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: Wrong Answer)

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


public class Main {

  class Pair implements Comparable<Pair> {
    int first;
    int second;

    public Pair(int first, int second) {
      this.first = first;
      this.second = second;
    }

    @Override
    public int compareTo(Pair o) {
      return first - o.first;
    }
  }

  void solve() throws IOException {
    int n = nextInt();
    int d = nextInt();
    int a = nextInt();
    Pair[] m = new Pair[n];
    for (int i = 0; i < n; i++) {
      m[i] = new Pair(nextInt(), nextInt());
    }
    Arrays.sort(m);
    PriorityQueue<Pair> toDecCount = new PriorityQueue<>();
    int x = 0;
    int ind = 0;
    long ans = 0;
    long damage = 0;
    while (x < n) {
      while (ind + 1 < m.length) {
        if (m[ind + 1].first - d <= m[x].first) {
          ind++;
        } else {
          break;
        }
      }
      while (!toDecCount.isEmpty() && m[ind].first - d > toDecCount.peek().first) {
        damage -= toDecCount.poll().second;
      }
      m[x].second -= damage * a;
      if (m[x].second > 0) {
        int count = (m[x].second - 1) / a + 1;
        damage += count;
        m[x].second = 0;
        ans += count;
        toDecCount.add(new Pair(m[ind].first + d, count));
      }
      x++;
    }
    out.println(ans);
  }

  public static void main(String[] args) throws IOException {
    new Main().run();
  }

  void run() throws IOException {
    reader = new BufferedReader(new InputStreamReader(System.in));
//		reader = new BufferedReader(new FileReader("input.txt"));
    tokenizer = null;
    out = new PrintWriter(new OutputStreamWriter(System.out));
//		out = new PrintWriter(new FileWriter("output.txt"));
    solve();
    reader.close();
    out.flush();

  }

  BufferedReader reader;
  StringTokenizer tokenizer;
  PrintWriter out;

  int nextInt() throws IOException {
    return Integer.parseInt(nextToken());
  }

  long nextLong() throws IOException {
    return Long.parseLong(nextToken());
  }

  double nextDouble() throws IOException {
    return Double.parseDouble(nextToken());
  }

  String nextToken() throws IOException {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine());
    }
    return tokenizer.nextToken();
  }
}