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.Arrays;
import java.util.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class Main {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int d = sc.nextInt();
		int a = sc.nextInt();
		Obj[] arr = new Obj[n];
		for (int i = 0; i < n; i++) {
			Obj o = new Obj();
			o.x = sc.nextInt();
			o.h = sc.nextInt();
			arr[i] = o;
		}
		sc.close();

		Arrays.sort(arr, (o1, o2) -> o1.x - o2.x);
		long ans = 0;
		long rem = 0;
		TreeMap<Long, Long> map = new TreeMap<>();
		for (Obj o : arr) {
			int time = (o.h + a - 1) / a;
			Map<Long,Long> hm = map.headMap((long) o.x);
			for (long l : hm.values()) {
				rem += l;
			}
			long val = ans - rem;
			val = Math.max(time - val, 0);
			ans += val;
			hm.clear();
			map.put((long) o.x + 2 * d, val);
		}
		System.out.println(ans);
	}

	static class Obj {
		int x, h;
	}
}