codeforces 593B Anton and Lines

B. 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 = 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 are1 ≤ 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.

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 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.

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).

Sample test(s)

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.

 

 

#include<cstdio>
#include<algorithm>
using namespace std;

struct line
{
    long long sy,ey;
}p[100005];

bool cmp(line a,line b)
{
    if(a.sy==b.sy)return a.ey<b.ey;
    return a.sy<b.sy;
}

int main()
{
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        int x1,x2;
        scanf("%d%d",&x1,&x2);
        for(int i=0;i<n;i++)
        {
            int k,b;
            scanf("%d%d",&k,&b);
            p[i].sy=(long long)k*x1+b;
            p[i].ey=(long long)k*x2+b;
        }
        sort(p,p+n,cmp);
        int k=0;
        for(;k<n-1;k++)
            if(p[k].sy<p[k+1].sy&&p[k].ey>p[k+1].ey)break;
        if(k==n-1)
            puts("NO");
        else
            puts("YES");
    }
    return 0;
}