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;
#define ll long long
const int N=2e5+5;
ll n,d,a,x[N],pos,di,sub[N],ans;
struct mos{
	ll x,h;
}q[N];
bool cmp(mos a,mos b){
	return a.x<b.x;
}
int main(){
	cin>>n>>d>>a;
	for(int i=1;i<=n;i++){
		cin>>q[i].x>>q[i].h;
		x[i]=q[i].x;
	}
	sort(q+1,q+n+1,cmp);
	sort(x+1,x+n+1);
	for(int i=1;i<=n;i++){
		di-=sub[i];
		ll xx=q[i].x+d+d;
		int pos=upper_bound(x+1,x+n+1,xx)-x;
		q[i].h-=di;
		ll need=(q[i].h>0?(q[i].h-1)/a+1:0);
		sub[pos]+=need*a;
		di+=need*a;
		ans+=need;
	}
	cout<<ans<<endl;
	return 0;
}