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>
#define Int int64_t

using namespace std;

int main() {
	Int N;
	cin >> N;

	Int ans = (N > 2 ? 2 : 1);
	for (Int i = 2; i * i <= N; ++i) {
		if (N % i == 0) {
			Int n = N;
			while (n % i == 0) { n /= i; }
			ans += (n % i == 1);
		}
		if (N % i == 1) {
			++ans;
			ans += (i != (N - 1) / i);
		}
	}
	cout << ans << endl;

	return 0;
}
