






# 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 				A		(					lowercase__  :  Dict  )		-> List[Any]:
	UpperCamelCase__ :List[str]						=      [False] * len(lowercase__  )
	UpperCamelCase__ :List[str]						=      [-1] * len(lowercase__  )

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

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

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

	return True


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




print(check_bipartite_dfs(graph))



'''simple docstring'''





from collections import OrderedDict
from typing import TYPE_CHECKING, Any, Mapping, Optional

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging


if TYPE_CHECKING:
    from ... import FeatureExtractionMixin, TensorType

__lowerCamelCase												=						logging.get_logger(__name__)

__lowerCamelCase												=						{
    '''openai/imagegpt-small''': '''''',
    '''openai/imagegpt-medium''': '''''',
    '''openai/imagegpt-large''': '''''',
}




class 				UpperCAmelCase			(			_snake_case						):
 UpperCAmelCase				=					"imagegpt"
 UpperCAmelCase				=					["past_key_values"]
 UpperCAmelCase				=					{
     "hidden_size": "n_embd",
     "max_position_embeddings": "n_positions",
     "num_attention_heads": "n_head",
     "num_hidden_layers": "n_layer",
 }


 def __init__(      self							:	List[Any]			,       __lowerCamelCase							:	List[Any]=5_1_2 + 1			,       __lowerCamelCase							:	Dict=3_2 * 3_2			,       __lowerCamelCase							:	List[str]=5_1_2			,       __lowerCamelCase							:	List[Any]=2_4			,       __lowerCamelCase							:	Any=8			,       __lowerCamelCase							:	Tuple=None			,       __lowerCamelCase							:	Any="quick_gelu"			,       __lowerCamelCase							:	Optional[int]=0.1			,       __lowerCamelCase							:	str=0.1			,       __lowerCamelCase							:	int=0.1			,       __lowerCamelCase							:	Tuple=1e-5			,       __lowerCamelCase							:	Dict=0.02			,       __lowerCamelCase							:	Tuple=True			,       __lowerCamelCase							:	str=True			,       __lowerCamelCase							:	Union[str, Any]=False			,       __lowerCamelCase							:	Union[str, Any]=False			,       __lowerCamelCase							:	Dict=False			,       **__lowerCamelCase							:	str			,       ):
    UpperCAmelCase__	:Dict      =      vocab_size
    UpperCAmelCase__	:str      =      n_positions
    UpperCAmelCase__	:Tuple      =      n_embd
    UpperCAmelCase__	:Dict      =      n_layer
    UpperCAmelCase__	:List[Any]      =      n_head
    UpperCAmelCase__	:str      =      n_inner
    UpperCAmelCase__	:Optional[Any]      =      activation_function
    UpperCAmelCase__	:str      =      resid_pdrop
    UpperCAmelCase__	:Optional[Any]      =      embd_pdrop
    UpperCAmelCase__	:Tuple      =      attn_pdrop
    UpperCAmelCase__	:int      =      layer_norm_epsilon
    UpperCAmelCase__	:List[Any]      =      initializer_range
    UpperCAmelCase__	:List[Any]      =      scale_attn_weights
    UpperCAmelCase__	:List[str]      =      use_cache
    UpperCAmelCase__	:Tuple      =      scale_attn_by_inverse_layer_idx
    UpperCAmelCase__	:Union[str, Any]      =      reorder_and_upcast_attn
    UpperCAmelCase__	:List[Any]      =      tie_word_embeddings

    super().__init__(tie_word_embeddings=__lowerCamelCase			,       **__lowerCamelCase )




class 				UpperCAmelCase			(			_snake_case						):


 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	str ):
    return OrderedDict(
        [
            ('''input_ids''', {0: '''batch''', 1: '''sequence'''}),
        ] )





 def        __SCREAMING_SNAKE_CASE					(      self							:	Dict			,       __lowerCamelCase							:	"FeatureExtractionMixin"			,       __lowerCamelCase							:	int = 1			,       __lowerCamelCase							:	int = -1			,       __lowerCamelCase							:	bool = False			,       __lowerCamelCase							:	Optional["TensorType"] = None			,       __lowerCamelCase							:	int = 3			,       __lowerCamelCase							:	int = 3_2			,       __lowerCamelCase							:	int = 3_2			,       ):
    UpperCAmelCase__	:Tuple      =      self._generate_dummy_images(__lowerCamelCase			,       __lowerCamelCase			,       __lowerCamelCase			,       __lowerCamelCase )
    UpperCAmelCase__	:Dict      =      dict(preprocessor(images=__lowerCamelCase			,       return_tensors=__lowerCamelCase ) )

    return inputs



