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 = 0
for i in range(2,10**6+1):
  m = int(n)
  while True:
    if m % i == 0:
      m //= i
    elif m % i == 1:
      #print(i)
      ans += 1
      break
    else:
      break
for i in range(1,10**6+1):
  if (n-1) % i == 0 and (n-1) // i > 10**6:
    #print((n-1)//i,i)
    ans += 1
if n > 10**6:
  ans += 1
print(ans)