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;
long long int n,ans=0;
void check(long long x) {
	long long nn=n;
	while(nn%x==0) nn/=x;
	if(nn%x==1) ans++;
}
int main(){
    
    cin>>n;
    for(long long i=1;i*i<=n;i++){
    	if((n-1)%i==0) {
			if(i>1) ans++;
			if(i*i!=n-1) ans++;
		}
	}
	for(long long i=1;i*i<=n;i++){
	
		if(n%i==0) {
			if(i>1) check(i);
			if(i*i!=n) check(n/i);
		}
	}
	cout<<ans<<endl;
	return 0;
	
}