


from itertools import permutations
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	: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
						__magic_name__					:				str				=   list(range(gon_side + 1   ,    0   ,    -1					)					)
						__magic_name__					:				List[str]				=   list(range(gon_side + 2   ,    gon_side * 2 + 1					)					)

						for perm in permutations(small_numbers + big_numbers					):
												__magic_name__					:				Any				=   generate_gon_ring(lowercase__   ,    list(lowercase__					)					)
												if is_magic_gon(lowercase__					):
																		return int(''.join(str(lowercase__					) for n in numbers					)					)

						__magic_name__					:				Dict				=   f"Magic {gon_side}-gon ring is impossible"
						raise ValueError(lowercase__					)
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:int   ,    lowercase__	:list[int]					)							->	list[int]:
						__magic_name__					:				List[Any]				=   [0] * (gon_side * 3)
						__magic_name__					:				List[str]				=   perm[0:3]
						perm.append(perm[1]					)

						__magic_name__					:				List[str]				=   1 if gon_side < 5 else 2

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

						return result
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:list[int]					)							->	bool:
						if len(lowercase__					) % 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

						__magic_name__					:				Optional[int]				=   sum(numbers[:3]					)

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


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






import math
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:int					)							->	list:
						if n <= 0:
												raise ValueError('Only positive integers have prime factors'					)
						__magic_name__					:				Union[str, Any]				=   []
						while n % 2 == 0:
												pf.append(2					)
												__magic_name__					:				Union[str, Any]				=   int(n / 2					)
						for i in range(3   ,    int(math.sqrt(lowercase__					)					) + 1   ,    2					):
												while n % i == 0:
																		pf.append(lowercase__					)
																		__magic_name__					:				List[str]				=   int(n / i					)
						if n > 2:
												pf.append(lowercase__					)
						return pf
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:int					)							->	int:
						if n <= 0:
												raise ValueError('Only positive numbers are accepted'					)
						__magic_name__					:				Union[str, Any]				=   1
						__magic_name__					:				Tuple				=   1
						while n % 2 == 0:
												temp += 1
												__magic_name__					:				Any				=   int(n / 2					)
						div *= temp
						for i in range(3   ,    int(math.sqrt(lowercase__					)					) + 1   ,    2					):
												__magic_name__					:				List[Any]				=   1
												while n % i == 0:
																		temp += 1
																		__magic_name__					:				Any				=   int(n / i					)
												div *= temp
						if n > 1:
												div *= 2
						return div
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:int					)							->	int:
						if n <= 0:
												raise ValueError('Only positive numbers are accepted'					)
						__magic_name__					:				int				=   1
						__magic_name__					:				List[str]				=   1
						while n % 2 == 0:
												temp += 1
												__magic_name__					:				List[Any]				=   int(n / 2					)
						if temp > 1:
												s *= (2**temp - 1) / (2 - 1)
						for i in range(3   ,    int(math.sqrt(lowercase__					)					) + 1   ,    2					):
												__magic_name__					:				int				=   1
												while n % i == 0:
																		temp += 1
																		__magic_name__					:				Optional[Any]				=   int(n / i					)
												if temp > 1:
																		s *= (i**temp - 1) / (i - 1)
						return int(lowercase__					)
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:int					)							->	int:
						__magic_name__					:				Dict				=   n
						for x in set(prime_factors(lowercase__					)					):
												s *= (x - 1) / x
						return int(lowercase__					)


if __name__ == "__main__":
			import doctest

			doctest.testmod()


