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: Accepted)

import java.util.*;

public class Main {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int d = sc.nextInt();
		int a = sc.nextInt();
		Monster[] monsters = new Monster[n];
		for (int i = 0; i < n; i++) {
		    monsters[i] = new Monster(sc.nextInt(), sc.nextInt());
		}
		Arrays.sort(monsters);
		int damage = 0;
		long total = 0;
		ArrayDeque<Time> deq = new ArrayDeque<>();
		for (int i = 0; i < n; i++) {
		    while (deq.size() > 0 && deq.peek().point < monsters[i].point) {
		        damage -= deq.poll().times * a;
		    }
		    monsters[i].helth -= damage;
		    if (monsters[i].helth > 0) {
		        int count = (monsters[i].helth + a - 1) / a;
		        deq.add(new Time(count, monsters[i].point + 2 * d));
		        damage += count * a;
		        total += count;
		    }
		}
		System.out.println(total);
	}
	
	
	static class Time {
	    int times;
	    int point;
	    
	    public Time(int times, int point) {
	        this.times = times;
	        this.point = point;
	    }
	}
	static class Monster implements Comparable<Monster> {
	    int point;
	    int helth;
	    
	    public Monster(int point, int helth) {
	        this.point = point;
	        this.helth = helth;
	    }
	    
	    public int compareTo(Monster another) {
	        return point - another.point;
	    }
	}
}