




import math

def   A   (   _SCREAMING_SNAKE_CASE					)			->				Optional[int]:
       lowerCamelCase     :   Union[str, Any]    				=      0
       if n % 2 == 0:
              count += 1
              while n % 2 == 0:
                     lowerCamelCase     :   List[Any]    				=      int(n / 2					)
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

       lowerCamelCase     :   int    				=      3

       while i <= int(math.sqrt(lowercase__					)					):
              if n % i == 0:
                     count += 1
                     while n % i == 0:
                            lowerCamelCase     :   List[str]    				=      int(n / i					)
              lowerCamelCase     :   Optional[int]    				=      i + 2

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

       if n > 2:
              count += 1
       return count


if __name__ == "__main__":
       SCREAMING_SNAKE_CASE__ :   Optional[int]						=     51242183
       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}''')








from __future__ import annotations

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				list:
       lowerCamelCase     :   int    				=      [None] * (len(_SCREAMING_SNAKE_CASE					) + len(_SCREAMING_SNAKE_CASE					))

       lowerCamelCase     :   Any    				=      0  # pointer to current index for left Half
       lowerCamelCase     :   int    				=      0  # pointer to current index for the right Half
       lowerCamelCase     :   Optional[int]    				=      0  # pointer to current index for the sorted array Half

       while pointera < len(_SCREAMING_SNAKE_CASE					) and pointera < len(_SCREAMING_SNAKE_CASE					):
              if left_half[pointera] < right_half[pointera]:
                     lowerCamelCase     :   Any    				=      left_half[pointera]
                     pointera += 1
                     index += 1
              else:
                     lowerCamelCase     :   Any    				=      right_half[pointera]
                     pointera += 1
                     index += 1
       while pointera < len(_SCREAMING_SNAKE_CASE					):
              lowerCamelCase     :   Optional[Any]    				=      left_half[pointera]
              pointera += 1
              index += 1

       while pointera < len(_SCREAMING_SNAKE_CASE					):
              lowerCamelCase     :   str    				=      right_half[pointera]
              pointera += 1
              index += 1

       return sorted_array

def   A   (   _SCREAMING_SNAKE_CASE					)			->				list:
       if len(_SCREAMING_SNAKE_CASE					) <= 1:
              return array
       # the actual formula to calculate the middle element = left + (right - left) // 2
       # this avoids integer overflow in case of large N
       lowerCamelCase     :   int    				=      0 + (len(_SCREAMING_SNAKE_CASE					) - 0) // 2

       # Split the array into halves till the array length becomes equal to One
       # merge the arrays of single length returned by mergeSort function and
       # pass them into the merge arrays function which merges the array
       lowerCamelCase     :   Optional[Any]    				=      array[:middle]
       lowerCamelCase     :   Optional[Any]    				=      array[middle:]

       return merge(merge_sort(_SCREAMING_SNAKE_CASE					)				,merge_sort(_SCREAMING_SNAKE_CASE					)					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()






