You are given a rectangular playing field of size $13 \times 2$ and any number of dominoes of sizes $2 \times 1$ and $3 \times 1$. The playing field should be completely covered with these dominoes without any overlaps, and no domino should protrude beyond the playing field. Furthermore, all dominoes must be aligned in the same direction, meaning their longer sides must be parallel to each other. How many such coverings are possible?

Let's think step by step and output the final answer within \boxed{}.
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