





"""simple docstring"""





class    _lowerCAmelCase  :
       """simple docstring"""




       def __init__(       self       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase ):



         '''simple docstring'''

         lowerCAmelCase__     :Tuple											=				None
         lowerCAmelCase__     :Any											=				None
         lowerCAmelCase__     :Any											=				graph

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






       def 	snake_case		(       self       ,					__UpperCAmelCase       ,					__UpperCAmelCase ):



         '''simple docstring'''

         if sources is int:
           lowerCAmelCase__     :List[Any]											=				[sources]
         if sinks is int:
           lowerCAmelCase__     :int											=				[sinks]

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

         lowerCAmelCase__     :List[str]											=				sources[0]
         lowerCAmelCase__     :str											=				sinks[0]

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

           lowerCAmelCase__     :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:
             lowerCAmelCase__     :Optional[Any]											=				max_input_flow
           lowerCAmelCase__     :int											=				0

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






       def 	snake_case		(       self ):



         '''simple docstring'''

         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       ,					__UpperCAmelCase ):



         '''simple docstring'''

         lowerCAmelCase__     :List[str]											=				algorithm(self )






class    _lowerCAmelCase  :
       """simple docstring"""




       def __init__(       self       ,					__UpperCAmelCase ):



         '''simple docstring'''

         lowerCAmelCase__     :str											=				flow_network
         lowerCAmelCase__     :Optional[int]											=				flow_network.verticesCount
         lowerCAmelCase__     :Optional[Any]											=				flow_network.sourceIndex
         lowerCAmelCase__     :Dict											=				flow_network.sinkIndex
         # it's just a reference, so you shouldn't change
         # it in your algorithms, use deep copy before doing that
         lowerCAmelCase__     :Optional[int]											=				flow_network.graph
         lowerCAmelCase__     :Optional[Any]											=				False






       def 	snake_case		(       self ):



         '''simple docstring'''

         if not self.executed:
           self._algorithm()
           lowerCAmelCase__     :List[Any]											=				True






       def 	snake_case		(       self ):



         '''simple docstring'''

         pass






class    _lowerCAmelCase  (	a			):
       """simple docstring"""




       def __init__(       self       ,					__UpperCAmelCase ):



         '''simple docstring'''

         super().__init__(__UpperCAmelCase )
         # use this to save your result
         lowerCAmelCase__     :Optional[int]											=				-1






       def 	snake_case		(       self ):



         '''simple docstring'''

         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       ,					__UpperCAmelCase ):



         '''simple docstring'''

         super().__init__(__UpperCAmelCase )

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

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






       def 	snake_case		(       self ):



         '''simple docstring'''

         lowerCAmelCase__     :Dict											=				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__     :List[str]											=				[
             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(__UpperCAmelCase ):
           lowerCAmelCase__     :Any											=				vertices_list[i]
           lowerCAmelCase__     :List[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 ) )
             lowerCAmelCase__     :int											=				0
           else:
             i += 1

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






       def 	snake_case		(       self       ,					__UpperCAmelCase ):



         '''simple docstring'''

         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       ,					__UpperCAmelCase       ,					__UpperCAmelCase ):



         '''simple docstring'''

         lowerCAmelCase__     :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 	snake_case		(       self       ,					__UpperCAmelCase ):



         '''simple docstring'''

         lowerCAmelCase__     :Union[str, Any]											=				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__     :Union[str, Any]											=				self.heights[to_index]

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


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

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

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


'''simple docstring'''





def snake_case_     (					lowercase__		):
  return sum(i for i in range(1   ,       number // 2 + 1		) if number % i == 0		) == number


if __name__ == "__main__":
      print("""Program to check whether a number is a Perfect number or not...""")
      SCREAMING_SNAKE_CASE     =       int(input("""Enter number: """).strip())
      print(F'{number} is {"" if perfect(number) else "not "}a Perfect Number.')



