




'''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"""
from typing import Any





class   __A  :





							'''simple docstring'''

							def __init__(					self				:   List[Any]							)       ->int:



														"""simple docstring"""



														snake_case_     							=		[]
														snake_case_     							=		0



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



														"""simple docstring"""



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



							def 		lowerCAmelCase							(					self				:   List[Any]		,							UpperCAmelCase_				:   Any							)       ->None:



														"""simple docstring"""



														self.stack.append(UpperCAmelCase_							)
														snake_case_     							=		self.length + 1



							def 		lowerCAmelCase							(					self				:   List[str]							)       ->Any:



														"""simple docstring"""



														self.rotate(1							)
														snake_case_     							=		self.stack[self.length - 1]
														snake_case_     							=		self.stack[:-1]
														self.rotate(self.length - 1							)
														snake_case_     							=		self.length - 1
														return dequeued



							def 		lowerCAmelCase							(					self				:   List[str]		,							UpperCAmelCase_				:   int							)       ->None:



														"""simple docstring"""



														for _ in range(UpperCAmelCase_							):
																					snake_case_     							=		self.stack[0]
																					snake_case_     							=		self.stack[1:]
																					self.put(UpperCAmelCase_							)
																					snake_case_     							=		self.length - 1



							def 		lowerCAmelCase							(					self				:   Dict							)       ->Any:



														"""simple docstring"""



														snake_case_     							=		self.get()
														self.put(UpperCAmelCase_							)
														self.rotate(self.length - 1							)
														return front



							def 		lowerCAmelCase							(					self				:   Optional[Any]							)       ->int:



														"""simple docstring"""



														return self.length



