What size AC unit for a 3 chamber fermenter?

I am looking to build a 3 chamber "cooler" out of a window mounted AC unit and some 2" foam board so that I can lager and control fermentation temps. What size AC unit do you think would be sufficient? This would have to be big enough to keep 3 5 gallon batches down to roughly 55 degrees for a few weeks. The chamber will be in my basement so ambient should not get above 70 degrees. I'm currently looking at a 9,000 BTU unit. Thanks

How big is your chamber ? I built a two chamber system that holds 2+ kegs in either
chamber + a conical. Its probably 16-18 cu ft. But this is powered by a mini refrigerator.
It will get down to 25 if the chamber is made very small (1 keg). It easily holds 2 kegs at
35 (small chamber) + 1 keg at 60. Soon I'll get move the 60 to 54 and add a conical.

2" of iso foam should be a good barrier - the more the better.

I haven't built it yet but I'd like it to hold three 7.5 gallon conicals. From everything that I've read so far it looks like the smallest AC unit that I can buy will be plenty big.