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.

Examples

Input

6


Output

3


Input

3141


Output

13


Input

314159265358


Output

9
import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long a = n-1;
        Set<Long> set = new HashSet<>();
        set.add(n);
        for (int i = 2; i < Math.sqrt(n)+1; i++) {
            if(n%i == 0){
                long b = n/i;
                while(b%i==0)b/=i;
                if(b%i == 1){
                    set.add((long)i);
                }
            }
        }
        for (int i = 1; i < Math.sqrt(a)+1; i++) {
            if(a%i == 0){
                long b = a/i;
                set.add((long)i);
                set.add(b);
            }
        }
        set.remove(Long.valueOf(1));
        System.out.println(set.size());
        sc.close();

    }

}
