A9161. Ciel and Flipboard

Fox Ciel has a board with $n$ rows and $n$ columns, there is one integer in each cell.

It's known that $n$ is an odd number, so let's introduce . Fox Ciel can do the following operation many times: she choose a sub-board with size $x$ rows and $x$ columns, then all numbers in it will be multiplied by -1.

Return the maximal sum of numbers in the board that she can get by these operations.

The first line contains an integer $n$ , ( $1<=n<=33$ , and $n$ is an odd integer) — the size of the board.

Each of the next $n$ lines contains $n$ integers — the numbers in the board. Each number doesn't exceed $1000$ by its absolute value.

Output a single integer: the maximal sum of numbers in the board that can be accomplished.

In the first test, we can apply this operation twice: first on the top left $2×2$ sub-board, then on the bottom right $2×2$ sub-board. Then all numbers will become positive.