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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n=int(input())
nn=n-1
ans=set([nn])
for i in range(2,int(nn*0.5)+1):
  if nn%i==0:
    ans.add(i)
    ans.add(nn//i)
l=[n]
for i in range(2,int(nn*0.5)+1):
  if n%i==0:
    l.append(i)
    l.append(n//i)
for j in l:
  m=n
  while m%j==0:
    m//=j
  if m%j==1:
    ans.add(j)
print(len(ans))