

def  _snake_case		(snake_case_					:     int  )							->		int:
  if not isinstance(snake_case_    ,       snake_case_  ):
    raise ValueError('double_factorial() only accepts integral values'  )
  if n < 0:
    raise ValueError('double_factorial() not defined for negative values'  )
  return 1 if n <= 1 else n * double_factorial(n - 2  )


if __name__ == "__main__":
      import doctest

      doctest.testmod()






'''simple docstring'''
import math







def 				__UpperCamelCase (					__UpperCAmelCase  :					str			)							->	Optional[int]:
  lowercase				:							Tuple									=   0
  if n % 2 == 0:
    count += 1
    while n % 2 == 0:
      lowercase				:							Optional[int]									=   int(n / 2			)
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

  lowercase				:							Dict									=   3

  while i <= int(math.sqrt(__UpperCAmelCase			)			):
    if n % i == 0:
      count += 1
      while n % i == 0:
        lowercase				:							Dict									=   int(n / i			)
    lowercase				:							List[Any]									=   i + 2

  # this condition checks the prime
  # number n is greater than 2

  if n > 2:
    count += 1
  return count


if __name__ == "__main__":
 _A		:      List[Any]						   =5_1_2_4_2_1_8_3
 print(f"""The number of distinct prime factors is/are {exact_prime_factor_count(n)}""")
 print(f"""The value of log(log(n)) is {math.log(math.log(n)):.4f}""")