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)

pub fn main() {
    use std::collections::BinaryHeap;
    use std::collections::VecDeque;
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let nda = s
        .split_whitespace()
        .map(|w| w.parse().unwrap())
        .collect::<Vec<i64>>();
    let n = nda[0];
    let d = nda[1];
    let a = nda[2];
    let mut heap = BinaryHeap::with_capacity(n as usize);
    for _ in 0..n {
        s.clear();
        std::io::stdin().read_line(&mut s).unwrap();
        let xh = s
            .split_whitespace()
            .map(|w| w.parse().unwrap())
            .collect::<Vec<i64>>();
        heap.push((xh[0], xh[1]));
    }
    let mut count = 0;
    let mut damage = 0;
    let mut queue: VecDeque<(i64, i64)> = VecDeque::new();
    while !heap.is_empty() {
        if queue.is_empty() || heap.peek().unwrap().0 >= queue.front().unwrap().0 {
            let (x, h) = heap.pop().unwrap();
            if h > damage {
                let q = (h - damage + a - 1) / a;
                count += q;
                damage += q * a;
                queue.push_back((x - 2 * d, q * a));
            }
        } else {
            let (_, h) = queue.pop_front().unwrap();
            damage -= h;
        }
    }
    println!("{}", count);
}