CZ-SK-MO 2013 Problem 4

On the board is written in decimal the integer positive number $N$ . If it is not a single digit number, wipe its last digit $c$ and replace the number $m$ that remains on the board with a number $m -3c$ . (For example, if $N = 1,204$ on the board, $120 - 3 \cdot 4 = 108$ .) Find all the natural numbers $N$ , by repeating the adjustment described eventually we get the number $0$ .