Let A be a $3 \times 3$ matrix such that $|{\mathop{\rm adj}\nolimits} ({\mathop{\rm adj}\nolimits} ({\mathop{\rm adj}\nolimits} {\rm{A}}))| = 81$.
If $S = \left\{ {n \in :{{(|{\mathop{\rm adj}\nolimits} ({\mathop{\rm adj}\nolimits} A)|)}^{\frac{{{{(n - 1)}^2}}}{2}}} = |A{|^{\left( {3{n^2} - 5n - 4} \right)}}} \right\}$ , then $\sum\limits_{n \in S} {\left| {{A^{\left( {{n^2} + n} \right)}}} \right|} $ is equal to