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())

if n == 2:
  count = 1
else:
  count = 2
divisor = []

d = 2
while d * d < n - 1:
  if (n - 1) % d == 0:
    count += 2
  d += 1
if d * d == n - 1:
  count += 1

d = 2
while d * d < n:
  if n % d == 0:
    divisor.append(d)
    divisor.append(n // d)
  d += 1
if d * d == n:
  divisor.append(d)

for d in divisor:
  tmp = n
  while tmp % d == 0:
    tmp //= d
  if tmp % d == 1:
    count += 1

print(count)