How to implement `__setitem__` for `pathlib.Path`

Question

As above. I made this attempt below but it throws an error: I don't know how to mutate self to get what I want.

from pathlib import Path

class P(type(Path()), Path):

    def __setitem__(self, key, value):
        fullparts = list(self.parts)
        fullparts[key] = value
        return P(*fullparts)

    def __getitem__(self, key):
        return P(self.parts[key])

p = P("folder/subfolder/file.txt")
p[1] = "haha"  # 

Desired outcome folder/haha/file.txt.

Actual outcome: object not changed!