The Exponentorial of \(2018\)

Define \(n¡\) to be \[\LARGE n¡=n^{{(n-1)}^{{(n-2)}^{.^{.^{.^{2^{\small1}}}}}}}.\] What are the last two digits of the number \(2018¡?\)

Note: \(\large ¡\) is the factorial notation \(!\) turned upside down. Note that \(\large ¡\) keeps exponentiating while \(!\) keeps multiplying.

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