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: Time Limit Exceeded)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;

fn main() {
    // 結局左のやつを倒せるように順番にやっていけばよい
    input!(n: usize, d: usize, a: usize);
    input!(mut hs: [(usize, usize); n]);
    hs.sort();

    let mut idx = 0;
    let mut min = 0;

    'bomb: loop {
        'find_left: loop {
            let (_, v) = hs[idx];
            if v > 0 {
                break 'find_left;
            }
            idx += 1;
            if idx >= n {
                break 'bomb;
            }
        }

        let (left_x, left_h) = hs[idx];

        let bombs = if left_h % a == 0 {
            left_h / a
        } else {
            left_h / a + 1
        };
        min += bombs;
        let damage = a * bombs;

        let mut tmp_idx = idx;
        let target = left_x + d;
        let right = target + d; // 端点含む

        // println!(
        //     "left = {}, target = {}, right = {} d = {}",
        //     left_x, target, right, d
        // );
        loop {
            if tmp_idx >= n {
                break;
            }
            let (i, h) = hs[tmp_idx];
            if i > right {
                break;
            }

            //            println!("found! i = {}", i);

            if h <= damage {
                hs[tmp_idx] = (i, 0);
            } else {
                hs[tmp_idx] = (i, h - damage);
            }

            //             println!(" -> hs = {:?}", hs);
            tmp_idx += 1;
        }
    }
    println!("{}", min);
}
*/

fn main() {
    let exe = "/tmp/bin4690A787";
    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>";