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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {

		try (Scanner sc = new Scanner(System.in)) {
			int n = sc.nextInt();
			int d = sc.nextInt();
			int a = sc.nextInt();
			List<Enemy> list = new ArrayList<Enemy>();
			for (int i = 0; i < n; i++) {
				list.add(new Enemy(sc.nextInt(), sc.nextInt()));
			}
			Collections.sort(list, (Enemy e1, Enemy e2) -> {
				return e1.x - e2.x;
			});

			long cnt = 0;

			int lsize = list.size();
			for (int i = 0; i < lsize; i++) {
				Enemy e = list.get(i);
				if (e.h > 0) {
					long r = e.x + d * 2;
					int c = e.h / a + (e.h % a > 0 ? 1 : 0);
					long damage = c * a;
					for (int j = i; j < lsize; j++) {
						Enemy ed = list.get(j);
						if (r < ed.x) break;
						if (e.x <= ed.x) {
							ed.h -= damage;
						}
					}
					cnt += c;
				}
			}

			System.out.println(cnt);

		}
	}

}

class Enemy {
	int x;
	int h;
	Enemy(int x, int h) {
		this.x = x;
		this.h = h;
	}
}