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.

Examples

Input

6


Output

3


Input

3141


Output

13


Input

314159265358


Output

9
n = int(input())
lst = set()

for i in range(2, int(n ** (1 / 2)) + 1):
  k = i
  while k <= n * i:
    k *= i
    if n % k == k // i:
      lst.add(i)
      break

for i in range(2, int(n ** (1 / 2)) + 1):
  if n % i == 1:
    lst.add(i)
    lst.add((n - 1) // i)

if n > 2:
  lst.add(n - 1)
lst.add(n)
print(len(lst))