Problem:
Score : 600 points

Problem Statement

Given is a positive integer N.

We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.

Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.

In how many choices of K will N become 1 in the end?

Constraints

2 \leq N \leq 10^{12}

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of choices of K in which N becomes 1 in the end.

Sample Input 1

6

Sample Output 1

3

There are three choices of K in which N becomes 1 in the end: 2, 5, and 6.

In each of these choices, N will change as follows:

When K=2: 6 \to 3 \to 1

When K=5: 6 \to 1

When K=6: 6 \to 1

Sample Input 2

3141

Sample Output 2

13

Sample Input 3

314159265358

Sample Output 3

9

Solution in Rust (1.42.0) (judge verdict: Wrong Answer)

use text_io::*;
use std::process::exit;

fn main() {
    let n:usize = read!();
    let mut divisors = Vec::new();
    let mut p:usize = 0;
    for i in 1..=(f64::sqrt(n as f64) + 1e-9) as usize {
        if n % i == 0 {
            divisors.push(i);
            if i != n / i {
                divisors.push(n / i);
            }
        }
    }
    for i in 0..divisors.len() {
        let mut o:usize = divisors[i];
        let mut nn:usize = n;
        let mut a:usize = 1;
        while a == 0{
            if nn % o == 0 {
                nn = nn/o;
                if nn == 1 {
                    p += 1;
                    a = 0;
                }else if nn < o {
                    a = 0;
                }
            }
            else if nn < o {
                a = 0;
            }
            else {
                nn = nn-o;
              if nn == 1 {
                    p += 1;
                    a = 0;
              }
            }
        }
    }
        for i in 1..=(f64::sqrt(n as f64) + 1e-9) as usize {
        if (n-1) % i == 0 {
            p += 1;
            if i != n / i {
                p += 1;
            }
        }
    }
    println!("{}",p+1);
}