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: Accepted)

from math import ceil, sqrt


def main():
    n = int(input())
    if n == 2:
        print(1)
        return
    c = 2 + (int(sqrt(n))**2 == n) + (int(sqrt(n - 1))**2 == (n - 1))
    # print(c)
    for k in range(2, ceil(sqrt(n - 1))):
        m = n % k
        if m > 1:
            # print(k, 0)
            continue
        elif m == 1:
            # print(k, 2)
            c += 2
        else:
            p = n // k
            while p % k == 0:
                p //= k
            if p % k == 1:
                # print(k, 1)
                c += 1
            # else:
                # print(k, 0)
    print(c)


if __name__ == '__main__':
    main()