
"""simple docstring"""




class 			lowercase_       :
       def __init__(     self ,				A_ ,				A_ ,				A_       )     ->	Union[str, Any]:





         """simple docstring"""




         _lowercase:			int       =     None
         _lowercase:			Union[str, Any]       =     None
         _lowercase:			Any       =     graph

         self._normalize_graph(A_ ,				A_       )
         _lowercase:			Any       =     len(A_       )
         _lowercase:			int       =     None
       def 							lowercase_							(     self ,				A_ ,				A_       )     ->	str:





         """simple docstring"""




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

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

         _lowercase:			str       =     sources[0]
         _lowercase:			Any       =     sinks[0]

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

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

           _lowercase:			Union[str, Any]       =     len(self.graph       ) + 1
           for room in self.graph:
             room.append(0       )
           self.graph.append([0] * size       )
           for i in sinks:
             _lowercase:			int       =     max_input_flow
           _lowercase:			List[Any]       =     size - 1
       def 							lowercase_							(     self       )     ->	Dict:





         """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 							lowercase_							(     self ,				A_       )     ->	List[Any]:





         """simple docstring"""




         _lowercase:			List[Any]       =     algorithm(self       )


class 			lowercase_       :
       def __init__(     self ,				A_       )     ->	List[Any]:





         """simple docstring"""




         _lowercase:			List[Any]       =     flow_network
         _lowercase:			List[Any]       =     flow_network.verticesCount
         _lowercase:			Optional[Any]       =     flow_network.sourceIndex
         _lowercase:			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
         _lowercase:			Union[str, Any]       =     flow_network.graph
         _lowercase:			Union[str, Any]       =     False
       def 							lowercase_							(     self       )     ->	Dict:





         """simple docstring"""




         if not self.executed:
           self._algorithm()
           _lowercase:			Union[str, Any]       =     True



       def 							lowercase_							(     self       )     ->	Dict:





         """simple docstring"""




         pass


class 			lowercase_       (       _SCREAMING_SNAKE_CASE ):
       def __init__(     self ,				A_       )     ->	List[Any]:





         """simple docstring"""




         super().__init__(A_       )
         # use this to save your result
         _lowercase:			Union[str, Any]       =     -1



       def 							lowercase_							(     self       )     ->	Optional[int]:





         """simple docstring"""




         if not self.executed:
           raise Exception('''You should execute algorithm before using its result!'''       )

         return self.maximum_flow


class 			lowercase_       (       _SCREAMING_SNAKE_CASE ):
       def __init__(     self ,				A_       )     ->	List[str]:





         """simple docstring"""




         super().__init__(A_       )

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

         _lowercase:			Dict       =     [0] * self.verticies_count
         _lowercase:			Any       =     [0] * self.verticies_count
       def 							lowercase_							(     self       )     ->	List[str]:





         """simple docstring"""




         _lowercase:			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
         _lowercase:			List[str]       =     [
             i
             for i in range(self.verticies_count       )
             if i != self.source_index and i != self.sink_index
         ]

         # move through list
         _lowercase:			Union[str, Any]       =     0
         while i < len(A_       ):
           _lowercase:			Optional[Any]       =     vertices_list[i]
           _lowercase:			Tuple       =     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_       )       )
             _lowercase:			Tuple       =     0
           else:
             i += 1

         _lowercase:			Union[str, Any]       =     sum(self.preflow[self.source_index]       )
       def 							lowercase_							(     self ,				A_       )     ->	List[Any]:





         """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(A_ ,				A_       )

           self.relabel(A_       )
       def 							lowercase_							(     self ,				A_ ,				A_       )     ->	Dict:





         """simple docstring"""




         _lowercase:			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 							lowercase_							(     self ,				A_       )     ->	Tuple:





         """simple docstring"""




         _lowercase:			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):
             _lowercase:			Dict       =     self.heights[to_index]

         if min_height is not None:
           _lowercase:			Union[str, Any]       =     min_height + 1


if __name__ == "__main__":
  A__   :					str							=   [0]
  A__   :					List[str]							=   [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__   :					Optional[Any]							=   [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

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

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


"""simple docstring"""




def  _lowerCAmelCase		(		_UpperCamelCase ,				_UpperCamelCase						):






  """simple docstring"""



  return number | (1 << position)




def  _lowerCAmelCase		(		_UpperCamelCase ,				_UpperCamelCase						):






  """simple docstring"""



  return number & ~(1 << position)




def  _lowerCAmelCase		(		_UpperCamelCase ,				_UpperCamelCase						):






  """simple docstring"""



  return number ^ (1 << position)




def  _lowerCAmelCase		(		_UpperCamelCase ,				_UpperCamelCase						):






  """simple docstring"""



  return ((number >> position) & 1) == 1




def  _lowerCAmelCase		(		_UpperCamelCase ,				_UpperCamelCase						):






  """simple docstring"""



  return int((number & (1 << position)) != 0						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
