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:
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 ≤ 100 000) — the number of lines in the task given to Anton. The second line contains integers x_{1} and x_{2} ( - 1 000 000 ≤ x_{1} < x_{2} ≤ 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 k_{i}, b_{i} ( - 1 000 000 ≤ k_{i}, b_{i} ≤ 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 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).
4
1 2
1 2
1 0
0 1
0 2
NO
2
1 3
1 0
-1 3
YES
2
1 3
1 0
0 2
YES
2
1 3
1 0
0 3
NO
In the first sample there are intersections located on the border of the strip, but there are no intersections located strictly inside it.
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