



"""simple docstring"""


def 					_lowerCAmelCase (  lowercase_		):
						UpperCAmelCase			 =					1
						UpperCAmelCase			 =					0
						UpperCAmelCase			 =					1
						UpperCAmelCase			 =					1
						UpperCAmelCase			 =					3
						UpperCAmelCase			 =					3
						UpperCAmelCase			 =					limit
						UpperCAmelCase			 =					0

						UpperCAmelCase			 =					''
						while counter != decimal + 1:
												if 4 * q + r - t < n * t:
																		result += str(lowercase_		)
																		if counter == 0:
																								result += "."

																		if decimal == counter:
																								break

																		counter += 1
																		UpperCAmelCase			 =					10 * (r - n * t)
																		UpperCAmelCase			 =					((10 * (3 * q + r)) // t) - 10 * n
																		q *= 10
																		UpperCAmelCase			 =					nr
												else:
																		UpperCAmelCase			 =					(2 * q + r) * l
																		UpperCAmelCase			 =					(q * (7 * k) + 2 + (r * l)) // (t * l)
																		q *= k
																		t *= l
																		l += 2
																		k += 1
																		UpperCAmelCase			 =					nn
																		UpperCAmelCase			 =					nr
						return result

def 					_lowerCAmelCase (  ):
						print(F"""{calculate_pi(50		) = }"""		)
						import doctest

						doctest.testmod()


if __name__ == "__main__":
				main()










"""simple docstring"""


from itertools import permutations

def 					_lowerCAmelCase (  lowercase_ = 5		):
						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
						UpperCAmelCase			 =					list(range(gon_side + 1						,      0						,      -1		)		)
						UpperCAmelCase			 =					list(range(gon_side + 2						,      gon_side * 2 + 1		)		)

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

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

def 					_lowerCAmelCase (  lowercase_						,      lowercase_		):
						UpperCAmelCase			 =					[0] * (gon_side * 3)
						UpperCAmelCase			 =					perm[0:3]
						perm.append(perm[1]		)

						UpperCAmelCase			 =					1 if gon_side < 5 else 2

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

						return result

def 					_lowerCAmelCase (  lowercase_		):
						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

						UpperCAmelCase			 =					sum(numbers[:3]		)

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


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





