A10158 | Anton and Lines

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 $y=k_{i}·x+b_{i}$ . 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 $x_{1}<x_{2}$ . In other words, is it true that there are $1<=i<j<=n$ and $x',y'$ , such that:

- $y'=k_{i}*x'+b_{i}$ , that is, point $(x',y')$ belongs to the line number $i$ ;
- $y'=k_{j}*x'+b_{j}$ , that is, point $(x',y')$ belongs to the line number $j$ ;
- $x_{1}<x'<x_{2}$ , that is, point $(x',y')$ lies inside the strip bounded by $x_{1}<x_{2}$ .

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

The first line of the input contains an integer $n$ ( $2<=n<=100000$ ) — the number of lines in the task given to Anton. The second line contains integers $x_{1}$ and $x_{2}$ ( $-1000000<=x_{1}<x_{2}<=1000000$ ) defining the strip inside which you need to find a point of intersection of at least two lines.

The following $n$ lines contain integers $k_{i}$ , $b_{i}$ ( $-1000000<=k_{i},b_{i}<=1000000$ ) — 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 $k_{i}≠k_{j}$ , or $b_{i}≠b_{j}$ .

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).