#include <bits/stdc++.h>
struct egyenes {
  long int m;
  long int b;
  long long int y1;
  long long int y2;
};
bool compareegyenes(egyenes node1, egyenes node2) {
  if (node1.y1 < node2.y1) return true;
  if (node1.y1 == node2.y1) return node1.y2 < node2.y2;
  return false;
}
using namespace std;
int main() {
  long int n;
  cin >> n;
  long long int x1, x2;
  cin >> x1 >> x2;
  vector<egyenes> ossz;
  for (int i = 1; i <= n; i++) {
    egyenes e;
    cin >> e.m >> e.b;
    e.y1 = e.m * x1 + e.b;
    e.y2 = e.m * x2 + e.b;
    ossz.push_back(e);
  }
  sort(ossz.begin(), ossz.end(), compareegyenes);
  int van;
  van = 0;
  for (int i = 0; i < n - 1; i++) {
    if (ossz[i].y1 < ossz[i + 1].y1 && ossz[i].y2 > ossz[i + 1].y2) {
      van = 1;
    }
  }
  if (van == 1) cout << "YES";
  if (van == 0) cout << "NO";
  return 0;
}

### Prompt

Develop a solution in CPP 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>
struct egyenes {
  long int m;
  long int b;
  long long int y1;
  long long int y2;
};
bool compareegyenes(egyenes node1, egyenes node2) {
  if (node1.y1 < node2.y1) return true;
  if (node1.y1 == node2.y1) return node1.y2 < node2.y2;
  return false;
}
using namespace std;
int main() {
  long int n;
  cin >> n;
  long long int x1, x2;
  cin >> x1 >> x2;
  vector<egyenes> ossz;
  for (int i = 1; i <= n; i++) {
    egyenes e;
    cin >> e.m >> e.b;
    e.y1 = e.m * x1 + e.b;
    e.y2 = e.m * x2 + e.b;
    ossz.push_back(e);
  }
  sort(ossz.begin(), ossz.end(), compareegyenes);
  int van;
  van = 0;
  for (int i = 0; i < n - 1; i++) {
    if (ossz[i].y1 < ossz[i + 1].y1 && ossz[i].y2 > ossz[i + 1].y2) {
      van = 1;
    }
  }
  if (van == 1) cout << "YES";
  if (van == 0) cout << "NO";
  return 0;
}

```