


class 						_UpperCAmelCase      :






		def __init__(						self				:     str   ,  UpperCAmelCase				:     Optional[int]   ,  UpperCAmelCase				:     Optional[Any]   ,  UpperCAmelCase				:     Any):
				SCREAMING_SNAKE_CASE_				:List[Any]				     =						None
				SCREAMING_SNAKE_CASE_				:Optional[int]				     =						None
				SCREAMING_SNAKE_CASE_				:List[Any]				     =						graph

				self._normalize_graph(UpperCAmelCase   ,  UpperCAmelCase)
				SCREAMING_SNAKE_CASE_				:int				     =						len(UpperCAmelCase)
				SCREAMING_SNAKE_CASE_				:Any				     =						None






		def _snake_case		(						self				:     List[str]   ,  UpperCAmelCase				:     Dict   ,  UpperCAmelCase				:     int):
				if sources is int:
						SCREAMING_SNAKE_CASE_				:Optional[int]				     =						[sources]
				if sinks is int:
						SCREAMING_SNAKE_CASE_				:List[Any]				     =						[sinks]

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

				SCREAMING_SNAKE_CASE_				:Optional[int]				     =						sources[0]
				SCREAMING_SNAKE_CASE_				:int				     =						sinks[0]

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

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

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






		def _snake_case		(						self				:     Union[str, 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 _snake_case		(						self				:     Any   ,  UpperCAmelCase				:     List[str]):
				SCREAMING_SNAKE_CASE_				:List[str]				     =						algorithm(self)




class 						_UpperCAmelCase      :






		def __init__(						self				:     List[str]   ,  UpperCAmelCase				:     Optional[Any]):
				SCREAMING_SNAKE_CASE_				:int				     =						flow_network
				SCREAMING_SNAKE_CASE_				:Optional[int]				     =						flow_network.verticesCount
				SCREAMING_SNAKE_CASE_				:List[str]				     =						flow_network.sourceIndex
				SCREAMING_SNAKE_CASE_				: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
				SCREAMING_SNAKE_CASE_				:int				     =						flow_network.graph
				SCREAMING_SNAKE_CASE_				:Union[str, Any]				     =						False






		def _snake_case		(						self				:     List[str]):
				if not self.executed:
						self._algorithm()
						SCREAMING_SNAKE_CASE_				:Optional[Any]				     =						True







		def _snake_case		(						self				:     List[Any]):
				pass




class 						_UpperCAmelCase      (     _SCREAMING_SNAKE_CASE							):






		def __init__(						self				:     Optional[int]   ,  UpperCAmelCase				:     List[str]):
				super().__init__(UpperCAmelCase)
				# use this to save your result
				SCREAMING_SNAKE_CASE_				:int				     =						-1







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

				return self.maximum_flow




class 						_UpperCAmelCase      (     _SCREAMING_SNAKE_CASE							):






		def __init__(						self				:     List[str]   ,  UpperCAmelCase				:     Union[str, Any]):
				super().__init__(UpperCAmelCase)

				SCREAMING_SNAKE_CASE_				:Union[str, Any]				     =						[[0] * self.verticies_count for i in range(self.verticies_count)]

				SCREAMING_SNAKE_CASE_				:Dict				     =						[0] * self.verticies_count
				SCREAMING_SNAKE_CASE_				:int				     =						[0] * self.verticies_count






		def _snake_case		(						self				:     str):
				SCREAMING_SNAKE_CASE_				: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
				SCREAMING_SNAKE_CASE_				:Dict				     =						[
				    i
				    for i in range(self.verticies_count)
				    if i != self.source_index and i != self.sink_index
				]

				# move through list
				SCREAMING_SNAKE_CASE_				:int				     =						0
				while i < len(UpperCAmelCase):
						SCREAMING_SNAKE_CASE_				:Dict				     =						vertices_list[i]
						SCREAMING_SNAKE_CASE_				:Union[str, Any]				     =						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))
								SCREAMING_SNAKE_CASE_				:Dict				     =						0
						else:
								i += 1

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






		def _snake_case		(						self				:     Optional[Any]   ,  UpperCAmelCase				:     int):
				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 _snake_case		(						self				:     str   ,  UpperCAmelCase				:     str   ,  UpperCAmelCase				:     Dict):
				SCREAMING_SNAKE_CASE_				:Dict				     =						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 _snake_case		(						self				:     Dict   ,  UpperCAmelCase				:     List[Any]):
				SCREAMING_SNAKE_CASE_				:List[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):
								SCREAMING_SNAKE_CASE_				:List[str]				     =						self.heights[to_index]

				if min_height is not None:
						SCREAMING_SNAKE_CASE_				:Optional[Any]				     =						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}''')










'''simple docstring'''






from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors







def 							UpperCamelCase_     (       A__   :  int   ):
  '''simple docstring'''





  lowerCAmelCase_     : Any     =  prime_factors(A__   )
  if is_square_free(A__   ):
    return -1 if len(A__   ) % 2 else 1
  return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()



