Problem: Silver Fox is fighting with N monsters.

The monsters are standing in a row, and we can assume them to be standing on a number line. The i-th monster, standing at the coordinate X_i, has the health of H_i.

Silver Fox can use bombs to attack the monsters. Using a bomb at the coordinate x decreases the healths of all monsters between the coordinates x-D and x+D (inclusive) by A. There is no way other than bombs to decrease the monster's health.

Silver Fox wins when all the monsters' healths become 0 or below.

Find the minimum number of bombs needed to win.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 0 \leq D \leq 10^9
* 1 \leq A \leq 10^9
* 0 \leq X_i \leq 10^9
* 1 \leq H_i \leq 10^9
* X_i are distinct.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N D A
X_1 H_1
:
X_N H_N


Output

Print the minimum number of bombs needed to win.

Examples

Input

3 3 2
1 2
5 4
9 2


Output

2


Input

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5


Output

5


Input

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000


Output

3000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int main()
{
  int64_t N, D, A, x, h, ans = 0;
  cin >> N >> D >> A;
  vector<pair<int64_t, int64_t>> xh(N);
  for (int i = 0; i < N; i++)
  {
    cin >> x >> h;
    xh[i] = {x, h};
  }
  sort(xh.begin(), xh.end());
  int64_t total = 0;
  queue<pair<int64_t, int64_t>> Q;
  for (int i = 0; i < N; i++)
  {
    tie(x, h) = xh[i];
    while (Q.size() && Q.front().first < x)
    {
      total -= Q.front().second;
      Q.pop();
    }
    h -= total;
    if (h > 0)
    {
      int64_t n = (h + A - 1) / A;
      ans += n;
      int64_t damage = n * A;
      total += damage;
      Q.emplace(x + 2 * D, damage);
    }
  }
  cout << ans << endl;
}