Starting with a $5 \times 5$ grid, choose a $4 \times 4$ square in it. Then, choose a $3 \times 3$ square in the $4 \times 4$ square, and a $2 \times 2$ square in the $3 \times 3$ square, and a $1 \times 1$ square in the $2 \times 2$ square. Assuming all squares chosen are made of unit squares inside the grid, in how many ways can the squares be chosen so that the final $1 \times 1$ square is the center of the original $5 \times 5$ grid?

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