For any positive integer $n$, let $f_{1}(n)$ denote the square of the sum of the digits of $n$ plus $r+1$, where $r$ is the integer such that $n=3q+r, 0 \leqslant r<3$. For $k \geqslant 2$, let $f_{k}(n)=f_{1}\left(f_{k-1}(n)\right)$. Therefore, $f_{1990}(2345)$ $=$ $\qquad$.
55 3. It is easy to calculate $f_{1}(2345)=199, f_{2}(2345)=363, f_{3}(2345)=145$,
$$
\begin{array}{l}
f_{4}(2345)=102, f_{5}(2345)=10, f_{6}(2345)=3, f_{7}(2345)=10, \\
f_{8}(2345)=3, \cdots, f_{1990}(2345)=3 .
\end{array}
$$