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));
    try{
      long N = Long.parseLong(br.readLine());
      Set<Long> set = new HashSet<>();
      int ans = 0;
      for(long i = 2; i <= Math.sqrt(N); i++){
        if(func(N, i) == 1){
            set.add(i);
        }
      }
      for(long i = 1; i <= Math.sqrt(N-1); i++){
        if((N-1)%i == 0){
            set.add(i);
            set.add((N-1)/i);
        }
      }
      System.out.println(set.size()); 
    }catch(Exception e){
    }
  }
  static long func(long N, long i){
    if(N%i == 0){
        return func(N/i, i);
    }
    return N%i;
  }
}