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.io.*;
import java.util.*;

class Main {
    public static void main(String args[]) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        Long n = Long.parseLong(br.readLine());
        long res = 1 + (n>2?1:0);
        for(long i = 2;i*i <= n; ++i){
            long t = n;
            long mod = t%i;
            if(mod==0){
                while(t%i==0){
                    t/=i;
                }
                if(t==1 || t%i==1)
                    res++;
            }
            else if(mod==1) {
                res += 1 + (i*i!=n-1?1:0);
            }
        }
        System.out.println(res);
        
    }
}
