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: Accepted)

fn main() {
    let n: usize = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.trim_end().parse().unwrap()
    };

    let mut ans = 0;
    
    {
        let mut k = 1;
        while k * k <= n - 1 {
            if (n - 1) % k == 0 {
                ans += if k == (n - 1) / k { 1 } else { 2 };
            }
            k += 1;
        }
        ans -= 1;
    }

    {
        let mut k = 2;
        while k * k <= n {
            if n % k == 0 {
                let mut x = n;
                while x % k == 0 { x /= k; }
                if x % k == 1 { ans += 1; }
                let l = n / k;
                if k != l {
                    let mut y = n;
                    while y % l == 0 { y /= l; }
                    if y % l == 1 { ans += 1; }    
                }
            }
            k += 1;
        }
        ans += 1;
    }

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