#include <bits/stdc++.h>
using namespace std;
double const eps = 1e-8;
struct Line {
  long long y1, y2;
} l[100005];
int cmp(const Line& a, const Line& b) {
  if (a.y1 != b.y1) return a.y1 > b.y1;
  return a.y2 > b.y2;
}
int main() {
  int n;
  long long x1, x2, k, b;
  while (scanf("%d", &n) != EOF) {
    scanf("%I64d%I64d", &x1, &x2);
    for (int i = 0; i < n; i++) {
      scanf("%I64d%I64d", &k, &b);
      l[i].y1 = k * x1 + b;
      l[i].y2 = k * x2 + b;
    }
    sort(l, l + n, cmp);
    long long maxy = l[0].y2;
    int flag = 0;
    for (int i = 1; i < n; i++) {
      if (l[i].y2 > maxy) {
        flag = 1;
        break;
      }
      maxy = l[i].y2;
    }
    if (flag)
      printf("YES\n");
    else
      printf("NO\n");
  }
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;
double const eps = 1e-8;
struct Line {
  long long y1, y2;
} l[100005];
int cmp(const Line& a, const Line& b) {
  if (a.y1 != b.y1) return a.y1 > b.y1;
  return a.y2 > b.y2;
}
int main() {
  int n;
  long long x1, x2, k, b;
  while (scanf("%d", &n) != EOF) {
    scanf("%I64d%I64d", &x1, &x2);
    for (int i = 0; i < n; i++) {
      scanf("%I64d%I64d", &k, &b);
      l[i].y1 = k * x1 + b;
      l[i].y2 = k * x2 + b;
    }
    sort(l, l + n, cmp);
    long long maxy = l[0].y2;
    int flag = 0;
    for (int i = 1; i < n; i++) {
      if (l[i].y2 > maxy) {
        flag = 1;
        break;
      }
      maxy = l[i].y2;
    }
    if (flag)
      printf("YES\n");
    else
      printf("NO\n");
  }
  return 0;
}

```