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: Accepted)

import sys
n=int(input())
if n==2:
  print(1)
  sys.exit()
l=[n]
for i in range(2,int(n**0.5)+1):
  if n%i==0:
    l.append(i)
l=list(set(l))
L=[]
for j in range(len(l)):
  x=n
  k=l[j]
  while x%k==0:
    x=x//k
  if x%k==1:
    L.append(l[j])

l2=[n-1]
for i in range(2,int((n-1)**0.5)+1):
  if (n-1)%i==0:
    l2.append(i)
    l2.append((n-1)//i)
l2=list(set(l2))
l2.sort()

print(len(L+l2))