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>
#include <vector>
using namespace std;
using ll = long long;

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;
        if (tmp%x == 1)ans++;
    }
    ans += enumDivisor(n-1).size()-1;
    cout << ans << endl;
    return 0;
}