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
// ABC 161 D LUNLUN number.


#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int main()

{
  ll n,i,count=2,temp;
  cin>>n;
  n-=1;
  if(n==1){
    cout<<1<<"\n";
    return 0;
  }

  for(i=2;i*i<n;i++)
    {
      if(n%i==0)count+=2;
    }
    if(n/i==i)count++;

    n++;

    for(i=2;i*i<=n;i++)
    {
       if(n%i==0)
       {
        temp=n;
        while(temp%i==0)
        {
          temp/=i;
        }
        if(temp%i==1)count++;
       }
    }

cout<<count<<"\n";


      return 0;
}


