# 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 $-1$.

Sample Input 1 | Sample Output 1 |
---|---|

123456789 |
9 |

Sample Input 2 | Sample Output 2 |
---|---|

1000000000 |
-1 |

Sample Input 3 | Sample Output 3 |
---|---|

11 |
-1 |

Sample Input 4 | Sample Output 4 |
---|---|

1324 |
-1 |