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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
import java.io.*;

public class Main {

  void solve(InputReader in, PrintWriter out) {
    int n = in.nextInt();
    int d = in.nextInt();
    int a = in.nextInt();
    
    Pair[] arr = new Pair[n];
    for (int i = 0; i < n; ++i)
      arr[i] = new Pair(in.nextInt(), in.nextInt());

    Arrays.sort(arr);
    ArrayDeque<Pair> q = new ArrayDeque<>();
    int i = 0; 
    long ans = 0;
    while (i < n) {
      ArrayDeque<Pair> qq = new ArrayDeque<>();
      while (!q.isEmpty()) {
        Pair p = q.poll();
        if (p.f < arr[i].f) {
          continue;
        }

        //System.err.println(i + " " + arr[i].f + " " + arr[i].s + " " + p.f + ", " + p.s);
        arr[i].s -= p.s;
        qq.offer(p);
      }
      q = qq;
      if (arr[i].s > 0) {
        int attacks = arr[i].s / a;
        attacks += arr[i].s % a != 0 ? 1 : 0;
        ans += attacks;
        q.offer(new Pair(arr[i].f + d + d, attacks * a));
        //System.err.println(i + ">> " + attacks + " " + arr[i].f + " | " + arr[i].s + " " + (arr[i].f + d + d));
      }
      ++i;
    }

    out.println(ans);
  }

  public static void main(String[] args) throws Exception {
    InputReader in = new InputReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    Main solver = new Main();
    solver.solve(in, out);
    out.close();
  }

  static class Pair implements Comparable<Pair> {
    int f, s;

    public Pair(int f, int s) {
      this.f = f;
      this.s = s;
    }

    @Override
    public int compareTo(Pair p) {
      return this.f - p.f;
    }
  }

  static class InputReader {
    BufferedReader in;
    StringTokenizer st;

    public InputReader(InputStream is) {
      in = new BufferedReader(new InputStreamReader(is));
    }

    public String next() {
      try {
        while (st == null || !st.hasMoreTokens()) {
          st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }

    public long nextLong() {
      return Long.parseLong(next());
    }
  }
}