Anydice to compare dice pools and then do math

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What id like to be able to do is have Anydice make the following calculation.

Roll 1 or more dice in one dice pool against 1 or more dice in another pool. Those two pools can be variable in number of dice and types of dice. Take the highest die from each pool and then compare them. If pool A is higher or equal to pool B then add their results together. If pool A is lower than pool B than just return the result on A.

I also want to be able to change the equation so that you can take lowest of a dice pool as well. You could end up with (take lowest of pool A) and (take highest of pool B).

Let me know if this makes sense. Thanks so much for your help out there!

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