Problem: Once a walrus professor Plato asked his programming students to perform the following practical task. 

The students had to implement such a data structure that would support a convex hull on some set of points S. The input to the program had q queries of two types: 

1. Add a point with coordinates (x, y) into the set S. Note that in this case the convex hull of S could have changed, and could have remained the same. 

2. Say whether a point with coordinates (x, y) belongs to an area limited by the convex hull, including the border. 

All the students coped with the task. What about you?

Input

The first line contains an integer q (4 ≤ q ≤ 105). 

Then follow q lines in the following way: "t x y", where t is the query type (1 or 2), and (x, y) are the coordinates of the point ( - 106 ≤ x, y ≤ 106, x and y are integers). 

There is at least one query of type 2.

It is guaranteed that the three queries of the first type follow first and the points given in the queries form a non-degenerative triangle. Also all the points added in S are distinct.

Output

For each query of the second type print one string containing "YES", if the point lies inside the convex hull or on its border. Otherwise, print "NO".

Examples

Input

8
1 0 0
1 2 0
1 2 2
2 1 0
1 0 2
2 1 1
2 2 1
2 20 -1


Output

YES
YES
YES
NO

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-10;
const double inf = 1e20;
const double pi = acos(-1.0);
const int maxp = 50200;
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, ang;
  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 {
    if (sgn(this->ang - b.ang) == 0) return this->x < b.x;
    return this->ang < b.ang;
  }
  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 dispointtoray(Point p) {
    if (sgn((p - s) * (e - s)) < 0) return p.distance(s);
    return dispointtoline(p);
  }
  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);
  }
} ll1, ll2, ll3, ll4;
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;
  }
  double dis(Point a, Point b) {
    return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
  }
  Point o;
  double ri;
  void tt(Point p1, Point p2, Point p3) {
    double a, b, c, d, e, f;
    a = p2.y - p1.y;
    b = p3.y - p1.y;
    c = p2.x - p1.x;
    d = p3.x - p1.x;
    f = p3.x * p3.x + p3.y * p3.y - p1.x * p1.x - p1.y * p1.y;
    e = p2.x * p2.x + p2.y * p2.y - p1.x * p1.x - p1.y * p1.y;
    o.x = (a * f - b * e) / (2 * a * d - 2 * b * c);
    o.y = (d * e - c * f) / (2 * a * d - 2 * b * c);
    ri = dis(o, p1);
  }
  void getmincircover(Point p[], int n, circle &c) {
    random_shuffle(p, p + n);
    o = p[0];
    ri = 0;
    for (int i = 1; i < n; i++) {
      if (dis(p[i], o) > ri + eps) {
        o = p[i];
        ri = 0;
        for (int j = 0; j <= i - 1; j++) {
          if (dis(o, p[j]) > ri + eps) {
            o.x = (p[i].x + p[j].x) / 2;
            o.y = (p[i].y + p[j].y) / 2;
            ri = dis(o, p[j]);
            for (int k = 0; k <= j - 1; k++) {
              if (dis(o, p[k]) > ri + eps) {
                tt(p[i], p[j], p[k]);
              }
            }
          }
        }
      }
    }
    c.p = o;
    c.r = ri;
  }
} cc, ccc;
const int maxn = 1010;
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;
      }
    }
  }
} C;
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();
  }
  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]);
    }
  }
  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 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--;
  }
  double dis(Point a, Point b, Point c) {
    return fabs((a - c) ^ (b - c) / (a - b).len());
  }
  double getD(polygon &convex, int &pos1, int &pos2) {
    double ans = 0.0;
    int pos = 1;
    convex.p[convex.n + 1] = convex.p[1];
    convex.p[convex.n] = convex.p[0];
    if (convex.n == 0 || convex.n == 1) return 0;
    if (convex.n == 2) return (convex.p[1] - convex.p[0]).len();
    for (int i = 1; i <= convex.n; i++) {
      while (dis(convex.p[i], convex.p[i + 1], convex.p[pos]) <=
             dis(convex.p[i], convex.p[i + 1], convex.p[pos + 1]))
        pos = pos % convex.n + 1;
      double tmp1 = (convex.p[i] - convex.p[pos]).len(),
             tmp2 = (convex.p[i + 1] - convex.p[pos]).len();
      if (tmp1 > ans) {
        ans = tmp1;
        pos1 = i % n;
        pos2 = pos % n;
      }
      if (tmp2 > ans) {
        ans = tmp2;
        pos1 = (i + 1) % n;
        pos2 = pos % n;
      }
    }
    convex.p[convex.n + 1] = Point(0, 0);
    convex.p[convex.n] = Point(0, 0);
    return ans;
  }
  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;
  }
  int relationpoint(Point q) {
    for (int i = 0; i < n; i++) {
      if (p[i] == q) return 3;
    }
    getline();
    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 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() {
    if (n < 3) return 0.0;
    p[n] = p[0];
    double ans = -1;
    int r = 1, pp = 1, q;
    for (int i = 0; i < n; i++) {
      while (sgn(cross(p[i], p[i + 1], p[r + 1]) -
                 cross(p[i], p[i + 1], p[r])) >= 0)
        r = (r + 1) % n;
      while (sgn(dot(p[i], p[i + 1], p[pp + 1]) - dot(p[i], p[i + 1], p[pp])) >=
             0)
        pp = (pp + 1) % n;
      if (i == 0) q = pp;
      while (sgn(dot(p[i], p[i + 1], p[q + 1]) - dot(p[i], p[i + 1], p[q])) <=
             0)
        q = (q + 1) % n;
      double d = (p[i] - p[i + 1]).len2();
      double tmp = cross(p[i], p[i + 1], p[r]) *
                   (dot(p[i], p[i + 1], p[pp]) - dot(p[i], p[i + 1], p[q])) / d;
      if (ans < 0 || ans > tmp) {
        ans = tmp;
        ll1.s = p[i];
        ll1.e = p[i + 1];
        double an1 = ll1.angle();
        double an2 = an1 + pi / 2;
        if (an2 >= pi) an2 -= pi;
        ll2 = Line(p[pp], an2);
        ll3 = Line(p[q], an2);
        ll4 = Line(p[r], an1);
      }
    }
    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;
  }
} PO, po;
Point s1[maxp], s2[maxp];
void getMinkowski(polygon thi, polygon convex, polygon &po) {
  for (int i = 0; i < thi.n - 1; i++) s1[i] = thi.p[i + 1] - thi.p[i];
  s1[thi.n - 1] = thi.p[0] - thi.p[thi.n - 1];
  for (int i = 0; i < convex.n - 1; i++) s2[i] = convex.p[i + 1] - convex.p[i];
  s2[convex.n - 1] = convex.p[0] - convex.p[convex.n - 1];
  int tot;
  po.p[tot = 0] = thi.p[0] + convex.p[0];
  int pos1 = 0, pos2 = 0;
  while (pos1 < thi.n && pos2 < convex.n) {
    ++tot;
    po.p[tot] =
        po.p[tot - 1] + ((s1[pos1] ^ s2[pos2]) >= 0 ? s1[pos1++] : s2[pos2++]);
  }
  while (pos1 < thi.n) {
    ++tot;
    po.p[tot] = po.p[tot - 1] + s1[pos1++];
  }
  while (pos2 < convex.n) {
    ++tot;
    po.p[tot] = po.p[tot - 1] + s2[pos2++];
  }
  po.n = tot + 1;
  po.p[po.n] = po.p[0];
}
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];
  }
} HP;
set<Point> sp;
set<Point>::iterator pre, suc;
set<Point>::iterator PRE(set<Point>::iterator x) {
  if (x == sp.begin()) return --sp.end();
  return --x;
}
set<Point>::iterator SUC(set<Point>::iterator x) {
  if ((++x) == sp.end()) return sp.begin();
  return x;
}
Point pp[202];
int main() {
  int t;
  scanf("%d", &t);
  Point pt = Point(0, 0);
  int num;
  scanf("%d", &num);
  pp[0].input();
  pt = pt + pp[0];
  scanf("%d", &num);
  pp[1].input();
  pt = pt + pp[1];
  scanf("%d", &num);
  pp[2].input();
  pt = pt + pp[2];
  pt = pt / 3.0;
  pp[0] = pp[0] - pt;
  pp[1] = pp[1] - pt;
  pp[2] = pp[2] - pt;
  pp[0].ang = atan2(pp[0].y, pp[0].x);
  pp[1].ang = atan2(pp[1].y, pp[1].x);
  pp[2].ang = atan2(pp[2].y, pp[2].x);
  sp.insert(pp[0]);
  sp.insert(pp[1]);
  sp.insert(pp[2]);
  t -= 3;
  int op;
  Point ppt;
  while (t--) {
    scanf("%d", &op);
    ppt.input();
    ppt = ppt - pt;
    ppt.ang = atan2(ppt.y, ppt.x);
    if ((suc = sp.lower_bound(ppt)) == sp.end()) suc = sp.begin();
    pre = PRE(suc);
    if (op == 1) {
      double dt = (*pre - ppt) ^ (*suc - ppt);
      if (dt >= 0) continue;
      sp.insert(ppt);
      set<Point>::iterator it = sp.find(ppt);
      set<Point>::iterator itq = PRE(it);
      set<Point>::iterator itqq = PRE(itq);
      while (((*itqq - *itq) ^ (*it - *itq)) >= 0) {
        sp.erase(itq);
        itq = itqq;
        itqq = PRE(itq);
      }
      itq = SUC(it);
      itqq = SUC(itq);
      while (((*it - *itq) ^ (*itqq - *itq)) >= 0) {
        sp.erase(itq);
        itq = itqq;
        itqq = SUC(itq);
      }
    } else {
      double dt = (*pre - ppt) ^ (*suc - ppt);
      if (sgn(dt) >= 0)
        puts("YES");
      else
        puts("NO");
    }
  }
  return 0;
}