For a positive integer $n$, let $f(n)$ be the sum of the squares of the digits (in base $10$) of $n$, e.g.

$$\begin{array}{rl}f(3)& =3^2=9,\\ f(25)& =2^2+5^2=4+25=29,\\ f(442)& =4^2+4^2+2^2=16+16+4=36\end{array}$$

Find the last nine digits of the sum of all $n$, $0<n<{10}^{20}$, such that $f(n)$ is a perfect square.