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 <iostream>
using namespace std;
typedef long long ll;
ll ans,n;
ll f(ll n,ll k){
    while(n%k==0){
        n/=k;
    }
    if(n%k==1)return 1;
    else return 0;
}
int main(void){
    cin>>n;
    if(n==2){cout<<1<<endl;return 0;}
    for(ll i=2;i*i<=n;i++){
        if(n%i==0){
            ans+=f(n,i);
            if(i*i!=n){ans+=f(n,n/i);}
        }
    }
    for(ll i=2;i*i<=n-1;i++){
        if((n-1)%i==0){
            ans+=f(n,i);
            if(i*i!=(n-1)){ans+=f(n,(n-1)/i);}
        }
    }
    cout<<ans+2<<endl;
}
