CF593B.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.

老师给安东布置了一大堆几何作业，但他没有做（像往常一样），因为他参加了 Codeforces 上的一场常规比赛。题目中给出了一组 $n$ 条直线，每条直线由方程 $y = k_i \cdot x + b_i$ 定义。要求判断：是否存在至少一对直线，其交点严格位于 $x_1 < x_2$ 所定义的竖直条带内部。换言之，是否满足：存在 $1 \le i < j \le n$ 以及点 $(x', y')$，使得：

• $y' = k_i \cdot x' + b_i$，即点 $(x', y')$ 在第 $i$ 条直线上；
• $y' = k_j \cdot x' + b_j$，即点 $(x', y')$ 在第 $j$ 条直线上；
• $x_1 < x' < x_2$，即点 $(x', y')$ 位于由 $x_1 < x_2$ 界定的条带内部。

你总不能让安东陷入困境吧？请编写一个程序来解决该问题。

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.

输入的第一行包含一个整数 $n$（$2 \leq n \leq 100\,000$）—— 表示 Anton 所需处理的直线数量。
第二行包含两个整数 $x_1$ 和 $x_2$（$-1\,000\,000 \leq x_1 < x_2 \leq 1\,000\,000$），定义了需要寻找至少两条直线交点的竖直条带区间。

接下来的 $n$ 行，每行包含两个整数 $k_i$ 和 $b_i$（$-1\,000\,000 \leq k_i, b_i \leq 1\,000\,000$）—— 描述第 $i$ 条直线。
保证所有直线两两互不相同，即对任意 $i \neq j$，均有 $k_i \neq k_j$ 或 $b_i \neq b_j$。

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).

如果存在至少一个位于条带内部（不包括边界）的两条不同直线的交点，则输出 "Yes"（不含引号）；否则输出 "No"（不含引号）。

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

在第一个样例中，存在位于条带边界的交点，但不存在严格位于条带内部的交点。