

# 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        lowerCAmelCase__				(						SCREAMING_SNAKE_CASE_:				Optional[Any]   )      ->   Any:




				'''simple docstring'''





				A__          =      [False] * len(SCREAMING_SNAKE_CASE_   )
				A__          =      [-1] * len(SCREAMING_SNAKE_CASE_   )

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

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

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

				return True


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





print(check_bipartite_dfs(graph))







import math

import tensorflow as tf
from packaging import version




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						str										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						List[str]										=0.5 * (1.0 + tf.math.erf(x / tf.cast(tf.sqrt(2.0 )						,  x.dtype ) ))

				return x * cdf




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						str										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						Optional[Any]										=tf.cast(math.pi						,  x.dtype )
				__magic_name__						:						int										=tf.cast(0.0_4_4_7_1_5						,  x.dtype )
				__magic_name__						:						Tuple										=0.5 * (1.0 + tf.tanh(tf.sqrt(2.0 / pi ) * (x + coeff * tf.pow(lowerCamelCase						,  3 )) ))

				return x * cdf




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						Any										=tf.convert_to_tensor(lowerCamelCase )

				return x * tf.tanh(tf.math.softplus(lowerCamelCase ) )




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						Optional[Any]										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						Union[str, Any]										=tf.cast(0.0_4_4_7_1_5						,  x.dtype )
				__magic_name__						:						Tuple										=tf.cast(0.7_9_7_8_8_4_5_6_0_8						,  x.dtype )

				return 0.5 * x * (1.0 + tf.tanh(x * coeffa * (1.0 + coeffa * x * x) ))




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						List[str]										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						Dict										=tf.cast(1.7_0_2						,  x.dtype )
				return x * tf.math.sigmoid(coeff * x )




def 		lowerCAmelCase_ (						lowerCamelCase ):
				return tf.clip_by_value(_gelu(lowerCamelCase )						,  -10						,  10 )




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase=-1 ):
				__magic_name__					,			__magic_name__						:						List[Any]										=tf.split(lowerCamelCase						,  2						,  axis=lowerCamelCase )
				return a * tf.math.sigmoid(lowerCamelCase )


if version.parse(tf.version.VERSION) >= version.parse("2.4"):




							def 		lowerCAmelCase_ (						lowerCamelCase ):
											return tf.keras.activations.gelu(lowerCamelCase						,  approximate=lowerCamelCase )

							UpperCAmelCase_		:					List[str]          =  tf.keras.activations.gelu



							UpperCAmelCase_		:					Dict          =  approximate_gelu_wrap
else:
							UpperCAmelCase_		:					Dict          =  _gelu
							UpperCAmelCase_		:					str          =  _gelu_new


UpperCAmelCase_		:					Any          =  {
    "gelu": gelu,
    "gelu_10": gelu_aa,
    "gelu_fast": gelu_fast,
    "gelu_new": gelu_new,
    "glu": glu,
    "mish": mish,
    "quick_gelu": quick_gelu,
    "relu": tf.keras.activations.relu,
    "sigmoid": tf.keras.activations.sigmoid,
    "silu": tf.keras.activations.swish,
    "swish": tf.keras.activations.swish,
    "tanh": tf.keras.activations.tanh,
}




def 		lowerCAmelCase_ (						lowerCamelCase ):
				if activation_string in ACTaFN:
								return ACTaFN[activation_string]
				else:
								raise KeyError(F"function {activation_string} not found in ACT2FN mapping {list(ACTaFN.keys() )}" )




