We have four registers, $R_1, R_2, R_3, R_4$, such that $R_i$ initially contains the number $i$ for $1 \leq i \leq 4$. We are allowed two operations:

1. Simultaneously swap the contents of $R_1$ and $R_3$ as well as $R_2$ and $R_4$.

2. Simultaneously transfer the contents of $R_2$ to $R_3$, the contents of $R_3$ to $R_4$, and the contents of $R_4$ to $R_2$. For example, if we do this once, then $(R_1, R_2, R_3, R_4) = (1, 4, 2, 3)$.

Using these two operations as many times as desired and in whatever order, what is the total number of possible outcomes?

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