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>
#define int long long
using namespace std;
signed main(){
	int n,d,a;
	cin>>n>>d>>a;
	pair<int,int>m[n+1LL];
	for(int i=1LL;i<=n;++i){
		cin>>m[i].first>>m[i].second;
		m[i].second=(m[i].second+a-1LL)/a;
	}
	sort(m+1LL,m+n+1LL);
	int j=1LL,sum=0LL,tot=0LL;
	int bomb[n+1LL];
	for(int i=1LL;i<=n;++i){
		while(j<i&&m[i].first-m[j].first>d*2){
			sum-=bomb[j];
			++j;
		}
		bomb[i]=max(m[i].second-sum,0LL);
		sum+=bomb[i];
		tot+=bomb[i];
	}
	cout<<tot<<endl;
	return 0;
}