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 ll long long
int main()
{
	ll n;
	cin>>n;
	ll ans=0;
	set<ll>s;
	for(ll k=2;k*k<=n;k++)
	{
		ll n1=n;
		if(n%k==0)
		{
			while(n1%k==0)
				n1/=k;
		}
		if(n1%k==1)
		{
			ans++;
			s.insert(k);
		}
		ll div=n/k;
		n1=n;
		if(n%div==0)
		{
			while(n1%div==0)
				n1/=div;
		}
		if(n1%div==1)
		{
			ans++;
			s.insert(div);
		}
	}
	if(n>2)
	{
		s.insert(n);
		s.insert(n-1);
	}
	s.insert(n);
	cout<<s.size();
}
