DFA recognizing the language {w | top(w) mod 3 = bottom(w) mod 3}

I am stumped on constructing this DFA. Can anyone offer any pointers?

For the alphabet:

| 0 | | 0 | | 1 | | 1 |
| 0 | | 1 | | 0 | | 1 |

where the strings over this alphabet represent a "top row" and a "bottom row" and each row represents a number in binary starting with the least significant bit.

Design a DFA to recognize the language {w | top(w) mod 3 = bottom(w) mod 3}.

This can be solved with 18 = 3 x 3 x 2 states or 6 = 3 x 2 states but I can't seem to figure it out.

Any help?

.

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