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
#include <bits/stdc++.h>
using namespace std;

int main() {
  int64_t N;
  cin>>N;
  int64_t Z=2;
  for(int64_t i=2;i<=sqrt(N);i++){
    int64_t a=N;
    if((N-1)%i==0){
      Z++;
    }
    while(a>0){
      if(a%i==0){
        a/=i;
      }
      else if(a%i==1){
        Z++;
        break;
      }
      else{
        break;
      }
    }
    if(i*i==N-1){
      Z--;
    }
  }
  if(N==2){
    Z=1;
  }
  cout<<Z<<endl;
            
}