






def 						_UpperCamelCase (     UpperCamelCase_							:       str		)	-> int:

						"""simple docstring"""



						lowerCAmelCase__         =    5381
						for x in s:
												lowerCAmelCase__         =    ((hash_value << 5) + hash_value) + ord(UpperCamelCase_		)
						return hash_value & 0XFFFFFFFF













from __future__ import annotations







def 						_UpperCamelCase (     UpperCamelCase_							:       list[int]		)	-> list[int]:

						"""simple docstring"""



						if not list_of_ints:
												return []

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

						lowerCAmelCase__         =    max(len(bin(UpperCamelCase_		)[2:]		) for x in list_of_ints		)
						return _msd_radix_sort(UpperCamelCase_     ,							UpperCamelCase_		)







def 						_UpperCamelCase (     UpperCamelCase_							:       list[int]     ,							UpperCamelCase_							:       int		)	-> list[int]:

						"""simple docstring"""



						if bit_position == 0 or len(UpperCamelCase_		) 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(UpperCamelCase_		)
												else:
																		# number has a zero at bit bit_position
																		zeros.append(UpperCamelCase_		)

    # recursively split both lists further
						lowerCAmelCase__         =    _msd_radix_sort(UpperCamelCase_     ,							bit_position - 1		)
						lowerCAmelCase__         =    _msd_radix_sort(UpperCamelCase_     ,							bit_position - 1		)

						# recombine lists
						lowerCAmelCase__         =    zeros
						res.extend(UpperCamelCase_		)

						return res







def 						_UpperCamelCase (     UpperCamelCase_							:       list[int]		)	-> Any:

						"""simple docstring"""



						lowerCAmelCase__         =    len(UpperCamelCase_		)
						if not list_of_ints or length == 1:
												return

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

						lowerCAmelCase__         =    max(len(bin(UpperCamelCase_		)[2:]		) for x in list_of_ints		)
						_msd_radix_sort_inplace(UpperCamelCase_     ,							UpperCamelCase_     ,							0     ,							UpperCamelCase_		)







def 						_UpperCamelCase (     UpperCamelCase_							:       list[int]     ,							UpperCamelCase_							:       int     ,							UpperCamelCase_							:       int     ,							UpperCamelCase_							:       int		)	-> int:

						"""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(UpperCamelCase_     ,							UpperCamelCase_     ,							UpperCamelCase_     ,							UpperCamelCase_		)
						_msd_radix_sort_inplace(UpperCamelCase_     ,							UpperCamelCase_     ,							UpperCamelCase_     ,							UpperCamelCase_		)


if __name__ == "__main__":
					import doctest

					doctest.testmod()





