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,k,c,i,m;
  cin>>n;
  m=n-1;
  c=1;
  for(k=2;k*k<=m;k++){
    if(m%k==0){
      m/=k;
      i=1;
      while(m%k==0){
        m/=k;
        i++;
      }
      c*=(i+1);
    }
  }
  if(m>1) c*=2;
  c--;
  
  for(k=2;k*k<=n;k++){
    if(n%k==0){
      m=n/k;
      while(m%k==0) m/=k;
      if (m%k==1) c++;
    }
  }
  c++;
  cout<<c<<endl;
}