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>

#define pb push_back
#define ff first
#define ss second
#define all(x) (x).begin(), (x).end()
#define ll long long
#define ii pair<ll,ll>
#define vi vector<int>
#define vll vector<ll>
#define vii vector<ii>

using namespace std;

int32_t main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	ll n,d,a,ans=0;
	cin>>n>>d>>a;
	vii vs(n);
	for(int i=0;i<n;++i){
		cin>>vs[i].ff>>vs[i].ss;
	}
	sort(all(vs));
	ll s=0;
	queue<ii> q;
	for(int i=0;i<n;++i){
		while(!q.empty() && q.front().ff <vs[i].ff){
			s-=q.front().ss;q.pop();
		}
		vs[i].ss=max(0LL,vs[i].ss-s);
		ll k = (vs[i].ss+a-1)/a;
		ans+=k;
		s+=a*k;
		q.push({vs[i].ff+2*d,a*k});
	}
	cout<<ans<<endl;
	return 0;
}