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
import sys
n = int(input())
if n == 2:
	print(1)
	sys.exit()
divs = []
i = 2
while i*i <= n:
	if n%i == 0:
		divs.append(i)
		if i*i < n:
			divs.append(n//i)
	i += 1
divs.append(n)

ans = set()
i = 2
while i*i <= n-1:
	if (n-1)%i == 0:
		ans.add(i)
		if i*i < (n-1):
			ans.add((n-1)//i)
	i += 1
ans.add(n-1)

for d in divs:
	tmp = n
	while tmp%d == 0:
		tmp //= d
	if tmp%d == 1:
		ans.add(d)
print(len(ans))