Get 2024

All positive integers from $1$ to $n$ are written consecutively from left to right: $\mathrm{123456789101112134...}n$.

How many ways are there to cross out all the digits of the obtained number, except four, so that the remaining digits form the number $2024$ without rearrangement?

For example, for n = 20 from the number $1234567891011121314151617181920$, you can obtain $2024$ only in one way:

1 $2$ 34567891 0 111 2 131 4 151617181920