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.*;
import static java.lang.Math.*;

public class Main {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		
		// 入力
		long n = sc.nextLong();
		
		// 計算
		long result = 2;
		if(n == 2) result = 1;
		for(int k = 2; k <= sqrt(n); k++){
		    if(n%k == 0){
		        long tmp = n;
		        while(tmp%k == 0){
		            tmp /= k;
		        }
		        if(tmp%k == 1) result++;
		    }
		}
		for(int k = 2; k <= sqrt(n); k++){
		    if(n%k != 0){
		        if((n-1)%k == 0){
		            result++;
		            if(k != 1 && (long)k*k != n) result++;
		        }
		    }
		}
		
		// 出力
		System.out.println(result);
	}
}