code: 
  
  
  """simple docstring"""
  
  
  
  
  import math
  
  
  
  
  
  def 			a_   (  lowercase__   :Tuple    ):
  			__lowerCamelCase        =			0
  			if n % 2 == 0:
  						count += 1
  						while n % 2 == 0:
  									__lowerCamelCase        =			int(n / 2    )
      # the n input value must be odd so that
      # we can skip one element (ie i += 2)
  
  			__lowerCamelCase        =			3
  
  			while i <= int(math.sqrt(lowercase__    )    ):
  						if n % i == 0:
  									count += 1
  									while n % i == 0:
  												__lowerCamelCase        =			int(n / i    )
  						__lowerCamelCase        =			i + 2
  
  			# this condition checks the prime
  			# number n is greater than 2
  
  			if n > 2:
  						count += 1
  			return count
  
  
  if __name__ == "__main__":
  					__magic_name__	:   Optional[int]          =							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}""")
  
  
  
  
  
style_context: 
  
  
  """simple docstring"""
  
  
  
  
  from __future__ import annotations
  
  import re
  
  
  
  
  
  def 			a_   (  lowercase__   :list[str]    ):
  
  			def alphanum_key(lowercase__   :int    ):
  						return [int(lowercase__    ) if s.isdigit() else s.lower() for s in re.split("""([0-9]+)""", lowercase__    )]
  
  			return sorted(lowercase__, key=lowercase__    )
  
  
  if __name__ == "__main__":
  					import doctest
  
  					doctest.testmod()
  
  
  
  
  