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.

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import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Solution {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader fi = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, fi, out);
        out.close();
    }

    static class Task {
        public void solve(int testNumber, InputReader fi, PrintWriter out) {
            int i,j,n,k;
            n=fi.nextInt();
            Node[] a=new Node[n];
            for (i=0;i<n;i++){
                a[i]=new Node(fi.nextLong(),fi.nextLong());
            }

            if(n<=4){
                out.println("YES");
                return;
            }
            ArrayList<Integer> st=new ArrayList<>();
            for (k=0;k<3;k++){

                for (j=k+1;j<3;j++){
                    st.clear();
                    for (i=0;i<n;i++){
                        if (!collinear(a[k],a[j],a[i])) st.add(i);
                    }
                    if(st.size() <=2 ){
                     out.println("YES");
                     return;
                    }
                    boolean good=true;
                    for (i=2;i<st.size();i++){
                        if (!collinear(a[st.get(0)],a[st.get(1)],a[st.get(i)])) {
                            good=false;
                            break;
                        }
                    }
                    if (good){
                        out.println("YES");
                        return;
                    }
                }
            }
            out.println("NO");
            return;
        }
    }


    static  boolean collinear(Node a,Node b,Node c){
        long d1x=b.x-a.x;
        long d1y=b.y-a.y;
        long d2x=c.x-a.x;
        long d2y=c.y-a.y;
        return (d1x*d2y)==(d1y*d2x);
    }
}

class Node{
    long x,y;
    Node(long x,long y){
        this.x=x;
        this.y=y;
    }
}






class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[8192];
    private int curChar, snumChars;
    private SpaceCharFilter filter;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int snext() {
        if (snumChars == -1)
            throw new InputMismatchException();
        if (curChar >= snumChars) {
            curChar = 0;
            try {
                snumChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (snumChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int nextInt() {
        int c = snext();
        while (isSpaceChar(c))
            c = snext();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = snext();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = snext();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public long nextLong() {
        int c = snext();
        while (isSpaceChar(c))
            c = snext();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = snext();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = snext();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public int[] nextIntArray(int n) {
        int a[] = new int[n+1];
        for (int i = 1; i <= n; i++)
            a[i] = nextInt();
        return a;
    }

    public String readString() {
        int c = snext();
        while (isSpaceChar(c))
            c = snext();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = snext();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}