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 make_yakusuu(n):
    r_list = []
    i = 1
    while i * i <= n:
        if n % i == 0:
            r_list.append(i)
            r_list.append(n // i)
        i += 1
    return sorted(r_list)
n = int(input())
tmp = make_yakusuu(n)
out = []
for i in tmp:
    m = n
    if i == 1:
        continue
    while m % i == 0:
        m //= i
    if m % i == 1 or m % i == 0:
        out.append(i)

out += make_yakusuu(n - 1)
print(len(set(out)) - 1)