[Python] Clear output then lose control of IPython debugger in jupyterhub notebook

So I import a module:

from IPython.core.debugger import Pdb


Then I initiate an object for debugging:

ipdb = Pdb()


I define a function to test debug mode:

def f(a=1):
ipdb.set_trace()
print(a)


After I run the function:

f()


I am in the debug mode, but if someone clear the output or switch the mode of the cell from code to markdown or NBconvert, then I lose the control of the debug mode,and to make things worse the interrupt key will not work any more(which is a very helpful weapon if you run a cell never ending), is there a way to get back the control of the debugger or at least quit the debugger mode instead of kill the whole kernel?

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