### Problem Statement

A magic square is a 3x3 array of numbers, such that the sum of each row, column, and diagonal are all the same. For example:

```
8 1 6
3 5 7
4 9 2
```

In this example, all rows, columns, and diagonals sum to 15.

You will be given a int[] representing the nine numbers of a magic square, listed left-to-right, top-to-bottom. However, one of these numbers will be replaced by a -1. Write a method to determine which number was removed. For example, if the 7 was removed from the magic square above, you would be given { 8, 1, 6, 3, 5, -1, 4, 9, 2 }, and your program should return 7.

The completed magic square will consist of exactly 9 distinct positive integers.

### Definition

 Class: MagicSquare Method: missing Parameters: int[] Returns: int Method signature: int missing(int[] square) (be sure your method is public)

### Constraints

-square will contain exactly 9 elements.
-Each element of square will either be -1 or be between 1 and 100, inclusive.
-Exactly one element of square will be -1.
-The eight elements of square that are not -1 will be distinct.
-The input will be such that a number between 1 and 100, inclusive, can be found to complete the magic square, and it will not be equal to any of the other 8 numbers in the square.

### Examples

0)

 `{ 8, 1, 6, 3, 5, -1, 4, 9, 2 }`
`Returns: 7`
 This is the example from the problem statement.
1)

 `{ -1, 1, 6, 3, 5, 7, 4, 9, 2 }`
`Returns: 8`
 The same square, but this time with the number 8 removed.
2)

 `{ 5, 15, 13, 19, 11, 3, 9, 7, -1 }`
`Returns: 17`
 The missing number is 17.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=2366

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4760&pm=2366

legakis

#### Testers:

lbackstrom , brett1479

Simple Math