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)

//created by Whiplash99
import java.io.*;
import java.util.*;

public class Main
{
    private static int countFactors(long N)
    {
        int ans=1;
        for (long i = 2; i * i <= N; i++)
        {
            int count=0;
            while (N%i==0)
            {
                N /=i;
                count++;
            }
            ans*=(count+1);
        }
        return N>1?ans*2:ans;
    }
    private static int check(long N, long fact)
    {
        while (N%fact==0) N/=fact;
        return N%fact==1?1:0;
    }
    private static int solve(long N)
    {
        int ans=0;

        for(long i=2;i*i<=N;i++)
        {
            if(N%i==0)
            {
                ans += check(N, i);
                if(i*i!=N) ans+=check(N,N/i);
            }
        }
        return ans+1;
    }
    public static void main(String[] args) throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        long N=Long.parseLong(br.readLine().trim());
        int ans=solve(N)+countFactors(N-1)-1;

        System.out.println(ans);
    }
}