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::cmp::*;
use std::io::*;

fn lower_bound<T: PartialOrd>(x: T, a: &Vec<T>) -> usize {
    let mut l: usize = 0;
    let mut r: usize = a.len();
    while r != l {
        let mid = (l + r) >> 1;
        if a[mid] < x {
            l = mid + 1;
        } else {
            r = mid;
        }
    }
    l
}

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();

    let n: usize = itr.next().unwrap().parse().unwrap();
    let d: i64 = itr.next().unwrap().parse().unwrap();
    let a: i64 = itr.next().unwrap().parse().unwrap();
    let mut xh: Vec<(i64, i64)> = (0..n)
        .map(|_| {
            (
                itr.next().unwrap().parse().unwrap(),
                itr.next().unwrap().parse().unwrap(),
            )
        })
        .collect();
    xh.sort();
    // 体力と座標をかんり

    let mut sum = vec![0i64; n + 5];
    let mut ans = 0;
    for i in 0..n {
        if xh[i].1 + sum[i] > 0 {
            let num = (xh[i].1 + sum[i] + a - 1) / a;
            // d * 2 hani
            let idx = lower_bound((xh[i].0 + d * 2 + 1, -(1 << 30)), &xh);
            sum[i] -= num * a;
            sum[idx] += num * a;
            ans += num;
        }
        sum[i + 1] += sum[i];
    }
    println!("{}", ans);
}