





"""simple docstring"""


def        lowercase__     (       lowercase_      )       ->		Optional[int]:  # noqa: E741




      """simple docstring"""

      _UpperCamelCase   :						List[Any]    =							len(lowercase_      )
      _UpperCamelCase   :						str    =							0
      _UpperCamelCase   :						List[Any]    =							[0] * n
      _UpperCamelCase   :						Any    =							[False] * n
      _UpperCamelCase   :						Optional[int]    =							[False] * n

      def dfs(lowercase_		,lowercase_		,lowercase_		,lowercase_      ):
            if parent == root:
                  out_edge_count += 1
            _UpperCamelCase   :						Union[str, Any]    =							True
            _UpperCamelCase   :						Any    =							at

            for to in l[at]:
                  if to == parent:
                        pass
                  elif not visited[to]:
                        _UpperCamelCase   :						str    =							dfs(lowercase_		,lowercase_		,lowercase_		,lowercase_      )
                        _UpperCamelCase   :						Optional[Any]    =							min(low[at]		,low[to]      )

                        # AP found via bridge
                        if at < low[to]:
                              _UpperCamelCase   :						str    =							True
                        # AP found via cycle
                        if at == low[to]:
                              _UpperCamelCase   :						Optional[int]    =							True
                  else:
                        _UpperCamelCase   :						Tuple    =							min(low[at]		,lowercase_      )
            return out_edge_count

      for i in range(lowercase_      ):
            if not visited[i]:
                  _UpperCamelCase   :						Optional[int]    =							0
                  _UpperCamelCase   :						Optional[int]    =							dfs(lowercase_		,lowercase_		,-1		,lowercase_      )
                  _UpperCamelCase   :						List[str]    =							out_edge_count > 1

      for x in range(len(lowercase_      )      ):
            if is_art[x] is True:
                  print(lowercase_      )


# Adjacency list of graph
lowerCamelCase__						= {
    0: [1, 2],
    1: [0, 2],
    2: [0, 1, 3, 5],
    3: [2, 4],
    4: [3],
    5: [2, 6, 8],
    6: [5, 7],
    7: [6, 8],
    8: [5, 7],
}

compute_ap(data)







"""simple docstring"""


from collections.abc import Callable

import numpy as np




def        lowercase__     (       lowercase_		,lowercase_		,lowercase_		,lowercase_		,lowercase_      )       ->		np.ndarray:




      """simple docstring"""

      _UpperCamelCase   :						List[str]    =							int(np.ceil((x_end - xa) / step_size      )      )
      _UpperCamelCase   :						Tuple    =							np.zeros((n + 1,)      )
      _UpperCamelCase   :						List[str]    =							ya
      _UpperCamelCase   :						List[Any]    =							xa

      for k in range(lowercase_      ):
            _UpperCamelCase   :						List[str]    =							y[k] + step_size * ode_func(lowercase_		,y[k]      )
            x += step_size

      return y


if __name__ == "__main__":
  import doctest

  doctest.testmod()
