




'''simple docstring'''

from itertools import permutations




def    snake_case__     (  a = 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
			snake_case__          =						list(range(gon_side + 1       ,      0       ,      -1	)	)
			snake_case__          =						list(range(gon_side + 2       ,      gon_side * 2 + 1	)	)

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

			snake_case__          =						F"""Magic {gon_side}-gon ring is impossible"""
			raise ValueError(a	)




def    snake_case__     (  a       ,      a	)			->       list[int]:





			'''simple docstring'''






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

			snake_case__          =						1 if gon_side < 5 else 2

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

			return result




def    snake_case__     (  a	)			->       bool:





			'''simple docstring'''






			if len(a	) % 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

			snake_case__          =						sum(numbers[:3]	)

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


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





'''simple docstring'''

class __magic_name__:






						def __init__(   self						:						List[Any]       ):



									'''simple docstring'''






									snake_case__          =						[]
									snake_case__          =						0
									snake_case__          =						0






						def __str__(   self						:						Union[str, Any]       ):



									'''simple docstring'''






									snake_case__          =						"""<""" + str(self.entries       )[1:-1] + """>"""
									return printed






						def       __lowerCAmelCase(   self						:						List[Any]					,   __UpperCamelCase						:						List[Any]       ):



									'''simple docstring'''






									self.entries.append(__UpperCamelCase       )
									snake_case__          =						self.length + 1






						def       __lowerCAmelCase(   self						:						int       ):



									'''simple docstring'''






									snake_case__          =						self.length - 1
									snake_case__          =						self.entries[self.front]
									# self.front-=1
									# self.entries = self.entries[self.front:]
									snake_case__          =						self.entries[1:]
									return dequeued






						def       __lowerCAmelCase(   self						:						str					,   __UpperCamelCase						:						Optional[Any]       ):



									'''simple docstring'''






									for _ in range(__UpperCamelCase       ):
												self.put(self.get()       )






						def       __lowerCAmelCase(   self						:						List[Any]       ):



									'''simple docstring'''






									return self.entries[0]






						def       __lowerCAmelCase(   self						:						str       ):



									'''simple docstring'''






									return self.length