






"""simple docstring"""


from itertools import permutations




def 			snake_case  (A_      :int = 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
  a     :			List[str]				=   list(range(gon_side + 1	,			0	,			-1      )      )
  a     :			str				=   list(range(gon_side + 2	,			gon_side * 2 + 1      )      )

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

  a     :			Union[str, Any]				=   f'''Magic {gon_side}-gon ring is impossible'''
  raise ValueError(A_      )




def 			snake_case  (A_      :int	,			A_      :list[int]      ):







  '''simple docstring'''

  a     :			Any				=   [0] * (gon_side * 3)
  a     :			List[Any]				=   perm[0:3]
  perm.append(perm[1]      )

  a     :			Tuple				=   1 if gon_side < 5 else 2

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

  return result




def 			snake_case  (A_      :list[int]      ):







  '''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

  a     :			int				=   sum(numbers[:3]      )

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


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










def  lowerCAmelCase  (	UpperCAmelCase       )  ->int:






					"""simple docstring"""






					return n * (2 * n - 1)







def  lowerCAmelCase  (	UpperCAmelCase       )  ->bool:






					"""simple docstring"""






					__magic_name__					:							Any		   =							(1 + 24 * n) ** 0.5
					return ((1 + root) / 6) % 1 == 0







def  lowerCAmelCase  (	UpperCAmelCase = 144       )  ->int:






					"""simple docstring"""






					__magic_name__					:							Optional[int]		   =							start
					__magic_name__					:							int		   =							hexagonal_num(UpperCAmelCase       )
					while not is_pentagonal(UpperCAmelCase       ):
										n += 1
										__magic_name__					:							Optional[int]		   =							hexagonal_num(UpperCAmelCase       )
					return num


if __name__ == "__main__":
				print(f"{solution()} = ")



