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.Arrays;
import java.util.HashMap;
import java.util.Scanner;

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();

		HashMap<Integer, Integer> map = new HashMap<>();
		int[] zahyo = new int[n];

		for (int i = 0; i < n; i++) {
			zahyo[i] = sc.nextInt();
			map.put(zahyo[i], ((sc.nextInt() - 1) / a) + 1);
		}

		Arrays.sort(zahyo);

		long attackSum = 0;

		for (int i = 0; i < n; i++) {
			int x = zahyo[i];
			int attackNum = map.get(x);
			if (attackNum < 1) {
				continue;
			}
			attackSum = attackSum + attackNum;
			int p = 1;
			while (true) {
				if (i + p > n - 1) {
					p--;
					break;
				}
				if (zahyo[i + p] <= x + 2 * d) {
					p++;
				} else {
					p--;
					break;
				}
			}
			for (int j = 0; j <= p; j++) {
				map.put(zahyo[i + j], map.get(zahyo[i + j]) - attackNum);
			}
		}

		print(attackSum);
		sc.close();
	}

	public static void print(Object obj) {
		System.out.println(obj);
	}

}