Problem:
Score : 300 points

Problem Statement

Given is a positive integer N.
How many tuples (A,B,C) of positive integers satisfy A \times B + C = N?

Constraints

2 \leq N \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

3

Sample Output 1

3

There are 3 tuples of integers that satisfy A \times B + C = 3: (A, B, C) = (1, 1, 2), (1, 2, 1), (2, 1, 1).

Sample Input 2

100

Sample Output 2

473

Sample Input 3

1000000

Sample Output 3

13969985

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        n: i128
    };

    let mut x = n + 1;
    let mut base = 0;
    let mut sum = 0;
    while x > 0 {
        let mut y = n / (base + 1);
        if y * (base + 1) >= n {
            y -= 1;
        }
        if x != n + 1 {
            sum += (x - y) * base;
        }

        base += 1;
        x = y;
    }

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