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 (1.15.1) (judge verdict: Accepted)

use std::io;
use std::str::FromStr;
use std::collections::VecDeque;

struct Monster {
    pos: u64,
    life: u64,
}

type Pair = (u64, u64);

fn input_tuple() -> (u64, u64) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<u64> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1])
}

fn input_tuple_three() -> (u64, u64, u64) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<u64> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1], vec[2])
}

fn dru(n: u64, m: u64) -> u64 {
    if n % m == 0 {
        return n / m;
    } 
    n / m + 1
}

fn main() {
    let (n, d, a) = input_tuple_three();
    let mut monsters: Vec<Monster> = Vec::new();
    for _ in 0..n {
        let (x, h) = input_tuple();
        monsters.push(Monster {pos: x, life: h});
    }

    monsters.sort_by(|x, y| x.pos.cmp(&y.pos));

    let mut sum = 0;
    let mut cache: VecDeque<Pair> = VecDeque::new();
    let mut current_count = 0;
    for i in 0..n as usize {
        while cache.len() > 0 && cache.front().unwrap().0 < monsters[i].pos {
            current_count -= cache.pop_front().unwrap().1;
        }
        if monsters[i].life < a * current_count {
            continue;
        }
        monsters[i].life -= a * current_count;
        let count = dru(monsters[i].life, a);
        sum += count;
        current_count += count;
        cache.push_back((monsters[i].pos + 2 * d, count));
    }
    println!("{}", sum);
}