
class       __A:

					def __init__(	self					:     Optional[int]   ,					__UpperCamelCase					:     Dict   ,					__UpperCamelCase					:     Optional[Any]   ,					__UpperCamelCase					:     List[Any]   ):
												lowerCamelCase_							  =					None
												lowerCamelCase_							  =					None
												lowerCamelCase_							  =					graph

												self._normalize_graph(__UpperCamelCase   ,					__UpperCamelCase   )
												lowerCamelCase_							  =					len(__UpperCamelCase   )
												lowerCamelCase_							  =					None

					def    lowercase__      (	self					:     Tuple   ,					__UpperCamelCase					:     Optional[Any]   ,					__UpperCamelCase					:     List[str]   ):
												if sources is int:
																			lowerCamelCase_							  =					[sources]
												if sinks is int:
																			lowerCamelCase_							  =					[sinks]

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

												lowerCamelCase_							  =					sources[0]
												lowerCamelCase_							  =					sinks[0]

												# make fake vertex if there are more
												# than one source or sink
												if len(__UpperCamelCase   ) > 1 or len(__UpperCamelCase   ) > 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    lowercase__      (	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    lowercase__      (	self					:     List[Any]   ,					__UpperCamelCase					:     List[str]   ):
												lowerCamelCase_							  =					algorithm(self   )





class       __A:

					def __init__(	self					:     Optional[Any]   ,					__UpperCamelCase					:     int   ):
												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    lowercase__      (	self					:     int   ):
												if not self.executed:
																			self._algorithm()
																			lowerCamelCase_							  =					True



					def    lowercase__      (	self					:     int   ):
												pass





class       __A(				UpperCAmelCase       ):

					def __init__(	self					:     Union[str, Any]   ,					__UpperCamelCase					:     Tuple   ):
												super().__init__(__UpperCamelCase   )
												# use this to save your result
												lowerCamelCase_							  =					-1



					def    lowercase__      (	self					:     List[str]   ):
												if not self.executed:
																			raise Exception("""You should execute algorithm before using its result!"""   )

												return self.maximum_flow





class       __A(				UpperCAmelCase       ):

					def __init__(	self					:     Dict   ,					__UpperCamelCase					:     List[str]   ):
												super().__init__(__UpperCamelCase   )

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

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

					def    lowercase__      (	self					:     Tuple   ):
												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(__UpperCamelCase   ):
																			lowerCamelCase_							  =					vertices_list[i]
																			lowerCamelCase_							  =					self.heights[vertex_index]
																			self.process_vertex(__UpperCamelCase   )
																			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(__UpperCamelCase   )   )
																										lowerCamelCase_							  =					0
																			else:
																										i += 1

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

					def    lowercase__      (	self					:     Optional[int]   ,					__UpperCamelCase					:     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(__UpperCamelCase   ,					__UpperCamelCase   )

																			self.relabel(__UpperCamelCase   )

					def    lowercase__      (	self					:     Any   ,					__UpperCamelCase					:     Dict   ,					__UpperCamelCase					:     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    lowercase__      (	self					:     Optional[int]   ,					__UpperCamelCase					:     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}""")







from abc import ABC, abstractmethod
from argparse import ArgumentParser





class       __A(				UpperCAmelCase       ):

					@staticmethod
					@abstractmethod
					def    lowercase__      (	__UpperCamelCase					:     ArgumentParser   ):
												raise NotImplementedError()



					@abstractmethod
					def    lowercase__      (	self					:     Any   ):
												raise NotImplementedError()





