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: Time Limit Exceeded)

#include <iostream>
#include <boost/range/algorithm/sort.hpp>
#include <vector>
#include <cmath>

struct monster {
  int64_t x;
  int64_t h;
};

int main() {
  int64_t n, d, a;
  std::cin >> n;
  std::cin >> d;
  std::cin >> a;

  std::vector<monster> ms(n);
  for (int64_t i = 0; i < n; ++i) {
    std::cin >> ms[i].x;
    std::cin >> ms[i].h;
  }

  boost::sort(ms, [](auto x, auto y) {return x.x < y.x;});

  int64_t nbomb = 0;
  for (int64_t i = 0; i < n; ++i) {
    const auto b =
        static_cast<int64_t>(std::ceil(static_cast<double>(ms[i].h) / a));
    if (b > 0) {
      for (int64_t j = i; j < n && ms[j].x - ms[i].x <= d * 2; ++j)
        ms[j].h = std::max<int64_t>(0, ms[j].h - b * a);
      nbomb += b;
    }
  }

  std::cout << nbomb << std::endl;

  return 0;
}