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::Read;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().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();
    let mut p = vec![(0i64, 0i64); n];
    for p in p.iter_mut() {
        p.0 = it.next().unwrap().parse().unwrap();
        p.1 = it.next().unwrap().parse().unwrap();
    }
    p.sort();
    let mut deq = std::collections::VecDeque::<(i64, i64)>::new();
    let mut ans = 0;
    let mut sum = 0;
    for (x, h) in p.into_iter() {
        while let Some(&(y, s)) = deq.front() {
            if y >= x {
                break;
            }
            sum -= s;
            deq.pop_front();
        }
        if sum >= h {
            continue;
        }
        let c = (h - sum + a - 1) / a;
        ans += c;
        sum += c * a;
        deq.push_back((x + 2 * d, c * a));
    }
    println!("{}", ans);
}

fn main() {
    run();
}