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: Wrong Answer)

#include <iostream>
#include <vector>
#include <algorithm>
#include <math.h>
using namespace std;

#define ll long long
#define loop(__x, __start, __end) for(int __x = __start; __x < __end; __x++)

struct Monster {
  ll x, h;
  bool operator< (const Monster &other) const {
    return x < other.x;
  }
};

#define MAX_X 1000000000LL
#define INFTY 1e9
ll N, D, A;
vector<Monster> M;

// 1)
// 0 1 2 3 4 5 6 7 8 9
//   2       4       2
//       - - - o - - -
//   - - - o - - -
//
// 2)
// 1 2 3 4 5 6 7 8 9
// 5 4 3 2 1 2 3 4 5
// - - - - o - - - -
// - - - - o - - - -
// - - - - o - - - -
// - - - - o - - - -
// - - - - o - - - -
// 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
// 3   3   3   3   3     3     3     3
// - - o - -
// - - o - -
// - - o - -

void input() {
  cin >> N >> D >> A;
  ll x, h;
  for (int i=0; i<N; i++) {
    cin >> x >> h;
    M.push_back({ x, h });
  }
}

void solve() {
  sort(M.begin(), M.end());
  ll total = 0;
  ll correction = 0;
  ll max_x = 0;

  // 10^5
  for (ll i=0; i<M.size(); i++) {
    auto &m = M.at(i);
    if (m.h <= 0) continue;
    ll count = 0;
    if (m.x <= max_x) count = ceil((double)(m.h-correction) / A);
    else count = ceil((double)m.h / A);
    if (count <= 0) continue;
    total += count;
    correction = count*A;
    max_x = min(m.x + 2*D, MAX_X);
  }

  cout << total << endl;
}

int main() {
  input();solve();
  return 0;
}