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;
typedef long long ll;
typedef pair<ll,ll> P;
#define rep(i,m,n) for(int i=m;i<n;i++)
ll mod=1e9+7;

int main(){
  int n;
  ll d,a;
  cin>>n>>d>>a;
  vector<P> b(n);
  rep(i,0,n){
    cin>>b[i].first;
    cin>>b[i].second;
  }
  sort(b.begin(),b.end());
  
  ll total=0;
  ll ans=0;
  queue<P> q;
  rep(i,0,n){
    ll x=b[i].first;
    ll h=b[i].second;
    while(q.size() && q.front().first<x){
      total-=q.front().second;
      q.pop();
    }
    h-=total;
    if(h>0){
      ll num=(h+a-1)/a;
      ans+=num;
      ll damage=num*a;
      q.push(P(x+2*d,damage));
      total+=damage;
    }
  }
  cout<<ans<<endl;
}