# Anton and Lines

Time Limit: 1 second

Memory Limit: 256 megabytes

## Description

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).

## Sample Input

Input41 21 21 00 10 2OutputNOInput21 31 0-1 3OutputYESInput21 31 00 2OutputYESInput21 31 00 3OutputNO

## Sample Output

None

## Hint

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

None