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: Accepted)

#include <stdio.h>
#include <stdlib.h>

typedef struct {
	long x;
	long hp;
} S_MONSTER;

int cmpAscVal(const void * n1, const void * n2)
{
	if (((S_MONSTER *)n1)->x > ((S_MONSTER *)n2)->x)
	{
		return 1;
	}
	else if (((S_MONSTER *)n1)->x < ((S_MONSTER *)n2)->x)
	{
		return -1;
	}
	else
	{
		return 0;
	}
}

int main(void) {

  long n,d,a;
  scanf("%ld %ld %ld", &n, &d, &a);
  S_MONSTER monster[n];
  for (long i = 0; i < n; i++) {
    scanf("%ld %ld", &monster[i].x, &monster[i].hp);
  }
  qsort(monster, n, sizeof(S_MONSTER), cmpAscVal);
  long list[n][2];
  long start = 0;
  long end = -1;
  long attack;
  long count = 0;
  for (long i = 0; i < n; i++) {
    for (long j = start; j <= end; j++) {
      if (monster[i].hp <= 0) {
        break;
      }
      if (list[j][0] >= monster[i].x) {
        monster[i].hp -= list[end][1];
        if (j != 0) {
          monster[i].hp += list[j-1][1];
        }
        start = j;
        break;
      }
      if (j == end) {
        start = end+1;
      }
    }
    if (monster[i].hp > 0) {
      attack = (monster[i].hp+a-1)/a;
      end++;
      list[end][0] = monster[i].x+d*2;
      list[end][1] = attack*a;
      if (end != 0) {
        list[end][1] += list[end-1][1];
      }
      count += attack;
    }
  }
  printf("%ld\n", count);

  return 0;
}