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>
#define fast ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
using namespace std;


int main() {
    fast

    int n,d,a;
    cin>>n>>d>>a;

    vector<pair<long long ,long long >>arr(n);

    for(int i=0;i<n;i++){
        cin>>arr[i].first>>arr[i].second;
    }
    sort(arr.begin(),arr.end());
    vector<long long>pref(n+1);
    int i=0;
    int j=0;
    long long ans=0;
    for(int i=0;i<n;i++){

        while(j<n && arr[i].first+2*d>=arr[j].first)
        j++;

        long long need=max((arr[i].second-pref[i]*a+a-1)/a,0LL);
        ans+=need;
        pref[i]+=need;
        pref[j]-=need;
        pref[i+1]+=pref[i];


    }
    cout<<ans<<endl;



	return 0;
}