




'''simple docstring'''



def 				SCREAMING_SNAKE_CASE_				(							__A       :				list[int]						)				->				int:

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

   citations.sort()
   _SCREAMING_SNAKE_CASE =   len(__A						)

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

   return len_citations


if __name__ == "__main__":
 import doctest

 doctest.testmod()







'''simple docstring'''



import math
def 				SCREAMING_SNAKE_CASE_				(							__A       :				Tuple						)				->				List[Any]:
   _SCREAMING_SNAKE_CASE =   0
   if n % 2 == 0:
      count += 1
      while n % 2 == 0:
         _SCREAMING_SNAKE_CASE =   int(n / 2						)
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

   _SCREAMING_SNAKE_CASE =   3

   while i <= int(math.sqrt(__A						)						):
      if n % i == 0:
         count += 1
         while n % i == 0:
            _SCREAMING_SNAKE_CASE =   int(n / i						)
      _SCREAMING_SNAKE_CASE =   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_24_21_83
 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}''')

