Is it okay to get a Pap smear on your period?

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Okay so, I am scheduled to get my first ever Pap smear tomorrow. It takes a really long time to get an appointment at my doctor, this one took over two months (!). 
As of today, I am on day 5 of my flow, and that is usually my last day, however (tmi) I do have the brown discharge a tiny bit on day 6, but nothing is actively flowing if you catch my drift. 
How does the pap smear even work?? Should I reschedule just out of respect for my doctor or does it not matter? I would shower right before I go so it's as clean as possible...
Help me, dear knowledgable women of the world, I am a bad adult! 😁😊