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())
k=2
ans=1
factors=[]
i=1
while i*i<N-1:
  if (N-1)%i==0:
    ans+=1
  i+=1
while k*k<=N:
  n=0
  while pow(k,n)<=N:
    if (N-pow(k,n))%(pow(k,n+1))==0:
      ans+=1
      break
    n+=1
  k+=1
print(ans)