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