


"""simple docstring"""



from __future__ import annotations
def     UpperCAmelCase    (					_lowercase   :      Any  )	->   list[int]:


	"""simple docstring"""




	if not list_of_ints:
		return []

	if min(_lowercase  ) < 0:
		raise ValueError('''All numbers must be positive'''  )

	lowerCAmelCase_			       = max(len(bin(_lowercase  )[2:]  ) for x in list_of_ints  )
	return _msd_radix_sort(_lowercase ,      _lowercase  )
def     UpperCAmelCase    (					_lowercase   :      Optional[int] ,      _lowercase   :      Tuple  )	->   list[int]:


	"""simple docstring"""




	if bit_position == 0 or len(_lowercase  ) in [0, 1]:
		return list_of_ints

	lowerCAmelCase_			       = []
	lowerCAmelCase_			       = []
	# Split numbers based on bit at bit_position from the right
	for number in list_of_ints:
		if (number >> (bit_position - 1)) & 1:
			# number has a one at bit bit_position
			ones.append(_lowercase  )
		else:
			# number has a zero at bit bit_position
			zeros.append(_lowercase  )

    # recursively split both lists further
	lowerCAmelCase_			       = _msd_radix_sort(_lowercase ,      bit_position - 1  )
	lowerCAmelCase_			       = _msd_radix_sort(_lowercase ,      bit_position - 1  )

	# recombine lists
	lowerCAmelCase_			       = zeros
	res.extend(_lowercase  )

	return res
def     UpperCAmelCase    (					_lowercase   :      Dict  )	->   List[Any]:


	"""simple docstring"""




	lowerCAmelCase_			       = len(_lowercase  )
	if not list_of_ints or length == 1:
		return

	if min(_lowercase  ) < 0:
		raise ValueError('''All numbers must be positive'''  )

	lowerCAmelCase_			       = max(len(bin(_lowercase  )[2:]  ) for x in list_of_ints  )
	_msd_radix_sort_inplace(_lowercase ,      _lowercase ,      0 ,      _lowercase  )
def     UpperCAmelCase    (					_lowercase   :      int ,      _lowercase   :      Any ,      _lowercase   :      Dict ,      _lowercase   :      Union[str, Any]  )	->   List[str]:


	"""simple docstring"""




	if bit_position == 0 or end_index - begin_index <= 1:
		return

	bit_position -= 1

	lowerCAmelCase_			       = begin_index
	lowerCAmelCase_			       = end_index - 1
	while i <= j:
		lowerCAmelCase_			       = False
		if not (list_of_ints[i] >> bit_position) & 1:
			# found zero at the beginning
			i += 1
			lowerCAmelCase_			       = True
		if (list_of_ints[j] >> bit_position) & 1:
			# found one at the end
			j -= 1
			lowerCAmelCase_			       = True

		if changed:
			continue

		lowerCAmelCase_       ,  lowerCAmelCase_			       = list_of_ints[j], list_of_ints[i]
		j -= 1
		if j != i:
			i += 1

	_msd_radix_sort_inplace(_lowercase ,      _lowercase ,      _lowercase ,      _lowercase  )
	_msd_radix_sort_inplace(_lowercase ,      _lowercase ,      _lowercase ,      _lowercase  )


if __name__ == "__main__":
			import doctest

			doctest.testmod()



"""simple docstring"""



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


	"""simple docstring"""




	lowerCAmelCase_			       = len(_lowercase  )
	if n in (0, 1):
		return 0
	return sum(query * (n - i - 1) for i, query in enumerate(sorted(_lowercase  )  )  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()