SimpleGuess | Topcoder Archive

Problem Statement

A cat and a rabbit are playing a simple number guessing game. The cat chose two different positive integers X and Y. He then told the rabbit several numbers. One of those numbers was X + Y and another was X - Y. The others were simply made up.

The rabbit thinks the cat prefers large numbers. Given a int[] hints containing the numbers the cat told the rabbit, return the largest possible value of X * Y.

Definition

Class:: SimpleGuess
Method:: getMaximum
Parameters:: int[]
Returns:: int
Method signature:: int getMaximum(int[] hints)
(be sure your method is public)

Constraints

hints will contain between 2 and 50 elements, inclusive.
Each element of hints will be between 1 and 100, inclusive.
All elements of hints will be distinct.
There will exist at least one pair of positive integers (X, Y) such that both X + Y and X - Y are elements of hints.

Examples

```
{ 1, 4, 5 }
```
```
Returns: 6
```
The rabbit can determine that (X, Y) = (3, 2).
```
{ 1, 4, 5, 8 }
```
```
Returns: 12
```
Possible pairs (X, Y) are (3, 2) and (6, 2). The values of X * Y are 6 and 12, respectively, and the largest is 12.

{ 9, 8, 7, 6, 5, 4, 3, 2, 1 }

Returns: 20

```
{ 2, 100 }
```
```
Returns: 2499
```
```
{ 50, 58, 47, 57, 40 }
```
```
Returns: 441
```

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