





'''simple docstring'''
def 				lowercase__   (   __lowercase						:  int				,  __lowercase						:  int     ) ->      int:



       """simple docstring"""






       while a != 0:
              __UpperCamelCase       ,						__UpperCamelCase       =  b % a, a
       return b


def 				lowercase__   (   __lowercase						:  int				,  __lowercase						:  int     ) ->      int:



       """simple docstring"""






       if gcd(__lowercase				,  __lowercase     ) != 1:
              __UpperCamelCase       =  F'''mod inverse of {a!r} and {m!r} does not exist'''
              raise ValueError(__lowercase     )
       __UpperCamelCase       ,						__UpperCamelCase       ,						__UpperCamelCase       =  1, 0, a
       __UpperCamelCase       ,						__UpperCamelCase       ,						__UpperCamelCase       =  0, 1, m
       while va != 0:
              __UpperCamelCase       =  ua // va
              __UpperCamelCase       ,						__UpperCamelCase       ,						__UpperCamelCase       ,						__UpperCamelCase       ,						__UpperCamelCase       ,						__UpperCamelCase       =  (ua - q * va), (ua - q * va), (ua - q * va), va, va, va
       return ua % m







"""simple docstring"""



def 		__lowercase     (   snake_case_  :  dict						)   ->set:



    '''simple docstring'''







    __A    :						List[str]						 =     set()
    # edges = list of graph's edges
    __A    :						Optional[int]						 =     get_edges(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:
        __A ,       __A    :						str						 =     edges.pop()
        chosen_vertices.add(snake_case_						)
        chosen_vertices.add(snake_case_						)
        for edge in edges.copy():
            if from_node in edge or to_node in edge:
                edges.discard(snake_case_						)
    return chosen_vertices







def 		__lowercase     (   snake_case_  :  dict						)   ->set:



    '''simple docstring'''







    __A    :						Tuple						 =     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)}")




