#include <bits/stdc++.h>
using namespace std;
struct node {
  double h1, h2;
  int num;
} s[100010];
bool cmp(node a, node b) {
  if (a.h1 == b.h1) return a.h2 < b.h2;
  return a.h1 < b.h1;
}
int main() {
  long long int n;
  int i, j, judge;
  double x1, x2, k[100010], b[100010];
  scanf("%lld", &n);
  scanf("%lf%lf", &x1, &x2);
  for (i = 1; i <= n; i++) {
    scanf("%lf%lf", &k[i], &b[i]);
    s[i].h1 = k[i] * x1 + b[i];
    s[i].h2 = k[i] * x2 + b[i];
  }
  sort(s + 1, s + 1 + n, cmp);
  judge = 0;
  for (i = 2; i <= n; i++)
    if (s[i].h2 < s[i - 1].h2) {
      judge = 1;
      break;
    }
  if (judge)
    printf("YES\n");
  else
    printf("NO\n");
}

### Prompt

Create a solution in CPP for the following problem:

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.

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).

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>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
struct node {
  double h1, h2;
  int num;
} s[100010];
bool cmp(node a, node b) {
  if (a.h1 == b.h1) return a.h2 < b.h2;
  return a.h1 < b.h1;
}
int main() {
  long long int n;
  int i, j, judge;
  double x1, x2, k[100010], b[100010];
  scanf("%lld", &n);
  scanf("%lf%lf", &x1, &x2);
  for (i = 1; i <= n; i++) {
    scanf("%lf%lf", &k[i], &b[i]);
    s[i].h1 = k[i] * x1 + b[i];
    s[i].h2 = k[i] * x2 + b[i];
  }
  sort(s + 1, s + 1 + n, cmp);
  judge = 0;
  for (i = 2; i <= n; i++)
    if (s[i].h2 < s[i - 1].h2) {
      judge = 1;
      break;
    }
  if (judge)
    printf("YES\n");
  else
    printf("NO\n");
}

```