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
N = int(input())


def divisors(n):
    x = []
    for i in range(1, int(n**0.5) + 1):
        if n % i == 0:
            x.append(i)
            if i != n // i:
                x.append(n // i)
    return sorted(x)


def test(N, K):
    if K == 1:
        return False
    while N % K == 0:
        N //= K
    return N % K == 1


cand = divisors(N) + divisors(N - 1)

ans = 0
for d in cand:
    if test(N, d):
        ans += 1
print(ans)
