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 <string>

using namespace std;

int main()
{
  long long n; cin >> n;
  
  int ans = 1;
  if (n != 2) ++ans;
  for (long long i = 2; i * i <= n; ++i) {
    if (n % i == 1) ans += (i * i == n-1 ? 1 : 2);
    if (n % i == 0) {
      long long tmp = n;
      while (tmp % i == 0) tmp /= i;
      if (tmp % i == 1) ++ans;
    }
  }
  
  cout << ans << endl;
  return 0;
}