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
#import<bits/stdc++.h>
#define endl '\n'
using namespace std;
typedef long long LL;
LL i,j,k,m,n,s=1,a[100005];
LL P(LL x,LL y)
{
	for(;x%y<1;)x/=y;
	return x%y<2;
}
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin>>n;
	for(i=1;++i*i<n;)
	{
		if(n%i<1)
		{
			s+=P(n,i);
			s+=P(n,n/i);
		}
	}
	if(i*i==n)s+=P(n,i);
	m=n-1;
	for(i=1;++i*i<m;)
	{
		if(m%i<1)
		{
			s+=2;
		}
	}
	if(i*i==m)s++;
	if(n>2)s++;
	cout<<s;
}