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.*;
import java.io.*;
public class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(System.out);
        long n=Long.parseLong(br.readLine());
        int cntr=0;
        if(n==2)
        {
            pw.println(1);
            pw.flush();
            pw.close();
            return;
        }
        for(long i=2;i*i<=n;i++)
        {
            if(n%i==0)
            {
                if(i!=n/i)
                {
                    long temp=n;
                    while(temp%i==0)
                    temp/=i;
                    if(temp==1||temp%i==1)
                    cntr++;
                    temp=n;
                    long div=n/i;
                    while(temp%div==0)
                    temp/=div;
                    if(temp==1||temp%div==1)
                    cntr++;
                }
                else
                {
                    long temp=n;
                    while(temp%i==0)
                    temp/=i;
                    if(temp==1||temp%i==1)
                    cntr++;
                }
            }
            else
            {
                if(n%i==1)
                cntr++;
                long temp=n;
                long div=n/i;
                if(div!=i)
                {
                if(temp%div==1)
                cntr++;
                else
                {
                    while(temp%div==0)
                    temp/=div;
                    if(temp==1||temp%div==1)
                    cntr++;
                }
                }
            }
        }
        pw.println(cntr+2);
        pw.flush();
        pw.close();
    }
}