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;

bool check(long long N, long long i){
  while(N%i==0) N /= i;
  if(N%i==1) return true;
  else return false;
}

int main(){
  long long N;
  cin >> N;
  
  if(N==2){
    cout << 1 << endl;
    return 0;
  }
  
  long long ans=2;
  for(long long i=2;i*i<=N-1;i++){
    if((N-1)%i==0){
      if(i*i==N-1) ans++;
      else ans += 2;
    }
  }
  for(long long i=2;i*i<=N;i++){
    if(N%i==0){
      if(check(N,i)) ans++;
      if(i*i!=N) if(check(N,N/i)) ans++;
    }
  }
  
  cout << ans << endl;
  return 0;
}
