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
s=set()
a=s.add
def f(n):
  for i in range(1,int(n**.5)+1):
    if n%i<1:
      a(i)
      if i!=n//i:a(n//i)
n=int(input())
f(n-1),f(n)
a=0
for i in s-{1}:
  m=n
  while m%i<1:m//=i
  a+=m%i<2
print(a)