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 int long long
#define rep(i,a,b) for(int i=a;i<=b;i++)
#define per(i,a,b) for(int i=a;i>=b;i--)
using namespace std;
const int N=1e6+50;
int n,d,A,ans=0,r=1,v[N];
struct node{ int x,z; }a[N];
bool mycmp(node a,node b){ return a.x<b.x; }
int solv(int x){
	if(x%A==0) return x/A;
	else return x/A+1;
}
signed main(){
	scanf("%lld%lld%lld",&n,&d,&A);
	rep(i,1,n) scanf("%lld%lld",&a[i].x,&a[i].z);
	sort(a+1,a+n+1,mycmp);
	rep(i,1,n){
		v[i]+=v[i-1]; a[i].z-=v[i];
		if(a[i].z<=0) continue;
		while(a[r].x-a[i].x<=2*d&&r<=n) r++;
		int t=solv(a[i].z);
		v[i]+=t*A; v[r]-=t*A;
		ans+=t;
	}
	printf("%lld\n",ans);
	return 0;
}