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[] m = new Monster[n];
		for(int i=0;i<n;i++) {
			int x = sc.nextInt();
			int h = sc.nextInt();
			int t = (int)Math.ceil((double)h/a);
			m[i] = new Monster(x, t);
		}
		
		Arrays.sort(m, new Comparator<Monster>() {

			@Override
			public int compare(Monster o1, Monster o2) {
				if(o1.x>o2.x)
					return 1;
				else if(o1.x==o2.x)
					return 0;
				else
					return -1;
			}
			
		});
		
		int[] attack = new int[n];
		int l = 0, r = 1;
		while(l<n && r<n) {
			if(m[r].x - m[l].x <= 2*d) {
				r++;
			}
			else {
				attack[l] = r-1;
				l++;
			}
		}
		for(int i=l;i<n;i++) {
			attack[i] = r-1;
		}
		
		
		int[] reduce = new int[n+1];
		int sum = 0;
		long time = 0;
		for(int i=0;i<n;i++) {
			sum += reduce[i];
			int t = m[i].t + sum;
			if(t>0) {
				time += t;
				sum -= t;
				reduce[i] -= t;
				reduce[attack[i]+1] += t;
			}
		}
		
		System.out.println(time);
	}
}
class Monster{
	int x, t;
	Monster(int x, int t){
		this.x = x;
		this.t = t;
	}
}