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

using namespace std;
using LL = long long;
using P = pair<int, int>;
using Tapris = tuple<int, int, int>;

#define FOR(i, a, n) for(int i = (int)(a); i < (int)(n); ++i)
#define REP(i, n) FOR(i, 0, n)

#define pb(a) push_back(a)
#define all(x) (x).begin(),(x).end()

const int INF = (int)1e9;
const LL INFL = (LL)1e15;
const int MOD = 1e9 + 7;

int dy[]={0, 0, 1, -1, 0};
int dx[]={1, -1, 0, 0, 0};

typedef long double LD;
typedef complex<LD> Point;
typedef pair<Point, Point> Line;
typedef vector<Point> Polygon;
const LD EPS = 1e-10;
#define X real() // x座標を取得
#define Y imag() // y座標を取得
#define LE(n,m) ((n) < (m) + EPS)
#define GE(n,m) ((n) + EPS > (m))
#define EQ(n,m) (abs((n)-(m)) < EPS)

// 内積 Dot(a, b) = |a||b|cosθ
LD Dot(Point a, Point b){
    return (conj(a)*b).X;
}

// 外積 Cross(a, b) = |a||b|sinθ
LD Cross(Point a, Point b){
    return (conj(a)*b).Y;
}

int CCW(Point a, Point b, Point 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
    return 0;
}

//*********************************************
//          点と線(Point and Line)            *
//*********************************************

// 交差判定 (Isec) ****************************
// 点　 := 平面座標にある点
// 直線 := 点と点を通るどこまでも続く線
// 線分 := 点と点を結んでその両端で止まっている線

// 直線と点
bool IsecLP(Point a1, Point a2, Point b){
    return abs(CCW(a1, a2, b)) != 1;
}

// 直線と直線
bool IsecLL(Point a1, Point a2, Point b1, Point b2) {
    return !IsecLP(a2-a1, b2-b1, 0) || IsecLP(a1, b1, b2);
}

// 直線と線分
bool IsecLS(Point a1, Point a2, Point b1, Point b2) {
    return Cross(a2-a1, b1-a1) * Cross(a2-a1, b2-a1) < EPS;
}

// 線分と線分
bool IsecSS(Point a1, Point a2, Point b1, Point b2) {
    return CCW(a1, a2, b1)*CCW(a1, a2, b2) <= 0 && CCW(b1, b2, a1)*CCW(b1, b2, a2) <= 0;
}

// 線分と点
bool IsecSP(Point a1, Point a2, Point b) {
    return !CCW(a1, a2, b);
}

// ********************************************


// 距離 (Dist) ********************************
// 点pの直線aへの射影点を返す
Point Proj(Point a1, Point a2, Point p){
    return a1 + Dot(a2-a1, p-a1) / norm(a2-a1) * (a2-a1);
}

// 点pの直線aへの反射点を返す
Point Reflection(Point a1, Point a2, Point p){
    return 2.0L*Proj(a1, a2, p) - p;
}

// 点と点
LD DistPP(Point a, Point b){
    return abs(a-b);
}

// 直線と点
LD DistLP(Point a1, Point a2, Point p){
    return abs(Proj(a1, a2, p) - p);
}

// 直線と直線
LD DistLL(Point a1, Point a2, Point b1, Point b2) {
    return IsecLL(a1, a2, b1, b2) ? 0 : DistLP(a1, a2, b1);
}

// 直線と線分
LD DistLS(Point a1, Point a2, Point b1, Point b2) {
    return IsecLS(a1, a2, b1, b2) ? 0 : min(DistLP(a1, a2, b1), DistLP(a1, a2, b2));
}

// 線分と点
LD DistSP(Point a1, Point a2, Point p) {
    if(Dot(a2-a1,p-a1) < EPS) return abs(p-a1);
    if(Dot(a1-a2,p-a2) < EPS) return abs(p-a2);
    return abs(Cross(a2-a1,p-a1)) / abs(a2-a1);
}

// 線分と線分
LD DistSS(Point a1, Point a2, Point b1, Point b2) {
    if(IsecSS(a1, a2, b1, b2)) return 0;
    return min(min(DistSP(a1, a2, b1), DistSP(a1, a2, b2)), min(DistSP(b1, b2, a1), DistSP(b1, b2, a2)));
}

// ********************************************


// 2直線の交点 (CrossPoint) *******************
Point CrossPointLL(Point a1, Point a2, Point b1, Point b2){
    LD d1 = Cross(b2-b1, b1-a1);
    LD d2 = Cross(b2-b1, a2-a1);
    if (EQ(d1, 0) && EQ(d2, 0)) return a1;
    if (EQ(d2, 0)) throw "not exist crosspoint";
    return a1 + d1/d2 * (a2-a1);
}
// ********************************************


//*********************************************
//             多角形(Polygon)                *
//*********************************************

namespace std {
    bool operator < (Point a, Point b){
        return a.X != b.X ? a.X < b.X : a.Y < b.Y;
    }
}

// 多角形の面積 (PolygonErea) *****************
LD PolygonErea(Polygon p){
    LD area = 0;
    int n = p.size();
    for(int i = 0; i < n; i++){
        area += Cross(p[i], p[(i+1) % n]);
    }
    return area / 2;
}
// ********************************************


// 凸性判定 (IsConvex) ************************
bool IsConvex(Polygon pol){
    int n = pol.size();
    for(int i = 0; i < n; i++){
        if(CCW(pol[i], pol[(i+1) % n], pol[(i+2) % n]) == -1) return false;
    }
    return true;
}
// ********************************************


// 多角形-点包含関係 (PolygonPointContainment)
int PolygonPointContainment(Polygon pol, Point p){
    enum {OUT, ON, IN};
    bool in = false;
    int n = pol.size();
    for(int i = 0; i < n; i++){
        Point a = pol[i] - p, b = pol[(i+1) % n] - p;
        if(a.Y > b.Y) swap(a, b);
        if(a.Y <= 0 && 0 < b.Y && Cross(a, b) < 0) in = !in;
        if(Cross(a, b) == 0 && Dot(a, b) <= 0) return ON;
    }
    return in ? IN : OUT;
}
// ********************************************


//*********************************************
//          凸多角形(ConvexPolygon)           *
//*********************************************

// 凸包[θ<=180] (ConvexHull) *****************
Polygon ConvexHull(Polygon pol){
    int n = pol.size(), k = 0;
    sort(pol.begin(), pol.end());
    Polygon ch(2*n);
    for(int i = 0; i < n; ch[k++] = pol[i++])
        while(k >= 2 && CCW(ch[k-2], ch[k-1], pol[i]) == -1) --k;

    for(int i = n-2, t = k+1; i >= 0; ch[k++] = pol[i--])
        while(k >= t && CCW(ch[k-2], ch[k-1], pol[i]) == -1) --k;

    ch.resize(k-1);
    return ch;
}
// ********************************************

// 凸包[θ<180] (ConvexHull2) *****************
Polygon ConvexHull2(Polygon pol){
    int n = pol.size(), k = 0;
    sort(pol.begin(), pol.end());
    Polygon ch(2*n);
    for(int i = 0; i < n; ch[k++] = pol[i++])
        while(k >= 2 && CCW(ch[k-2], ch[k-1], pol[i]) <= 0) --k;

    for(int i = n-2, t = k+1; i >= 0; ch[k++] = pol[i--])
        while(k >= t && CCW(ch[k-2], ch[k-1], pol[i]) <= 0) --k;

    ch.resize(k-1);
    return ch;
}
// ********************************************

// 凸多角形の直径 (ConvexPolygonDiameter) *****
pair<int, int> ConvexPolygonDiameter(Polygon cpol){
    int n = cpol.size();
    int is = 0, js = 0;
    for (int i = 1; i < n; ++i) {
        if (imag(cpol[i]) > imag(cpol[is])) is = i;
        if (imag(cpol[i]) < imag(cpol[js])) js = i;
    }
    LD maxd = norm(cpol[is]-cpol[js]);

    int i, maxi, j, maxj;
    i = maxi = is;
    j = maxj = js;
    do{
        if(Cross(cpol[(i+1)%n] - cpol[i], cpol[(j+1)%n] - cpol[j]) >= 0) j = (j+1) % n;
        else i = (i+1) % n;
        if(norm(cpol[i]-cpol[j]) > maxd) {
            maxd = norm(cpol[i]-cpol[j]);
            maxi = i; maxj = j;
        }
    } while(i != is || j != js);
    return make_pair(maxi, maxj);
}
// ********************************************


// 凸多角形の切断 (ConvexPolygonCut) **********
Polygon ConvexPolygonCut(Polygon cpol, Line l){
    int n = cpol.size();
    Polygon q;
    for(int i = 0; i < n; i++){
        Point a = cpol[i], b = cpol[(i+1)%n];
        if(CCW(l.first, l.second, a) != -1) q.push_back(a);
        if(CCW(l.first, l.second, a) * CCW(l.first, l.second, b) < 0) q.push_back(CrossPointLL(a, b, l.first, l.second));
    }
    return q;
}
// ********************************************


// 凸多角形-点包含関係 (ConvexPolygonPointContainment)
int ConvexPolygonPointContainment(Polygon cpol, Point p){
    enum {OUT, ON, IN};
    int n = cpol.size();
    Point g = (cpol[0] + cpol[n/3] + cpol[2*n/3]) / 3.0L;
    int a = 0, b = n;
    while(a+1 < b){
        int c = (a + b) / 2;
        if(Cross(cpol[a]-g, cpol[c]-g) > 0){
            if(Cross(cpol[a]-g, p-g) > 0 && Cross(cpol[c]-g, p-g) < 0) b = c;
            else a = c;
        }else{
            if(Cross(cpol[a]-g, p-g) < 0 && Cross(cpol[c]-g, p-g) > 0) a = c;
            else b = c;
        }
    }
    b %= n;
    if(Cross(cpol[a]-p, cpol[b]-p) < 0) return OUT;
    if(Cross(cpol[a]-p, cpol[b]-p) > 0) return IN;
    return ON;
}
// ********************************************


/************** using variables ***************/
Polygon p;
int n;
int q;
/**********************************************/

signed main(){
    cin >> n;
    REP(i, n){
        LD xp, yp;
        cin >> xp >> yp;
        p.pb(Point(xp, yp));
    }

    cin >> q;
    REP(i, q){
        LD x1p, y1p, x2p, y2p;
        cin >> x1p >> y1p >> x2p >> y2p;
        Polygon ans = ConvexPolygonCut(p, Line(Point(x1p, y1p), Point(x2p, y2p)));
        printf("%.9Lf\n", PolygonErea(ans));
    }
}