





class        UpperCAmelCase     :
 def __init__(    self				:Optional[Any]						,	lowercase_				:Dict						,	lowercase_				:Dict						,	lowercase_				:Union[str, Any]							)->							Optional[Any]:
     A__    =      None
     A__    =      None
     A__    =      graph

     self._normalize_graph(lowercase_						,	lowercase_							)
     A__    =      len(lowercase_							)
     A__    =      None
 def 					UpperCAmelCase_							(    self				:Tuple						,	lowercase_				:Dict						,	lowercase_				:Union[str, Any]							)->							Union[str, Any]:
     if sources is int:
         A__    =      [sources]
     if sinks is int:
         A__    =      [sinks]

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

     A__    =      sources[0]
     A__    =      sinks[0]

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

         A__    =      len(self.graph							) + 1
         for room in self.graph:
             room.insert(0						,	0							)
         self.graph.insert(0						,	[0] * size							)
         for i in sources:
             A__    =      max_input_flow
         A__    =      0

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






class        UpperCAmelCase     :
 def __init__(    self				:str						,	lowercase_				:Union[str, Any]							)->							Union[str, Any]:
     A__    =      flow_network
     A__    =      flow_network.verticesCount
     A__    =      flow_network.sourceIndex
     A__    =      flow_network.sinkIndex
     # it's just a reference, so you shouldn't change
     # it in your algorithms, use deep copy before doing that
     A__    =      flow_network.graph
     A__    =      False
 def 					UpperCAmelCase_							(    self				:Optional[int]							)->							Optional[Any]:
     if not self.executed:
         self._algorithm()
         A__    =      True



 def 					UpperCAmelCase_							(    self				:List[Any]							)->							Optional[Any]:
     pass






class        UpperCAmelCase     (	UpperCamelCase__    ):
 def __init__(    self				:List[str]						,	lowercase_				:Optional[Any]							)->							Optional[Any]:
     super().__init__(lowercase_							)
     # use this to save your result
     A__    =      -1



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

     return self.maximum_flow






class        UpperCAmelCase     (	UpperCamelCase__    ):
 def __init__(    self				:Tuple						,	lowercase_				:Optional[Any]							)->							List[str]:
     super().__init__(lowercase_							)

     A__    =      [[0] * self.verticies_count for i in range(self.verticies_count							)]

     A__    =      [0] * self.verticies_count
     A__    =      [0] * self.verticies_count
 def 					UpperCAmelCase_							(    self				:Union[str, Any]							)->							Optional[Any]:
     A__    =      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__    =      [
         i
         for i in range(self.verticies_count							)
         if i != self.source_index and i != self.sink_index
     ]

     # move through list
     A__    =      0
     while i < len(lowercase_							):
         A__    =      vertices_list[i]
         A__    =      self.heights[vertex_index]
         self.process_vertex(lowercase_							)
         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(lowercase_							)							)
             A__    =      0
         else:
             i += 1

     A__    =      sum(self.preflow[self.source_index]							)
 def 					UpperCAmelCase_							(    self				:Any						,	lowercase_				:str							)->							Dict:
     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(lowercase_						,	lowercase_							)

         self.relabel(lowercase_							)
 def 					UpperCAmelCase_							(    self				:List[str]						,	lowercase_				:Optional[int]						,	lowercase_				:Any							)->							Any:
     A__    =      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				:Tuple						,	lowercase_				:Dict							)->							int:
     A__    =      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__    =      self.heights[to_index]

     if min_height is not None:
         A__    =      min_height + 1


if __name__ == "__main__":
  __lowerCAmelCase							:     Optional[int]		     =[0]
  __lowerCAmelCase							:     Optional[int]		     =[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							:     str		     =[[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

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

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










'''simple docstring'''

def 						UpperCamelCase    (							_lowerCamelCase : int	):

    if not isinstance(_lowerCamelCase						,	_lowerCamelCase	):
        A__    =      F"Input value of [number={number}] must be an integer"
        raise TypeError(_lowerCamelCase	)

    if number < 1:
        A__    =      F"Input value of [number={number}] must be > 0"
        raise ValueError(_lowerCamelCase	)

    A__    =      1

    for i in range(1						,	_lowerCamelCase	):
        current_number *= 4 * i - 2
        current_number //= i + 1

    return current_number


if __name__ == "__main__":
  import doctest

  doctest.testmod()



