





def 	lowerCAmelCase_					(			__a						)	->						Any:







  """simple docstring"""





  return [
      {
          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],
      },
      {
          0: [6],
          1: [9],
          2: [4, 5],
          3: [4],
          4: [2, 3],
          5: [2],
          6: [0, 7],
          7: [6],
          8: [],
          9: [1],
      },
      {
          0: [4],
          1: [6],
          2: [],
          3: [5, 6, 7],
          4: [0, 6],
          5: [3, 8, 9],
          6: [1, 3, 4, 7],
          7: [3, 6, 8, 9],
          8: [5, 7],
          9: [5, 7],
      },
      {
          0: [1, 3],
          1: [0, 2, 4],
          2: [1, 3, 4],
          3: [0, 2, 4],
          4: [1, 2, 3],
      },
  ][index]





def 	lowerCAmelCase_					(			__a						)	->						list[tuple[int, int]]:







  """simple docstring"""





  lowerCamelCase__: Dict         =0
  lowerCamelCase__: Union[str, Any]         =len(__a						)  # No of vertices in graph
  lowerCamelCase__: Optional[int]         =[0] * n
  lowerCamelCase__: List[str]         =[False] * n

  def dfs(__a      ,       __a      ,       __a      ,       __a						):
    lowerCamelCase__: Dict         =True
    lowerCamelCase__: List[Any]         =id_
    id_ += 1
    for to in graph[at]:
      if to == parent:
        pass
      elif not visited[to]:
        dfs(__a      ,       __a      ,       __a      ,       id_						)
        lowerCamelCase__: str         =min(low[at]      ,       low[to]						)
        if id_ <= low[to]:
          bridges.append((at, to) if at < to else (to, at)						)
      else:
        # This edge is a back edge and cannot be a bridge
        lowerCamelCase__: str         =min(low[at]      ,       low[to]						)

  lowerCamelCase__: list[tuple[int, int]]         =[]
  for i in range(__a						):
    if not visited[i]:
      dfs(__a      ,       -1      ,       __a      ,       id_						)
  return bridges


if __name__ == "__main__":
     import doctest

     doctest.testmod()




from collections.abc import Callable

import numpy as np





def 	__a     (      A__			:  Callable			,  A__			:  float			,  A__			:  float			,  A__			:  float			,  A__			:  float       ):
    SCREAMING_SNAKE_CASE										=   int(np.ceil((x_end - xa) / step_size       )       )
    SCREAMING_SNAKE_CASE										=   np.zeros((n + 1,)       )
    SCREAMING_SNAKE_CASE										=   ya
    SCREAMING_SNAKE_CASE										=   xa

    for k in range(A__       ):
        SCREAMING_SNAKE_CASE										=   y[k] + step_size * ode_func(A__			,  y[k]       )
        SCREAMING_SNAKE_CASE										=   y[k] + (
            (step_size / 2) * (ode_func(A__			,  y[k]       ) + ode_func(x + step_size			,  A__       ))
        )
        x += step_size

    return y


if __name__ == "__main__":
    import doctest

    doctest.testmod()