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;
ll N;
unordered_set<ll> v;
int f(ll k) {
	if (k < 2) return 0;
	if (!v.insert(k).second) return 0;
	ll n = N;
	while (n >= k) {
		if (n % k == 0) n /= k;
		else n %= k;
	}
	return n == 1 ? 1 : 0;
}
int main() {
	cin >> N;
	ll r = 0;
	for (ll n = N-1; n <= N; ++ n) {
		r += f(n);
		for (ll i = 2; i*i <= n; ++ i) if (n % i == 0) {
			r += f(i);
			r += f(n/i);
		}
	}
	cout << r << endl;
}
