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 = LazySegmentTree::new(n);

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

    let x = ene.iter().map(|&x| x.0).collect::<Vec<_>>();
    let mut ans = 0;
    for i in 0..n {
        let res = seg.getsum(i, i + 1, 0, 0, n);
        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);
        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,
    data: Vec<i64>,
    datb: Vec<i64>,
}

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

    fn add(&mut self, a: usize, b: usize, x: i64, k: usize, l: usize, r: usize) {
        if a <= l && r <= b {
            self.data[k] += x;
        } else if l < b && a < r {
            self.datb[k] += (min(b, r) - max(a, l)) as i64 * x;
            self.add(a, b, x, k * 2 + 1, l, (l + r) / 2);
            self.add(a, b, x, k * 2 + 2, (l + r) / 2, r);
        }
    }

    fn getsum(&mut self, a: usize, b: usize, k: usize, l: usize, r: usize) -> i64 {
        if b <= l || r <= a {
            return 0;
        }
        if a <= l && r <= b {
            return self.data[k] * (r - l) as i64 + self.datb[k];
        } else {
            let mut res = (min(b, r) - max(a, l)) as i64 * self.data[k];
            res += self.getsum(a, b, k * 2 + 1, l, (l + r) / 2);
            res += self.getsum(a, b, k * 2 + 2, (l + r) / 2, r);
            return res;
        }
    }
}

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
    }
}