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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.TreeMap;

class Main {
    public static void main(String[] args) {
        int n = 0;
        int radius = 0;
        List<Integer> coordinates = null;
        List<Integer> hps = null;
        List<Integer> neighbour = null;
        try (InputStreamReader isr = new InputStreamReader(System.in); BufferedReader br = new BufferedReader(isr);) {
            String line;
            String[] arrayString;
            line = br.readLine();
            arrayString = line.split(" ");
            n = Integer.parseInt(arrayString[0]);
            radius = Integer.parseInt(arrayString[1]);
            int attack = Integer.parseInt(arrayString[2]);
            coordinates = new ArrayList<>(n);
            hps = new ArrayList<>(n);
            neighbour = new ArrayList<>(n);
            Map<Integer, Integer> monsters = new TreeMap<>();
            for (int i = 0; i < n; i++) {
                line = br.readLine();
                arrayString = line.split(" ");
                int x = Integer.parseInt(arrayString[0]);
                int hp = Integer.parseInt(arrayString[1]);
                hp = divideCeil(hp, attack);
                monsters.put(x,hp);
            }
            for (int x : monsters.keySet()) {
                int hp = monsters.get(x);
                coordinates.add(x);
                hps.add(hp);
            }
        } catch (IOException e) {

        }
        for (int i = 0; i < n; i++) {
            int coordinate = coordinates.get(i);
            int nei = i;
            long range_inclusive = 2L * radius + coordinate;
            for (; nei < n; nei++) {
                int temp_coordinate = coordinates.get(nei);
                if (temp_coordinate > range_inclusive)
                    break;
            }
            neighbour.add(nei);
        }

        int[] damages = new int[n];
        long total = 0;
        for (int i = 0; i < n; i++) {
            int current_hp = hps.get(i) - damages[i];
            if (current_hp < 0)
                continue;
            total += current_hp;
            for (int j = i; j < neighbour.get(i); j++) {
                damages[j] += current_hp;
            }
        }
        System.out.println(total);
    }

    static int divideCeil(int numerator, int denominator) {
        double a = numerator;
        double b = denominator;
        return (int) Math.ceil(a / b);
    }
}