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;
typedef long long ll;

int main(){
  ll n,a;
  cin>>n;
  ll ans=1;
  for(ll i=2;i*i<=n;i++){
    if(n%i==1){
      if(i*i==n-1) ans++; 
      else ans+=2;
    }
    else if(n%i==0){
      a=n;
      while(a%i==0){
        a/=i;
      }
      if(a%i==1) ans++;
    }
  }
  if(n!=2) ans++;
  cout<<ans<<endl;
  
}
 