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;
#define int long long
signed main(){
  int N,ans=0;
  cin>>N;
  for(int i=2;i<=N/i;i++){
    if(N%i==0){
      int j=N;
      for(;j%i==0;j/=i);
      if(j%i==1)
        ans++;
    }
  }
  N--;
  for(int i=1;i<=N/i;i++){
    if(N%i==0)
      ans+=2;
    if(i*i==N)
      ans--;
  }
  cout<<ans<<endl;
}