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;
  cin>>N>>D>>A;
  vector<pair<int64_t,int64_t>> p(N);
  vector<int64_t> q(N+1);
  for(int i=0;i<N;i++){
    int64_t a,b;
    cin>>a>>b;
    p[i]=make_pair(a,b);
    q[i]=a;
  }
  q[N]=167167167167;
  sort(p.begin(),p.end());
  sort(q.begin(),q.end());
  vector<int64_t> kez(N+1);
  int64_t Z=0;
  for(int i=0;i<N;i++){
    int64_t X,H;
    tie(X,H)=p[i];
    H-=kez[i];
    if(H>0){
      int64_t L=X+2*D+1;
      int b=lower_bound(q.begin(),q.end(),L)-q.begin();
      int64_t Q=(H-1)/A+1;
      Z+=Q;
      kez[i]+=Q*A;
      kez[b]-=Q*A;
    }
    kez[i+1]+=kez[i];
  }
  cout<<Z<<endl;

    
}