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>
#define int long long

using namespace std;

signed main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	
	int n;
	cin >> n;
	
	int res = 1;
	for (int i = 1; i * i <= (n - 1); i++) {
		int m = n - 1;
		if (m % i == 0) {
			if (i != 1) res++;
			if (i * i != m) res++;
		}
	}
	for (int i = 2; i * i <= n; i++) {
		int m = n;
		while (m % i == 0) m /= i;
		if (m != n && m % i == 1) res++;
	}
	 
	cout << res << '\n';
	
	return 0;
}