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 (1.42.0) (judge verdict: Wrong Answer)

#![allow(unused_parens)]
#![allow(unused_imports)]
#![allow(non_upper_case_globals)]
#![allow(non_snake_case)]
#![allow(unused_mut)]
#![allow(unused_variables)]
#![allow(dead_code)]

use itertools::Itertools;
use proconio::input;
use proconio::marker::{Chars, Usize1};

#[allow(unused_macros)]
#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    //($arg:expr) => (println!("{:?}",$arg));
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
      }
}
#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}

macro_rules! echo {
    ($($a:expr),*) => {
          $(println!("{}",$a))*
      }
}

use std::cmp::*;
use std::collections::*;
use std::ops::{Add, Div, Mul, Sub};

#[allow(dead_code)]
static INF_I64: i64 = 92233720368547758;
#[allow(dead_code)]
static INF_I32: i32 = 21474836;
#[allow(dead_code)]
static INF_USIZE: usize = 18446744073709551;
#[allow(dead_code)]
static M_O_D: usize = 1000000007;
#[allow(dead_code)]
static PAI: f64 = 3.1415926535897932;

trait IteratorExt: Iterator {
    fn toVec(self) -> Vec<Self::Item>;
}

impl<T: Iterator> IteratorExt for T {
    fn toVec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

trait CharExt {
    fn toNum(&self) -> usize;
    fn toAlphabetIndex(&self) -> usize;
    fn toNumIndex(&self) -> usize;
}
impl CharExt for char {
    fn toNum(&self) -> usize {
        return *self as usize;
    }
    fn toAlphabetIndex(&self) -> usize {
        return self.toNum() - 'a' as usize;
    }
    fn toNumIndex(&self) -> usize {
        return self.toNum() - '0' as usize;
    }
}

trait VectorExt {
    fn joinToString(&self, s: &str) -> String;
}
impl<T: ToString> VectorExt for Vec<T> {
    fn joinToString(&self, s: &str) -> String {
        return self
            .iter()
            .map(|x| x.to_string())
            .collect::<Vec<_>>()
            .join(s);
    }
}

trait StringExt {
    fn get_reverse(&self) -> String;
}
impl StringExt for String {
    fn get_reverse(&self) -> String {
        self.chars().rev().collect::<String>()
    }
}

trait UsizeExt {
    fn pow(&self, n: usize) -> usize;
}
impl UsizeExt for usize {
    fn pow(&self, n: usize) -> usize {
        return ((*self as u64).pow(n as u32)) as usize;
    }
}

fn main() {
    input! {
       N: usize,
       D:usize,
       A:usize,
    }

    let mut ans: usize = 0;
    let mut tmp = VecDeque::new();
    let mut b = vec![];
    for _ in 0..N {
        input! {
            x:usize,
            h:usize,
        }
        b.push((x, h));
    }
    b.sort_by_key(|&x| x.0);
    let mut c = vec![];
    for i in 0..N {
        c.push((b[i].0, b[i].1, i));
    }
    let mut s = vec![0; N + 1];
    let mut s_i = 0;
    let mut sum = vec![0; N + 2];
    let mut cur = 0;
    let mut r = 0;
    let mut l = 0;
    let mut m = 0;
    let mut index = 0;
    while true {
        while cur < N {
            let (x, h, i) = c[cur];
            if tmp.len() == 0 || x <= r {
                tmp.push_back((x, h, i));
                cur += 1;
            } else {
                break;
            }
            if tmp.len() == 1 {
                let &(x, h, i) = tmp.get(0).unwrap();
                l = x;
                r = x + D + D;
                m = h;
                index = i;
            }
        }

        let life = m.saturating_sub((sum[index] + s[index]) * A);
        let mut y = 0;
        if life > 0 {
            y = (life + A - 1) / A;
        }
        ans += y;
        mydbg!(y);
        let (x1, h1, i1) = tmp.pop_front().unwrap();
        s[i1] += y;
        let mut last = i1;
        while !tmp.is_empty() {
            let &(x2, h2, i2) = tmp.get(0).unwrap();
            let life = m.saturating_sub(sum[i2 + 1] * A);
            if life > y * A {
                s[last + 1] -= y;
                break;
            } else {
                last = i2;
                sum[s_i + 1] = sum[s_i] + s[s_i];
                tmp.pop_front();
            }
        }
        if tmp.len() > 0 {
            let &(x, h, i) = tmp.get(0).unwrap();
            l = x;
            r = x + D + D;
            m = h;
            index = i;
        }
        if cur == N && tmp.len() == 0 {
            break;
        }
    }

    mydbg!(sum);

    echo!(ans);
}