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: Accepted)

#![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_U64: u64 = 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;
    }
}

pub trait Monoid {
    type T: Clone + PartialEq + std::fmt::Debug;
    fn id() -> Self::T;
    fn op(a: &Self::T, b: &Self::T) -> Self::T;
    fn op2(a: &Self::T, b: &Self::T) -> Self::T;
    fn op3(a: &Self::T, b: &Self::T) -> Self::T;
}
struct SUB;
impl Monoid for SUB {
    type T = u64;
    fn id() -> Self::T {
        0
    }
    fn op(a: &Self::T, b: &Self::T) -> Self::T {
        max(*a, *b)
    }
    fn op2(a: &Self::T, b: &Self::T) -> Self::T {
        *a + *b
    }
    fn op3(a: &Self::T, b: &Self::T) -> Self::T {
        (*a).saturating_sub(*b)
    }
}

struct SqrtDecomposition<M: Monoid> {
    sqrt_N: usize,
    sub: Vec<M::T>,
    lazy: Vec<M::T>,
    a: Vec<M::T>,
}
impl<M: Monoid> SqrtDecomposition<M> {
    //fn new(N: usize) -> SqrtDecomposition<M> {
    fn new(a: &Vec<M::T>) -> SqrtDecomposition<M> {
        let sqrt_N = (a.len() + 511) / 512;
        let mut sub = vec![M::id(); sqrt_N];
        let mut lazy = vec![M::id(); sqrt_N];
        let mut b = vec![M::id(); sqrt_N * 512];
        for i in 0..a.len() {
            b[i] = a[i].clone();
            sub[i / 512] = M::op(&sub[i / 512], &b[i]);
        }
        SqrtDecomposition {
            sqrt_N: sqrt_N,
            sub: sub,
            a: b,
            lazy: lazy,
        }
    }
    fn update_range(&mut self, l: usize, r: usize, v: M::T) {
        let sub_l = l / 512;
        let sub_r = (r + 511) / 512;
        for i in sub_l..sub_r {
            let s = i * 512;
            let e = s + 512;
            if s >= l && e < r {
                self.lazy[i] = M::op2(&self.lazy[i], &v);
            } else {
                for j in max(s, l)..min(e, r) {
                    self.a[j] = M::op3(&self.a[j], &v);
                }
            }
        }
    }
    fn query(&mut self, l: usize) -> M::T {
        let sub_index = l / 512;
        if self.lazy[sub_index] != M::id() {
            let s = sub_index * 512;
            let e = s + 512;
            for j in s..e {
                self.a[j] = M::op3(&self.a[j], &self.lazy[sub_index]);
            }
            self.lazy[sub_index] = M::id();
        }
        self.a[l].clone()
    }
}

fn main() {
    use superslice::*;
    input! {
       N: usize,
       D:usize,
       A:u64,
       mut mon:[(usize,u64);N],
    }

    mydbg!(mon);
    mon.sort_by_key(|x| x.0);
    let mut x = vec![];
    let mut hp = vec![];
    for &(a, b) in &mon {
        x.push(a);
        hp.push(b);
    }

    let mut sd: SqrtDecomposition<SUB> = SqrtDecomposition::new(&hp);

    let mut ans: usize = 0;
    for i in 0..N {
        let p = x[i] + D + D;
        let t = x.upper_bound(&p);
        let h = sd.query(i);
        if h != 0 {
            let c = (h + A - 1) / A;
            sd.update_range(i, t, c * A);
            ans += c as usize;
        }
    }

    echo!(ans);
}