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 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<math.h>
#define max(x,y)(x>y?x:y)
#define min(x,y)(x>y?y:x)
typedef long long int ll;
typedef unsigned long long int ull;
int asc_cmp(const void* X,const void* Y){int x=*(int*)X,y=*(int*)Y;if(x<y)return -1;else if(x==y)return 0;else return 1;}
int desc_cmp(const void* X,const void* Y){int x=*(int*)X,y=*(int*)Y;if(x<y)return 1;else if(x==y)return 0;else return -1;}

typedef struct{
    int x;
    int h;
}pair_t;

typedef struct{
    int x;
    int index;
}start_t;
int pair__cmp(const void* X,const void* Y){
    int x=((pair_t*)X)->x;
    int y=((pair_t*)Y)->x;
    if(x<y)return -1;else if(x==y)return 0;else return 1;
}
int main(){
    int n,d,a;scanf("%d %d %d",&n,&d,&a);
    pair_t pair[n];for(int i=0;i<n;i++)scanf("%d %d",&pair[i].x,&pair[i].h);

    qsort(pair,n,sizeof(pair_t),pair__cmp);

    start_t start;
    
    ll ans=0,ss;
    while(1){
        for(int i=0;i<n;i++){
            if(pair[i].h>0){
                start.x=pair[i].x;
                start.index=i;
                break;
            }
        }
        //printf("start:x%d h:%d\n",start.x,pair[start.index].h);
        int cnt=(pair[start.index].h%a)?pair[start.index].h/a+1:pair[start.index].h/a;
        int dist=0;
        int flg=0;
        for(int i=start.index;i<n;i++){
            if(pair[i].h>0)flg=1;
            if(pair[i].x-start.x<=2*d){
                pair[i].h-=a*cnt;
            }else{
                break;
            }
        }
        if(!flg)break;
        ans+=cnt;
    }
    
    printf("%lld\n",ans);
}