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:
#pragma GCC optimize(2)
#include <bits/stdc++.h>
#define int long long
#define INF 1000000000000000007ll
using namespace std;

int n,d,a,sum[200010];
pair<int,int> m[200010];

signed main()
{
	ios::sync_with_stdio(false);
	cin>>n>>d>>a;
	for(int i=1;i<=n;i++){
		cin>>m[i].first>>m[i].second;
	}
	sort(m+1,m+n+1);
	m[n+1]=make_pair(INF,INF);
	int cnt=0ll;
	for(int i=1;i<=n;i++){
		sum[i]+=sum[i-1];
		int num=m[i].second-sum[i];
		if(num>0){
			int e=m[i].first+2*d;
			int pos=upper_bound(m+1,m+n+2,make_pair(e+1,0ll))-m-1;
			int val=num/a+(num%a!=0);
			sum[i]+=val*a;
			sum[pos+1]-=val*a;
			cnt+=val;
		}
	}
	cout<<cnt<<endl;
	return 0;
}