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 alga::general::{AbstractGroup, AbstractMonoid, Additive, Operator};
use proconio::input;

use std::cmp;
use std::marker::PhantomData;
use std::ops::{RangeInclusive, RangeTo, RangeToInclusive};

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

    xhs.sort_by_key(|&(x, _)| x);
    let monsters = xhs
        .into_iter()
        .map(|(x, h)| (x, (h + a - 1) / a))
        .collect::<Vec<_>>();

    let mut ans = 0;
    let mut bit = Bit::<i64, Additive>::new(n);

    let mut j = 0;
    for i in 0..n {
        let bombs = cmp::max(0, monsters[i].1 - bit.query(..=i));
        while j < n - 1 && monsters[i].0 + 2 * d >= monsters[j + 1].0 {
            j += 1;
        }
        bit.plus(i, &bombs);
        if j < n - 1 {
            bit.plus(j + 1, &-bombs);
        }
        ans += bombs;
    }
    println!("{}", ans);
}

#[derive(Debug)]
struct Bit<M, O> {
    nodes: Vec<M>,
    phantom: PhantomData<fn() -> O>,
}

impl<M: AbstractMonoid<O>, O: Operator> Bit<M, O> {
    fn new(n: usize) -> Self {
        Self {
            nodes: vec![M::identity(); n],
            phantom: PhantomData,
        }
    }

    fn query<R: BitRange<M, O>>(&self, range: R) -> M {
        range.query(&self.nodes)
    }

    fn plus(&mut self, i: usize, x: &M) {
        let mut i_plus1 = i + 1;
        while i_plus1 <= self.nodes.len() {
            self.nodes[i_plus1 - 1] = self.nodes[i_plus1 - 1].operate(x);
            i_plus1 += 1 << i_plus1.trailing_zeros();
        }
    }
}

trait BitRange<M: AbstractMonoid<O>, O: Operator> {
    fn query(&self, nodes: &[M]) -> M;
}

impl<M: AbstractMonoid<O>, O: Operator> BitRange<M, O> for RangeTo<usize> {
    fn query(&self, nodes: &[M]) -> M {
        #[allow(clippy::range_minus_one)]
        match self.end {
            0 => M::identity(),
            end => (..=end - 1).query(nodes),
        }
    }
}

impl<M: AbstractMonoid<O>, O: Operator> BitRange<M, O> for RangeToInclusive<usize> {
    fn query(&self, nodes: &[M]) -> M {
        let mut acc = M::identity();
        let mut i_plus1 = self.end + 1;
        while i_plus1 > 0 {
            acc = acc.operate(&nodes[i_plus1 - 1]);
            i_plus1 -= 1 << i_plus1.trailing_zeros();
        }
        acc
    }
}

impl<M: AbstractGroup<O>, O: Operator> BitRange<M, O> for RangeInclusive<usize> {
    fn query(&self, nodes: &[M]) -> M {
        let l = (..*self.start()).query(nodes);
        let r = (..=*self.end()).query(nodes);
        r.operate(&l.two_sided_inverse())
    }
}
*/

fn main() {
    let exe = "/tmp/bin63FF56E5";
    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>";