



class 	lowerCamelCase_    :






						'''simple docstring'''







						def __init__(	self      :			int	,	__lowerCamelCase      :			List[Any]	,	__lowerCamelCase      :			int	,	__lowerCamelCase      :			Union[str, Any] )      ->				str:
									A							:					Tuple              =						None
									A							:					Union[str, Any]              =						None
									A							:					int              =						graph

									self._normalize_graph(__lowerCamelCase	,	__lowerCamelCase )
									A							:					Optional[Any]              =						len(__lowerCamelCase )
									A							:					Any              =						None







						def 			SCREAMING_SNAKE_CASE__		(	self      :			Any	,	__lowerCamelCase      :			Optional[int]	,	__lowerCamelCase      :			Union[str, Any] )      ->				str:
									if sources is int:
												A							:					str              =						[sources]
									if sinks is int:
												A							:					int              =						[sinks]

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

									A							:					Tuple              =						sources[0]
									A							:					List[str]              =						sinks[0]

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

												A							:					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:
															A							:					str              =						max_input_flow
												A							:					List[str]              =						0

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







						def 			SCREAMING_SNAKE_CASE__		(	self      :			Dict )      ->				List[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 			SCREAMING_SNAKE_CASE__		(	self      :			Union[str, Any]	,	__lowerCamelCase      :			List[Any] )      ->				Union[str, Any]:
									A							:					Any              =						algorithm(self )







class 	lowerCamelCase_    :






						'''simple docstring'''







						def __init__(	self      :			Optional[int]	,	__lowerCamelCase      :			int )      ->				List[str]:
									A							:					Optional[int]              =						flow_network
									A							:					List[Any]              =						flow_network.verticesCount
									A							:					Tuple              =						flow_network.sourceIndex
									A							:					Any              =						flow_network.sinkIndex
									# it's just a reference, so you shouldn't change
									# it in your algorithms, use deep copy before doing that
									A							:					int              =						flow_network.graph
									A							:					int              =						False







						def 			SCREAMING_SNAKE_CASE__		(	self      :			Optional[int] )      ->				Tuple:
									if not self.executed:
												self._algorithm()
												A							:					Optional[Any]              =						True







						def 			SCREAMING_SNAKE_CASE__		(	self      :			Any )      ->				List[str]:
									pass







class 	lowerCamelCase_    ( _A						):






						'''simple docstring'''







						def __init__(	self      :			int	,	__lowerCamelCase      :			Tuple )      ->				Dict:
									super().__init__(__lowerCamelCase )
									# use this to save your result
									A							:					List[Any]              =						-1







						def 			SCREAMING_SNAKE_CASE__		(	self      :			Optional[Any] )      ->				int:
									if not self.executed:
												raise Exception("You should execute algorithm before using its result!" )

									return self.maximum_flow







class 	lowerCamelCase_    ( _A						):






						'''simple docstring'''







						def __init__(	self      :			Dict	,	__lowerCamelCase      :			Any )      ->				Tuple:
									super().__init__(__lowerCamelCase )

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

									A							:					Optional[int]              =						[0] * self.verticies_count
									A							:					Dict              =						[0] * self.verticies_count







						def 			SCREAMING_SNAKE_CASE__		(	self      :			str )      ->				List[Any]:
									A							:					Tuple              =						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
									A							:					List[Any]              =						[
									    i
									    for i in range(self.verticies_count )
									    if i != self.source_index and i != self.sink_index
									]

									# move through list
									A							:					List[Any]              =						0
									while i < len(__lowerCamelCase ):
												A							:					int              =						vertices_list[i]
												A							:					Optional[int]              =						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 ) )
															A							:					Any              =						0
												else:
															i += 1

									A							:					List[Any]              =						sum(self.preflow[self.source_index] )







						def 			SCREAMING_SNAKE_CASE__		(	self      :			str	,	__lowerCamelCase      :			str )      ->				List[str]:
									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 			SCREAMING_SNAKE_CASE__		(	self      :			Dict	,	__lowerCamelCase      :			List[str]	,	__lowerCamelCase      :			Tuple )      ->				int:
									A							:					List[str]              =						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 			SCREAMING_SNAKE_CASE__		(	self      :			Optional[Any]	,	__lowerCamelCase      :			Dict )      ->				int:
									A							:					int              =						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):
															A							:					Dict              =						self.heights[to_index]

									if min_height is not None:
												A							:					List[str]              =						min_height + 1


if __name__ == "__main__":
							__SCREAMING_SNAKE_CASE           =  [0]
							__SCREAMING_SNAKE_CASE           =  [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],
							# ]
							__SCREAMING_SNAKE_CASE           =  [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

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

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




from __future__ import annotations

from math import pi

# Define the Reduced Planck Constant ℏ (H bar), speed of light C, value of
# Pi and the function
__SCREAMING_SNAKE_CASE           =  1.0_5_4_5_7_1_8_1_7e-3_4  # unit of ℏ : J * s

__SCREAMING_SNAKE_CASE           =  3e8  # unit of c : m * s^-1




def 	UpperCAmelCase   (						_lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase    ):

			if (force, area, distance).count(0    ) != 1:
						raise ValueError("One and only one argument must be 0"    )
			if force < 0:
						raise ValueError("Magnitude of force can not be negative"    )
			if distance < 0:
						raise ValueError("Distance can not be negative"    )
			if area < 0:
						raise ValueError("Area can not be negative"    )
			if force == 0:
						A							:					int              =						(REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (
						    240 * (distance) ** 4
						)
						return {"force": force}
			elif area == 0:
						A							:					Tuple              =						(240 * force * (distance) ** 4) / (
						    REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2
						)
						return {"area": area}
			elif distance == 0:
						A							:					Dict              =						(
						    (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (240 * force)
						) ** (1 / 4)
						return {"distance": distance}
			raise ValueError("One and only one argument must be 0"    )


# Run doctest
if __name__ == "__main__":
							import doctest

							doctest.testmod()