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 <stdio.h>
long long n, x, y, ans, z, w;
int main() {
	scanf("%lld", &n);
	if (n == 2) {
		printf("1\n");
		return 0;
	}
	x = n - 1;
	y = 2;
	while (y * y <= x) {
		if (x % y == 0) {
			ans += 2;
			if (y * y == x)ans--;
		}
		y++;
	}
	y = 2;
	while (y * y <= n) {
		if (n % y == 0) {
			z = n;
			while (z % y == 0)z /= y;
			if (z % y == 1)ans++;
			if (y * y != n) {
				z = n;
				w = n / y;
				while (z % w == 0)z /= w;
				if (z % w == 1)ans++;
			}
		}
		y++;
	}
	printf("%lld\n", ans + 2);
}