#include <bits/stdc++.h>
using namespace std;
const int Maxn = 100020;
int k[Maxn], b[Maxn];
int xx1, xx2;
int idd1[Maxn];
bool cmp1(int id1, int id2) {
  long long t1 = 1LL * k[id1] * xx1 + b[id1];
  long long t2 = 1LL * k[id2] * xx1 + b[id2];
  if (t1 != t2) return t1 < t2;
  return id1 < id2;
}
long long cal1(int id) { return 1LL * k[id] * xx1 + b[id]; }
long long cal2(int id) { return 1LL * k[id] * xx2 + b[id]; }
int main() {
  int n;
  scanf("%d", &n);
  scanf("%d%d", &xx1, &xx2);
  for (int i = 0; i < n; i++) {
    scanf("%d%d", k + i, b + i);
    idd1[i] = i;
  }
  sort(idd1, idd1 + n, cmp1);
  long long maxx = -1LL << 60;
  for (int i = 0, j; i < n; i = j) {
    for (j = i; j < n && cal1(idd1[j]) == cal1(idd1[i]); j++) {
      if (cal2(idd1[j]) < maxx) {
        puts("YES");
        return 0;
      }
    }
    for (int k = i; k < j; k++) maxx = max(maxx, cal2(idd1[k]));
  }
  puts("NO");
}

### 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;
const int Maxn = 100020;
int k[Maxn], b[Maxn];
int xx1, xx2;
int idd1[Maxn];
bool cmp1(int id1, int id2) {
  long long t1 = 1LL * k[id1] * xx1 + b[id1];
  long long t2 = 1LL * k[id2] * xx1 + b[id2];
  if (t1 != t2) return t1 < t2;
  return id1 < id2;
}
long long cal1(int id) { return 1LL * k[id] * xx1 + b[id]; }
long long cal2(int id) { return 1LL * k[id] * xx2 + b[id]; }
int main() {
  int n;
  scanf("%d", &n);
  scanf("%d%d", &xx1, &xx2);
  for (int i = 0; i < n; i++) {
    scanf("%d%d", k + i, b + i);
    idd1[i] = i;
  }
  sort(idd1, idd1 + n, cmp1);
  long long maxx = -1LL << 60;
  for (int i = 0, j; i < n; i = j) {
    for (j = i; j < n && cal1(idd1[j]) == cal1(idd1[i]); j++) {
      if (cal2(idd1[j]) < maxx) {
        puts("YES");
        return 0;
      }
    }
    for (int k = i; k < j; k++) maxx = max(maxx, cal2(idd1[k]));
  }
  puts("NO");
}

```