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



