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_imports)]
#![allow(unused_macros)]
use itertools::Itertools;
use std::cmp::{max, min};
use std::collections::*;
use std::i64;
use std::io::{stdin, Read};
use std::usize;

trait ChMinMax {
    fn chmin(&mut self, other: Self);
    fn chmax(&mut self, other: Self);
}
impl<T> ChMinMax for T
where
    T: PartialOrd,
{
    fn chmin(&mut self, other: Self) {
        if *self > other {
            *self = other
        }
    }
    fn chmax(&mut self, other: Self) {
        if *self < other {
            *self = other
        }
    }
}

#[allow(unused_macros)]
macro_rules! parse {
    ($it: ident ) => {};
    ($it: ident, ) => {};
    ($it: ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
    ($it: ident, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
    ($it: ident, $var:ident $($r:tt)*) => {
        let $var = parse_val!($it, usize);
        parse!($it $($r)*);
    };
}

#[allow(unused_macros)]
macro_rules! parse_val {
    ($it: ident, [$t:tt; $len:expr]) => {
        (0..$len).map(|_| parse_val!($it, $t)).collect::<Vec<_>>();
    };
    ($it: ident, ($($t: tt),*)) => {
        ($(parse_val!($it, $t)),*)
    };
    ($it: ident, u1) => {
        $it.next().unwrap().parse::<usize>().unwrap() -1
    };
    ($it: ident, $t: ty) => {
        $it.next().unwrap().parse::<$t>().unwrap()
    };
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    parse!(it, n: usize, d: i64, a: i64);
    let div = |x, y| {
        let ret = x / y;
        let r = x % y;
        if r == 0 {
            ret
        } else {
            ret + 1
        }
    };
    let mut xh = vec![];
    for _ in 0..n {
        parse!(it, x: i64, h: i64);
        xh.push((x, h));
    }
    xh.sort();
    let mut ret = 0;
    let mut dq = VecDeque::new();
    let mut ds = 0;
    for (x, mut h) in xh {
        while let Some(&(dd, xd)) = dq.front() {
            if x > xd {
                ds += dd;
                dq.pop_front();
            } else {
                break;
            }
        }
        assert!(ds <= 0);
        h += ds;
        if h <= 0 {
            continue;
        }
        let y = div(h, a);
        ret += y;
        let dd = y * a;
        ds -= dd;
        let r = x + 2 * d;
        dq.push_back((dd, r));
    }
    println!("{}", ret);
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}