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;

int main()
{
    long long n ,ans = 2 ,N ,i;
    cin >> n;
    if(n == 2){
        cout << 1 << endl;
        return 0;
    }
    for(N,i=2; i*i<=n; i++){
        for(N=n; N%i==0; N/=i);
        ans += (N%i==1) + (n%i==1);
    }
    cout << ans-((i-1)*(i-1)==n-1) << endl;
}
