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(){
  int N, D, A;
  cin >> N >> D >> A;
  
  vector<pair<int, int>> monster(N);
  for(int i = 0; i < N; i++){
    int X, H;
    cin >> X >> H;
    monster[i] = make_pair(X, H);
  }
  sort(monster.begin(), monster.end());
  
  long long cnt = 0;
  vector<long long> damage(N + 1, 0);
  int right = 0;
  for(int i = 0; i < N; i++){
    if(i > 0) damage[i] += damage[i - 1];
    while(right < N && monster[right].first <= monster[i].first + 2 * D) right++;
    long long d = max((monster[i].second - damage[i] - 1 + A) / A, 0ll);
    cnt += d;
    damage[i] += d * A;
    damage[right] -= d * A;
  }
  
  cout << cnt << endl;
  
  return 0;
}