const P& b) { return cmpX(a, b); }
}

P linearTransform(P p, P q, P fp, P fq, P r) {
    return fp + (r - p) * (fq - fp) / (q - p);
}

int ccw(P a, P b, P c) {
    b -= a; c -= a;
    if (cross(b, c) > 0) return +1;      // counter clockwise
    if (cross(b, c) < 0) return -1;      // clockwise
    if (dot(b, c) < 0) return +2;        // c--a--b on line
    if (norm(b) < norm(c)) return -2;    // a--b--c on line or a==b
    return 0;                            // a--c--b on line or a==c or b==c
}

T angle(P v, P w) {
    T cosTheta = dot(v, w) / abs(v) / abs(w);
    return acos(max(-1.0, min(1.0, cosTheta)));
}
T orientedAngle(P a, P b, P c) {
    if (orient(a, b, c) >= 0) return angle(b - a, c - a);
    return 2 * M_PI - angle(b - a, c - a);
}
bool inAngle(P a, P b, P c, P p) {
    assert(abs(orient(a, b, c)) != 0);
    if (orient(a, b, c) < 0) swap(b, c);
    return orient(a, b, p) >= 0 && orient(a, c, p) <= 0;
}

// polar sort
bool half(P p) {
    assert(p.x != 0 || p.y != 0);
    return p.y > 0 || (p.y == 0 && p.x < 0);
}
void polarSort(vector<P>& v, P o = P(0.0, 0.0)) {
    sort(v.begin(), v.end(), [&](P v, P w) {
        return make_tuple(half(v - o), 0, norm(v - o)) <
            make_tuple(half(w - o), cross(v - o, w - o), norm(w - o));
    });
}

/* Line */
struct L : array<P, 2> {
    P v; T c;
    L(P a = P(0.0, 0.0), P b = P(0.0, 0.0)) : array<P, 2>({a, b}), v(b - a), c(cross(v, a)) {}
    T side(P p) { return cross(v, p) - c; }
    P proj(P p) { return p - rot90(v) * side(p) / norm(v); }
    P refl(P p) { return p - rot90(v) * T(2) * side(p) / norm(v); }
    friend istream& operator>>(istream& is, L& l) { P a, b; is >> a >> b; l = L(a, b); return is; }
    friend ostream& operator<<(ostream& os, const L& l) { return os << '{' << l[0] << ", " << l[1] << '}'; }
};

/* Circle */
struct C : P {
    T r;
    C(P p = P(0.0, 0.0), T r = 0.0) : P(p), r(r) {}
    friend ostream& operator<<(ostream& os, const C& c) { return os << '(' << c.x << ", " << c.y << ", " << c.r << ')'; }
};

P circumCenter(P a, P b, P c) {
    b -= a, c -= a;
    assert(cross(b, c) != 0);
    return a + rot90(b * norm(c) - c * norm(b)) / cross(b, c) / T(2);
}

vector<P> tangentPoints(C c, P p) {
    if (eq(abs(p - c), c.r)) return vector<P>{p};
    vector<P> res;
    T t = acos(c.r / abs(p - c));
    P q = (p - c) / abs(p - c) * c.r;
    res.push_back(c + q * polar(1.0, t));
    res.push_back(c + q * polar(1.0, -t));
    sort(res.begin(), res.end(), cmpX);
    return res;
}

vector<L> tangentLines(C c1, C c2, bool inner) {
    if (inner) c2.r = -c2.r;
    vector<L> res;
    P d = c2 - c1;
    T dr = c1.r - c2.r, d2 = norm(d), h2 = d2 - dr * dr;
    if (d2 == 0 || h2 < 0) { assert(h2 != 0); return res; }
    for (T sign : {-1, 1}) {
        P v = (d * dr + rot90(d) * sqrt(h2) * sign) / d2;
        res.emplace_back(c1 + v * c1.r, c2 + v * c2.r);
    }
    return res;
}

// intersect
bool isInterPL(P p, L l) { return (ccw(l[0], l[1], p) != 1); }
bool isInterPS(P p, L s) { return (ccw(s[0], s[1], p) == 0); }
bool isInterLL(L l, L m) { return (!isPara(l.v, m.v)); }
bool isInterLS(L l, L s) {
    if (eq(s[0], s[1])) return isInterPL(s[0], l);
    return (ccw(l[0], l[1], s[0]) * ccw(l[0], l[1], s[1]) <= 0);
}
bool isInterSS(L s, L t) {
    if (eq(s[0], s[1])) return isInterPL(s[0], t);
    if (eq(t[0], t[1])) return isInterPL(t[0], s);
    return (ccw(s[0], s[1], t[0]) * ccw(s[0], s[1], t[1]) <= 0 &&
            ccw(t[0], t[1], s[0]) * ccw(t[0], t[1], s[1]) <= 0);
}
int isInterCC(C a, C b) {
    T d = abs(b - a);
    if (a == b && a.r == b.r) return 0;         // ∞ cp (A = B)
    if (a.r + d - b.r < -EPS) return +1;        // 0 cp (A in B)
    if (b.r + d - a.r < -EPS) return -1;        // 0 cp (B in A)
    if (abs(a.r + d - b.r) < EPS) return +2;    // 1 cp (A in B)
    if (abs(b.r + d - a.r) < EPS) return -2;    // 1 cp (B in A)
    if (abs(a.r + b.r - d) < EPS) return 3;     // 1 cp (outside)
    if (a.r + b.r - d < -EPS) return 4;         // 0 cp (outside)
    return 5;                                   // 2 cp
}
 
// distance
T distancePL(P p, L l) { return (abs(p - l.proj(p))); }
T distancePS(P p, L s) {
    P h = s.proj(p);
    if (isInterPS(h, s)) return abs(p - h);
    return min(abs(p - s[0]), abs(p - s[1]));
}
T distanceLL(L l, L m) {
    if (isInterLL(l, m)) return T(0);
    return distancePL(m[0], l);
}
T distanceLS(L l, L s) {
    if (isInterLS(l, s)) return 0;
    return min(distancePL(s[0], l), distancePL(s[1], l));
}
T distanceSS(L s, L t) {
    if (isInterSS(s, t)) return 0;
    return min({distancePS(s[0], t), distancePS(s[1], t), distancePS(t[0], s), distancePS(t[1], s)});
}

// crosspoint
vector<P> crosspointLL(L l, L m) {
    if (!isInterLL(l, m)) return vector<P>();
    vector<P> res;
    T d = cross(m[1] - m[0], l[1] - l[0]);
    res.push_back(l[0] + (l[1] - l[0]) * cross(m[1] - m[0], m[1] - l[0]) / d);
    return res;
}
vector<P> crosspointLS(L l, L s) {
    if (!isInterLS(l, s)) return vector<P>();
    vector<P> res;
    T d = cross(s[1] - s[0], l[1] - l[0]);
    res.push_back(l[0] + (l[1] - l[0]) * cross(s[1] - s[0], s[1] - l[0]) / d);
    return res;
}
vector<P> crosspointLC(L l, C c) {
    if (abs(c - l.proj(c)) > c.r) return vector<P>();
    vector<P> res;
    T d = distancePL(c, l), h2 = c.r * c.r - d * d;
    assert(h2 >= 0);
    P p = l.proj(c), h = l.v * sqrt(h2) / abs(l.v);
    res.push_back(p - h);
    if (abs(h) > 0) res.push_back(p + h);
    return res;
}
vector<P> crosspointSS(L s, L t) {
    if (!isInterSS(s, t)) return vector<P>();
    vector<P> res;
    if (unit(s.v) != unit(t.v)) {
        T d = cross(t[1] - t[0], s[1] - s[0]);
        res.push_back(s[0] + (s[1] - s[0]) * cross(t[1] - t[0], t[1] - s[0]) / d);
    } else {
        if (ccw(s[0], s[1], t[0]) == 0) res.push_back(t[0]);
        if (ccw(s[0], s[1], t[1]) == 0) res.push_back(t[1]);
        if (ccw(t[0], t[1], s[0]) == 0) res.push_back(s[0]);
        if (ccw(t[0], t[1], s[1]) == 0) res.push_back(s[1]);
    }
    return res;
}
vector<P> crosspointSC(L s, C c) {
    if (abs(c - s.proj(c)) > c.r) return vector<P>();
    vector<P> res;
    T d = distancePL(c, s), h2 = c.r * c.r - d * d;
    assert(h2 >= 0);
    P p = s.proj(c), h = s.v * sqrt(h2) / abs(s.v);
    if (ccw(s[0], s[1], p - h) == 0) res.push_back(p - h);
    if (abs(h) > 0 && ccw(s[0], s[1], p + h) == 0) res.push_back(p + h);
    return res;
}
vector<P> crosspointCC(C c1, C c2) {
    P d = c2 - c1; T d2 = norm(d);
    if (d2 == 0) { assert(c1.r != c2.r); return vector<P>(); }
    vector<P> res;
    T pd = (d2 + c1.r * c1.r - c2.r * c2.r) / 2;
    T h2 = c1.r * c1.r - pd * pd / d2;
    if (h2 >= 0) {
        P p = c1 + d * pd / d2, h = rot90(d) * sqrt(h2 / d2);
        res.push_back(p - h);
        if (abs(h) > 0) res.push_back(p + h);
    }
    return res;
}

/* Polygon */
// p[0] has minimum y and p is counterclockwise
vector<P> makeStandard(vector<P> p) {
    int n = p.size(), j = -1;
    for (int i = 0; i < n; ++i) {
        if (j == -1 || p[i].y < p[j].y) j = i;
    }
    vector<P> res;
    if (p[(j - 1 + n) % n].x <= p[j].x && p[j].x <= p[(j + 1) % n].x) {
        for (int i = 0; i < n; ++i) {
            res.push_back(p[(i + j) % n]);
        }
    } else {
        for (int i = 0; i < n; ++i) {
            res.push_back(p[(i - j + n) % n]);
        }
    }
    return res;
}
bool isConvex(vector<P> p) {
    p = makeStandard(p);
    for (int i = 0, n = p.size(); i < n; ++i) {
        P a = p[i], b = p[(i + 1) % n], c = p[(i + 2) % n];
        if (orient(a, b, c) < 0) return false;
        if (b.y != p[0].y && b.y < min(a.y, c.y)) return false;
        if (b.y != p[0].y && a.y == b.y && b.y == c.y && a.x <= b.x && b.x <= c.x) return false;
    }
    return true;
}
T areaTriangle(P a, P b, P c) {
    return abs(cross(b - a, c - a)) / T(2);
}
T area(vector<P> p) {
    T res = 0;
    for (int i = 0, n = p.size(); i < n; ++i) {
        res += cross(p[i], p[(i + 1) % n]);
    }
    return abs(res) / T(2);
}
bool above(P a, P p) { return p.y >= a.y; }
bool crossesRay(P a, P p, P q) {
    return (above(a, q) - above(a, p)) * orient(a, p, q) > 0;
}
// if strict, returns false when A is on the boundary
bool inPolygon(vector<P> p, P a, bool strict = true) {
    int numCrossing = 0;
    for (int i = 0, n = p.size(); i < n; ++i) {
        if (ccw(p[i], p[(i + 1) % n], a) == 0)
            return !strict;
        numCrossing += crossesRay(a, p[i], p[(i + 1) % n]);
    }
    return numCrossing & 1;
}
vector<P> convexHull(vector<P> p) {
    int n = p.size(), k = 0;
    sort(p.begin(), p.end(), cmpX);
    vector<P> res(2 * n);
    for (int i = 0; i < n; res[k++] = p[i++])
        while (k >= 2 && ccw(res[k - 2], res[k - 1], p[i]) <= 0) --k;
    for (int i = n - 2, t = k + 1; i >= 0; res[k++] = p[i--])
        while (k >= t && ccw(res[k - 2], res[k - 1], p[i]) <= 0) --k;
    res.resize(k - 1);
    return res;
}
vector<P> convexHullCollinearOK(vector<P> p) {
    int n = p.size(), k = 0;
    sort(p.begin(), p.end(), cmpX);
    vector<P> res(2 * n);
    for (int i = 0; i < n; res[k++] = p[i++])
        while (k >= 2 && ccw(res[k - 2], res[k - 1], p[i]) == -1) --k;
    for (int i = n - 2, t = k + 1; i >= 0; res[k++] = p[i--])
        while (k >= t && ccw(res[k - 2], res[k - 1], p[i]) == -1) --k;
    res.resize(k - 1);
    return res;
}
vector<P> convexCut(vector<P> p, L l) {
    vector<P> res;
    for (int i = 0, n = p.size(); i < n; ++i) {
        int ccwc = ccw(l[0], l[1], p[i]);
        if (ccwc != -1) res.push_back(p[i]);
        int ccwn = ccw(l[0], l[1], p[(i + 1) % n]);
        if (ccwc * ccwn == -1) res.push_back(crosspointLL(l, L(p[i], p[(i + 1) % n]))[0]);
    }
    return res;
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(10);

    int n;
    cin >> n;
    vector<P> p(n);
    REP (i, n) cin >> p[i];
    int q;
    cin >> q;
    REP (i, q) {
        L l;
        cin >> l;
        cout << area(convexCut(p, l)) << endl;
    }
}