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 f first
#define s second
#define pb push_back
#define M (L+R)/2
#define N 500009
#define inf 99999999999
#define ll long long
#define mod 1000000007
using namespace std;
int n,d,a,j;
pair <int,int> mas[N];
vector <pair<int,int> > v;
ll ans,sum,zum;
int main(){

	ios::sync_with_stdio(0);
	
	cin>>n>>d>>a;
	for(int i=1;i<=n;i++){
		cin>>mas[i].f>>mas[i].s;
	}
	sort(mas+1,mas+1+n);
	
	for(int i=1;i<=n;i++){
		for(j;j<v.size();j++){
			if(v[j].f>=mas[i].f)break;
			zum-=v[j].s;
		}
		mas[i].s-=zum;
		if(mas[i].s<=0)continue;
		sum=mas[i].s/a;
		if(mas[i].s%a!=0)sum++;
		v.pb({mas[i].f+2*d,sum*a});
		zum+=sum*a;
		ans+=sum;
	}
	cout<<ans<<endl;

	return 0;
}