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: Accepted)

use std::collections::VecDeque;

fn main() {
    let (n, d, a) = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let mut it = buf.trim_end().split_whitespace();
        let n: usize = it.next().unwrap().parse().unwrap();
        let d: i64 = it.next().unwrap().parse().unwrap();
        let a: i64 = it.next().unwrap().parse().unwrap();
        (n, d, a)
    };
    let mut monsters: Vec<Vec<i64>> = Vec::new();
    for _ in 0..n {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let mut it = buf.trim_end().split_whitespace();
        let x: i64 = it.next().unwrap().parse().unwrap();
        let h: i64 = it.next().unwrap().parse().unwrap();
        monsters.push(vec![x, h]);
    }
    monsters.sort_by(|a, b| a[0].cmp(&b[0]));
    let mut ans: i64 = 0;
    let mut total: i64 = 0;
    let mut q: VecDeque<Vec<i64>> = VecDeque::new();
    for i in 0..n {
        let x = monsters[i][0];
        let mut h = monsters[i][1];
        while (q.len() > 0) && (q.front().unwrap()[0] < x) {
            let damage = q.pop_front().unwrap();
            total -= damage[1];
        }
        h -= total;
        if h > 0 {
            let mut cnt = h / a;
            if cnt * a < h {
                cnt += 1;
            }
            ans += cnt;
            let damage = cnt * a;
            total += damage;

            q.push_back(vec![x + 2 * d, damage])
        }
    }
    println!("{}", ans);
}