Mega 2560 and two 26650 Rechargeable Batteries

@Paul_B
So what exactly IS the difference between 30000mAh, and 30Ah? Isn't that just another way of saying the same thing?
I measured the draw of my project and it's 1012mA. I don't suppose it HAS to last 48 hrs on battery, but if there is a long power outage, I want it to stay alive during that time. Even if it has to turn off the screen to last the power outage, that's fine, but I'd like it to last 24hrs minimum.
What would you suggest I use, that isn't stupidly large or expensive?
This is the inside unit, so it can't be solar powered. The external one can be, but this one can't.
I really don't care WHAT I have to use, as long as it lasts 24 hours.