You and your friend play a game on a $7 \times 7$ grid of buckets. Your friend chooses $5$ "lucky" buckets by marking an "X" on the bottom that you cannot see. However, he tells you that they either form a vertical or horizontal line of length $5$. To clarify, he will select either of the following sets of buckets:

- Either $\{(a, b), (a, b + 1), (a, b + 2), (a, b + 3), (a, b + 4)\}$,
- Or $\{(b, a), (b + 1, a), (b + 2, a), (b + 3, a), (b + 4, a)\}$,

where $1 \le a \le 7$, and $1 \le b \le 3$. Your friend lets you pick up at most $n$ buckets, and you win if one of the buckets you picked was a "lucky" bucket. What is the minimum possible value of $n$ such that, if you pick your buckets optimally, you can guarantee that at least one is "lucky"?

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