[Python] Compress PDFs using Python

So I have a gazillion pdfs in a folder, I want to recursively (using os.path.walk) shrink them. I see that adobe pro has a save as reduced size. Would I be able to use this / how do you suggest I do it otherwise.

Note: Yes, I would like them to stay as pdfs because I find that to be the most commonly used and installed fileviewer.

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