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)

from math import sqrt

N = int(input())


def f(x):
    n = N
    while n % x == 0:
        n //= x
    return n % x == 1


ans = 1
for k in range(2, int(sqrt(N)) + 1):
    res = N % k
    if res == 0:
        k1, k2 = k, N // k
        ans += 1 if f(k1) else 0
        ans += 1 if k1 != k2 and f(k2) else 0
    elif res == 1:
        ans += 1 if k == (N - 1) // k else 2
if N >= 3:
    ans += 1

print(ans)