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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.util.*;

public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        long n = sc.nextLong();
        long m = 1;
        while(m * m <= n) m++;
        Set<Long> set = new HashSet<>();
        m--;
        if(n == 2) {
            System.out.println(1);
            return;
        }
        int res = 2;
        set.add(n);
        set.add(n-1);
        long p = n - 1;
        for(long i=2; i<=m; i++) {
            if(i * i == p) {
                set.add(i);
                res += 1;
            } else if (p % i == 0 && i < (p/i)) {
                set.add(i);
                set.add(p/i);
                res += 2;
            }
        }
        for(long i=2; i<=m; i++) {
            long num = n;
            while(num % i == 0) num /= i;
            if(num % i == 1) {
                res++;
                set.add(i);
            }
        }

        System.out.println(set.size());
    }

}