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 (3.4.3) (judge verdict: Runtime Error)

N = int(input())

KMAX = math.floor(math.sqrt(N)) + 1
# KMAX = 1000

Kn = [N]  # N の約数であるような K
Kn1 = [N-1]  # N - 1 の約数であるような K

# N の約数であるような K (Kn)を求める
for K in range(2,KMAX):
    
    if N % K == 0:
        Kn.append(K)
        tmp = N//K
        if tmp == K:
            continue
        Kn.append(N//K)
        
Knn = []

# Kn のうち、割れるだけ割った(tN)あと、tN mod Kn == 1 であるような Kn
for K in Kn:
    tN = N
    while tN % K == 0:
        tN = tN // K  # K で割れなくなるまで割る
    
    if (tN - 1) % K == 0:
        Knn.append(K)
        
# N-1 の約数であるような K を求める
for K in range(2,KMAX):

    if (N - 1) % K == 0:
        Kn1.append(K)
        tmp = (N-1) // K
        if tmp == K:
            continue
        Kn1.append(tmp)

Knn.extend(Kn1)
print(len(Knn))
# print(sorted(Knn))