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(){
	
	cin.tie(0); ios_base::sync_with_stdio(0);
	long long n,x;
	cin>>n;
	int res = 0;
	for(long long i = 2;i*i<=n;i++)if(n%i==0){
		x = n;
		while(x%i==0)x/=i;
		if(x%i==1)res++;
		if(n/i!=i){
			long long d = n/i;
			x = n;
			while(x%d==0)x/=d;
			if(x%d==1)res++;
		}
	}
	else if((n-1)%i==0){
		res++;
		if((n-1)/i!=i)res++;
	}
	res+=1;
	if(n>2)res++;
	cout<<res<<endl;
	
	return 0;
}