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

n=int(input())
ans=0
t=d(n)
for i in t:
    if i==1:
        continue
    tn=n
    while tn>=i:
        if tn%i==0:
            tn//=i
        else:
            tn%=i
    if tn==1:
        ans+=1
ans+=len(d(n-1))-1
print(ans)