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 n,m,ans;
set<long long>st;
int main()
{
  cin>>n;
  m=n-1;
  for(long long i=2;i*i<=n;i++)
  {
	if(n%i!=0)continue;
	long long qwq=n;
	while(qwq%i==0)qwq/=i;
	qwq%=i;
	if(qwq==1)
    	st.insert(i);
  }
	for(long long i=2;i*i<=m;i++)
		if(m%i==0)
			st.insert(i),st.insert(m/i);
	st.insert(n);
	if(m!=1)st.insert(m);
	cout<<st.size()<<"\n";
}
