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;
#define ll long long
#define m 1000000007
int main() {
	ll n,ans=0,i;
	cin>>n;
	if(n==2)
    {
        cout<<"1";
        return 0;
    }
	for(i=2;i*i<=n;i++)
    {
        if(n%i==0)
        {
            ll ch=n;
            while(ch%i==0)
            ch=ch/i;
            if(ch%i==1)
                ans++;
        }
    }
    for(i=2;i*i<n-1;i++)
    {
        if((n-1)%i==0)
            ans+=2;
    }
    if(i*i==n-1)
        ans++;
    cout<<ans+2<<endl;

}
