How to evaluate power towers?

Logic Level 3

\[\Large 2 \; \underbrace{\square \; 2 \; \square \; \cdots \; \square \; 2 \; \square}_{n \text{ number of }\square\text{'s}} \; 2 = 2^{2^{2^{2^2}}} \]

What is the minimum value of positive integer \(n\) such that we can fill in the boxes above with the four mathematical operators ( \(+, -, \times , \div \) ) and the equation holds true?

Note: Order of operations (BODMAS) applied.

Bonus: What would the answer be if we were to find the maximum value of integer \(n\)?

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