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: Accepted)

def divisor(i):
    s = []
    for j in range(1, int(i ** (1 / 2)) + 1):
        if i % j == 0:
            s.append(i // j)
            s.append(j)
    return sorted(set(s))

n = int(input())
ans = 0
d = divisor(n)
d.pop(0)
for i in d:
    x = n
    while True:
        if not x % i == 0:
            break
        x //= i
    if x % i == 1:
        ans += 1
d = divisor(n - 1)
ans += len(d)
ans -= 1
print(ans)