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 rep(i,n) for(int i=0;i<(n);++i)
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
const int inf = 1001001001;

int main() {
	int n, d, a;
	cin >> n >> d >> a;
	vector<P> p(n);
	rep(i, n) cin >> p[i].first >> p[i].second;
	sort(p.begin(), p.end());
	d = d * 2;
	ll ans = 0;
	ll tot = 0;
	queue<pair<ll, ll>> que;
	rep(i, n) {
		ll x = p[i].first;
		ll h = p[i].second;
		while (que.size() && que.front().second < x) {
			tot -= que.front().first;
			que.pop();
		}
		h -= tot;
		if (h > 0) {
			ll num = (h + a - 1) / a;
			ans += num;
			ll damage = num * a;
			tot += damage;
			que.emplace(damage, x + d);
		}
	}
	cout << ans << endl;
	return 0;
}