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
def divisors(N):
  result = {1, N}
  for i in range(2, int(N**0.5)+2):
    if N % i == 0:
      result.add(i)
      result.add(N//i)
  return result

N = int(input().strip())
if N == 2: print(1)
else:
  ans = len(divisors(N-1))-1
  for k in divisors(N):
    if k == 1: continue
    n = N
    while n%k == 0: n = n//k
    if n%k == 1: ans += 1
  print(ans)