593_B. Anton and Lines_8832
The teacher gave Anton a large geometry homework, but he didn't do it (as usual) as he participated in a regular round on Codeforces. In the task he was given a set of n lines defined by the equations y = ki·x + bi. It was necessary to determine whether there is at least one point of intersection of two of these lines, that lays strictly inside the strip between x1 < x2. In other words, is it true that there are 1 ≤ i < j ≤ n and x', y', such that: 

  * y' = ki * x' + bi, that is, point (x', y') belongs to the line number i; 
  * y' = kj * x' + bj, that is, point (x', y') belongs to the line number j; 
  * x1 < x' < x2, that is, point (x', y') lies inside the strip bounded by x1 < x2. 



You can't leave Anton in trouble, can you? Write a program that solves the given task.

Input

The first line of the input contains an integer n (2 ≤ n ≤ 100 000) — the number of lines in the task given to Anton. The second line contains integers x1 and x2 ( - 1 000 000 ≤ x1 < x2 ≤ 1 000 000) defining the strip inside which you need to find a point of intersection of at least two lines.

The following n lines contain integers ki, bi ( - 1 000 000 ≤ ki, bi ≤ 1 000 000) — the descriptions of the lines. It is guaranteed that all lines are pairwise distinct, that is, for any two i ≠ j it is true that either ki ≠ kj, or bi ≠ bj.

Output

Print "Yes" (without quotes), if there is at least one intersection of two distinct lines, located strictly inside the strip. Otherwise print "No" (without quotes).

Examples

Input

4
1 2
1 2
1 0
0 1
0 2


Output

NO

Input

2
1 3
1 0
-1 3


Output

YES

Input

2
1 3
1 0
0 2


Output

YES

Input

2
1 3
1 0
0 3


Output

NO

Note

In the first sample there are intersections located on the border of the strip, but there are no intersections located strictly inside it.

<image>
import java.util.*;


public class MyTest{


    public static class Obj implements Comparable<Obj> {
        long x;
        long y;
        public Obj(long x, long y)
        {
            this.x =x;
            this.y =y;
        }
        public int compareTo(Obj o)
        {
            if(o.x > this.x)
                return -1;
                
            if(o.x < this.x)
                return 1;
                
            if(o.x == this.x)
            {
                if(o.y > this.y)
                    return -1;
                else
                    return 1;
            }          
            return 0;
        }
    }
    
    public static boolean solve(ArrayList<Obj> list)
    {
        for(int i=list.size()-1; i>0;i--)
        {
            long y1 = list.get(i).y;
            long y2 = list.get(i-1).y;
            if(y2 > y1)
                return true;
        }
        return false;
    }
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        int m = sc.nextInt();
        long x1 = sc.nextInt();
        long x2 = sc.nextInt();
        ArrayList<Obj> list = new ArrayList<Obj>();
        
        for(int i=0; i<m; i++)
        {
            long k = sc.nextInt();
            long b = sc.nextInt();
            long y1 = k*x1 + b;
            long y2 = k*x2 + b;
            
            list.add(new Obj(y1,y2));
        }
        Collections.sort(list);
            
        /*    
        for(int i=0; i<list.size()-1;i++)
        {
            long max;
            if(list.get(i).x == list.get(i+1).x)
            {
                max = Math.max(list.get(i).y, list.get(i+1).y);
                list.get(i).y = max;
                list.get(i+1).y = max;
            }
        }
        */

        if(solve(list))
            System.out.println("YES");
        else
            System.out.println("NO");
    }
    
}