# Set Theory is difficult, isn't it?

Logic Level 4

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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