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;
#define int long long

typedef pair<int,int> P;
int n,d,a,now,ans;
priority_queue<P,vector<P>,greater<P>> que;

signed main(){
  cin>>n>>d>>a;
  while(n--){
    int x,h;cin>>x>>h;
    que.push(P(x,h));
  }
  while(que.size()){
    P p=que.top();que.pop();
    int x=p.first,h=p.second;
    if(h<0)now+=h;
    if(h-now>0){
      int A=(h-now-1)/a+1;
      ans+=A;now+=A*a;
      que.push(P(x+d*2+1,-A*a));
    }
  }
  cout<<ans<<endl;
}