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 <iostream>
#include <stdio.h>
using namespace std;
int main(){
  long long N,NN;
  scanf("%lld",&N);
  if(N==2){printf("1");return 0;}
  long long ans=2;
  for(long long K=2;K*K<=N;K++){
    if((N-1)%K){
      NN=N;
      while(!(NN%K)){
        NN=NN/K;
      }
      if(NN%K==1)ans++;
    }else{
      if(K*K==N-1)ans++;
      else ans+=2;
    }
  }
  printf("%d",ans);
}