

class _UpperCamelCase							:
			'''simple docstring'''







			def __init__(			self							: Tuple      ,      a							: Any      ,      a							: List[Any]      ,      a							: Any	)							->       Dict:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE   :      List[Any]				     =       None
				SCREAMING_SNAKE_CASE   :      List[Any]				     =       None
				SCREAMING_SNAKE_CASE   :      int				     =       graph

				self._normalize_graph(a      ,      a	)
				SCREAMING_SNAKE_CASE   :      str				     =       len(a	)
				SCREAMING_SNAKE_CASE   :      Dict				     =       None
			def 							__UpperCamelCase (			self							: List[Any]      ,      a							: Optional[int]      ,      a							: List[str]	)							->       Tuple:

				"""simple docstring"""

				if sources is int:
					SCREAMING_SNAKE_CASE   :      Any				     =       [sources]
				if sinks is int:
					SCREAMING_SNAKE_CASE   :      List[str]				     =       [sinks]

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

				SCREAMING_SNAKE_CASE   :      List[Any]				     =       sources[0]
				SCREAMING_SNAKE_CASE   :      List[Any]				     =       sinks[0]

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

					SCREAMING_SNAKE_CASE   :      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:
						SCREAMING_SNAKE_CASE   :      List[Any]				     =       max_input_flow
					SCREAMING_SNAKE_CASE   :      List[Any]				     =       0

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

				"""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 							__UpperCamelCase (			self							: List[str]      ,      a							: Tuple	)							->       Optional[int]:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE   :      List[str]				     =       algorithm(self	)






class _UpperCamelCase							:
			'''simple docstring'''







			def __init__(			self							: Dict      ,      a							: Optional[Any]	)							->       List[str]:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE   :      Optional[Any]				     =       flow_network
				SCREAMING_SNAKE_CASE   :      List[Any]				     =       flow_network.verticesCount
				SCREAMING_SNAKE_CASE   :      str				     =       flow_network.sourceIndex
				SCREAMING_SNAKE_CASE   :      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
				SCREAMING_SNAKE_CASE   :      Optional[int]				     =       flow_network.graph
				SCREAMING_SNAKE_CASE   :      List[str]				     =       False
			def 							__UpperCamelCase (			self							: Optional[int]	)							->       List[str]:

				"""simple docstring"""

				if not self.executed:
					self._algorithm()
					SCREAMING_SNAKE_CASE   :      Dict				     =       True






			def 							__UpperCamelCase (			self							: Union[str, Any]	)							->       Any:

				"""simple docstring"""

				pass






class _UpperCamelCase							(							A_   ):
			'''simple docstring'''







			def __init__(			self							: str      ,      a							: Optional[int]	)							->       int:

				"""simple docstring"""

				super().__init__(a	)
				# use this to save your result
				SCREAMING_SNAKE_CASE   :      str				     =       -1






			def 							__UpperCamelCase (			self							: List[str]	)							->       Optional[Any]:

				"""simple docstring"""

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

				return self.maximum_flow






class _UpperCamelCase							(							A_   ):
			'''simple docstring'''







			def __init__(			self							: List[Any]      ,      a							: str	)							->       Optional[int]:

				"""simple docstring"""

				super().__init__(a	)

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

				SCREAMING_SNAKE_CASE   :      str				     =       [0] * self.verticies_count
				SCREAMING_SNAKE_CASE   :      int				     =       [0] * self.verticies_count
			def 							__UpperCamelCase (			self							: Tuple	)							->       Optional[Any]:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE   :      List[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
				SCREAMING_SNAKE_CASE   :      Any				     =       [
				    i
				    for i in range(self.verticies_count	)
				    if i != self.source_index and i != self.sink_index
				]

				# move through list
				SCREAMING_SNAKE_CASE   :      int				     =       0
				while i < len(a	):
					SCREAMING_SNAKE_CASE   :      List[Any]				     =       vertices_list[i]
					SCREAMING_SNAKE_CASE   :      Any				     =       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	)	)
						SCREAMING_SNAKE_CASE   :      Optional[Any]				     =       0
					else:
						i += 1

				SCREAMING_SNAKE_CASE   :      Tuple				     =       sum(self.preflow[self.source_index]	)
			def 							__UpperCamelCase (			self							: List[Any]      ,      a							: Dict	)							->       List[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 							__UpperCamelCase (			self							: Optional[Any]      ,      a							: List[str]      ,      a							: Tuple	)							->       int:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE   :      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 							__UpperCamelCase (			self							: Tuple      ,      a							: List[Any]	)							->       Dict:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE   :      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):
						SCREAMING_SNAKE_CASE   :      Dict				     =       self.heights[to_index]

				if min_height is not None:
					SCREAMING_SNAKE_CASE   :      str				     =       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}''')


def  lowerCamelCase__ (					_a = 50):
	SCREAMING_SNAKE_CASE   :      int				     =       [1] * (length + 1)

	for row_length in range(length + 1):
		for tile_length in range(2							,			5):
			for tile_start in range(row_length - tile_length + 1):
				ways_number[row_length] += ways_number[
				    row_length - tile_start - tile_length
				]

	return ways_number[length]


if __name__ == "__main__":
			print(F'''{solution() = }''')