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.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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);
        DPairOfLines solver = new DPairOfLines();
        solver.solve(1, in, out);
        out.close();
    }

    static class DPairOfLines {
        int n;
        Point[] arr;

        public void readInput(Scanner sc) {
            n = sc.nextInt();
            arr = new Point[n];
            for (int i = 0; i < n; i++)
                arr[i] = new Point(sc.nextInt(), sc.nextInt());
        }

        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            int q = 1;
            while (q-- > 0) {
                readInput(sc);
                if (n <= 4) {
                    pw.println("YES");
                    return;
                }
                boolean f = false;
                for (int i = 0; i < 150; i++) {
                    int rand = (int) (Math.random() * n);
                    int rand2 = (int) (Math.random() * n);
                    if (rand == rand2)
                        continue;
                    boolean[] out = new boolean[n];
                    int c = 0;
                    int first = -1, second = -1;
                    for (int j = 0; j < n; j++) {
                        if (j == rand || j == rand2)
                            continue;
                        if (!arr[j].onLine(arr[rand], arr[rand2])) {
                            c++;
                            out[j] = true;
                            if (first == -1)
                                first = j;
                            else if (second == -1)
                                second = j;
                        }
                    }
                    if (c <= 2)
                        f = true;
                    else {
                        boolean ff = true;
                        for (int j = 0; j < n; j++) {
                            if (!out[j])
                                continue;
                            if (j == first || j == second)
                                continue;
                            if (!arr[j].onLine(arr[first], arr[second]))
                                ff = false;
                        }
                        f |= ff;
                    }
                }
                pw.println(f ? "YES" : "NO");
            }
        }

        public class Point implements Comparable<Point> {
            static final double EPS = 1e-9;
            long x;
            long y;

            Point(long a, long b) {
                x = a;
                y = b;
            }

            public int compareTo(Point p) {
                if (Math.abs(x - p.x) > EPS) return x > p.x ? 1 : -1;
                if (Math.abs(y - p.y) > EPS) return y > p.y ? 1 : -1;
                return 0;
            }

            boolean onLine(Point a, Point b) {
                if (a.compareTo(b) == 0) return compareTo(a) == 0;
                Point temp = new Point(b.x - a.x, b.y - a.y);
                Point temp2 = new Point(this.x - a.x, this.y - a.y);
                return Math.abs(temp.x * temp2.y - temp.y * temp2.x) < EPS;
            }

        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() {
            try {
                while (st == null || !st.hasMoreTokens())
                    st = new StringTokenizer(br.readLine());
                return st.nextToken();
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

