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
#define pii pair<LL,LL>
const int N=2e5+5;

LL n,d,p,ans;
pii a[N];
LL too[N];

int main()
{
	ios_base::sync_with_stdio(0);
	scanf("%lld%lld%lld",&n,&d,&p);
	for(int i=1;i<=n;i++)
		scanf("%lld%lld",&a[i].first,&a[i].second);
	d<<=1;
	sort(a+1,a+n+1);
	for(int i=1,j=1;i<=n;i++)
	{
		too[i]+=too[i-1];
		a[i].second-=too[i];
		if(a[i].second<=0) continue;
		LL tt=(a[i].second+p-1)/p*p;
		ans+=(a[i].second+p-1)/p;
		while(a[i].first+d>=a[j].first && j<=n) j++;
		j--;
		too[i+1]+=tt;
		too[j+1]-=tt;
	}
	printf("%lld\n",ans);
	
	return 0;
}