## LQDNUMS - LQDNUMBERS

He choose a number N ( 1 ≤ N ≤ 10^18 ),

then wrote all the numbers from 1 to N to form a continuous string of digits. Next he replaced substrings of indentical digits with a single digit. For example string fragment "14445556677666" would be changed to "145676". He named this shortened string S. Then he specified a problem for his fellow professors: given a length of string S determine the number N witch results in that kind of string S. The task has proven to be too much for Mathematicans. can you solve it?

During a meeting with professors in the Asian Confederation of Mathematics, a Russian professor came up with a problem:

He choose a number N ( 1 ≤ N ≤ 10^18 ), then wrote all the numbers from 1 to N to form a continuous string of digits. Next he replaced substrings of indentical digits with a single digit. For example string fragment "14445556677666" would be changed to "145676". Then he specified a problem for his fellow professors: given a length of string S determine the number N witch results in that kind of string S. The task has proven to be too much for Mathematicans. can you solve it?

### Input

A single number M, length of the string S  ( 1 ≤ M ≤ 1018 )

### Output

A single number N, the number which Russian professor selected.

### Example

Input:

`13`

Output:

`12`

Explaination:

```With N = 12, we get the string:
- 123456789101112
Because three consecutive number one in the same location adjacent to the end, we delete the first two numbers, then we have
- 1234567891012
The length of this string is 13```

 Được gửi lên bởi: Tmbao Ngày: 2011-05-29 Thời gian chạy: 3s Giới hạn mã nguồn: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Ngôn ngữ cho phép: Tất cả ngoại trừ: ASM64 GOSU PERL6 PYPY RUST SED Nguồn bài: Ukrana OI