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::stdin;
use std::collections::VecDeque;

fn read_line() -> Vec<i64> {
    let mut a_str = String::new();
    stdin().read_line(&mut a_str).expect("read error");
    a_str.split_whitespace()
        .map(|x| x.parse::<i64>().expect("parse error"))
        .collect::<Vec<i64>>()
}

fn main() {
    let v = read_line();
    let n = v[0] as usize;
    let d = v[1] as usize;
    let a = v[2];

    let mut m = Vec::<(i64, i64)>::new();
    for _i in 0..n as usize {
        let v = read_line();
        m.push((v[0], v[1]));
    }

    m.sort_by(|x, y| x.0.cmp(&y.0));

    let mut ret = 0;
    let mut total = 0;
    let mut queue = VecDeque::<(i64, i64)>::new();

    for i in 0..n {
        while queue.len() > 0 {
            let x = queue[0];
            if x.0 < m[i].0 {
                total -= queue[0].1;
                queue.pop_front();
            } else {
                break;
            }
        }

        m[i].1 -= total;

        if m[i].1 > 0 {
            let c = (m[i].1 + a - 1) / a;
            ret += c;
            total += c * a;
            queue.push_back((m[i].0 + 2 * d as i64, c * a));
        }
    }
    
    println!("{}", ret);
}