### Problem Statement

You are given a rectangular matrix with odd numbers of rows and columns. Each cell of the matrix contains either 0 or 1. In one move, you can select any one row or column of the matrix and replace all 0's with 1's and all 1's with 0's in that row/column. Your aim is to have an even number of 1's in each row and each column.

The elements of the String[] matrix correspond to the rows of the matrix. Return the minimal number of moves needed to achieve your aim, or -1 if it's impossible.

### Definition

 Class: EvenOnes Method: minOperations Parameters: String[] Returns: int Method signature: int minOperations(String[] matrix) (be sure your method is public)

### Constraints

-matrix will contain between 1 and 49 elements, inclusive.
-Each element of matrix will contain between 1 and 49 characters, inclusive.
-All elements in matrix will contain the same number of characters.
-The number of elements in matrix will be odd.
-The number of characters in each element of matrix will be odd.
-Each character in each element of matrix will be '0' (zero) or '1' (one).

### Examples

0)

 ```{ "111", "011", "001" }```
`Returns: 2`
 We can first apply the operation to the middle row of the matrix, and then to the middle column.
1)

 ```{ "111", "111", "111", "111", "111" }```
`Returns: 3`
 We must apply the operations either to all rows or to all columns. As the number of columns is less than the number of rows, we choose the second variant.
2)

 ```{ "00000", "00000", "00000" }```
`Returns: 0`
 The matrix initially contains an even number of ones in each row and column, so we don't apply any operations.
3)

 ```{ "10101", "01010", "10101", "01010", "10101" }```
`Returns: 5`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8018

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=12058&pm=8018

ivan_metelsky

#### Testers:

PabloGilberto , vorthys , Olexiy , misof

Simple Math