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
def f(n):
  d=[]
  for i in range(1,int(n**0.5)+1):
    if n%i<1:
      d+=i,
      if i!=n//i:d+=n//i,
  return d[1:]
n=int(input())
a=f(n-1)
for i in f(n):
  m=n
  while m%i<1:m//=i
  if m%i<2:a+=i,
print(len(set(a)))