






"""simple docstring"""







class  lowerCamelCase__ :






    def __init__(			self     ,A     ,A     ,A ):
          UpperCAmelCase          =	None
          UpperCAmelCase          =	None
          UpperCAmelCase          =	graph

          self._normalize_graph(A     ,A )
          UpperCAmelCase          =	len(A )
          UpperCAmelCase          =	None






    def     _UpperCamelCase							(			self     ,A     ,A ):
          if sources is int:
                UpperCAmelCase          =	[sources]
          if sinks is int:
                UpperCAmelCase          =	[sinks]

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

          UpperCAmelCase          =	sources[0]
          UpperCAmelCase          =	sinks[0]

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

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

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






    def     _UpperCamelCase							(			self ):
          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     ,A ):
          UpperCAmelCase          =	algorithm(self )







class  lowerCamelCase__ :






    def __init__(			self     ,A ):
          UpperCAmelCase          =	flow_network
          UpperCAmelCase          =	flow_network.verticesCount
          UpperCAmelCase          =	flow_network.sourceIndex
          UpperCAmelCase          =	flow_network.sinkIndex
          # it's just a reference, so you shouldn't change
          # it in your algorithms, use deep copy before doing that
          UpperCAmelCase          =	flow_network.graph
          UpperCAmelCase          =	False






    def     _UpperCamelCase							(			self ):
          if not self.executed:
                self._algorithm()
                UpperCAmelCase          =	True






    def     _UpperCamelCase							(			self ):
          pass







class  lowerCamelCase__ (	snake_case			):






    def __init__(			self     ,A ):
          super().__init__(A )
          # use this to save your result
          UpperCAmelCase          =	-1






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

          return self.maximum_flow







class  lowerCamelCase__ (	snake_case			):






    def __init__(			self     ,A ):
          super().__init__(A )

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

          UpperCAmelCase          =	[0] * self.verticies_count
          UpperCAmelCase          =	[0] * self.verticies_count






    def     _UpperCamelCase							(			self ):
          UpperCAmelCase          =	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          =	[
              i
              for i in range(self.verticies_count )
              if i != self.source_index and i != self.sink_index
          ]

          # move through list
          UpperCAmelCase          =	0
          while i < len(A ):
                UpperCAmelCase          =	vertices_list[i]
                UpperCAmelCase          =	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          =	0
                else:
                      i += 1

          UpperCAmelCase          =	sum(self.preflow[self.source_index] )






    def     _UpperCamelCase							(			self     ,A ):
          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     _UpperCamelCase							(			self     ,A     ,A ):
          UpperCAmelCase          =	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     ,A ):
          UpperCAmelCase          =	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          =	self.heights[to_index]

          if min_height is not None:
                UpperCAmelCase          =	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"""







from __future__ import annotations

def _a			(		_snake_case				,	_snake_case = None				,	_snake_case = None							):







      """simple docstring"""






      if start is None:
            UpperCAmelCase          =	0

      if end is None:
            UpperCAmelCase          =	len(_snake_case							) - 1

      if start >= end:
            return

      UpperCAmelCase          =	(start + end) // 2

      slowsort(_snake_case				,	_snake_case				,	_snake_case							)
      slowsort(_snake_case				,	mid + 1				,	_snake_case							)

      if sequence[end] < sequence[mid]:
            UpperCAmelCase      , UpperCAmelCase          =	sequence[mid], sequence[end]

      slowsort(_snake_case				,	_snake_case				,	end - 1							)


if __name__ == "__main__":
  from doctest import testmod

  testmod()



