


def       _a	(					SCREAMING_SNAKE_CASE						:					list[int]  ):







 """simple docstring"""



 if len(_a  ) > 1:
  UpperCamelCase__       :     Any 							= len(_a  ) // 2  # Finds the middle of the array
  UpperCamelCase__       :     Tuple 							= arr[
      :middle_length
  ]  # Creates an array of the elements in the first half.
  UpperCamelCase__       :     int 							= arr[
      middle_length:
  ]  # Creates an array of the elements in the second half.
  UpperCamelCase__       :     Dict 							= len(_a  )
  UpperCamelCase__       :     str 							= len(_a  )
  merge(_a  )  # Starts sorting the left.
  merge(_a  )  # Starts sorting the right
  UpperCamelCase__       :     List[str] 							= 0  # Left Counter
  UpperCamelCase__       :     Tuple 							= 0  # Right Counter
  UpperCamelCase__       :     str 							= 0  # Position Counter
  while (
      left_index < left_size and right_index < right_size
  ):  # Runs until the lowers size of the left and right are sorted.
   if left_array[left_index] < right_array[right_index]:
    UpperCamelCase__       :     Tuple 							= left_array[left_index]
    left_index += 1
   else:
    UpperCamelCase__       :     int 							= right_array[right_index]
    right_index += 1
   index += 1
  while (
      left_index < left_size
  ):  # Adds the left over elements in the left half of the array
   UpperCamelCase__       :     Union[str, Any] 							= left_array[left_index]
   left_index += 1
   index += 1
  while (
      right_index < right_size
  ):  # Adds the left over elements in the right half of the array
   UpperCamelCase__       :     Tuple 							= right_array[right_index]
   right_index += 1
   index += 1
 return arr


if __name__ == "__main__":
       import doctest

       doctest.testmod()







import math







def       lowerCamelCase_  (    _a       :						int    ):



    '''simple docstring'''




    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5   ,		int(math.sqrt(_a    ) + 1    )   ,		6    ):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True







def       lowerCamelCase_  (    _a       :						int = 6008_5147_5143    ):



    '''simple docstring'''




    try:
        UpperCAmelCase_     :       str  		=					int(_a    )
    except (TypeError, ValueError):
        raise TypeError("""Parameter n must be int or castable to int."""    )
    if n <= 0:
        raise ValueError("""Parameter n must be greater than or equal to one."""    )
    UpperCAmelCase_     :       Optional[int]  		=					0
    if is_prime(_a    ):
        return n
    while n % 2 == 0:
        n //= 2
    if is_prime(_a    ):
        return n
    for i in range(3   ,		int(math.sqrt(_a    )    ) + 1   ,		2    ):
        if n % i == 0:
            if is_prime(n // i    ):
                UpperCAmelCase_     :       Optional[int]  		=					n // i
                break
            elif is_prime(_a    ):
                UpperCAmelCase_     :       str  		=					i
    return max_number


if __name__ == "__main__":
      print(F"{solution() = }")
