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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Swatantra
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            Point p[] = new Point[n];
            int i;
            for (i = 0; i < n; i++) {
                int x = in.nextInt();
                int y = in.nextInt();
                p[i] = new Point(x, y);

            }

            if (n <= 3) {
                out.println("YES");
                return;
            }

            Line l1 = new Line(p[0], p[1]);
            Line l2 = new Line(p[0], p[2]);
            Line l3 = new Line(p[1], p[2]);

            if (find(l1, p) || find(l2, p) || find(l3, p)) {
                out.println("YES");
                return;
            }

            out.println("NO");

        }

        boolean find(Line l, Point p[]) {

            boolean used[] = new boolean[p.length];
            int i;

            for (i = 0; i < p.length; i++) {
                if (l.colinear(p[i])) {

                    used[i] = true;
                }
            }
            int m = -1;
            int n = -1;

            for (i = 0; i < p.length; i++) {
                if (!used[i]) {

                    //System.out.println("Entered");
                    if (m != -1) {
                        n = i;
                        break;

                    } else {
                        m = i;
                    }

                }
            }
            // System.out.println("m="+m+" n="+n);

            if (m == -1 || n == -1)
                return true;

            //System.out.println("Reached");
            Line newl = new Line(p[m], p[n]);

            for (i = 0; i < p.length; i++) {
                if (!used[i] && newl.colinear(p[i])) {

                    used[i] = true;
                }
            }

            for (i = 0; i < p.length; i++) {
                if (!used[i]) {

                    return false;
                }
            }

            return true;
        }

        long det(long mat[][]) {
            return (mat[0][0] * mat[1][1] - mat[1][0] * mat[0][1]);
        }

        class Point {
            int x;
            int y;

            Point(int a, int b) {
                this.x = a;
                this.y = b;
            }

        }

        class Line {
            Point a;
            Point b;

            Line(Point a, Point b) {

                this.a = a;
                this.b = b;

            }

            boolean colinear(Point p) {

                int mat[][] = {{a.x, a.y, 1}, {b.x, b.y, 1}, {p.x, p.y, 1}};

                int i;
                long res = 0;

                for (i = 0; i < 3; i++) {

                    long sub[][] = {{mat[1][(i + 1) % 3], mat[1][(i + 2) % 3]},
                            {mat[2][(i + 1) % 3], mat[2][(i + 2) % 3]}};
                    res += (mat[0][i] * det(sub));
                    //System.out.println("res="+res);
                }

                return res == 0l;
            }

        }

    }
}

