



def      lowerCAmelCase_					(  _lowercase    :       list[int]						,       _lowercase    :       list[int]						,       _lowercase    :       int)							->	bool:







			"""simple docstring"""
			return not any(
			    neighbour == 1 and colored_vertices[i] == color
			    for i, neighbour in enumerate(_lowercase))

def      lowerCAmelCase_					(  _lowercase    :       list[list[int]]						,       _lowercase    :       int						,       _lowercase    :       list[int]						,       _lowercase    :       int)							->	bool:







			"""simple docstring"""

			# Base Case
			if index == len(_lowercase):
						return True

			# Recursive Step
			for i in range(_lowercase):
						if valid_coloring(graph[index]						,       _lowercase						,       _lowercase):
									# Color current vertex
									a__       :						Union[str, Any]							=  i
									# Validate coloring
									if util_color(_lowercase						,       _lowercase						,       _lowercase						,       index + 1):
												return True
									# Backtrack
									a__       :						List[str]							=  -1
			return False





def      lowerCAmelCase_					(  _lowercase    :       list[list[int]]						,       _lowercase    :       int)							->	list[int]:







			"""simple docstring"""
			a__       :						Union[str, Any]							=  [-1] * len(_lowercase)

			if util_color(_lowercase						,       _lowercase						,       _lowercase						,       0):
						return colored_vertices

			return []









from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_flax_available, is_torch_available


_lowercase		:				int      		={
    "configuration_longt5": ["LONGT5_PRETRAINED_CONFIG_ARCHIVE_MAP", "LongT5Config", "LongT5OnnxConfig"],
}

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		_lowercase		:				Optional[Any]      		=[
		    "LONGT5_PRETRAINED_MODEL_ARCHIVE_LIST",
		    "LongT5EncoderModel",
		    "LongT5ForConditionalGeneration",
		    "LongT5Model",
		    "LongT5PreTrainedModel",
		]

try:
		if not is_flax_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		_lowercase		:				List[Any]      		=[
		    "FlaxLongT5ForConditionalGeneration",
		    "FlaxLongT5Model",
		    "FlaxLongT5PreTrainedModel",
		]


if TYPE_CHECKING:
		from .configuration_longta import LONGT5_PRETRAINED_CONFIG_ARCHIVE_MAP, LongTaConfig, LongTaOnnxConfig

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_longta import (
				    LONGT5_PRETRAINED_MODEL_ARCHIVE_LIST,
				    LongTaEncoderModel,
				    LongTaForConditionalGeneration,
				    LongTaModel,
				    LongTaPreTrainedModel,
				)

		try:
				if not is_flax_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_flax_longta import (
				    FlaxLongTaForConditionalGeneration,
				    FlaxLongTaModel,
				    FlaxLongTaPreTrainedModel,
				)


else:
		import sys

		_lowercase		:				Any      		=_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)




