


def 					lowerCamelCase_   (	_a	):




		"""simple docstring"""






		if not isinstance(_a     ,       _a	):
				raise ValueError('''multiplicative_persistence() only accepts integral values'''	)
		if num < 0:
				raise ValueError('''multiplicative_persistence() does not accept negative values'''	)

		lowerCAmelCase__       :      Union[str, Any]   					= 0
		lowerCAmelCase__       :      str   					= str(_a	)

		while len(_a	) != 1:
				lowerCAmelCase__       :      str   					= [int(_a	) for i in num_string]

				lowerCAmelCase__       :      Any   					= 1
				for i in range(0     ,       len(_a	)	):
						total *= numbers[i]

				lowerCAmelCase__       :      Tuple   					= str(_a	)

				steps += 1
		return steps






def 					lowerCamelCase_   (	_a	):




		"""simple docstring"""






		if not isinstance(_a     ,       _a	):
				raise ValueError('''additive_persistence() only accepts integral values'''	)
		if num < 0:
				raise ValueError('''additive_persistence() does not accept negative values'''	)

		lowerCAmelCase__       :      Dict   					= 0
		lowerCAmelCase__       :      Tuple   					= str(_a	)

		while len(_a	) != 1:
				lowerCAmelCase__       :      List[Any]   					= [int(_a	) for i in num_string]

				lowerCAmelCase__       :      Optional[int]   					= 0
				for i in range(0     ,       len(_a	)	):
						total += numbers[i]

				lowerCAmelCase__       :      List[Any]   					= str(_a	)

				steps += 1
		return steps


if __name__ == "__main__":
		import doctest

		doctest.testmod()








class  _a							:




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

			self._normalize_graph(_SCREAMING_SNAKE_CASE		, _SCREAMING_SNAKE_CASE		)
			lowerCAmelCase__       :      Tuple   					= len(_SCREAMING_SNAKE_CASE		)
			lowerCAmelCase__       :      Optional[int]   					= None




	def 							UpperCAmelCase__( self						:		Union[str, Any]		, _SCREAMING_SNAKE_CASE						:		Optional[Any]		, _SCREAMING_SNAKE_CASE						:		Union[str, Any]		)->	Union[str, Any]:
			if sources is int:
					lowerCAmelCase__       :      List[Any]   					= [sources]
			if sinks is int:
					lowerCAmelCase__       :      Optional[Any]   					= [sinks]

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

			lowerCAmelCase__       :      Union[str, Any]   					= sources[0]
			lowerCAmelCase__       :      Dict   					= sinks[0]

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

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

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




	def 							UpperCAmelCase__( self						:		Union[str, Any]		)->	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 							UpperCAmelCase__( self						:		str		, _SCREAMING_SNAKE_CASE						:		List[Any]		)->	int:
			lowerCAmelCase__       :      int   					= algorithm(self		)





class  _a							:




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




	def 							UpperCAmelCase__( self						:		List[str]		)->	Dict:
			if not self.executed:
					self._algorithm()
					lowerCAmelCase__       :      Any   					= True




	def 							UpperCAmelCase__( self						:		Optional[Any]		)->	int:
			pass





class  _a							(    _lowercase):




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




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

			return self.maximum_flow





class  _a							(    _lowercase):




	def __init__( self						:		Any		, _SCREAMING_SNAKE_CASE						:		List[str]		)->	List[str]:
			super().__init__(_SCREAMING_SNAKE_CASE		)

			lowerCAmelCase__       :      Any   					= [[0] * self.verticies_count for i in range(self.verticies_count		)]

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




	def 							UpperCAmelCase__( self						:		Any		)->	List[Any]:
			lowerCAmelCase__       :      Optional[Any]   					= 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__       :      Any   					= [
			    i
			    for i in range(self.verticies_count		)
			    if i != self.source_index and i != self.sink_index
			]

			# move through list
			lowerCAmelCase__       :      str   					= 0
			while i < len(_SCREAMING_SNAKE_CASE		):
					lowerCAmelCase__       :      Union[str, Any]   					= vertices_list[i]
					lowerCAmelCase__       :      Any   					= self.heights[vertex_index]
					self.process_vertex(_SCREAMING_SNAKE_CASE		)
					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(_SCREAMING_SNAKE_CASE		)		)
							lowerCAmelCase__       :      Optional[Any]   					= 0
					else:
							i += 1

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




	def 							UpperCAmelCase__( self						:		List[str]		, _SCREAMING_SNAKE_CASE						:		Optional[Any]		)->	Optional[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(_SCREAMING_SNAKE_CASE		, _SCREAMING_SNAKE_CASE		)

					self.relabel(_SCREAMING_SNAKE_CASE		)




	def 							UpperCAmelCase__( self						:		int		, _SCREAMING_SNAKE_CASE						:		Optional[Any]		, _SCREAMING_SNAKE_CASE						:		Union[str, Any]		)->	Union[str, Any]:
			lowerCAmelCase__       :      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						:		Optional[int]		, _SCREAMING_SNAKE_CASE						:		Any		)->	Optional[int]:
			lowerCAmelCase__       :      Optional[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):
							lowerCAmelCase__       :      List[Any]   					= self.heights[to_index]

			if min_height is not None:
					lowerCAmelCase__       :      Optional[Any]   					= min_height + 1


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

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

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




