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
def div(n):
    r = int(n**(1/2))
    for i in range(1, r + 1):
        if n % i == 0:
            yield i
            if i*i != n:
                yield n // i


n = int(input())
count = len(list(div(n-1)))-1
for i in div(n):
    if i > 1:
        x = n
        while x % i == 0:
            x //= i
        if x % i == 1:
            count += 1

print(count)
