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>
using namespace std;
typedef long long ll;

int main()
{
    ll n;
    cin >> n;
    int ans = 0;
    ll r = 0;
    for(ll i = 2; i * i <= n; i++){
        ll m = n;
        while(m % i == 0) m /= i;
        m %= i;
        if(m == 1) ans++;
        r = i;
    }
    for(ll i = 1; i * i <= n * 2; i++){
        if((n - 1) % i == 0){
            ll l = (n - 1) / i;
            if(l > r) ans++;
        }
    }
    if(n == 2) cout << 1 << endl;
    else cout << ans + 1 << endl;
}
