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())
if n==2:
  print(1)
  exit()
nn=n-1
ans=set([nn])
for i in range(2,int(nn**0.5)+1):
  if nn%i==0:
    ans.add(i)
    ans.add(nn//i)
l=set()
l.add(n)
for i in range(2,int(n**0.5)+1):
  if n%i==0:
    l.add(i)
    l.add(n//i)
for j in l:
  m=n
  while m%j==0:
    m//=j
  if m%j==1:
    ans.add(j)
print(len(ans))