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.

-----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 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}.

-----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]