




'''simple docstring'''





from itertools import permutations


def 					UpperCamelCase						(	snake_case = 5 ):




   '''simple docstring'''

   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
   SCREAMING_SNAKE_CASE__      :					List[str]							    =			list(range(gon_side + 1						,  0						,  -1 ) )
   SCREAMING_SNAKE_CASE__      :					Optional[Any]							    =			list(range(gon_side + 2						,  gon_side * 2 + 1 ) )

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

   SCREAMING_SNAKE_CASE__      :					Optional[Any]							    =			f"""Magic {gon_side}-gon ring is impossible"""
   raise ValueError(snake_case )


def 					UpperCamelCase						(	snake_case						,  snake_case ):




   '''simple docstring'''

   SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			[0] * (gon_side * 3)
   SCREAMING_SNAKE_CASE__      :					List[str]							    =			perm[0:3]
   perm.append(perm[1] )

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

   for i in range(1						,  len(snake_case ) // 3 + magic_number ):
      SCREAMING_SNAKE_CASE__      :					str							    =			perm[2 * i + 1]
      SCREAMING_SNAKE_CASE__      :					str							    =			result[3 * i - 1]
      SCREAMING_SNAKE_CASE__      :					int							    =			perm[2 * i + 2]

   return result


def 					UpperCamelCase						(	snake_case ):




   '''simple docstring'''

   if len(snake_case ) % 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

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

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


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







'''simple docstring'''

from typing import TYPE_CHECKING

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


a__         =     {'''configuration_gptj''': ['''GPTJ_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''GPTJConfig''', '''GPTJOnnxConfig''']}

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		a__         =     [
		    '''GPTJ_PRETRAINED_MODEL_ARCHIVE_LIST''',
		    '''GPTJForCausalLM''',
		    '''GPTJForQuestionAnswering''',
		    '''GPTJForSequenceClassification''',
		    '''GPTJModel''',
		    '''GPTJPreTrainedModel''',
		]

try:
		if not is_tf_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		a__         =     [
		    '''TFGPTJForCausalLM''',
		    '''TFGPTJForQuestionAnswering''',
		    '''TFGPTJForSequenceClassification''',
		    '''TFGPTJModel''',
		    '''TFGPTJPreTrainedModel''',
		]

try:
		if not is_flax_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		a__         =     [
		    '''FlaxGPTJForCausalLM''',
		    '''FlaxGPTJModel''',
		    '''FlaxGPTJPreTrainedModel''',
		]


if TYPE_CHECKING:
		from .configuration_gptj import GPTJ_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTJConfig, GPTJOnnxConfig

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_gptj import (
				    GPTJ_PRETRAINED_MODEL_ARCHIVE_LIST,
				    GPTJForCausalLM,
				    GPTJForQuestionAnswering,
				    GPTJForSequenceClassification,
				    GPTJModel,
				    GPTJPreTrainedModel,
				)

		try:
				if not is_tf_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_tf_gptj import (
				    TFGPTJForCausalLM,
				    TFGPTJForQuestionAnswering,
				    TFGPTJForSequenceClassification,
				    TFGPTJModel,
				    TFGPTJPreTrainedModel,
				)

		try:
				if not is_flax_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_flax_gptj import FlaxGPTJForCausalLM, FlaxGPTJModel, FlaxGPTJPreTrainedModel

else:
		import sys

		a__         =     _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)