





def      A__       (    SCREAMING_SNAKE_CASE_   :      int						)  ->  int:






   """simple docstring"""







   if not isinstance(SCREAMING_SNAKE_CASE_				,	SCREAMING_SNAKE_CASE_						):
      raise ValueError('''multiplicative_persistence() only accepts integral values'''						)
   if num < 0:
      raise ValueError('''multiplicative_persistence() does not accept negative values'''						)

   _UpperCAmelCase           =   0
   _UpperCAmelCase           =   str(SCREAMING_SNAKE_CASE_						)

   while len(SCREAMING_SNAKE_CASE_						) != 1:
      _UpperCAmelCase           =   [int(SCREAMING_SNAKE_CASE_						) for i in num_string]

      _UpperCAmelCase           =   1
      for i in range(0				,	len(SCREAMING_SNAKE_CASE_						)						):
         total *= numbers[i]

      _UpperCAmelCase           =   str(SCREAMING_SNAKE_CASE_						)

      steps += 1
   return steps
def      A__       (    SCREAMING_SNAKE_CASE_   :      int						)  ->  int:






   """simple docstring"""







   if not isinstance(SCREAMING_SNAKE_CASE_				,	SCREAMING_SNAKE_CASE_						):
      raise ValueError('''additive_persistence() only accepts integral values'''						)
   if num < 0:
      raise ValueError('''additive_persistence() does not accept negative values'''						)

   _UpperCAmelCase           =   0
   _UpperCAmelCase           =   str(SCREAMING_SNAKE_CASE_						)

   while len(SCREAMING_SNAKE_CASE_						) != 1:
      _UpperCAmelCase           =   [int(SCREAMING_SNAKE_CASE_						) for i in num_string]

      _UpperCAmelCase           =   0
      for i in range(0				,	len(SCREAMING_SNAKE_CASE_						)						):
         total += numbers[i]

      _UpperCAmelCase           =   str(SCREAMING_SNAKE_CASE_						)

      steps += 1
   return steps


if __name__ == "__main__":
   import doctest

   doctest.testmod()


'''simple docstring'''



def       snake_case   (	snake_case      : dict			) ->  set:


    """simple docstring"""


    lowerCAmelCase 						=							set()
    # edges = list of graph's edges
    lowerCAmelCase 						=							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:
        lowerCAmelCase						,   lowerCAmelCase 						=							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       snake_case   (	snake_case      : dict			) ->  set:


    """simple docstring"""


    lowerCAmelCase 						=							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)}")





