



from __future__ import annotations






def        a( A			:       list[int]			)						->			list[int]:
					"""simple docstring"""





					if not list_of_ints:
										return []

					if min(A			) < 0:
										raise ValueError("All numbers must be positive"			)

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






def        a( A			:       list[int]					,	A			:       int			)						->			list[int]:
					"""simple docstring"""





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

					a   	=  []
					a   	=  []
					# 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(A			)
										else:
															# number has a zero at bit bit_position
															zeros.append(A			)

    # recursively split both lists further
					a   	=  _msd_radix_sort(A					,	bit_position - 1			)
					a   	=  _msd_radix_sort(A					,	bit_position - 1			)

					# recombine lists
					a   	=  zeros
					res.extend(A			)

					return res






def        a( A			:       list[int]			)						->			Optional[int]:
					"""simple docstring"""





					a   	=  len(A			)
					if not list_of_ints or length == 1:
										return

					if min(A			) < 0:
										raise ValueError("All numbers must be positive"			)

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






def        a( A			:       list[int]					,	A			:       int					,	A			:       int					,	A			:       int			)						->			Any:
					"""simple docstring"""





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

					bit_position -= 1

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

										if changed:
															continue

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

					_msd_radix_sort_inplace(A					,	A					,	A					,	A			)
					_msd_radix_sort_inplace(A					,	A					,	A					,	A			)


if __name__ == "__main__":
				import doctest

				doctest.testmod()





_lowercase:					Optional[Any]      =						[[0, 1, 1], [0, 0, 1], [1, 0, 0]]



class       _lowercase				:





	"""simple docstring"""




	def __init__(self						,			lowerCamelCase_						):
						"""simple docstring"""

						a   	=  name
						a   	=  []
						a   	=  []




	def 	UpperCamelCase_			(self						,			lowerCamelCase_						):
						"""simple docstring"""

						self.inbound.append(lowerCamelCase_						)




	def 	UpperCamelCase_			(self						,			lowerCamelCase_						):
						"""simple docstring"""

						self.outbound.append(lowerCamelCase_						)




	def __repr__(self						):
						"""simple docstring"""

						return F'''<node={self.name} inbound={self.inbound} outbound={self.outbound}>'''






def        a( A			:       Optional[Any]					,	A			:       Optional[int]=3					,	A			:       str=0.85			)						->			Optional[Any]:
					"""simple docstring"""





					a   	=  {}
					for node in nodes:
										a   	=  1

					a   	=  {}
					for node in nodes:
										a   	=  len(node.outbound			)

					for i in range(A			):
										print(f'''======= Iteration {i + 1} ======='''			)
										for _, node in enumerate(A			):
															a   	=  (1 - d) + d * sum(
															    ranks[ib] / outbounds[ib] for ib in node.inbound			)
										print(A			)






def        a( )						->			List[Any]:
					"""simple docstring"""





					a   	=  list(input("Enter Names of the Nodes: "			).split()			)

					a   	=  [Node(A			) for name in names]

					for ri, row in enumerate(A			):
										for ci, col in enumerate(A			):
															if col == 1:
																				nodes[ci].add_inbound(names[ri]			)
																				nodes[ri].add_outbound(names[ci]			)

					print("======= Nodes ======="			)
					for node in nodes:
										print(A			)

					page_rank(A			)


if __name__ == "__main__":
				main()
