Difference from Reversal

Time limit2sMemory limit128 MB

Summary

Find the smallest nonnegative integer x whose value minus its decimal reversal equals a given natural number D, or report that none exists.

Level: Medium7 of 10
Topics: Math, Brute force, Number theory, Implementation
Solved: No attempts yet

Problem

For a nonnegative integer, define its reversal as the integer obtained by reading its decimal digits from right to left. Any zeros that become leading zeros after the reversal disappear when the value is interpreted as an integer.

Given a natural number D, find the smallest nonnegative integer x such that x - reverse(x) = D. Here, reverse(x) denotes the reversal of x.

Input

D is given. D is a natural number not greater than 1,000,000.

Output

Print the smallest x satisfying the condition. If no such x exists, print -1.

Examples7

Example 1
Input
```
18
```
Expected output
```
20
```
Example 2
Input
```
15
```
Expected output
```
-1
```
Example 3
Input
```
4275
```
Expected output
```
5080
```
Example 4
Input
```
900
```
Expected output
```
101001
```
Example 5
Input
```
1989
```
Expected output
```
100990
```
Example 6
Input
```
857232
```
Expected output
```
860300
```
Example 7
Input
```
45
```
Expected output
```
50
```