## REVADD - Special Numbers (Reverse and Add)

A number $N$ is called special iff it can be written as $$N = \mathrm{reverse}(N_1) + N_1 = \mathrm{reverse}(N_2) + N_2,$$ where $N_1$ and $N_2$ are some positive integers and their number of digits (lengths) are different.

For example, $121$ is a special number since \begin{aligned} 121 &= \mathrm{reverse}(74) + 74 = \mathrm{reverse}(110) + 110 \\ &= 47 + 74 = 11 + 110. \end{aligned}

There are only two special number less than $10,000$.

Find the first 5,000 smallest special numbers.

### Input

This problem has no input data.

### Output

Output the first 5,000 special numbers in ascending order. (One special number per one line.)

### Example

#### Output:

121
1111
...
[4998 lines]
...


### Information

Source Limit is 10 KB.

hide comments [Rampage] Blue.Mary: 2016-05-02 10:42:47 To debug the wrong program of this problem is a very challenging work... Min_25: 2016-05-01 18:09:16 @Amaterasu Yes. Amaterasu: 2016-05-01 15:01:51 Is my understanding of problem statement correct: number k is special number IFF there exists at least 2 integers a and b such that a + reverse(a) == b + reverse(b) == k AND digitNum(a) != digitNum(b). Is that what you meant by "two distinct digit number"? S.Y.P.Lai: 2014-10-21 08:23:24 @Min_25 OK, I see. I'd made a false assumption. Those numbers are not special. Min_25: 2014-10-21 08:23:24 @S.Y.P.Lai Please check special numbers (< 10^7) using a brute force approach. S.Y.P.Lai: 2014-10-21 08:23:24 @Min_25 Could you check the submissions with WAs? I think your standard solution has some errors.

 Added by: Min_25 Date: 2014-09-05 Time limit: 3s Source limit: 10240B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM64