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<stdlib.h>

void swap(long int array[],long int lo,long int hi){
  long int temp=array[lo];
  array[lo]=array[hi];
  array[hi]=temp;
}

void shuffle(long int array[],long int array2[],long int size){
  for(long int i=0;i<size;i++){
    long int j=rand()%size;
    swap(array,i,j);
    swap(array2,i,j);
  }
}

int partition(long int array[],long int array2[],long int low,long int hig){
  long int i=low;
  long int j=hig+1;
  while(1){
    while(array[++i]<array[low]){
      if(i == hig) break;}
    while(array[low]<array[--j]){
      if(j==low) break;}
    if(i>=j) break;
    swap(array,i,j);
    swap(array2,i,j);
  }
  swap(array,low,j);
  swap(array2,low,j);
  return j;
}

void sort(long int array[],long int array2[],long int lo,long int hi){
  if(hi<=lo) return;
  long int j=partition(array,array2,lo,hi);
  sort(array,array2,lo,j-1);
  sort(array,array2,j+1,hi);
}

void quicksort(long int array[],long int array2[],long int size){
  shuffle(array,array2,size);
  sort(array,array2,0,size-1);
}

int main(){
  long int n,d,a;
  scanf("%ld%ld%ld",&n,&d,&a);
  long int x[n];
  long int h[n];
  for(long int i=0;i<n;i++){
    scanf("%ld%ld",&x[i],&h[i]);}
  quicksort(x,h,n);

  long int kaisu=0;
  long int sum=0;
  for(long int i=0;i<n;i++){
    if(h[i]<=0) continue;
    kaisu=h[i]/a;
    if(h[i]%a>0) kaisu++;
    sum+=kaisu;
    for(long int j=i+1;j<n;j++){
      if(x[i]+2*d >= x[j]){
	h[j]-=a*kaisu;}
      else{
	break;}
    }}
  printf("%ld\n",sum);

  return 0;
}