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;

#define ll long long int

vector<ll> enumDivisor(ll n){
    vector<ll> res;
    for(ll i=1; i*i <=n; ++i){
        if(n%i !=0) continue;
        res.push_back(i);
        if(i*i != n) res.push_back(n/i);
    }
    return res;
}

int main(){
    ll n;
    cin>>n;
    int ans=0;
    for(ll x : enumDivisor(n)){
        if(x==1) continue;
        ll tmp=n;
        while(tmp%x == 0) tmp /= x;
        tmp %= x;
        if(tmp==1) ++ans;
    }
    ans+=enumDivisor(n-1).size()-1;
    cout << ans << endl;
    return 0;
}
