'''simple docstring'''




from typing import Optional
from urllib.parse import quote

import huggingface_hub as hfh
from packaging import version

def 	UpperCamelCase_							(					_UpperCAmelCase  :      str			,	_UpperCAmelCase  :      str			,	_UpperCAmelCase  :      Optional[str] = None    )    ->    str:


       """simple docstring"""







       if version.parse(hfh.__version__    ).release < version.parse("0.11.0"    ).release:
              # old versions of hfh don't url-encode the file path
              _UpperCAmelCase     :  Union[str, Any]							      =    quote(_UpperCAmelCase    )
       return hfh.hf_hub_url(_UpperCAmelCase			,	_UpperCAmelCase			,	repo_type="dataset"			,	revision=_UpperCAmelCase    )


'''simple docstring'''




class 	lowerCamelCase_	:
      '''simple docstring'''

      def __init__(       self						:				Tuple						,					A						:				Any						,					A						:				str						,					A						:				Union[str, Any]       ):
             _UpperCAmelCase     :  Optional[int]							      =    None
             _UpperCAmelCase     :  Optional[int]							      =    None
             _UpperCAmelCase     :  Any							      =    graph

             self._normalize_graph(A						,					A       )
             _UpperCAmelCase     :  List[str]							      =    len(A       )
             _UpperCAmelCase     :  Tuple							      =    None




      def      _A	(       self						:				Any						,					A						:				List[Any]						,					A						:				str       ):
             if sources is int:
                    _UpperCAmelCase     :  List[Any]							      =    [sources]
             if sinks is int:
                    _UpperCAmelCase     :  List[Any]							      =    [sinks]

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

             _UpperCAmelCase     :  str							      =    sources[0]
             _UpperCAmelCase     :  Union[str, Any]							      =    sinks[0]

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

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

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




      def      _A	(       self						:				Union[str, 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      _A	(       self						:				Tuple						,					A						:				Dict       ):
             _UpperCAmelCase     :  str							      =    algorithm(self       )

class 	lowerCamelCase_	:
      '''simple docstring'''

      def __init__(       self						:				Any						,					A						:				str       ):
             _UpperCAmelCase     :  Optional[int]							      =    flow_network
             _UpperCAmelCase     :  Any							      =    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     :  Any							      =    flow_network.graph
             _UpperCAmelCase     :  Union[str, Any]							      =    False




      def      _A	(       self						:				List[str]       ):
             if not self.executed:
                    self._algorithm()
                    _UpperCAmelCase     :  int							      =    True





      def      _A	(       self						:				List[Any]       ):
             pass

class 	lowerCamelCase_	(snake_case__    ):
      '''simple docstring'''

      def __init__(       self						:				Optional[int]						,					A						:				Union[str, Any]       ):
             super().__init__(A       )
             # use this to save your result
             _UpperCAmelCase     :  Any							      =    -1





      def      _A	(       self						:				Union[str, Any]       ):
             if not self.executed:
                    raise Exception("You should execute algorithm before using its result!"       )

             return self.maximum_flow

class 	lowerCamelCase_	(snake_case__    ):
      '''simple docstring'''

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

             _UpperCAmelCase     :  List[str]							      =    [[0] * self.verticies_count for i in range(self.verticies_count       )]

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




      def      _A	(       self						:				Dict       ):
             _UpperCAmelCase     :  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
             _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     :  int							      =    vertices_list[i]
                    _UpperCAmelCase     :  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     :  Union[str, Any]							      =    0
                    else:
                           i += 1

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




      def      _A	(       self						:				Union[str, Any]						,					A						:				str       ):
             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      _A	(       self						:				int						,					A						:				Dict						,					A						:				List[str]       ):
             _UpperCAmelCase     :  int							      =    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      _A	(       self						:				Optional[int]						,					A						:				Union[str, Any]       ):
             _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     :  Tuple							      =    self.heights[to_index]

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


if __name__ == "__main__":
  __SCREAMING_SNAKE_CASE       :     Optional[int]     =  [0]
  __SCREAMING_SNAKE_CASE       :     Union[str, Any]     =  [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],
  # ]
  __SCREAMING_SNAKE_CASE       :     List[Any]     =  [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

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

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

