




# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.





def        __UpperCAmelCase						(							lowerCamelCase_ :     str  )       ->  Optional[int]:







			"""simple docstring"""





			SCREAMING_SNAKE_CASE_   : List[Any]					  =      [False] * len(lowerCamelCase_  )
			SCREAMING_SNAKE_CASE_   : str					  =      [-1] * len(lowerCamelCase_  )

			def dfs(lowerCamelCase_ :     Any  ,							lowerCamelCase_ :     Any  ):
						SCREAMING_SNAKE_CASE_   : str					  =      True
						SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      c
						for u in graph[v]:
									if not visited[u]:
												dfs(lowerCamelCase_  ,							1 - c  )

			for i in range(len(lowerCamelCase_  )  ):
						if not visited[i]:
									dfs(lowerCamelCase_  ,							0  )

			for i in range(len(lowerCamelCase_  )  ):
						for j in graph[i]:
									if color[i] == color[j]:
												return False

			return True


# Adjacency list of graph
UpperCamelCase__ :   Any						=							{0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}




print(check_bipartite_dfs(graph))










import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging


_lowerCamelCase 					=      logging.get_logger(__name__)




class 	UpperCamelCase_							(  UpperCamelCase__     ):
							lowerCamelCase_							     =       "encoder-decoder"
							lowerCamelCase_							     =       True


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



									"""simple docstring"""



									super().__init__(**__A		)
									assert (
									    "encoder" in kwargs and "decoder" in kwargs
									), "Config has to be initialized with encoder and decoder config"
									SCREAMING_SNAKE_CASE__								=   kwargs.pop("""encoder"""		)
									SCREAMING_SNAKE_CASE__								=   encoder_config.pop("""model_type"""		)
									SCREAMING_SNAKE_CASE__								=   kwargs.pop("""decoder"""		)
									SCREAMING_SNAKE_CASE__								=   decoder_config.pop("""model_type"""		)

									from ..auto.configuration_auto import AutoConfig

									SCREAMING_SNAKE_CASE__								=   AutoConfig.for_model(__A				,					**__A		)
									SCREAMING_SNAKE_CASE__								=   AutoConfig.for_model(__A				,					**__A		)
									SCREAMING_SNAKE_CASE__								=   True


							@classmethod
							def   _snake_case	(				cls     :str				,					__A     :PretrainedConfig				,					__A     :PretrainedConfig				,					**__A     :List[str]		) -> PretrainedConfig:



									"""simple docstring"""



									logger.info("""Set `config.is_decoder=True` and `config.add_cross_attention=True` for decoder_config"""		)
									SCREAMING_SNAKE_CASE__								=   True
									SCREAMING_SNAKE_CASE__								=   True

									return cls(encoder=encoder_config.to_dict()				,					decoder=decoder_config.to_dict()				,					**__A		)


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



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								=   copy.deepcopy(self.__dict__		)
									SCREAMING_SNAKE_CASE__								=   self.encoder.to_dict()
									SCREAMING_SNAKE_CASE__								=   self.decoder.to_dict()
									SCREAMING_SNAKE_CASE__								=   self.__class__.model_type
									return output