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 CFD {

    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    private static final long MOD = 1000L * 1000L * 1000L + 7;
    private static final int[] dx = {0, -1, 0, 1};
    private static final int[] dy = {1, 0, -1, 0};
    private static final String yes = "Yes";
    private static final String no = "No";

    int n;
    long[] x;
    long[] y;
    void solve() throws IOException {
        n = nextInt();
        x = new long[n];
        y = new long[n];
        for (int i = 0; i < n; i++) {
            x[i] = nextInt();
            y[i] = nextInt();
        }

        if (n <= 4) {
            outln(yes.toUpperCase());
            return;
        }

        boolean res = check(0, 1);
        res |= check(0, 2);
        res |= check(1, 2);
        if (res) {
            outln(yes.toUpperCase());
        }
        else {
            outln(no.toUpperCase());
        }
    }

    boolean check(int f, int s) {
        int n1 = -1;
        int n2 = -1;
        for (int i = 0; i < n; i++) {
            if (isLine(f, s, i)) {
                continue;
            }
            if (n1 == -1) {
                n1 = i;
            }
            else {
                if (n2 == -1) {
                    n2 = i;
                }
                else {
                    if (!isLine(n1, n2, i)) {
                        return false;
                    }
                }
            }
        }

        return true;
    }

    boolean isLine(int i, int j, int k) {
        long dx1 = x[k] - x[i];
        long dy1 = y[k] - y[i];
        long dx2 = x[j] - x[i];
        long dy2 = y[j] - y[i];

        return dy2 * dx1 == dy1 * dx2;
    }

    void shuffle(int[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            int tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }
    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    private void formatPrint(double val) {
        System.out.format("%.9f%n", val);
    }
    public CFD() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFD();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}
