Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

6

Sample Output 1

3

There are three choices of K in which N becomes 1 in the end: 2, 5, and 6.

In each of these choices, N will change as follows:

When K=2: 6 \to 3 \to 1

When K=5: 6 \to 1

When K=6: 6 \to 1

Sample Input 2

3141

Sample Output 2

13

Sample Input 3

314159265358

Sample Output 3

9

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

def gen(x):
    root = int(pow(x, 0.5))

    yield x

    for k in range(2, root):
        if x % k == 0:
            yield k
            yield x // k

    if x % root == 0:
        yield root
        if root != x // root:
            yield x // root


def main():
    N = int(input())

    # N%K!=0
    cnt = sum(1 for _ in filter(lambda x: x > 1, gen(N - 1)))

    # N%K==0
    for k in filter(lambda x: x > 1, gen(N)):
        x = N
        while x % k == 0:
            x //= k

        if x % k == 1:
            cnt += 1

    print(cnt)


if __name__ == '__main__':
    main()