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 LL;
typedef unsigned int UI;

const int N=200000;

int n,a;
UI d;
struct mobs{
  UI x;
  int h;
}b[N+9];

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

UI x[N+9];
int h[N+9],ad[N+9];
LL ans;

int main(){
  scanf("%d%u%d",&n,&d,&a);
  for (int i=1;i<=n;++i)
	scanf("%u%d",&b[i].x,&b[i].h);
  sort(b+1,b+n+1,cmp);
  for (int i=1;i<=n;++i) x[i]=b[i].x,h[i]=b[i].h;
  x[n+1]=x[n]+d*2+1;
  int add=0;
  for (int i=1;i<=n;++i){
	int r=upper_bound(x+1,x+n+2,x[i]+d*2)-x;
	h[i]+=add+=ad[i];
	if (h[i]<=0) continue;
	int t=h[i]%a?h[i]/a+1:h[i]/a;
	ans+=t;add-=t*a;ad[r]+=t*a;
  }
  printf("%lld\n",ans);
  return 0;
}