
def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					lowercase					=		set()
					# edges = list of graph's edges
					lowercase					=		get_edges(lowerCAmelCase__	)

					# 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(lowerCAmelCase__	)
										chosen_vertices.add(lowerCAmelCase__	)
										for edge in edges.copy():
															if from_node in edge or to_node in edge:
																				edges.discard(lowerCAmelCase__	)
					return chosen_vertices



def  UpperCamelCase					(							lowerCAmelCase__	):
					'''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)}")








def  UpperCamelCase					(							lowerCAmelCase__ = 1000	):
					'''simple docstring'''
					lowercase					=		-1
					lowercase					=		0
					for a in range(1				,    n // 3	):
										# Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
										lowercase					=		(n * n - 2 * a * n) // (2 * n - 2 * a)
										lowercase					=		n - a - b
										if c * c == (a * a + b * b):
															lowercase					=		a * b * c
															if candidate >= product:
																				lowercase					=		candidate
					return product


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




