#include <bits/stdc++.h>
int f(const void* p, const void* q);
using namespace std;
typedef struct pp {
  double x1;
  double x2;
  double t;
  double p;
} ss;
ss a[100005];
int main(void) {
  int n, i, j, k, p, q;
  double x1, x2, y1, y2;
  while (scanf("%d", &n) != EOF) {
    scanf("%lf %lf", &x1, &x2);
    for (i = 0; i < n; i++) {
      scanf("%lf %lf", &a[i].x1, &a[i].x2);
      a[i].t = a[i].x1 * x1 + a[i].x2;
      a[i].p = a[i].x1 * x2 + a[i].x2;
    }
    qsort(a, n, sizeof(ss), f);
    int flag = 0;
    for (i = 1; i < n; i++) {
      if (a[i].p < a[i - 1].p) {
        flag = 1;
        break;
      }
    }
    if (flag) {
      printf("YES\n");
    } else
      printf("NO\n");
  }
  return 0;
}
int f(const void* p, const void* q) {
  ss* ww = (ss*)p;
  ss* ee = (ss*)q;
  if (ww->t == ee->t) {
    return ww->p > ee->p ? 1 : -1;
  } else
    return ww->t > ee->t ? 1 : -1;
}

### Prompt

Please formulate a cpp solution to 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>
int f(const void* p, const void* q);
using namespace std;
typedef struct pp {
  double x1;
  double x2;
  double t;
  double p;
} ss;
ss a[100005];
int main(void) {
  int n, i, j, k, p, q;
  double x1, x2, y1, y2;
  while (scanf("%d", &n) != EOF) {
    scanf("%lf %lf", &x1, &x2);
    for (i = 0; i < n; i++) {
      scanf("%lf %lf", &a[i].x1, &a[i].x2);
      a[i].t = a[i].x1 * x1 + a[i].x2;
      a[i].p = a[i].x1 * x2 + a[i].x2;
    }
    qsort(a, n, sizeof(ss), f);
    int flag = 0;
    for (i = 1; i < n; i++) {
      if (a[i].p < a[i - 1].p) {
        flag = 1;
        break;
      }
    }
    if (flag) {
      printf("YES\n");
    } else
      printf("NO\n");
  }
  return 0;
}
int f(const void* p, const void* q) {
  ss* ww = (ss*)p;
  ss* ee = (ss*)q;
  if (ww->t == ee->t) {
    return ww->p > ee->p ? 1 : -1;
  } else
    return ww->t > ee->t ? 1 : -1;
}

```