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)

use std::collections::VecDeque;
use std::io::{stdin, Read};

macro_rules! parse {
    ($iter: ident) => {
        $iter.next().unwrap().parse().unwrap()
    };
    ($iter: ident,2) => {
        (parse!($iter), parse!($iter))
    };
    ($iter: ident,3) => {
        (parse!($iter), parse!($iter), parse!($iter))
    };
    ($iter: ident,4) => {
        (parse!($iter), parse!($iter), parse!($iter), parse!($iter))
    };
    ($iter: ident, $n: ident) => {
        (&mut $iter).take($n).map(|e| e.parse().unwrap()).collect();
    };
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    let mut iter = s.split_whitespace();
    let (n, d, a): (usize, usize, isize) = parse!(iter, 3);
    let mut s = 0;
    let mut xhs: Vec<(usize, isize)> = (0..n).map(|x| parse!(iter, 2)).collect();
    xhs.sort();
    let mut s = 0;
    let mut ret = 0;
    let mut attacks = VecDeque::new();
    for (x, mut h) in xhs {
        while attacks.len() > 0 {
            let (xr, p) = attacks[0];
            if xr < x {
                attacks.pop_front();
                s -= p;
            } else {
                break;
            }
        }
        h -= s;
        if h > 0 {
            let pi = h / a + if h % a == 0 { 0 } else { 1 };
            ret += pi;
            s += pi * a;
            attacks.push_back((x + 2 * d, pi * a));
        }
    }
    println!("{}", ret);
}