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;
using ll = long long;

int main() {
  ll n;
  cin >> n;

  ll r = n < 3 ? 1 : 2;
  for (ll k = 2; k * k <= n; k++) {
    ll t = n;
    while (t >= k) t % k ? t %= k : t /= k;
    if (t == 1) r++;

    if ((n - 1) % k == 0 && (n - 1) / k != k) r++;
  }

  cout << r << endl;
}
