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;

const int lim = 1000000;

int res;

int main()
{
    ll n; cin >> n;
    for (ll i = 2; i <= lim && i <= n; i++) {
        ll num = n;
        while (num % i == 0) num /= i;
        if (num % i == 1) res++;
    }
    if (n > lim) res++;
    n--;
    for (ll i = 1; i * i <= n; i++) if (n % i == 0) {
        if (i > lim) res++;
        if (i * i < n && n / i > lim) res++;
    }
    cout << res << endl;
    return 0;
}
