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)

n = int(input())

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

cnt = 0
for i in range(1, int((n-1)**0.5)+1):
    if (n - 1) % i == 0:
        if i ** 2 == n - 1:
            cnt += 1
        else:
            cnt += 2

res = cnt - 1
for v in div[1:]:
    tmp = n
    while tmp % v == 0:
        tmp //= v
    if tmp % v == 1:
        res += 1

print(res)