

"""simple docstring"""




class      __lowercase			:

  def __init__(  self		:			int					,A		:			List[Any]					,A		:			List[str]					,A		:			List[str]    ):






   '''simple docstring'''
   UpperCAmelCase__					:  Optional[int]					   =					None
   UpperCAmelCase__					:  Tuple					   =					None
   UpperCAmelCase__					:  List[Any]					   =					graph

   self._normalize_graph(A					,A    )
   UpperCAmelCase__					:  Tuple					   =					len(A    )
   UpperCAmelCase__					:  Tuple					   =					None

  def    __lowercase       (  self		:			str					,A		:			Union[str, Any]					,A		:			Union[str, Any]    ):






   '''simple docstring'''
   if sources is int:
    UpperCAmelCase__					:  int					   =					[sources]
   if sinks is int:
    UpperCAmelCase__					:  Optional[Any]					   =					[sinks]

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

   UpperCAmelCase__					:  List[Any]					   =					sources[0]
   UpperCAmelCase__					:  Dict					   =					sinks[0]

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

    UpperCAmelCase__					:  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:
     UpperCAmelCase__					:  str					   =					max_input_flow
    UpperCAmelCase__					:  str					   =					0

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

  def    __lowercase       (  self		:			Tuple    ):






   '''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		:			List[Any]					,A		:			str    ):






   '''simple docstring'''
   UpperCAmelCase__					:  Tuple					   =					algorithm(self    )







class      __lowercase			:

  def __init__(  self		:			Dict					,A		:			str    ):






   '''simple docstring'''
   UpperCAmelCase__					:  Optional[int]					   =					flow_network
   UpperCAmelCase__					:  Dict					   =					flow_network.verticesCount
   UpperCAmelCase__					:  List[str]					   =					flow_network.sourceIndex
   UpperCAmelCase__					:  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
   UpperCAmelCase__					:  Union[str, Any]					   =					flow_network.graph
   UpperCAmelCase__					:  Any					   =					False

  def    __lowercase       (  self		:			Optional[Any]    ):






   '''simple docstring'''
   if not self.executed:
    self._algorithm()
    UpperCAmelCase__					:  Optional[int]					   =					True




  def    __lowercase       (  self		:			List[Any]    ):






   '''simple docstring'''
   pass







class      __lowercase			(    __lowerCamelCase					):

  def __init__(  self		:			Dict					,A		:			Union[str, Any]    ):






   '''simple docstring'''
   super().__init__(A    )
   # use this to save your result
   UpperCAmelCase__					:  Tuple					   =					-1




  def    __lowercase       (  self		:			Dict    ):






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

   return self.maximum_flow







class      __lowercase			(    __lowerCamelCase					):

  def __init__(  self		:			List[str]					,A		:			Dict    ):






   '''simple docstring'''
   super().__init__(A    )

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

   UpperCAmelCase__					:  Optional[int]					   =					[0] * self.verticies_count
   UpperCAmelCase__					:  Optional[int]					   =					[0] * self.verticies_count

  def    __lowercase       (  self		:			List[str]    ):






   '''simple docstring'''
   UpperCAmelCase__					:  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
   UpperCAmelCase__					:  Optional[int]					   =					[
       i
       for i in range(self.verticies_count    )
       if i != self.source_index and i != self.sink_index
   ]

   # move through list
   UpperCAmelCase__					:  Any					   =					0
   while i < len(A    ):
    UpperCAmelCase__					:  Any					   =					vertices_list[i]
    UpperCAmelCase__					:  Optional[int]					   =					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    )    )
     UpperCAmelCase__					:  str					   =					0
    else:
     i += 1

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

  def    __lowercase       (  self		:			int					,A		:			Optional[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		:			List[str]					,A		:			Tuple					,A		:			Optional[Any]    ):






   '''simple docstring'''
   UpperCAmelCase__					:  List[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		:			Optional[Any]					,A		:			Union[str, Any]    ):






   '''simple docstring'''
   UpperCAmelCase__					:  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):
     UpperCAmelCase__					:  Optional[Any]					   =					self.heights[to_index]

   if min_height is not None:
    UpperCAmelCase__					:  int					   =					min_height + 1


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

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

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








"""simple docstring"""




__UpperCAmelCase =				'Tobias Carryer'

from time import time







class      __lowercase			:

  def __init__(  self		:			Union[str, Any]					,A		:			Dict					,A		:			Optional[int]					,A		:			Union[str, Any]					,A		:			int=int(time()    )    ):  # noqa: B008






   '''simple docstring'''
   UpperCAmelCase__					:  int					   =					multiplier
   UpperCAmelCase__					:  Union[str, Any]					   =					increment
   UpperCAmelCase__					:  Dict					   =					modulo
   UpperCAmelCase__					:  Tuple					   =					seed




  def    __lowercase       (  self		:			Dict    ):






   '''simple docstring'''
   UpperCAmelCase__					:  Any					   =					(self.multiplier * self.seed + self.increment) % self.modulo
   return self.seed


if __name__ == "__main__":
      # Show the LCG in action.
      __UpperCAmelCase =				LinearCongruentialGenerator(166_4525, 10_1390_4223, 2 << 31)
      while True:
            print(lcg.next_number())





