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: Wrong Answer)

def gen_divs(n):
    divs = []
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            divs.append(i)
            if i != n // i:
                divs.append(n // i)
    return divs


def divthensub(v, div):
    while v % div == 0:
        v //= div
    if v % div == 1:
        return True
    else:
        return False


n = int(input())
if n == 2:
    print(2)
else:
    print(len([i for i in gen_divs(n) if divthensub(n, i)]) + len(gen_divs(n - 1)) + 2)