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;

int main(){
    ll n,ans=2;
    cin>>n;
    if(n==2) ans=1;
    for(ll k=2;k*k<=n;k++){
        ll m=n;
        while(m>=k) m%k?m%=k:m/=k;
        if(m==1) ans++;
        if((n-1)%k==0&&k*k!=(n-1) ) ans++;
    }
    cout<<ans<<endl;
    return 0;
}
