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)

N = int(input())

def divider(n):
  dividers = []
  for i in range(1, int(n**0.5) + 1):
    if n % i == 0:
      dividers.append(i)
      if i != n // i:
        dividers.append(n // i)
  dividers.sort()
  dividers.remove(1)
  return dividers
#nの約数を抽出する関数を定義(1以外)

cnt = len(divider(N - 1))
for k in divider(N):
  n = N
  while n % k == 0:
    n /= k
  if n % k == 1:
    cnt += 1
print(cnt)