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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let v = read_vec::<i64>();
    let (n, d, a) = (v[0] as usize, v[1], v[2]);
    let mut ene = vec![];
    for i in 0..n {
        let v = read_vec::<i64>();
        let (x, h) = (v[0], v[1]);
        ene.push((x, h));
    }
    ene.sort();

    let mut seg: SEG<RangeAddSum> = SEG::new(n, (0, 0));

    for i in 0..n {
        seg.update(i, (ene[i].1, 0));
    }

    /*
    let mut seg = LazySegmentTree::new(n);
    for i in 0..n {
        seg.add(i, i + 1, ene[i].1, 0, 0, n);
    }
    */

    let mut ans = 0;
    let x = ene.iter().map(|&x| x.0).collect::<Vec<_>>();
    for i in 0..n {
        // let res = seg.getsum(i, i + 1, 0, 0, n);
        let res = seg.query(i, i + 1).unwrap_or(0);
        if res <= 0 {
            continue;
        }

        let count = (a + res - 1) / a;
        let end = x.upper_bound(&(x[i] + 2 * d));
        //seg.add(i, end, -count * a, 0, 0, n);
        seg.range_add(&(-count * a), i, end);
        ans += count;
    }
    println!("{}", ans);
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

#[derive(Debug)]
struct LazySegmentTree {
    n: usize,
    node: Vec<i64>,
    lazy: Vec<i64>,
}

impl LazySegmentTree {
    fn new(sz: usize) -> LazySegmentTree {
        let mut n = 1;
        while n < sz {
            n *= 2;
        }
        LazySegmentTree {
            n: n,
            node: vec![0i64; n * 2],
            lazy: vec![0i64; n * 2],
        }
    }

    fn eval(&mut self, k: usize, l: usize, r: usize) {
        if self.lazy[k] != 0 {
            self.node[k] += self.lazy[k];
            if r - l > 1 {
                self.lazy[2 * k + 1] += self.lazy[k] / 2;
                self.lazy[2 * k + 2] += self.lazy[k] / 2;
            }
            self.lazy[k] = 0;
        }
    }

    fn add(&mut self, a: usize, b: usize, x: i64, k: usize, l: usize, r: usize) {
        self.eval(k, l, r);

        // if out of range, do nothing.
        if b <= l || r <= a {
            return;
        }

        if a <= l && r <= b {
            self.lazy[k] += (r - l) as i64 * x;
            self.eval(k, l, r);
        } else {
            self.add(a, b, x, 2 * k + 1, l, (l + r) / 2);
            self.add(a, b, x, 2 * k + 2, (l + r) / 2, r);
            self.node[k] = self.node[2 * k + 1] + self.node[2 * k + 2];
        }
    }

    fn getsum(&mut self, a: usize, b: usize, k: usize, l: usize, r: usize) -> i64 {
        if b <= l || r <= a {
            return 0;
        }

        self.eval(k, l, r);
        if a <= l && r <= b {
            return self.node[k];
        }

        self.getsum(a, b, 2 * k + 1, l, (l + r) / 2) + self.getsum(a, b, 2 * k + 2, (l + r) / 2, r)
    }
}

pub trait BinarySearch<T> {
    fn lower_bound(&self, x: &T) -> usize;
    fn upper_bound(&self, x: &T) -> usize;
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();

        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }

    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();

        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}

#[allow(dead_code)]
/// Lazy Segment Tree
pub struct SEG<T: SEGimpl> {
    n: usize,
    buf: Vec<T::Elem>,
    zero: T::Elem,
    phantom: std::marker::PhantomData<T>,
}

impl<T: SEGimpl> SEG<T> {
    #[allow(dead_code)]
    pub fn new(n: usize, zero: T::Elem) -> SEG<T> {
        let n = (1..).map(|i| 1 << i).find(|&x| x >= n).unwrap();
        SEG {
            n: n,
            buf: vec![zero.clone(); 2 * n],
            zero: zero,
            phantom: std::marker::PhantomData,
        }
    }

    #[allow(dead_code)]
    fn eval(&mut self, k: usize, l: usize, r: usize) {
        if r - l > 1 {
            let (l, r) = self.buf.split_at_mut(2 * k + 1);
            let (c1, c2) = r.split_at_mut(1);
            T::eval(&mut l[k], Some((&mut c1[0], &mut c2[0])));
        } else {
            T::eval(&mut self.buf[k], None);
        }
    }

    #[allow(dead_code)]
    pub fn update(&mut self, i: usize, x: T::Elem) {
        let mut k = i + self.n - 1;
        self.buf[k] = x;
        self.eval(k, i, i + 1);

        while k > 0 {
            k = (k - 1) / 2;
            let (l, r) = self.buf.split_at_mut(2 * k + 1);
            let (c1, c2) = r.split_at_mut(1);
            T::reduce(&mut l[k], &c1[0], &c2[0]);
        }
    }

    #[allow(dead_code)]
    pub fn get(&mut self, i: usize) -> Option<T::R> {
        self.query(i, i + 1)
    }

    #[allow(dead_code)]
    fn r(&mut self, x: &T::A, a: usize, b: usize, k: usize, l: usize, r: usize) {
        self.eval(k, l, r);
        if r <= a || b <= l {
            return;
        }
        if a <= l && r <= b {
            T::range(x, &mut self.buf[k], l, r);
            self.eval(k, l, r);
            return;
        }

        self.r(x, a, b, 2 * k + 1, l, (l + r) / 2);
        self.r(x, a, b, 2 * k + 2, (l + r) / 2, r);
        let (l, r) = self.buf.split_at_mut(2 * k + 1);
        let (c1, c2) = r.split_at_mut(1);
        T::reduce(&mut l[k], &c1[0], &c2[0]);
    }

    #[allow(dead_code)]
    pub fn range_add(&mut self, x: &T::A, a: usize, b: usize) {
        let n = self.n;
        self.r(x, a, b, 0, 0, n);
    }

    #[allow(dead_code)]
    pub fn add(&mut self, x: &T::A, i: usize) {
        self.range_add(x, i, i + 1);
    }

    #[allow(dead_code)]
    fn q(&mut self, a: usize, b: usize, k: usize, l: usize, r: usize) -> Option<T::Elem> {
        self.eval(k, l, r);
        if r <= a || b <= l {
            return None;
        }
        if a <= l && r <= b {
            Some(self.buf[k].clone())
        } else {
            let vl = self.q(a, b, k * 2 + 1, l, (l + r) / 2);
            let vr = self.q(a, b, k * 2 + 2, (l + r) / 2, r);
            match (vl, vr) {
                (Some(l), Some(r)) => {
                    let mut res = self.zero.clone();
                    T::reduce(&mut res, &l, &r);
                    Some(res)
                }
                (Some(l), None) => Some(l),
                (None, Some(r)) => Some(r),
                _ => None,
            }
        }
    }
    #[allow(dead_code)]
    pub fn query(&mut self, a: usize, b: usize) -> Option<T::R> {
        let n = self.n;
        self.q(a, b, 0, 0, n).map(T::to_result)
    }
}

pub trait SEGimpl {
    type Elem: Clone;
    type A;
    type R;

    fn eval(parent: &mut Self::Elem, children: Option<(&mut Self::Elem, &mut Self::Elem)>);
    fn range(x: &Self::A, elem: &mut Self::Elem, l: usize, r: usize);
    fn reduce(parent: &mut Self::Elem, c1: &Self::Elem, c2: &Self::Elem);
    fn to_result(elem: Self::Elem) -> Self::R;
}

#[allow(dead_code)]
struct RangeAddSum();
impl SEGimpl for RangeAddSum {
    type Elem = (i64, i64);
    type A = i64;
    type R = i64;

    fn eval(parent: &mut Self::Elem, children: Option<(&mut Self::Elem, &mut Self::Elem)>) {
        let x = parent.1;
        parent.0 += x;
        parent.1 = 0;
        if let Some((c1, c2)) = children {
            c1.1 += x / 2;
            c2.1 += x / 2;
        }
    }
    fn range(x: &Self::A, elem: &mut Self::Elem, l: usize, r: usize) {
        elem.1 += (r - l) as i64 * x;
    }
    fn reduce(parent: &mut Self::Elem, c1: &Self::Elem, c2: &Self::Elem) {
        parent.0 = c1.0 + c2.0;
    }
    fn to_result(elem: Self::Elem) -> Self::R {
        elem.0
    }
}

#[allow(dead_code)]
struct NonCommutative;
impl SEGimpl for NonCommutative {
    type Elem = Vec<i64>;
    type A = i64;
    type R = Vec<i64>;

    fn eval(_parent: &mut Self::Elem, _children: Option<(&mut Self::Elem, &mut Self::Elem)>) {}
    fn range(x: &Self::A, elem: &mut Self::Elem, _l: usize, _r: usize) {
        elem.push(*x);
    }
    fn reduce(parent: &mut Self::Elem, c1: &Self::Elem, c2: &Self::Elem) {
        parent.clear();
        parent.extend(c1.iter());
        parent.extend(c2.iter());
    }
    fn to_result(elem: Self::Elem) -> Self::R {
        elem
    }
}