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 Rust (1.42.0) (judge verdict: Time Limit Exceeded)

use proconio::input;
use superslice::*;

fn main() {
    input! {
        n: usize,
        d: usize,
        a: isize,
        mut monsters: [(usize, isize); n],
    }

    monsters.sort();

    let mut count = 0;
    for i in 0..n {
        if monsters[i].1 > 0 {
            let index = monsters.upper_bound_by(|x| x.0.cmp(&(monsters[i].0 + 2 * d)));
            if index > n - 1 {
                let max = monsters
                    .iter()
                    .skip(i)
                    .max_by(|x, y| x.1.cmp(&y.1))
                    .unwrap();
                /* 
                print!("Monsters:");
                for m in monsters.iter().skip(i-1) {
                    print!(" {}", m.1)
                }
                println!();
                println!("max {}", max.1);
                */
                let times = (max.1 +(a - 1)) / a;
                count += times;
                break;
            }
            let times = (monsters[i].1 + (a - 1)) / a;
            let damage = times * a;
            //println!("index {} times {} damage {}", index, times, damage);
            for j in 0..(index-i) {
                monsters[i + j].1 -= damage;
            }
            count += times;
        }
    }

    println!("{}", count);
}