Katie has a chocolate bar that is a $5$-by-$5$ grid of square pieces, but she only wants to eat the center piece. To get to it, she performs the following operations:
i. Take a gridline on the chocolate bar, and split the bar along the line.
ii. Remove the piece that doesn’t contain the center.
iii. With the remaining bar, repeat steps $1$ and $2$.
Determine the number of ways that Katie can perform this sequence of operations so that eventually she ends up with just the center piece.

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