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.util.*;
import java.io.*;

import static java.lang.Math.*;

public class Edu41D {
    static final double EPS = 0.0000000001;
    static Point[] points;
    static int n;
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        StringBuilder sb = new StringBuilder();
        n = sc.nextInt();
        ArrayList<Line> lines = new ArrayList<Line>();
        points = new Point[n];
        for (int i = 0; i < n; i++)
            points[i] = new Point(sc.nextLong(), sc.nextLong());
        sb.append(tryLines(0, new ArrayList<Line>()) ? "YES" : "NO");
        System.out.print(sb);
    }
    static ArrayList<Line> getClone(ArrayList<Line> lines) {
        ArrayList<Line> clone = new ArrayList<Line>();
        for (int j = 0; j < lines.size(); j++) {
            Line l = lines.get(j);
            Line lClone = new Line(l.a.clone());
            if (l.b != null) {
                lClone.addPoint(l.b.clone());
            }
            clone.add(lClone);
        }
        return clone;
    }
    static boolean tryLines(int i, ArrayList<Line> lines) {
        loop:
        for (; i < n; i++) {
            Point p = points[i];
            for  (int j = 0; j < lines.size(); j++) {
                if (lines.get(j).isColinear(p)) {
                    continue loop;
                }
            }
            ArrayList<Line> clone = getClone(lines);
            for (int j = 0; j < lines.size(); j++) {
                // try adding point to an already existing line
                if (clone.get(j).addPoint(p)) {
                    if (tryLines(i+1, clone)) {
                        return true;
                    }
                    clone = getClone(lines);
                }
            }
            if (lines.size() <= 1) {
                lines.add(new Line(p));
            } else {
                return false;
            }
        }
        return true;
    }


    public static class Point {
        long x, y;
        public Point(long x, long y) {
            this.x = x; this.y = y;
        }
        public Point add(Point b) {
            return new Point(x + b.x, y + b.y);
        }
        public Point subtract(Point b) {
            return new Point(x - b.x, y - b.y);
        }
        public Point scale(long s) {
            return new Point(s * x, s * y);
        }
        public boolean equals(Point o) {
            return (Math.abs(x - o.x) < EPS &&
                    Math.abs(y - o.y) < EPS);
        }
        public Point clone() {
            return new Point(x, y);
        }
        public double divide(Point o) {
            double check1 = x * o.y;
            double check2 = o.x * y;
            if (Math.abs(check1 - check2) < EPS) {
                return x / o.x;
            } else {
                return 0;
            }
        }
        public String toString() {
            return "[" + x + ", " + y + "]";
        }
    }
    public static class Line {
        Point a, b = null;
        boolean isVertical;
        public Line(Point a) {
            this.a = a;
        }
        boolean isColinear(Point c) {
            if (a.equals(c)) return true;
            if (b == null) return false;
            if (isVertical && c.x == a.x) return true;
            /*
            Point diff = b.subtract(a);
            double xDiff2 = c.x - a.x;
            double xDiff1 = b.x - a.x;
            double scale = xDiff2 / xDiff1;
            Point predict = a.add(diff.scale(scale));
            return predict.equals(c);*/
            return (c.x - a.x) * (b.y - a.y) == (b.x - a.x) * (c.y - a.y);
        }
        boolean addPoint(Point b) {
            if (this.b == null) {
                this.b = b;
                isVertical = (b.x == a.x);
                return true;
            }
            return false;
        }
    }


    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner() {
            this(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }

        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextLong();
            }
            return a;
        }
    }
}
