Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3 3 2
1 2
5 4
9 2

Sample Output 1

2

First, let us use a bomb at the coordinate 4 to decrease the first and second monsters' health by 2.

Then, use a bomb at the coordinate 6 to decrease the second and third monsters' health by 2.

Now, all the monsters' healths are 0.
We cannot make all the monsters' health drop to 0 or below with just one bomb.

Sample Input 2

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5

Sample Output 2

5

We should use five bombs at the coordinate 5.

Sample Input 3

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000

Sample Output 3

3000000000

Watch out for overflow.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<cstdio>
#include<iostream>
#include<cmath>
#include<algorithm>
#include<cstring>
#include<queue>
#include<map> 
#include<bitset>
#include<vector>
using namespace std;
#define int __int128
#define re register int
inline int read(){
    int x=0,ff=1;char c=getchar();
    while(c<'0'||c>'9'){if(c=='-')ff=-1;c=getchar();}
    while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
    return x*ff;
}
struct tt{
	int x,y;
	bool friend operator <(tt xx,tt yy){
		return xx.x<yy.x;
	}
}a[200005];
int n,d,k,f[200005],ans;
void write(__int128 x){
	if(x>9)write(x/10);
	short y=x%10;cout<<y;
}
signed main(){
	n=read();d=read();k=read();
	for(re i=1;i<=n;i++)a[i].x=read(),a[i].y=read();
	for(re i=1;i<=n;i++)a[i].y=(a[i].y+k-1)/k;
	sort(a+1,a+n+1);
	for(re i=1;i<=n;i++){
		f[i]=f[i-1]+f[i];
		if(f[i]+a[i].y<=0)continue;
		int u=a[i].x+2*d,l,r,mid;l=i+1,r=n;
		while(l<=r){
			mid=(l+r)>>1;
			if(a[mid].x<=u)l=mid+1;
			else r=mid-1;
		}
		f[l]+=f[i]+a[i].y;ans+=f[i]+a[i].y;f[i]-=a[i].y+f[i];
	}
	write(ans);puts("");
   	return 0;
}