

"""simple docstring"""





__UpperCamelCase						:   Dict							   =	{0: [1, 2], 1: [0, 3], 2: [0], 3: [1], 4: [5, 6], 5: [4, 6], 6: [4, 5]}

__UpperCamelCase						:   Tuple							   =	{0: [1, 2, 3], 1: [0, 3], 2: [0], 3: [0, 1], 4: [], 5: []}

def 						__SCREAMING_SNAKE_CASE						(   A_		,  A_		,  A_				):
	lowerCAmelCase__			:		Optional[Any]						       =			True
	lowerCAmelCase__			:		Optional[Any]						       =			[]

	for neighbour in graph[vert]:
		if not visited[neighbour]:
			connected_verts += dfs(A_		,  A_		,  A_				)

	return [vert, *connected_verts]

def 						__SCREAMING_SNAKE_CASE						(   A_				):
	lowerCAmelCase__			:		Optional[int]						       =			len(A_				)
	lowerCAmelCase__			:		Tuple						       =			graph_size * [False]
	lowerCAmelCase__			:		int						       =			[]

	for i in range(A_				):
		if not visited[i]:
			lowerCAmelCase__			:		Dict						       =			dfs(A_		,  A_		,  A_				)
			components_list.append(A_				)

	return components_list


if __name__ == "__main__":
							import doctest

							doctest.testmod()







"""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())




