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: Runtime Error)


def make_divisors(n):
    divisors = []
    for i in range(2, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    divisors.sort()
    divisors.append(n)
    return divisors

def check(N,K):
    if N == K:
        return True
    if N % K ==1:
        return True
    if N<K:
        return False
    
    if N % K ==0:
        return check(N//K,K)
    else:
        return False


def resolve():
    N = int(input())
    ys= set(make_divisors(N))
    ys2= set([i   for i in make_divisors(N-1) if check(N,i)])
    x =set([i for i in ys|ys2 if check(N,i)])

    print(len(x | ys2))


if __name__ == "__main__":
    resolve()