2462: Anton and Lines
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.
The first line of the input contains an integer n (2≤n≤100000)− the number of lines in the task given to Anton. The second line contains integers x1 and x2 (-1000000≤x1<x2≤1000000) 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 (-1000000≤ki,bi≤1000000)− 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.
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.
