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 = []
l = int(math.log2(N))
for i in range(1,l+1):
  if round(N**(1/i))**i==N:
    ans.append(round(N**(1/i)))

for i in range(2,round((N-1)**0.5)+1):
  if (N-1)%i == 0:
    ans.append(i)
    if (N-1)//i != i:
      ans.append((N-1)//i)
if N>2:
  ans.append(N-1)

for i in range(2,round(N**0.5)+1):
  if N%i == 0:
    n = N
    while n%i==0:
      n//=i
    if n != 1 and n%i==1:
      ans.append(i)

print(len(ans))