Plumbing and Piping - Adding check value to drain stack? Need help

This is my main drain stack in my basement. I want to add a check valve near the bottom. Our main sewer line backs up when the area gets allot of heavy rains of long periods of time. And I want to stop it from going up this stack.

The stack material it as follows:

(TOP)
Brass pipe
Some type of PVD clamp w/ bolts
PVC pipe
PVC tee
PVC pipe
PVC tee
PVC pipe
Some type of pvc clamp w/ bolts
Brass pipe
Cast Iron
(BOTTOM)

Any suggestions on how and where the Check valve should go and what type of check valve I can hopefully install would be great appreciated.
http://www.yankeetackleshop.com/drain.JPG

Jpmd: What your looking for is called a Vertical Back Water Valve. While it is the thing you need to prevent backflow into your home, while the condition exists your drains will not exit the home. Google "Vertical Backwater Valve".

What gonna be the easiest way to cut the brass pipe and attach a PVC to it?
Thanks for your help.

The pipe you refer to is copper DWV not brass. To cut it you can use a sawzall or a hack saw, make sure you get a straight line around it. :)

I can't find any 3" vertical backwater valves on the net.
Found one but it appears that the ends are always off set from each other.

I forgot to ask, how is rain water going up that stack? :confused:

Our street sewers over flow and back up when it rains really hard. I'm assuming that it is the rain water that is climbing up the drain line.