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;

typedef long long lli;

const int N = 200000 + 10;

struct Item
{
	int x, h;
};

Item monster[N];
lli add[N];

bool cmp(const Item& a, const Item& b)
{
	return a.x < b.x;
}

int main()
{
	lli res, s;
	int n, d, a, x, i, j;
	cin>>n>>d>>a;
	d *= 2;
	for (i=0; i<n; i++) 
	{
		cin>>monster[i].x>>monster[i].h;
		if (monster[i].h % a) monster[i].h = monster[i].h / a + 1; else monster[i].h /= a;
	}
	sort(monster, monster + n, cmp);
	res = s = 0;
	for (i=0,j=1; i<n; i++)
	{
		s += add[i];
		if (monster[i].h > s)
		{
			x = monster[i].h - s;
			res += x;
			add[i+1] += x;
			for (; j<n&&monster[j].x-monster[i].x<=d; j++);
			add[j] -= x;
		}
	}
	cout<<res<<endl;
	return 0;
}