code: '''simple docstring'''
  
  
  
  
  
  import math
  
  
  def 					__lowerCAmelCase			(  _A					):
  
  
  
  							"""simple docstring"""
  
  
  							_lowercase				=	0
  							if n % 2 == 0:
  														count += 1
  														while n % 2 == 0:
  																					_lowercase				=	int(n / 2					)
      # the n input value must be odd so that
      # we can skip one element (ie i += 2)
  
  							_lowercase				=	3
  
  							while i <= int(math.sqrt(_A					)					):
  														if n % i == 0:
  																					count += 1
  																					while n % i == 0:
  																												_lowercase				=	int(n / i					)
  														_lowercase				=	i + 2
  
  							# this condition checks the prime
  							# number n is greater than 2
  
  							if n > 2:
  														count += 1
  							return count
  
  
  if __name__ == "__main__":
  				A_:      Optional[Any]        =			5124_2183
  				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: import math
  from timeit import timeit
  
  
  def 					__lowerCAmelCase			(  _A					):
  
  
  
  							"""simple docstring"""
  
  
  							_lowercase				=	0
  							_lowercase				=	abs(_A					)
  							while True:
  														_lowercase				=	n // 10
  														digits += 1
  														if n == 0:
  																					break
  							return digits
  
  
  def 					__lowerCAmelCase			(  _A					):
  
  
  
  							"""simple docstring"""
  
  
  							return 1 if n == 0 else math.floor(math.log(abs(_A					) ,10					) + 1					)
  
  
  def 					__lowerCAmelCase			(  _A					):
  
  
  
  							"""simple docstring"""
  
  
  							return len(str(abs(_A					)					)					)
  
  
  def 					__lowerCAmelCase			(  ):
  
  
  
  							"""simple docstring"""
  
  
  							from collections.abc import Callable
  
  							def benchmark_a_function(_A ,_A					) -> None:
  														_lowercase				=	f'''{func.__name__}({value})'''
  														_lowercase				=	timeit(f'''__main__.{call}''' ,setup="""import __main__"""					)
  														print(f'''{call}: {func(_A					)} -- {timing} seconds'''					)
  
  							for value in (262_144, 1_125_899_906_842_624, 1_267_650_600_228_229_401_496_703_205_376):
  														for func in (num_digits, num_digits_fast, num_digits_faster):
  																					benchmark_a_function(_A ,_A					)
  														print()
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  				benchmark()
  
  
  