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;
using PP = pair<long, long>;
long n, d, a;
set<PP> st;
int main() {
  cin >> n >> d >> a;
  for (int i = 0; i < n; ++i) {
    int x, h;
    cin >> x >> h;
    h = (h + a - 1) / a;
    st.insert(PP(x, -h));
  }
  
  long sum = 0;
  long cnt = 0;
  for (auto it = st.begin(); it != st.end(); ++it) {
    PP p = *it;
    long x = p.first;
    long k = p.second;
    if (k < 0) {
      long h = -k;
      long at = h - cnt;
      if (at > 0) {
        sum += at;
        cnt += at;
        st.insert(PP(x + 2 * d, at));
      }
    } else {
      int at = k;
      cnt -= at;
    }
  }
  cout << sum << endl;
}