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;cin>>n;
    if(n==2){cout<<1<<endl;return 0;}
    int ans=2;
    for(ll i=2;i*i<=n;i++){
        if((n-1)%i==0)ans+=(i*i==n-1)?1:2;
        else if(n%i==0){
            ll x=n;
            while(x%i==0)x/=i;
            if(x%i==1)ans++;
        }
    }cout<<ans<<endl;
}