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;
  int64_t M;
  int sum=0;
  cin >> N;
  for(int64_t i=2;i*i<=N;i++){
    M=N;
    while(M%i==0){
      M /= i;
    }
    if(M%i==1){
      sum++;
    }
    if(N%i==1){
      sum++;
    }
    if(N==i*i+1){
      sum--;
    }
  }
  sum += 2;
  if(N==2){sum=1;}
  cout << sum << endl;
}