


"""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}""")








"""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()




