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>
using namespace std;

#define ll long long
#define ar array

const int mxN=2e5;
int n;
ll d, a, ans, c[mxN+1];
ar<int, 2> b[mxN];

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

	cin >> n >> d >> a;
	for(int i=0; i<n; ++i) {
		cin >> b[i][0] >> b[i][1];
	}
	sort(b, b+n);
	for(int i=0, j=0; i<n; ++i) {
		while(j<n&&b[j][0]<=b[i][0]+2*d)
			++j;
		ll need=max((b[i][1]-c[i]*a+a-1)/a, 0ll);
		ans+=need;
		c[i]+=need;
		c[j]-=need;
		c[i+1]+=c[i];
	}
	cout << ans;
}