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 k,ans=0;
map<long long,bool>vis;
void fun(long long x)
{

	if(x==1)return;
	long long y=k;
	while(y%x==0)y/=x;
	y%=x;
	if(y==1)
	{
		if(!vis[x])
		{
			ans++;vis[x]=1;
		}
	}
}
int main()
{
	cin>>k;
	for(long long i=1;i*i<=k;i++)
	{
		if(k%i==0)
		{
			fun(i);fun(k/i);
		}
	}
	for(long long i=1;i*i<=k-1;i++)
	{
		if((k-1)%i==0)
		{
			fun(i);fun((k-1)/i);
		}
		
	}
	cout<<ans;
	return 0;
}