Earliest Occurrence in the Infinite Number Sequence

We define an infinite sequence \(S\) as the concatenation of all natural numbers in ascending order: \(\texttt{1234567891011121314\ldots}\). Let \(S_i\) denote the \(i\)-th digit of \(S\) (1-indexed).

You are given a digit sequence \(A\). Your task is to determine the smallest index \(i\) such that the substring of \(S\) starting at \(i\) matches \(A\) exactly.

inputFormat

The input consists of a single line containing the digit sequence \(A\) (a non-empty string of digits).

outputFormat

Output a single integer representing the 1-indexed position in \(S\) where \(A\) first appears.

sample

12

1