### Problem Statement

A quadratic equation has the format ax^2 + bx + c = 0 where a != 0. To solve this equation the quadratic formula is used:
`x = (-b (+|-) sqrt(b^2 - 4ac)) / 2a ,`
where (+|-) means plus or minus, sqrt means square root, and x is the solution.

Given a list of values for a, b and c your method will return a sorted int[] of all integer solutions to the corresponding quadratic equations. The sorted values should be in ascending order with no repeats. For example, if
```    a = {1} ,
b = {2,3} ,
and c = {2,1} ,```
your method would have to solve the quadratic equations corresponding to all combinations of values from a, b and c. This would amount to solving:
``` x^2 + 2x + 2 = 0  (Solutions : not integers)
x^2 + 2x + 1 = 0  (Solutions : -1)
x^2 + 3x + 2 = 0  (Solutions : -2,-1)
x^2 + 3x + 1 = 0  (Solutions : not integers)  .```
Notice that all combinations have been tried. The return value would be {-2,-1}.

### Definition

 Class: QuadraticRoots Method: findRoots Parameters: int[], int[], int[] Returns: int[] Method signature: int[] findRoots(int[] a, int[] b, int[] c) (be sure your method is public)

### Constraints

-a, b, and c will each contain between 1 and 50 elements inclusive.
-Each element of a will be nonzero, between -10000 and 10000 inclusive.
-Each element of b and c will be between -10000 and 10000 inclusive.
-The returned int[] will contain at most 100 elements.

### Examples

0)

 `{1}` `{2,3}` `{2,1}`
`Returns: { -2,  -1 }`
 Example from above.
1)

 `{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}` `{1}` `{1}`
`Returns: { }`
 No roots here.
2)

 `{1}` `{0}` `{-1,-2,-3,-4,-5,-6,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16}`
`Returns: { -4,  -3,  -2,  -1,  1,  2,  3,  4 }`
3)

 `{1,1,2,2,3,3,4,4}` `{1,1,2,2,3,3,4,4}` `{1,1,2,2,3,3,4,4}`
`Returns: { -3,  -2,  -1 }`
 Tons of repeats.
4)

 `{1,10000,-10000}` `{0,1,10000,-10000}` `{0,1,10000,-10000}`
`Returns: { -10000,  -100,  -1,  0,  1,  100,  10000 }`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=893

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4704&pm=893

brett1479

#### Problem categories:

Brute Force, Simple Math