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 ll long long
using namespace std;
ll n,d,a;
struct st{ ll x,h; }arr[200002];
ll bmb[200002],now=0;
ll e, ans=0;
int main(){
	ios_base::sync_with_stdio(0); cin.tie(0);
	cin>>n>>d>>a;
	for(ll i=1;i<=n;i++) cin>>arr[i].x>>arr[i].h;
	sort(arr+1,arr+n+1,[&](st aa, st bb){
		if(aa.x==bb.x) return aa.h<bb.h;
		return aa.x<bb.x;
	}); e=1;
	for(ll i=1;i<=n;i++){
		now+=bmb[i];
		while(e<n && arr[e+1].x<=arr[i].x+2*d) e++;
		if(arr[i].h>0){
			ll imsi=(max(arr[i].h-now*a,(ll)0)+a-1)/a;
			now+=imsi; bmb[e+1]+=-imsi;
			ans+=imsi;
		}
	}
	cout<<ans;
}