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)

fn read<T: std::str::FromStr>(
    stdin_lock: &mut std::io::StdinLock,
    buf: &mut Vec<u8>,
    delimiter: u8,
) -> T {
    buf.clear();
    let l = std::io::BufRead::read_until(stdin_lock, delimiter, buf).unwrap();
    buf.truncate(l - 1); // remove delimiter
    let s = unsafe { std::str::from_utf8_unchecked(&buf) };
    s.parse().unwrap_or_else(|_| panic!("read"))
}

fn main() {
    let stdin = std::io::stdin();
    let mut stdin_lock = stdin.lock();
    let mut buf: Vec<u8> = Vec::new();

    // input
    let n: usize = read(&mut stdin_lock, &mut buf, b' ');
    let d: usize = read(&mut stdin_lock, &mut buf, b' ');
    let a: usize = read(&mut stdin_lock, &mut buf, b'\n');
    let mut xhv = vec![(0usize, 0usize); n];
    for i in 0..n {
        xhv[i].0 = read(&mut stdin_lock, &mut buf, b' ');
        xhv[i].1 = read(&mut stdin_lock, &mut buf, b'\n');
    }

    xhv.sort();

    let mut ans = 0;
    let mut i = 0;
    while i < n {
        let (x, h) = xhv[i];
        let c = (h + a - 1) / a;
        let damage = c * a;
        let mut streak = true;
        let mut next_i = i + 1;
        for j in i + 1..xhv.len() {
            let (jx, jh) = xhv[j];
            if jx > x + 2 * d {
                break;
            }
            xhv[j].1 = jh.saturating_sub(damage);
            if streak && xhv[j].1 > 0 {
                streak = false;
                next_i = j;
            }
        }
        i = next_i;
        ans += c;
    }
    println!("{}", ans);
}