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>
typedef long long ll;
const ll mod=1e9+7;
const ll inf=0x3f3f3f3f;
const int N=1e2+5;
using namespace std;
int main()
{
    ll n;cin>>n;
    ll ans=2;
    if(n==2) ans=1;
    for(ll i=2;i*i<=n;i++)
    {
        ll m=n;
        while(m>=i)
        {
            m%i?m%=i:m/=i;
        }
        if(m==1) ans++;
        if((n-1)%i==0&&i*i!=(n-1)) ans++;
    }
    cout<<ans;
    return 0;
}
