





def 	UpperCamelCase__(       UpperCamelCase__			:       dict  )->Optional[int]:
       A__											=						set()
       # edges = list of graph's edges
       A__											=						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:
              A__											=						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__(       UpperCamelCase__			:       dict  )->Any:
       A__											=						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)}")






import operator

def 			lowercase_				(			_lowerCamelCase							:       list		,	_lowerCamelCase							:       bool = False		,	_lowerCamelCase							:       list | None = None):
    lowercase__ :   int    					=				operator.lt if reverse else operator.gt
    lowercase__ :   str    					=				solution or []

    if not arr:
        return solution

    lowercase__ :   List[str]    					=				[arr.pop(0)]
    for i, item in enumerate(_lowerCamelCase):
        if _operator(_lowerCamelCase		,	sublist[-1]):
            sublist.append(_lowerCamelCase)
            arr.pop(_lowerCamelCase)

    #  merging sublist into solution list
    if not solution:
        solution.extend(_lowerCamelCase)
    else:
        while sublist:
            lowercase__ :   str    					=				sublist.pop(0)
            for i, xx in enumerate(_lowerCamelCase):
                if not _operator(_lowerCamelCase		,	_lowerCamelCase):
                    solution.insert(_lowerCamelCase		,	_lowerCamelCase)
                    break
            else:
                solution.append(_lowerCamelCase)

    strand_sort(_lowerCamelCase		,	_lowerCamelCase		,	_lowerCamelCase)
    return solution


if __name__ == "__main__":
      assert strand_sort([4, 3, 5, 1, 2]) == [1, 2, 3, 4, 5]
      assert strand_sort([4, 3, 5, 1, 2], reverse=True) == [5, 4, 3, 2, 1]



