'''simple docstring'''

class   SCREAMING_SNAKE_CASE			:







		"""simple docstring"""






		def __init__(   self		,						__A		,						__A		,						__A				) ->     Tuple:
								_lowerCAmelCase										=None
								_lowerCAmelCase										=None
								_lowerCAmelCase										=graph

								self._normalize_graph(__A		,						__A				)
								_lowerCAmelCase										=len(__A				)
								_lowerCAmelCase										=None






		def 		UpperCamelCase__       (   self		,						__A		,						__A				) ->     Optional[int]:
								if sources is int:
														_lowerCAmelCase										=[sources]
								if sinks is int:
														_lowerCAmelCase										=[sinks]

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

								_lowerCAmelCase										=sources[0]
								_lowerCAmelCase										=sinks[0]

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

														_lowerCAmelCase										=len(self.graph				) + 1
														for room in self.graph:
																				room.insert(0		,						0				)
														self.graph.insert(0		,						[0] * size				)
														for i in sources:
																				_lowerCAmelCase										=max_input_flow
														_lowerCAmelCase										=0

														_lowerCAmelCase										=len(self.graph				) + 1
														for room in self.graph:
																				room.append(0				)
														self.graph.append([0] * size				)
														for i in sinks:
																				_lowerCAmelCase										=max_input_flow
														_lowerCAmelCase										=size - 1






		def 		UpperCamelCase__       (   self				) ->     Optional[Any]:
								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 		UpperCamelCase__       (   self		,						__A				) ->     Dict:
								_lowerCAmelCase										=algorithm(self				)

class   SCREAMING_SNAKE_CASE			:







		"""simple docstring"""






		def __init__(   self		,						__A				) ->     Dict:
								_lowerCAmelCase										=flow_network
								_lowerCAmelCase										=flow_network.verticesCount
								_lowerCAmelCase										=flow_network.sourceIndex
								_lowerCAmelCase										=flow_network.sinkIndex
								# it's just a reference, so you shouldn't change
								# it in your algorithms, use deep copy before doing that
								_lowerCAmelCase										=flow_network.graph
								_lowerCAmelCase										=False






		def 		UpperCamelCase__       (   self				) ->     List[str]:
								if not self.executed:
														self._algorithm()
														_lowerCAmelCase										=True






		def 		UpperCamelCase__       (   self				) ->     Tuple:
								pass

class   SCREAMING_SNAKE_CASE			(						__lowercase):







		"""simple docstring"""






		def __init__(   self		,						__A				) ->     List[Any]:
								super().__init__(__A				)
								# use this to save your result
								_lowerCAmelCase										=-1






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

								return self.maximum_flow

class   SCREAMING_SNAKE_CASE			(						__lowercase):







		"""simple docstring"""






		def __init__(   self		,						__A				) ->     List[str]:
								super().__init__(__A				)

								_lowerCAmelCase										=[[0] * self.verticies_count for i in range(self.verticies_count				)]

								_lowerCAmelCase										=[0] * self.verticies_count
								_lowerCAmelCase										=[0] * self.verticies_count






		def 		UpperCamelCase__       (   self				) ->     List[str]:
								_lowerCAmelCase										=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										=[
								    i
								    for i in range(self.verticies_count				)
								    if i != self.source_index and i != self.sink_index
								]

								# move through list
								_lowerCAmelCase										=0
								while i < len(__A				):
														_lowerCAmelCase										=vertices_list[i]
														_lowerCAmelCase										=self.heights[vertex_index]
														self.process_vertex(__A				)
														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(__A				)				)
																				_lowerCAmelCase										=0
														else:
																				i += 1

								_lowerCAmelCase										=sum(self.preflow[self.source_index]				)






		def 		UpperCamelCase__       (   self		,						__A				) ->     Union[str, Any]:
								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(__A		,						__A				)

														self.relabel(__A				)






		def 		UpperCamelCase__       (   self		,						__A		,						__A				) ->     List[Any]:
								_lowerCAmelCase										=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 		UpperCamelCase__       (   self		,						__A				) ->     Optional[int]:
								_lowerCAmelCase										=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										=self.heights[to_index]

								if min_height is not None:
														_lowerCAmelCase										=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 							UpperCamelCase__			(			a__      ):


						'''simple docstring'''






						_lowerCAmelCase										=set()
						# To detect a back edge, keep track of vertices currently in the recursion stack
						_lowerCAmelCase										=set()
						return any(
						    node not in visited and depth_first_search(a__			,      a__			,      a__			,      a__      )
						    for node in graph      )



def 							UpperCamelCase__			(			a__			,      a__			,      a__			,      a__      ):


						'''simple docstring'''






						visited.add(a__      )
						rec_stk.add(a__      )

						for node in graph[vertex]:
												if node not in visited:
																		if depth_first_search(a__			,      a__			,      a__			,      a__      ):
																								return True
												elif node in rec_stk:
																		return True

    # The node needs to be removed from recursion stack before function ends
						rec_stk.remove(a__      )
						return False


if __name__ == "__main__":
							from doctest import testmod

							testmod()





