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.io.*;
import java.util.*;

public class ed {
	
	static InputStream is;

	public static void main(String[] args) throws IOException {
		is = System.in;
		int n = ni();
		long[] x = new long[n];
		long[] y = new long[n];
		
		for (int i = 0; i < y.length; i++) {
			x[i] = ni();
			y[i] = ni();
		}
		
		
		
		if(n <= 4){
			System.out.println("YES");
		}
		else{
			
			boolean found = false;
			
			for(int q = 0; q < 3; q++){
				int a = q;
				int b = (q+1)%3;
				
				boolean[] covered = new boolean[n];
				
				long cross = x[a]*y[b]-x[b]*y[a];
				
				for(int c =0; c < n; c++){
					long ncross = cross + x[b]*y[c]+x[c]*y[a]-x[a]*y[c]-x[c]*y[b];
					if(ncross == 0) covered[c] = true;
				}
				
				boolean good = true;
				for(a =0; a < n; a++){
					if(!covered[a]){
						for(b=a+1; b < n; b++){
							if(!covered[b]){
								cross = x[a]*y[b]-x[b]*y[a];
								
								for(int c = b+1; c < n; c++){
									long ncross = cross + x[b]*y[c]+x[c]*y[a]-x[a]*y[c]-x[c]*y[b];
									if(ncross == 0) covered[c] = true;
									
									if(!covered[c]) good = false;
									
								}
								
								break;
							}
						}
						break;
					}
				}
				
				if(good){
					found = true;
					break;
				}
				
			}
			
			System.out.println((found ? "YES" : "NO"));
			
		}
		
		
		
		
	}
	
	private static byte[] inbuf = new byte[1024];
	public static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
}