"""simple docstring"""






class     UpperCAmelCase						:



    """simple docstring"""

    def __init__(   self    ,			_UpperCAmelCase    ,			_UpperCAmelCase    ,			_UpperCAmelCase							):
       lowercase__:   int					=      None
       lowercase__:   Tuple					=      None
       lowercase__:   Optional[int]					=      graph

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






    def _snake_case			(   self    ,			_UpperCAmelCase    ,			_UpperCAmelCase							):
       if sources is int:
          lowercase__:   List[str]					=      [sources]
       if sinks is int:
          lowercase__:   int					=      [sinks]

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

       lowercase__:   int					=      sources[0]
       lowercase__:   List[Any]					=      sinks[0]

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

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

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






    def _snake_case			(   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 _snake_case			(   self    ,			_UpperCAmelCase							):
       lowercase__:   Optional[Any]					=      algorithm(self							)



class     UpperCAmelCase						:



    """simple docstring"""

    def __init__(   self    ,			_UpperCAmelCase							):
       lowercase__:   Any					=      flow_network
       lowercase__:   int					=      flow_network.verticesCount
       lowercase__:   Union[str, Any]					=      flow_network.sourceIndex
       lowercase__:   List[Any]					=      flow_network.sinkIndex
       # it's just a reference, so you shouldn't change
       # it in your algorithms, use deep copy before doing that
       lowercase__:   Tuple					=      flow_network.graph
       lowercase__:   Tuple					=      False






    def _snake_case			(   self							):
       if not self.executed:
          self._algorithm()
          lowercase__:   Any					=      True






    def _snake_case			(   self							):
       pass



class     UpperCAmelCase						(_UpperCAmelCase  ):



    """simple docstring"""

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






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

       return self.maximum_flow



class     UpperCAmelCase						(_UpperCAmelCase  ):



    """simple docstring"""

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

       lowercase__:   Tuple					=      [[0] * self.verticies_count for i in range(self.verticies_count							)]

       lowercase__:   Optional[Any]					=      [0] * self.verticies_count
       lowercase__:   int					=      [0] * self.verticies_count






    def _snake_case			(   self							):
       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__:   Tuple					=      [
           i
           for i in range(self.verticies_count							)
           if i != self.source_index and i != self.sink_index
       ]

       # move through list
       lowercase__:   int					=      0
       while i < len(_UpperCAmelCase							):
          lowercase__:   List[str]					=      vertices_list[i]
          lowercase__:   str					=      self.heights[vertex_index]
          self.process_vertex(_UpperCAmelCase							)
          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(_UpperCAmelCase							)							)
             lowercase__:   str					=      0
          else:
             i += 1

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






    def _snake_case			(   self    ,			_UpperCAmelCase							):
       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(_UpperCAmelCase    ,			_UpperCAmelCase							)

          self.relabel(_UpperCAmelCase							)






    def _snake_case			(   self    ,			_UpperCAmelCase    ,			_UpperCAmelCase							):
       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 _snake_case			(   self    ,			_UpperCAmelCase							):
       lowercase__:   Any					=      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__:   Tuple					=      self.heights[to_index]

       if min_height is not None:
          lowercase__:   Dict					=      min_height + 1


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

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

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

"""simple docstring"""






def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase )  ->  List[str]:
   lowercase__:   Optional[Any]					=      0
   lowercase__:   List[Any]					=      len(__UpperCAmelCase ) - 1

   while left <= right:
      # avoid divided by 0 during interpolation
      if sorted_collection[left] == sorted_collection[right]:
         if sorted_collection[left] == item:
            return left
         else:
            return None

      lowercase__:   Tuple					=      left + ((item - sorted_collection[left]) * (right - left)) // (
          sorted_collection[right] - sorted_collection[left]
      )

      # out of range check
      if point < 0 or point >= len(__UpperCAmelCase ):
         return None

      lowercase__:   Optional[int]					=      sorted_collection[point]
      if current_item == item:
         return point
      else:
         if point < left:
            lowercase__:   List[Any]					=      left
            lowercase__:   int					=      point
         elif point > right:
            lowercase__:   Dict					=      right
            lowercase__:   List[str]					=      point
         else:
            if item < current_item:
               lowercase__:   int					=      point - 1
            else:
               lowercase__:   int					=      point + 1
   return None



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )  ->  List[str]:

   # avoid divided by 0 during interpolation
   if sorted_collection[left] == sorted_collection[right]:
      if sorted_collection[left] == item:
         return left
      else:
         return None

   lowercase__:   Optional[int]					=      left + ((item - sorted_collection[left]) * (right - left)) // (
       sorted_collection[right] - sorted_collection[left]
   )

   # out of range check
   if point < 0 or point >= len(__UpperCAmelCase ):
      return None

   if sorted_collection[point] == item:
      return point
   elif point < left:
      return interpolation_search_by_recursion(__UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )
   elif point > right:
      return interpolation_search_by_recursion(__UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )
   else:
      if sorted_collection[point] > item:
         return interpolation_search_by_recursion(
             __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    point - 1 )
      else:
         return interpolation_search_by_recursion(
             __UpperCAmelCase       ,    __UpperCAmelCase       ,    point + 1       ,    __UpperCAmelCase )



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  List[Any]:
   if collection != sorted(__UpperCAmelCase ):
      raise ValueError('''Collection must be ascending sorted''' )
   return True


if __name__ == "__main__":
       import sys
       __A			   = 0
       if debug == 1:
              __A			   = [1_0, 3_0, 4_0, 4_5, 5_0, 6_6, 7_7, 9_3]
              try:
                     __assert_sorted(collection)
              except ValueError:
                     sys.exit("Sequence must be ascending sorted to apply interpolation search")
              __A			   = 6_7

       __A			   = interpolation_search(collection, target)
       if result is not None:
              print(f'''{target} found at positions: {result}''')
       else:
              print("Not found")
