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: Wrong Answer)

N = int(input())
A = []
B = []
for i in range(2,int(N**0.5)+1):
    if N%i==0:
        A.append(i)
        A.append(N//i)
    if (N-1)%i==0:
        B.append(i)
        B.append((N-1)//i)
A.append(N)
B.append(N-1)
A = sorted(A)
for a in A:
    m = 1
    while True:
        if a**m==N:
            B.append(a)
            break
        elif a**m>N:
            break
        m += 1
for a in A:
    m=0
    while a**m<N:
        if N%a**m==0:
            if (N//(a**m)-1)%a==0:
                B.append(a)
        m += 1
B = sorted(list(set(B)))
print(len(B))