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):
    ret = set()
    for i in range(1, int(n**0.5)+2):
        if n % i == 0:
            ret.add(i)
            ret.add(n // i)
    ret.remove(1)
    return ret


def main():
    N = int(input())
    s = divisors(N)
    ans = divisors(N-1)

    for x in s:
        n = N
        if x == 1:
            continue
        while(n % x == 0):
            n = n // x
        if n % x == 1:
            ans.add(x)
    print(len(ans))


main()
