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:
#import<bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef struct{LL x;LL h;}H;
LL a,d,h,i,j,k,m,n,s,t,z[200040];
H w[200040];
int C(H a,H b){return a.x<b.x;}
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	cin>>n>>d>>a;
	for(;i<n;i++)cin>>w[i].x>>w[i].h;
	sort(w,w+n,C);
	w[n].x=w[n].h=4000000000;
	d*=2;
	for(i=0;j<n;)
	{
		if(w[j].x-w[i].x>d)t-=z[i++];
		else
		{
			if(w[j].h>t)
			{
				m=(w[j].h-t-1)/a+1;
				s+=m;
				m*=a;
				z[j]=m;
				t+=m;
			}
			
			j++;
		}
	}
	cout<<s;
}