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.BufferedInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.util.*;

public class D {

	static int N;
	public static void main(String[] args) {
		JS in = new JS();
		N = in.nextInt();
		point ar[] = new point[N];
		for(int i = 0; i < N; i++) {
			ar[i] = new point(in.nextLong(),in.nextLong());
		}	
		
		if(N < 5) {
			System.out.println("YES");
			return;
		}
		
		boolean found = false;
		ArrayList<Integer> line1 = new ArrayList<Integer>();
		String curD = "";
		for(int start = 0; start < 5; start++) {
			
			HashMap<String, Integer> map = new HashMap<String, Integer>();
			point st = ar[start];
			
			for(int i = 0; i < N; i++) {
				if(i==start)continue;
				long dx = ar[i].x-st.x;
				long dy = ar[i].y-st.y;
				if(dx < 0) {
					dx*=-1;
					dy*=-1;
				}
				if(dx==0)dy=Math.abs(dy);
				if(dy==0)dx=Math.abs(dx);
				long gcd = gcd(Math.abs(dx),Math.abs(dy));
				dx/=gcd;
				dy/=gcd;
				String ss = dx+"#"+dy;
				if(map.containsKey(ss)) {
					//This is line
					line1.add(start);
					line1.add(map.get(ss));
					line1.add(i);
					curD=ss;
					found=true;
					break;
				}
				else {
					map.put(ss, i);
				}
			}
			if(found)break;
		}
		//System.out.println(line1.toString()+" "+curD);
		if(line1.size() == 0) {
			System.out.println("NO");
			return;
		}
		
		boolean done[] = new boolean[N];
		for(Integer ii : line1)done[ii]=true;
		point p1 = ar[line1.get(0)];
		for(int i = 0; i < N; i++) {
			if(done[i])continue;
			
			long dx = ar[i].x-p1.x;
			long dy = ar[i].y-p1.y;
			if(dx < 0) {
				dx*=-1;
				dy*=-1;
			}
			if(dx==0)dy=Math.abs(dy);
			if(dy==0)dx=Math.abs(dx);
			long gcd = gcd(Math.abs(dx),Math.abs(dy));
			dx/=gcd;
			dy/=gcd;
			
			String ss = dx+"#"+dy;
			if(curD.equals(ss))done[i]=true;
		}
		
		
		//Now do second line
		boolean first = false;
		point p2 = null;
		String dd = "";
		for(int i = 0; i < N; i++) {
			if(done[i])continue;
			if(first==false) {
				p2 = ar[i];
				done[i]=true;
				first = true;
			}
			else {
				long dx = ar[i].x-p2.x;
				long dy = ar[i].y-p2.y;
				if(dx < 0) {
					dx*=-1;
					dy*=-1;
				}
				if(dx==0)dy=Math.abs(dy);
				if(dy==0)dx=Math.abs(dx);
				long gcd = gcd(Math.abs(dx),Math.abs(dy));
				dx/=gcd;
				dy/=gcd;
				String ss = dx+"#"+dy;
				if(dd.length()<1) {
					dd=ss;
					//System.out.println(dd);
					done[i]=true;
				}
				else {
					if(dd.equals(ss))done[i]=true;					
				}
			}
		}
		
		boolean good = true;
		for(int i = 0; i < N; i++) {
			if(!done[i])good=false;
		}
		System.out.println(good?"YES":"NO");

	}
	static class point{
		long x, y;
		public point(long xx, long yy) {
			x=xx;
			y=yy;
		}
	}
	
	static long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}

	long lcm(int a, int b){
		return a*(b/gcd(a, b));
	}
	
	static class JS{
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;
		
		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}
		
		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}
		
		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}				
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}
		
		public int nextInt() {
			return (int)nextLong();
		}
		
		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}
		
		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}
		
		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}
		
		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}
}
