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() {
	// your code goes here
    long long n,d,a;
    cin>>n>>d>>a;
    vector<pair<long long,long long>>monsters;
    int x,h;
    for(int i=0;i<n;i++)
    {
        cin>>x>>h;
        monsters.emplace_back(x,h);
    }
    sort(monsters.begin(),monsters.end());
    vector<long long>change(n+1);
    long long ans=0;
    for(int i=0,j=0;i<n;i++)
    {
        while(j<n&&monsters[j].first<=monsters[i].first+2*d)
            j++;
        int bombs=max(((monsters[i].second-change[i]*a+a-1)/a),0LL);
        ans+=bombs;
        change[i]+=bombs;
        change[j]-=bombs;
        change[i+1]+=change[i];
    }
    cout<<ans;
	
	return 0;
}