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 whiteread::Reader;
use contest::misc::{arr, ceil_mod, ceil_div};
use contest::segment_tree::SegRangeAdd;
use contest::binary_search::upper_bound;

fn main() {
    let mut scan = Reader::from_stdin_naive();
    let n = scan.p::<usize>();
    let d = scan.p::<i64>();
    let a = scan.p::<i64>();
    let mut xh = arr(n, |_| (scan.p::<i64>(), scan.p::<i64>()));
    xh.sort();
    let x = xh.iter().map(|&p| p.0).collect::<Vec<_>>();
    let mut seg= SegRangeAdd::new(xh.iter().map(|&p| p.1).collect::<Vec<_>>());
    let mut cnt = 0;
    for i in 0..n {
        let hi = seg.sum(i..i+1);
        if hi > 0 {
            let until = upper_bound(&x, &(x[i] + 2 * d));
            cnt += ceil_div(hi, a);
            seg.add(i..until, -ceil_mod(hi, a));
        }
    }
    println!("{}", cnt);
}
*/

fn main() {
    let exe = "/tmp/bin0BD2E055";
    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: &[u8]) -> Vec<u8> {
    let mut ret = Vec::with_capacity(v.len() * 3 / 4);
    let mut buf = 0;
    let mut tbl = [64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.iter().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 [u8] = b"<base64-encoded ELF executable removed>";