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):
    U = int(N ** 0.5) + 1
    L = [i for i in range(1, U) if N % i == 0]
    return L + [N // i for i in reversed(L) if N != i * i]

def solve(k):
    n = N
    while n % k == 0:
        n //= k
    return (n % k == 1)

N = int(input())

K = set(divisors(N) + divisors(N - 1)) - {1}
print(sum(solve(k) for k in K))