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(){
  long long int n,i,kari;
  cin>>n;
  if(n==2){
    cout<<1;
    return 0;
  }
  set<long long int>st{};
  st.insert(n-1);
  for(i=2;i<=sqrt(n-1);i++){
    if((n-1)%i==0){
      st.insert(i);
      st.insert(n/i);
    }
  }
  st.insert(n);
  for(i=2;i<=sqrt(n);i++){
    if(n%i==0){
      kari=n/i;
      for(;;){
        if(kari%i==0){
          kari=kari/i;
        }else{
          if(kari%i==1){
            st.insert(i);
          }
          break;
        }
      }
    }
  }
  cout<<st.size();
}  