10. If the three-digit number $n=\overline{a b c}$ is a perfect square, and the sum of its digits $a+b+c$ is also a perfect square, then $n$ is called a super square number. Let the set of super square numbers be $A$, and the sum of all elements in set $A$ be denoted as $S(A)$. Then the integer closest to $\frac{S(A)}{|A|}$ is $\qquad$.
Rong 376.
Analysis It is not difficult to list the three-digit square numbers as:
$$
100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,784,841,900,961
$$

There are a total of 22, among which the super square numbers are 13, that is,
$$
\begin{array}{c}
A=\{100,121,144,169,196,225,324,400,441,484,529,900,961\} \\
S(A)=100+121+144+169+196+225+324+400+441+484+529+900+961=4994
\end{array}
$$

So $\frac{S(A)}{|A|}=\frac{4994}{13} \approx 384.15$, therefore the integer closest to $\frac{S(A)}{|A|}$ is 384.