Kata

Every book has n pages with page numbers 1 to n. The summary is made by adding up the number of digits of all page numbers.

Task: Given the summary, find the number of pages n the book has.

Example

If the input is summary=25, then the output must be n=17: The numbers 1 to 17 have 25 digits in total: 1234567891011121314151617.

Be aware that you'll get enormous books having up to 100.000 pages.

All inputs will be valid.

Here's the opposite kata, which is more complex (Paginating a huge book)