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
import math
def prime(x):
  L = []
  last = math.floor(x ** 0.5) 
  for i in range(1, last + 1):
    if x % i == 0:
      L.append(i)
      if x // i != i:
        L.append(x // i)
  return L

N = int(input())

if N == 2:
  print(1)
  exit()

L = prime(N - 1)

ans = len(L) - 1

D = prime(N)

for i in D:
  if i == 1: continue
  t = N
  while (t / i == t // i):
    t //= i

  t -= 1
  if t / i == t // i:
    ans += 1

print(ans)
