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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use lib_competition::prelude::*;
use std::collections::VecDeque;

fn main() {
    input! {
        n: usize,
        d: i64,
        a: i64,
        mut monsters: [(i64, i64); n]
    };

    monsters.sort_by(|(ax, _ah), (bx, _bh)| { ax.cmp(bx) });

    let mut acc_atk = 0i64;
    let mut atk_count = 0i64;
    let mut atk_position_queue = VecDeque::<(i64, i64)>::new();
    for i in 0..n {
        let (m_pos, m_h) = monsters[i];

        // println!("- {} {}", m_pos, m_h);

        // println!("A {}, {}, {:?}", acc_atk, atk_count, atk_position_queue);

        while let Some((a, p)) = atk_position_queue.front() {
            if m_pos <= p + d * 2 {
                break;
            }
            acc_atk -= a;
            atk_position_queue.pop_front();
        }

        // println!("B {}, {}, {:?}", acc_atk, atk_count, atk_position_queue);

        if acc_atk < m_h {
            let atk = (m_h - acc_atk + a - 1) / a;
            atk_count += atk;
            acc_atk += atk * a;
            atk_position_queue.push_back((atk * a, m_pos));
        }

        // println!("C {}, {}, {:?}", acc_atk, atk_count, atk_position_queue);
    }
    println!("{}", atk_count);
}

// fn main() {
//     input! {
//         n: usize,
//         d: i64,
//         a: i64,
//         mut monsters: [(i64, i64); n]
//     };

//     monsters.sort_by(|(ax, _ah), (bx, _bh)| { ax.cmp(bx) });

//     let mut first = 0usize;
//     let mut last = 0usize;
//     let mut atk = 0u64;
//     while first < n {
//         // println!("{}, {}, A {:?}", first, last, monsters);
//         while last < n && monsters[last].0 <= monsters[first].0 + d * 2 {
//             last += 1;
//         }
//         // println!("{}, {}, B {:?}", first, last, monsters);
//         let atk_cnt = ((monsters[first].1 + a - 1) / a) as u64;
//         for i in first..last {
//             monsters[i].1 -= atk_cnt as i64 * a;
//         }
//         atk += atk_cnt;
//         // println!("{}, {}, C {:?}", first, last, monsters);
//         while first < n && monsters[first].1 <= 0 {
//             first += 1;
//         }
//     }
//     println!("{}", atk);
// }
*/

fn main() {
    let exe = "/tmp/binC0380829";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";