Smallest Beautiful Number

Let's call a positive integer $M$ a *beautiful number* if the following conditions are satisfied: - The decimal representation of $M$ (without leading zeros) does not contain any zeros. - The sum of squares of all decimal digits of $M$ is a perfect square. For example, $1$, $4$ and $221$ are beautiful, but $10$ and $333$ are not. You are given a positive integer $N$. Find the smallest $N$-