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.Scanner;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();
        HashSet<Long> set = new HashSet<>();
        for (long i = 1; i * i <= N; i++) {
            if (N % i == 0) {
                set.add(i);
                set.add(N / i);
            }
        }
        for (long i = 1; i * i <= N - 1; i++) {
            if ((N - 1) % i == 0) {
                set.add(i);
                set.add((N - 1) / i);
            }
        }
        int res = 0;
        for (long i : set) {
            if (i == 1) continue;
            long temp = N;
            while (temp % i == 0) {
                temp /= i;
            }
            temp %= i;
            if (temp == 1) res++;
        }
        System.out.println(res);
    }
}