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>
#include <cstdio>
using namespace std;

typedef long long ll;
ll n, cnt;
void f(ll p, ll q) {
	while (p % q == 0) p /= q;
	if (p % q == 1) cnt++;
}

int main()
{
	ll i, j;
	cin >> n;
	if (n == 2) {
		cout << 1;
		return 0;
	}
	for (i = 2; i * i <= n; i++) {
        if (n % i == 0) {
			f(n, i);
			if (n / i != i) f(n, n / i);
        }
	}
	for (i = 2; i * i <= n - 1; i++) {
		if ((n - 1) % i == 0) {
			cnt += 2;
			if (i * i == n - 1) cnt--;
		}
	}
	cout << cnt + 2;
    return 0;
}
