

def 							__SCREAMING_SNAKE_CASE     (   a__    :   str       )					->				list:
	__A :			int		    =			[0] * len(a__       )

	for i in range(1			,len(a__       )       ):
		# use last results for better performance - dynamic programming
		__A :			List[Any]		    =			prefix_result[i - 1]
		while j > 0 and input_string[i] != input_string[j]:
			__A :			str		    =			prefix_result[j - 1]

		if input_string[i] == input_string[j]:
			j += 1
		__A :			Union[str, Any]		    =			j

	return prefix_result
def 							__SCREAMING_SNAKE_CASE     (   a__    :   str       )					->				int:
	return max(prefix_function(a__       )       )


if __name__ == "__main__":
			import doctest

			doctest.testmod()








class      lowerCamelCase_      :




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

		self._normalize_graph(__A					,      __A							)
		__A :			str		    =			len(__A							)
		__A :			Optional[int]		    =			None




	def        lowerCAmelCase_       (     self						:     int					,      __A						:     Any					,      __A						:     Optional[Any]							):
		if sources is int:
			__A :			Dict		    =			[sources]
		if sinks is int:
			__A :			Optional[int]		    =			[sinks]

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

		__A :			str		    =			sources[0]
		__A :			Dict		    =			sinks[0]

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

			__A :			List[Any]		    =			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 :			Union[str, Any]		    =			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 :			int		    =			max_input_flow
			__A :			Optional[Any]		    =			size - 1




	def        lowerCAmelCase_       (     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        lowerCAmelCase_       (     self						:     Optional[Any]					,      __A						:     Dict							):
		__A :			Dict		    =			algorithm(self							)






class      lowerCamelCase_      :




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




	def        lowerCAmelCase_       (     self						:     List[Any]							):
		if not self.executed:
			self._algorithm()
			__A :			Any		    =			True




	def        lowerCAmelCase_       (     self						:     List[str]							):
		pass






class      lowerCamelCase_      (	_lowercase	):




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




	def        lowerCAmelCase_       (     self						:     Any							):
		if not self.executed:
			raise Exception("""You should execute algorithm before using its result!"""							)

		return self.maximum_flow






class      lowerCamelCase_      (	_lowercase	):




	def __init__(     self						:     List[Any]					,      __A						:     Dict							):
		super().__init__(__A							)

		__A :			Tuple		    =			[[0] * self.verticies_count for i in range(self.verticies_count							)]

		__A :			Optional[Any]		    =			[0] * self.verticies_count
		__A :			Union[str, Any]		    =			[0] * self.verticies_count




	def        lowerCAmelCase_       (     self						:     int							):
		__A :			Optional[int]		    =			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[str]		    =			[
		    i
		    for i in range(self.verticies_count							)
		    if i != self.source_index and i != self.sink_index
		]

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

		__A :			Optional[int]		    =			sum(self.preflow[self.source_index]							)




	def        lowerCAmelCase_       (     self						:     Optional[Any]					,      __A						:     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(__A					,      __A							)

			self.relabel(__A							)




	def        lowerCAmelCase_       (     self						:     Dict					,      __A						:     List[str]					,      __A						:     Optional[Any]							):
		__A :			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        lowerCAmelCase_       (     self						:     Optional[Any]					,      __A						:     Tuple							):
		__A :			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):
				__A :			Dict		    =			self.heights[to_index]

		if min_height is not None:
			__A :			Optional[int]		    =			min_height + 1


if __name__ == "__main__":
			UpperCAmelCase_							:					Union[str, Any]		 =   [0]
			UpperCAmelCase_							:					Dict		 =   [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],
			# ]
			UpperCAmelCase_							:					int		 =   [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

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

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





