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 divisors(n):
    x = set()
    m = 1
    while m * m <= n:
        if n % m == 0:
            x.add(m)
            x.add(n // m)
        m += 1
    return x

n = int(input())
d = divisors(n)
ans = 0
for k in d:
    if k == 1:
        continue
    nn = n
    while nn % k == 0:
        nn = nn // k
    ans += nn % k == 1

d1 = divisors(n - 1)
ans += len(d1) - 1
print(ans)
