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;
typedef long long ll;
int main()
{
	ll n;cin>>n;
	set<ll> st;
	for(ll i=2;i*i<=n;i++){
		if(n%i==0){
			ll t=n;
			while(t%i==0){
				if(t/i%i==1) st.insert(i);
				t/=i;
			}
		}
	}
	for(ll i=1;i*i<=n-1;i++){
		if((n-1)%i==0){
			st.insert(i);
			st.insert((n-1)/i);
		} 
	}
	st.erase(1);
  	st.insert(n);
	cout<<st.size()<<"\n";
	return 0;
}