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: Wrong Answer)

import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		long a = sc.nextLong()-1;		
        long c = 0;
        for(long i=1;i<=Math.sqrt(a);i++){if(a%i==0){c+=2;}if(i==Math.sqrt(a)){c--;}
                                         }
        c--;
        a++; 
        long e,f,g;
        for(long i=2;i<=Math.sqrt(a);i++){
          if(a%i==0){
          if(i<Math.sqrt(a)){g=a;e=i;f=a/i;                                                              
                             while(g%e==0){g/=e;}                                                                     
                             if(g%e==1){c++;}                                                                     
                             g=a;
                             while(g%f==0){g/=f;}                                                                  
                             if(g%f==1){c++;}                                                                  
                            }
                              else{c++;}                                                                          
                    }                                        
        }
        System.out.println(c);                                  
	}
}