**self-descriptive number** is an integer $m$ in which each digit $d$ at position $n$ (the most significant digit being at position $0$ and the least significant at position $9$) counts how many instances of digit $n$ are in $m$. The smallest self-descriptive number is $1210$, as it has 1 zero, 2 ones, 1 two and 0 threes. Find the largest self-descriptive number.