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 n = sc.nextLong();
        int count = 2;
        for (long i = 2; i <= Math.sqrt(n); i++) {
            if (n % i == 0) {
                if (getMod(n, i) == 1) {
                    count++;
                }
                if (i * i != n) {
                    if (getMod(n, n / i) == 1) {
                        count++;
                    }
                }
            }
            if ((n - 1) % i == 0 && i * i <= n - 1) {
                count++;
                if (i * i != n - 1) {
                    count++;
                }
            }
        }
        System.out.println(count);
    }
    
    static long getMod(long x, long y) {
        while (x % y == 0) {
            x /= y;
        }
        return x % y;
    }
}