#include <bits/stdc++.h>
using namespace std;
const int MAX_INT = 0x7FFFFFFF;
const int INF = 0x3f3f3f3f;
const int maxn = 1050;
const double eps = 1e-8;
const double inf = 1e20;
;
const double pi = acos(-1.0);
const int maxp = 1e5 + 50;
int sgn(double x) {
  if (fabs(x) < eps) return 0;
  if (x < 0)
    return -1;
  else
    return 1;
}
inline double sqr(double x) { return x * x; }
struct Point {
  double x, y;
  int info;
  Point() {}
  Point(double _x, double _y) {
    x = _x;
    y = _y;
  }
  void input() { scanf("%lf%lf", &x, &y); }
  void output() { printf("%.2f␣%.2f\n", x, y); }
  bool operator==(Point b) const {
    return sgn(x - b.x) == 0 && sgn(y - b.y) == 0;
  }
  bool operator<(Point b) const {
    return sgn(x - b.x) == 0 ? sgn(y - b.y) < 0 : x < b.x;
  }
  Point operator-(const Point &b) const { return Point(x - b.x, y - b.y); }
  double operator^(const Point &b) const { return x * b.y - y * b.x; }
  double operator*(const Point &b) const { return x * b.x + y * b.y; }
  double len() { return hypot(x, y); }
  double len2() { return x * x + y * y; }
  double distance(Point p) { return hypot(x - p.x, y - p.y); }
  Point operator+(const Point &b) const { return Point(x + b.x, y + b.y); }
  Point operator*(const double &k) const { return Point(x * k, y * k); }
  Point operator/(const double &k) const { return Point(x / k, y / k); }
  double rad(Point a, Point b) {
    Point p = *this;
    return fabs(atan2(fabs((a - p) ^ (b - p)), (a - p) * (b - p)));
  }
  Point trunc(double r) {
    double l = len();
    if (!sgn(l)) return *this;
    r /= l;
    return Point(x * r, y * r);
  }
  Point rotleft() { return Point(-y, x); }
  Point rotright() { return Point(y, -x); }
  Point rotate(Point p, double angle) {
    Point v = (*this) - p;
    double c = cos(angle), s = sin(angle);
    return Point(p.x + v.x * c - v.y * s, p.y + v.x * s + v.y * c);
  }
};
struct Line {
  Point s, e;
  Line() {}
  Line(Point _s, Point _e) {
    s = _s;
    e = _e;
  }
  bool operator==(Line v) { return (s == v.s) && (e == v.e); }
  Line(Point p, double angle) {
    s = p;
    if (sgn(angle - pi / 2) == 0) {
      e = (s + Point(0, 1));
    } else {
      e = (s + Point(1, tan(angle)));
    }
  }
  Line(double a, double b, double c) {
    if (sgn(a) == 0) {
      s = Point(0, -c / b);
      e = Point(1, -c / b);
    } else if (sgn(b) == 0) {
      s = Point(-c / a, 0);
      e = Point(-c / a, 1);
    } else {
      s = Point(0, -c / b);
      e = Point(1, (-c - a) / b);
    }
  }
  void input() {
    s.input();
    e.input();
  }
  void adjust() {
    if (e < s) swap(s, e);
  }
  double length() { return s.distance(e); }
  double angle() {
    double k = atan2(e.y - s.y, e.x - s.x);
    if (sgn(k) < 0) k += pi;
    if (sgn(k - pi) == 0) k -= pi;
    return k;
  }
  int relation(Point p) {
    int c = sgn((p - s) ^ (e - s));
    if (c < 0)
      return 1;
    else if (c > 0)
      return 2;
    else
      return 3;
  }
  bool pointonseg(Point p) {
    return sgn((p - s) ^ (e - s)) == 0 && sgn((p - s) * (p - e)) <= 0;
  }
  bool parallel(Line v) { return sgn((e - s) ^ (v.e - v.s)) == 0; }
  int segcrossseg(Line v) {
    int d1 = sgn((e - s) ^ (v.s - s));
    int d2 = sgn((e - s) ^ (v.e - s));
    int d3 = sgn((v.e - v.s) ^ (s - v.s));
    int d4 = sgn((v.e - v.s) ^ (e - v.s));
    if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 2;
    return (d1 == 0 && sgn((v.s - s) * (v.s - e)) <= 0) ||
           (d2 == 0 && sgn((v.e - s) * (v.e - e)) <= 0) ||
           (d3 == 0 && sgn((s - v.s) * (s - v.e)) <= 0) ||
           (d4 == 0 && sgn((e - v.s) * (e - v.e)) <= 0);
  }
  int linecrossseg(Line v) {
    int d1 = sgn((e - s) ^ (v.s - s));
    int d2 = sgn((e - s) ^ (v.e - s));
    if ((d1 ^ d2) == -2) return 2;
    return (d1 == 0 || d2 == 0);
  }
  int linecrossline(Line v) {
    if ((*this).parallel(v)) return v.relation(s) == 3;
    return 2;
  }
  Point crosspoint(Line v) {
    double a1 = (v.e - v.s) ^ (s - v.s);
    double a2 = (v.e - v.s) ^ (e - v.s);
    return Point((s.x * a2 - e.x * a1) / (a2 - a1),
                 (s.y * a2 - e.y * a1) / (a2 - a1));
  }
  double dispointtoline(Point p) { return fabs((p - s) ^ (e - s)) / length(); }
  double dispointtoseg(Point p) {
    if (sgn((p - s) * (e - s)) < 0 || sgn((p - e) * (s - e)) < 0)
      return min(p.distance(s), p.distance(e));
    return dispointtoline(p);
  }
  double dissegtoseg(Line v) {
    return min(min(dispointtoseg(v.s), dispointtoseg(v.e)),
               min(v.dispointtoseg(s), v.dispointtoseg(e)));
  }
  Point lineprog(Point p) {
    return s + (((e - s) * ((e - s) * (p - s))) / ((e - s).len2()));
  }
  Point symmetrypoint(Point p) {
    Point q = lineprog(p);
    return Point(2 * q.x - p.x, 2 * q.y - p.y);
  }
};
struct circle {
  Point p;
  double r;
  circle() {}
  circle(Point _p, double _r) {
    p = _p;
    r = _r;
  }
  circle(double x, double y, double _r) {
    p = Point(x, y);
    r = _r;
  }
  circle(Point a, Point b, Point c) {
    Line u = Line((a + b) / 2, ((a + b) / 2) + ((b - a).rotleft()));
    Line v = Line((b + c) / 2, ((b + c) / 2) + ((c - b).rotleft()));
    p = u.crosspoint(v);
    r = p.distance(a);
  }
  circle(Point a, Point b, Point c, bool t) {
    Line u, v;
    double m = atan2(b.y - a.y, b.x - a.x), n = atan2(c.y - a.y, c.x - a.x);
    u.s = a;
    u.e = u.s + Point(cos((n + m) / 2), sin((n + m) / 2));
    v.s = b;
    m = atan2(a.y - b.y, a.x - b.x), n = atan2(c.y - b.y, c.x - b.x);
    v.e = v.s + Point(cos((n + m) / 2), sin((n + m) / 2));
    p = u.crosspoint(v);
    r = Line(a, b).dispointtoseg(p);
  }
  void input() {
    p.input();
    scanf("%lf", &r);
  }
  void output() { printf("%.2lf␣%.2lf␣%.2lf\n", p.x, p.y, r); }
  bool operator==(circle v) { return (p == v.p) && sgn(r - v.r) == 0; }
  bool operator<(circle v) const {
    return ((p < v.p) || ((p == v.p) && sgn(r - v.r) < 0));
  }
  double area() { return pi * r * r; }
  double circumference() { return 2 * pi * r; }
  int relation(Point b) {
    double dst = b.distance(p);
    if (sgn(dst - r) < 0)
      return 2;
    else if (sgn(dst - r) == 0)
      return 1;
    return 0;
  }
  int relationseg(Line v) {
    double dst = v.dispointtoseg(p);
    if (sgn(dst - r) < 0)
      return 2;
    else if (sgn(dst - r) == 0)
      return 1;
    return 0;
  }
  int relationline(Line v) {
    double dst = v.dispointtoline(p);
    if (sgn(dst - r) < 0)
      return 2;
    else if (sgn(dst - r) == 0)
      return 1;
    return 0;
  }
  int relationcircle(circle v) {
    double d = p.distance(v.p);
    if (sgn(d - r - v.r) > 0) return 5;
    if (sgn(d - r - v.r) == 0) return 4;
    double l = fabs(r - v.r);
    if (sgn(d - r - v.r) < 0 && sgn(d - l) > 0) return 3;
    if (sgn(d - l) == 0) return 2;
    if (sgn(d - l) < 0) return 1;
  }
  int pointcrosscircle(circle v, Point &p1, Point &p2) {
    int rel = relationcircle(v);
    if (rel == 1 || rel == 5) return 0;
    double d = p.distance(v.p);
    double l = (d * d + r * r - v.r * v.r) / (2 * d);
    double h = sqrt(r * r - l * l);
    Point tmp = p + (v.p - p).trunc(l);
    p1 = tmp + ((v.p - p).rotleft().trunc(h));
    p2 = tmp + ((v.p - p).rotright().trunc(h));
    if (rel == 2 || rel == 4) return 1;
    return 2;
  }
  int pointcrossline(Line v, Point &p1, Point &p2) {
    if (!(*this).relationline(v)) return 0;
    Point a = v.lineprog(p);
    double d = v.dispointtoline(p);
    d = sqrt(r * r - d * d);
    if (sgn(d) == 0) {
      p1 = a;
      p2 = a;
      return 1;
    }
    p1 = a + (v.e - v.s).trunc(d);
    p2 = a - (v.e - v.s).trunc(d);
    return 2;
  }
  int gercircle(Point a, Point b, double r1, circle &c1, circle &c2) {
    circle x(a, r1), y(b, r1);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r;
    return t;
  }
  int getcircle(Line u, Point q, double r1, circle &c1, circle &c2) {
    double dis = u.dispointtoline(q);
    if (sgn(dis - r1 * 2) > 0) return 0;
    if (sgn(dis) == 0) {
      c1.p = q + ((u.e - u.s).rotleft().trunc(r1));
      c2.p = q + ((u.e - u.s).rotright().trunc(r1));
      c1.r = c2.r = r1;
      return 2;
    }
    Line u1 = Line((u.s + (u.e - u.s).rotleft().trunc(r1)),
                   (u.e + (u.e - u.s).rotleft().trunc(r1)));
    Line u2 = Line((u.s + (u.e - u.s).rotright().trunc(r1)),
                   (u.e + (u.e - u.s).rotright().trunc(r1)));
    circle cc = circle(q, r1);
    Point p1, p2;
    if (!cc.pointcrossline(u1, p1, p2)) cc.pointcrossline(u2, p1, p2);
    c1 = circle(p1, r1);
    if (p1 == p2) {
      c2 = c1;
      return 1;
    }
    c2 = circle(p2, r1);
    return 2;
  }
  int getcircle(Line u, Line v, double r1, circle &c1, circle &c2, circle &c3,
                circle &c4) {
    if (u.parallel(v)) return 0;
    Line u1 = Line(u.s + (u.e - u.s).rotleft().trunc(r1),
                   u.e + (u.e - u.s).rotleft().trunc(r1));
    Line u2 = Line(u.s + (u.e - u.s).rotright().trunc(r1),
                   u.e + (u.e - u.s).rotright().trunc(r1));
    Line v1 = Line(v.s + (v.e - v.s).rotleft().trunc(r1),
                   v.e + (v.e - v.s).rotleft().trunc(r1));
    Line v2 = Line(v.s + (v.e - v.s).rotright().trunc(r1),
                   v.e + (v.e - v.s).rotright().trunc(r1));
    c1.r = c2.r = c3.r = c4.r = r1;
    c1.p = u1.crosspoint(v1);
    c2.p = u1.crosspoint(v2);
    c3.p = u2.crosspoint(v1);
    c4.p = u2.crosspoint(v2);
    return 4;
  }
  int getcircle(circle cx, circle cy, double r1, circle &c1, circle &c2) {
    circle x(cx.p, r1 + cx.r), y(cy.p, r1 + cy.r);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r1;
    return t;
  }
  int tangentline(Point q, Line &u, Line &v) {
    int x = relation(q);
    if (x == 2) return 0;
    if (x == 1) {
      u = Line(q, q + (q - p).rotleft());
      v = u;
      return 1;
    }
    double d = p.distance(q);
    double l = r * r / d;
    double h = sqrt(r * r - l * l);
    u = Line(q, p + ((q - p).trunc(l) + (q - p).rotleft().trunc(h)));
    v = Line(q, p + ((q - p).trunc(l) + (q - p).rotright().trunc(h)));
    return 2;
  }
  double areacircle(circle v) {
    int rel = relationcircle(v);
    if (rel >= 4) return 0.0;
    if (rel <= 2) return min(area(), v.area());
    double d = p.distance(v.p);
    double hf = (r + v.r + d) / 2.0;
    double ss = 2 * sqrt(hf * (hf - r) * (hf - v.r) * (hf - d));
    double a1 = acos((r * r + d * d - v.r * v.r) / (2.0 * r * d));
    a1 = a1 * r * r;
    double a2 = acos((v.r * v.r + d * d - r * r) / (2.0 * v.r * d));
    a2 = a2 * v.r * v.r;
    return a1 + a2 - ss;
  }
  double areatriangle(Point a, Point b) {
    if (sgn((p - a) ^ (p - b)) == 0) return 0.0;
    Point q[5];
    int len = 0;
    q[len++] = a;
    Line l(a, b);
    Point p1, p2;
    if (pointcrossline(l, q[1], q[2]) == 2) {
      if (sgn((a - q[1]) * (b - q[1])) < 0) q[len++] = q[1];
      if (sgn((a - q[2]) * (b - q[2])) < 0) q[len++] = q[2];
    }
    q[len++] = b;
    if (len == 4 && sgn((q[0] - q[1]) * (q[2] - q[1])) > 0) swap(q[1], q[2]);
    double res = 0;
    for (int i = 0; i < len - 1; i++) {
      if (relation(q[i]) == 0 || relation(q[i + 1]) == 0) {
        double arg = p.rad(q[i], q[i + 1]);
        res += r * r * arg / 2.0;
      } else {
        res += fabs((q[i] - p) ^ (q[i + 1] - p)) / 2.0;
      }
    }
    return res;
  }
};
struct polygon {
  int n;
  Point p[maxp];
  Line l[maxp];
  void input(int _n) {
    n = _n;
    for (int i = 0; i < n; i++) {
      p[i].input();
      p[i].info = 0;
    }
  }
  void input(int _n, int info) {
    n = _n;
    for (int i = 0; i < n; i++) {
      p[i].input();
      p[i].info = info;
    }
  }
  void add(Point q) { p[n++] = q; }
  void getline() {
    for (int i = 0; i < n; i++) {
      l[i] = Line(p[i], p[(i + 1) % n]);
    }
  }
  inline Point &operator[](int i) {
    if (n == 0) return p[i];
    return p[(i + n) % n];
  }
  struct cmp {
    Point p;
    cmp(const Point &p0) { p = p0; }
    bool operator()(const Point &aa, const Point &bb) {
      Point a = aa, b = bb;
      int d = sgn((a - p) ^ (b - p));
      if (d == 0) {
        return sgn(a.distance(p) - b.distance(p)) < 0;
      }
      return d > 0;
    }
  };
  void norm() {
    Point mi = p[0];
    for (int i = 1; i < n; i++) mi = min(mi, p[i]);
    sort(p, p + n, cmp(mi));
  }
  void getconvex(polygon &convex) {
    sort(p, p + n);
    convex.n = n;
    for (int i = 0; i < min(n, 2); i++) {
      convex.p[i] = p[i];
    }
    if (convex.n == 2 && (convex.p[0] == convex.p[1])) convex.n--;
    if (n <= 2) return;
    int &top = convex.n;
    top = 1;
    for (int i = 2; i < n; i++) {
      while (top &&
             sgn((convex.p[top] - p[i]) ^ (convex.p[top - 1] - p[i])) <= 0)
        top--;
      convex.p[++top] = p[i];
    }
    int temp = top;
    convex.p[++top] = p[n - 2];
    for (int i = n - 3; i >= 0; i--) {
      while (top != temp &&
             sgn((convex.p[top] - p[i]) ^ (convex.p[top - 1] - p[i])) <= 0)
        top--;
      convex.p[++top] = p[i];
    }
    if (convex.n == 2 && (convex.p[0] == convex.p[1])) convex.n--;
    convex.norm();
  }
  void getconvex_hull(polygon &convex) {
    sort(p, p + n);
    int k = 0;
    for (int i = 0; i < n; i++) {
      while (k > 1 &&
             ((convex[k - 1] - convex[k - 2]) ^ (p[i] - convex[k - 1])) < 0)
        k--;
      convex[k++] = p[i];
    }
    for (int i = n - 2, t = k; i >= 0; i--) {
      while (k > t &&
             ((convex[k - 1] - convex[k - 2]) ^ (p[i] - convex[k - 1])) < 0)
        k--;
      convex[k++] = p[i];
    }
    convex.n = k;
  }
  void Graham(polygon &convex) {
    norm();
    int &top = convex.n;
    top = 0;
    if (n == 1) {
      top = 1;
      convex.p[0] = p[0];
      return;
    }
    if (n == 2) {
      top = 2;
      convex.p[0] = p[0];
      convex.p[1] = p[1];
      if (convex.p[0] == convex.p[1]) top--;
      return;
    }
    convex.p[0] = p[0];
    convex.p[1] = p[1];
    top = 2;
    for (int i = 2; i < n; i++) {
      while (top > 1 && sgn((convex.p[top - 1] - convex.p[top - 2]) ^
                            (p[i] - convex.p[top - 2])) <= 0)
        top--;
      convex.p[top++] = p[i];
    }
    if (convex.n == 2 && (convex.p[0] == convex.p[1])) convex.n--;
  }
  bool isconvex() {
    bool s[2];
    memset(s, false, sizeof(s));
    for (int i = 0; i < n; i++) {
      int j = (i + 1) % n;
      int k = (j + 1) % n;
      s[sgn((p[j] - p[i]) ^ (p[k] - p[i])) + 1] = true;
      if (s[0] && s[2]) return false;
    }
    return true;
  }
  bool inedge(Point q) {
    for (int i = 0; i < n; i++) {
      if (p[i] == q) return true;
    }
    for (int i = 0; i < n; i++) {
      if (l[i].pointonseg(q)) return true;
    }
    return false;
  }
  int relationpoint(Point q) {
    for (int i = 0; i < n; i++) {
      if (p[i] == q) return 3;
    }
    for (int i = 0; i < n; i++) {
      if (l[i].pointonseg(q)) return 2;
    }
    int cnt = 0;
    for (int i = 0; i < n; i++) {
      int j = (i + 1) % n;
      int k = sgn((q - p[j]) ^ (p[i] - p[j]));
      int u = sgn(p[i].y - q.y);
      int v = sgn(p[j].y - q.y);
      if (k > 0 && u < 0 && v >= 0) cnt++;
      if (k < 0 && v < 0 && u >= 0) cnt--;
    }
    return cnt != 0;
  }
  void convexcut(Line u, polygon &po) {
    int &top = po.n;
    top = 0;
    for (int i = 0; i < n; i++) {
      int d1 = sgn((u.e - u.s) ^ (p[i] - u.s));
      int d2 = sgn((u.e - u.s) ^ (p[(i + 1) % n] - u.s));
      if (d1 >= 0) po.p[top++] = p[i];
      if (d1 * d2 < 0) po.p[top++] = u.crosspoint(Line(p[i], p[(i + 1) % n]));
    }
  }
  double getcircumference() {
    double sum = 0;
    for (int i = 0; i < n; i++) {
      sum += p[i].distance(p[(i + 1) % n]);
    }
    return sum;
  }
  double getarea() {
    double sum = 0;
    for (int i = 0; i < n; i++) {
      sum += (p[i] ^ p[(i + 1) % n]);
    }
    return fabs(sum) / 2;
  }
  bool getdir() {
    double sum = 0;
    for (int i = 0; i < n; i++) sum += (p[i] ^ p[(i + 1) % n]);
    if (sgn(sum) > 0) return 1;
    return 0;
  }
  Point getbarycentre() {
    Point ret(0, 0);
    double area = 0;
    for (int i = 1; i < n - 1; i++) {
      double tmp = (p[i] - p[0]) ^ (p[i + 1] - p[0]);
      if (sgn(tmp) == 0) continue;
      area += tmp;
      ret.x += (p[0].x + p[i].x + p[i + 1].x) / 3 * tmp;
      ret.y += (p[0].y + p[i].y + p[i + 1].y) / 3 * tmp;
    }
    if (sgn(area)) ret = ret / area;
    return ret;
  }
  double areacircle(circle c) {
    double ans = 0;
    for (int i = 0; i < n; i++) {
      int j = (i + 1) % n;
      if (sgn((p[j] - c.p) ^ (p[i] - c.p)) >= 0)
        ans += c.areatriangle(p[i], p[j]);
      else
        ans -= c.areatriangle(p[i], p[j]);
    }
    return fabs(ans);
  }
  int relationcircle(circle c) {
    getline();
    int x = 2;
    if (relationpoint(c.p) != 1) return 0;
    for (int i = 0; i < n; i++) {
      if (c.relationseg(l[i]) == 2) return 0;
      if (c.relationseg(l[i]) == 1) x = 1;
    }
    return x;
  }
};
double cross(Point A, Point B, Point C) { return (B - A) ^ (C - A); }
double dot(Point A, Point B, Point C) { return (B - A) * (C - A); }
double minRectangleCover(polygon A) {
  if (A.n < 3) return 0.0;
  A.p[A.n] = A.p[0];
  double ans = -1;
  int r = 1, p = 1, q;
  for (int i = 0; i < A.n; i++) {
    while (sgn(cross(A.p[i], A.p[i + 1], A.p[r + 1]) -
               cross(A.p[i], A.p[i + 1], A.p[r])) >= 0)
      r = (r + 1) % A.n;
    while (sgn(dot(A.p[i], A.p[i + 1], A.p[p + 1]) -
               dot(A.p[i], A.p[i + 1], A.p[p])) >= 0)
      p = (p + 1) % A.n;
    if (i == 0) q = p;
    while (sgn(dot(A.p[i], A.p[i + 1], A.p[q + 1]) -
               dot(A.p[i], A.p[i + 1], A.p[q])) <= 0)
      q = (q + 1) % A.n;
    double d = (A.p[i] - A.p[i + 1]).len2();
    double tmp =
        cross(A.p[i], A.p[i + 1], A.p[r]) *
        (dot(A.p[i], A.p[i + 1], A.p[p]) - dot(A.p[i], A.p[i + 1], A.p[q])) / d;
    if (ans < 0 || ans > tmp) ans = tmp;
  }
  return ans;
}
vector<Point> convexCut(const vector<Point> &ps, Point q1, Point q2) {
  vector<Point> qs;
  int n = ps.size();
  for (int i = 0; i < n; i++) {
    Point p1 = ps[i], p2 = ps[(i + 1) % n];
    int d1 = sgn((q2 - q1) ^ (p1 - q1)), d2 = sgn((q2 - q1) ^ (p2 - q1));
    if (d1 >= 0) qs.push_back(p1);
    if (d1 * d2 < 0) qs.push_back(Line(p1, p2).crosspoint(Line(q1, q2)));
  }
  return qs;
}
struct halfplane : public Line {
  double angle;
  halfplane() {}
  halfplane(Point _s, Point _e) {
    s = _s;
    e = _e;
  }
  halfplane(Line v) {
    s = v.s;
    e = v.e;
  }
  void calcangle() { angle = atan2(e.y - s.y, e.x - s.x); }
  bool operator<(const halfplane &b) const { return angle < b.angle; }
};
struct halfplanes {
  int n;
  halfplane hp[maxp];
  Point p[maxp];
  int que[maxp];
  int st, ed;
  void push(halfplane tmp) { hp[n++] = tmp; }
  void unique() {
    int m = 1;
    for (int i = 1; i < n; i++) {
      if (sgn(hp[i].angle - hp[i - 1].angle) != 0)
        hp[m++] = hp[i];
      else if (sgn((hp[m - 1].e - hp[m - 1].s) ^ (hp[i].s - hp[m - 1].s)) > 0)
        hp[m - 1] = hp[i];
    }
    n = m;
  }
  bool halfplaneinsert() {
    for (int i = 0; i < n; i++) hp[i].calcangle();
    sort(hp, hp + n);
    unique();
    que[st = 0] = 0;
    que[ed = 1] = 1;
    p[1] = hp[0].crosspoint(hp[1]);
    for (int i = 2; i < n; i++) {
      while (st < ed && sgn((hp[i].e - hp[i].s) ^ (p[ed] - hp[i].s)) < 0) ed--;
      while (st < ed && sgn((hp[i].e - hp[i].s) ^ (p[st + 1] - hp[i].s)) < 0)
        st++;
      que[++ed] = i;
      if (hp[i].parallel(hp[que[ed - 1]])) return false;
      p[ed] = hp[i].crosspoint(hp[que[ed - 1]]);
    }
    while (st < ed &&
           sgn((hp[que[st]].e - hp[que[st]].s) ^ (p[ed] - hp[que[st]].s)) < 0)
      ed--;
    while (st < ed && sgn((hp[que[ed]].e - hp[que[ed]].s) ^
                          (p[st + 1] - hp[que[ed]].s)) < 0)
      st++;
    if (st + 1 >= ed) return false;
    return true;
  }
  void getconvex(polygon &con) {
    p[st] = hp[que[st]].crosspoint(hp[que[ed]]);
    con.n = ed - st + 1;
    for (int j = st, i = 0; j <= ed; i++, j++) con.p[i] = p[j];
  }
};
struct circles {
  circle c[maxn];
  double ans[maxn];
  double pre[maxn];
  int n;
  circles() {}
  void add(circle cc) { c[n++] = cc; }
  bool inner(circle x, circle y) {
    if (x.relationcircle(y) != 1) return 0;
    return sgn(x.r - y.r) <= 0 ? 1 : 0;
  }
  void init_or() {
    bool mark[maxn] = {0};
    int i, j, k = 0;
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++)
        if (i != j && !mark[j]) {
          if ((c[i] == c[j]) || inner(c[i], c[j])) break;
        }
      if (j < n) mark[i] = 1;
    }
    for (i = 0; i < n; i++)
      if (!mark[i]) c[k++] = c[i];
    n = k;
  }
  void init_add() {
    int i, j, k;
    bool mark[maxn] = {0};
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++)
        if (i != j && !mark[j]) {
          if ((c[i] == c[j]) || inner(c[j], c[i])) break;
        }
      if (j < n) mark[i] = 1;
    }
    for (i = 0; i < n; i++)
      if (!mark[i]) c[k++] = c[i];
    n = k;
  }
  double areaarc(double th, double r) { return 0.5 * r * r * (th - sin(th)); }
  void getarea() {
    memset(ans, 0, sizeof(ans));
    vector<pair<double, int>> v;
    for (int i = 0; i < n; i++) {
      v.clear();
      v.push_back(make_pair(-pi, 1));
      v.push_back(make_pair(pi, -1));
      for (int j = 0; j < n; j++)
        if (i != j) {
          Point q = (c[j].p - c[i].p);
          double ab = q.len(), ac = c[i].r, bc = c[j].r;
          if (sgn(ab + ac - bc) <= 0) {
            v.push_back(make_pair(-pi, 1));
            v.push_back(make_pair(pi, -1));
            continue;
          }
          if (sgn(ab + bc - ac) <= 0) continue;
          if (sgn(ab - ac - bc) > 0) continue;
          double th = atan2(q.y, q.x),
                 fai = acos((ac * ac + ab * ab - bc * bc) / (2.0 * ac * ab));
          double a0 = th - fai;
          if (sgn(a0 + pi) < 0) a0 += 2 * pi;
          double a1 = th + fai;
          if (sgn(a1 - pi) > 0) a1 -= 2 * pi;
          if (sgn(a0 - a1) > 0) {
            v.push_back(make_pair(a0, 1));
            v.push_back(make_pair(pi, -1));
            v.push_back(make_pair(-pi, 1));
            v.push_back(make_pair(a1, -1));
          } else {
            v.push_back(make_pair(a0, 1));
            v.push_back(make_pair(a1, -1));
          }
        }
      sort(v.begin(), v.end());
      int cur = 0;
      for (int j = 0; j < v.size(); j++) {
        if (cur && sgn(v[j].first - pre[cur])) {
          ans[cur] += areaarc(v[j].first - pre[cur], c[i].r);
          ans[cur] += 0.5 * (Point(c[i].p.x + c[i].r * cos(pre[cur]),
                                   c[i].p.y + c[i].r * sin(pre[cur])) ^
                             Point(c[i].p.x + c[i].r * cos(v[j].first),
                                   c[i].p.y + c[i].r * sin(v[j].first)));
        }
        cur += v[j].second;
        pre[cur] = v[j].first;
      }
    }
    for (int i = 1; i < n; i++) ans[i] -= ans[i + 1];
  }
};
polygon pol;
polygon pol2;
polygon pol3;
int main() {
  int n;
  scanf("%d", &n);
  pol.input(n, 1);
  int m;
  scanf("%d", &m);
  pol2.input(m, 2);
  for (int i = 0; i < m; i++) {
    pol.add(pol2[i]);
  }
  pol.getconvex_hull(pol3);
  bool flag = true;
  for (int i = 0; i < pol3.n; i++) {
    if (pol3[i].info == 2) {
      flag = false;
      break;
    }
  }
  if (flag)
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

You've got another geometrical task. You are given two non-degenerate polygons A and B as vertex coordinates. Polygon A is strictly convex. Polygon B is an arbitrary polygon without any self-intersections and self-touches. The vertices of both polygons are given in the clockwise order. For each polygon no three consecutively following vertices are located on the same straight line.

Your task is to check whether polygon B is positioned strictly inside polygon A. It means that any point of polygon B should be strictly inside polygon A. "Strictly" means that the vertex of polygon B cannot lie on the side of the polygon A.

Input

The first line contains the only integer n (3 ≤ n ≤ 105) — the number of vertices of polygon A. Then n lines contain pairs of integers xi, yi (|xi|, |yi| ≤ 109) — coordinates of the i-th vertex of polygon A. The vertices are given in the clockwise order.

The next line contains a single integer m (3 ≤ m ≤ 2·104) — the number of vertices of polygon B. Then following m lines contain pairs of integers xj, yj (|xj|, |yj| ≤ 109) — the coordinates of the j-th vertex of polygon B. The vertices are given in the clockwise order.

The coordinates of the polygon's vertices are separated by a single space. It is guaranteed that polygons A and B are non-degenerate, that polygon A is strictly convex, that polygon B has no self-intersections and self-touches and also for each polygon no three consecutively following vertices are located on the same straight line.

Output

Print on the only line the answer to the problem — if polygon B is strictly inside polygon A, print "YES", otherwise print "NO" (without the quotes).

Examples

Input

6
-2 1
0 3
3 3
4 1
3 -2
2 -2
4
0 1
2 2
3 1
1 0


Output

YES


Input

5
1 2
4 2
3 -3
-2 -2
-2 1
4
0 1
1 2
4 1
2 -1


Output

NO


Input

5
-1 2
2 3
4 1
3 -2
0 -3
5
1 0
1 1
3 1
5 -1
2 -1


Output

NO

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MAX_INT = 0x7FFFFFFF;
const int INF = 0x3f3f3f3f;
const int maxn = 1050;
const double eps = 1e-8;
const double inf = 1e20;
;
const double pi = acos(-1.0);
const int maxp = 1e5 + 50;
int sgn(double x) {
  if (fabs(x) < eps) return 0;
  if (x < 0)
    return -1;
  else
    return 1;
}
inline double sqr(double x) { return x * x; }
struct Point {
  double x, y;
  int info;
  Point() {}
  Point(double _x, double _y) {
    x = _x;
    y = _y;
  }
  void input() { scanf("%lf%lf", &x, &y); }
  void output() { printf("%.2f␣%.2f\n", x, y); }
  bool operator==(Point b) const {
    return sgn(x - b.x) == 0 && sgn(y - b.y) == 0;
  }
  bool operator<(Point b) const {
    return sgn(x - b.x) == 0 ? sgn(y - b.y) < 0 : x < b.x;
  }
  Point operator-(const Point &b) const { return Point(x - b.x, y - b.y); }
  double operator^(const Point &b) const { return x * b.y - y * b.x; }
  double operator*(const Point &b) const { return x * b.x + y * b.y; }
  double len() { return hypot(x, y); }
  double len2() { return x * x + y * y; }
  double distance(Point p) { return hypot(x - p.x, y - p.y); }
  Point operator+(const Point &b) const { return Point(x + b.x, y + b.y); }
  Point operator*(const double &k) const { return Point(x * k, y * k); }
  Point operator/(const double &k) const { return Point(x / k, y / k); }
  double rad(Point a, Point b) {
    Point p = *this;
    return fabs(atan2(fabs((a - p) ^ (b - p)), (a - p) * (b - p)));
  }
  Point trunc(double r) {
    double l = len();
    if (!sgn(l)) return *this;
    r /= l;
    return Point(x * r, y * r);
  }
  Point rotleft() { return Point(-y, x); }
  Point rotright() { return Point(y, -x); }
  Point rotate(Point p, double angle) {
    Point v = (*this) - p;
    double c = cos(angle), s = sin(angle);
    return Point(p.x + v.x * c - v.y * s, p.y + v.x * s + v.y * c);
  }
};
struct Line {
  Point s, e;
  Line() {}
  Line(Point _s, Point _e) {
    s = _s;
    e = _e;
  }
  bool operator==(Line v) { return (s == v.s) && (e == v.e); }
  Line(Point p, double angle) {
    s = p;
    if (sgn(angle - pi / 2) == 0) {
      e = (s + Point(0, 1));
    } else {
      e = (s + Point(1, tan(angle)));
    }
  }
  Line(double a, double b, double c) {
    if (sgn(a) == 0) {
      s = Point(0, -c / b);
      e = Point(1, -c / b);
    } else if (sgn(b) == 0) {
      s = Point(-c / a, 0);
      e = Point(-c / a, 1);
    } else {
      s = Point(0, -c / b);
      e = Point(1, (-c - a) / b);
    }
  }
  void input() {
    s.input();
    e.input();
  }
  void adjust() {
    if (e < s) swap(s, e);
  }
  double length() { return s.distance(e); }
  double angle() {
    double k = atan2(e.y - s.y, e.x - s.x);
    if (sgn(k) < 0) k += pi;
    if (sgn(k - pi) == 0) k -= pi;
    return k;
  }
  int relation(Point p) {
    int c = sgn((p - s) ^ (e - s));
    if (c < 0)
      return 1;
    else if (c > 0)
      return 2;
    else
      return 3;
  }
  bool pointonseg(Point p) {
    return sgn((p - s) ^ (e - s)) == 0 && sgn((p - s) * (p - e)) <= 0;
  }
  bool parallel(Line v) { return sgn((e - s) ^ (v.e - v.s)) == 0; }
  int segcrossseg(Line v) {
    int d1 = sgn((e - s) ^ (v.s - s));
    int d2 = sgn((e - s) ^ (v.e - s));
    int d3 = sgn((v.e - v.s) ^ (s - v.s));
    int d4 = sgn((v.e - v.s) ^ (e - v.s));
    if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 2;
    return (d1 == 0 && sgn((v.s - s) * (v.s - e)) <= 0) ||
           (d2 == 0 && sgn((v.e - s) * (v.e - e)) <= 0) ||
           (d3 == 0 && sgn((s - v.s) * (s - v.e)) <= 0) ||
           (d4 == 0 && sgn((e - v.s) * (e - v.e)) <= 0);
  }
  int linecrossseg(Line v) {
    int d1 = sgn((e - s) ^ (v.s - s));
    int d2 = sgn((e - s) ^ (v.e - s));
    if ((d1 ^ d2) == -2) return 2;
    return (d1 == 0 || d2 == 0);
  }
  int linecrossline(Line v) {
    if ((*this).parallel(v)) return v.relation(s) == 3;
    return 2;
  }
  Point crosspoint(Line v) {
    double a1 = (v.e - v.s) ^ (s - v.s);
    double a2 = (v.e - v.s) ^ (e - v.s);
    return Point((s.x * a2 - e.x * a1) / (a2 - a1),
                 (s.y * a2 - e.y * a1) / (a2 - a1));
  }
  double dispointtoline(Point p) { return fabs((p - s) ^ (e - s)) / length(); }
  double dispointtoseg(Point p) {
    if (sgn((p - s) * (e - s)) < 0 || sgn((p - e) * (s - e)) < 0)
      return min(p.distance(s), p.distance(e));
    return dispointtoline(p);
  }
  double dissegtoseg(Line v) {
    return min(min(dispointtoseg(v.s), dispointtoseg(v.e)),
               min(v.dispointtoseg(s), v.dispointtoseg(e)));
  }
  Point lineprog(Point p) {
    return s + (((e - s) * ((e - s) * (p - s))) / ((e - s).len2()));
  }
  Point symmetrypoint(Point p) {
    Point q = lineprog(p);
    return Point(2 * q.x - p.x, 2 * q.y - p.y);
  }
};
struct circle {
  Point p;
  double r;
  circle() {}
  circle(Point _p, double _r) {
    p = _p;
    r = _r;
  }
  circle(double x, double y, double _r) {
    p = Point(x, y);
    r = _r;
  }
  circle(Point a, Point b, Point c) {
    Line u = Line((a + b) / 2, ((a + b) / 2) + ((b - a).rotleft()));
    Line v = Line((b + c) / 2, ((b + c) / 2) + ((c - b).rotleft()));
    p = u.crosspoint(v);
    r = p.distance(a);
  }
  circle(Point a, Point b, Point c, bool t) {
    Line u, v;
    double m = atan2(b.y - a.y, b.x - a.x), n = atan2(c.y - a.y, c.x - a.x);
    u.s = a;
    u.e = u.s + Point(cos((n + m) / 2), sin((n + m) / 2));
    v.s = b;
    m = atan2(a.y - b.y, a.x - b.x), n = atan2(c.y - b.y, c.x - b.x);
    v.e = v.s + Point(cos((n + m) / 2), sin((n + m) / 2));
    p = u.crosspoint(v);
    r = Line(a, b).dispointtoseg(p);
  }
  void input() {
    p.input();
    scanf("%lf", &r);
  }
  void output() { printf("%.2lf␣%.2lf␣%.2lf\n", p.x, p.y, r); }
  bool operator==(circle v) { return (p == v.p) && sgn(r - v.r) == 0; }
  bool operator<(circle v) const {
    return ((p < v.p) || ((p == v.p) && sgn(r - v.r) < 0));
  }
  double area() { return pi * r * r; }
  double circumference() { return 2 * pi * r; }
  int relation(Point b) {
    double dst = b.distance(p);
    if (sgn(dst - r) < 0)
      return 2;
    else if (sgn(dst - r) == 0)
      return 1;
    return 0;
  }
  int relationseg(Line v) {
    double dst = v.dispointtoseg(p);
    if (sgn(dst - r) < 0)
      return 2;
    else if (sgn(dst - r) == 0)
      return 1;
    return 0;
  }
  int relationline(Line v) {
    double dst = v.dispointtoline(p);
    if (sgn(dst - r) < 0)
      return 2;
    else if (sgn(dst - r) == 0)
      return 1;
    return 0;
  }
  int relationcircle(circle v) {
    double d = p.distance(v.p);
    if (sgn(d - r - v.r) > 0) return 5;
    if (sgn(d - r - v.r) == 0) return 4;
    double l = fabs(r - v.r);
    if (sgn(d - r - v.r) < 0 && sgn(d - l) > 0) return 3;
    if (sgn(d - l) == 0) return 2;
    if (sgn(d - l) < 0) return 1;
  }
  int pointcrosscircle(circle v, Point &p1, Point &p2) {
    int rel = relationcircle(v);
    if (rel == 1 || rel == 5) return 0;
    double d = p.distance(v.p);
    double l = (d * d + r * r - v.r * v.r) / (2 * d);
    double h = sqrt(r * r - l * l);
    Point tmp = p + (v.p - p).trunc(l);
    p1 = tmp + ((v.p - p).rotleft().trunc(h));
    p2 = tmp + ((v.p - p).rotright().trunc(h));
    if (rel == 2 || rel == 4) return 1;
    return 2;
  }
  int pointcrossline(Line v, Point &p1, Point &p2) {
    if (!(*this).relationline(v)) return 0;
    Point a = v.lineprog(p);
    double d = v.dispointtoline(p);
    d = sqrt(r * r - d * d);
    if (sgn(d) == 0) {
      p1 = a;
      p2 = a;
      return 1;
    }
    p1 = a + (v.e - v.s).trunc(d);
    p2 = a - (v.e - v.s).trunc(d);
    return 2;
  }
  int gercircle(Point a, Point b, double r1, circle &c1, circle &c2) {
    circle x(a, r1), y(b, r1);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r;
    return t;
  }
  int getcircle(Line u, Point q, double r1, circle &c1, circle &c2) {
    double dis = u.dispointtoline(q);
    if (sgn(dis - r1 * 2) > 0) return 0;
    if (sgn(dis) == 0) {
      c1.p = q + ((u.e - u.s).rotleft().trunc(r1));
      c2.p = q + ((u.e - u.s).rotright().trunc(r1));
      c1.r = c2.r = r1;
      return 2;
    }
    Line u1 = Line((u.s + (u.e - u.s).rotleft().trunc(r1)),
                   (u.e + (u.e - u.s).rotleft().trunc(r1)));
    Line u2 = Line((u.s + (u.e - u.s).rotright().trunc(r1)),
                   (u.e + (u.e - u.s).rotright().trunc(r1)));
    circle cc = circle(q, r1);
    Point p1, p2;
    if (!cc.pointcrossline(u1, p1, p2)) cc.pointcrossline(u2, p1, p2);
    c1 = circle(p1, r1);
    if (p1 == p2) {
      c2 = c1;
      return 1;
    }
    c2 = circle(p2, r1);
    return 2;
  }
  int getcircle(Line u, Line v, double r1, circle &c1, circle &c2, circle &c3,
                circle &c4) {
    if (u.parallel(v)) return 0;
    Line u1 = Line(u.s + (u.e - u.s).rotleft().trunc(r1),
                   u.e + (u.e - u.s).rotleft().trunc(r1));
    Line u2 = Line(u.s + (u.e - u.s).rotright().trunc(r1),
                   u.e + (u.e - u.s).rotright().trunc(r1));
    Line v1 = Line(v.s + (v.e - v.s).rotleft().trunc(r1),
                   v.e + (v.e - v.s).rotleft().trunc(r1));
    Line v2 = Line(v.s + (v.e - v.s).rotright().trunc(r1),
                   v.e + (v.e - v.s).rotright().trunc(r1));
    c1.r = c2.r = c3.r = c4.r = r1;
    c1.p = u1.crosspoint(v1);
    c2.p = u1.crosspoint(v2);
    c3.p = u2.crosspoint(v1);
    c4.p = u2.crosspoint(v2);
    return 4;
  }
  int getcircle(circle cx, circle cy, double r1, circle &c1, circle &c2) {
    circle x(cx.p, r1 + cx.r), y(cy.p, r1 + cy.r);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r1;
    return t;
  }
  int tangentline(Point q, Line &u, Line &v) {
    int x = relation(q);
    if (x == 2) return 0;
    if (x == 1) {
      u = Line(q, q + (q - p).rotleft());
      v = u;
      return 1;
    }
    double d = p.distance(q);
    double l = r * r / d;
    double h = sqrt(r * r - l * l);
    u = Line(q, p + ((q - p).trunc(l) + (q - p).rotleft().trunc(h)));
    v = Line(q, p + ((q - p).trunc(l) + (q - p).rotright().trunc(h)));
    return 2;
  }
  double areacircle(circle v) {
    int rel = relationcircle(v);
    if (rel >= 4) return 0.0;
    if (rel <= 2) return min(area(), v.area());
    double d = p.distance(v.p);
    double hf = (r + v.r + d) / 2.0;
    double ss = 2 * sqrt(hf * (hf - r) * (hf - v.r) * (hf - d));
    double a1 = acos((r * r + d * d - v.r * v.r) / (2.0 * r * d));
    a1 = a1 * r * r;
    double a2 = acos((v.r * v.r + d * d - r * r) / (2.0 * v.r * d));
    a2 = a2 * v.r * v.r;
    return a1 + a2 - ss;
  }
  double areatriangle(Point a, Point b) {
    if (sgn((p - a) ^ (p - b)) == 0) return 0.0;
    Point q[5];
    int len = 0;
    q[len++] = a;
    Line l(a, b);
    Point p1, p2;
    if (pointcrossline(l, q[1], q[2]) == 2) {
      if (sgn((a - q[1]) * (b - q[1])) < 0) q[len++] = q[1];
      if (sgn((a - q[2]) * (b - q[2])) < 0) q[len++] = q[2];
    }
    q[len++] = b;
    if (len == 4 && sgn((q[0] - q[1]) * (q[2] - q[1])) > 0) swap(q[1], q[2]);
    double res = 0;
    for (int i = 0; i < len - 1; i++) {
      if (relation(q[i]) == 0 || relation(q[i + 1]) == 0) {
        double arg = p.rad(q[i], q[i + 1]);
        res += r * r * arg / 2.0;
      } else {
        res += fabs((q[i] - p) ^ (q[i + 1] - p)) / 2.0;
      }
    }
    return res;
  }
};
struct polygon {
  int n;
  Point p[maxp];
  Line l[maxp];
  void input(int _n) {
    n = _n;
    for (int i = 0; i < n; i++) {
      p[i].input();
      p[i].info = 0;
    }
  }
  void input(int _n, int info) {
    n = _n;
    for (int i = 0; i < n; i++) {
      p[i].input();
      p[i].info = info;
    }
  }
  void add(Point q) { p[n++] = q; }
  void getline() {
    for (int i = 0; i < n; i++) {
      l[i] = Line(p[i], p[(i + 1) % n]);
    }
  }
  inline Point &operator[](int i) {
    if (n == 0) return p[i];
    return p[(i + n) % n];
  }
  struct cmp {
    Point p;
    cmp(const Point &p0) { p = p0; }
    bool operator()(const Point &aa, const Point &bb) {
      Point a = aa, b = bb;
      int d = sgn((a - p) ^ (b - p));
      if (d == 0) {
        return sgn(a.distance(p) - b.distance(p)) < 0;
      }
      return d > 0;
    }
  };
  void norm() {
    Point mi = p[0];
    for (int i = 1; i < n; i++) mi = min(mi, p[i]);
    sort(p, p + n, cmp(mi));
  }
  void getconvex(polygon &convex) {
    sort(p, p + n);
    convex.n = n;
    for (int i = 0; i < min(n, 2); i++) {
      convex.p[i] = p[i];
    }
    if (convex.n == 2 && (convex.p[0] == convex.p[1])) convex.n--;
    if (n <= 2) return;
    int &top = convex.n;
    top = 1;
    for (int i = 2; i < n; i++) {
      while (top &&
             sgn((convex.p[top] - p[i]) ^ (convex.p[top - 1] - p[i])) <= 0)
        top--;
      convex.p[++top] = p[i];
    }
    int temp = top;
    convex.p[++top] = p[n - 2];
    for (int i = n - 3; i >= 0; i--) {
      while (top != temp &&
             sgn((convex.p[top] - p[i]) ^ (convex.p[top - 1] - p[i])) <= 0)
        top--;
      convex.p[++top] = p[i];
    }
    if (convex.n == 2 && (convex.p[0] == convex.p[1])) convex.n--;
    convex.norm();
  }
  void getconvex_hull(polygon &convex) {
    sort(p, p + n);
    int k = 0;
    for (int i = 0; i < n; i++) {
      while (k > 1 &&
             ((convex[k - 1] - convex[k - 2]) ^ (p[i] - convex[k - 1])) < 0)
        k--;
      convex[k++] = p[i];
    }
    for (int i = n - 2, t = k; i >= 0; i--) {
      while (k > t &&
             ((convex[k - 1] - convex[k - 2]) ^ (p[i] - convex[k - 1])) < 0)
        k--;
      convex[k++] = p[i];
    }
    convex.n = k;
  }
  void Graham(polygon &convex) {
    norm();
    int &top = convex.n;
    top = 0;
    if (n == 1) {
      top = 1;
      convex.p[0] = p[0];
      return;
    }
    if (n == 2) {
      top = 2;
      convex.p[0] = p[0];
      convex.p[1] = p[1];
      if (convex.p[0] == convex.p[1]) top--;
      return;
    }
    convex.p[0] = p[0];
    convex.p[1] = p[1];
    top = 2;
    for (int i = 2; i < n; i++) {
      while (top > 1 && sgn((convex.p[top - 1] - convex.p[top - 2]) ^
                            (p[i] - convex.p[top - 2])) <= 0)
        top--;
      convex.p[top++] = p[i];
    }
    if (convex.n == 2 && (convex.p[0] == convex.p[1])) convex.n--;
  }
  bool isconvex() {
    bool s[2];
    memset(s, false, sizeof(s));
    for (int i = 0; i < n; i++) {
      int j = (i + 1) % n;
      int k = (j + 1) % n;
      s[sgn((p[j] - p[i]) ^ (p[k] - p[i])) + 1] = true;
      if (s[0] && s[2]) return false;
    }
    return true;
  }
  bool inedge(Point q) {
    for (int i = 0; i < n; i++) {
      if (p[i] == q) return true;
    }
    for (int i = 0; i < n; i++) {
      if (l[i].pointonseg(q)) return true;
    }
    return false;
  }
  int relationpoint(Point q) {
    for (int i = 0; i < n; i++) {
      if (p[i] == q) return 3;
    }
    for (int i = 0; i < n; i++) {
      if (l[i].pointonseg(q)) return 2;
    }
    int cnt = 0;
    for (int i = 0; i < n; i++) {
      int j = (i + 1) % n;
      int k = sgn((q - p[j]) ^ (p[i] - p[j]));
      int u = sgn(p[i].y - q.y);
      int v = sgn(p[j].y - q.y);
      if (k > 0 && u < 0 && v >= 0) cnt++;
      if (k < 0 && v < 0 && u >= 0) cnt--;
    }
    return cnt != 0;
  }
  void convexcut(Line u, polygon &po) {
    int &top = po.n;
    top = 0;
    for (int i = 0; i < n; i++) {
      int d1 = sgn((u.e - u.s) ^ (p[i] - u.s));
      int d2 = sgn((u.e - u.s) ^ (p[(i + 1) % n] - u.s));
      if (d1 >= 0) po.p[top++] = p[i];
      if (d1 * d2 < 0) po.p[top++] = u.crosspoint(Line(p[i], p[(i + 1) % n]));
    }
  }
  double getcircumference() {
    double sum = 0;
    for (int i = 0; i < n; i++) {
      sum += p[i].distance(p[(i + 1) % n]);
    }
    return sum;
  }
  double getarea() {
    double sum = 0;
    for (int i = 0; i < n; i++) {
      sum += (p[i] ^ p[(i + 1) % n]);
    }
    return fabs(sum) / 2;
  }
  bool getdir() {
    double sum = 0;
    for (int i = 0; i < n; i++) sum += (p[i] ^ p[(i + 1) % n]);
    if (sgn(sum) > 0) return 1;
    return 0;
  }
  Point getbarycentre() {
    Point ret(0, 0);
    double area = 0;
    for (int i = 1; i < n - 1; i++) {
      double tmp = (p[i] - p[0]) ^ (p[i + 1] - p[0]);
      if (sgn(tmp) == 0) continue;
      area += tmp;
      ret.x += (p[0].x + p[i].x + p[i + 1].x) / 3 * tmp;
      ret.y += (p[0].y + p[i].y + p[i + 1].y) / 3 * tmp;
    }
    if (sgn(area)) ret = ret / area;
    return ret;
  }
  double areacircle(circle c) {
    double ans = 0;
    for (int i = 0; i < n; i++) {
      int j = (i + 1) % n;
      if (sgn((p[j] - c.p) ^ (p[i] - c.p)) >= 0)
        ans += c.areatriangle(p[i], p[j]);
      else
        ans -= c.areatriangle(p[i], p[j]);
    }
    return fabs(ans);
  }
  int relationcircle(circle c) {
    getline();
    int x = 2;
    if (relationpoint(c.p) != 1) return 0;
    for (int i = 0; i < n; i++) {
      if (c.relationseg(l[i]) == 2) return 0;
      if (c.relationseg(l[i]) == 1) x = 1;
    }
    return x;
  }
};
double cross(Point A, Point B, Point C) { return (B - A) ^ (C - A); }
double dot(Point A, Point B, Point C) { return (B - A) * (C - A); }
double minRectangleCover(polygon A) {
  if (A.n < 3) return 0.0;
  A.p[A.n] = A.p[0];
  double ans = -1;
  int r = 1, p = 1, q;
  for (int i = 0; i < A.n; i++) {
    while (sgn(cross(A.p[i], A.p[i + 1], A.p[r + 1]) -
               cross(A.p[i], A.p[i + 1], A.p[r])) >= 0)
      r = (r + 1) % A.n;
    while (sgn(dot(A.p[i], A.p[i + 1], A.p[p + 1]) -
               dot(A.p[i], A.p[i + 1], A.p[p])) >= 0)
      p = (p + 1) % A.n;
    if (i == 0) q = p;
    while (sgn(dot(A.p[i], A.p[i + 1], A.p[q + 1]) -
               dot(A.p[i], A.p[i + 1], A.p[q])) <= 0)
      q = (q + 1) % A.n;
    double d = (A.p[i] - A.p[i + 1]).len2();
    double tmp =
        cross(A.p[i], A.p[i + 1], A.p[r]) *
        (dot(A.p[i], A.p[i + 1], A.p[p]) - dot(A.p[i], A.p[i + 1], A.p[q])) / d;
    if (ans < 0 || ans > tmp) ans = tmp;
  }
  return ans;
}
vector<Point> convexCut(const vector<Point> &ps, Point q1, Point q2) {
  vector<Point> qs;
  int n = ps.size();
  for (int i = 0; i < n; i++) {
    Point p1 = ps[i], p2 = ps[(i + 1) % n];
    int d1 = sgn((q2 - q1) ^ (p1 - q1)), d2 = sgn((q2 - q1) ^ (p2 - q1));
    if (d1 >= 0) qs.push_back(p1);
    if (d1 * d2 < 0) qs.push_back(Line(p1, p2).crosspoint(Line(q1, q2)));
  }
  return qs;
}
struct halfplane : public Line {
  double angle;
  halfplane() {}
  halfplane(Point _s, Point _e) {
    s = _s;
    e = _e;
  }
  halfplane(Line v) {
    s = v.s;
    e = v.e;
  }
  void calcangle() { angle = atan2(e.y - s.y, e.x - s.x); }
  bool operator<(const halfplane &b) const { return angle < b.angle; }
};
struct halfplanes {
  int n;
  halfplane hp[maxp];
  Point p[maxp];
  int que[maxp];
  int st, ed;
  void push(halfplane tmp) { hp[n++] = tmp; }
  void unique() {
    int m = 1;
    for (int i = 1; i < n; i++) {
      if (sgn(hp[i].angle - hp[i - 1].angle) != 0)
        hp[m++] = hp[i];
      else if (sgn((hp[m - 1].e - hp[m - 1].s) ^ (hp[i].s - hp[m - 1].s)) > 0)
        hp[m - 1] = hp[i];
    }
    n = m;
  }
  bool halfplaneinsert() {
    for (int i = 0; i < n; i++) hp[i].calcangle();
    sort(hp, hp + n);
    unique();
    que[st = 0] = 0;
    que[ed = 1] = 1;
    p[1] = hp[0].crosspoint(hp[1]);
    for (int i = 2; i < n; i++) {
      while (st < ed && sgn((hp[i].e - hp[i].s) ^ (p[ed] - hp[i].s)) < 0) ed--;
      while (st < ed && sgn((hp[i].e - hp[i].s) ^ (p[st + 1] - hp[i].s)) < 0)
        st++;
      que[++ed] = i;
      if (hp[i].parallel(hp[que[ed - 1]])) return false;
      p[ed] = hp[i].crosspoint(hp[que[ed - 1]]);
    }
    while (st < ed &&
           sgn((hp[que[st]].e - hp[que[st]].s) ^ (p[ed] - hp[que[st]].s)) < 0)
      ed--;
    while (st < ed && sgn((hp[que[ed]].e - hp[que[ed]].s) ^
                          (p[st + 1] - hp[que[ed]].s)) < 0)
      st++;
    if (st + 1 >= ed) return false;
    return true;
  }
  void getconvex(polygon &con) {
    p[st] = hp[que[st]].crosspoint(hp[que[ed]]);
    con.n = ed - st + 1;
    for (int j = st, i = 0; j <= ed; i++, j++) con.p[i] = p[j];
  }
};
struct circles {
  circle c[maxn];
  double ans[maxn];
  double pre[maxn];
  int n;
  circles() {}
  void add(circle cc) { c[n++] = cc; }
  bool inner(circle x, circle y) {
    if (x.relationcircle(y) != 1) return 0;
    return sgn(x.r - y.r) <= 0 ? 1 : 0;
  }
  void init_or() {
    bool mark[maxn] = {0};
    int i, j, k = 0;
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++)
        if (i != j && !mark[j]) {
          if ((c[i] == c[j]) || inner(c[i], c[j])) break;
        }
      if (j < n) mark[i] = 1;
    }
    for (i = 0; i < n; i++)
      if (!mark[i]) c[k++] = c[i];
    n = k;
  }
  void init_add() {
    int i, j, k;
    bool mark[maxn] = {0};
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++)
        if (i != j && !mark[j]) {
          if ((c[i] == c[j]) || inner(c[j], c[i])) break;
        }
      if (j < n) mark[i] = 1;
    }
    for (i = 0; i < n; i++)
      if (!mark[i]) c[k++] = c[i];
    n = k;
  }
  double areaarc(double th, double r) { return 0.5 * r * r * (th - sin(th)); }
  void getarea() {
    memset(ans, 0, sizeof(ans));
    vector<pair<double, int>> v;
    for (int i = 0; i < n; i++) {
      v.clear();
      v.push_back(make_pair(-pi, 1));
      v.push_back(make_pair(pi, -1));
      for (int j = 0; j < n; j++)
        if (i != j) {
          Point q = (c[j].p - c[i].p);
          double ab = q.len(), ac = c[i].r, bc = c[j].r;
          if (sgn(ab + ac - bc) <= 0) {
            v.push_back(make_pair(-pi, 1));
            v.push_back(make_pair(pi, -1));
            continue;
          }
          if (sgn(ab + bc - ac) <= 0) continue;
          if (sgn(ab - ac - bc) > 0) continue;
          double th = atan2(q.y, q.x),
                 fai = acos((ac * ac + ab * ab - bc * bc) / (2.0 * ac * ab));
          double a0 = th - fai;
          if (sgn(a0 + pi) < 0) a0 += 2 * pi;
          double a1 = th + fai;
          if (sgn(a1 - pi) > 0) a1 -= 2 * pi;
          if (sgn(a0 - a1) > 0) {
            v.push_back(make_pair(a0, 1));
            v.push_back(make_pair(pi, -1));
            v.push_back(make_pair(-pi, 1));
            v.push_back(make_pair(a1, -1));
          } else {
            v.push_back(make_pair(a0, 1));
            v.push_back(make_pair(a1, -1));
          }
        }
      sort(v.begin(), v.end());
      int cur = 0;
      for (int j = 0; j < v.size(); j++) {
        if (cur && sgn(v[j].first - pre[cur])) {
          ans[cur] += areaarc(v[j].first - pre[cur], c[i].r);
          ans[cur] += 0.5 * (Point(c[i].p.x + c[i].r * cos(pre[cur]),
                                   c[i].p.y + c[i].r * sin(pre[cur])) ^
                             Point(c[i].p.x + c[i].r * cos(v[j].first),
                                   c[i].p.y + c[i].r * sin(v[j].first)));
        }
        cur += v[j].second;
        pre[cur] = v[j].first;
      }
    }
    for (int i = 1; i < n; i++) ans[i] -= ans[i + 1];
  }
};
polygon pol;
polygon pol2;
polygon pol3;
int main() {
  int n;
  scanf("%d", &n);
  pol.input(n, 1);
  int m;
  scanf("%d", &m);
  pol2.input(m, 2);
  for (int i = 0; i < m; i++) {
    pol.add(pol2[i]);
  }
  pol.getconvex_hull(pol3);
  bool flag = true;
  for (int i = 0; i < pol3.n; i++) {
    if (pol3[i].info == 2) {
      flag = false;
      break;
    }
  }
  if (flag)
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}

```