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;

ll n;
int ans=2;

bool check(ll x){
    ll c=n;
    while(c%x==0)c/=x;
    return c%x==1;
}

int main(){

    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    cin>>n;if(n==2)ans--;
    for(ll i=2;i*i<=n;i++){
        ans+=check(i);
        if(n%i==0&&i*i<n)ans+=check(n/i);
        if((n-1)%i==0&&i*i<n-1)ans+=check((n-1)/i);
    }
    cout<<ans<<endl;

    return 0;
}