#include <bits/stdc++.h>
using namespace std;
template <class T>
T pwr(T b, T p) {
  T r = 1, x = b;
  while (p) {
    if (p & 1) r *= x;
    x *= x;
    p = (p >> 1);
  }
  return r;
}
template <class T>
T lcm(T a, T b) {
  return (a / __gcd(a, b)) * b;
}
template <class T>
T sqr(T a) {
  return a * a;
}
template <class T>
void xswap(T &x, T &y) {
  if (x != y) {
    x ^= y;
    y ^= x;
    x ^= y;
  }
}
template <typename T>
inline bool is_on(T &mask, int pos) {
  return ((mask) & (1LL << pos));
}
template <typename T>
inline T setf(T mask, int pos) {
  return mask = ((mask) & (~(1LL << pos)));
}
template <typename T>
inline T sett(T mask, int pos) {
  return mask = ((mask) | (1LL << pos));
}
template <typename T>
inline T flip(T mask, int pos) {
  return mask = ((mask) ^ (1LL << pos));
}
template <class T1>
void put(T1 e) {
  cout << e << endl;
}
template <class T1, class T2>
void put(T1 e1, T2 e2) {
  cout << e1 << " " << e2 << endl;
}
template <class T1, class T2, class T3>
void put(T1 e1, T2 e2, T3 e3) {
  cout << e1 << " " << e2 << " " << e3 << endl;
}
template <class T1, class T2, class T3, class T4>
void put(T1 e1, T2 e2, T3 e3, T4 e4) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << endl;
}
template <class T1, class T2, class T3, class T4, class T5>
void put(T1 e1, T2 e2, T3 e3, T4 e4, T5 e5) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << " " << e5 << endl;
}
template <class T1>
void putv(vector<T1> e1) {
  for (int i = 0; i < e1.size(); i++)
    (!i ? cout << e1[i] : cout << " " << e1[i]);
  cout << endl;
}
template <class T1>
void puta(T1 arr[], int l) {
  for (int i = 0; i < l; i++) (!i ? cout << arr[i] : cout << " " << arr[i]);
  cout << endl;
}
template <class T1>
bool tk(T1 &e1) {
  return (cin >> e1 ? true : false);
}
template <class T1, class T2>
bool tk(T1 &e1, T2 &e2) {
  return (cin >> e1 >> e2 ? true : false);
}
template <class T1, class T2, class T3>
bool tk(T1 &e1, T2 &e2, T3 &e3) {
  return (cin >> e1 >> e2 >> e3 ? true : false);
}
template <class T1, class T2, class T3, class T4>
bool tk(T1 &e1, T2 &e2, T3 &e3, T4 &e4) {
  return (cin >> e1 >> e2 >> e3 >> e4 ? true : false);
}
pair<long long, long long> ranges[200007];
int main() {
  long long n, mi, ci, x1, x2;
  cin >> n;
  cin >> x1 >> x2;
  for (int i = 0; i <= n - 1; ++i) {
    cin >> mi >> ci;
    ranges[i].first = x1 * mi + ci;
    ranges[i].second = x2 * mi + ci;
  }
  sort(ranges, ranges + n);
  for (int i = 1; i <= n - 1; ++i) {
    pair<long long, long long> pre = ranges[i - 1];
    pair<long long, long long> now = ranges[i];
    if (pre.first < now.first && now.second < pre.second) {
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
  return 0;
}

### Prompt

Your challenge is to write 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>
using namespace std;
template <class T>
T pwr(T b, T p) {
  T r = 1, x = b;
  while (p) {
    if (p & 1) r *= x;
    x *= x;
    p = (p >> 1);
  }
  return r;
}
template <class T>
T lcm(T a, T b) {
  return (a / __gcd(a, b)) * b;
}
template <class T>
T sqr(T a) {
  return a * a;
}
template <class T>
void xswap(T &x, T &y) {
  if (x != y) {
    x ^= y;
    y ^= x;
    x ^= y;
  }
}
template <typename T>
inline bool is_on(T &mask, int pos) {
  return ((mask) & (1LL << pos));
}
template <typename T>
inline T setf(T mask, int pos) {
  return mask = ((mask) & (~(1LL << pos)));
}
template <typename T>
inline T sett(T mask, int pos) {
  return mask = ((mask) | (1LL << pos));
}
template <typename T>
inline T flip(T mask, int pos) {
  return mask = ((mask) ^ (1LL << pos));
}
template <class T1>
void put(T1 e) {
  cout << e << endl;
}
template <class T1, class T2>
void put(T1 e1, T2 e2) {
  cout << e1 << " " << e2 << endl;
}
template <class T1, class T2, class T3>
void put(T1 e1, T2 e2, T3 e3) {
  cout << e1 << " " << e2 << " " << e3 << endl;
}
template <class T1, class T2, class T3, class T4>
void put(T1 e1, T2 e2, T3 e3, T4 e4) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << endl;
}
template <class T1, class T2, class T3, class T4, class T5>
void put(T1 e1, T2 e2, T3 e3, T4 e4, T5 e5) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << " " << e5 << endl;
}
template <class T1>
void putv(vector<T1> e1) {
  for (int i = 0; i < e1.size(); i++)
    (!i ? cout << e1[i] : cout << " " << e1[i]);
  cout << endl;
}
template <class T1>
void puta(T1 arr[], int l) {
  for (int i = 0; i < l; i++) (!i ? cout << arr[i] : cout << " " << arr[i]);
  cout << endl;
}
template <class T1>
bool tk(T1 &e1) {
  return (cin >> e1 ? true : false);
}
template <class T1, class T2>
bool tk(T1 &e1, T2 &e2) {
  return (cin >> e1 >> e2 ? true : false);
}
template <class T1, class T2, class T3>
bool tk(T1 &e1, T2 &e2, T3 &e3) {
  return (cin >> e1 >> e2 >> e3 ? true : false);
}
template <class T1, class T2, class T3, class T4>
bool tk(T1 &e1, T2 &e2, T3 &e3, T4 &e4) {
  return (cin >> e1 >> e2 >> e3 >> e4 ? true : false);
}
pair<long long, long long> ranges[200007];
int main() {
  long long n, mi, ci, x1, x2;
  cin >> n;
  cin >> x1 >> x2;
  for (int i = 0; i <= n - 1; ++i) {
    cin >> mi >> ci;
    ranges[i].first = x1 * mi + ci;
    ranges[i].second = x2 * mi + ci;
  }
  sort(ranges, ranges + n);
  for (int i = 1; i <= n - 1; ++i) {
    pair<long long, long long> pre = ranges[i - 1];
    pair<long long, long long> now = ranges[i];
    if (pre.first < now.first && now.second < pre.second) {
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
  return 0;
}

```