--description--

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

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

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

--hints--

lastDigitsSumOfPerfectSquare() should return 142989277.

assert.strictEqual(lastDigitsSumOfPerfectSquare(), 142989277);

--seed--

--seed-contents--

function lastDigitsSumOfPerfectSquare() {

  return true;
}

lastDigitsSumOfPerfectSquare();

--solutions--

// solution required