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;

#define i64 long long int

i64 n;

int main() {
	cin>>n;
	
	int ans = 1; // n
	int lim = 2;
	for(i64 i=2;i*i<=n;i++) {
		i64 t = n;
		while(t%i==0) t/=i;
		if(t%i==1) ans++;
		
		lim = i;
	}
	for(i64 i=1;n/i>lim;i++)
		if((n-1)%i==0) ans++;
	
	cout<<ans<<endl;
	
	return 0;
}