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 JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NavigableSet;
import java.util.TreeSet;

public class Code_Forces_70_D 
{
	public static void main(String[] args) 
	{
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Task solver = new Task();
		solver.solve(1, in, out);
		out.close();
	}

	static class Task 
	{
		public void solve(int testNumber, InputReader in, PrintWriter out) 
		{
			int q = in.nextInt();

			PointContainer ref = new PointContainer();
			TreeSet<Point> S = new TreeSet<>((o1, o2) -> 
			{
				int sgn = signCrossProduct(ref.e, o1, o2);
				if (sgn != 0) 
				{
					return -sgn;
				} 
				else if (o1.x != o2.x) 
				{
					return Integer.compare(o1.x, o2.x);
				} else 
				{
					return Integer.compare(o1.y, o2.y);
				}
			});

			int maxx = -0x3f3f3f3f;

			while (q-- > 0) 
			{
				int type = in.nextInt();
				Point p = new Point(in.nextInt(), in.nextInt());

				if (type == 1) 
				{
					maxx = Math.max(maxx, p.x);
					if (ref.e == null) 
					{
						ref.e = p;
						continue;
					}

					if (p.compareTo(ref.e) < 0) 
					{
						workHull(S, p, maxx);
						Point prev = ref.e;
						ref.e = p;
						p = prev;
					}

					NavigableSet<Point> smaller = S.headSet(p, false);

					while (smaller.size() >= 1) 
					{
						Point s = smaller.last();
						Point f = smaller.lower(s);
						if (f == null) f = ref.e;
						if (signCrossProduct(f, s, p) <= 0) 
						{
							smaller.pollLast();
						} 
						else
						{
							break;
						}
					}

					Point d = S.higher(p);

					if ((d == null || smaller.size() < 1) || (signCrossProduct(smaller.last(), p, d) > 0)) 
					{
						S.add(p);
						NavigableSet<Point> bigger = S.tailSet(p, false);

						while (bigger.size() >= 1)
						{
							Point f = bigger.first();
							Point s = bigger.higher(f);
							if (s == null) s = ref.e;
							if (signCrossProduct(p, f, s) <= 0) 
							{
								bigger.pollFirst();
							}
							else
							{
								break;
							}
						}
					}
				} 
				else
				{
					if (p.compareTo(ref.e) < 0) 
					{
						out.println("NO");
					} 
					else if (p.compareTo(ref.e) == 0)
					{
						out.println("YES");
					} 
					else
					{
						Point f = S.lower(p);
						Point s = S.ceiling(p);
						if (f != null && signCrossProduct(ref.e, p, f) == 0 && between(ref.e, p, f)) 
						{
							out.println("YES");
						} 
						else if (s != null && signCrossProduct(ref.e, p, s) == 0 && between(ref.e, p, s)) 
						{
							out.println("YES");
						} 
						else if (f == null || s == null) 
						{
							out.println("NO");
						} 
						else if (signCrossProduct(ref.e, f, s) * signCrossProduct(p, f, s) >= 0)
						{
							out.println("YES");
						} 
						else
						{
							out.println("NO");
						}
					}
				}
			}
		}

		private void workHull(TreeSet<Point> S, Point p, int maxx)
		{
			while (S.size() >= 2) 
			{
				Point f = S.first();
				Point s = S.higher(f);
				if (f.x == maxx) 
					break;
				if (signCrossProduct(p, f, s) <= 0) 
				{
					S.pollFirst();
				}
				else
				{
					break;
				}
			}

			while (S.size() >= 2)
			{
				Point s = S.last();
				Point f = S.lower(s);
				if (s.x == maxx) 
					break;
				if (signCrossProduct(p, f, s) <= 0)
				{
					S.pollLast();
				} 
				else
				{
					break;
				}
			}
		}

		private boolean between(Point a, Point b, Point c)
		{
			if (a.x == c.x)
			{
				return a.y <= b.y && b.y <= c.y;
			}
			else
			{
				return a.x <= b.x && b.x <= c.x;
			}
		}

		private int signCrossProduct(Point o, Point a, Point b) 
		{
			long c = (long) (a.x - o.x) * (b.y - o.y) - (long) (a.y - o.y) * (b.x - o.x);
			if (c < 0)
				return -1;
			else if (c > 0) 
				return 1;
			return 0;
		}

		private class Point
		{
			int x;
			int y;

			Point(int x, int y)
			{
				this.x = x;
				this.y = y;
			}

			private int compareTo(Point other)
			{
				return x != other.x ? Integer.compare(x, other.x) : Integer.compare(y, other.y);
			}

			public String toString()
			{
				return "(" + x + ", " + y + ")";
			}

		}

		private class PointContainer
		{
			public Point e;
		}

	}

	static class InputReader 
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public InputReader(InputStream stream)
		{
			this.stream = stream;
		}

		public int read()
		{
			if (numChars == -1)
				throw new UnknownError();
			if (curChar >= numChars)
			{
				curChar = 0;
				try
				{
					numChars = stream.read(buf);
				}
				catch (IOException e) 
				{
					throw new UnknownError();
				}

				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() 
		{
			return Integer.parseInt(next());
		}

		public String next() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuffer res = new StringBuffer();
			do
			{
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));

			return res.toString();
		}

		private boolean isSpaceChar(int c) 
		{
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	}
}