

"""simple docstring"""





def 						__SCREAMING_SNAKE_CASE						(   A_				):
	lowerCAmelCase__			:		Any						       =			1
	lowerCAmelCase__			:		int						       =			0
	lowerCAmelCase__			:		Any						       =			1
	lowerCAmelCase__			:		Tuple						       =			1
	lowerCAmelCase__			:		List[str]						       =			3
	lowerCAmelCase__			:		str						       =			3
	lowerCAmelCase__			:		str						       =			limit
	lowerCAmelCase__			:		Dict						       =			0

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

			if decimal == counter:
				break

			counter += 1
			lowerCAmelCase__			:		Dict						       =			10 * (r - n * t)
			lowerCAmelCase__			:		Any						       =			((10 * (3 * q + r)) // t) - 10 * n
			q *= 10
			lowerCAmelCase__			:		List[Any]						       =			nr
		else:
			lowerCAmelCase__			:		List[Any]						       =			(2 * q + r) * l
			lowerCAmelCase__			:		Any						       =			(q * (7 * k) + 2 + (r * l)) // (t * l)
			q *= k
			t *= l
			l += 2
			k += 1
			lowerCAmelCase__			:		Optional[int]						       =			nn
			lowerCAmelCase__			:		Optional[Any]						       =			nr
	return result

def 						__SCREAMING_SNAKE_CASE						(   ):
	print(f'{calculate_pi(50				) = }'				)
	import doctest

	doctest.testmod()


if __name__ == "__main__":
							main()







"""simple docstring"""





from itertools import permutations

def 						__SCREAMING_SNAKE_CASE						(   A_ = 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
	lowerCAmelCase__			:		str						       =			list(range(gon_side + 1		,  0		,  -1				)				)
	lowerCAmelCase__			:		int						       =			list(range(gon_side + 2		,  gon_side * 2 + 1				)				)

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

	lowerCAmelCase__			:		Tuple						       =			f'Magic {gon_side}-gon ring is impossible'
	raise ValueError(A_				)

def 						__SCREAMING_SNAKE_CASE						(   A_		,  A_				):
	lowerCAmelCase__			:		Dict						       =			[0] * (gon_side * 3)
	lowerCAmelCase__			:		Optional[int]						       =			perm[0:3]
	perm.append(perm[1]				)

	lowerCAmelCase__			:		int						       =			1 if gon_side < 5 else 2

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

	return result

def 						__SCREAMING_SNAKE_CASE						(   A_				):
	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

	lowerCAmelCase__			:		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())




