How Many Digits between 1 and N

Imagine you took all the numbers between 0 and n and concatenated them together into a long string. How many digits are there between 0 and n? Write a function that can calculate this.

There are 0 digits between 0 and 1, there are 9 digits between 0 and 10 and there are 189 digits between 0 and 100.

Examples

digits(1) ➞ 0

digits(10) ➞ 9

digits(100) ➞ 189

digits(2020) ➞ 6969

Notes

The numbers are going to be rather big so creating that string won't be practical.