




'''simple docstring'''




from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


snake_case__ 							=    {"""configuration_t5""": ["""T5_PRETRAINED_CONFIG_ARCHIVE_MAP""", """T5Config""", """T5OnnxConfig"""]}

try:
							if not is_sentencepiece_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							snake_case__ 							=    ["""T5Tokenizer"""]

try:
							if not is_tokenizers_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							snake_case__ 							=    ["""T5TokenizerFast"""]

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							snake_case__ 							=    [
							    """T5_PRETRAINED_MODEL_ARCHIVE_LIST""",
							    """T5EncoderModel""",
							    """T5ForConditionalGeneration""",
							    """T5Model""",
							    """T5PreTrainedModel""",
							    """load_tf_weights_in_t5""",
							    """T5ForQuestionAnswering""",
							]

try:
							if not is_tf_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							snake_case__ 							=    [
							    """TF_T5_PRETRAINED_MODEL_ARCHIVE_LIST""",
							    """TFT5EncoderModel""",
							    """TFT5ForConditionalGeneration""",
							    """TFT5Model""",
							    """TFT5PreTrainedModel""",
							]

try:
							if not is_flax_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							snake_case__ 							=    [
							    """FlaxT5EncoderModel""",
							    """FlaxT5ForConditionalGeneration""",
							    """FlaxT5Model""",
							    """FlaxT5PreTrainedModel""",
							]


if TYPE_CHECKING:
							from .configuration_ta import T5_PRETRAINED_CONFIG_ARCHIVE_MAP, TaConfig, TaOnnxConfig

							try:
														if not is_sentencepiece_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_ta import TaTokenizer

							try:
														if not is_tokenizers_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_ta_fast import TaTokenizerFast

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_ta import (
														    T5_PRETRAINED_MODEL_ARCHIVE_LIST,
														    TaEncoderModel,
														    TaForConditionalGeneration,
														    TaForQuestionAnswering,
														    TaModel,
														    TaPreTrainedModel,
														    load_tf_weights_in_ta,
														)

							try:
														if not is_tf_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_tf_ta import (
														    TF_T5_PRETRAINED_MODEL_ARCHIVE_LIST,
														    TFTaEncoderModel,
														    TFTaForConditionalGeneration,
														    TFTaModel,
														    TFTaPreTrainedModel,
														)

							try:
														if not is_flax_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_flax_ta import (
														    FlaxTaEncoderModel,
														    FlaxTaForConditionalGeneration,
														    FlaxTaModel,
														    FlaxTaPreTrainedModel,
														)


else:
							import sys

							snake_case__ 							=    _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)









'''simple docstring'''




from itertools import permutations




def     snake_case__     (			lowerCamelCase__					: int = 5      ) -> int:
					if gon_side < 3 or gon_side > 5:
										raise ValueError('''gon_side must be in the range [3, 5]'''      )

					# Since it's 16, we know 10 is on the outer ring
					# Put the big numbers at the end so that they are never the first number
					A_			:  int			=				list(range(gon_side + 1      ,		0      ,		-1      )      )
					A_			:  List[Any]			=				list(range(gon_side + 2      ,		gon_side * 2 + 1      )      )

					for perm in permutations(small_numbers + big_numbers      ):
										A_			:  Optional[int]			=				generate_gon_ring(lowerCamelCase__      ,		list(lowerCamelCase__      )      )
										if is_magic_gon(lowerCamelCase__      ):
															return int(''''''.join(str(lowerCamelCase__      ) for n in numbers      )      )

					A_			:  Optional[Any]			=				f'Magic {gon_side}-gon ring is impossible'
					raise ValueError(lowerCamelCase__      )




def     snake_case__     (			lowerCamelCase__					: int      ,		lowerCamelCase__					: list[int]      ) -> list[int]:
					A_			:  List[Any]			=				[0] * (gon_side * 3)
					A_			:  Optional[Any]			=				perm[0:3]
					perm.append(perm[1]      )

					A_			:  Optional[Any]			=				1 if gon_side < 5 else 2

					for i in range(1      ,		len(lowerCamelCase__      ) // 3 + magic_number      ):
										A_			:  List[str]			=				perm[2 * i + 1]
										A_			:  str			=				result[3 * i - 1]
										A_			:  Union[str, Any]			=				perm[2 * i + 2]

					return result




def     snake_case__     (			lowerCamelCase__					: list[int]      ) -> bool:
					if len(lowerCamelCase__      ) % 3 != 0:
										raise ValueError('''a gon ring should have a length that is a multiple of 3'''      )

					if min(numbers[::3]      ) != numbers[0]:
										return False

					A_			:  Union[str, Any]			=				sum(numbers[:3]      )

					return all(sum(numbers[i : i + 3]      ) == total for i in range(3      ,		len(lowerCamelCase__      )      ,		3      )      )


if __name__ == "__main__":
							print(solution())



