Pillows under winter cover--what size?

I'm getting ready to order all of our winter "stuff" so we're fully ready when it comes time to close the pool. I'm set that we're going to go with a solid cover (a cheapo for at least this year until we can assess what kind of wind, snow, ice, etc issues we can expect each year--we live in Central Illinois but I've never had a pool here). I fully plan on keeping the cover pumped off and as clean as possible throughout the winter season (we're also getting a leaf net to get the bulk of the "big dump" this fall and next spring).

So, that said, I think it would be wise to get a pillow or two to assist w/keeping the water and gunk towards the edges. My questions: What size pillow(s) should I be getting for a 21' round AGP and how many should I get? Any particular kind I should be looking for or are they all about the same?

Also, any other tips you have for covering our AGP would be greatly appreciated!
 
My pool came with a 4×4 pillow and it always deflated and sank within a couple of months. Bought a new one, same thing. So, I went to my favorite tire guy and purchased a 10.00×20 inner tube used by the 18-wheelers. The guy said trucks hardly ever use them as they are pretty much tubeless, but he keeps two cases of tubes handy for the pool folks. This'll be the third season for the same tube. Point the valve down so it doesn't poke a hole in the cover. I also tied four small loops around the tube inside to outside, tied to a small loop around the inside of the hole, and around the outside, much like I've seen on life rings on board ships, then I have lines tied from the outside loop to the pool edges. This way any tension is carried to the rope array, not to the tube rubber itself. This holds the tube on center.
 
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