comparing two 3-bit numbers with a 2-bit output

Question

I have two 3-bit numbers A2A1A0 and B2B1B0 and I have to compare them and generate a 2-bit output based on if A > B, A < B , and A = B.

The only circuit I can use to implement this is a multiplexer.

I've made a truth table; however, i'm not sure how to implement the 2-bit outputs. I was thinking of labeling A > B as 01, A < B as 10, and A = B as 11. But I can't find a way to put this in a multiplexer successfully, because each block of inputs will never have the same output.

Any help would be appreciated.