Sally the snail sits on the $3 \times  24$ lattice of points $(i, j)$ for all $1 \le  i  \le  3$ and $1 \le  j \le 24$. She wants to visit every point in the lattice exactly once. In a move, Sally can move to a point in the lattice exactly one unit away. Given that Sally starts at $(2, 1)$, compute the number of possible paths Sally can take.

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