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.text.DecimalFormat;
import java.util.*;
import java.io.*;

public class Main {
    private static int [] X,Y;
    private static int n;

    private static long cross(int o,int a,int b) {
        long x1 = X[a] - X[o],y1 = Y[a] - Y[o];
        long x2 = X[b] - X[o],y2 = Y[b] - Y[o];
        return x1*y2 - x2*y1;
    }

    private static ArrayList<Integer> pass(ArrayList<Integer> P,int a,int b) {
        if (P.size() <= 1) return new ArrayList<>();
        ArrayList<Integer> Q = new ArrayList<>();
        if (a == -1) {
            a = P.get(0);
            b = P.get(1);
        }

        for (int x : P){
            if (x == a || x == b) continue;
            if (a==b || cross(a,b,x) != 0)
                Q.add(x);
        }
        return Q;
    }

    private static ArrayList<Integer> work(ArrayList<Integer> P) {
        ArrayList<Integer> R = new ArrayList<>();
        int siz = 0;
        for (int p : P) {
            while (siz > 1 && cross(R.get(siz-2),R.get(siz-1),p) >= 0)
                R.remove(--siz);
            R.add(p);
            siz++;
        }
        return R;
    }

    private static ArrayList<Integer> getCorners(ArrayList<Integer> P){
        ArrayList<Integer> C = new ArrayList<>();
        Collections.sort(P, new Comparator<Integer>() {
            @Override
            public int compare(Integer a, Integer b) {
                if (X[a] == X[b]) return Y[a] - Y[b];
                return X[a] - X[b];
            }
        });

        ArrayList<Integer> U = work(P);
        Collections.reverse(P);
        ArrayList<Integer> D = work(P);

        C.addAll(U);
        C.addAll(D);
        return C;
    }

    public static void main(String[] args) throws Exception {
        IO io = new IO(null, null);
        n = io.getNextInt();
        X = new int[n];
        Y = new int[n];
        ArrayList<Integer> P = new ArrayList<>(n);
        for (int i = 0;i < n;i++){
            X[i] = io.getNextInt();
            Y[i] = io.getNextInt();
            P.add(i);
        }

        boolean f = false;
        ArrayList<Integer> C = getCorners(P);
//        System.err.println(C);

        if (C.size() - 2 <= 4) {
            for (int i = 0; i < C.size() && !f; i++) {
                for (int j = 0; j <= i && !f; j++) {
                    ArrayList<Integer> Q = pass(P, C.get(i), C.get(j));
                    Q = pass(Q, -1, -1);
                    f = Q.isEmpty();
                }
            }

        }
        io.println(f ? "YES" : "NO");
        io.close();
    }


}

class pair implements Comparable<pair>{
    long v;
    int siz;
    public pair(long x,int y) {
        v = x;
        siz = y;
    }
    @Override
    public int compareTo(pair o) {
        long diff = v - o.v;
        if (diff < 0) return -1;
        if (diff == 0) return 0;
        return 1;
    }
}

class IO{
    private BufferedReader br;
    private StringTokenizer st;
    private PrintWriter writer;
    private String inputFile,outputFile;

    public boolean hasMore() throws IOException{
        if(st != null && st.hasMoreTokens()) return true;
        if(br != null && br.ready()) return true;
        return false;
    }

    public String getNext() throws FileNotFoundException, IOException{
        while(st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public String getNextLine() throws FileNotFoundException, IOException{
        return br.readLine().trim();
    }

    public int getNextInt() throws FileNotFoundException, IOException{
        return Integer.parseInt(getNext());
    }
    public long getNextLong() throws FileNotFoundException, IOException{
        return Long.parseLong(getNext());
    }

    public void print(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f" ,x);
    }
    public void println(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f\n" ,x);
    }
    public void print(Object o) throws  IOException{
        writer.print(o.toString());
    }

    public void println(Object o) throws  IOException{
        writer.println(o.toString());
    }
    public IO(String x,String y) throws FileNotFoundException, IOException{
        inputFile = x;
        outputFile = y;
        if(x != null) br = new BufferedReader(new FileReader(inputFile));
        else br = new BufferedReader(new InputStreamReader(System.in));
        if(y != null) writer = new PrintWriter(new BufferedWriter(new FileWriter(outputFile)));
        else writer = new PrintWriter(new OutputStreamWriter(System.out));
    }

    protected void close() throws IOException{
        br.close();
        writer.close();
    }
    public void outputArr(Object [] A) throws IOException{
        int L = A.length;
        for (int i = 0;i < L;i++) {
            if(i > 0) writer.print(" ");
            writer.print(A[i]);
        }
        writer.print("\n");
    }
}
