Find the largest positive integer \(n\) that satisfies these conditions:

**1**. \(n\) is not divisible by \(3\).

**2**. The \(n\)-by-\(n\) *cannot* be covered by 1 I-shaped-tetromino piece and \(\dfrac{n^2-4}{3}\) I-shaped-triomino pieces.

Image of an I-shaped-tetromino:

Image of an I-shaped-triomino:

*This problem is not original*

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