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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Random;
import java.util.StringTokenizer;

public class T3 {
	
	static int n;
    static long[] x;
    static long[] y;
    
	public static void main(String[] args) {
		MyScanner sc = new MyScanner();
		n = sc.nextInt();  
		x = new long[n];
		y = new long[n];
		
		if (n <= 2) {
			System.out.println("YES");
			return;
		}
		
		for (int i = 0; i < n; i++) {
			x[i] = sc.nextLong();
			y[i] = sc.nextLong();
		}
		
		for (int step = 0; step < 100; step++) {
			Random r = new Random();  
			int ind1 = r.nextInt(n);
			int ind2 = r.nextInt(n);
			if (ind1 == ind2) continue;
			
			long a = y[ind2]-y[ind1]; 
			long b = x[ind1]-x[ind2]; 
			long c = -x[ind1]*(y[ind2]-y[ind1])+y[ind1]*(x[ind2]-x[ind1]); 
			
			List<Long> newx = new ArrayList<Long>();
			List<Long> newy = new ArrayList<Long>();
			
			for (int i = 0; i < n; i++) {
				if (a*x[i] + b*y[i] + c != 0) {
					newx.add(x[i]);
					newy.add(y[i]);
				}
			}
			
			if (newx.size() <= 2) {
				System.out.println("YES");
				return;
			
			}
			
			long a1 = newy.get(1)-newy.get(0); 
			long b1 = newx.get(0)-newx.get(1); 
			long c1 = -newx.get(0)* (newy.get(1)-newy.get(0)) + newy.get(0) * (newx.get(1)-newx.get(0)); 
			
			boolean fl = true;
			for (int i = 2; i < newx.size(); i++) {
				if (a1*newx.get(i) + b1*newy.get(i) + c1 != 0) {
					fl=false;
					break;
				}
			}
			if (fl) {
				System.out.println("YES");
				return;
			}
			
		}
		
		System.out.println("NO");
	
	}
	
	 public static class MyScanner {
	      BufferedReader br;
	      StringTokenizer st;
	 
	      public MyScanner() {
	         br = new BufferedReader(new InputStreamReader(System.in));
	      }
	 
	      String next() {
	          while (st == null || !st.hasMoreElements()) {
	              try {
	                  st = new StringTokenizer(br.readLine());
	              } catch (IOException e) {
	                  e.printStackTrace();
	              }
	          }
	          return st.nextToken();
	      }
	 
	      int nextInt() {
	          return Integer.parseInt(next());
	      }
	 
	      long nextLong() {
	          return Long.parseLong(next());
	      }
	 
	      double nextDouble() {
	          return Double.parseDouble(next());
	      }
	 
	      String nextLine(){
	          String str = "";
		  try {
		     str = br.readLine();
		  } catch (IOException e) {
		     e.printStackTrace();
		  }
		  return str;
	      }

	   }
}
