



'''simple docstring'''
import torch






def A__   (					):
						if torch.cuda.is_available():
												_UpperCamelCase :		Optional[Any]			    =       torch.cuda.device_count()
						else:
												_UpperCamelCase :		str			    =       0
						print(f'Successfully ran on {num_gpus} GPUs'							)


if __name__ == "__main__":
					main()







'''simple docstring'''
class 							lowercase__     :





	def __init__(			self :    List[str]			,lowerCamelCase__ :    List[Any]			,lowerCamelCase__ :    Optional[int]			,lowerCamelCase__ :    Any			):







							'''simple docstring'''
							_UpperCamelCase :		Dict			    =       None
							_UpperCamelCase :		List[Any]			    =       None
							_UpperCamelCase :		int			    =       graph

							self._normalize_graph(lowerCamelCase__			,lowerCamelCase__			)
							_UpperCamelCase :		List[str]			    =       len(lowerCamelCase__			)
							_UpperCamelCase :		Tuple			    =       None





	def      UpperCamelCase_  (			self :    Any			,lowerCamelCase__ :    Optional[Any]			,lowerCamelCase__ :    Any			):







							'''simple docstring'''
							if sources is int:
													_UpperCamelCase :		Optional[int]			    =       [sources]
							if sinks is int:
													_UpperCamelCase :		Union[str, Any]			    =       [sinks]

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

							_UpperCamelCase :		List[str]			    =       sources[0]
							_UpperCamelCase :		str			    =       sinks[0]

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

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

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





	def      UpperCamelCase_  (			self :    List[str]			):







							'''simple docstring'''
							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 :    Any			,lowerCamelCase__ :    Any			):







							'''simple docstring'''
							_UpperCamelCase :		str			    =       algorithm(self			)






class 							lowercase__     :





	def __init__(			self :    List[str]			,lowerCamelCase__ :    Optional[int]			):







							'''simple docstring'''
							_UpperCamelCase :		Optional[Any]			    =       flow_network
							_UpperCamelCase :		List[str]			    =       flow_network.verticesCount
							_UpperCamelCase :		List[str]			    =       flow_network.sourceIndex
							_UpperCamelCase :		Any			    =       flow_network.sinkIndex
							# it's just a reference, so you shouldn't change
							# it in your algorithms, use deep copy before doing that
							_UpperCamelCase :		List[Any]			    =       flow_network.graph
							_UpperCamelCase :		Any			    =       False





	def      UpperCamelCase_  (			self :    str			):







							'''simple docstring'''
							if not self.executed:
													self._algorithm()
													_UpperCamelCase :		Any			    =       True





	def      UpperCamelCase_  (			self :    Any			):







							'''simple docstring'''
							pass






class 							lowercase__     (							lowercase       ):





	def __init__(			self :    Union[str, Any]			,lowerCamelCase__ :    List[str]			):







							'''simple docstring'''
							super().__init__(lowerCamelCase__			)
							# use this to save your result
							_UpperCamelCase :		Tuple			    =       -1





	def      UpperCamelCase_  (			self :    Dict			):







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

							return self.maximum_flow






class 							lowercase__     (							lowercase       ):





	def __init__(			self :    Optional[Any]			,lowerCamelCase__ :    Dict			):







							'''simple docstring'''
							super().__init__(lowerCamelCase__			)

							_UpperCamelCase :		Dict			    =       [[0] * self.verticies_count for i in range(self.verticies_count			)]

							_UpperCamelCase :		Optional[Any]			    =       [0] * self.verticies_count
							_UpperCamelCase :		List[str]			    =       [0] * self.verticies_count





	def      UpperCamelCase_  (			self :    Union[str, Any]			):







							'''simple docstring'''
							_UpperCamelCase :		Dict			    =       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
							_UpperCamelCase :		List[str]			    =       [
							    i
							    for i in range(self.verticies_count			)
							    if i != self.source_index and i != self.sink_index
							]

							# move through list
							_UpperCamelCase :		int			    =       0
							while i < len(lowerCamelCase__			):
													_UpperCamelCase :		List[Any]			    =       vertices_list[i]
													_UpperCamelCase :		str			    =       self.heights[vertex_index]
													self.process_vertex(lowerCamelCase__			)
													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(lowerCamelCase__			)			)
																			_UpperCamelCase :		Dict			    =       0
													else:
																			i += 1

							_UpperCamelCase :		Optional[Any]			    =       sum(self.preflow[self.source_index]			)





	def      UpperCamelCase_  (			self :    Union[str, Any]			,lowerCamelCase__ :    Dict			):







							'''simple docstring'''
							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(lowerCamelCase__			,lowerCamelCase__			)

													self.relabel(lowerCamelCase__			)





	def      UpperCamelCase_  (			self :    Tuple			,lowerCamelCase__ :    List[Any]			,lowerCamelCase__ :    List[str]			):







							'''simple docstring'''
							_UpperCamelCase :		Union[str, 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      UpperCamelCase_  (			self :    List[str]			,lowerCamelCase__ :    Optional[int]			):







							'''simple docstring'''
							_UpperCamelCase :		Tuple			    =       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):
																			_UpperCamelCase :		List[Any]			    =       self.heights[to_index]

							if min_height is not None:
													_UpperCamelCase :		Any			    =       min_height + 1


if __name__ == "__main__":
					snake_case_			:     List[str]  	=  [0]
					snake_case_			:     int  	=  [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],
					# ]
					snake_case_			:     int  	=  [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

					# prepare our network
					snake_case_			:     List[Any]  	=  FlowNetwork(graph, entrances, exits)
					# set algorithm
					flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
					# and calculate
					snake_case_			:     Tuple  	=  flow_network.find_maximum_flow()

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


