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
import math
n=int(input())
ans=0
s=set()
s.add(1)
s.add(n)
s.add(n-1)
for i in range(2,math.ceil(math.sqrt(n))+1):
  nn=n
  key=0
  while nn % i ==0:
    nn=nn//i
    key=1
  if nn % i ==1:
    s.add(i)
    if key==0:
      s.add((nn-1)//i)
s.remove(1)
print(len(s))