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)

#![allow(non_snake_case)]
#![allow(unused_imports)]
use proconio::input;
use std::cmp::max;
use std::cmp::min;
use std::collections::HashMap;
use std::collections::VecDeque;

fn main() {
    input! {
        N: usize,
    }

    let mut ans: i64 = 0;

    for a in 1..N {
        // a * 1, a * 2, ... a * ?
        // 最も大きいのは、A * B = N -1
        // 最も小さいのは、A * 1 = A;

        let b_max = (N - 1) / a;
        let c_max = N - a * b_max;
        if c_max <= 0 {
            return;
        }

        let _b_min = 1;
        let c_min = N - a;
        if c_min <= 0 {
            return;
        }

        ans += b_max as i64;
    }

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