Problem M
Champernowne Verification

The $k^{\text{th}}$ Champernowne word is obtained by writing down the first $k$ positive integers and concatenating them together. For example, the ${10}^{\text{th}}$ Champernowne word is $12345678910$.

Given a positive integer $n$, determine if it is a Champernowne word, and if so, which word.

Input

The first line contains a single integer, $n$ ($1\le n\le {10}^9$). $n$ will not have leading zeroes.

Output

If $n$ is the $k^{\text{th}}$ Champernowne word, output $k$. Otherwise, output $-1$.

123456789

9

1000000000

-1

11

-1

1324

-1