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;
const int N=200010;
typedef long long LL;
typedef pair<int,int>pa;
pa a[N];
queue<pa>q;
LL ans;
int n,m,k;
int main(){
#ifdef WK
	freopen("in.txt","r",stdin);
#endif
	scanf("%d%d%d",&n,&m,&k);
	for(int i=1;i<=n;i++){
		int aa,bb;
		scanf("%d%d",&aa,&bb);
		a[i]=make_pair(aa,bb);
	}
	sort(a+1,a+1+n);
	LL nowD=0;
	for(int i=1;i<=n;i++){
		int xx=a[i].first,yy=a[i].second;
		while(!q.empty()&&q.front().first+m<xx){
			nowD-=1ll*q.front().second*k;
			q.pop();
		}
		yy-=nowD;
		if(yy>0){
			int aa=xx+m,bb=(yy-1)/k+1;
			q.push(make_pair(aa,bb));
			nowD+=1ll*bb*k;
			ans+=bb;
		}
	}
	printf("%lld\n",ans);
    return 0;
}