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 (2.4.0) (judge verdict: Accepted)

def rest(n, i):
    while n%i == 0:
        n //= i
    return n

N = int(input())
if N == 2:
    print(1)
    exit()

ans = [N-1, N]

for i in range(2, int(N**0.5) + 1):
    if (N-1)%i == 0:
        ans.append(i)
        ans.append((N-1)//i)
    elif N%i == 0:
        if rest(N,i) % i == 1 or rest(N,N//i) % (N//i) == 1:
            ans.append(i)

print(len(set(ans)))