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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

from sys import stdin, setrecursionlimit


def check(n, k):
    tmp = n
    while tmp % k == 0:
        tmp = tmp // k
    return tmp % k == 1


def main():
    input = stdin.buffer.readline
    n = int(input())
    ans = 2
    for i in range(2, int((n - 1) ** 0.5) + 1):
        if (n - 1) % i == 0:
            ans += 2
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            if check(n, i):
                ans += 1
            if check(n, n // i):
                ans += 1
    print(ans)


if __name__ == "__main__":
    setrecursionlimit(10000)
    main()