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());div=[];ans=[]
for i in range(1,int(n**0.5)+2):
  if n%i == 0:
    div.append(i);div.append(n//i)
    
for i in div:
  if i == 1:
    continue
  tmp = n
  while tmp % i == 0:
    tmp //= i
  if tmp % i ==1:
    ans.append(i)
    
n -= 1
for i in range(1,int(n**0.5)+2):
  if n%i == 0:
    ans.append(i);ans.append(n//i)
    
print(len(set(ans))-1)