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;
typedef long long ll;
struct node{
	int l;
	int r;
	int h;
}a[200000];
ll c[200000]={0};
bool cmp(struct node a1,struct node a2)
{
	return a1.l<a2.l;
}
int main(void)
{
	int n,d,health;
	scanf("%d%d%d",&n,&d,&health);
	int i;
	for(i=0;i<n;i++)
	{
		int x,h;
		scanf("%d%d",&x,&h);
		a[i].l=x-d;
		a[i].r=x+d;
		int c=h/health;
		if(h%health!=0)
		{
			c++;
		}
		a[i].h=c;
	}
	sort(a,a+n,cmp);
	ll sum=0;
	int j=0;
	for(i=0;i<n;i++)
	{
		while(j<n&&a[i].r>=a[j].l)
		{
			j++;
		}
		ll ok;
		ok=a[i].h-c[i];
		if(ok<0) ok=0;
		sum+=ok;
		c[i]+=ok;
		c[j]-=ok;
		c[i+1]+=c[i];
	}
	printf("%lld",sum);
}