

class        a	:




							"""simple docstring"""


							def __init__(							self :						str					,			lowerCamelCase :						Dict					,			lowerCamelCase :						Dict					,			lowerCamelCase :						List[str]       )			->					Dict:
														__snake_case	:    Dict											=     None
														__snake_case	:    Optional[int]											=     None
														__snake_case	:    List[Any]											=     graph

														self._normalize_graph(SCREAMING_SNAKE_CASE_					,			SCREAMING_SNAKE_CASE_       )
														__snake_case	:    int											=     len(SCREAMING_SNAKE_CASE_       )
														__snake_case	:    List[str]											=     None

							def 					__snake_case      (							self :						Dict					,			lowerCamelCase :						List[Any]					,			lowerCamelCase :						List[Any]       )			->					Optional[Any]:
														if sources is int:
																					__snake_case	:    List[str]											=     [sources]
														if sinks is int:
																					__snake_case	:    Tuple											=     [sinks]

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

														__snake_case	:    List[str]											=     sources[0]
														__snake_case	:    List[str]											=     sinks[0]

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

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

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

							def 					__snake_case      (							self :						Optional[int]       )			->					str:
														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 :						List[str]					,			lowerCamelCase :						str       )			->					Optional[Any]:
														__snake_case	:    Any											=     algorithm(self       )

class        a	:




							"""simple docstring"""


							def __init__(							self :						List[Any]					,			lowerCamelCase :						Optional[Any]       )			->					Union[str, Any]:
														__snake_case	:    List[str]											=     flow_network
														__snake_case	:    Union[str, Any]											=     flow_network.verticesCount
														__snake_case	:    Any											=     flow_network.sourceIndex
														__snake_case	:    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
														__snake_case	:    Dict											=     flow_network.graph
														__snake_case	:    Union[str, Any]											=     False

							def 					__snake_case      (							self :						Dict       )			->					int:
														if not self.executed:
																					self._algorithm()
																					__snake_case	:    List[Any]											=     True






							def 					__snake_case      (							self :						str       )			->					str:
														pass

class        a	(__lowerCamelCase   ):




							"""simple docstring"""


							def __init__(							self :						List[Any]					,			lowerCamelCase :						Tuple       )			->					Any:
														super().__init__(SCREAMING_SNAKE_CASE_       )
														# use this to save your result
														__snake_case	:    str											=     -1






							def 					__snake_case      (							self :						Tuple       )			->					Dict:
														if not self.executed:
																					raise Exception("You should execute algorithm before using its result!"       )

														return self.maximum_flow

class        a	(__lowerCamelCase   ):




							"""simple docstring"""


							def __init__(							self :						str					,			lowerCamelCase :						Optional[int]       )			->					Union[str, Any]:
														super().__init__(SCREAMING_SNAKE_CASE_       )

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

														__snake_case	:    int											=     [0] * self.verticies_count
														__snake_case	:    Any											=     [0] * self.verticies_count

							def 					__snake_case      (							self :						int       )			->					List[str]:
														__snake_case	:    Tuple											=     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
														__snake_case	:    Dict											=     [
														    i
														    for i in range(self.verticies_count       )
														    if i != self.source_index and i != self.sink_index
														]

														# move through list
														__snake_case	:    int											=     0
														while i < len(SCREAMING_SNAKE_CASE_       ):
																					__snake_case	:    Optional[Any]											=     vertices_list[i]
																					__snake_case	:    str											=     self.heights[vertex_index]
																					self.process_vertex(SCREAMING_SNAKE_CASE_       )
																					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(SCREAMING_SNAKE_CASE_       )       )
																												__snake_case	:    Union[str, Any]											=     0
																					else:
																												i += 1

														__snake_case	:    List[str]											=     sum(self.preflow[self.source_index]       )

							def 					__snake_case      (							self :						Tuple					,			lowerCamelCase :						Dict       )			->					List[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(SCREAMING_SNAKE_CASE_					,			SCREAMING_SNAKE_CASE_       )

																					self.relabel(SCREAMING_SNAKE_CASE_       )

							def 					__snake_case      (							self :						Tuple					,			lowerCamelCase :						List[Any]					,			lowerCamelCase :						Tuple       )			->					Optional[int]:
														__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 					__snake_case      (							self :						Any					,			lowerCamelCase :						Union[str, Any]       )			->					Any:
														__snake_case	:    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):
																												__snake_case	:    Dict											=     self.heights[to_index]

														if min_height is not None:
																					__snake_case	:    Any											=     min_height + 1


if __name__ == "__main__":
			_snake_case  :	str			      =       [0]
			_snake_case  :	str			      =       [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],
			# ]
			_snake_case  :	str			      =       [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

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

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





import logging
import os
from logging import (
    CRITICAL,  # NOQA
    DEBUG,  # NOQA
    ERROR,  # NOQA
    FATAL,  # NOQA
    INFO,  # NOQA
    NOTSET,  # NOQA
    WARN,  # NOQA
    WARNING,  # NOQA
)
from typing import Optional

from tqdm import auto as tqdm_lib


_snake_case  :	int			      =       {
    "debug": logging.DEBUG,
    "info": logging.INFO,
    "warning": logging.WARNING,
    "error": logging.ERROR,
    "critical": logging.CRITICAL,
}

_snake_case  :	Dict			      =       logging.WARNING







def        lowerCAmelCase_  (      ):
							__snake_case	:    Union[str, Any]											=     os.getenv("DATASETS_VERBOSITY"							,			__lowerCamelCase			)
							if env_level_str:
														if env_level_str in log_levels:
																					return log_levels[env_level_str]
														else:
																					logging.getLogger().warning(
																					    F'Unknown option DATASETS_VERBOSITY={env_level_str}, '
																					    F'has to be one of: { ", ".join(log_levels.keys()			) }'			)
							return _default_log_level







def        lowerCAmelCase_  (      ):
							return __name__.split("."			)[0]







def        lowerCAmelCase_  (      ):
							return logging.getLogger(_get_library_name()			)







def        lowerCAmelCase_  (      ):
							# Apply our default configuration to the library root logger.
							__snake_case	:    str											=     _get_library_root_logger()
							library_root_logger.setLevel(_get_default_logging_level()			)







def        lowerCAmelCase_  (      ):
							__snake_case	:    Dict											=     _get_library_root_logger()
							library_root_logger.setLevel(logging.NOTSET			)







def        lowerCAmelCase_  (      __lowerCamelCase = None			):
							if name is None:
														__snake_case	:    Tuple											=     _get_library_name()
							return logging.getLogger(__lowerCamelCase			)







def        lowerCAmelCase_  (      ):
							return _get_library_root_logger().getEffectiveLevel()







def        lowerCAmelCase_  (      __lowerCamelCase			):
							_get_library_root_logger().setLevel(__lowerCamelCase			)







def        lowerCAmelCase_  (      ):
							return set_verbosity(__lowerCamelCase			)







def        lowerCAmelCase_  (      ):
							return set_verbosity(__lowerCamelCase			)







def        lowerCAmelCase_  (      ):
							return set_verbosity(__lowerCamelCase			)







def        lowerCAmelCase_  (      ):
							return set_verbosity(__lowerCamelCase			)







def        lowerCAmelCase_  (      ):
							__snake_case	:    List[str]											=     False







def        lowerCAmelCase_  (      ):
							__snake_case	:    Tuple											=     True


# Configure the library root logger at the module level (singleton-like)
_configure_library_root_logger()

class        a	:




							"""simple docstring"""


							def __init__(							self :						int					,			*lowerCamelCase :						Optional[Any]					,			**lowerCamelCase :						List[str]       )			->					Optional[int]:  # pylint: disable=unused-argument
														__snake_case	:    int											=     args[0] if args else None

							def __iter__(							self :						Dict       )			->					Optional[int]:
														return iter(self._iterator       )

							def __getattr__(							self :						int					,			lowerCamelCase :						Optional[Any]       )			->					List[Any]:

														def empty_fn(*lowerCamelCase :						Optional[int]					,			**lowerCamelCase :						List[Any]       ):  # pylint: disable=unused-argument
																					return

														return empty_fn

							def __enter__(							self :						List[str]       )			->					int:
														return self






							def __exit__(							self :						Dict					,			lowerCamelCase :						Any					,			lowerCamelCase :						List[Any]					,			lowerCamelCase :						str       )			->					Dict:
														return
_snake_case  :	Optional[Any]			      =       True

class        a	:




							"""simple docstring"""


							def __call__(							self :						str					,			*lowerCamelCase :						Optional[Any]					,			lowerCamelCase :						Tuple=False					,			**lowerCamelCase :						Union[str, Any]       )			->					Optional[Any]:
														if _tqdm_active and not disable:
																					return tqdm_lib.tqdm(*lowerCamelCase					,			**lowerCamelCase       )
														else:
																					return EmptyTqdm(*lowerCamelCase					,			**lowerCamelCase       )

							def 					__snake_case      (							self :						str					,			*lowerCamelCase :						str					,			**lowerCamelCase :						Tuple       )			->					str:
														__snake_case	:    Optional[Any]											=     None
														if _tqdm_active:
																					return tqdm_lib.tqdm.set_lock(*lowerCamelCase					,			**lowerCamelCase       )






							def 					__snake_case      (							self :						List[Any]       )			->					List[Any]:
														if _tqdm_active:
																					return tqdm_lib.tqdm.get_lock()
_snake_case  :	int			      =       _tqdm_cls()







def        lowerCAmelCase_  (      ):
							global _tqdm_active
							return bool(_tqdm_active			)







def        lowerCAmelCase_  (      ):
							global _tqdm_active
							__snake_case	:    Tuple											=     True







def        lowerCAmelCase_  (      ):
							global _tqdm_active
							__snake_case	:    List[Any]											=     False

