





import math

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

		UpperCamelCase__								=						3

		while i <= int(math.sqrt(_SCREAMING_SNAKE_CASE							)							):
				if n % i == 0:
						count += 1
						while n % i == 0:
								UpperCamelCase__								=						int(n / i							)
				UpperCamelCase__								=						i + 2

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

		if n > 2:
				count += 1
		return count


if __name__ == "__main__":
				__lowerCAmelCase 	=      51_242_183
				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"""







def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				list[int]						)    ->     int:







     '''simple docstring'''


     if not isinstance(_SCREAMING_SNAKE_CASE  ,       _SCREAMING_SNAKE_CASE						) or not all(
         isinstance(_SCREAMING_SNAKE_CASE  ,       _SCREAMING_SNAKE_CASE						) and item >= 0 for item in citations						):
          raise ValueError('The citations should be a list of non negative integers.'						)

     citations.sort()
     __A					:					Any								=		len(_SCREAMING_SNAKE_CASE						)

     for i in range(_SCREAMING_SNAKE_CASE						):
          if citations[len_citations - 1 - i] <= i:
               return i

     return len_citations


if __name__ == "__main__":
       import doctest

       doctest.testmod()



