#include <bits/stdc++.h>
using namespace std;
const int N = 100005;
const int M = 1005;
const int INF = 0x3f3f3f3f;
const int MOD = 1000000007;
struct Node {
  long long x, y;
  bool operator<(const Node &ah) const {
    if (x != ah.x) return x < ah.x;
    return y < ah.y;
  }
} a[N];
long long ma[N];
int main() {
  int n;
  while (~scanf("%d", &n)) {
    int x, y;
    scanf("%d%d", &x, &y);
    for (int i = 0; i < n; ++i) {
      int x1, y1;
      scanf("%d%d", &x1, &y1);
      a[i].x = 1LL * x * x1 + y1;
      a[i].y = 1LL * y * x1 + y1;
    }
    sort(a, a + n);
    ma[0] = a[0].y;
    for (int i = 1; i < n; ++i) ma[i] = max(ma[i - 1], a[i].y);
    bool flag = false;
    for (int i = n - 1; i >= 0; --i) {
      long long mi = a[i].y, j;
      for (j = i; j >= 0; --j)
        if (a[i].x == a[j].x)
          mi = min(mi, a[j].y);
        else
          break;
      if (j >= 0 && ma[j] > mi) {
        flag = true;
        break;
      }
      i = j + 1;
    }
    if (flag)
      puts("YES");
    else
      puts("NO");
  }
  return 0;
}

### 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;
const int N = 100005;
const int M = 1005;
const int INF = 0x3f3f3f3f;
const int MOD = 1000000007;
struct Node {
  long long x, y;
  bool operator<(const Node &ah) const {
    if (x != ah.x) return x < ah.x;
    return y < ah.y;
  }
} a[N];
long long ma[N];
int main() {
  int n;
  while (~scanf("%d", &n)) {
    int x, y;
    scanf("%d%d", &x, &y);
    for (int i = 0; i < n; ++i) {
      int x1, y1;
      scanf("%d%d", &x1, &y1);
      a[i].x = 1LL * x * x1 + y1;
      a[i].y = 1LL * y * x1 + y1;
    }
    sort(a, a + n);
    ma[0] = a[0].y;
    for (int i = 1; i < n; ++i) ma[i] = max(ma[i - 1], a[i].y);
    bool flag = false;
    for (int i = n - 1; i >= 0; --i) {
      long long mi = a[i].y, j;
      for (j = i; j >= 0; --j)
        if (a[i].x == a[j].x)
          mi = min(mi, a[j].y);
        else
          break;
      if (j >= 0 && ma[j] > mi) {
        flag = true;
        break;
      }
      i = j + 1;
    }
    if (flag)
      puts("YES");
    else
      puts("NO");
  }
  return 0;
}

```