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: Time Limit Exceeded)

macro_rules! scan_sub {
    ( $itr:ident, $t:ty ) => {
        let mut buf = String::new();
        let $itr = {
            while buf.trim().len() == 0 {
                buf = String::new();
                std::io::stdin().read_line(&mut buf).unwrap();
            }
            buf.split_whitespace().map(|n| n.parse::<$t>().unwrap())
        };
    };
}

macro_rules! scan {
    ( $x:ident; Vec<$t:ty> ) => {
        scan_sub!(itr, $t);
        let $x = itr.collect::<Vec<_>>();
    };
    ( $( $x:ident ),*; $t:ty ) => {
        scan_sub!(itr, $t);
        let mut itr = itr;
        $(
            let $x = itr.next().unwrap();
        )*
    };
}

use std::collections::HashMap;
use std::cmp::max;

fn main() {
    scan!(n, d, a; usize);
    let mut hp_book = HashMap::new();
    let mut last_pos = 0;
    let mut monsters = (0..n).map(|_| {
        scan!(x, h; usize);
        hp_book.insert(x, h);
        last_pos = max(x, last_pos);
        x
    }).collect::<Vec<_>>();

    monsters.sort();

    let mut index = 0;
    let mut ans = 0;
    while index < n {
        while hp_book[&monsters[index]] == 0 { index += 1; }
        let here = monsters[index];
        let times = (hp_book[&here] as f64 / a as f64).ceil() as usize;
        ans += times;
        let damage = a * times;
        let mut target_ind = index;
        let mut target = monsters[index];
        let to = here + 2 * d;
        let mut flag = true;
        while target <= to {
            let hp = hp_book.get_mut(&target).unwrap();
            *hp = if *hp > damage { *hp - damage } else { 0 };
            if flag && *hp == 0 {
                index = target_ind;
            } else {
                flag = false;
            }
            target_ind += 1;
            if target_ind >= n { break; }
            target = monsters[target_ind];
        }
        index += 1;
    }

    println!("{}", ans);
}