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;

vector<ll> enumDivisor(ll n) {
	vector<ll> res;
	for (ll i = 1; i * i <= n; ++i) {
		if (n % i != 0) continue;
		res.emplace_back(i);
		if (i * i != n) res.emplace_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;
		tmp %= x;
		if (tmp == 1) ans++;
	}
	ans += enumDivisor(n - 1).size() - 1;
	cout << ans << endl;
	return 0;
}