


"""simple docstring"""
from __future__ import annotations






def 						lowercase				(	_snake_case		: list	,  _snake_case		: list	)	->list:
	"""simple docstring"""





	__snake_case      :		List[Any]         =							[None] * (len(_snake_case	) + len(_snake_case	))

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

	while pointera < len(_snake_case	) and pointera < len(_snake_case	):
		if left_half[pointera] < right_half[pointera]:
			__snake_case      :		str         =							left_half[pointera]
			pointera += 1
			index += 1
		else:
			__snake_case      :		List[str]         =							right_half[pointera]
			pointera += 1
			index += 1
	while pointera < len(_snake_case	):
		__snake_case      :		List[Any]         =							left_half[pointera]
		pointera += 1
		index += 1

	while pointera < len(_snake_case	):
		__snake_case      :		str         =							right_half[pointera]
		pointera += 1
		index += 1

	return sorted_array






def 						lowercase				(	_snake_case		: list	)	->list:
	"""simple docstring"""





	if len(_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
	__snake_case      :		int         =							0 + (len(_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
	__snake_case      :		Union[str, Any]         =							array[:middle]
	__snake_case      :		List[Any]         =							array[middle:]

	return merge(merge_sort(_snake_case	)	,  merge_sort(_snake_case	)	)


if __name__ == "__main__":
			import doctest

			doctest.testmod()











def       lowerCAmelCase_      (	lowerCamelCase:							str    )       ->      int:


      '''simple docstring'''




      lowerCamelCase__   	=					53_81
      for x in s:
            lowerCamelCase__   	=					((hash_value << 5) + hash_value) + ord(lowerCamelCase    )
      return hash_value & 0Xffff_ffff