### Problem Statement

You are given three integers: a, b and c. Convert each of them into their binary representations with no leading zeroes. Let x be the number of binary digits in the longest of the three. Add leading zeroes to the others until all of them have exactly x digits.

Transform a, b and c into a', b' and c', such that a'+b'=c', by optionally reordering the digits within each number. Leading zeroes are allowed. If there are several ways to do this, use the one that minimizes c'.

For example, let a = 7, b = 6 and c = 9. In binary notation, a = 111, b = 110 and c = 1001. We add leading zeroes to a and b so that all of them have exactly four digits: a = 0111, b = 0110, c = 1001. Now, if we reorder the digits within each number to get a' = 0111, b' = 0011 and c' = 1010, we satisfy a' + b' = c' (7 + 3 = 10). There is another way to do this as well (7 + 5 = 12), but this is the way that minimizes c'.

You are given ints a, b and c. Return the minimal possible value of c'. If there is no solution, return -1.

### Definition

 Class: BinarySum Method: rearrange Parameters: int, int, int Returns: int Method signature: int rearrange(int a, int b, int c) (be sure your method is public)

### Constraints

-a, b and c will each be between 1 and 2^30, inclusive.

### Examples

0)

 `7` `6` `9`
`Returns: 10`
 The example from the problem statement.
1)

 `1` `1` `2`
`Returns: 2`
2)

 `1` `1` `4`
`Returns: 2`
3)

 `3` `3` `9`
`Returns: 6`
4)

 `1` `1` `1`
`Returns: -1`
5)

 `32517565` `204650420` `4096`
`Returns: -1`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8711

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=12171&pm=8711

andrewzta

#### Testers:

PabloGilberto , Olexiy , marek.cygan , ivan_metelsky

#### Problem categories:

Dynamic Programming