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 (3.8.2) (judge verdict: Wrong Answer)

import math
import copy
def prime_factorize(n):
    a = [n]
    for i in range(2, math.floor(n ** 0.5) + 1):
        if n % i == 0:
            a.append(i)
            if n // i != i:
                a.append(n // i)
    return a

N = int(input())
prime_n = prime_factorize(N)
prime_n_1 = prime_factorize(N - 1)

ans = 0
for i in prime_n:
    n = copy.deepcopy(N)
    while (n % i) == 0:
            n = n // i
    if (n % i) == 1:
        ans += 1
ans += len(prime_n_1)
print(ans)