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<iostream>
#include<algorithm>
#include<array>
using namespace std;
const int N=2e5+10;
long long d[N],n,f,l;
array<int,2> a[N];
int main(){
	cin>>n>>f>>l;
	for(int i=0;i<n;i++) cin>>a[i][0]>>a[i][1];
	sort(a,a+n);
	long long ans=0;
	for(int i=0,j=0;i<n;i++){
		while(j<n&&a[j][0]-2*f<=a[i][0]) j++;
		long long tmp=max((a[i][1]-d[i]*l+l-1)/l,0LL);
		d[i]+=tmp;
		d[j]-=tmp;
		ans+=tmp;
		d[i+1]+=d[i];
	}
	cout<<ans;
	return 0;
}