Set Theory is difficult, isn't it?

Logic Level 3

The set \( S \) is formed according to the following rules:

\( 1) \) \( 2 \in S \).

\( 2) \) If \( n \) is in \( S \), then \( (n+5) \) is also in \( S \).

\( 3) \) If \( n \) is in \( S \), then \( 3n \) is also in \( S \).

Find the largest integer in the set \( { 1,2,3, \ldots, 2008 } \) that does not belong to \( S \).

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