


def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		lowercase__						=				set()
		# edges = list of graph's edges
		lowercase__						=				get_edges(SCREAMING_SNAKE_CASE					)

		# While there are still elements in edges list, take an arbitrary edge
		# (from_node, to_node) and add his extremity to chosen_vertices and then
		# remove all arcs adjacent to the from_node and to_node
		while edges:
				lowercase__					,		lowercase__						=				edges.pop()
				chosen_vertices.add(SCREAMING_SNAKE_CASE					)
				chosen_vertices.add(SCREAMING_SNAKE_CASE					)
				for edge in edges.copy():
						if from_node in edge or to_node in edge:
								edges.discard(SCREAMING_SNAKE_CASE					)
		return chosen_vertices
def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		lowercase__						=				set()
		for from_node, to_nodes in graph.items():
				for to_node in to_nodes:
						edges.add((from_node, to_node)					)
		return edges


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			# graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
			# print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")






lowerCAmelCase	=							[sum(int(c, 10) ** 2 for c in i.__str__()) for i in range(10_0000)]
def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		lowercase__						=				0
		while number:
				# Increased Speed Slightly by checking every 5 digits together.
				sum_of_digits_squared += DIGITS_SQUARED[number % 10_00_00]
				number //= 10_00_00

		return sum_of_digits_squared


# There are 2 Chains made,
# One ends with 89 with the chain member 58 being the one which when declared first,
# there will be the least number of iterations for all the members to be checked.

# The other one ends with 1 and has only one element 1.

# So 58 and 1 are chosen to be declared at the starting.

# Changed dictionary to an array to quicken the solution
lowerCAmelCase	=							[None] * 1000_0000
lowerCAmelCase	=							True
lowerCAmelCase	=							False
def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		if CHAINS[number - 1] is not None:
				return CHAINS[number - 1]  # type: ignore

		lowercase__						=				chain(next_number(SCREAMING_SNAKE_CASE					)					)
		lowercase__						=				number_chain

		while number < 10_00_00_00:
				lowercase__						=				number_chain
				number *= 10

		return number_chain
def       _a			(				SCREAMING_SNAKE_CASE = 10_00_00_00					):


		"""simple docstring"""




		for i in range(1						,    SCREAMING_SNAKE_CASE					):
				if CHAINS[i] is None:
						chain(i + 1					)

		return CHAINS[:number].count(SCREAMING_SNAKE_CASE					)


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			print(f"""{solution() = }""")


