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>
#define int long long
#define mod 1000000007
#define mx 1000002
#define fastio ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
using namespace std;
int f(int a,int b)
{
	while(a%b==0)
		a/=b;
	return a%b==1;
}	
int32_t main() {	
	int n,i,b;
	cin>>n;
	if(n==2)
	{	cout<<"1\n";
		exit(0);
	}
	b=n-1;
	int ans=0;
	for(i=2;i*i<=b;i++)
	{
		if(b%i==0)
		{	ans++;
		if(i*i!=b)
		{
			ans++;
		}
		}
	}
	for(i=2;i*i<=n;i++)
	{
		if(n%i==0)
		{
			ans+=f(n,i);
			if(i*i!=n)
			{
				ans+=f(n,n/i);
			}
		}
	}
	cout<<ans+2<<"\n";
}	