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())
ans = 1
pr = []
if n == 2:
  print(1)
  exit()
if n == 3:
  print(2)
  exit()
for i in range(1,int(n**0.5)):
  if (n-1)%i == 0:
    pr.append((n-1)//i)
ans += len(pr)
for i in range(2,int(n**0.5+2)):
  t = n
  while t > i:
    if t%i:
      t %= i
    else:
      t //= i
  if t == 1 or t == i:
    ans += 1
if int(n**0.5+0.5)**2 == n:
  ans -= 1
print(ans)