


def 							UpperCamelCase_( lowerCamelCase_					)       ->		set:
    _lowercase			:				Optional[Any] 						=						set()
    # edges = list of graph's edges
    _lowercase			:				List[Any] 						=						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			:				str 						=						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_					)       ->		set:
    _lowercase			:				List[Any] 						=						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)}")






from maths.prime_factors import prime_factors



def 							UpperCamelCase_( lowerCamelCase_					)       ->		int:
    if not isinstance(lowerCamelCase_				,					lowerCamelCase_					):
        _lowercase			:				str 						=						F'''Input value of [number={number}] must be an integer'''
        raise TypeError(lowerCamelCase_					)
    if number < 1:
        raise ValueError('Input must be a positive integer'					)
    return -1 if len(prime_factors(lowerCamelCase_					)					) % 2 else 1


if __name__ == "__main__":
 import doctest

 doctest.testmod()


