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)

import math
N = int(input())
if N == 2:
    print(1)
else:
    ans = [N-1,N]

    #N-1
    for i in range(2,int(math.sqrt(N-1)+1)):
        if (N-1) % i == 0:
            ans.append(i)
            if i != (N-1)//i:
                ans.append((N-1)//i)

    #N
    for j in range(2,int(math.sqrt(N))+1):
        if N % j == 0:
            n1 = N
            n2 = N
            while n1 % j == 0:
                n1 = n1/j
            if n1 % j == 1:
                ans.append(j)
            if j != N//j:
                while n2 % N//j == 0:
                    n2 = n2*j//N
                if n2 % j == 1:
                    ans.append(N//j)
        
    print(len(ans))