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)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String {
            bytes
                .by_ref()
                .map(|r| r.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{min, max};

fn main() {
    input!{
        n: usize,
        d: usize,
        a: usize,
        mut v: [(usize, usize); n]
    }
    v.sort_by_key(|x| x.0);
    let xs: Vec<usize> = v.iter().map(|x| x.0).collect();
    let mut seg = LSegT::new(n);
    let mut ans = 0;
    for i in 0..n {
        let (x, h) = v[i];
        let bin = xs.binary_search(&(x + 2 * d));
        let pos = bin.unwrap_or_else(|p| p - 1);
        let s = seg.get(i, i);
        if h <= s {
            continue;
        }
        let c = (h - s - 1) / a + 1;
        ans += c;
        seg.add(i, pos, c * a);
    }
    println!("{}", ans);
}

struct LSegT {
    v: Vec<usize>,
    lazy: Vec<usize>,
    n: usize
}

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

    fn eval(&mut self, p: usize) {
        if self.lazy[p] == 0 {
            return;
        }
        self.v[p] += self.lazy[p];
        if p < self.n - 1 {
            self.lazy[2 * p + 1] += self.lazy[p];
            self.lazy[2 * p + 2] += self.lazy[p];
        }
        self.lazy[p] = 0;
    }

    fn add(&mut self, l: usize, r: usize, x: usize) {
        let n = self.n;
        self.add_rec(l, r, x, 0, 0, n - 1);
    }

    fn add_rec(&mut self, l: usize, r: usize, x: usize, p: usize, pl: usize, pr: usize) {
        self.eval(p);
        if pl > r || pr < l {
            return;
        } else if l <= pl && pr <= r {
            self.lazy[p] += x;
            self.eval(p);
        } else {
            self.add_rec(l, r, x, 2 * p + 1, pl, (pl + pr - 1) / 2);
            self.add_rec(l, r, x, 2 * p + 2, (pl + pr + 1) / 2, pr);
            self.v[p] = std::cmp::max(self.v[2 * p + 1], self.v[2 * p + 2]);
        }
    }

    fn get(&mut self, l: usize, r: usize) -> usize {
        let n = self.n;
        self.get_rec(l, r, 0, 0, n - 1)
    }

    fn get_rec(&mut self, l: usize, r: usize, p: usize, pl: usize, pr: usize) -> usize {
        self.eval(p);
        if pl > r || pr < l {
            0
        } else if l <= pl && pr <= r {
            self.v[p]
        } else {
            let a = self.get_rec(l, r, 2 * p + 1, pl, (pl + pr - 1) / 2);
            let b = self.get_rec(l, r, 2 * p + 2, (pl + pr + 1) / 2, pr);
            std::cmp::max(a, b)
        }
    }
}