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.*;

public class Main {
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		HashSet<Long> l = new HashSet<>();
		long j = s.nextLong();
		long k = j - 1;

		for (long i = 2; i * i <= j; ++i) {
			if (j % i == 0) {
				f(i, j, l);
				f(j / i, j, l);
			}

			if (k % i == 0) {
				f(i, j, l);
				f(k / i, j, l);
			}
		}
		System.out.println(j <= 3 ? j - 1 : l.size() + 2);
	}

	private static void f(long i, long k, HashSet<Long> l) {
		while (k % i == 0) {
			k /= i;
		}
		if (k % i == 1)
			l.add(i);
	}
}