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 n,d;
long long a;
pair<int,long long> mon[200100];//(x,h)
long long de[200100];
int main(){
	cin>>n>>d>>a;
	for(int i=1;i<=n;i++){
		cin>>mon[i].first>>mon[i].second;
	}
	sort(mon+1,mon+n+1);
	long long ch=0LL;
	long long blows=0LL;
	long long res=0;
	memset(de,0,sizeof(de));
	int it=1;
	int ccc;
	for(int i=1;i<=n;i++){
		//possible:i,......,it
		//cur_hp:HP(i)
		ch=mon[i].second;//blood
		ch-=blows*a;
		ccc=0;
		if(ch>0){
			blows+=(ch+a-1)/a;//KO!
			res+=(ch+a-1)/a;
			ccc=(ch+a-1)/a;
		}
		while(it<=n&&mon[it].first-mon[i].first<=2*d)
			it++;
		it--;
		de[it]+=ccc;
		blows-=de[i];
	}
	cout<<res<<endl;
	return 0;
}