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())
import math
ans=0
for i in range(1,int(math.sqrt(N-1))+1):
  if (N-1)%i==0:
    ans+=2
    i+=1
  else:
    i+=1
ans-=1

if int(math.sqrt(N-1))==math.sqrt(N-1):
  ans-=1
for i in range(2,int(math.sqrt(N))+1):
  if N%i==0:
    temp=N
    while temp%i==0:
      temp=temp/i
    if temp%i==1:
      ans+=1
      i+=1
    else:
      i+=1
ans+=1
print(ans)
               