Three. (50 points) Given sets $A_{1}, A_{2}, \cdots, A_{n}$ are different subsets of the set $\{1,2, \cdots, n\}$, satisfying the following conditions:
( i ) $i \notin A_{i}$ and $\operatorname{Card}\left(A_{i}\right) \geqslant 3, i=1,2, \cdots, n$;
(ii) $i \in A_{j}$ if and only if $j \notin A_{i}(i \neq j$, and $i, j=1,2, \cdots, n)$.
Try to answer the following questions:
(1) Find $\sum_{i=1}^{n} \operatorname{Card}\left(A_{i}\right)$;
(2) Find the minimum value of $n$.