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 calc_factors(N):
    """
    約数をlistでreturn
    この問題はK>1なので、約数に1を含めてない
    """
    i=2
    factors={N}
    while i*i<=N:
        if N%i==0:
            factors.add(i)
            factors.add(N//i)
        i+=1
    return list(sorted(factors))


N = int(input())


if N==2:
    print(1)
    exit()
#割り算しない場合
ans = len(calc_factors(N-1))
#割り算する場合
for fac in calc_factors(N):
    tmp=N
    while tmp%fac==0:
        tmp//=fac
    if tmp%fac==1:
        ans+=1
print(ans)