"""simple docstring"""


from itertools import permutations





def 			lowerCamelCase_ (					__lowerCAmelCase = 5				)							->					int:




						'''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
						lowerCamelCase__					=list(range(gon_side + 1   ,    0   ,    -1				)				)
						lowerCamelCase__					=list(range(gon_side + 2   ,    gon_side * 2 + 1				)				)

						for perm in permutations(small_numbers + big_numbers				):
												lowerCamelCase__					=generate_gon_ring(__lowerCAmelCase   ,    list(__lowerCAmelCase				)				)
												if is_magic_gon(__lowerCAmelCase				):
																		return int("".join(str(__lowerCAmelCase				) for n in numbers				)				)

						lowerCamelCase__					=F'''Magic {gon_side}-gon ring is impossible'''
						raise ValueError(__lowerCAmelCase				)





def 			lowerCamelCase_ (					__lowerCAmelCase   ,    __lowerCAmelCase				)							->					list[int]:




						'''simple docstring'''



						lowerCamelCase__					=[0] * (gon_side * 3)
						lowerCamelCase__					=perm[0:3]
						perm.append(perm[1]				)

						lowerCamelCase__					=1 if gon_side < 5 else 2

						for i in range(1   ,    len(__lowerCAmelCase				) // 3 + magic_number				):
												lowerCamelCase__					=perm[2 * i + 1]
												lowerCamelCase__					=result[3 * i - 1]
												lowerCamelCase__					=perm[2 * i + 2]

						return result





def 			lowerCamelCase_ (					__lowerCAmelCase				)							->					bool:




						'''simple docstring'''



						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

						lowerCamelCase__					=sum(numbers[:3]				)

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


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



"""simple docstring"""


from ..utils import DummyObject, requires_backends






class    __UpperCAmelCase						(	metaclass=__lowerCAmelCase	):
				A__      :   List[Any]  							=       ['''torch''', '''librosa''']

				def __init__(      self	, *_lowerCamelCase	, **_lowerCamelCase      ):
										requires_backends(self	, ["torch", "librosa"]      )

				@classmethod
				def 		_a	(      cls	, *_lowerCamelCase	, **_lowerCamelCase      ):
										requires_backends(cls	, ["torch", "librosa"]      )






				@classmethod
				def 		_a	(      cls	, *_lowerCamelCase	, **_lowerCamelCase      ):
										requires_backends(cls	, ["torch", "librosa"]      )






class    __UpperCAmelCase						(	metaclass=__lowerCAmelCase	):
				A__      :   List[str]  							=       ['''torch''', '''librosa''']

				def __init__(      self	, *_lowerCamelCase	, **_lowerCamelCase      ):
										requires_backends(self	, ["torch", "librosa"]      )

				@classmethod
				def 		_a	(      cls	, *_lowerCamelCase	, **_lowerCamelCase      ):
										requires_backends(cls	, ["torch", "librosa"]      )






				@classmethod
				def 		_a	(      cls	, *_lowerCamelCase	, **_lowerCamelCase      ):
										requires_backends(cls	, ["torch", "librosa"]      )


