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())

def D(n):
  A = []
  for i in range(1,int(n**0.5)+1,1):
    if n % i == 0:
      A.append(i)
      if i != n//i:
        A.append(n//i)
  return A

a = 0

for i in D(N):
  M = N
  if i == 1:
    continue
  else:
    while M % i == 0:
      M = M//i
    if M % i == 1:
      a += 1

print(len(D(N-1))-1+a)
