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.Random;
import java.util.StringTokenizer;

public class D {

	static long MOD=1_000_000_007;
	
	public static void main(String[] args) {
		FastScanner fs=new FastScanner();
		int n=fs.nextInt();
		Vec[] points=new Vec[n];
		for (int i=0; i<n; i++)
			points[i]=new Vec(fs.nextLong(), fs.nextLong());
		if (n<5) {
			System.out.println("YES");
			return;
		}
		
		Random r=new Random();
		boolean[] marked=new boolean[n];
		Vec[] open=new Vec[n];
		outer: for (int tt=0; tt<50; tt++) {
			int first=r.nextInt(n);
			int second=r.nextInt(n);
			while (second==first)
				second=r.nextInt(n);
			Seg toTry=new Seg(points[first], points[second]);
			for (int i=0; i<n; i++)
				marked[i]=toTry.contains(points[i]);
			int openCount=0;
			for (int i=0; i<n; i++)
				if (!marked[i])
					open[openCount++]=points[i];
			if (openCount<3) {
				System.out.println("YES");
				return;
			}
			Seg other=new Seg(open[0], open[1]);
			for (int i=0; i<n; i++)
				if (other.contains(points[i]))
					marked[i]=true;
			for (boolean b:marked)
				if (!b)
					continue outer;
			System.out.println("YES");
			return;
		}
		System.out.println("NO");
	}
	
	static class Seg {
		Vec a, b;
		public Seg(Vec a, Vec b) {
			this.a=a;
			this.b=b;
		}
		
		public boolean contains(Vec o) {
			Vec dir=b.sub(a);
			Vec oDir=o.sub(a);
			return dir.cross(oDir)==0;
		}
	}
	
	static class Vec {
		long x, y;
		public Vec(long x, long y) {
			this.x=x;
			this.y=y;
		}
		
		public Vec add(Vec o) {
			return new Vec(x+o.x, y+o.y);
		}
		
		public Vec scale(long s) {
			return new Vec(x*s, y*s);
		}
		
		public Vec sub(Vec o) {
			return add(o.scale(-1));
		}
		
		public String toString() {
			return "("+x+", "+y+")";
		}
		
		public long cross(Vec o) {
			return x*o.y-y*o.x;
		}
		
		public long dot(Vec o) {
			return x*o.x+y*o.y;
		}
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		
		public String next() {
			while (!st.hasMoreElements())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
		
		public int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) {
				a[i]=nextInt();
			}
			return a;
		}
		
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		
	}

}
