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)

import math


def main():
    N = int(input())
    cnt = 0

    N1 = N - 1
    cnt = 1
    for i in range(2, int(math.sqrt(N1)) + 1):
        if N1 % i == 0:
            cnt += 2

    cnt += 1
    for i in range(2, int(math.sqrt(N)) + 1):
        if N % i != 0:
            continue

        n = N // i
        while n % i == 0:
            n //= i
        if n % i == 1:
            cnt += 1

    print(cnt)


main()