# Subnumber

Time Limit: Java: 10000 ms / Others: 10000 ms

Memory Limit: Java: 32768 KB / Others: 32768 KB

## Description

George likes arithmetics very much. Especially he likes the natural numbers series. His most favourite thing is the infinite sequence of digits, which results as the concatenation of all natural numbers in ascending order. The beginning of this sequence is 1234567891011121314... Let us call this sequence S. Then S = 1, S = 2, ..., S = 1, S = 0, ... , and so on.

George takes a sequence of digits A and wants to know when it first appears in S. Help him to solve this difficult problem.

## Input

The first line of the input file contains A - the given sequence of digits. The number of digits in A does not exceed 200.

Process to the end of file.

## Output

Output file must contain the only number - the least k such that A = S[k], A = S[k+1], ... A[len(A)] = S[k + len(A) - 1], where len(A) denotes the length of A (i.e. the number of digits in it).

## Sample Input

101
123

## Sample Output

10
1

None

## Source

Northeastern Europe 2001, Northern Subregion