Let $S=\{\sqrt{n}: 1 \leq n \leq 50$ and $n$ is odd $\}$
Let $a \in S$ and $A=\left[\begin{array}{ccc}1 & 0 & a \\ -1 & 1 & 0 \\ -a & 0 & 1\end{array}\right]$
If $\sum_{a \in S} \operatorname{det}(\operatorname{adj} A)=100 \lambda$, then $\lambda$ is equal to
