




"""simple docstring"""






class lowerCAmelCase__			:






			'''simple docstring'''



			def __init__(						self						,   lowercase						,   lowercase						,   lowercase						):
							_lowerCamelCase  :    List[str]					=					None
							_lowerCamelCase  :    int					=					None
							_lowerCamelCase  :    List[Any]					=					graph

							self._normalize_graph(lowercase						,   lowercase						)
							_lowerCamelCase  :    str					=					len(lowercase						)
							_lowerCamelCase  :    Optional[Any]					=					None
			def       A_					(						self						,   lowercase						,   lowercase						):
							if sources is int:
											_lowerCamelCase  :    str					=					[sources]
							if sinks is int:
											_lowerCamelCase  :    str					=					[sinks]

							if len(lowercase						) == 0 or len(lowercase						) == 0:
											return

							_lowerCamelCase  :    Optional[Any]					=					sources[0]
							_lowerCamelCase  :    Optional[int]					=					sinks[0]

							# make fake vertex if there are more
							# than one source or sink
							if len(lowercase						) > 1 or len(lowercase						) > 1:
											_lowerCamelCase  :    int					=					0
											for i in sources:
															max_input_flow += sum(self.graph[i]						)

											_lowerCamelCase  :    Optional[int]					=					len(self.graph						) + 1
											for room in self.graph:
															room.insert(0						,   0						)
											self.graph.insert(0						,   [0] * size						)
											for i in sources:
															_lowerCamelCase  :    Optional[int]					=					max_input_flow
											_lowerCamelCase  :    List[Any]					=					0

											_lowerCamelCase  :    int					=					len(self.graph						) + 1
											for room in self.graph:
															room.append(0						)
											self.graph.append([0] * size						)
											for i in sinks:
															_lowerCamelCase  :    Dict					=					max_input_flow
											_lowerCamelCase  :    Any					=					size - 1
			def       A_					(						self						):
							if self.maximum_flow_algorithm is None:
											raise Exception('You need to set maximum flow algorithm before.'						)
							if self.source_index is None or self.sink_index is None:
											return 0

							self.maximum_flow_algorithm.execute()
							return self.maximum_flow_algorithm.getMaximumFlow()






			def       A_					(						self						,   lowercase						):
							_lowerCamelCase  :    List[Any]					=					algorithm(self						)






class lowerCAmelCase__			:






			'''simple docstring'''



			def __init__(						self						,   lowercase						):
							_lowerCamelCase  :    Optional[Any]					=					flow_network
							_lowerCamelCase  :    List[str]					=					flow_network.verticesCount
							_lowerCamelCase  :    Dict					=					flow_network.sourceIndex
							_lowerCamelCase  :    List[str]					=					flow_network.sinkIndex
							# it's just a reference, so you shouldn't change
							# it in your algorithms, use deep copy before doing that
							_lowerCamelCase  :    Tuple					=					flow_network.graph
							_lowerCamelCase  :    Optional[int]					=					False
			def       A_					(						self						):
							if not self.executed:
											self._algorithm()
											_lowerCamelCase  :    int					=					True






			def       A_					(						self						):
							pass






class lowerCAmelCase__			(  lowercase		):






			'''simple docstring'''



			def __init__(						self						,   lowercase						):
							super().__init__(lowercase						)
							# use this to save your result
							_lowerCamelCase  :    Dict					=					-1






			def       A_					(						self						):
							if not self.executed:
											raise Exception('You should execute algorithm before using its result!'						)

							return self.maximum_flow






class lowerCAmelCase__			(  lowercase		):






			'''simple docstring'''



			def __init__(						self						,   lowercase						):
							super().__init__(lowercase						)

							_lowerCamelCase  :    Optional[int]					=					[[0] * self.verticies_count for i in range(self.verticies_count						)]

							_lowerCamelCase  :    Tuple					=					[0] * self.verticies_count
							_lowerCamelCase  :    int					=					[0] * self.verticies_count
			def       A_					(						self						):
							_lowerCamelCase  :    int					=					self.verticies_count

							# push some substance to graph
							for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]						):
											self.preflow[self.source_index][nextvertex_index] += bandwidth
											self.preflow[nextvertex_index][self.source_index] -= bandwidth
											self.excesses[nextvertex_index] += bandwidth

							# Relabel-to-front selection rule
							_lowerCamelCase  :    List[Any]					=					[
							    i
							    for i in range(self.verticies_count						)
							    if i != self.source_index and i != self.sink_index
							]

							# move through list
							_lowerCamelCase  :    Dict					=					0
							while i < len(lowercase						):
											_lowerCamelCase  :    Union[str, Any]					=					vertices_list[i]
											_lowerCamelCase  :    int					=					self.heights[vertex_index]
											self.process_vertex(lowercase						)
											if self.heights[vertex_index] > previous_height:
															# if it was relabeled, swap elements
															# and start from 0 index
															vertices_list.insert(0						,   vertices_list.pop(lowercase						)						)
															_lowerCamelCase  :    Any					=					0
											else:
															i += 1

							_lowerCamelCase  :    int					=					sum(self.preflow[self.source_index]						)
			def       A_					(						self						,   lowercase						):
							while self.excesses[vertex_index] > 0:
											for neighbour_index in range(self.verticies_count						):
															# if it's neighbour and current vertex is higher
															if (
															    self.graph[vertex_index][neighbour_index]
															    - self.preflow[vertex_index][neighbour_index]
															    > 0
															    and self.heights[vertex_index] > self.heights[neighbour_index]
															):
																			self.push(lowercase						,   lowercase						)

											self.relabel(lowercase						)
			def       A_					(						self						,   lowercase						,   lowercase						):
							_lowerCamelCase  :    Any					=					min(
							    self.excesses[from_index]						,   self.graph[from_index][to_index] - self.preflow[from_index][to_index]						,   )
							self.preflow[from_index][to_index] += preflow_delta
							self.preflow[to_index][from_index] -= preflow_delta
							self.excesses[from_index] -= preflow_delta
							self.excesses[to_index] += preflow_delta






			def       A_					(						self						,   lowercase						):
							_lowerCamelCase  :    str					=					None
							for to_index in range(self.verticies_count						):
											if (
											    self.graph[vertex_index][to_index]
											    - self.preflow[vertex_index][to_index]
											    > 0
											) and (min_height is None or self.heights[to_index] < min_height):
															_lowerCamelCase  :    Optional[int]					=					self.heights[to_index]

							if min_height is not None:
											_lowerCamelCase  :    int					=					min_height + 1


if __name__ == "__main__":
			lowercase__  		=		[0]
			lowercase__  		=		[3]
			# graph = [
			#     [0, 0, 4, 6, 0, 0],
			#     [0, 0, 5, 2, 0, 0],
			#     [0, 0, 0, 0, 4, 4],
			#     [0, 0, 0, 0, 6, 6],
			#     [0, 0, 0, 0, 0, 0],
			#     [0, 0, 0, 0, 0, 0],
			# ]
			lowercase__  		=		[[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

			# prepare our network
			lowercase__  		=		FlowNetwork(graph, entrances, exits)
			# set algorithm
			flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
			# and calculate
			lowercase__  		=		flow_network.find_maximum_flow()

			print(F"maximum flow is {maximum_flow}")





"""simple docstring"""






def   _snake_case    (       lowercase__ = 1000	):
				_lowerCamelCase,				_lowerCamelCase  :    Optional[int]					=					1, 1
				_lowerCamelCase  :    int					=					[]
				for i in range(1							,					n + 1	):
								_lowerCamelCase  :    Tuple					=					prev_numerator + 2 * prev_denominator
								_lowerCamelCase  :    str					=					prev_numerator + prev_denominator
								if len(str(lowercase__	)	) > len(str(lowercase__	)	):
												result.append(lowercase__	)
								_lowerCamelCase  :    Dict					=					numerator
								_lowerCamelCase  :    Optional[int]					=					denominator

				return len(lowercase__	)


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