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;

LL n,ans;
bool check(LL k,LL n)
{
	if (n%k!=0) return false;
	while (n%k==0) n/=k;
	if ((n-1)%k!=0) return false;
	return true;
}
int main()
{
	cin>>n;
	for (LL i=2;i*i<=n-1;++i)
	{
		if ((n-1)%i==0) 
		{
			ans++;
			if ((n-1)/i!=i) ans++;
		}
	}
	if (n-1!=1) ans++;
	for (LL i=2;i*i<=n;++i)
	{
		if (check(i,n)) ans++;
	}
	ans++;
	cout<<ans<<endl;
	return 0;
}