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: Accepted)

def yakusu(x):
    ya = []
    for i in range(1,int(x**0.5)+1):
        if x % i == 0:
            ya.append(i)
            if i != x//i:
                ya.append(x //i)
    return ya

n = int(input())
l,m,ans = yakusu(n),yakusu(n-1),0
for i in range(1,len(l)):
    a = n
    while a % l[i] == 0:
        a = a // l[i]
    if (a-1) % l[i] == 0:
        ans += 1
ans += len(m)
print(ans-1)