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.
输入描述:
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.
输出描述:
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).
示例1
输入
4<br />1 2<br />1 2<br />1 0<br />0 1<br />0 2<br />2<br />1 3<br />1 0<br />-1 3<br />2<br />1 3<br />1 0<br />0 2<br />2<br />1 3<br />1 0<br />0 3<br />
备注:
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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