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:
//This code was made by Chinese_zjc_.
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<string>
#define int long long
#define INF 0x3fffffffffffffff
using namespace std;
int n,d,a,now,ans,tmp;
struct M{
	int x,h,l;
}m[200002];
bool cmp(const M &A,const M &B)
{
	return A.x<B.x;
}
signed main()
{
	std::ios::sync_with_stdio(false);
	cin>>n>>d>>a;
	d<<=1;
	for(int i=1;i<=n;++i)
	{
		cin>>m[i].x>>m[i].h;
	}
	sort(m+1,m+1+n,cmp);
	for(int i=1;i<=n;++i)
	{
		while(m[now].x<=m[i].x+d&&now<=n)
		{
			++now;
		}
		tmp=max((m[i].h-m[i].l*a)/a+((m[i].h-m[i].l*a)%a>0),i-i);
		ans+=tmp;
		m[now].l-=tmp;
		m[i].l+=tmp;
		m[i+1].l+=m[i].l;
	}
	cout<<ans;
	return 0;
}