You are given n points on Cartesian plane. Every point is a lattice point (i. e. both of its coordinates are integers), and all points are distinct.

You may draw two straight lines (not necessarily distinct). Is it possible to do this in such a way that every point lies on at least one of these lines?

Input

The first line contains one integer n (1 ≤ n ≤ 105) — the number of points you are given.

Then n lines follow, each line containing two integers xi and yi (|xi|, |yi| ≤ 109)— coordinates of i-th point. All n points are distinct.

Output

If it is possible to draw two straight lines in such a way that each of given points belongs to at least one of these lines, print YES. Otherwise, print NO.

Examples

Input

5
0 0
0 1
1 1
1 -1
2 2


Output

YES


Input

5
0 0
1 0
2 1
1 1
2 3


Output

NO

Note

In the first example it is possible to draw two lines, the one containing the points 1, 3 and 5, and another one containing two remaining points.

<image>


import java.util.*;

import java.io.*;

public class file {
	static long mod = (long) Math.pow(10, 9) + 7;

	public static void main(String[] args) throws Exception {

		Scan scn = new Scan();
		int n = scn.scanInt();
		point[] arr = new point[n];

		for (int i = 0; i < arr.length; i++) {
			arr[i] = new point(scn.scanInt(), scn.scanInt());
		}

		if (n <= 2) {
			System.out.println("YES");
			return;
		}

		if (check(0, 1, arr))
			System.out.println("YES");
		else if (check(0, 2, arr))
			System.out.println("YES");
		else if (check(1, 2, arr))
			System.out.println("YES");
		else
			System.out.println("NO");

	}

	public static boolean check(int x, int y, point[] arr) {
		int n = arr.length;
		boolean[] used = new boolean[n];

		point a = arr[x];
		point b = arr[y];
		used[x] = used[y] = true;

		for (int i = 0; i < n; i++) {
			if (used[i])
				continue;

			if (areOnSameLine(a, b, arr[i]))
				used[i] = true;

		}

		point one = null;
		point two = null;

		int j = 0;
		while (j < n) {
			if (used[j]) {
				j++;
				continue;
			}

			if (one == null) {
				one = arr[j];
			} else {
				two = arr[j];
				j++;
				break;
			}
			j++;
		}

		if (one == null || two == null)
			return true;

		for (int i = j; i < n; i++) {

			if (used[i] == true)
				continue;

			if (areOnSameLine(one, two, arr[i]) == false)
				return false;
		}

		return true;
	}

	public static boolean areOnSameLine(point a, point b, point c) {

		point one = new point();
		one.x = b.x - a.x;
		one.y = b.y - a.y;

		point two = new point();
		two.x = c.x - a.x;
		two.y = c.y - a.y;

		long l = 1;

		if (one.x * l * two.y - one.y * l * two.x == 0)
			return true;

		return false;
	}

	public static class point {
		int x;
		int y;

		public point() {
			x = 0;
			y = 0;
		}

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

		@Override
		public String toString() {
			// TODO Auto-generated method stub
			return "[" + this.x + "," + this.y + "]";
		}
	}

	static class Scan {
		private InputStream in;
		private byte[] buf = new byte[1024 * 1024];
		private int index;
		private int total;

		public Scan() {
			in = System.in;
			// try {
			// in = new FileInputStream(new File("/home/ujjwal/test/test"));
			// } catch (Exception ex) {
			//
			// }
		}

		public int scan() throws IOException {
			if (total < 0)
				throw new InputMismatchException();
			if (index >= total) {
				index = 0;
				total = in.read(buf);
				if (total <= 0)
					return -1;
			}
			return buf[index++];
		}

		public int scanInt() throws IOException {
			int integer = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n)) {
				if (n >= '0' && n <= '9') {
					integer *= 10;
					integer += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			return neg * integer;
		}

		public long scanLong() throws IOException {
			long integer = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n)) {
				if (n >= '0' && n <= '9') {
					integer *= 10;
					integer += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			return neg * integer;
		}

		public double scanDouble() throws IOException {
			double doub = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n) && n != '.') {
				if (n >= '0' && n <= '9') {
					doub *= 10;
					doub += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			if (n == '.') {
				n = scan();
				double temp = 1;
				while (!isWhiteSpace(n)) {
					if (n >= '0' && n <= '9') {
						temp /= 10;
						doub += (n - '0') * temp;
						n = scan();
					} else
						throw new InputMismatchException();
				}
			}
			return doub * neg;
		}

		public String scanString() throws IOException {
			StringBuilder sb = new StringBuilder();
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			while (!isWhiteSpace(n)) {
				sb.append((char) n);
				n = scan();
			}
			return sb.toString();
		}

		private boolean isWhiteSpace(int n) {
			if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
				return true;
			return false;
		}
	}

	static class Print {
		private final BufferedWriter bw;

		public Print() {
			bw = new BufferedWriter(new OutputStreamWriter(System.out));
		}

		public void print(String str) throws IOException {
			bw.append(str);
		}

		public void printLine(String str) throws IOException {
			print(str);
			bw.append("\n");
		}

		public void close() throws IOException {
			bw.close();
		}
	}

}
